tag:blogger.com,1999:blog-61957831210739280872024-03-13T19:57:23.377-07:00Matemática FantásticaAnonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.comBlogger38125tag:blogger.com,1999:blog-6195783121073928087.post-50607729814929146472013-11-03T06:18:00.000-08:002013-11-03T06:18:17.690-08:00VÍDEOS ANÁLISESAUDAÇÕES VENCEDORES: APÓS UMA MINUCIOSA SELEÇÃO DAS QUESTÕES, TEREMOS FINALMENTE O VÍDEO DE TODAS AS QUESTÕES DE ANÁLISE ( MAIS DE 5O QUESTÕES) ATÉ O DOMINGO DIA 10/11. AGUARDEMAnonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com3tag:blogger.com,1999:blog-6195783121073928087.post-52932935378082846242013-09-29T17:30:00.003-07:002013-11-03T06:16:23.081-08:00Análise Combinatória 4 - Combinação<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
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<b><span style="font-family: "Arial","sans-serif"; font-size: 20.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">COMBINAÇÃO<o:p></o:p></span></b></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">1 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Sete diferentes figuras foram
criadas para ilustrar, em grupos de quatro, o Manual do Candidato do Vestibular
Estadual 2007.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Um desses
grupos está apresentado a seguir.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxXsHhsl6Ka4Bf37PXa4nCTRE7E-EAaKNXdFJ6Er-uwJ1yqPvfhnWhOf35oEzUPXxBgbkTpZvP9ER01b0FJ6uff8SapChdXDb7a8pJSls1-sP6WSjz-z40CBDwg4W-ZN-44oLuF3mZCZc/s1600/c+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxXsHhsl6Ka4Bf37PXa4nCTRE7E-EAaKNXdFJ6Er-uwJ1yqPvfhnWhOf35oEzUPXxBgbkTpZvP9ER01b0FJ6uff8SapChdXDb7a8pJSls1-sP6WSjz-z40CBDwg4W-ZN-44oLuF3mZCZc/s1600/c+1.png" /></a></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Considere
que cada grupo de quatro figuras que poderia ser formado é distinto de outro
somente quando pelo menos uma de suas figuras for diferente.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Nesse
caso, o número total de grupos distintos entre si que poderiam ser formados
para ilustrar o Manual é igual a: </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">24 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">35 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">70 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">140 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">2<b>.</b>
(Uftm 2011) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A prova da primeira fase de
um vestibular terá 8 questões objetivas de Matemática, com 5 alternativas.
Pretende-se que apenas duas dessas questões tenham a resposta correta indicada
na alternativa E. O número de formas de se escolher essas duas questões é </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">28. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">36. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">48. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">56. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">68. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">3 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Em uma sorveteria, há sorvetes
nos sabores morango, chocolate, abacaxi e flocos.<o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">De quantas maneiras podemos montar uma casquinha,
com dois sabores diferentes, nessa sorveteria? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">6 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">7 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">8 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">9 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">10 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">4</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">
</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Em uma
sorveteria há sorvetes nos sabores morango, chocolate, abacaxi e flocos.</span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">De quantas maneiras podemos montar uma casquinha
com duas bolas nessa sorveteria? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">10 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">9 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">8 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">7 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">6 maneiras </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">5 Num grupo de 8 pessoas incluem-se Ana e Bia e
deseja-se formar uma comissão de 5 pessoas.
Atenda as solicitações seguintes:</span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="margin: 0cm 0cm 0.0001pt; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Qual o número total de comissões que podem ser
formadas<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin: 0cm 0cm 0.0001pt; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">b)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Em quantas das comissões do item A) Bia e Ana não
estão presentes ?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin: 0cm 0cm 0.0001pt; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">c)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Em quantas das comissões do item A) Bia ou Ana
estão presentes ?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin: 0cm 0cm 0.0001pt; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">d)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Em quantas das comissões do item A) Bia e Ana estão
presentes ?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">6 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Uma família do interior, composta
por 10 pessoas, necessita fazer uma viagem de retorno à cidade de origem após
passar férias no litoral. A viagem será feita de ônibus, no domingo, e apenas
dois horários estão disponíveis. De quantas maneiras poderão viajar essas
pessoas de forma que a metade da família viaje num ônibus e a outra metade no
outro? </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">45 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-hansi-font-family: Arial;">252</span><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">136 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">90 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">7 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Oito garotas chegam de férias a
uma pequena cidade do litoral norte. Dirigem-se a um hotel onde somente estão
disponíveis dois quartos triplos e um quarto duplo.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> De quantos
modos diferentes elas podem alojar-se no hotel?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="margin: 0cm 0cm 0.0001pt; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">320 b)
240 c)120 d) 480 e) 560<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin: 0cm 0cm 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">8<b>.</b>
(Enem 2ª aplicação 2010) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Considere que um professor
de arqueologia tenha obtido recursos para visitar 5 museus, sendo 3 deles no
Brasil e 2 fora do país. Ele decidiu restringir sua escolha aos museus
nacionais e internacionais relacionados na tabela a seguir.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 5.65pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Museus nacionais<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: none; border-top: solid windowtext 1.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Museus internacionais<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Masp </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">—<b> </b>São Paulo<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Louvre — </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Paris<o:p></o:p></span></div>
</td>
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<tr>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">MAM — </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">São Paulo<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Prado </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">— Madri<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Ipiranga — </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">São Paulo<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">British Museum — </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Londres<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Imperial — </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Petrópolis<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border: none; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Metropolitan — </span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Nova York<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">De acordo com os recursos obtidos, de
quantas maneiras diferentes esse professor pode escolher os 5 museus para
visitar? </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">6 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">8 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">20 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">24 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">36 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">9 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">O início da década de oitenta foi marcado por um estilo que ficou
conhecido como <i>new wave</i>. Um grande
sucesso dessa época foi a música <i>Safety Dance </i>do grupo canadense <i>Men
Without Hats</i>. No videoclipe da<i> </i>música, ambientado num cenário
medieval, um casal dança ao som da música e, no refrão “<i>Oh Well the safety
dance, ah yes the safety dance”</i>, forma com os braços a letra S, inicial de <i>Safety</i>. Essa representação ficou sendo a
marca registrada do sucesso alcançado. Alguns programas e séries da TV atual
apresentaram a sua versão para o <i>Safety
Dance</i>. Nas figuras a seguir, estão representadas a versão original, a
versão da série animada <i>Uma família da
pesada</i> e a versão da série <i>Glee</i>.</span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-no-proof: yes;"><v:shape id="Imagem_x0020_18" o:spid="_x0000_i1041" style="height: 303.75pt; mso-wrap-style: square; visibility: visible; width: 438.75pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image002.png">
</v:imagedata></v:shape></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqgSwJDQ62fO8jMMRrYBLhgLYmqBL0OKZsKQtBzaMHAQWSumVi1CPLZa6NO-Y-x28tB4AlQOi75HMstNBKEVsBGA2Aju5rkf4PZkCe_Erwd7t6dxcX8_hsNn041bR3TQzznnOL-lWbt10/s1600/c+9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="221" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqgSwJDQ62fO8jMMRrYBLhgLYmqBL0OKZsKQtBzaMHAQWSumVi1CPLZa6NO-Y-x28tB4AlQOi75HMstNBKEVsBGA2Aju5rkf4PZkCe_Erwd7t6dxcX8_hsNn041bR3TQzznnOL-lWbt10/s320/c+9.png" width="320" /></a></div>
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span><br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Na versão da série <i>Glee</i> do <i>Safety Dance</i>, um grupo de atores dança no<i> hall</i> de um <i>shopping center</i>,
enquanto os demais apenas observam. Suponha que, para a execução da cena, foi
necessário escolher, dentre 6 atores e 8 atrizes, um grupo formado por 5 atores
e 5 atrizes. Quantos grupos de dançarinos podem ser escolhidos dessa forma? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">336. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">168. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">70. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">48. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">25. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">10 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Um juiz dispõe de 10 pessoas, das
quais somente 4 são advogados, para formar um único júri com 7 jurados. O
número de formas de compor o júri, com pelo menos um advogado é </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">70 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><v:shape id="_x0000_i1025" o:ole="" style="height: 15pt; width: 14.25pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025"
DrawAspect="Content" ObjectID="_1441994661">
</o:OLEObject>
</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">120 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><v:shape id="_x0000_i1026" o:ole="" style="height: 15pt; width: 14.25pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image004.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026"
DrawAspect="Content" ObjectID="_1441994662">
</o:OLEObject>
</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">140 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">11<b>.</b> (Uerj 2010) </span><b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR; mso-no-proof: yes;"><o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt;">
<b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR; mso-no-proof: yes;"><v:shape alt="Descrição: uerj2010_1f_ciencias_natureza_mat_39.gif" id="Imagem_x0020_21" o:spid="_x0000_i1040" style="height: 149.25pt; mso-wrap-style: square; visibility: visible; width: 408.75pt;" type="#_x0000_t75">
<v:imagedata o:title="uerj2010_1f_ciencias_natureza_mat_39" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png">
</v:imagedata></v:shape></span></b><b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><o:p></o:p></span></b></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdFARCgmb6d441wfEpr-_dUJwsvzypb8cux78yztbYZ1HYKnmu2OJCpMaZry6Dpeule69uWr3CJzOsBp4HPxYx8SgNg4Hk2JvyU17HRNnjeEOve0AFpum7IvCTwNtf0hyphenhyphen0MQSoDz1mu4E/s1600/c+11.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdFARCgmb6d441wfEpr-_dUJwsvzypb8cux78yztbYZ1HYKnmu2OJCpMaZry6Dpeule69uWr3CJzOsBp4HPxYx8SgNg4Hk2JvyU17HRNnjeEOve0AFpum7IvCTwNtf0hyphenhyphen0MQSoDz1mu4E/s400/c+11.png" width="400" /></a></div>
<br />
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Considere como um único conjunto as 8 crianças – 4
meninos e 4 meninas – personagens da tirinha. A partir desse conjunto, podem-se
formar <i>n </i>grupos, não vazios, que apresentam um número igual de meninos e
de meninas. <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">O maior valor de <i>n </i>é equivalente a: </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">45 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">56 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">69 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">81 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">12 Um
cientista recebeu 5 cobaias para usar em seu estudo sobre uma nova vacina. Seus
cálculos indicaram que o número de maneiras possíveis de escolher pelo menos 3
cobaias é: <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) 10.
b) 16. c) 50. d) 120. e) 60. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div style="border-bottom: solid #4F81BD 1.0pt; border: none; mso-border-bottom-themecolor: accent1; mso-element: para-border-div; padding: 0cm 0cm 4.0pt 0cm;">
<div class="MsoTitleCxSpFirst">
<span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-family: 'Times New Roman', serif; font-size: 12pt;">13,Na Rua do Amparo, na
Cidade de Olinda, Pernambuco, forma escolhidas 10 casas distintas, sendo 6 do
lado direito e 4 do lado esquerdo da rua.</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><br />
<span style="background: white;">Se for escolhida uma pessoa ao acaso em cada uma
das nove casas, quantas comissões de <i>três pessoas podem ser formadas, de modo que
elas não morem no mesmo lado da rua? a) 74 b) 82 c) 96 d) 112 e) 144 <o:p></o:p></i></span></span></div>
<div class="MsoTitleCxSpLast">
<br /></div>
</div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">14</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Régis está em uma loja de roupas e deseja
selecionar 3 camisas dentre 10 modelos diferentes, sendo essas 6 brancas e 4
azuis. De quantas maneiras ele poderá escolher as 3 camisas de forma que pelo
menos uma delas tenha cor distinta das demais? </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) 74 b) 82
c) 96 d) 112 e) 144 <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">15<b>.</b>
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A tabela abaixo apresenta os critérios adotados por
dois países para a formação de placas de automóveis. Em ambos os casos, podem
ser utilizados quaisquer dos 10 algarismos de 0 a 9 e das 26 letras do alfabeto
romano.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 5.65pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">País<o:p></o:p></span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Descrição<o:p></o:p></span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 103.6pt;" width="138"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Exemplo de placa<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">X<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">3 letras e 3
algarismos, em qualquer ordem<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 103.6pt;" width="138"><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguDfD1hcb6UPH-Bh87K99Pwz6V1Jw_FY1X3H7vifjHfzpuQt4v41rEg8DU2WzkakJ-7iBMeCWZs0RoDnnjdSA06gslfHqvD_pQmfj18vARkv1ddRHG4uRoiOUywo0lXTccbFu-j6FswGM/s1600/15a.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguDfD1hcb6UPH-Bh87K99Pwz6V1Jw_FY1X3H7vifjHfzpuQt4v41rEg8DU2WzkakJ-7iBMeCWZs0RoDnnjdSA06gslfHqvD_pQmfj18vARkv1ddRHG4uRoiOUywo0lXTccbFu-j6FswGM/s1600/15a.png" /></a></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR; mso-no-proof: yes;"><v:shape id="Imagem_x0020_22" o:spid="_x0000_i1039" style="height: 39pt; mso-wrap-style: square; visibility: visible; width: 84.75pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image006.wmz">
</v:imagedata></v:shape></span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<br /></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Y<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">um bloco de 3
letras, em qualquer ordem,<o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">à esquerda de
outro bloco de 4 algarismos,<o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">também em
qualquer ordem<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 103.6pt;" width="138"><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgS6DSZRjFTHLDDnGjZIq7U1CpKH7HvrdgSTVqa_JR4u14r8dF0PWZUJ4ICS3r1EDKKXRPgVkib929wTYgljUUl2llKADS6F8-qvR39RnKVySMlH_PQEsjtQ5E2mDsHOewVUD04_EyfX4/s1600/15b.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgS6DSZRjFTHLDDnGjZIq7U1CpKH7HvrdgSTVqa_JR4u14r8dF0PWZUJ4ICS3r1EDKKXRPgVkib929wTYgljUUl2llKADS6F8-qvR39RnKVySMlH_PQEsjtQ5E2mDsHOewVUD04_EyfX4/s1600/15b.png" /></a></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR; mso-no-proof: yes;"><v:shape id="Imagem_x0020_23" o:spid="_x0000_i1038" style="height: 39pt; mso-wrap-style: square; visibility: visible; width: 93.75pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image007.wmz">
</v:imagedata></v:shape></span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<br /></div>
</td>
</tr>
</tbody></table>
</div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Considere o número máximo de placas
distintas que podem ser confeccionadas no país X<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">igual a <i>n </i>e no país Y igual a <i>p. </i>A<i> <span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"><v:shape id="_x0000_i1027" o:ole="" style="height: 29.25pt; width: 11.25pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image008.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027"
DrawAspect="Content" ObjectID="_1441994664">
</o:OLEObject>
</xml><![endif]--></span> </i>razão
corresponde a: </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">1 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">2 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">3 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">6 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Enunciado
para as questões 16 e 17 <o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">A escrita
Braile para cegos é um sistema de símbolos no qual cada caractere é um conjunto
de 6 pontos dispostos em forma retangular, dos quais pelo menos um se destaca
em relação aos demais.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0PP3ALz_1Rg2kNW7HTNX-4joeCb8bxfl7N_NL3WAR2S2YfN0bfv8PbgCPzCWa1xeZ50CynNGwYrFxOnT9uehb4XQUqmA1jhSPjKOM0ke4j54xJEzLrTrngdXmt7lPrKf1giCjSn9UYP8/s1600/c+16.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0PP3ALz_1Rg2kNW7HTNX-4joeCb8bxfl7N_NL3WAR2S2YfN0bfv8PbgCPzCWa1xeZ50CynNGwYrFxOnT9uehb4XQUqmA1jhSPjKOM0ke4j54xJEzLrTrngdXmt7lPrKf1giCjSn9UYP8/s1600/c+16.png" /></a></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Por
exemplo, a letra </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><v:shape id="_x0000_i1028" o:ole="" style="height: 12pt; width: 11.25pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image009.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028"
DrawAspect="Content" ObjectID="_1441994665">
</o:OLEObject>
</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> A representada por<br />
</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-no-proof: yes;"><br />
<v:shape id="Imagem_x0020_19" o:spid="_x0000_i1037" style="height: 72.75pt; mso-wrap-style: square; visibility: visible; width: 65.25pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image010.wmz">
</v:imagedata></v:shape><br />
<!--[if !supportLineBreakNewLine]--><br />
<!--[endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">16. O
número total de caracteres que podem ser representados no sistema Braile é </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><v:shape id="_x0000_i1029" o:ole="" style="height: 12pt; width: 17.25pt;" type="#_x0000_t75">
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><v:shape id="_x0000_i1030" o:ole="" style="height: 12.75pt; width: 17.25pt;" type="#_x0000_t75">
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</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><v:shape id="_x0000_i1031" o:ole="" style="height: 12.75pt; width: 17.25pt;" type="#_x0000_t75">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1031"
DrawAspect="Content" ObjectID="_1441994668">
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</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><v:shape id="_x0000_i1032" o:ole="" style="height: 12.75pt; width: 17.25pt;" type="#_x0000_t75">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
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</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><v:shape id="_x0000_i1033" o:ole="" style="height: 12.75pt; width: 23.25pt;" type="#_x0000_t75">
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</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1033"
DrawAspect="Content" ObjectID="_1441994670">
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</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">17 Se </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">a escrita
Braile apresentasse um conjunto de 7 pontos ao invés dos 6 atuais. O número de
caracteres, em relação ao atual, aumentaria de:</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoListParagraph" style="line-height: 105%; margin-bottom: 2.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l4 level1 lfo1; mso-pagination: none; text-autospace: none; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">24 b) 32
c) 48 d) 64
e) 78<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<u><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></u></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">18 (Fgv 2011) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">As saladas de frutas de um restaurante são feitas
misturando pelo menos duas frutas escolhidas entre: banana, laranja, maçã,
abacaxi e melão.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Quantos tipos diferentes de saladas de
frutas podem ser feitos considerando apenas os tipos de frutas e não as
quantidades? </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">26 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">24 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">22 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">30 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">28 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<u><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></u></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">19.As
frutas são alimentos que não podem faltar na nossa alimentação, pelas suas
vitaminas e pela energia que nos fornecem. Vera consultou um nutricionista que
lhe sugeriu uma dieta que incluísse a ingestão de três frutas diariamente,
dentre as seguintes opções: abacaxi, banana, caqui, laranja, maçã, pera e uva.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Suponha
que Vera siga rigorosamente a sugestão do nutricionista, ingerindo três frutas
por dia, sendo pelo menos duas diferentes. Então, ela pode montar sua dieta
diária, com as opções diferentes de frutas recomendadas, de: </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">57 maneiras. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">50 maneiras. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">56 maneiras. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">77 maneiras. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">98 maneiras. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<u><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></u></div>
<div class="MsoNormal">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">20<b>.</b> Um
casal está fazendo uma trilha junto com outras 10 pessoas. Em algum momento,
eles devem cruzar um rio em 4 jangadas, cada uma com capacidade para 3 pessoas
(excluindo o jangadeiro). De quantas maneiras, os grupos podem ser organizados
para a travessia, se o casal quer ficar na mesma jangada? <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) 2200
b) 2400 c) 2600 d) 2800 e) 3000<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">21. Em um jogo lotérico, com 40 dezenas distintas e
possíveis de serem escolhidas para aposta, são sorteadas 4 dezenas e o ganhador
do prêmio maior deve acertar todas elas. Se aposta mínima, em 4 dezenas, custa
R$ 2,00,<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">uma aposta em seis dezenas deve custar:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; mso-layout-grid-align: none; mso-list: l2 level1 lfo5; tab-stops: list 36.0pt; text-autospace: none; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">R$ 15,00<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; mso-layout-grid-align: none; mso-list: l2 level1 lfo5; tab-stops: list 36.0pt; text-autospace: none; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">b)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">R$ 30,00<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; mso-layout-grid-align: none; mso-list: l2 level1 lfo5; tab-stops: list 36.0pt; text-autospace: none; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">c)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">R$ 35,00<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; mso-layout-grid-align: none; mso-list: l2 level1 lfo5; tab-stops: list 36.0pt; text-autospace: none; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">d)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">R$ 70,00<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; mso-layout-grid-align: none; mso-list: l2 level1 lfo5; tab-stops: list 36.0pt; text-autospace: none; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">e)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">R$ 140,00<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<u><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></u><u><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></u></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">22. No jogo da quina são
sorteadas 5 dezenas de um total de 80. O apostador deve marcar um mínimo de 5 e
um máximo de 7 dezenas em um volante.O valor da aposta varia de acordo com u
número de dezenas marcadas. Para 5 dezenas, o valor é R$ 0,75. Para 6, R$ 3,00
e para 7,R$ 7,50. Um apostador tem R$ 15,00 e observou que com este valor ele
tem ,dentre outras possibilidades, 5 opções para jogar: <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Opção 1: 2 volantes distintos de 7 dezenas cada<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Opção 2: 5 volantes distintos de 6 dezenas cada<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Opção 3: 20 volantes distintos de 5 dezenas cada<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Opção 4: 10 volantes distintos de 5 dezenas cada e 1
volante com 7 dezenas<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">Opção 5: 4 volantes distintos de 5 dezenas cada e 4
volante com 6 dezenas<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">A opção que permite a maior
chance para o apostador será a:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoListParagraph" style="margin: 0cm 0cm 0.0001pt; text-indent: 0cm;">
<!--[if !supportLists]--><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">primeira b) segunda c) terceira<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> d)
quarta e) quinta<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">23. Maria faz uma aposta de 8
números na Mega-sena tentando acertar os 6 números. Se tivesse feito uma aposta
de 10 números suas chances teriam aumentado, em relação a aposta de 8 números
em:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) 200%
b) 360%
c) 480% d) 650% e) 800%<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">24<b>.</b>
(Pucpr 2010) </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">No jogo da
Mega Sena, um apostador pode assinalar entre 6 e 15 números, de um total de 60
opções disponíveis. O valor da aposta é igual a R$ 2,00 multiplicado pelo
número de sequencias de seis números que são possíveis, a partir daqueles
números assinalados pelo apostador.</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaWINAfaK9ltMpulysMACwxcohF78ob1e2KlP-zFC41WXzZWVuHHmQ0Angug36YF0By52zqWTxtwIw7972qA6mmdYXHSoGqtA2f_b_QnVMG4V1yJAXg49Oa2y7kfAwq-XYoZNEK5fo7l0/s1600/c+24.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaWINAfaK9ltMpulysMACwxcohF78ob1e2KlP-zFC41WXzZWVuHHmQ0Angug36YF0By52zqWTxtwIw7972qA6mmdYXHSoGqtA2f_b_QnVMG4V1yJAXg49Oa2y7kfAwq-XYoZNEK5fo7l0/s320/c+24.png" width="320" /></a></div>
<o:p></o:p><br />
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Por exemplo: se o apostador assinala 6 números, tem
apenas uma sequencia favorável e paga R$ 2,00 pela aposta. Se o apostador
assinala 7 números, tem sete sequencias favoráveis, ou seja, é possível formar
sete sequencias de seis números a partir dos sete números escolhidos. Neste
caso, o valor da aposta é R$ 14,00.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR; mso-no-proof: yes;"><v:shape id="Imagem_x0020_24" o:spid="_x0000_i1036" style="height: 270pt; mso-wrap-style: square; visibility: visible; width: 5in;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image016.png">
</v:imagedata></v:shape></span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Considerando que se trata de uma aplicação de
matemática, sem apologia a qualquer tipo de jogo, assinale a única alternativa CORRETA. </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A aposta máxima custará R$
5.005,00. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Uma aposta com 14 números
assinalados custará entre R$ 3.000,00 e R$ 3.050,00. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Apostar dois cartões com
dez números assinalados, ou cinco cartões com nove números assinalados, são
opções equivalentes em termos de custo e de chance de ser ganhador do prêmio
máximo. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O custo de uma aposta com
12 números assinalados será inferior a R$ 1.830,00. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Apostar um cartão com 13
números assinalados custará o dobro da aposta de um cartão com 12 números
assinalados. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Enunciado para as questões 25 e 26<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">A população brasileira sabe, pelo menos
intuitivamente, que a probabilidade de acertar as seis dezenas da mega sena não
é zero, mas é quase.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Mesmo assim, milhões de pessoas são atraídas por
essa loteria, especialmente quando o prêmio se acumula em valores altos. Até
junho de 2009, cada aposta de seis dezenas, pertencentes ao conjunto {01, 02,
03, ..., 59, 60}, custava R$ 1,50.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div align="right" class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-align: right; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Disponível
em: www.caixa.gov.br. Acesso em: 7 jul. 2009.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">25. Considere que uma pessoa decida apostar
exatamente R$ 126,00 e que esteja mais interessada em acertar apenas cinco das
seis dezenas da mega sena, justamente pela dificuldade desta última. Nesse
caso, é melhor que essa pessoa faça 84 apostas de seis dezenas diferentes, que
não tenham cinco números em comum, do que uma única aposta com nove dezenas,
porque a probabilidade de acertar a quina no segundo caso em relação ao
primeiro é, aproximadamente, </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -11.0pt; position: relative; top: 11.0pt;"><v:shape id="_x0000_i1034" o:ole="" style="height: 29.25pt; width: 17.25pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image017.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1034"
DrawAspect="Content" ObjectID="_1441994671">
</o:OLEObject>
</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> vez menor. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-text-raise: -11.0pt; position: relative; top: 11.0pt;"><v:shape id="_x0000_i1035" o:ole="" style="height: 29.25pt; width: 18.75pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image018.wmz">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1035"
DrawAspect="Content" ObjectID="_1441994672">
</o:OLEObject>
</xml><![endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">vezes
menor. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">4 vezes menor. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">9 vezes menor. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">14 vezes menor. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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26. A possibilidade de acertar a quina jogando um cartão simples de 6 unidades em relação a acertar a sena é cerca de: <br />
a) 14 vezes maior
<br />
b) 68 vezes maior
<br />
c) 178 vezes maior
<br />
d) 384 vezes maior
<br />
e) 520 vezes maior
<br />
<br />
27. Num acampamento militar, serão instaladas três barracas: I, II e III. Nelas, serão alojados 10 soldados, dentre eles o soldado A e o soldado B, de tal maneira que fiquem 4 soldados na barraca I, 3 na barraca II e 3 na barraca III.
