tag:blogger.com,1999:blog-8103401095338906452024-03-13T06:56:38.849-07:00Prof. Fellipe ArraisBlog contendo questões direcionadas para vestibulares e concursos,um abraço do Professor e Amigo, FELLIPE ARRAIS.PROFESSOR FELLIPE ARRAIShttp://www.blogger.com/profile/08017683679638452640noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-810340109533890645.post-51564473594234417852011-06-21T03:56:00.000-07:002011-06-21T04:34:30.627-07:00COMBINATÓRIA<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:trackmoves/> <w:trackformatting/> <w:hyphenationzone>21</w:HyphenationZone> <w:punctuationkerning/> <w:validateagainstschemas/> <w:saveifxmlinvalid>false</w:SaveIfXMLInvalid> <w:ignoremixedcontent>false</w:IgnoreMixedContent> <w:alwaysshowplaceholdertext>false</w:AlwaysShowPlaceholderText> <w:donotpromoteqf/> <w:lidthemeother>PT-BR</w:LidThemeOther> <w:lidthemeasian>X-NONE</w:LidThemeAsian> <w:lidthemecomplexscript>X-NONE</w:LidThemeComplexScript> 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Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} </style> <!--[endif]--> <p class="MsoNormal">1. (UFSM) Para efetuar suas compras, o usuário que necessita sacar dinheiro no caixa eletrônico deve realizar duas operações: digitar uma senha composta por 6 algarismos distintos e outra composta por 3 letras, escolhidas num alfabeto de 26 letras. Se essa pessoa esqueceu a senha, mas lembra que 8, 6 e 4 fazem parte dos três primeiros algarismos e que as letras são todas vogais distintas, sendo E a primeira delas, o número máximo de tentativas necessárias para acessar sua conta será</p> <p class="MsoNormal">(A) 230</p> <p class="MsoNormal">(B) 2.520 </p> <p class="MsoNormal">(C) 3.360</p> <p class="MsoNormal">(D) 15.120</p><p class="MsoNormal">2. Um cientista recebeu <span style="font-weight: bold;">cinco</span> cobaias para usar em seu estudo sobre uma nova vacina. Seus cálculos indicaram que o número de maneiras possíveis de escolher pelo menos<span style="font-weight: bold;"> três</span> cobaias é:</p><p class="MsoNormal">(A) 10.</p><p class="MsoNormal">(B) 16.</p><p class="MsoNormal">(C) 50.</p><p class="MsoNormal">(D) 60.</p><p class="MsoNormal">3. (UFF) A administração de determinado condomínio é feita por uma comissão colegiada formada de <span style="font-weight: bold;">oito</span> membros: <span style="font-weight: bold;">síndico</span>, <span style="font-weight: bold;">subsíndico</span> e um <span style="font-weight: bold;">conselho consultivo</span> composto de seis pessoas. Note que há distinção na escolha de síndico e subsíndico enquanto não há esta distinção entre os membros do conselho consultivo. Sabendo que dez pessoas se dispõem a fazer parte de tal comissão, determine o número total de comissões colegiadas distintas que poderão ser formadas com essas dez pessoas.</p><p class="MsoNormal">4. (UEL) Gabi e Ana Paula são membros atuantes do Grêmio Estudantil e estão se formando numa turma de 27 alunos, no total. Uma comissão de formatura, com <span style="font-weight: bold;">cinco</span> membros, deve ser formada para a organização dos festejos. Quantas comissões podem ser formadas de modo que Gabi e Ana Paula sejam membros?</p><p class="MsoNormal">(A) 2300<br /></p><p class="MsoNormal">(B) 9828<br /></p><p class="MsoNormal">(C) 9288<br /></p><p class="MsoNormal">(D) 3276<br /></p><p class="MsoNormal">5. (FGV) Uma empresa tem n vendedores que, com exceção de dois deles, podem ser promovidos a duas vagas de gerente de vendas. Se há 105 possibilidades de se efetuar essa promoção, então o número n é igual a:</p><p class="MsoNormal">(A) 10.<br /></p><p class="MsoNormal">(B) 11.<br /></p><p class="MsoNormal">(C) 13.<br /></p><p class="MsoNormal">(D) 17.