Se o soldado A deve ficar na barraca I e o soldado B NÃO deve ficar na barraca III, então o número de maneiras distintas de distribuí-los é igual a
<br />
a) 560
<br />
b) 1120
<br />
c) 1680
<br />
d) 2240
<br />
e) 2480 </div>
<br />
28. As pedras de um dominó usual são compostas por dois quadrados, com 7 possíveis marcas (de zero pontos até 6 pontos). Quantas pedras terá um dominó se cada quadrado puder ter até 9 pontos? Veja no desenho abaixo um exemplo de uma nova pedra do dominó.
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwqMS4N6vfH9sHR6jMghYnU3oKU7EVxSUNXa9MO7YW62CvdHuP_5psxM65Lq_lx088cNdA2xAb181ipHhtdbS37I-GhfyHCAijakbVJk7zhoq0PPcnLkx_alz9kMOAMmb83ICY3ig127s/s1600/d.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwqMS4N6vfH9sHR6jMghYnU3oKU7EVxSUNXa9MO7YW62CvdHuP_5psxM65Lq_lx088cNdA2xAb181ipHhtdbS37I-GhfyHCAijakbVJk7zhoq0PPcnLkx_alz9kMOAMmb83ICY3ig127s/s320/d.png" /></a></div>
<br />
a) 36.
<br />
b) 40.
<br />
c) 46.
<br />
d) 55.
<br />
e) 62.<br />
<br />
29.Cinco pescadores, pescando individualmente, conseguiram pegar ao todo 10 peixes. Uma pessoa, que não participou da pescaria, propôs descobrir quantos peixes cada um havia pescado. O número mínimo de tentativas que garante que essa pessoa acerte é:
<br />
a) 1001
<br />
b )10
<br />
c) 252
<br />
d) 30240
<br />
e) 120 Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-14602851076836538952013-09-29T17:06:00.000-07:002013-11-03T06:12:03.182-08:00Análise Combinatória 3 - Arranjo<div align="center" class="MsoNormal" style="text-align: center;">
<b><span style="font-size: 48.0pt; line-height: 115%; mso-fareast-language: ZH-CN;">ARRANJO<o:p></o:p></span></b></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">1<b>.</b> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Doze
times se inscreveram em um torneio de futebol amador. O jogo de abertura do
torneio foi escolhido da seguinte forma: primeiro foram sorteados 4 times para
compor o Grupo A. Em seguida, entre os times do Grupo A, foram sorteados 2
times para realizar o jogo de abertura do torneio, sendo que o primeiro deles
jogaria em seu próprio campo, e o segundo seria o time visitante.<o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">A quantidade total de escolhas possíveis para o
Grupo A e a quantidade total de escolhas dos times do jogo de abertura podem
ser calculadas através de </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">uma combinação e um arranjo,
respectivamente. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">um arranjo e uma combinação,
respectivamente. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">um arranjo e uma permutação,
respectivamente. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">duas combinações. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">dois arranjos. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">2<b>.</b> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Em virtude de uma crise financeira, uma fábrica dispõe de apenas quatro
vigilantes para ocuparem sete postos de vigilância.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Considerando
que, em cada posto, fica, no máximo, um vigilante e que o posto da entrada
principal não pode ficar desguarnecido, indique a opção correspondente ao
número de maneiras distintas de que o chefe de segurança pode dispor para
distribuir os vigilantes.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Obs.:
Duas maneiras são ditas idênticas se, em ambas, os vigilantes ocupam os mesmos
postos e cada posto é ocupado pelo mesmo vigilante; caso contrário, são ditas
distintas. </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">35 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">80 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">480 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">840 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">3<b>.</b> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Para mostrar aos seus clientes alguns dos produtos que vende, um
comerciante reservou um espaço em uma vitrine, para colocar exatamente 3 latas
de refrigerante, lado a lado. Se ele vende 6 tipos diferentes de refrigerante,
de quantas maneiras distintas pode expô-los na vitrine? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">144 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">132 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">120 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">72 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">20 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">4<b>.</b> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">O conselho administrativo de um sindicato é constituído por doze
pessoas, das quais uma é o presidente deste conselho. A diretoria do sindicato
tem quatro cargos a serem preenchidos por membros do conselho, sendo que o
presidente da diretoria e do conselho não devem ser a mesma pessoa. De quantas
maneiras diferentes esta diretoria poderá ser formada? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">40. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">7920. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">10890. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">11!. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">12!. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">5 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Uma prova
de atletismo é disputada por 9 atletas, dos quais apenas 4 são brasileiros. Os
resultados possíveis para a prova, de modo que pelo menos um brasileiro fique
numa das três primeiras colocações, são em número de: </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">426 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">444 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">468 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">480 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">504 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">6</span></b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> ( </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Vinte times de futebol disputam a Série A do
Campeonato Brasileiro, sendo seis deles paulistas. Cada time joga duas vezes
contra cada um dos seus adversários. A porcentagem de jogos nos quais os dois
oponentes são paulistas é </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">menor que 7%. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">maior que 7%, mas menor que 10%. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">maior que 10%, mas menor que 13%.
</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">maior que 13%, mas menor que 16%.
</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">maior que 16%. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">7. Seis amigos, entre eles Alice e Bernardo, vão
jantar em uma mesa triangular, cujos
lados têm 2, 3 e 4 lugares, como na fi gura. De quantas maneiras esses amigos
podem sentar-se à mesa de modo que Alice
e Bernardo fiquem </span><span style="font-family: Arial, sans-serif; font-size: 10pt;">juntos e em um mesmo lado da mesa?</span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-no-proof: yes;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
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</span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAUov5Sg7ur5iWwwczkVn40IuItZc5El8CGjGfk4tzbZjn8hSzJTh-V2YVoukRGD4rSbT6v0SxB3WjW_7YH_ZYeBsZaLhH1-u9jiuvnhecGaiqNWWIlcRnsVLybbBOj5kmVpCFLidUqsw/s1600/arranjo+7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAUov5Sg7ur5iWwwczkVn40IuItZc5El8CGjGfk4tzbZjn8hSzJTh-V2YVoukRGD4rSbT6v0SxB3WjW_7YH_ZYeBsZaLhH1-u9jiuvnhecGaiqNWWIlcRnsVLybbBOj5kmVpCFLidUqsw/s1600/arranjo+7.png" /></a></div>
<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) 288 <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) 6720 <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) 10080 <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) 15120 <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) 60480<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">8. (Pucsp 2011)
</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Na sala de reuniões de certa empresa há uma mesa
retangular com 10 poltronas dispostas da forma como é mostrado na figura
abaixo.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-no-proof: yes;"><v:shape id="Imagem_x0020_8" o:spid="_x0000_i1025" style="height: 108.75pt; mso-wrap-style: square; visibility: visible; width: 207.75pt;" type="#_x0000_t75">
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</v:imagedata></v:shape></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmU8ggaWC6h6apuSE-Fh1ZF7lt6PhDfRxVeTqg0Z9hARBpUX3wugwi-kO-AxpyWommzhQJzZ-Z0Lx8RsdSZcU9QrXBiF1OrEgaq2RA8mQBB321wyj7PNVC7Tp_rx70NNZwpDaneEtjJAc/s1600/arranjo+8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmU8ggaWC6h6apuSE-Fh1ZF7lt6PhDfRxVeTqg0Z9hARBpUX3wugwi-kO-AxpyWommzhQJzZ-Z0Lx8RsdSZcU9QrXBiF1OrEgaq2RA8mQBB321wyj7PNVC7Tp_rx70NNZwpDaneEtjJAc/s1600/arranjo+8.png" /></a></div>
<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Certo dia, sete pessoas foram
convocadas para participar de uma reunião a ser realizada nessa sala: o
presidente, o vice-presidente, um secretário e quatro membros da diretoria.
Sabe-se que: o presidente e o vice-presidente deverão ocupar exclusivamente as
poltronas das cabeceiras da mesa; o secretário deverá ocupar uma poltrona ao
lado do presidente.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Considerando que tais poltronas
são fixas no piso da sala, de quantos modos as sete pessoas podem nelas se
acomodar para participar de tal reunião?</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">3.360 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">2.480</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">1.680 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">1.240 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">840</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">9<b>.</b> (Ufjf 2011) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Para uma viagem, seis amigos alugaram três
motocicletas distintas, com capacidade para duas pessoas cada. Sabe-se que
apenas quatro desses amigos são habilitados para pilotar motocicletas e que não
haverá troca de posições ao longo do percurso. De quantas maneiras distintas
esses amigos podem se dispor nas motocicletas para realizar a viagem? </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">24 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">72 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">120 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">144 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">720 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
</div>
<div class="MsoNormal">
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10. Um vagão de metrô tem 10 bancos individuais, sendo 5 de frente e 5 de costas. De 10 passageiros, 4 preferem sentar de frente, 3 preferem sentar de costas e os demais não têm preferência. De quantos modos eles podem sentar, respeitadas as preferências?
<br />
a) Um número inteiro maior que 40000.
<br />
b) Um número inteiro entre 167 e 40000.
<br />
c) Exatamente 166.
<br />
d) Um número inteiro menor que 100.
<br />
e) Exatamente 40000.
Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-16724241224391395542013-09-29T14:03:00.003-07:002013-11-03T05:39:56.873-08:00Análise Combinatória 2 - Permutação<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Arial","sans-serif"; font-size: 36.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">PERMUTAÇÃO<o:p></o:p></span></b></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
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<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">1 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Um clube
resolve fazer uma Semana de Cinema. Para isso, os organizadores escolhem sete
filmes, que serão exibidos um por dia. Porém, ao elaborar a programação, eles
decidem que três desses filmes, que são de ficção científica, devem ser exibidos
em dias consecutivos.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Nesse
caso, o número de maneiras DIFERENTES de se fazer a programação dessa semana é </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">144 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">576 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">720 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">1040 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">2</span></b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Seis pessoas, entre elas João e Pedro, vão ao cinema. Existem seis
lugares vagos, alinhados e consecutivos. O número de maneiras distintas como as
seis podem sentar-se sem que João e Pedro fiquem juntos é </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">720 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">600 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">480 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">240 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">120 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">3 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">O setor de recursos humanos de uma empresa vai
realizar uma entrevista com 120 candidatos a uma vaga de contador. Por sorteio,
eles pretendem atribuir a cada candidato um número, colocar a lista de números
em ordem numérica crescente e usá-la para convocar os interessados. Acontece
que, por um defeito do computador, foram gerados números com 5 algarismos
distintos e, em nenhum deles, apareceram dígitos pares. <o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Em razão
disso, a ordem de chamada do candidato que tiver recebido o número 75.913 é </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">24. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">31. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">32. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">88. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">89. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">4 Seguindo a etiqueta japonesa, um restaurante
tipicamente oriental solicita aos seus clientes que retirem seus calçados na
entrada do estabelecimento. Em certa noite, 6 pares de sapato e 2 pares de
sandálias, todos distintos, estavam dispostos na entrada do restaurante, em
duas fileiras com quatro pares de calçados cada uma. Se esses pares de calçados
forem organizados nessas fileiras de tal forma que as sandálias devam ocupar as
extremidades da primeira fila, de quantas formas diferentes podem-se organizar
esses calçados nas duas fileiras? </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> a)
6! b) 2 . 6!
c) 4 .
6! d)
6 . 6! e)
8! <o:p></o:p></span></div>
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<br /></div>
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<br /></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">5.Em cada ingresso vendido para um show de música,
é impresso o número da mesa onde o comprador deverá se sentar. Cada mesa possui
seis lugares, dispostos conforme o esquema a seguir.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI11UNhW8FrohtIf1RmZgi8JeCz4DkuK_kgiLHGAPRezzLfdkZ14H7Ffnlc-cTqWoKbml40daZMnTwxeIiBjWAqb17EBSGblM4OkOQiYU3yv5PjOWdnQ3F0WTWjGM7Ch9RRXIOdyFDP5M/s1600/permu+5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI11UNhW8FrohtIf1RmZgi8JeCz4DkuK_kgiLHGAPRezzLfdkZ14H7Ffnlc-cTqWoKbml40daZMnTwxeIiBjWAqb17EBSGblM4OkOQiYU3yv5PjOWdnQ3F0WTWjGM7Ch9RRXIOdyFDP5M/s1600/permu+5.png" /></a></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">O lugar da mesa em que cada comprador se sentará
não vem especificado no ingresso, devendo os seis ocupantes entrar em acordo.
Os ingressos para uma dessas mesas foram adquiridos por um casal de namorados e
quatro membros de uma mesma família. Eles acordaram que os namorados poderiam
sentar-se um ao lado do outro. Nessas condições, o número de maneiras distintas
em que as seis pessoas poderão ocupar os lugares da mesa é </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">96. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">120. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">192. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">384. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">720. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">6. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Oito amigos entraram em um restaurante para
jantar e sentaram-se numa mesa retangular, com oito lugares, como mostra a
figura a seguir:</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFLWHH8zJUmyQ4_ZLuLEHXbVJMUxAYPrgbsuTiD-15uae7FF4dEk7v1j0IDink5e0gmj71WXA_NJk6evCAY2UtcdXqRC97eSIDnb53dLtNq_qPTAQsWZVAxhhVMIhyphenhyphenIachTsDYHXDVtyQ/s1600/permu+6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFLWHH8zJUmyQ4_ZLuLEHXbVJMUxAYPrgbsuTiD-15uae7FF4dEk7v1j0IDink5e0gmj71WXA_NJk6evCAY2UtcdXqRC97eSIDnb53dLtNq_qPTAQsWZVAxhhVMIhyphenhyphenIachTsDYHXDVtyQ/s1600/permu+6.png" /></a></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Dentre todas as configurações possíveis, quantas
são as possibilidades de dois desses amigos, Amaro e Danilo, ficarem sentados
em frente um do outro? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">1 440 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">1 920 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">2 016 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">4 032 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">5 760 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">7<b>.</b> </span><b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> </span></b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">As ruas da cidade interceptam-se em ângulos retos,
como mostra a figura. Certo dia, uma pessoa decide almoçar no único restaurante
da cidade. Quantos caminhos diferentes ela podem escolher para ir do hotel ao
restaurante? Elas caminham somente para o norte ou para o leste. A figura
indica um possível caminho.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFdwGn6DHEmw7nat1HtSC3p0Nd8H1GBPlsY2PjFLlB2M8hu59GhqFfNkwzZKyjbaf5sq5fFk8p_DI3VEgo1ZckleG5k9VWsjbG20TIIWYvGoB1DBF1rGQVEIUUFsZ9fhn6N7CpBwX80l4/s1600/permuta+7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFdwGn6DHEmw7nat1HtSC3p0Nd8H1GBPlsY2PjFLlB2M8hu59GhqFfNkwzZKyjbaf5sq5fFk8p_DI3VEgo1ZckleG5k9VWsjbG20TIIWYvGoB1DBF1rGQVEIUUFsZ9fhn6N7CpBwX80l4/s320/permuta+7.png" width="320" /></a></div>
<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span><br />
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8. Num episódio de uma série policial de televisão, um
agente secreto encontra-se diante do
desafio de descobrir a senha de quatro dígitos digitada no teclado
numérico, instalado na porta de entrada de num laboratório. Para isso, o agente
utiliza o seguinte artifício: borrifa um spray sobre o teclado, fazendo
com que os algarismos recém-digitados
para abrir a porta fiquem destacados, como mostra a figura. Para sua surpresa,
apenas três dígitos são ressaltados pelo spray, indicando que um dos dígitos
aparece duas vezes na senha.<o:p></o:p></div>
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a)36 b) 24 c) 16 d) 13 e)4 <br />
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9. Uma
equipe de natação, composta por 8 atletas (6 homens e 2 mulheres), ficará
hospedada no sexto andar de um hotel durante a realização de um torneio de
natação. Este andar possui oito quartos numerados e dispostos de forma
circular, conforme a figura abaixo. Sabendo que os atletas ficarão em quartos
individuais e que as mulheres não ficarão em quartos adjacentes, então o número
de maneiras distintas de alocar estes atletas nestes oito quartos é igual a:]<o:p></o:p></div>
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a)
40.6!. b) 4.5!.5! c) 8.<span style="font-family: "Cambria Math","serif"; mso-bidi-font-family: "Cambria Math"; mso-fareast-language: ZH-CN;">⋅</span>
5!. d) 5!.6!/4!<o:p></o:p></div>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-1404807771350562902013-09-29T13:44:00.004-07:002013-11-03T05:36:58.983-08:00Análise Combinatória 1- Princípio Fundamental da Contagem<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span style="font-family: "Arial","sans-serif"; font-size: 20.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">PRINCÍPIO
FUNDAMENTAL DA CONTAGEM<o:p></o:p></span></b></div>
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<br /></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">1</span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Um profissional de design de interiores precisa
planejar as cores que serão utilizadas em quatro paredes de uma casa, para isso
possui seis cores diferentes de tinta. O número de maneiras diferentes que esse
profissional poderá utilizar as seis cores nas paredes, sabendo-se que somente
utilizará uma cor em cada parede, é: </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">24 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">30 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">120 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">360 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">400 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">2 </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: Arial, sans-serif; font-size: 10pt;">O diretor de uma escola convidou os 280
alunos de terceiro ano a participarem de uma brincadeira. Suponha que existem 5
objetos e 6 personagens numa casa de 9 cômodos; um dos personagens esconde um
dos objetos em um dos cômodos da casa. O objetivo da brincadeira é adivinhar
qual objeto foi escondido por qual personagem e em qual cômodo da casa o objeto
foi escondido.</span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: Arial, sans-serif; font-size: 10pt;">Todos os alunos decidiram participar. A
cada vez um aluno é sorteado e dá a sua resposta. As respostas devem ser sempre
distintas das anteriores, e um mesmo aluno não pode ser sorteado mais de uma
vez. Se a resposta do aluno estiver correta, ele é declarado vencedor e a
brincadeira é encerrada. <o:p></o:p></span></div>
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<span style="font-family: Arial, sans-serif; font-size: 10pt;">O diretor sabe que algum aluno acertará
a resposta porque há </span><span style="font-family: Arial, sans-serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: Arial, sans-serif; font-size: 10pt;">10 alunos a mais do
que possíveis respostas distintas. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: Arial, sans-serif; font-size: 10pt;">20 alunos a mais do
que possíveis respostas distintas. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: Arial, sans-serif; font-size: 10pt;">119 alunos a mais do
que possíveis respostas distintas. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: Arial, sans-serif; font-size: 10pt;">260 alunos a mais do
que possíveis respostas distintas. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">270 alunos a mais do que
possíveis respostas distintas. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoHeader">
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<span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">3</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um
encontro científico conta com a participação de pesquisadores de três áreas,
sendo eles: 7 químicos, 5 físicos e 4 matemáticos. No encerramento do encontro,
o grupo decidiu formar uma comissão de dois cientistas para representá-lo em um
congresso. Tendo sido estabelecido que a dupla deveria ser formada por
cientistas de áreas diferentes, o total de duplas distintas que podem
representar o grupo no congresso é igual a </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">46.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">59.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">77.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">83.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">91.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">4 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Uma empresa escolherá um chefe
para cada uma de suas repartições A e
B. Cada chefe deve ser escolhido
entre os funcionários das respectivas repartições e não devem ser ambos do
mesmo sexo.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Abaixo é apresentado o quadro de funcionários das
repartições A e B.<o:p></o:p></span></div>
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<br /></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 5.65pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
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<td rowspan="2" style="border: solid windowtext 1.0pt; height: 14.15pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">FUNCIONÁRIOS<o:p></o:p></span></div>
</td>
<td colspan="2" style="border-left: none; border: solid windowtext 1.0pt; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">REPARTIÇÕES<o:p></o:p></span></div>
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<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">A<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">B<o:p></o:p></span></div>
</td>
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<tr style="height: 14.15pt; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Mulheres<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">4<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 14.15pt; mso-yfti-irow: 3; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Homens<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">6<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 14.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; page-break-after: avoid; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">3<o:p></o:p></span></div>
</td>
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</tbody></table>
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<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">De quantas maneiras é possível ocupar esses dois
cargos? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">12. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">24. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">42. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">54. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">72. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
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<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">5</span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">De acordo com o Conselho Nacional de Trânsito - CONTRAN, os veículos
licenciados no Brasil são identificados externamente por meio de placas cujos
caracteres são três letras do alfabeto e quatro algarismos.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Nas
placas a seguir, as letras estão em sequência e os algarismos também.<o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR1aULgxtAsFUjbOaGMjm61tH0vDDISvPDm6-Dv8FMr2m8aWsjv8cOKczZghSfQzr9TiCuKDtTAbWbenMIq4ulW47mblwwKHv0Bt2YF18smIg03mdv9Y5ZB_adkADfMyHZPDFPh-t31I8/s1600/pfc+5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR1aULgxtAsFUjbOaGMjm61tH0vDDISvPDm6-Dv8FMr2m8aWsjv8cOKczZghSfQzr9TiCuKDtTAbWbenMIq4ulW47mblwwKHv0Bt2YF18smIg03mdv9Y5ZB_adkADfMyHZPDFPh-t31I8/s1600/pfc+5.png" /></a></div>
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<br /></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">O
número de placas que podemos formar com as letras e os algarismos distribuídos
em sequência, como nos exemplos, é </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">192
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">168
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">184
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">208
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<br /></div>
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<br /></div>
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6<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10pt;">O quadro de
avisos de uma escola de ensino médio foi dividido em quatro partes, como mostra
a figura a seguir.</span><o:p></o:p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdEFd54npUScFpJWaMCxpk3rl-Do-t7W52MZogzBN4njaNOZImj3IGaQ6MSLMjnvG2-sVZloVKW-yax94TIGZhebQ6tBInuAht9M4TERrUOqtL2CUGPNnD-oHZ0X-ux1Z_pzfDp7IQ-LM/s1600/pfc+6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdEFd54npUScFpJWaMCxpk3rl-Do-t7W52MZogzBN4njaNOZImj3IGaQ6MSLMjnvG2-sVZloVKW-yax94TIGZhebQ6tBInuAht9M4TERrUOqtL2CUGPNnD-oHZ0X-ux1Z_pzfDp7IQ-LM/s1600/pfc+6.png" /></a></div>
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<span style="font-size: 10pt;">No retângulo à esquerda, são colocados os avisos da diretoria, e, nos
outros três retângulos, serão colocados, respectivamente, de cima para baixo,
os avisos dos 1º, 2º e 3º anos do ensino médio. <o:p></o:p></span></div>
<div class="MsoHeader">
<span style="font-size: 10pt;">A escola resolveu que retângulos adjacentes (vizinhos) fossem pintados,
no quadro, com cores diferentes. Para isso, disponibilizou cinco cores e
solicitou aos servidores e alunos sugestões para a disposição das cores no
quadro. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> O número máximo de sugestões diferentes que
podem ser apresentadas pelos servidores e alunos. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 36pt; text-indent: -18pt;">
<!--[if !supportLists]--><span style="font-size: 10.0pt; mso-bidi-font-family: Calibri; mso-bidi-font-size: 11.0pt; mso-bidi-theme-font: minor-latin; mso-fareast-language: PT-BR;">A)<span style="font-size: 7pt;"> </span></span><!--[endif]--><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">150 B) 160 C) 170 D) 180 E) 190</span><span style="font-family: "Arial","sans-serif"; font-size: 10pt; text-indent: -18pt;"><span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 10pt; text-indent: -18pt;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12pt; text-indent: -18pt;"> </span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">7 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">No
Nordeste brasileiro, é comum encontrarmos peças de artesanato constituídas por
garrafas preenchidas com areia de diferentes cores, formando desenhos. Um artesão
deseja fazer peças com areia de cores cinza, azul, verde e amarela, mantendo o
mesmo desenho, mas variando as cores da paisagem (casa, palmeira e fundo),
conforme a figura.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-KY9TFqHTdJiZ7B8UrPI15_1zgcuXja_TG7lJ7sAfz_-KM7w1ub9AzXEdb2JboB2V2SktHwYUx6PanOa1KEUFT8ZXMqGwcWZ_vCsoie0KxkwepZQSnaY7WM1_1_sZz4TWpaOrHbBX_U/s1600/pfc+7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-KY9TFqHTdJiZ7B8UrPI15_1zgcuXja_TG7lJ7sAfz_-KM7w1ub9AzXEdb2JboB2V2SktHwYUx6PanOa1KEUFT8ZXMqGwcWZ_vCsoie0KxkwepZQSnaY7WM1_1_sZz4TWpaOrHbBX_U/s1600/pfc+7.png" /></a></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">O fundo
pode ser representado nas cores azul ou cinza; a casa, nas cores azul, verde ou
amarela; e a palmeira, nas cores cinza ou verde. Se o fundo não pode ter a
mesma cor nem da casa nem da palmeira, por uma questão de contraste, então o
número de variações que podem ser obtidas para a paisagem é </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">6. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">7.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">8. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">9. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">10. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">8</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A
prefeitura de certo município solicitou ao Governo Federal uma verba para a
execução das seguintes obras:</span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">• saneamento básico;<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">• calçamento de ruas;<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">• construção de uma escola;<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">• construção de uma creche;<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">• construção de casas populares.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O Governo Federal aprovou a concessão da
verba solicitada, na condição de que fosse estabelecida uma ordem na execução
das obras, de modo que, tendo sido liberada a verba para a primeira obra, a
verba para a segunda só seria liberada após a conclusão da primeira, e assim
sucessivamente até a execução da última obra. Nesse contexto, considere o
planejamento feito pela prefeitura:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">• a primeira obra escolhida foi a construção
das casas populares;<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">• o calçamento das ruas só poderá ser
executado com o saneamento básico concluído.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Atendendo às condições estabelecidas pelo
Governo Federal e ao planejamento da prefeitura, é correto afirmar que o número
de maneiras possíveis e distintas para a realização dessas 5 obras é: </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">8 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">10 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">12 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">14 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">16 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">9 O estudo
da genética estabelece que, com as bases adenina (A), timina (T), citosina (C)
e guanina (G), podem-se formar, apenas, quatro tipos de pares: A-T, T-A, C-G e G-C.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Certo
cientista deseja sintetizar um fragmento de DNA com dez desses pares, de modo
que:<o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3d1YHxxzVtm67E6MuYyRo4Jqb5U_gooLCXhnmkxMSjBzw-qZvYTDed6gH-H8VvCAoy-mT2-YEqYclUtrq7zq7VIQmIqGS9gGTLoJ2wpq36U1CaznTUSFvvox01cuOvxZmJHTPv8OyTbA/s1600/pfc+9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3d1YHxxzVtm67E6MuYyRo4Jqb5U_gooLCXhnmkxMSjBzw-qZvYTDed6gH-H8VvCAoy-mT2-YEqYclUtrq7zq7VIQmIqGS9gGTLoJ2wpq36U1CaznTUSFvvox01cuOvxZmJHTPv8OyTbA/s1600/pfc+9.png" /></a></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">- dois
pares consecutivos não sejam iguais;<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">- um par
A-T não seja seguido por um par T-A e vice-versa;<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">- um par
C-G não seja seguido por um par G-C e vice-versa.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Sabe-se
que dois fragmentos de DNA são idênticos se constituídos por pares iguais
dispostos na mesma ordem.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Logo, o
número de maneiras distintas que o cientista pode formar esse fragmento de DNA
é: </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> 2<sup>11</sup> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> 2<sup>20</sup> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> 2 × 10 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> 2<sup>10</sup> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"> 2<sup>2</sup> × 10 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">10 </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Dois
rapazes e duas moças irão viajar de ônibus, ocupando as poltronas de números 1
a 4, com 1 e 2 juntas e 3 e 4 juntas, conforme o esquema.</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4yi5U4EefH7Yh_ipofeExQnr5zZ9euIXQnW2P3IEF1xZXemCCzNRNlbnsh0B5tGnN-x0KXlq0t9-RlaN31pKpiEsUOxFUP6hf3n4dUx24m8NZEtWyTJs4TkohvykC1LutSN_5SQKWheI/s1600/pfc+10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4yi5U4EefH7Yh_ipofeExQnr5zZ9euIXQnW2P3IEF1xZXemCCzNRNlbnsh0B5tGnN-x0KXlq0t9-RlaN31pKpiEsUOxFUP6hf3n4dUx24m8NZEtWyTJs4TkohvykC1LutSN_5SQKWheI/s1600/pfc+10.png" /></a></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">O
número de maneiras de ocupação dessas quatro poltronas, garantindo que, em duas
poltronas juntas, ao lado de uma moça sempre viaje um rapaz, é </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">4.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">6.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">8.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">12.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">16.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">11</span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Uma pessoa vai retirar dinheiro num caixa
eletrônico de um banco, mas na hora de digitar a senha, esquece-se do número.
Ela lembra que o número tem 5 algarismos, começa com 6, não tem algarismos
repetidos e tem o algarismo 7 em alguma posição. O número máximo de tentativas
para acertar a senha é </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">1
680 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">1
344 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">720
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">224
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">136
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">12.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Os clientes de um banco, ao utilizarem seus cartões nos caixas
eletrônicos, digitavam uma senha numérica composta por cinco algarismos. Com o
intuito de melhorar a segurança da utilização desses cartões, o banco solicitou
a seus clientes que cadastrassem senhas numéricas com seis algarismos.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Se a segurança for definida pela quantidade de
possíveis senhas, em quanto aumentou percentualmente a segurança na utilização
dos cartões? </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">10% </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">90% </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">100% </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">900% </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">1900% </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">13</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Na
ilustração abaixo, as 52 cartas de um baralho estão agrupadas em linhas com 13
cartas de mesmo naipe e colunas com 4 cartas de mesmo valor.</span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje__zi3xuUWddjVyWJDyB0tgdw2hSOnUXjWDUKzCYnRojmju68ymC3JRlC48STnaQLIIy_y1W1EFZ9xA7cU5TyCM-LbdRBvIzqLVtSVKOasVrYmL7Iuosj3iRFiRPov1goz2na4eKAzkQ/s1600/pfc+13+a.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="209" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje__zi3xuUWddjVyWJDyB0tgdw2hSOnUXjWDUKzCYnRojmju68ymC3JRlC48STnaQLIIy_y1W1EFZ9xA7cU5TyCM-LbdRBvIzqLVtSVKOasVrYmL7Iuosj3iRFiRPov1goz2na4eKAzkQ/s320/pfc+13+a.png" width="320" /></a></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Imagem_x0020_15"
o:spid="_x0000_i1026" type="#_x0000_t75" style='width:254.25pt;height:166.5pt;
visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Denomina-se quadra a reunião de quatro cartas de
mesmo valor. Observe, em um conjunto de cinco cartas, um exemplo de quadra:<o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Imagem_x0020_16"
o:spid="_x0000_i1025" type="#_x0000_t75" style='width:72.75pt;height:76.5pt;
visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image008.png"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_qOnJDf_NtI8peY34f3sJZoxQ2KxUFmBac4-qC2mvPSyB1pnDhMFS4_rlgWiCUryBEQRKq1l7a08zRBELF43O0lbYfrYVZI_qLgc95khslIXMnMjBQSH9PPRNjJBtOciZyLQDzH7kp9o/s1600/pfc+13+b.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_qOnJDf_NtI8peY34f3sJZoxQ2KxUFmBac4-qC2mvPSyB1pnDhMFS4_rlgWiCUryBEQRKq1l7a08zRBELF43O0lbYfrYVZI_qLgc95khslIXMnMjBQSH9PPRNjJBtOciZyLQDzH7kp9o/s1600/pfc+13+b.png" /></a></div>
<br />
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">O número total de conjuntos distintos de cinco
cartas desse baralho que contêm uma quadra é igual a: </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">624 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">676 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">715 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">720 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">14 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Um número
capicua é um número que se pode ler indistintamente em ambos os sentidos, da
esquerda para a direita ou da direita para a esquerda (exemplo: 5335). Em um
hotel de uma cidade, onde os jogadores de um time se hospedaram, o número de
quartos era igual ao número de capicuas pares de 3 algarismos. Quantos eram os
quartos do hotel? </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">20 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">40 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">80 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">90 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">100 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">15 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Para acomodar a crescente quantidade de veículos, estuda-se mudar as
placas, atualmente com três letras e quatro algarismos numéricos, para quatro
letras e três algarismos numéricos, como está ilustrado abaixo.</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 5.65pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 22.7pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0; mso-yfti-lastrow: yes;">
<td style="border: solid windowtext 1.0pt; height: 22.7pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt;"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">ABC
1234<o:p></o:p></span></div>
</td>
<td style="border-right: solid windowtext 1.0pt; border: none; height: 22.7pt; mso-border-left-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 11.8pt;" width="16"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<br /></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 22.7pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 63.65pt;" width="85"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">ABCD
123<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Considere o alfabeto com 26 letras e os algarismos
de 0 a 9. O aumento obtido com essa modificação em relação ao número máximo de
placas em vigor seria </span><span style="font-family: "Arial","sans-serif"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">inferior ao dobro. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">superior ao dobro e inferior ao
triplo. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">superior ao triplo e inferior ao
quádruplo. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">mais que o quádruplo. </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">16. Um
sistema inovador de senhas utiliza 4 digitos dentre os 10 algarismos numéricos
disponíveis. No entanto, senhas com 4 algarismos distintos são consideradas
inválidas enquanto que senhas que possuam pelo menos um algarismo repetido são
válidas. Por exemplo, as senhas 0754 ou 1243 são inválidas enquanto as senhas
2245 ou 3444 são válidas. Assim, o número de senhas válidas que podem ser
geradas é:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">
</span></b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) 4960 b) 5670 c) 6230 d) 7120 e) 8040
</span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; text-align: justify; text-autospace: none;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">17<b>.</b> </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Maria
deve criar uma senha de 4 dígitos para sua conta bancária. Nessa senha, somente
os algarismos 1,2,3,4,5 podem ser usados e um mesmo algarismo pode aparecer
mais de uma vez. Contudo, supersticiosa, Maria não quer que sua senha contenha
o número 13, isto é, o algarismo 1 seguido imediatamente pelo algarismo 3. De
quantas maneiras distintas Maria pode escolher sua senha? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-align: justify; text-indent: -11.35pt;">
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: PT-BR;">551 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: PT-BR;">552 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: PT-BR;">553 </span><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN;"> d) 554 e) 555</span><v:shapetype coordsize="21600,21600" id="_x0000_t202" o:spt="202" path="m,l,21600r21600,l21600,xe"><v:stroke joinstyle="miter"><v:path gradientshapeok="t" o:connecttype="rect"></v:path></v:stroke></v:shapetype></div>
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<o:p></o:p>Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com1tag:blogger.com,1999:blog-6195783121073928087.post-1712777669152497212013-07-11T13:49:00.000-07:002013-10-05T13:45:40.112-07:00GEOMETRIA ANALÍTICA 4- CÔNICAS<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">1 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">O gráfico que melhor representa a curva de equação
x<sup>2</sup> + 16y<sup>2</sup> = 16 é:<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: 12px;">2 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: 12px;">Em uma praça dispõe-se de uma região retangular de 20 m de comprimento por 16 m de largura para construir um jardim. A exemplo de outros canteiros, este deverá ter a forma elíptica e estar inscrito nessa região retangular. Para aguá-lo, serão colocados dois aspersores nos pontos que correspondem aos focos da elipse. Qual será a distância entre os aspersores? <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">4 m </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">6 m </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">8 m </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">10 m </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;">12 m </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: normal; text-indent: -11.35pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Existem pessoas que nascem com problemas de saúde
relacionados ao consumo de leite de vaca. A pequena Laura, filha do Sr.
Antônio, nasceu com este problema. Para solucioná-lo, o Sr. Antônio adquiriu
uma cabra que pasta em um campo retangular medindo 20 m de comprimento e 16 m
de largura. Acontece que as cabras comem tudo o que aparece à sua frente,
invadindo hortas, jardins e chácaras vizinhas. O Sr. Antônio resolveu amarrar a
cabra em uma corda presa pelas extremidades nos pontos A e B que estão 12 m
afastados um do outro. A cabra tem uma argola na coleira por onde é passada a
corda, de tal modo que ela possa deslizar livremente por toda a extensão da
corda. Observe a figura e responda a questão a seguir.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Qual deve ser o comprimento da corda para que a
cabra possa pastar na maior área possível, dentro do campo retangular? <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">10 m. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">15 m. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">20 m. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">25 m. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Cambria Math"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">30 m. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: 105%;">4 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9pt; line-height: 105%;">Kepler, astrônomo alemão que viveu antes de Newton,
foi o primeiro a enunciar leis que regem o movimento dos planetas em torno do
Sol. A Primeira Lei de Kepler afirma que os planetas se movem em órbitas
elípticas, com o Sol em um dos focos. Em consequência, em alguns pontos, os
planetas estão mais próximos do Sol do que em outros. Por exemplo, a Terra
chega a 147 x 10<sup>6</sup> km do Sol, em seu periélio (o ponto mais próximo,
P), e atinge 152 x 10 <sup>6</sup> km do Sol, em seu afélio (o ponto mais
afastado, A), conforme a figura adiante.</span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></div>
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<o:p></o:p><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Sabe-se que a excentricidade da elipse é a razão entre a distância do
foco ao centro da elipse e a medida do semi-eixo maior. Então, no caso da
órbita da Terra, a excentricidade e vale:. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) 1/299 b)
2/299 c) 3/299 d) 4/299 e) 5/299 <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">
</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">5 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Na parede
retangular de um palácio renascentista, há um vitral circular e, acima dele, na
mesma parede, uma estreita faixa reta, conforme a figura:</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Essa parede foi ornamentada com um elemento
decorativo em forma de uma curva que tem a seguinte característica: cada ponto
da curva está situado a igual distância do centro do vitral e da faixa.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Pode-se afirmar que o elemento decorativo tem a
forma de um arco: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">de elipse </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">de hipérbole </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">de parábola </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">de circunferência </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">de senoide </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">6 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">O vértice, o foco e a reta diretriz da parábola de
equação y = x<sup>2</sup> são dados por: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Vértice: (0, 0); Foco: (0,
1/4); Reta diretriz y = -1/4 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Vértice: (0, 0); Foco: (0,
1/2); Reta diretriz y = -1/2 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Vértice: (0, 0); Foco: (0,
1); Reta diretriz y = -1 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Vértice: (0, 0); Foco: (0,
-1); Reta diretriz y = 1 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Vértice: (0, 0); Foco: (0,
2); Reta diretriz y = -2 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">7 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">O gráfico da equação x<sup>2</sup> - y<sup>2</sup>
= 1 representa uma hipérbole. Os focos dessa hipérbole são: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> a) (1/2,0) e (-1/2,0)
b) (2, 0) e
(-2, 0) c) (</span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">Ö</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"><b> </b>, 0) e (-</span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">Ö</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"><b> </b>,0) <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> d) (0,</span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">Ö</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> ) e (0, -</span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">Ö</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2<b> </b></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">) e) (0,1/2) e (0,-1/2) <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">8. Em certo sistema marítimo de navegação, duas
estações de rádio, localizadas na costa,
nos pontos A e B, transmitem simultaneamente sinais de rádio para qualquer embarcação
que se encontre no mar, na área de alcance dessas estações. Sendo P o ponto
onde está localizada uma embarcação que recebe esses sinais, o computador de bordo da embarcação calcula a diferença, PA -
PB , das distâncias da embarcação a cada
uma das estações. Um navio que estava ancorado no mar recebeu o sinal da estação localizada em
B e, 120 microssegundos (</span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">m</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">s) depois, recebeu o sinal da estação localizada em A, conforme a figura
<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> Considere
as estações de rádio e o ponto P onde esse
navio estava ancorado como pontos de um
plano cartesiano, onde a unidade de comprimento
é o quilômetO e</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">A(-30,0) e B(30 ,0)</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">Nesse contexto, pede-se</span><br />
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<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 36pt; text-align: justify; text-indent: -18pt;">
<!--[if !supportLists]--><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: Verdana; mso-fareast-font-family: Verdana; mso-fareast-language: ZH-CN;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">A partir da expressão d = PA – PB = V.</span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: ZH-CN; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">D</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">t calcule a medida a do semi eixo real.<o:p></o:p></span></div>
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</div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 36pt; text-align: justify; text-indent: -18pt;">
<!--[if !supportLists]--><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: Verdana; mso-fareast-font-family: Verdana; mso-fareast-language: PT-BR;">b)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Determine a equação da hipérbole com focos nos
pontos A e B e que contém o ponto P <o:p></o:p></span><span style="font-family: Verdana, sans-serif; font-size: 12px;"> </span></div>
Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-12952666321866981772013-07-11T13:43:00.002-07:002013-07-18T06:13:32.923-07:00GEOMETRIA ANALÍTICA 3 - CIRCUNFERÊNCIA<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-size: 10pt; line-height: 105%;">1 </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A equação da circunferência cuja representação
cartesiana está indicada NA FIGURA ABAIXO é: </span><o:p></o:p></div>
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<span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;">a) </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">x<sup>2</sup>
+ y<sup>2</sup> - 3x - 4y = 0 </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;">b) </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">x<sup>2</sup> + y<sup>2</sup> + 6x + 8y = 0 </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;">c) </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">x<sup>2</sup> + y<sup>2</sup> + 6x - 8y = 0 </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">x<sup>2</sup>
+ y<sup>2</sup> + 8x - 6y = 0 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">x<sup>2</sup>
+ y<sup>2</sup> - 8x + 6y = 0 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12pt;"> <i><o:p></o:p></i></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2 </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Considere
a reta s e os pontos A, B e C representados na figura a seguir.<o:p></o:p></span></div>
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<a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a)
Determine as coordenadas cartesianas dos pontos A, B e C.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">b)
Determine uma equação cuja representação gráfica seja a reta s.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">c)
Determine uma equação cuja representação gráfica seja a circunferência de
centro B que passa pelo ponto C. </span><o:p></o:p></div>
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<span style="font-size: 10pt; line-height: 105%;"><i>3</i><b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> A feira de Caruaru<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A feira de Caruaru<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Faz gosto da gente ver<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">De tudo que há no mundo<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Nela tem pra vender<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> http://luiz-gonzaga.letras.terra.com.br<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A cidade a que se refere Luiz Gonzaga em sua
canção está indicada no mapa a seguir como a origem de um sistema de eixos
ortogonais x0y.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Considere que a região de influência da feira
de Caruaru seja representada, nesse sistema de eixos, pela inequação x<sup>2</sup>
+ y<sup>2</sup> ≤ 2,25, com x e y medidos em centímetros.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Em relação à região de influência da feira,<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a) determine sua área, em km<sup>2</sup>,
supondo que a escala do mapa seja de 1:10.000.000;<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">b) demonstre que uma cidade situada nas
coordenadas (11/10,11/10)do sistema de eixos considerado não está nessa região. </span><i><o:p></o:p></i></div>
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<i><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></i><i><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></i><i><o:p></o:p></i></div>
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<i><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></i><i><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></i><i><o:p></o:p></i></div>
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<i><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></i><i><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></i><i><o:p></o:p></i></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">4 </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Pilates é um sistema de
exercícios físicos que integra o corpo e a mente como um todo, desenvolvendo a
estabilidade corporal necessária para uma vida mais saudável. A figura abaixo
mostra um dos exercícios trabalhado no Pilates e é observado que o corpo da
professora gera um arco AB. Supondo que o arco gerado pelo corpo da professora
seja um quarto de uma circunferência de equação <b>100x<sup>2</sup> + 100y<sup>2
</sup>- 600x - 800y + 2356 = 0</b> (com medidas x e y em metros).
o valor aproximado da altura da
professora é:<o:p></o:p></span></div>
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<span style="font-size: 10pt;">a) 1,72 m b)
1,76m c) 1,80m
d) 1,84 m e)
1,88 m <o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">5 </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">A reta r
de equação y =x/2 intercepta a
circunferência de centro na origem e raio</span><span style="background-color: white; color: #333333; font-family: arial, helvetica, clean, sans-serif; font-size: 13px;">√5 </span><span style="font-size: 10pt; line-height: 105%;">em dois pontos P e Q, sendo que as coordenadas de P são ambas
positivas.</span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">Determine:<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">a)
a equação da circunferência e os pontos P e Q;<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">b)
a equação da reta s, perpendicular a r, passando por P. <o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">6<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A reta y = mx (m > 0) é
tangente à circunferência (x - 4)<sup>2</sup> + y<sup>2</sup> = 4. Determine o
seno do ângulo que a reta forma com o eixo x. </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)</span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">1/5.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b)</span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">1/4. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c)</span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">1/3. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">1/2. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">2/5. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><br />
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-31480960187742433232013-07-11T13:33:00.001-07:002013-07-16T20:40:29.781-07:00GEOMETRIA ANALÍTICA 2 - RETA<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">1<b>.</b></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Ao ser inaugurada, uma represa possuía 8 mil m<sup>3</sup>
de água. A quantidade de água da represa vem diminuindo anualmente. O gráfico
mostra que a quantidade de água na represa 8 anos após a inauguração é de 5 mil
m<sup>3</sup>.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Se for mantida essa relação de linearidade entre o
tempo e a quantidade de água em m<sup>3</sup>, determine em quantos anos, após
a inauguração, a represa terá 2 mil m<sup>3</sup>. <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) 12 anos b) 13
anos c) 14 anos d) 15 anos e) 16 anos<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">A
equação da reta mostrada na figura a seguir é:<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">3x + 4y - 12 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">3x - 4y + 12 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">4x + 3y + 12 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">4x - 3y - 12 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">4x - 3y + 12 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">3 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">Considere as retas r e s
representadas no plano cartesiano abaixo.<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">a) Escreva a equação da reta r. <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">b) Qual deve ser o coeficiente angular da reta s,
de modo que ela divida o triângulo cinza em dois triângulos com áreas iguais?
Justifique sua resposta. <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">4 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">No plano cartesiano, seja r uma reta de equação ax
+ 2y - 2 = 0. Sabendo que P = (1,-1) é um ponto de r, determine:<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">a) o valor de a;<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">b) o coeficiente angular de r. <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">5 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Determine a equação geral da reta apresentada <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> </span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">6 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Dada a equação de reta (s):
2x - y +1 = 0 , a equação de reta paralela a s pelo ponto<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-style: italic; mso-fareast-language: PT-BR;">P</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">(1,1) será: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2x - y = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2x +
y +1 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2x +
y -1 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2x - y -1 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2x -
y + 2 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">7 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Uma formiga se desloca num plano, ao longo de uma
reta. Passa pelo ponto (1, -2) e percorre a MENOR distância até interceptar a
trajetória retilínea de outra formiga, nesse mesmo plano, descrita pela equação
y + 2x = 8.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">A equação da reta que representa a trajetória da
primeira formiga é: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2y - x + 5 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">y - x + 3 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">y + x + 1 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2y + x + 2 = 0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> e) y + x – 1 = 0<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">8 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Um bairro de uma cidade foi planejado em uma região plana, com ruas
paralelas e perpendiculares, delimitando quadras de mesmo tamanho. No plano de
coordenadas cartesianas seguinte, esse bairro localiza-se no segundo quadrante,
e as distâncias nos eixos são dadas em quilômetros. <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">A reta de equação y = x+ 4 <span style="mso-text-raise: -5.0pt; position: relative; top: 5.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75"
style='width:41.25pt;height:15pt' o:ole="">
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<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1032"
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</xml><![endif]-->representa o planejamento do percurso da linha do metrô
subterrâneo que atravessará o bairro e outras regiões da cidade. No ponto (-5,5) , localiza-se um hospital público. A comunidade solicitou ao
comitê de planejamento que fosse prevista uma estação do metrô de modo que sua
distância ao hospital, medida em linha reta, não fosse maior que 5 km. <br />
Atendendo ao pedido da comunidade, o comitê argumentou corretamente que isso
seja automaticamente satisfeito, pois já estava prevista a construção de uma
estação no ponto <o:p></o:p></span></div>
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<b><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) (-5,0)</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) (-3,1)</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) (-2,1)</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"><span style="mso-text-raise: -5.0pt; position: relative; top: 5.0pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1036" type="#_x0000_t75" style='width:27.75pt;height:15pt' o:ole="">
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</xml><![endif]--></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) (0,4)</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">e) (2,6)</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span></b><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><b> </b><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">9 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Um pássaro sobrevoa uma rampa conforme mostra a figura. A ave faz seu
voo em linha reta e paralela à calçada.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a) Sabendo-se que a rampa forma um ângulo de 135º com a calçada,
conforme mostra a figura, e que a distância do muro de apoio até o pé da rampa
é de 3 metros, calcule o comprimento da rampa.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">b) Determine a menor distância entre o pássaro e a rampa no instante em
que o pássaro se encontra a 5 metros do muro e a 6 metros da calçada em que se
apoia a rampa. Apresente os cálculos realizados na resolução de cada item. <o:p></o:p></span></div>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-36763013728375818192013-07-11T13:20:00.001-07:002013-07-16T20:31:39.732-07:00GEOMETRIA ANALÍTICA 1 - COORDENADAS CARTESIANAS<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">ENUNCIADO PARA AS QUESTÕES 1 E 2 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">No
sistema de coordenadas cartesianas a seguir, está representado o triângulo ABC.
<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">1.Sua área em unidades de superfície é: a ) 5
b) 6,5 c) 8 d) 9,5
e) 11 <o:p></o:p></span></div>
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2. Seu baricentro tem
coordenadas a) (5,3) b) (4,3/2) c) (7,5)
d) (10/3,4) e) (11/3,3)<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">A
área do triângulo, limitada pelas retas de equação 3x - 4y + 12 = 0 e os eixos
coordenados, é igual a <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">6 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">8 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">10 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">12 e) 14</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">4<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">As
transmissões de uma determinada emissora de rádio são feitas por meio de 4
antenas situadas nos pontos A(0,0), B(100,0), C(60,40) e D(0,40), sendo o
quilômetro a unidade de comprimento. Desprezando a altura das antenas e supondo
que o alcance máximo de cada antena é de 20 km, pergunta-se:<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">a) O ponto médio do segmento BC recebe as
transmissões dessa emissora? Justifique sua resposta apresentando os cálculos
necessários.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: left;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">b) Qual a área da região limitada pelo quadrilátero
ABCD que não é alcançada pelas transmissões da referida emissora? <o:p></o:p></span><br />
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-90214374296287939142013-07-01T18:58:00.002-07:002013-07-14T17:45:50.747-07:00RETAS E PLANOS NO ESPAÇO<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
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<b>VÍDEO COMPLETO PARA AS 4 QUESTÕES, INCLUINDO-SE A TEORIA</b></div>
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<object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i1.ytimg.com/vi/xTNe_GFYpHE/0.jpg"><param name="movie" value="http://www.youtube.com/v/xTNe_GFYpHE?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/xTNe_GFYpHE?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">1. </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Sobre
os conhecimentos de geometria tridimensional, considere as afirmativas:<o:p></o:p></span></div>
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<br /></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">I.
Se duas retas distintas não são paralelas, então elas são concorrentes.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">II.
Três pontos não colineares determinam um único plano.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">III.
Duas retas paralelas distintas determinam um plano.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">IV.
Se duas retas r e s são reversas, então elas não determinam um plano<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A
alternativa que contém todas as afirmativas corretas é: </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">I
e II </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> b</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">I e IV </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) II, </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">III e IV<span style="color: red;"> </span></span><span style="color: red; font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="color: red; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">I,
II e III </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">I, III e IV </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Na cadeira representada na figura
a seguir, o encosto é perpendicular ao assento e este é paralelo ao chão.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Sendo
assim, </span><o:p></o:p></div>
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<br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Os
planos EFN e FGJ são paralelos. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">HG
é um segmento de reta comum aos planos EFN e EFH. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Os
planos HIJ e EGN são paralelos. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">EF
é um segmento de reta comum aos planos EFN e EHG. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">O galpão da figura a seguir está no prumo e a cumeeira está "bem no
meio" da parede.<o:p></o:p></span></div>
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<br />
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Das
retas assinaladas podemos afirmar que: </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">t
e u são reversas </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">s e u são reversas </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">t e u são concorrentes </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">s
e r são concorrentes </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">t e r são perpendiculares </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">4. Dentre as
afirmativas abaixo,referentes à geometria de posição, assinale a única falsa: </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">I) Se dois
planos são paralelos e distintos,então toda reta de um deles é paralela ou
reversa a qualquer reta do outro </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">II) Se uma
reta é paralela a dois planos,então os planos são paralelos.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">III) Se duas
retas de um plano, distintas e concorrentes,são paralelas a um outro plano,então
os dois planos são paralelos entre si.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">IV) Se dois
planos são paralelos,então toda reta paralela a um deles é paralela ao outro ou
está contida nele<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><b><span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">GABARITO 1
C 2. D 3. A 4.
Alternativa II</span></b><br />
<!--[if !supportLineBreakNewLine]--><br />
<!--[endif]--></span>Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com1tag:blogger.com,1999:blog-6195783121073928087.post-66367215171214810742013-07-01T18:28:00.001-07:002013-07-14T09:16:51.605-07:00POLIEDROS<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">1<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">O número
de faces de um poliedro convexo com 20 vértices e com todas as faces
triangulares é igual a: </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">28 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">30 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">32 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">34 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">36 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/19kGOMRdkvE?feature=player_embedded' frameborder='0'></iframe></div>
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um
poliedro convexo só tem faces triangulares e quadrangulares. Se ele tem 20
arestas e 10 vértices, então, o número de faces triangulares é: </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">12 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">11 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">10 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">9 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">8 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/2rtDaonWMDU?feature=player_embedded' frameborder='0'></iframe></div>
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">3</span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">.</span></b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O fulereno é uma molécula
de carbono descoberta em 1985, e sua utilização tem sido proposta em muitas
áreas, como medicina, bioquímica e física, devido à sua grande estabilidade. O
modelo tridimensional da molécula do fulereno é um poliedro convexo
de faces regulares, que possui 12 faces pentagonais, 20 faces hexagonais e três
arestas (ligações entre os carbono) se encontrando em cada vértice ( átomo de
carbono), formando ângulos triédricos.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> Entre as aplicações deste poliedro está sua
utilização na bola de futebol que</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> é
formada por as mesmas 12 faces pentagonais e 20 faces hexagonais todas com
lados congruentes entre si. Sabe-se que ,para costurar essas face lado a lado ,
formando a superfície de um poliedro convexo, usam-se 20 cm de linha em cada
aresta do poliedro. <o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUjoRskHHiXX2PLyJjXJsvVcVdCE0SBLKdLtuZ0k0GNXrybtB-wsoN0GksD-EpbEnpERlevcY-SmzMY-_WV57br4fBoM6PyOXTYe7DsBSQXz-MlNQutIxBavS8WZJarmUx2XD9voJ7v1g/s312/POLI.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUjoRskHHiXX2PLyJjXJsvVcVdCE0SBLKdLtuZ0k0GNXrybtB-wsoN0GksD-EpbEnpERlevcY-SmzMY-_WV57br4fBoM6PyOXTYe7DsBSQXz-MlNQutIxBavS8WZJarmUx2XD9voJ7v1g/s312/POLI.png" /></a></div>
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<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/AFMJxSD7nnw?feature=player_embedded' frameborder='0'></iframe></div>
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">. Baseando-se nessas informações,
considere as afirmações<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 17pt; text-align: justify; text-indent: -17pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">I.
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O poliedro que
representa a molécula possui 90 arestas (ligações entre átomos de carbono)</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 17pt; text-align: justify; text-indent: -17pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">II.
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O poliedro que
representa a molécula possui 120 vértices (átomos de carbono) </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 17pt; text-align: justify; text-indent: -17pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">III.
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A soma dos
ângulos internos de todas as faces é 58 </span><span style="font-family: Symbol; font-size: 10.0pt; mso-ascii-font-family: Arial; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;">p</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> radiano. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 17pt; text-align: justify; text-indent: -17pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">IV.
Para costurar inteiramente a bola são necessários exatamente 18 m de linha.</span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 17pt; text-align: justify; text-indent: -17pt;">
<span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">A afirmação correta é:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 36pt; text-align: justify; text-indent: -18pt;">
<!--[if !supportLists]--><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Arial; mso-fareast-language: ZH-CN;">a)<span style="font-size: 7pt;"> </span></span><!--[endif]--><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">São corretas I e II</span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> b) </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">São
corretas I e IV</span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">
c) </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">São corretas II e III</span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 18pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">d) São corretas II e IV</span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> e) </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">São corretas III e IV</span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><b>Gabarito: </b></div>
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<br /></div>
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<span style="font-size: 12pt;"> </span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></b><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">1:</span></b><span style="color: blue; font-size: 10pt;"> </span><span style="font-size: 10pt;">[E]
</span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></b><span style="font-size: 12pt;"> </span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> 2:</span></b><span style="color: blue; font-size: 10pt;"> </span><span style="font-size: 10pt;">[E] </span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></b><span style="font-size: 12pt;"> </span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> 3: </span></b><span style="font-size: 10pt;">[B]
</span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></b><span style="font-size: 12pt;"> </span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></b><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span></div>
Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-61684553601617154102013-06-09T04:13:00.000-07:002013-07-14T09:09:45.845-07:00ESFERA <span style="font-size: 10pt; line-height: 105%; text-align: justify;">1<b>.</b>
</span><span style="font-size: 10pt; line-height: 105%; text-align: justify;">De um cristal de rocha, com o
formato de uma esfera, foi lapidada uma joia na forma de um <b>octaedro regular,</b>
como mostra a figura seguinte.</span><br />
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Se tal joia tem 9</span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; line-height: 105%;">cm<sup>3</sup> de volume, quantos centímetros cúbicos
de rocha foram retirados do cristal original para lapidá-la? (Use: </span><span style="font-family: Symbol; font-size: 10pt; line-height: 105%;">p</span><span style="font-size: 10pt; line-height: 105%;"> = 3)</span></div>
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<o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">36</span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 12pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;">b) </span><span style="font-size: 10pt; text-indent: -11.35pt;">32</span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 12pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;">c) </span><span style="font-size: 10pt; text-indent: -11.35pt;">24</span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; text-indent: -11.35pt;"><span style="mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"> </span> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> d) </span><span style="font-size: 10pt; text-indent: -11.35pt;">18 </span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; text-indent: -11.35pt;"> e) </span><span style="font-size: 10pt; text-indent: -11.35pt;">12 </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">2. </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Se pudéssemos reunir em
esferas toda a água do planeta, os diâmetros delas seriam:<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A razão entre o volume da
esfera que corresponde à água doce superficial e o volume da esfera que
corresponde à água doce do planeta é </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) 1/343</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) 1/49</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) 7</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) 29/136</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) 136/203</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b></span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um
troféu para um campeonato de futebol tem a forma de uma esfera de raio R = 10
cm cortada por um plano situado a uma distância de 5</span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" /><span style="font-size: 10pt; line-height: 105%;">cm do centro da esfera, determinando uma
circunferência de raio r cm, e sobreposta a um cilindro circular reto de 20 cm
de altura e raio r cm, como na figura (não em escala).</span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">O volume do cilindro, em cm<sup>3</sup>, é </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> 100 </span><span style="text-indent: -11.35pt;">π</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> 200 π</span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN; mso-hansi-font-family: Arial;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> 250 </span><span style="text-indent: -11.35pt;">π</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN; mso-hansi-font-family: Arial;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> 500 </span><span style="text-indent: -11.35pt;">π</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> 750 </span><span style="text-indent: -11.35pt;">π</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><br />
<span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">4. </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Considere uma bola de sorvete de 36</span><span style="font-family: Symbol; font-size: 10.0pt; line-height: 105%; mso-ascii-font-family: Arial; mso-bidi-font-size: 11.5pt; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;">p</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> cm<sup>3</sup>
de volume e uma casquinha cônica de 3 cm de raio. A altura da casquinha, para
que o sorvete, ao derreter, ocupe todo o seu espaço, em cm, é <o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">12 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">10 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">9 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">8 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> e) 6</span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">5. Pesquisadores da Fundação Osvaldo Cruz desenvolveram um sensor a
laser capaz de detectar bactérias no ar em até 5 horas, ou seja, 14 vezes mais
rápido do que o método tradicional. O equipamento, que aponta a presença de
microorganismos por meio de uma ficha ótica, pode se tornar um grande aliado no
combate às infecções hospitalares.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">(Adaptado de Karine Rodrigues. http:www.estadão.com.br/ciência/notícias/2004/julho/15)
</span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Em certo
momento, uma cultura tem 30 000 bactérias. Essas bactérias têm formato
esférico, com diâmetro de 4 micrômetros (1 micrômetro equivale à milésima parte
de 1 mm). Nesse momento, o espaço ocupado por essas bactérias é, em milímetros
cúbicos, igual a . Considere </span><span style="font-family: Symbol; font-size: 10.0pt; line-height: 105%; mso-ascii-font-family: Arial; mso-bidi-font-size: 11.5pt; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;">p</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">= 3,1</span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">3,72 × 10<sup>-1</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">9,92
× 10<sup>-2</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">3,72
× 10<sup>-3</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">9,92
× 10<sup>-4</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">9,92
× 10<sup>-5</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">6<b>.</b> </span><span style="font-size: 10pt;">Um artesão produz peças ornamentais com um material que pode ser
derretido quando elevado a certa temperatura. Uma dessas peças contém uma
esfera sólida e o artesão observa que as peças com esferas maiores são mais
procuradas e resolve desmanchar as esferas menores para construir esferas
maiores, com o mesmo material. Para cada 8 esferas de 10 cm de raio
desmanchada, ele constrói uma nova esfera.<o:p></o:p></span></div>
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<object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i1.ytimg.com/vi/-68Ac1uGe_A/0.jpg"><param name="movie" value="http://www.youtube.com/v/-68Ac1uGe_A?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/-68Ac1uGe_A?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
<span style="font-size: 10pt;"> O raio da nova esfera construída mede </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) 80 cm</span><span style="font-size: 10pt;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) 14,2 cm</span><span style="font-size: 10pt;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) 28,4 cm</span><span style="font-size: 10pt;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) 20 cm</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> d) 25 cm</span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">7<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Um
designer criou pesos para papel usando cubos e esferas. Nas peças criadas a
esfera está inscrita no cubo, que tem aresta medindo 6 cm. Para dar um efeito
visual, ele colocou na parte interna do cubo, e externa à esfera, um líquido
vermelho. Com 1 litro desse líquido o designer pode confeccionar no máximo
quantas peças? </span><o:p></o:p></div>
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<object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i1.ytimg.com/vi/vAdJMDaU_Jc/0.jpg"><param name="movie" value="http://www.youtube.com/v/vAdJMDaU_Jc?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/vAdJMDaU_Jc?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">9 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">12 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">18 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">24 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">27 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">8<b>.</b></span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um vaso
em forma de cilindro circular reto tem medida de raio da base 5 cm, altura 20
cm e contém água até a altura de 19 cm (despreze a espessura das paredes do
vaso). Assinale a alternativa na qual consta o maior número de esferas de aço,
de 1 cm de raio cada, que podemos colocar no vaso a fim de que a água não
transborde. </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">14 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">15
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">16
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">17 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10pt;">e) </span><span style="font-size: 10pt;">18 </span><span style="font-size: 10pt;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">9<b> </b></span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Oscar Niemayer foi um arquiteto brasileiro,
considerado um dos nomes mais influentes na arquitetura moderna internacional.
Ele contribuiu, através de uma doação de um croqui, para a construção do
planetário da UFSM, um marco arquitetônico importante da cidade de Santa Maria.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixJuR-io3x1r2oZd8SzRKsp6CjHL9hxRtw09NmFELlZ-vTW8M-ZcfzlY5P00WRGjVDFfxZxF9N7Jwjd0NdwVuN4PMkQocxPCX3hXh3zl0nnWT0vgffJQ7ZloiYmyniSRiE4I8eNtk7GJE/s1600/esfera9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixJuR-io3x1r2oZd8SzRKsp6CjHL9hxRtw09NmFELlZ-vTW8M-ZcfzlY5P00WRGjVDFfxZxF9N7Jwjd0NdwVuN4PMkQocxPCX3hXh3zl0nnWT0vgffJQ7ZloiYmyniSRiE4I8eNtk7GJE/s320/esfera9.png" width="320" /></a></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> Suponha que a cobertura da construção seja
uma semiesfera de 28 m de diâmetro, vazada por 12 partes iguais, as quais são
aproximadas por semicírculos de raio 3 m. Sabendo que uma lata de tinta é
suficiente para pintar 39 m<sup>2</sup> de área, qual a quantidade mínima de
latas de tinta necessária para pintar toda a cobertura do planetário? (Use </span><o:p></o:p><span style="font-family: Symbol; font-size: 13px; line-height: 13px;">p=3)</span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">20. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><b><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span></b><b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">26</span></b><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">.
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">40. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">52. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">60. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<br /></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">10<b>.</b>
</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um artista esculpiu a metade de
uma esfera de pedra-sabão, transformando-a num cone, ilustrado na figura a
seguir.<o:p></o:p></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/xkJzHa-XtW8?feature=player_embedded' frameborder='0'></iframe></div>
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> Supondo que a esfera tem raio R
e a altura do cone esculpido também é R, calcule:<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a) o volume do cone esculpido;<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">b) o volume do material retirado da metade da esfera para formar o cone.
<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizQnGzACUAY-OZjH0ESl_KmZgGhbHrfzwPyrk82K4brFe0W2dFJBaCtb3Pr6c_lifTdo5aVH3YEaO0LWZt_OlCxmNjGX9Vuci2h6HVn_eECrf3O77JtT-3-THKufy9u6focrouk_Lu1H0/s1600/esfera10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizQnGzACUAY-OZjH0ESl_KmZgGhbHrfzwPyrk82K4brFe0W2dFJBaCtb3Pr6c_lifTdo5aVH3YEaO0LWZt_OlCxmNjGX9Vuci2h6HVn_eECrf3O77JtT-3-THKufy9u6focrouk_Lu1H0/s1600/esfera10.png" /></a></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">11<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um cone
circular reto, cujo raio da base é 3 cm, está inscrito em uma esfera de raio 5
cm, conforme mostra a figura a seguir.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> O volume do cone corresponde a
que porcentagem do volume da esfera? </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">26,4% </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">21,4%
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">19,5%
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">18,6%
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">16,2%
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjC8pnY8w2PtGaycJOpoK4toen-h5Y2J958TOHgPo7q34QsxgyndaiFLEnqpa_0IRNaePKROcEE137O34oS-CHL6L_ewGNL2SVhLe_GySGUWMv0akkP3czXR4OdoXq1rbefQk8Or-QsN8/s1600/esfera11.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjC8pnY8w2PtGaycJOpoK4toen-h5Y2J958TOHgPo7q34QsxgyndaiFLEnqpa_0IRNaePKROcEE137O34oS-CHL6L_ewGNL2SVhLe_GySGUWMv0akkP3czXR4OdoXq1rbefQk8Or-QsN8/s1600/esfera11.png" /></a></div>
<o:p></o:p><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">12.</span><span style="font-size: 10pt; line-height: 105%;"> </span><span style="font-size: 10pt; line-height: 105%;">Um joalheiro resolveu presentear
uma amiga com uma joia exclusiva. Para isto, imaginou um pingente, com o
formato de um octaedro regular, contendo uma pérola inscrita, com o formato de
uma esfera de raio r, conforme representado na figura a seguir.</span><br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/PgnSuuC2KQ0?feature=player_embedded' frameborder='0'></iframe></div>
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Se
a aresta do octaedro regular tem 2 cm de comprimento. Determine o volume da pérola, em cm<sup>3</sup>,
é: </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">13<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um fabricante de cristais produz três tipos de taças para servir vinho.
Uma delas tem o bojo no formato de uma semiesfera de raio r; a outra, no
formato de um cone reto de base circular de raio 2r e altura h; e a última, no
formato de um cilindro reto de base circular de raio x e altura h.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD00om7KMzOlFAuqgfOYmiIIkC8Tnsj5Eg0Mwezst0pdwnLV5IOOwBQ3rMFW3e3pzjYNZGGPEw-YiZxqJ8fwZL3dNCNAgq9O3ywt7EVTTsBywPhu1Ephzk95WYnmWfBIu0xGb_jz2n6Gg/s1600/esfera13.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="93" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD00om7KMzOlFAuqgfOYmiIIkC8Tnsj5Eg0Mwezst0pdwnLV5IOOwBQ3rMFW3e3pzjYNZGGPEw-YiZxqJ8fwZL3dNCNAgq9O3ywt7EVTTsBywPhu1Ephzk95WYnmWfBIu0xGb_jz2n6Gg/s320/esfera13.png" width="320" /></a></div>
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<object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i1.ytimg.com/vi/RGRcaFVc_bs/0.jpg"><param name="movie" value="http://www.youtube.com/v/RGRcaFVc_bs?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/RGRcaFVc_bs?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> Sabendo-se que as taças dos três tipos,
quando completamente cheias, comportam a mesma quantidade de vinho, é correto
afirmar que a razão x/h é igual a: </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;"> <o:p></o:p></span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="text-align: justify;" />/6</div>
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<span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;"> </span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="line-height: 16px; text-align: justify;" />/3<span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) 2.</span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="line-height: 16px; text-align: justify;" />/3<span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;"> </span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="line-height: 16px; text-align: justify;" /><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span></div>
<span style="font-size: 10pt; text-indent: -11.35pt;">e) 4. </span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="line-height: 16px; text-align: justify;" />/3 <br />
<span style="text-align: justify;"><br /></span>
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<b><span style="font-size: 10pt;"><o:p></o:p></span></b></div>
Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com2tag:blogger.com,1999:blog-6195783121073928087.post-43274543246827030202013-05-30T07:41:00.003-07:002013-06-09T06:02:40.177-07:00CONE<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt -1cm; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><b><span style="font-size: large;">VÍDEO DE RESOLUÇÃO DIA 10/06/2013</span></b><span style="color: white; font-size: 13px;"> uma lanchonete, um casal de namorados res</span><br />
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1.Em uma lanchonete, um casal de namorados resolve dividir uma taça de milk shake
com as dimensões mostradas no desenho<span style="font-size: 10pt;">.</span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a)
Sabendo-se que a taça estava totalmente cheia e que eles beberam todo o milk
shake, calcule qual foi o volume, em mL, ingerido pelo casal. Adote </span><span style="font-family: Symbol; font-size: 10.0pt; line-height: 105%; mso-ascii-font-family: Arial; mso-bidi-font-size: 11.5pt; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;">p</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> = 3.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">b) Se um
deles beber sozinho até a metade da altura do copo, quanto do volume total, em
porcentagem, terá bebido? </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">2.</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Depois de encher de areia
um molde cilíndrico, uma criança virou-o sobre uma superfície horizontal. Após
a retirada do molde, a areia escorreu, formando um cone cuja base tinha raio
igual ao dobro do raio da base do cilindro.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> A altura
do cone formado pela areia era igual a </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) 3/4 </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">da altura do cilindro. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> b) 1/2 </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">da altura do cilindro. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> c) 2/3 </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">da altura do cilindro. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> d) 1/3 </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">da altura do cilindro. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></div>
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<o:p></o:p><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">3<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A prefeitura de certo
município realizou um processo de licitação para a construção de 100 cisternas
de placas de cimento para famílias da zona rural do município. Esse sistema de </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">armazenamento de água é
muito simples, de baixo custo e não poluente. A empreiteira vencedora estipulou
o preço de 40 reais por m<sup>2</sup>
construído, tomando por base a área externa da cisterna. O modelo de cisterna
pedido no processo tem a forma de um cilindro com uma cobertura em forma de
cone, conforme a figura abaixo.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">
Considerando que a construção da base das cisternas deve estar incluída nos
custos, é correto afirmar que o valor, em reais, a ser gasto pela prefeitura na
construção das 100 cisternas será, no máximo, de:<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Use:</span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" /><span style="font-size: 10pt;">= 3,14</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt -1cm; text-align: justify;">
<o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt -1cm; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">100.960 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">125.600 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">140.880 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt -1cm; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">202.888 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">213.520 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<br /></div>
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<span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnjDl7lUlkF6lL-dX4qvR3ANBzzcDuUHzd41X6XnfzPQV-Chcxb468AXsu3JvVwPsdM1aVkikL-MHBPcsF0H85Xb4IQ6IxWl9bmegA7bUrOM3QbJLUD83ixPpG2ggiV0ynps3KRSzF_fM/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnjDl7lUlkF6lL-dX4qvR3ANBzzcDuUHzd41X6XnfzPQV-Chcxb468AXsu3JvVwPsdM1aVkikL-MHBPcsF0H85Xb4IQ6IxWl9bmegA7bUrOM3QbJLUD83ixPpG2ggiV0ynps3KRSzF_fM/s1600/3.png" /></a></div>
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</div>
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<br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">4<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A figura indica a
planificação da lateral de um cone circular reto:<o:p></o:p></span></div>
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<br /></div>
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<span style="font-size: x-small;"> </span></div>
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<span style="font-size: x-small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWiFXLUSY-7G-nHYiTaRTu07KisiQxoeeLOZg-pgjYmbE7fi3EfEmA50jzXRrxMUGCMwUUs3waAQyU6nHuIcU78Ff4Z8vfwmcRjwjwoCix3Fpzh8kG01m1PT9FddPCEH66ojwA3RaD_VU/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWiFXLUSY-7G-nHYiTaRTu07KisiQxoeeLOZg-pgjYmbE7fi3EfEmA50jzXRrxMUGCMwUUs3waAQyU6nHuIcU78Ff4Z8vfwmcRjwjwoCix3Fpzh8kG01m1PT9FddPCEH66ojwA3RaD_VU/s1600/4.png" /></a></span></div>
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<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt -1cm; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O cone a que se refere tal
planificação é </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTxI1U71KJF3xbH_OUT4hLS1ZHqdBK94y4910WDf1KAuJvU2RjBPiuC4AhJAWsdde1-8cJPslL43P84kvymOIx3c7uVVuvZv05yGbGE-HKs1Oc2tUKiKFQqAI4iFrSkrEeImEJIJ_4U08/s1600/4R.png" imageanchor="1"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTxI1U71KJF3xbH_OUT4hLS1ZHqdBK94y4910WDf1KAuJvU2RjBPiuC4AhJAWsdde1-8cJPslL43P84kvymOIx3c7uVVuvZv05yGbGE-HKs1Oc2tUKiKFQqAI4iFrSkrEeImEJIJ_4U08/s320/4R.png" width="188" /></a></div>
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<span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">5<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Um arquiteto está fazendo
um projeto de iluminação de ambiente e necessita saber a altura que deverá
instalar a luminária ilustrada na figura<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTHKAQNtBW2ulu9nL3fjWEUR3DNDkMePFgAEm97LCyeoAB340qbhYslwbQj4L_UZmh28jfmHYGB46Kk6I_Qsz6sjBFEK0LpmBix87F3qKOPDg7EPrdKcg9k4lIpPpoF-KbbH3IoHsSa5A/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTHKAQNtBW2ulu9nL3fjWEUR3DNDkMePFgAEm97LCyeoAB340qbhYslwbQj4L_UZmh28jfmHYGB46Kk6I_Qsz6sjBFEK0LpmBix87F3qKOPDg7EPrdKcg9k4lIpPpoF-KbbH3IoHsSa5A/s1600/5.png" /></a></div>
<br />
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Sabendo-se que a luminária deverá iluminar uma área
circular de 28,26 metros quadrados <span style="mso-text-raise: -4.0pt; position: relative; top: 4.0pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1036" type="#_x0000_t75" style='width:45pt;height:18pt' o:ole="">
<v:imagedata src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image027.wmz"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1036"
DrawAspect="Content" ObjectID="_1431107012">
</o:OLEObject>
</xml><![endif]--></span>, considerando</span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" />= 3,14<span style="font-size: 10pt;">, a altura h será igual a</span></div>
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<o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">3 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">4 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">5 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">9 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">16 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">6<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Uma ampulheta é formada por dois
cones de revolução iguais, com eixos verticais e justapostos pelo vértice, o
qual tem um pequeno orifício que permite a passagem de areia da parte de cima
para a parte de baixo. Ao ser colocada para marcar um intervalo de tempo, toda
a areia está na parte de cima e, 35 minutos após, a altura da areia na parte de
cima reduziu-se à metade, como mostra a figura. Supondo que em cada minuto a
quantidade de areia que passa do cone de cima para o de baixo é constante, em
quanto tempo mais toda a areia terá passado para a parte de baixo?<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span></div>
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<o:p></o:p><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">5 minutos. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">10
minutos. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">15
minutos. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">20
minutos. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">30
minutos. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<o:p> </o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; margin-left: -1.0cm; margin-right: 0cm; margin-top: 0cm; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 9.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">7</span><b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">.</span></b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Considerando um lustre de formato cônico com altura e raio da base igual
a 0,25 m, a distância do chão (H) em que se deve pendurá-lo para obter um lugar
iluminado em forma de círculo com área de 25 </span><span style="font-family: Symbol; font-size: 10.0pt; line-height: 105%; mso-ascii-font-family: Arial; mso-bidi-font-size: 11.5pt; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;">p</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> m<sup>2</sup>, é de<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7vhMOZB-lWX2d1kBalmmKszw2UVSJjPtXqWuWEvfHFw6n7cZDjB89epypH7uewIlHgvMlMD_1gIdIkSdy8rZMInX-yqxpklx8JBWVZREr7sV5CzxZuT5Jm_kjV9Sf-RdPeSrCTdtY6rU/s1600/7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7vhMOZB-lWX2d1kBalmmKszw2UVSJjPtXqWuWEvfHFw6n7cZDjB89epypH7uewIlHgvMlMD_1gIdIkSdy8rZMInX-yqxpklx8JBWVZREr7sV5CzxZuT5Jm_kjV9Sf-RdPeSrCTdtY6rU/s1600/7.png" /></a></div>
<o:p></o:p><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">12 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">10
m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">8 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">6 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">5 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">8<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A
figura abaixo representa um recipiente cônico com solução aquosa de hipoclorito
de sódio a 27%. O nível desse líquido tem 12 cm de altura.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> Para o
preparo de um desinfetante, diluiu-se a solução inicial com água, até completar
o recipiente, obtendo-se a solução aquosa do hipoclorito de sódio a 8%.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Esse recipiente tem altura
H, em centímetros, equivalente a </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">16 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">18 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">20 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">22 e) 24 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<o:p> </o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">9<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">A
areia contida em um cone fechado, de altura 18 cm, ocupa 7/8<span style="mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"> </span>da capacidade do cone.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaCdvGbC9PQAUpALp4SKH2cuAkaIfMN723PJte4lEJZpET4shRhRi4TO3I4axtv_u21AJjpznp1odst6d4H-fv_4LNgRvwQktNF6QqxBBiCweIuZitw2rPuqztwMzfiEVsIgA3QG8BFrY/s1600/8888.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="155" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaCdvGbC9PQAUpALp4SKH2cuAkaIfMN723PJte4lEJZpET4shRhRi4TO3I4axtv_u21AJjpznp1odst6d4H-fv_4LNgRvwQktNF6QqxBBiCweIuZitw2rPuqztwMzfiEVsIgA3QG8BFrY/s320/8888.png" width="320" /></a></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Voltando-se o vértice do
cone para cima, conforme indica a figura, a altura h do tronco de cone ocupado
pela areia, em centímetros, é </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">7. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">8. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">9. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">10. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">11. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i.ytimg.com/vi/BviVU_WbDh4/0.jpg"><param name="movie" value="http://www.youtube.com/v/BviVU_WbDh4?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/BviVU_WbDh4?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">10 </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Para revestir externamente chapéus em forma de cones com h = 12 cm de
altura e diâmetro da base medindo 2r= 10 cm, serão utilizados um certo tipo de
tecido. <o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0fGKbCZU87V9pTVMft9sw2xo9qSCV26k5_g8tKT93jV9Df0mi5xn9THp0okUHNWmIBcYm6-48P9Ob15cARb2EkggRhmgJyZHWy6szKvw5yLN5FJqGZbIglZay0DCAKemYkBH4Czbzk4/s1600/10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0fGKbCZU87V9pTVMft9sw2xo9qSCV26k5_g8tKT93jV9Df0mi5xn9THp0okUHNWmIBcYm6-48P9Ob15cARb2EkggRhmgJyZHWy6szKvw5yLN5FJqGZbIglZay0DCAKemYkBH4Czbzk4/s1600/10.png" /></a></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A área <b>mínima, em cm<sup>2</sup></b> , necessária forrar 50 chapéus é igual a: </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">2750</span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" style="text-indent: 0px;" /><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">2825</span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" style="text-indent: 0px;" /><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> c</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">2975</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" style="text-indent: 0px;" /><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">3075</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" style="text-indent: 0px;" /><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">3250 </span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" style="text-indent: 0px;" /><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></div>
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<span style="font-size: 10pt; line-height: 115%;">11. Em um canteiro de obras, peças de concreto tem a forma de um tronco
de cone de raios</span><span style="font-size: 10pt; line-height: 115%;"> </span><span style="font-size: 10pt; line-height: 115%;">r = 4 m e R = 8 m e
altura h = 4 m. O volume de cada peça é :</span><br />
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<span style="font-size: 10.0pt; line-height: 115%; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="vertical-align: super;"> </span> <span style="font-family: 'Times New Roman', serif; font-size: 10pt;">a) 448 </span><span style="font-family: Symbol; font-size: 10pt;">p</span><span style="font-family: 'Times New Roman', serif; font-size: 10pt;">/ 3 m<sup>3</sup> b) 248 </span><span style="font-family: Symbol; font-size: 10pt;">p</span><span style="font-family: 'Times New Roman', serif; font-size: 10pt;">/ 3 m<sup>3</sup> c) 311 </span><span style="font-family: Symbol; font-size: 10pt;">p</span><span style="font-family: 'Times New Roman', serif; font-size: 10pt;">/ 3 m<sup>3</sup> d) 133 </span><span style="font-family: Symbol; font-size: 10pt;">p</span><span style="font-family: 'Times New Roman', serif; font-size: 10pt;">/ 3 m<sup>3</sup> e) 47 </span><span style="font-family: Symbol; font-size: 10pt;">p</span><span style="font-family: 'Times New Roman', serif; font-size: 10pt;">/ 3 m<sup>3</sup></span><br />
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<span style="font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com2tag:blogger.com,1999:blog-6195783121073928087.post-75214998928660452272013-05-13T16:48:00.001-07:002013-05-31T16:11:00.217-07:00PIRÂMIDE<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">1<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Se duplicarmos a medida da
aresta da base de uma pirâmide quadrangular
regular e reduzirmos sua altura
à metade, o volume desta pirâmide</span><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">será reduzido
à quarta parte. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">será reduzido à metade. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">permanecerá inalterado. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">será
duplicado. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">aumentará quatro vezes</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Em uma
indústria de velas, a parafina é armazenada em caixas cúbicas, cujo lado mede <i>a.</i><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Depois de derretida, a
parafina é derramada em moldes em formato de pirâmides de base quadrada, cuja
altura e cuja aresta da base medem, cada uma, a/2<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Considerando-se essas
informações, é CORRETO<b> </b>afirmar
que, com a parafina armazenada em apenas <b>uma </b>dessas caixas, enche-se um <b>total
</b>de </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">6 moldes. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">8 moldes. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">24 moldes. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">32 moldes. e) 40 moldes</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<div class="separator" style="clear: both; text-align: center;">
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Uma fábrica produz velas de parafina em forma de pirâmide quadrangular
regular com 19 cm de altura e 6 cm de aresta da base. Essas velas são formadas
por 4 blocos de mesma altura — 3 troncos de pirâmide de bases paralelas e 1
pirâmide na parte superior —, espaçados de 1 cm entre eles, sendo que a base
superior de cada bloco é igual à base inferior do bloco sobreposto, com uma
haste de ferro passando pelo centro de cada bloco, unindo-os, conforme a
figura.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> Se o dono da fábrica resolver diversificar o
modelo, retirando a pirâmide da parte superior, que tem 1,5 cm de aresta na
base, mas mantendo o mesmo molde, quanto ele passará a gastar com parafina para
fabricar uma vela? </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicyeVdVw_JTaJ5A7kyw2ywhB6Uua1Baoa8W2VmHU7dQC0FelJ3dSX3Lj_FrFkCztYIrqBpz-xeDc2wC_3jDsD3h31jegus64R8lfKRuQj_VnROsAjJz5cDK9PD6ovdKUFodHMw7UDHnfY/s1600/PI5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicyeVdVw_JTaJ5A7kyw2ywhB6Uua1Baoa8W2VmHU7dQC0FelJ3dSX3Lj_FrFkCztYIrqBpz-xeDc2wC_3jDsD3h31jegus64R8lfKRuQj_VnROsAjJz5cDK9PD6ovdKUFodHMw7UDHnfY/s1600/PI5.png" /></a></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">156 cm<sup>3</sup></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">189 cm<sup>3</sup></span><br />
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">192 cm<sup>3</sup></span><br />
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) 216</span><span style="height: 46px; left: 0px; margin-left: 300px; margin-top: 4px; mso-ignore: vglayout; position: absolute; width: 31px; z-index: 251655680;"> cm<sup>3 </sup></span><br />
<span style="height: 46px; left: 0px; margin-left: 300px; margin-top: 4px; mso-ignore: vglayout; position: absolute; width: 31px; z-index: 251655680;"><sup> </sup></span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) 540</span><span style="height: 46px; left: 0px; margin-left: 300px; margin-top: 4px; mso-ignore: vglayout; position: absolute; width: 31px; z-index: 251655680;"> cm<sup>3</sup></span><br />
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<br /></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">4<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um
telhado tem a forma da superfície lateral de uma pirâmide regular, de base
quadrada. O lado da base mede 8m e a altura da pirâmide 3m. As telhas para
cobrir esse telhado são vendidas em lotes que cobrem 1m<sup>2</sup>. Supondo
que possa haver 10 lotes de telhas desperdiçadas (quebras e emendas), o número
mínimo de lotes de telhas a ser comprado é: </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">90 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">100 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">110 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">120 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">130 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">5.</span></b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">
</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Uma pirâmide tem altura H. A que
distância do vértice deve-se passar um plano paralelo à base, para dividi-la em
duas partes de mesmo volume? </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<object class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i.ytimg.com/vi/M5RdV2i_ENM/0.jpg" height="266" width="320"><param name="movie" value="http://www.youtube.com/v/M5RdV2i_ENM?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/M5RdV2i_ENM?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">6<b>.</b> </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Seja
uma pirâmide regular de base hexagonal e altura 10 m. A que distância do
vértice devemos cortá-la por um plano paralelo à base de forma que o volume da
pirâmide obtida seja 1/8 do volume da pirâmide original? </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">2 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">4 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">5 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">6 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">8 m. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">7<b>.</b></span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um
octaedro regular é um poliedro constituído por 8 faces triangulares congruentes
entre si e ângulos poliédricos congruentes entre si, conforme mostra a figura a
seguir.</span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> Se o volume desse poliedro é 72</span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; line-height: 105%;"> cm</span><sup style="line-height: 105%;">3</sup><span style="font-size: 10pt; line-height: 105%;">, a medida de sua
aresta, em centímetros, é</span></div>
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<o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 12pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;">b) </span><span style="font-size: 10pt; text-indent: -11.35pt;">3 </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 12pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;">c) </span><span style="font-size: 10pt; text-indent: -11.35pt;">3 </span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 12pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;">d) </span><span style="font-size: 10pt; text-indent: -11.35pt;">6 </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 12pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;">e) </span><span style="font-size: 10pt; text-indent: -11.35pt;">6 </span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" /><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span></div>
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<object class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i.ytimg.com/vi/mGsFhO_poeM/0.jpg" height="266" width="320"><param name="movie" value="http://www.youtube.com/v/mGsFhO_poeM?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/mGsFhO_poeM?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
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<span style="font-size: 10pt; line-height: 105%;">8<b>.</b> </span><span style="font-size: 10pt; line-height: 105%;">Um
técnico agrícola utiliza um pluviômetro na forma de pirâmide quadrangular, para
verificar o índice pluviométrico de uma certa região. A água, depois de
recolhida, é colocada num cubo de 10 cm de aresta. Se, na pirâmide, a água
atinge uma altura de 8 cm e forma uma pequena pirâmide de 10 cm de apótema
lateral, então a altura atingida pela água no cubo é de</span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">2,24 cm </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">2,84 cm </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">3,84 cm </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">4,24 cm </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">6,72 cm </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><b><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><o:p></o:p></span></b></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">9<b>.</b>
</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um faraó projetou uma pirâmide de
100m de altura, cuja base é um quadrado de lado 100 m, dentro da qual estaria
seu túmulo. Para edificar 1000m<sup>3</sup>
a mão de obra escrava gastava, em média, 72 dias. Nessas condições, o
tempo necessário, em anos, para a construção dessa pirâmide foi,
aproximadamente, </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">76 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">66 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">56 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">46 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> e) 36</span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<object class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i.ytimg.com/vi/t_pWZQnr4gA/0.jpg" height="266" width="320"><param name="movie" value="http://www.youtube.com/v/t_pWZQnr4gA?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/t_pWZQnr4gA?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">10<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">Um
tetraedro regular tem arestas medindo </span><span style="background-color: white; color: #333333; font-family: arial, helvetica, clean, sans-serif; font-size: 13px;">√ 6 </span><span style="font-size: 10pt; line-height: 105%;">cm. Então a medida de suas alturas H é
igual a:</span></div>
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<o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) 1/2</span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;"> cm </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">1 cm</span> <span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) 3/2</span><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR; mso-hansi-font-family: Arial;"> cm</span> <span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">2
cm</span> <span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) 5/2</span><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;"> cm</span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com1tag:blogger.com,1999:blog-6195783121073928087.post-75643297315450804962013-05-07T18:31:00.002-07:002013-05-31T01:45:25.233-07:00CILINDRO<b>VÍDEO DE RESOLUÇÃO DIA 15/05</b><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">1</span><b><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">. </span></b><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Durante uma feira de exposição de animais, um tratador de cavalos é
encarregado de levar água a alguns animais em uma baia. É colocado um tanque
vazio na baia na forma de um paralelepípedo retangular com comprimento a = 80 cm, largura b = 2 m e altura c = 40 cm. O tratador transporta água de um
reservatório para o tanque, em um balde de formato cilíndrico com base de 40 cm
de diâmetro e 50 cm de altura. Estima-se que a cada vez que vai ao
reservatório, ele enche o balde e, no caminho, derrame 5% de seu conteúdo. Para
que o nível de água no tanque atinja a metade de sua capacidade, o número
mínimo de vezes que o tratador deverá buscar água no reservatório é igual a:<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">(Utilize </span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" /> = 3 <span style="font-family: Verdana, sans-serif; font-size: 9pt;">).</span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">6 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">5 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">7 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">8 e) 9 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><br /></span>VEJA VÍDEO DE RESOLUÇÃO:<br />
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<object width="320" height="266" class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i.ytimg.com/vi/oZ00ROLOD_o/0.jpg"><param name="movie" value="http://www.youtube.com/v/oZ00ROLOD_o?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/oZ00ROLOD_o?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Nove cubos
de gelo, cada um com aresta igual a 3 cm, derretem dentro de um copo
cilíndrico, inicialmente vazio, com raio da base também igual a 3 cm. <o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV9ilJ-1A54o1qDFKH9psD3gkI1vmlyFX1_C4S8dSMg1ZbDByHN0n6fa2KEHVrz3cQSHjIs2hkkz60BzK5JBcq9c487MwOD58lLRZOVB35z8WlGGAU90sB9t1lDtYRImo6jsKWchybEIM/s1600/ci2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV9ilJ-1A54o1qDFKH9psD3gkI1vmlyFX1_C4S8dSMg1ZbDByHN0n6fa2KEHVrz3cQSHjIs2hkkz60BzK5JBcq9c487MwOD58lLRZOVB35z8WlGGAU90sB9t1lDtYRImo6jsKWchybEIM/s1600/ci2.jpg" /></a></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> Após o gelo
derreter completamente, a altura do nível da água no copo será de
aproximadamente <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">8,5 cm. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">8,0 cm. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">7,5 cm. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">9,0 cm. e) 9,5 cm </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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VEJA VÍDEO DE RESOLUÇÃO:<br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/iTBXNrUKjZc?feature=player_embedded' frameborder='0'></iframe></div>
<br /></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">3<b>.</b> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">"Uma
das soluções encontradas para a escassez de água na região semiárida do
nordeste brasileiro é a captação da água da chuva que escorre dos telhados das
casas. A água captada é conduzida por meio de calhas para um reservatório com a
forma de um cilindro circular reto."</span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Superinteressante, Edição 177, junho de 2002.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Revista Globo Rural, setembro, 2003.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> </span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> O
reservatório citado tem raio da base R = 2,5 m e capacidade para armazenar a
quantidade média de água captada pela chuva em um ano acrescida de 25 %<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> O gráfico
representa a quantidade média mensal de
chuva na região onde o agricultor possui sua casa cuja área do telhado é de 10m por 8 m no período de 1 ano<o:p></o:p></span></div>
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<b><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> </span></b></div>
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<b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPSJSNil7zBVnkA4Nmn1_GwZoudqP48RG-YgdvYW-0wJpJLytgFRSGaE7v_PYhwMOHv00ZE0cHYJwETsf_JLcLgfFlgni5tQ15aHZJSQe5lvWP87ypoK4Q4H5E7O8bfnM8lHAYqc3X6Ug/s1600/image004.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="207" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPSJSNil7zBVnkA4Nmn1_GwZoudqP48RG-YgdvYW-0wJpJLytgFRSGaE7v_PYhwMOHv00ZE0cHYJwETsf_JLcLgfFlgni5tQ15aHZJSQe5lvWP87ypoK4Q4H5E7O8bfnM8lHAYqc3X6Ug/s320/image004.gif" width="320" /></a></b></div>
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<b><o:p></o:p></b><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> Podemos afirmar que a
profundidade (h) da cisterna para as condições apresentadas é de: Considere </span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">p</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"> = 3,2<o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: Verdana; mso-fareast-font-family: Verdana; mso-fareast-language: PT-BR;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><!--[endif]--><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">2,5 m b) 3,0 m c) 3,5 m d) 4,0 m e) 4,5 m <o:p></o:p></span></div>
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VEJA VÍDEO DE RESOLUÇÃO</div>
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<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/tzwpc0ezw7I?feature=player_embedded' frameborder='0'></iframe></div>
<br /></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">4<b>.</b></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Uma empresa de transporte armazena seu combustível
em um reservatório cilíndrico enterrado horizontalmente. Seu conteúdo é medido
com uma vara graduada em vinte intervalos, de modo que a distância entre duas
graduações consecutivas representa sempre o mesmo volume.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> A
ilustração que melhor representa a distribuição das graduações na vara é:<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">a)</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiByoow3X_010L_tFLzOlpdt6jQDITDW4Y9X3rV_wd0xH34GYwtP2qC2h-Wn2nluBaXxw-MHqvNV5FVfUx7bIciBwV3NshwzDaIaBGCHrmLdHcfpazT_3jwqa8f7JWhsYSsOO-EnfkCLus/s1600/4aa.png" imageanchor="1" style="font-family: Verdana, sans-serif; font-size: 9pt; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiByoow3X_010L_tFLzOlpdt6jQDITDW4Y9X3rV_wd0xH34GYwtP2qC2h-Wn2nluBaXxw-MHqvNV5FVfUx7bIciBwV3NshwzDaIaBGCHrmLdHcfpazT_3jwqa8f7JWhsYSsOO-EnfkCLus/s1600/4aa.png" /></a> <span style="font-family: Verdana, sans-serif; font-size: 9pt;">b)</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEircxtJr_rovp9bmDgn8mW8xroh6xH46po-YKKtlqa9x03A_pafBkx1DmXhYYzVD4N7qJm0vYCHhllbG69m7ronBkVBxeLHCW942KT6oFal79_UFifJV3HLhrElQuzMqSjezodKexP_X6E/s1600/ci4ab.png" imageanchor="1" style="font-family: Verdana, sans-serif; font-size: 9pt; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEircxtJr_rovp9bmDgn8mW8xroh6xH46po-YKKtlqa9x03A_pafBkx1DmXhYYzVD4N7qJm0vYCHhllbG69m7ronBkVBxeLHCW942KT6oFal79_UFifJV3HLhrElQuzMqSjezodKexP_X6E/s1600/ci4ab.png" /></a> <span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">c</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">)</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFoob0kajA8jmrioUHloZUfFQJBOzC0UQAqx_WQIqcIm-egEMkxEpf6W8DW2LVtPNMi4FuwM6t73WHGPutYtn1jr2HnbQLTkldHuVlvjQRSz58KOLtQ4zeyBRhfS8nPDMjHxUEvvCfvOw/s1600/ci4ac.png" imageanchor="1" style="font-family: Verdana, sans-serif; font-size: 9pt; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFoob0kajA8jmrioUHloZUfFQJBOzC0UQAqx_WQIqcIm-egEMkxEpf6W8DW2LVtPNMi4FuwM6t73WHGPutYtn1jr2HnbQLTkldHuVlvjQRSz58KOLtQ4zeyBRhfS8nPDMjHxUEvvCfvOw/s1600/ci4ac.png" /></a> <span style="font-family: Verdana, sans-serif; font-size: 9pt;">d)</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlRN6O1I2LLjVc3c0Szu1ISDqYzt2WP660ItlMHH52GAy2x8GipNUMcu5sCJubQWG33LKiFEFMem2LyM63rrOewITJ-gbUERl_7yRuFFiIa4HlgClGscWo8eAYpRTH0VgLNjxyFlMH0aw/s1600/ci4ae.png" imageanchor="1" style="font-family: Verdana, sans-serif; font-size: 9pt; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlRN6O1I2LLjVc3c0Szu1ISDqYzt2WP660ItlMHH52GAy2x8GipNUMcu5sCJubQWG33LKiFEFMem2LyM63rrOewITJ-gbUERl_7yRuFFiIa4HlgClGscWo8eAYpRTH0VgLNjxyFlMH0aw/s1600/ci4ae.png" /></a> <span style="font-family: Verdana, sans-serif; font-size: 9pt;">e)</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7fBPP9pPh3Z61VPnY1LDR_pMEYV9qt19pPytsYtbzUZfyitC77x7pf_XKyRJQ3hA-QQ5RX6-ZwuXJMFJCIjLCbaCI_Wf8UpwUhi8bw7FoXnhJmtdRAGIINPK-0iwbrq3bzWaEu9l1HyI/s1600/fi4ad.png" imageanchor="1" style="font-family: Verdana, sans-serif; font-size: 9pt; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7fBPP9pPh3Z61VPnY1LDR_pMEYV9qt19pPytsYtbzUZfyitC77x7pf_XKyRJQ3hA-QQ5RX6-ZwuXJMFJCIjLCbaCI_Wf8UpwUhi8bw7FoXnhJmtdRAGIINPK-0iwbrq3bzWaEu9l1HyI/s1600/fi4ad.png" /></a></div>
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;"></span><br />
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">
</span>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><br /></span>
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><span style="line-height: normal;">VEJA VÍDEO DE RESOLUÇÃO: </span></span><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">5<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Numa experiência em sala de aula, são utilizados
dois cilindros graduados com capacidade de um litro. Sabe-se que cada cilindro
tem a altura igual ao dobro do diâmetro de sua base. Um dos cilindros está
vazio e se encontra sobre a mesa, enquanto o outro, que está cheio de um
líquido, será inclinado suavemente de modo que o líquido seja derramado dentro
do primeiro. Veja ilustração na figura a seguir.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> Se o
líquido que foi derramado dentro do cilindro que está sobre a mesa marca 250 ml
em sua graduação, podemos concluir que a maior inclinação á ocorrida no outro
cilindro é de <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">60<sup>°</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">30<sup>°</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">35<sup>°</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">45<sup>°</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">15<sup>°</sup></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="line-height: normal;">VEJA VÍDEO DE RESOLUÇÃO:</span><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> 6<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Uma
artesã confecciona dois diferentes tipos de vela ornamental a partir de moldes
feitos com cartões de papel retangulares de 20 cm x 10 cm (conforme
ilustram as figuras abaixo). Unindo dois lados opostos do cartão, de duas
maneiras, a artesã forma cilindros e, em seguida, os preenche completamente com
parafina.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Supondo-se que o custo da vela seja diretamente
proporcional ao volume de parafina empregado, o custo da vela do tipo I, em
relação ao custo da vela do tipo II, será <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">o triplo. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">o dobro. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">igual. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a metade. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a terça
parte. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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VEJA VÍDEO DE RESOLUÇÃO:<br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: normal;">7. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: normal;">A figura abaixo mostra um reservatório de água na
forma de um cilindro circular reto, com 6 m de altura.
Quando está completamente cheio, o reservatório é suficiente para abastecer,
por um dia, 942 casas cujo
consumo médio diário é de 500 litros de água.
Devido a um vazamento nas parede laterais verificou-se a necessidade de uma
construtora impermeabilizar toda a superfície externa do reservatório com um impermeabilizante
de custo R$ 15,00 por metro quadrado.</span><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Atenda as solicitações seguintes<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a) Determinel o raio da base do reservatório<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">b) Determine o custo para impermeabilizar toda a superfície
lateral do reservatório <span style="background: yellow; mso-highlight: yellow;"> <o:p></o:p></span></span></div>
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VEJA VÍDEO DE RESOLUÇÃO:<br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">8<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">A Gestão Ambiental visa ao uso de práticas que garantem a conservação e
a preservação da biodiversidade, a reciclagem das matérias-primas e a redução
do impacto ambiental das atividades humanas sobre os recursos naturais.
Consciente da importância de reaproveitar sobras de madeira, uma serraria que
trabalha apenas com madeira de reflorestamento resolveu calcular a sobra de
madeira na confecção de peças cilíndricas. Para confeccionar uma peça
cilíndrica, a serraria faz os cortes adequados em um prisma quadrangular de
arestas da base 5 cm e altura 0,8 m e obtém um cilindro de 5 cm de diâmetro e
0,8 m de altura. A sobra de madeira na fabricação de mil destas peças é, em cm<sup>3</sup>
(utilize </span><img alt="\scriptstyle{\pi}" src="http://upload.wikimedia.org/math/4/a/f/4af6c37b09cf72658a73222be841877b.png" style="text-align: justify;" /><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> = 3,14), a
seguinte:</span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) 0,43</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">4,3. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) 43</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) 430</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) 43</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">00. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span><br />
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;">VEJA VÍDEO DE RESOLUÇÃO: </span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">9<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Para construir uma manilha de esgoto, um cilindro com 2 m de diâmetro e
4 m de altura (de espessura desprezível), foi envolvido homogeneamente por uma
camada de concreto, contendo 20 cm de espessura.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Supondo que cada metro cúbico de concreto custe R$ 10,00 e tomando 3,1
como valor aproximado de </span><span style="font-family: Symbol; font-size: 9.0pt; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">p</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">, então o preço dessa manilha é igual a <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">R$ 230,40. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">R$ 124,00. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: HE; mso-fareast-language: PT-BR;">R$
104,16. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">R$ 54,56. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">R$ 49,60. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><span style="line-height: normal;">VEJA VÍDEO DE RESOLUÇÃO: </span></span><br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/mRmP8IhFhuU?feature=player_embedded' frameborder='0'></iframe></div>
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><span style="line-height: normal;"><br /></span></span>
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">10<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Em um supermercado, podemos encontrar manteiga em
dois tipos de embalagens de forma cilíndrica:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">- a menor tem raio da base medindo 4 cm, altura
igual a 5 cm, contém 200 g e custa R$ 1,75;<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">- a maior tem raio da base medindo 5 cm,
altura igual a 8 cm e custa R$ 4,00.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Supondo que a densidade da manteiga seja constante,
determine:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">a) a quantidade de manteiga, em gramas, contida na
embalagem maior;<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">b) a embalagem mais vantajosa para o consumido (menor preço por grama)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: justify;">
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 2pt; text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><span style="font-size: 12px; line-height: 12px;">c) a embalagem que corresponde o menor gasto de material na fabricação</span></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
<span style="text-align: justify;">VEJA VÍDEO DE RESOLUÇÃO:</span><br />
<br />
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<br />
<div style="text-align: justify;">
<br /></div>
Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com1tag:blogger.com,1999:blog-6195783121073928087.post-82662983125714604252013-05-02T02:08:00.000-07:002013-05-07T18:54:13.828-07:00PRISMAS<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2pt; text-align: center;">
<br /></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">1<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um
arquiteto fez um projeto para construir colunas de concreto que vão sustentar
um viaduto. Cálculos mostram que 10 colunas com a forma de um prisma triangular
regular de aresta de 1 metro por 10 metros de altura são suficientes para
sustentar o viaduto.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkgA1HyQAf7ALRTo-iWBq2495NCy0hB7ZgECG2qKUVQS4c2VWBhuJFWUilfovwOPVbqExKfOCN-2bi4gE7EZ3QnqnQ45gyXya6pY1f8XiSRwxNf2zGkBuoVv9PMaHnWS_qffsVFZF_16M/s1600/triangulo.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkgA1HyQAf7ALRTo-iWBq2495NCy0hB7ZgECG2qKUVQS4c2VWBhuJFWUilfovwOPVbqExKfOCN-2bi4gE7EZ3QnqnQ45gyXya6pY1f8XiSRwxNf2zGkBuoVv9PMaHnWS_qffsVFZF_16M/s200/triangulo.png" width="183" /></a></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Se
1 metro cúbico de concreto custa R$ 800,00, qual será o custo total das
colunas? </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt;">Dado:</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt;"> <o:p></o:p></span><img alt="\sqrt{3}" class="tex" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="background-color: white; border: none; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; margin: 0px; vertical-align: middle;" /><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px;">,=1,7</span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a) R$ 8.000,00 <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">b) R$ 12.320, 00 <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">c) R$ 17.600, 00 <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">d) R$ 28.650, 00 <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">e) R$ 34.000, 00 <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p><br />
<div class="separator" style="clear: both; text-align: center;">
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<span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<br />
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> 2<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Uma caixa sem tampa é construída a partir de uma chapa retangular de metal, com 8 dm de largura de largura por 10 dmde comprimento, cortando-se, de cada canto da chapa, um quadrado de lado <i>x </i>decímetros e, a seguir, dobrando-se para cima as partes retangulares, conforme sugere a figura a seguir:<o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQc8jkQ6CmQ5TY8wOvnCaxc7kBwMXDFhr7xxjdCid89ZYtSUA5-ri_0eP_k2I6___U7Akb_bu9Erpi2CJkeIMPuHAFSPuh6NDH8g7I4yciz8L4CuxvamQ13NSto_8dnUfp-zuopg5KH_c/s1600/P4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="57" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQc8jkQ6CmQ5TY8wOvnCaxc7kBwMXDFhr7xxjdCid89ZYtSUA5-ri_0eP_k2I6___U7Akb_bu9Erpi2CJkeIMPuHAFSPuh6NDH8g7I4yciz8L4CuxvamQ13NSto_8dnUfp-zuopg5KH_c/s320/P4.png" width="320" /></a></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10pt;"> Determine o</span><span style="font-size: 10pt;"> volume, em função de x,</span><span style="font-size: 10pt;"> </span><span style="font-size: 10pt;">da caixa assim obtida :</span><br />
<span style="font-size: 10pt;"><br /></span>
<br />
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<span style="font-size: 10pt;"><br /></span>
<span style="font-size: 10pt;"><br /></span></div>
</div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b>
</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">De uma folha quadrada de papelão,
com 60 cm de lado, devem ser cortados os quatro cantos, para montar a base
inferior e as faces laterais de uma caixa de base quadrada, como mostram as
figuras a seguir.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivtjMBHo4kZbn37bO-Efs-X33Q_ZfsVnsF1MAqUkAXEqNvuB9zU5ZvrZFrbfLZjx-9d1ZlNcdhOjoaAaV9eeHggw8tbXmuH8xL5IQXObCcMcL14GDJg0Fwi0MXf7GaYFgBqGT3vNq5HDM/s1600/P2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivtjMBHo4kZbn37bO-Efs-X33Q_ZfsVnsF1MAqUkAXEqNvuB9zU5ZvrZFrbfLZjx-9d1ZlNcdhOjoaAaV9eeHggw8tbXmuH8xL5IQXObCcMcL14GDJg0Fwi0MXf7GaYFgBqGT3vNq5HDM/s1600/P2.png" /></a></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"><br /></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> Essa caixa será fechada com
uma tampa de acrílico e, no seu interior, serão colocadas bolas com 3 cm de
raio, acomodadas em uma única camada ou em várias camadas, dependendo da medida
x da altura da caixa. Se todas as camadas devem ter o mesmo número de bolas, a
maior quantidade de bolas que podem ser acomodadas é </span><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 11.35pt; text-align: justify; text-indent: -11.35pt;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">72 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">64 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">48 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">24 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">16 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p><br />
<div class="separator" style="clear: both; text-align: center;">
<object class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="http://i.ytimg.com/vi/tAFsJw2_ba0/0.jpg" height="266" width="320"><param name="movie" value="http://www.youtube.com/v/tAFsJw2_ba0?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="320" height="266" src="http://www.youtube.com/v/tAFsJw2_ba0?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
<span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><br /></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> 4<b>.</b> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Dona Margarida comprou terra adubada para sua nova jardineira, que tem a
forma de um paralelepípedo retângulo, cujas dimensões internas são: 1 m de
comprimento, 25 cm de largura e 20 cm de altura.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Sabe-se que 1 kg de terra ocupa um volume de 1,7 dm<sup>3</sup>.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 105%; margin-bottom: 2.0pt; mso-layout-grid-align: none; mso-pagination: none; text-align: justify; text-autospace: none;">
<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Nesse caso, para encher totalmente a jardineira, a quantidade de terra
que Dona Margarida deverá utilizar é, aproximadamente, </span><o:p></o:p></div>
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<span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;">a) </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">85,0 kg. </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 12.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;">b) </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">8,50 kg. </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 12.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;">c) </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">29,4 kg. </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 12.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN;">d) </span><span lang="EN-US" style="font-size: 10.0pt; mso-ansi-language: EN-US; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">294,1 kg. </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">e) 16,2 kg </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p><br />
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<span style="font-size: 10pt; text-align: justify;"> </span><span style="font-size: 12pt; text-align: justify;"> </span><span style="font-size: 12pt; text-align: justify;"> </span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">5<b>.</b> </span><span style="font-size: 10pt;">Uma indústria de cerâmica localizada no município de São Miguel do Guamá
no estado do Pará fabrica tijolos de argila (barro) destinados à construção
civil. Os tijolos de 6 furos possuem medidas externas: 9cm x 14cm x 19cm e
espessura uniforme de 8 milímetros, conforme a figura abaixo.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw6V0qKCzgcePh-vATY6dlvBVvkMsZygz5N93lAiHplvi4zWAL_ZNb_vxLFPMKqt1vTANADA8TmYwQQ7CNjcgNlH__V3rxnWqVqxoooin8Ez4rMSbH3P_BpXrIc_2YSjB9KcNRauo7Z9E/s1600/P5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw6V0qKCzgcePh-vATY6dlvBVvkMsZygz5N93lAiHplvi4zWAL_ZNb_vxLFPMKqt1vTANADA8TmYwQQ7CNjcgNlH__V3rxnWqVqxoooin8Ez4rMSbH3P_BpXrIc_2YSjB9KcNRauo7Z9E/s1600/P5.png" /></a></div>
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<span style="font-size: 10pt;"> Utilizando 1 metro cúbico de argila, o
número de tijolos inteiros que podem ser fabricados é, aproximadamente: </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10pt;">740
</span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10pt;">960 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10pt;">1020 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10pt;">1090 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10pt;">1280 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> 6<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Uma indústria precisa
fabricar 10.000 caixas em forma de pararerepípedo reãngulo com dimensões: comprimento: 40 cm, largura 20 cm e altura de 14 cm. Desprezando as abas,
aproximadamente, quantos m<sup>2</sup> de papelão serão necessários para a
confecção das caixas?<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">0,328 m<sup>2</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">1120 m<sup>2</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">112 m<sup>2</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">3280 m<sup>2</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">1640 m<sup>2</sup> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">7<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Uma
empresa de sorvete utiliza como embalagem um prisma reto, cuja altura mede 10
cm e cuja base é dada conforme descrição a seguir: de um retângulo de dimensões
20 cm por 10 cm, extrai-se em cada um dos quatro vértices um triângulo
retângulo isósceles de catetos de medida 1cm.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG8AAQezra-TOX9CZuP6DsJkZpJQuxLTd1D-dD9agMJOY5-tI2qeDtJSU0Dv-xYQVq3pM45gQkQySZERmtj_IDPKeZnrFZo3Nu5uvpfpxI7yB046VPrmkZKECcvu4Fnuft-tfUfHI7m3Y/s1600/P7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="88" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG8AAQezra-TOX9CZuP6DsJkZpJQuxLTd1D-dD9agMJOY5-tI2qeDtJSU0Dv-xYQVq3pM45gQkQySZERmtj_IDPKeZnrFZo3Nu5uvpfpxI7yB046VPrmkZKECcvu4Fnuft-tfUfHI7m3Y/s320/P7.png" width="320" /></a></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">a) Calcule o volume da
embalagem.<o:p></o:p></span><br />
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<span style="font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-language: PT-BR;">b)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Sabendo que o
volume ocupado por esse sorvete aumenta em 1/5<span style="mso-text-raise: -11.0pt; position: relative; top: 11.0pt;"><!--[if gte vml 1]><v:shape id="_x0000_i1037"
type="#_x0000_t75" style='width:11.25pt;height:27.75pt' o:ole="">
<v:imagedata src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image032.wmz"
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quando passa do estado líquido para o estado sólido, qual deve ser o volume
máximo ocupado por esse sorvete no estado líquido, nessa embalagem, para que,
ao congelar, o sorvete não transborde? </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> 8<b>.</b> </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Observe o tabuleiro de um jogo, mostrado na figura
abaixo. </span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Ele tem a forma de um paralelepípedo retângulo. Para construí-lo, um
marceneiro recebeu as seguintes instruções:<o:p></o:p></span></div>
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<b><i><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Instruções:<o:p></o:p></span></i></b></div>
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<i><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">1. as dimensões do
tabuleiro deveriam ser de 40 cm de comprimento por 20 cm de largura, por 5 cm
de altura;<o:p></o:p></span></i></div>
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<i><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">2. ele deveria ser
envernizado apenas na superfície superior e nas superfícies laterais;<o:p></o:p></span></i></div>
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<i><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">3. a madeira deveria ser o
ipê.<o:p></o:p></span></i></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Se esse marceneiro gasta,
em média, R$ 45,00 para revestir de verniz uma superfície de 1 m<sup>2</sup> e
paga R$ 3.900,00 por 1 m<sup>3</sup> de ipê ao seu fornecedor, é <b>CORRETO </b>afirmar
que, se consideradas apenas a madeira e a pintura, o custo para a confecção do
tabuleiro em R$ (reais) é: </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">27,00. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">6,30. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">12,90. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">21,90. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">18,00. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><br />
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><br /></span>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> 9<b>. </b></span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Alguns objetos, durante a
sua fabricação, necessitam passar por um processo de resfriamento. Para que
isso ocorra, uma fábrica utiliza um tanque de resfriamento, como mostrado na figura.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;"> O que aconteceria com o nível da água se
colocássemos no tanque um objeto cujo volume fosse de 2 400 cm<sup>3</sup>? </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O nível
subiria 0,2 cm, fazendo a água ficar com 20,2 cm de altura. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O nível
subiria 1 cm, fazendo a água ficar com 21 cm de altura. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O nível
subiria 2 cm, fazendo a água ficar com 22 cm de altura. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O nível
subiria 8 cm, fazendo a água transbordar. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e)
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O nível
subiria 20 cm, fazendo a água transbordar. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><br />
<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><br /></span>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">10<b>.</b>
</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Uma chapa metálica retangular com
500 cm de comprimento e 120 cm de largura deve ser dobrada, conforme a figura,
para obter-se uma calha. Quais devem ser as medidas a e b para que a vazão
nessa calha seja a maior possível?<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a = 60 cm, b = 60 cm </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a
= 50 cm, b = 35 cm </span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a = 40 cm, b = 40 cm </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a = 80 cm, b = 25 cm </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e)
</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a = 60 cm, b = 30 cm </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<br />Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com2tag:blogger.com,1999:blog-6195783121073928087.post-31122186524636001532013-04-25T13:53:00.000-07:002013-05-02T12:28:09.876-07:00ÁREAS<div style="text-align: center;">
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">1<b>.</b></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Em canteiros de obras de construção civil é comum perceber trabalhadores
realizando medidas de comprimento e de ângulos e fazendo demarcações por onde a
obra deve começar ou se erguer. Em um desses canteiros foram feitas algumas
marcas no chão plano. Foi possível perceber que, das seis estacas colocadas,
três eram vértices de um triângulo retângulo e as outras três eram os pontos
médios dos lados desse triângulo, conforme pode ser visto na figura, em que as
estacas foram indicadas por letras.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">A região demarcada pelas estacas A, B, M e N deveria ser calçada com
concreto.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Nessas condições, a área a ser calcada corresponde <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a mesma área do triângulo AMC. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a mesma área do triângulo BNC. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a metade da área formada pelo triângulo ABC. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">ao dobro da área do triângulo MNC. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">ao triplo da área do triângulo MNC. </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Na Figura I, está representado um retângulo, cuja
base mede 25 cm e cuja altura mede <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">9 cm. Esse retângulo está dividido nas regiões </span><span style="font-family: Symbol; font-size: 9.0pt; line-height: 105%; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">a</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">,
</span><span style="font-family: Symbol; font-size: 9.0pt; line-height: 105%; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">b</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> e </span><span style="font-family: Symbol; font-size: 9.0pt; line-height: 105%; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">g</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Sem que haja qualquer superposição delas, essas
regiões podem ser reagrupadas, formando um quadrado, como mostrado na Figura
II.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Então, é correto afirmar que a área da região </span><span style="font-family: Symbol; font-size: 9.0pt; line-height: 105%; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">a</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">
mede <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">24 cm<sup>2</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">28 cm<sup>2</sup>.
</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <span style="color: red;">c) </span></span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">30 cm<sup>2</sup>. </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">32 cm<sup>2</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">34 cm<sup>2</sup>.
</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b> (Ufrj 2007) ) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Para facilitar o estudo dos triângulos, uma menina foi orientada por sua
professora a trabalhar com jogos educativos</span><span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Tangram
é um antigo quebra-cabeça chinês formado por um quadrado decomposto em sete
peças: . É formado por cinco triângulos retângulos isósceles , um paralelogramo
e um quadrado, como mostra as figuras abaixo. A. <o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Se
a área de Q é 2, é correto afirmar:<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A
área do quadrado maior é 8. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A
área de T<sub>1</sub> é o dobro da área de T<sub>3</sub>. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A
área de T<sub>4</sub> é igual à área de T<sub>5</sub>. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A
área de T<sub>5</sub> é 1/4 da área do quadrado
maior. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="color: red; font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="color: red; font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A área de P é igual à área de Q. </span><span style="color: red; font-size: 10.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span><br />
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4. A figura ao lado é de um mosaico quadrado
de 1,5 m por 1,5 m,construído com cerâmicas quadradas de 0,30 m por 0,30
m,algumas cortadas em diagonal.<o:p></o:p></div>
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A
área, em metros quadrados, da região cinza que cerca as cerâmicas postas em diagonal é:</div>
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<o:p></o:p></div>
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<b><span style="font-family: "Arial,Bold","sans-serif"; mso-bidi-font-family: "Arial\,Bold"; mso-fareast-language: PT-BR;">A) </span></b>0,08 <b><span style="font-family: "Arial,Bold","sans-serif"; mso-bidi-font-family: "Arial\,Bold"; mso-fareast-language: PT-BR;">B) </span></b>0,09 <b><span style="font-family: "Arial,Bold","sans-serif"; mso-bidi-font-family: "Arial\,Bold"; mso-fareast-language: PT-BR;">C) </span></b>0,10 <b><span style="font-family: "Arial,Bold","sans-serif"; mso-bidi-font-family: "Arial\,Bold"; mso-fareast-language: PT-BR;">D) </span></b>0,11<o:p></o:p></div>
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5. Um terreno retangular, com 12 km de comprimento
por 9 km de largura, foi dividido em quatro regiões triangulares, ficando a
área sombreada para preservação de mata virgem, conforme a figura ao lado.<o:p></o:p></div>
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Sabendo que <i><span style="font-family: 'TimesNewRoman,Italic', serif;">AE </span></i><span style="font-family: Symbol;">= </span><i><span style="font-family: 'TimesNewRoman,Italic', serif;">EF </span></i><span style="font-family: Symbol;">= </span><i><span style="font-family: 'TimesNewRoman,Italic', serif;">FC </span></i>, atenda às solicitações que seguem.<o:p></o:p></div>
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<b><span style="font-family: 'Arial,Bold', sans-serif;">A) </span></b>Determine a área de cada uma das quatro regiões
triangulares.<o:p></o:p></div>
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<b><span style="font-family: 'Arial,Bold', sans-serif;">B) </span></b>Determine o percentual da área do terreno reservado
para preservação de mata<o:p></o:p></div>
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virgem.<o:p></o:p><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 115%; mso-fareast-language: ZH-CN;">6<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 115%; mso-fareast-language: PT-BR;">Uma empresa produz tampas circulares de alumínio
para tanques cilíndricos a partir de chapas quadradas de 2 metros de lado,
conforme a figura. Para 1 tampa grande, a
empresa produz 4 tampas médias e 16 tampas pequenas.<o:p></o:p></span></div>
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<!--[if !supportLineBreakNewLine]--><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 115%; mso-fareast-language: PT-BR;">Área do círculo: <o:p></o:p></span><strong style="color: red; font-family: Arial, Helvetica, sans-serif; line-height: 20.6875px;"><em>A = π * r²</em></strong></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">As sobras de material da
produção diária das tampas grandes, médias e pequenas dessa empresa são doadas,
respectivamente, a três entidades: I, II e III, para efetuarem reciclagem do
material. A partir dessas informações, pode-se concluir que <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a entidade I recebe mais material do que a entidade II. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a entidade I recebe metade de material do que a entidade III. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">a entidade II recebe o dobro de material do que a entidade III. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">as entidades I e II recebem, juntas, menos material do que a entidade
III. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">as três entidades recebem iguais quantidades de material. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">7<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">A figura representa um canteiro de forma circular
com 5 metros de raio.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">O canteiro tem uma região retangular que se destina
à plantação de flores e uma outra região, sombreada na figura, na qual se
plantará grama. Na figura, O é o centro do círculo, OB é o raio, o retângulo
está inscrito no círculo e CD mede 8 metros.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">a) Determine a medida do lado BD e a área da região
retangular destinada à plantação de flores.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">b) Sabendo-se que o metro quadrado de grama custa
R$3,00, determine quantos reais serão gastos em grama (para facilitar os
cálculos, use a aproximação </span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px;">π</span> = 3,2).<br />
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<b><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"> </span></b><b><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></b><b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">8.</span></b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">A
figura a seguir mostra uma circunferência de raio r , inscrita num triângulo retângulo de lados BC=4
cm e AC = 3 cm.<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">a) Calcule a medida AB<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">b) Calcule o raio r da circunferência .<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">9<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Um
cavalo se encontra preso num cercado de pastagem, cuja forma é um quadrado, com
lado medindo 50m. Ele está amarrado a uma corda de 40m que está fixada num dos
cantos do quadrado. Considerando </span><span style="font-family: Symbol; font-size: 9.0pt; line-height: 105%; mso-ascii-font-family: Verdana; mso-char-type: symbol; mso-fareast-language: PT-BR; mso-hansi-font-family: Verdana; mso-symbol-font-family: Symbol;">p</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> = 3,14, calcule a área, em metros quadrados, da
região do cercado que o cavalo não conseguirá alcançar, porque está amarrado. <o:p></o:p></span></div>
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<span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> a) </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">1244</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">1256. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">1422. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">1424. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">1444</span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">. </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span><br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">10<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Em uma cidade do interior, a praça principal, em
forma de um setor circular de 180 metros de raio e 200 metros de comprimento do
arco, ficou lotada no comício político de um candidato a prefeito.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Admitindo uma ocupação média de 4 pessoas por metro
quadrado, a melhor estimativa do número de pessoas presentes ao comício é: <o:p></o:p></span></div>
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<span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">70 mil </span><span style="color: red; font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">30 mil </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <span style="color: red;"> </span>c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">100 mil </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <span style="color: red;"> </span>d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">90 mil </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <span style="color: red;"> </span></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">11.</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">O mosaico
da figura adiante foi desenhado em papel quadriculado 1x1.<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">A razão entre a área da parte escura e a área da
parte clara, na região compreendida pelo quadrado ABCD, é igual a<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">12<b>.</b> (Fgv 2006) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Um fabricante produz um tipo de telha que tem a forma abaixo, cujas
medidas estão expressas em cm na figura 1.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Ele
pretende fabricar outro tipo de telha em que, como se observa na figura 2, há
semicircunferências de raio R.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a)
Se as áreas A<sub>1</sub> e A<sub>2</sub> (vide figura 3) devem ser iguais para
que a vazão de água da chuva se mantenha a mesma, qual é o valor de R?<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">b)
Qual é a economia de material, expressa em porcentagem, que o fabricante vai
obter com a mudança do tipo de telha? As duas chapas têm larguras iguais, L, e
comprimentos diferentes (vide figura 4). </span><o:p></o:p></div>
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<br /><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/0f9RN8mLAK4?feature=player_embedded' frameborder='0'></iframe></div>
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><br /></span>Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-48126808385884313442013-04-23T18:15:00.004-07:002013-04-25T12:52:45.851-07:00POTÊNCIA DO PONTO<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">1. </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Na figura a seguir, AB = 8 cm, BC = 10 cm, AD = 4 cm e o ponto O é o centro da circunferência. O raio da circunferência mede, em cm:</span><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) 1</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">6 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) 17</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) 1</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">8 </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) 19</span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) 20</span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">2<b>.</b> (Ufsc 2013) </span><span style="font-size: 10pt;">Em um centro de eventos na cidade de Madri, encontra-se um mural de Joan Miró (1893-1983) confeccionado pelo ceramista Artigas. O mural está colocado no alto da parede frontal externa do prédio e tem 60m de comprimento por 10m de altura. A borda inferior do mural está 8m acima do nível do olho de uma pessoa. A que distância da parede deve ficar essa pessoa para ter a melhor visão do mural, no sentido de que o ângulo vertical que subtende o mural, a partir de seu olho, seja o maior possível? O matemático Regiomontanus (1436-1476) propôs um problema semelhante em 1471 e o problema foi resolvido da seguinte maneira:<o:p></o:p></span></div>
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<span style="font-size: 10pt;">Imagine uma circunferência passando pelo olho O do observador e por dois pontos P e Q, verticalmente dispostos nas bordas superior e inferior do mural. O ângulo </span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; text-align: start; text-indent: 0px;"> </span><b style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; text-align: start; text-indent: 0px;">α</b><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><span style="font-size: 10pt; text-indent: -11.35pt;">será máximo quando esta circunferência for tangente à linha do nível do olho, que é perpendicular à parede onde se encontra o mural, como mostra a figura. Com estas informações, calcule a que distância OC da parede deve ficar o observador para ter a melhor visão do mural de Joan. </span><span style="font-size: 10pt; text-indent: -11.35pt;"> </span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"><b>3</b>. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Em
uma residência, há uma área de lazer com uma piscina redonda de 5 m de
diâmetro. Nessa área há um coqueiro, representado na figura por um ponto Q.<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Se a distância de Q (coqueiro) ao ponto de tangência T (da piscina) é 6
m, a distância d = QP, do coqueiro à piscina, é: <o:p></o:p></span></div>
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a) a) 4 m</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> 4,5 m. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> 5 m. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> 5,5 m. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e)
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> 6 m. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"><b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 12px;">4.</span></b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 12px;">Os satélites de comunicação são posicionados em sincronismo com a Terra, o que significa dizer que cada satélite fica sempre sobre o mesmo ponto da superfície da Terra. Considere um satélite cujo raio da órbita seja igual a 7 vezes o raio da Terra. Na figura, P e Q representam duas cidades na Terra, separadas pela maior distância possível em que um sinal pode ser enviado e recebido, em linha reta, por esse satélite.</span></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 12px;"> Se R é a medida do raio da Terra, para ir de P até Q, passando pelo satélite, o sinal percorrerá, em linha reta, a distância de<o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">6(</span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="text-align: justify; text-indent: -11.35pt;" /><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">)R. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> </span></span><br />
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">7(</span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="text-align: justify; text-indent: -11.35pt;" /><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">)R. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> </span></span><br />
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">8(</span><img alt="\sqrt{3}" src="http://upload.wikimedia.org/math/1/7/c/17c68e294ba0dc1356295bac633bf868.png" style="text-align: justify; text-indent: -11.35pt;" /><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">)R. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> </span></span><br />
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">10(</span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" style="text-align: justify; text-indent: -11.35pt;" /><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">)</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">R. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> </span></span><br />
<span style="font-family: "Arial","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">11(</span><img alt="\sqrt{2}" src="http://upload.wikimedia.org/math/e/f/5/ef5590434a387b3c4427e09d5b08baaf.png" style="text-align: justify; text-indent: -11.35pt;" /><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">)</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;">R. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-align: justify; text-indent: -11.35pt;"> </span></span><br />
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com2tag:blogger.com,1999:blog-6195783121073928087.post-15800493865748307752013-04-23T10:19:00.001-07:002013-04-25T14:53:00.086-07:00CIRCUNFERÊNCIA E CÍRCULO<b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">1</span></b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">.</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Deseja-se
construir um anel rodoviário circular em torno da cidade de São Paulo, distando
aproximadamente 20 km da Praça da Sé.</span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">a) Quantos quilômetros deverá ter essa rodovia?<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">b) Qual a densidade demográfica da região interior do anel (em
habitantes por km<sup>2</sup>), supondo que lá residam 12 milhões de pessoas,
adote o valor </span><span style="font-family: Symbol; font-size: 9pt; line-height: 105%;">p</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> = 3 <o:p></o:p></span><br />
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<b><span style="font-family: Verdana, sans-serif; font-size: 9pt;">2.</span></b><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">O
papelão utilizado na fabricação de caixas reforçadas é composto de três folhas
de papel, coladas uma nas outras, sendo que as duas folhas das faces são
“lisas” e a folha que se intercala entre elas é “sanfonada”, conforme mostrado
na figura.<o:p></o:p></span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> O fabricante desse papelão compra o papel em
bobinas, de comprimento variável. Supondo que a folha “sanfonada” descreva uma
curva composta por uma sequência de semicircunferências, com concavidades
alternadas e de raio externo (R<sub>Ext</sub>) de 1,5 mm, determine qual deve
ser a quantidade de papel da bobina que gerará a folha “sanfonada”, com
precisão de centímetros, para que, no processo de fabricação do papelão, esta
se esgote no mesmo instante das outras duas bobinas de 102 m de comprimento de
papel, que produzirão as faces “lisas”. <b>Dado:
</b></span><span style="font-family: Symbol; font-size: 9pt;">p</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">≈ 3,14.</span></div>
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a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">160 m e 07 cm. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">160 m e 14 cm. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">160 m e 21 cm. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">160 m e 28 cm. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">160 m e 35 cm. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span><br />
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</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">No processo inicial de criação de um
logotipo para uma empresa, um designer esboçou várias composições de formas
geométricas, na tentativa de encontrar algo simples e representativo. Em uma
dessas composições, um círculo de raio r = 6 cm foi sobreposto a um triângulo equilátero de lado l = 18 cm , de acordo com a figura.<o:p></o:p></span><br />
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<a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> Sabendo-se que as duas figuras têm centros
no mesmo ponto, pode-se afirmar que o perímetro do logotipo é,</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> em cm, igual a:</span><br />
<span style="font-family: Verdana, sans-serif; font-size: 9pt;"><br /></span>
<span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;">a) 6.(6 - </span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; text-align: start; text-indent: 0px;">π)</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> b) 6.(9 -</span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; text-align: start; text-indent: 0px;">π)</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> c) 6.(6+</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> </span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; text-align: start; text-indent: 0px;">π)</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> d) 9.(3+2</span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; text-align: start; text-indent: 0px;">π)</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> e) 9.(2-3</span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; text-align: start; text-indent: 0px;">π) </span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; text-indent: -11.35pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">4. Na figura abaixo, o triângulo ABC está inscrito na semicircunferência de
raio r = 5cm. Se a medida AC= 6 cm</span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">Atenda as solicitações:<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: Verdana, sans-serif; font-size: 9pt;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: Verdana, sans-serif; font-size: 9pt;">Justifique
porque o triângulo ABC é retângulo.<o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: Verdana, sans-serif; font-size: 9pt;">b)<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: Verdana, sans-serif; font-size: 9pt;">Determine
a medida AB.<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) Determine a área
do triângulo ABC.<o:p></o:p></span><br />
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com3tag:blogger.com,1999:blog-6195783121073928087.post-70646049954808372762013-04-11T15:17:00.000-07:002013-04-23T10:18:19.576-07:00POLÍGONOS<br />
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<b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">1.</span></b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Pentágonos
regulares congruentes podem ser conectados, lado a lado, formando uma estrela
de cinco pontas, conforme destacado na figura.</span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Nestas condições, o ângulo </span><span style="background-color: white; font-family: arial, helvetica, clean, sans-serif; font-size: 21px; line-height: 1.2;">θ mede:</span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">108<sup>°</sup>.
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">72<sup>°</sup>. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">54<sup>°</sup>. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">36<sup>°</sup>. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">18<sup>°</sup>. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span></div>
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<b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">2. </span></b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Na construção civil, é muito comum a utilização de
ladrilhos ou azulejos com a forma de polígonos para o revestimento de pisos ou
paredes. Entretanto, não são todas as combinações de polígonos que se prestam a
pavimentar uma superfície plana, sem que haja falhas ou superposições de
ladrilhos, como ilustram as figuras:<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">A tabela traz uma relação de alguns polígonos
regulares, com as respectivas medidas de seus ângulos internos.<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Nome<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Triângulo<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Quadrado<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Figura<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Ângulo interno<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">60°<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">90°<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">108°<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Nome<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Hexágono<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Octágono<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Eneágono<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Figura<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">Ângulo interno<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">120°<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">135°<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;">140°<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Se um arquiteto deseja utilizar uma combinação de dois tipos diferentes
de ladrilhos entre os polígonos da tabela, sendo um deles octogonal, o outro
tipo escolhido deverá ter a forma de um <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">
a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">triângulo. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">quadrado.
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">pentágono.
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">hexágono.
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e)
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">eneágono. </span><br />
<span style="font-family: Verdana, sans-serif; font-size: 9pt;"><br /></span>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"><o:p></o:p></span></div>
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<b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">3.</span></b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Na figura adiante, ABCDE é um pentágono
regular. A medida, em graus, do ângulo </span><span style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px;"> </span><b style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px;">α</b><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> é:</span></div>
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a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">32<sup>°</sup> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">34<sup>°</sup>
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c)
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">36<sup>°</sup> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">38<sup>°</sup>
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e)
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">40<sup>°</sup> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com0tag:blogger.com,1999:blog-6195783121073928087.post-40388968679661943072013-04-10T17:05:00.000-07:002013-05-01T14:13:48.017-07:00SEMELHANÇA DE TRIÂNGULOS<span style="font-family: Verdana, sans-serif; font-size: large;"> </span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">1<b>. </b></span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">Um telhado inclinado reto
foi construído sobre três suportes verticais de aço, colocados nos pontos A, B
e C, como mostra a figura ABAIXO. Os suportes nas extremidades A e C medem,
respectivamente, 4 metros e 6 metros de altura.</span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">A altura do suporte em B é, então, de: </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"><o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">4,2
metros. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">4,5
metros. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">5
metros. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">5,2
metros. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">5,5
metros.</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"><o:p></o:p></span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">2.</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">Observe os discos de raios 2 e 4, tangentes entre
si e às semirretas s e t, representados na figura abaixo. <o:p></o:p></span></div>
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A distância entre os pontos P e Q é <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">9. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">10. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">11. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">12. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">13<o:p></o:p></span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">3<b>.</b>
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Um observador situado num ponto O,
localizado na margem de um rio, precisa determinar sua distância até um ponto
P, localizado na outra margem, sem atravessar o rio. Para isso marca, com
estacas, outros pontos do lado da margem em que se encontra, de tal forma que
P, O e B estão alinhados entre si e P, A e C também. Além disso, OA é paralelo
a BC, OA = 25 m, BC = 40 m e OB = 30 m, conforme figura.<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">A distância, em metros, do observador em O até o ponto P, é: <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">30. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b)
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">35.
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">40. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">45.
</span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">50. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">4<b>.</b> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">A área
do quadrado assinalado na figura é igual a<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">15 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">20 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">12 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">18 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">16</span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"></span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><span style="font-family: Verdana, sans-serif; font-size: 9pt;">5<b>.</b> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">No triângulo retângulo abaixo, os catetos AB e AC medem,
respectivamente, 2 e 3. A área do quadrado ARST é que porcentagem da área do
triângulo ABC?<o:p></o:p></span></div>
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a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">42% </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">44% </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">46% </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">48% </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">50% </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">6<b>.</b></span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Um artesão precisa recortar um retângulo de couro com 10 cm x 2,5 cm. Os
dois retalhos de couro disponíveis para a obtenção dessa tira são mostrados nas
figuras a seguir.<b><o:p></o:p></b></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">a) O
retalho semicircular pode ser usado para a obtenção da tira? Justifique.<o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">b) O
retalho triangular pode ser usado para a obtenção da tira? Justifique.<o:p></o:p></span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">7 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Dois garotos estavam conversando ao lado de uma piscina, nas posições A
e B , como ilustra a figura abaixo. O garoto que estava na posição A observou
que o ângulo</span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">era de 90º e que as
distâncias BD e AD eram de 1m e 2m, respectivamente.</span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">Sabendo que o garoto da posição B gostava de estudar geometria, o da
posição A desafiou-o a dizer qual era a largura da piscina.<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7-u-NtYZNiYK49ykfyL1O6j8I45VetVbJXp0vTpdbJ8G-KKoIA-V84s21Fs5d80aE80Mdbp8gX5jsfH5wiO_rXJHgbG_AEkqFrftkrm6Ejod84Vi2NsW0O5VdFWdKKn5vSCLN_tlvwj4/s1600/se7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7-u-NtYZNiYK49ykfyL1O6j8I45VetVbJXp0vTpdbJ8G-KKoIA-V84s21Fs5d80aE80Mdbp8gX5jsfH5wiO_rXJHgbG_AEkqFrftkrm6Ejod84Vi2NsW0O5VdFWdKKn5vSCLN_tlvwj4/s1600/se7.png" /></a></div>
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<span style="line-height: 115%;">A resposta, correta, do garoto da
posição B deveria ser:<o:p></o:p></span></div>
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<span style="line-height: 115%;">a) <st1:metricconverter productid="4 m" w:st="on">4
m</st1:metricconverter> <o:p></o:p></span></div>
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<span style="line-height: 115%;">b) <st1:metricconverter productid="5 m" w:st="on">5
m</st1:metricconverter> <o:p></o:p></span></div>
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<span style="line-height: 115%;">c) <st1:metricconverter productid="3 m" w:st="on">3
m</st1:metricconverter><o:p></o:p></span></div>
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<span style="line-height: 115%;">d) <st1:metricconverter productid="2 m" w:st="on">2
m</st1:metricconverter><o:p></o:p></span><br />
<span style="line-height: 115%;"><st1:metricconverter productid="2 m" w:st="on"><br /></st1:metricconverter></span>
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<span style="line-height: 115%;"><st1:metricconverter productid="2 m" w:st="on"><br /></st1:metricconverter></span>
<span style="line-height: 115%;"><st1:metricconverter productid="2 m" w:st="on"><br /></st1:metricconverter></span>
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<span style="line-height: 115%;"><b><span style="font-size: 10pt;">8.</span></b><span style="font-size: 10pt;"> </span><span style="font-size: 10pt;">Uma folha de papel retangular foi dobrada como mostra a figura abaixo. De acordo com as medidas fornecidas, a região sombreada, que é a parte visível do verso da folha, tem área igual a:<o:p></o:p></span></span></div>
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<span style="line-height: 115%;"><o:p></o:p><br /></span></div>
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<span style="line-height: 115%;"><span style="font-size: 10pt;">a) </span><span style="font-size: 10pt;">24 cm<sup>2</sup> </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">b) </span><span style="font-size: 10pt;">25 cm<sup>2</sup> </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">c) </span><span style="font-size: 10pt;">28 cm<sup>2</sup> </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">d) </span><span style="font-size: 10pt;">35 cm<sup>2</sup> </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">e) </span><span style="font-size: 10pt;">36 cm<sup>2</sup></span></span><br />
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<span style="line-height: 115%;"><span style="font-size: 10pt;"><sup><br /></sup></span></span>
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<span style="line-height: 115%;"><span style="font-size: 10pt;"><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">9.Duas cidades X e Y são interligadas pela
rodovia R101, que é retilínea e apresenta 300 km de extensão. A 160 km de X, à
beira da R101, fica a cidade Z, por onde passa a rodovia R102, também retilínea
e perpendicular à R101. Está sendo construída uma nova rodovia retilínea, a
R103, que ligará X à capital do estado. A nova rodovia interceptará a R102 no
ponto P, distante 120 km da cidade Z.<o:p></o:p></span></span></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O governo está planejando, após a conclusão
da obra, construir uma estrada ligando a cidade Y até a R103. A menor extensão,
em quilômetros, que esta ligação poderá ter é </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">250. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">240. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">225. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">200. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">180. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"><o:p></o:p></span><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">8.</span></div>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com5tag:blogger.com,1999:blog-6195783121073928087.post-42541030456281368792013-04-06T03:43:00.001-07:002013-04-12T12:45:02.493-07:00TEOREMA DE TALES<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=6195783121073928087" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><b><span style="font-size: large;">VÍDEO DE RESOLUÇÃO 14 DE ABRIL</span></b><br />
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">1. </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">No desenho Ao lado, as frentes para a
rua A dos quarteirões I e II medem, respectivamente, 250 m e 200 m, e a frente
do quarteirão I para a rua B mede 40 m a mais do que a frente do quarteirão II
para a mesma rua. Sendo assim, pode-se afirmar que a medida, em metros, da
frente do menor dos dois quarteirões para a rua B é: <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;">
a) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">160 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> b) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">180 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> c) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">200 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> d) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">220 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> e) </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;">240 </span><span style="font-family: Verdana, sans-serif; font-size: 9pt;"> <o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">2<b>.</b>
</span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Para melhorar
a qualidade do solo, aumentando a produtividade do milho e da soja, em uma
fazenda é feito o rodízio entre essas culturas e a área destinada ao pasto. Com
essa finalidade, a área produtiva da fazenda foi dividida em três partes
conforme a figura.</span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Considere que<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">– os pontos A, B, C e D estão alinhados;<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">– os pontos H, G, F e E estão alinhados;<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">– os segmentos <span style="mso-text-raise: -4.0pt; position: relative; top: 4.0pt;"></span> AH,BG,CF e DE <span style="mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"></span> e <span style="mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"></span> são, dois a dois, paralelos entre si;<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">AB =500 m , BC = 600m , CD = 700 m, HE = 1980 m</span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Nessas condições, a medida do segmento GF é, em metros, </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">665. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">660. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">655. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">650. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">645. </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><o:p></o:p><br />
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3. </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A crise energética tem levado as médias e grandes empresas a buscarem
alternativas na geração de energia elétrica para a manutenção do maquinário.
Uma alternativa encontrada por uma fábrica foi a de construir uma pequena
hidrelétrica, aproveitando a correnteza de um rio que passa próximo às suas
instalações. Observando a figura e admitindo que as linhas retas r, s e t sejam
paralelas, pode-se afirmar que a barreira mede<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNJWewAWXOS6Hxul_xiwPzN_GzXfhY9fGE-akPvjKSeWwJVwPLov-W9Ghj3McYyt1mDLzBxp54nY_bNv9Ylo7SKJfLA7RPsI4gbT0y80SbZrCNiv-CQ4RrOZClSGKwee2Wc5RtV2F6b4M/s1600/t3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNJWewAWXOS6Hxul_xiwPzN_GzXfhY9fGE-akPvjKSeWwJVwPLov-W9Ghj3McYyt1mDLzBxp54nY_bNv9Ylo7SKJfLA7RPsI4gbT0y80SbZrCNiv-CQ4RrOZClSGKwee2Wc5RtV2F6b4M/s1600/t3.png" /></a></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;"><br /></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">33
m </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">38
m </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">43
m </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">d) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">48
m </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">e) </span><span style="font-size: 10.0pt; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">53
m </span><span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com2tag:blogger.com,1999:blog-6195783121073928087.post-53372058929637877462013-04-01T17:35:00.001-07:002013-04-26T10:21:22.992-07:00TRIÂNGULO RETÂNGULO<b style="text-align: justify;"><span style="font-size: 10pt;">1.</span></b><span style="font-size: 10pt; text-align: justify;"> </span><span style="font-size: 10pt; text-align: justify;">Uma estação de tratamento de água (ETA) localiza-se a 600 m de uma
estrada reta. Uma estação de rádio localiza-se nessa mesma entrada, a 1000 m da
ETA. Pretende-se construir um restaurante, na estrada, que fique à mesma
distância das duas estações. A distância do restaurante a cada uma das estações
deverá ser de</span><br />
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<span style="font-size: 10pt;">a) </span><span style="font-size: 10pt;"> 575 m </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">b) </span><span style="font-size: 10pt;"> 600 m </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">c) </span><span style="font-size: 10pt;"> 625 m </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">d) </span><span style="font-size: 10pt;"> 700 m </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">e) </span><span style="font-size: 10pt;"> 750 m</span><br />
<span style="font-size: 10pt;"><br /></span>
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<span style="font-size: 10pt;"></span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<b><span style="font-size: 10pt;">2.</span></b><span style="font-size: 10pt;"> </span><span style="font-size: 10pt;">Quatro estações
distribuidoras de energia A,B,C e D stão dispostas como
vértices de um quadrado de 40 km de lado. Deseja-se
construir uma estação central que seja ao mesmo tempo equidistante das estações A e B e da estrada (reta)
que liga as estações C e D . </span><br />
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<br /></div>
<span style="font-size: 10pt;">A nova estação deve
ser localizada</span><br />
<span style="font-size: 10pt;"><br /></span>
<o:p></o:p></div>
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<span style="font-size: 10pt;">a) </span><span style="font-size: 10pt;">no centro do quadrado. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-size: 10pt;">b) </span><span style="font-size: 10pt;">na perpendicular à estrada que liga C e D passando por seu ponto
médio, a 15 km dessa estrada. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-size: 10pt;">c) </span><span style="font-size: 10pt;">na perpendicular à estrada que liga C e D passando por seu ponto
médio, a 25 km dessa estrada. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-size: 10pt;">d) </span><span style="font-size: 10pt;">no vértice de um triângulo equilátero de base AB oposto a essa base. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-size: 10pt;">e) </span><span style="font-size: 10pt;">no ponto médio da estrada que liga as estações A e B </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span><br />
<span style="font-size: 10pt;"><br /></span>
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<b><span style="font-size: 10pt;">3.</span></b><span style="font-size: 10pt;"> </span><span style="font-size: 10pt;">Para trocar uma
lâmpada, Roberto encostou uma escada na parede de sua casa, de forma que o topo
da escada ficou a uma altura de 4 m. Enquanto Roberto subia os degraus, a base
da escada escorregou por 1 m, tocando o muro paralelo à parede, conforme
ilustração abaixo. Refeito do susto, Roberto reparou que, após deslizar, a
escada passou a fazer um ângulo de 45º com o piso horizontal. A distância entre
a parede da casa e o muro equivale a<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><span style="color: black;">a) 3<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" /> - 1 m</span><span style="font-size: 10pt; text-align: justify; text-indent: -11.35pt;"> b) </span></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;">3<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" /></a><span style="text-align: justify;">- </span><span style="text-align: justify;">2 m</span><span style="font-size: 10pt; text-align: justify; text-indent: -11.35pt;"> c) 4</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0UaxzFmIDEG1OUM-hPi3seYY-a8r-zvRXTQhrPi2gk08uvF-Z5bSnYByEfXMhyW4f7R1-DyjJZ8u7ekQFYJHzFUlvRD5gKIxNHrv-8ns99rb4KwgjSj5OTfmyCxVivWhaxP0c1AwizY/s1600/raiz+de+3.png" imageanchor="1" style="font-size: 10pt;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0UaxzFmIDEG1OUM-hPi3seYY-a8r-zvRXTQhrPi2gk08uvF-Z5bSnYByEfXMhyW4f7R1-DyjJZ8u7ekQFYJHzFUlvRD5gKIxNHrv-8ns99rb4KwgjSj5OTfmyCxVivWhaxP0c1AwizY/s1600/raiz+de+3.png" /></a><span style="text-align: justify;"> + 1 m d</span><span style="font-size: 10pt; text-align: justify; text-indent: -11.35pt;">) 4</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0UaxzFmIDEG1OUM-hPi3seYY-a8r-zvRXTQhrPi2gk08uvF-Z5bSnYByEfXMhyW4f7R1-DyjJZ8u7ekQFYJHzFUlvRD5gKIxNHrv-8ns99rb4KwgjSj5OTfmyCxVivWhaxP0c1AwizY/s1600/raiz+de+3.png" imageanchor="1" style="font-size: 10pt;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0UaxzFmIDEG1OUM-hPi3seYY-a8r-zvRXTQhrPi2gk08uvF-Z5bSnYByEfXMhyW4f7R1-DyjJZ8u7ekQFYJHzFUlvRD5gKIxNHrv-8ns99rb4KwgjSj5OTfmyCxVivWhaxP0c1AwizY/s1600/raiz+de+3.png" /></a><span style="text-align: justify;"> m </span></div>
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<b><span style="font-size: 10pt; line-height: 105%;">4.</span></b><span style="font-size: 10pt; line-height: 105%;"> </span><span style="font-size: 10pt; line-height: 105%;">Nesta figura,
estão representadas três circunferências, tangentes duas a duas, e uma reta
tangente às três circunferências:<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;"> Sabe-se que
o raio de cada uma das duas circunferências maiores mede 1 cm.<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;"> Então, é
CORRETO afirmar que a medida do raio da circunferência menor é <o:p></o:p></span></div>
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<span style="font-size: 10pt;">a) 1/3 </span><span style="font-size: 10pt;">cm. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">b) 1/4 </span><span style="font-size: 10pt;">cm. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">c) 1/5 </span><span style="font-size: 10pt;">cm. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> </span><span style="font-size: 10pt;">d) 1/6 </span><span style="font-size: 10pt;">cm. </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> <o:p></o:p></span></div>
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<b><span style="font-size: 10pt; line-height: 105%;">5.</span></b><span style="font-size: 10pt; line-height: 105%;"> Determine a</span><span style="font-size: 10pt; line-height: 105%;"> razão entre o lado do quadrado
inscrito e o lado do quadrado circunscrito em uma circunferência de raio R é: <o:p></o:p></span></div>
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<span style="font-size: 10pt;"> </span><span style="font-size: 10pt;"> </span><span style="font-size: 10pt;"> </span><span style="font-size: 12pt;"> a) 1/3 b) 1/2 c) </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" /></a> d<span style="font-size: 12pt; text-indent: -11.35pt;">) </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglu0BRd6DPkhuLOCGbrzUVE0qlW6iSp59Qdnru7-u_0FgLzwbYzjjAkH6wEncNKsiWf3_aIgqQzG75E-3TUSysseZi8YrjtNOFrdsUb3TWGmIE3Zd3lZKwxPZRjGNYGXfWr6HHxkZwL-g/s1600/raiz+de+2.png" /></a>/ 2 e) <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0UaxzFmIDEG1OUM-hPi3seYY-a8r-zvRXTQhrPi2gk08uvF-Z5bSnYByEfXMhyW4f7R1-DyjJZ8u7ekQFYJHzFUlvRD5gKIxNHrv-8ns99rb4KwgjSj5OTfmyCxVivWhaxP0c1AwizY/s1600/raiz+de+3.png" imageanchor="1" style="font-size: 10pt; text-indent: 0px;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0UaxzFmIDEG1OUM-hPi3seYY-a8r-zvRXTQhrPi2gk08uvF-Z5bSnYByEfXMhyW4f7R1-DyjJZ8u7ekQFYJHzFUlvRD5gKIxNHrv-8ns99rb4KwgjSj5OTfmyCxVivWhaxP0c1AwizY/s1600/raiz+de+3.png" /></a>/3<br />
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<o:p></o:p></div>
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<b><span style="font-size: 10pt; line-height: 105%;">6.</span></b><span style="font-size: 10pt; line-height: 105%;"> </span><span style="font-size: 10pt; line-height: 105%;">Seja MNPQ um quadrado de lado igual a 2 cm. Considere C o círculo que
contém os vértices P e Q do quadrado e o ponto médio do lado MN (ponto T). Veja
a figura a seguir.<o:p></o:p></span></div>
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<span style="font-size: 10pt; line-height: 105%;"> </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX6KbYGEZIU4rnXzYzwlaLDrctSbqBVAK1vETp6IP2af3cRsZAfI6xkJTFL41sMvRfshGbvGJTLWr-oNu-HC4flOUf_tbGjZTq7nGEKAvq-cbm2TTPuKl3aOk2NTwMrrfYIxnW_8w410Q/s1600/62.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX6KbYGEZIU4rnXzYzwlaLDrctSbqBVAK1vETp6IP2af3cRsZAfI6xkJTFL41sMvRfshGbvGJTLWr-oNu-HC4flOUf_tbGjZTq7nGEKAvq-cbm2TTPuKl3aOk2NTwMrrfYIxnW_8w410Q/s1600/62.png" /></a></div>
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<span style="font-size: 10pt; line-height: 105%;">O raio
do círculo C é de:<o:p></o:p></span><br />
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<!--[if !supportLists]--><span style="font-size: 10pt; line-height: 105%;">a)<span style="font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-size: 10pt; line-height: 105%;">3/4 cm</span> b) <span style="font-size: 10pt; line-height: 105%;">4/5 cm c) 5/4 cm</span> d) <span style="font-size: 10pt; line-height: 105%;">6/5 cm</span> e) <span style="font-size: 10pt; line-height: 105%;">7/6 cm</span><o:p></o:p><br />
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<span style="font-family: "Times New Roman","serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">7. </span><span style="font-family: "Times New Roman","serif"; font-size: 9.0pt; mso-bidi-font-weight: bold; mso-fareast-language: PT-BR;">Num projeto hidráulico, um cano com diâmetro externo de 6 cm será encaixado no vão triangular de uma superfície, como ilustra a figura abaixo. Que porção x da altura do cano permanecerá acima da superfície?</span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 9.0pt; mso-bidi-font-weight: bold; mso-fareast-language: PT-BR;">VÍDEO DE RESOLUÇÃO CLIQUE NO LINK :<a href="http://www.youtube.com/watch?v=ko3yVF9EKsw"> http://www.youtube.com/watch?v=ko3yVF9EKsw</a></span></div>
Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com1tag:blogger.com,1999:blog-6195783121073928087.post-9021043572062006242013-03-25T15:35:00.000-07:002013-04-01T17:29:24.418-07:00Fatoração e produtos notáveis<br />
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<span style="text-align: justify;">1<b style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;">.</b><span style="font-family: Verdana, sans-serif;"><span style="font-size: 9pt; line-height: 105%;"> (cftmg 2010) </span></span></span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%; text-align: justify;">Se <span style="mso-no-proof: yes; mso-text-raise: -12.0pt; position: relative; top: 12.0pt;"></span>,</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGrwfOa5Ht6iU6Jbox49XflYuTnTbe3ORlMpxR6yHAHLlrrae2mmBP-lUtjULhNdazlor0zIcYu7tSt-EaLbqv4nxXBNWSDgLgEbxttyD6Okfi_I1jDm9jkULwyXOkKgDrC3mTGa26SPY/s1600/1a.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGrwfOa5Ht6iU6Jbox49XflYuTnTbe3ORlMpxR6yHAHLlrrae2mmBP-lUtjULhNdazlor0zIcYu7tSt-EaLbqv4nxXBNWSDgLgEbxttyD6Okfi_I1jDm9jkULwyXOkKgDrC3mTGa26SPY/s1600/1a.png" /></a></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">então</span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">, é igual a <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">0 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">1 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">5 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">6 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">2<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Se x + (1/x) = 3, o valor de x<sup>3</sup> + (1/x<sup>3</sup>)
é: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">27 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">18 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">9 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">6 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">12 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Alguns
cálculos matemáticos ficam mais simples quando usamos identidades, tais como:</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">a<sup>2</sup> - b<sup>2</sup> = (a + b)(a – b) a<sup>3</sup>
+ b<sup>3</sup> = (a + b) (a<sup>2</sup> - ab + b<sup>2</sup>)<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">a) Determine </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-bidi-font-family: Verdana; mso-fareast-font-family: Verdana; mso-fareast-language: PT-BR;"><span style="font-family: 'Times New Roman'; font-size: 7pt;"> </span></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">(702)<sup>2</sup>
- (698)<sup>2</sup></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-bidi-font-family: Verdana; mso-fareast-font-family: Verdana; mso-fareast-language: PT-BR;"><br /></span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-bidi-font-family: Verdana; mso-fareast-font-family: Verdana; mso-fareast-language: PT-BR;">b) Simplifique: <span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"><u>P<sup>3</sup> +
q<sup>3</sup> </u></span></div>
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<span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%; text-indent: -18pt;"> p</span><sup style="font-family: Verdana, sans-serif; line-height: 105%; text-indent: -18pt;">2</sup><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%; text-indent: -18pt;"> – p.q + q</span><sup style="font-family: Verdana, sans-serif; line-height: 105%; text-indent: -18pt;">2</sup></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> </span><span style="font-family: Verdana, sans-serif; font-size: 9pt; line-height: 105%;"> </span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">4<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Sabendo-se que p + q = 4 e pq = 5, então o valor de
E = p<sup>3</sup> + q<sup>3</sup> + p<sup>2</sup>q + pq<sup>2</sup> é: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">24 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">26 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">30 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d)
</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">34 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e)
</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">36 </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">5<b>.</b> (cftmg
2012) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">Ao
simplificar a expressão </span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">x. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">x – 2. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">x + 2. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">x + 4. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span><br />
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Anonymoushttp://www.blogger.com/profile/13446395895435449681noreply@blogger.com2tag:blogger.com,1999:blog-6195783121073928087.post-24226352678682305852013-03-19T01:35:00.002-07:002013-03-25T15:34:10.275-07:00POTENCIAÇÃO E RADICIAÇÃO<br />
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">1<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Calcule o valor da expressão numérica</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;">2<b>.</b>
(Enem 2010) </span><span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">Embora o Índice de Massa
Corporal (IMC) seja amplamente utilizado, existem ainda inúmeras restrições
teóricas ao uso e as faixas de normalidade preconizadas.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">O Recíproco do Índice Ponderal (RIP), de
acordo com o modelo alométrico, possui uma melhor fundamentação matemática, já
que a massa é uma variável de dimensões cúbicas e a altura, uma variável de
dimensões lineares.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">As fórmulas que determinam esses índices
são:<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">IMC= Massa/ (altura).(altura) RIP= altura /</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPAcmVxc0H4fwBf6j2SckzZXE-o3fUPAjNY2kURJVDEtrNJ0NLGJDubTNkB9ZYq-UeaCYkUTCE-SVnoWtQ6WatfPSpyzIi35lLX5xivb32I8go4Sd-fRtsPf76FfI9kn5sZU8GsipG0-Q/s1600/P3.png" imageanchor="1" style="clear: right; line-height: 16px; margin-bottom: 1em; margin-left: 1em; text-align: justify;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPAcmVxc0H4fwBf6j2SckzZXE-o3fUPAjNY2kURJVDEtrNJ0NLGJDubTNkB9ZYq-UeaCYkUTCE-SVnoWtQ6WatfPSpyzIi35lLX5xivb32I8go4Sd-fRtsPf76FfI9kn5sZU8GsipG0-Q/s1600/P3.png" /></a></div>
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<span style="font-size: 10.0pt; line-height: 115%; mso-fareast-language: PT-BR;">ARAÚJO. C. G. S.; RICARDO, D.R. <i>Índice
de Massa Corporal: Um Questionamento Científicio Baseado em Evidências. </i>Arq.Bras.
Cardiologia, volume 79, n.o 1, 2002 (adaptado).<b><o:p></o:p></b></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">a)Se uma menina, com 64 kg de massa,
apresenta IMC igual a 25 kg/m<sup>2</sup>,. Qual sua altura ?<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; mso-fareast-language: PT-BR;">b) Determine seu RIP </span><br />
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">3<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Um grupo de alunos do Ensino Técnico realizou um
trabalho de pesquisa para determinar a área da superfície do corpo humano de
jovens de 15 a 20 anos. Chegaram a uma conclusão que aproximadamente a área
varia de acordo com a fórmula matemática </span></div>
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S=0,12.<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPAcmVxc0H4fwBf6j2SckzZXE-o3fUPAjNY2kURJVDEtrNJ0NLGJDubTNkB9ZYq-UeaCYkUTCE-SVnoWtQ6WatfPSpyzIi35lLX5xivb32I8go4Sd-fRtsPf76FfI9kn5sZU8GsipG0-Q/s1600/P3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPAcmVxc0H4fwBf6j2SckzZXE-o3fUPAjNY2kURJVDEtrNJ0NLGJDubTNkB9ZYq-UeaCYkUTCE-SVnoWtQ6WatfPSpyzIi35lLX5xivb32I8go4Sd-fRtsPf76FfI9kn5sZU8GsipG0-Q/s1600/P3.png" /></a></div>
<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> </span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">onde S é a área (m<sup>2</sup>) e
m a massa do corpo humano (kg). <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">Determine:<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">a) A área da superfície do corpo de um aluno S de
massa m = 64 kg, em m<sup>2</sup>:<o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">b) A massa m, em kg, quando a área da superfície
corporal S for igual a 3,00 m<sup>2</sup> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">4<b>.</b> Determine o</span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;"> valor da expressão </span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">5<b>.</b> (G1 - cp2 2008) </span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">O número de ouro, também conhecido como razão de ouro, tem sido
utilizado durante séculos por pintores e arquitetos. Hoje sabemos que Φ está
presente em algumas curvas que aparecem na natureza, como na margarida, no
girassol e na concha do molusco náutilo.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">Dizemos
que um ponto P (figura 1) divide um segmento AB na razão de ouro, se (AP)/(PB)
= (AB)/(AP) .<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">A
razão (AB)/(AP) é chamada razão de ouro e é representada pela letra grega
Φ (lê-se fi). Seu valor é constante, independente
da medida do segmento AB.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">a) Admitindo que o segmento
AB (figura 2) tenha comprimento1 determine o comprimento do segmento AP, de tal
modo que (AP)/(PB) = (AB)/(AP).<br />
<br />
</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;"> </span><span style="font-size: 10pt; line-height: 105%;"> </span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">b)
Determine a razão de ouro Φ.<o:p></o:p></span></div>
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<span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 11.5pt; mso-fareast-language: PT-BR;">c) Na figura 3, temos o
famoso desenho de Leonardo da Vinci conhecido como o Homem Vitruviano. Leonardo
utilizou a razão áurea na construção do desenho em vários momentos. Por
exemplo, o segmento que une o ponto A (extremidade da cabeça) ao ponto B (pé)
está dividido na razão áurea pelo ponto P (umbigo), sendo PB maior que AP.
Sabendo que o lado do quadrado CDEF mede 16,2 cm, utilize a razão de ouro
(AB/PB) para calcular o comprimento do segmento PB (a distância do umbigo até o
pé).<br />
Considere <b>somente neste item</b>, que RAIZ(5)</span><span style="font-size: 10.0pt; line-height: 105%; mso-bidi-font-size: 12.0pt; mso-fareast-language: PT-BR;">≈2,24<br />
<br />
Figura 3<br /> </span><o:p></o:p></div>
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<span style="font-size: 10.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-language: ZH-CN;"> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"><o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">6<b>.</b> </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">41.000 × 10<sup>-5</sup> + 3 × 10<sup>-4</sup> é
igual a: <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">0,4013. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">0,4103. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">0,0413. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">0,44. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">0,044. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: ZH-CN;">7<b>.</b>
(Ufrgs 2010) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; line-height: 105%; mso-fareast-language: PT-BR;">A distância que a luz percorre em um ano, chamada
ano-luz, é de aproximadamente 38.<span style="mso-no-proof: yes; mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape id="Imagem_x0020_16"
o:spid="_x0000_i1035" type="#_x0000_t75" style='width:6pt;height:8.25pt;
visibility:visible'>
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</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span>4<sup>5.</sup><span style="mso-no-proof: yes; mso-text-raise: -2.0pt; position: relative; top: 2.0pt;"><!--[if gte vml 1]><v:shape
id="Imagem_x0020_17" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:6pt;
height:8.25pt;visibility:visible'>
<v:imagedata src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image020.wmz"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span>5<sup>12</sup> quilômetros. A
notação científica desse número é <o:p></o:p></span></div>
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<span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;">a) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">9,5.10<sup>10</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> b) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">0,95.10<sup>12</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> c) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">9,5.10<sup>12</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> d) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">95.10<sup>12</sup>. </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: ZH-CN;"> e) </span><span style="font-family: "Verdana","sans-serif"; font-size: 9.0pt; mso-fareast-language: PT-BR;">9,5.10<sup>14</sup>.<o:p></o:p></span><br />
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