</p><p class="MsoNormal">6. (FUVEST) Em uma classe de <span style="font-weight: bold;">nove</span> alunos, todos se dão bem, com exceção de Andréia, que vive brigando com Manoel e Alberto. Nessa classe, será constituída uma comissão de cinco alunos, com a exigência de que cada membro se relacione bem com todos os outros. Quantas comissões podem ser formadas?</p><p class="MsoNormal">(A) 71<br /></p><p class="MsoNormal">(B) 75<br /></p><p class="MsoNormal">(C) 80<br /></p><p class="MsoNormal">(D) 83<br /></p><p class="MsoNormal">7. (UFJF) Um jornalista foi designado para cobrir uma reunião de ministros de estado. Ao chegar ao local da reunião, descobriu que havia terminado. Ao perguntar ao porteiro o número de ministros presentes, ele disse: "Ao saírem, todos os ministros se cumprimentaram mutuamente, num total de 15 apertos de mão". Com base nessa informação, qual foi o número de ministros presentes ao encontro?</p><p class="MsoNormal">8. (UFSM) Por ocasião da Feira de Ciências, 10 alunos da turma de Susanita foram incumbidos de monitorar as salas Meio Ambiente e Informática. A sala Meio Ambiente deve ter 6 monitores. Como um dos principais objetivos é desenvolver a capacidade de o aluno pensar, refletir e expressar seus conhecimentos perante os visitantes, todos deverão passar pelas duas salas. Assim, o número de maneiras diferentes que esses alunos podem ser distribuídos nas duas salas, sem que nenhum seja excluído é:</p><p class="MsoNormal">(A) 105<br /></p><p class="MsoNormal">(B) 210<br /></p><p class="MsoNormal">(C) 420<br /></p><p class="MsoNormal">(D) 5.040</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">GABARITO</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">1) D</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">2) B</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">3) 2520</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">4) A</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">5) D</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">6) A</p><p style="font-weight: bold; color: rgb(255, 0, 0);" class="MsoNormal">7) 6</p><p class="MsoNormal"><span style="font-weight: bold; color: rgb(255, 0, 0);">8) B</span><br /></p><p class="MsoNormal"><br /></p>PROFESSOR FELLIPE ARRAIShttp://www.blogger.com/profile/08017683679638452640noreply@blogger.com0tag:blogger.com,1999:blog-810340109533890645.post-39455249365486761712011-06-19T14:11:00.000-07:002011-06-19T14:12:15.070-07:00PERCENTAGEM<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:trackmoves/> <w:trackformatting/> <w:hyphenationzone>21</w:HyphenationZone> <w:punctuationkerning/> <w:validateagainstschemas/> <w:saveifxmlinvalid>false</w:SaveIfXMLInvalid> <w:ignoremixedcontent>false</w:IgnoreMixedContent> <w:alwaysshowplaceholdertext>false</w:AlwaysShowPlaceholderText> <w:donotpromoteqf/> <w:lidthemeother>PT-BR</w:LidThemeOther> <w:lidthemeasian>X-NONE</w:LidThemeAsian> <w:lidthemecomplexscript>X-NONE</w:LidThemeComplexScript> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> <w:dontgrowautofit/> <w:splitpgbreakandparamark/> 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mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} </style> <![endif]--> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">1<b style="">.</b> <span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">Um grupo de amigos tinha reservado um sítio para um fim de semana, e o aluguel seria dividido entre eles em partes iguais. Por algum motivo, o proprietário resolveu aumentar em 10% o preço combinado; isso fez com que três deles desistissem, ocasionando um acréscimo de 20% para cada um dos outros.</span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">Com base nessas informações, pode-se afirmar que o número de pessoas do grupo inicial era igual a: </span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) 27<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) 32<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) 36<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">d) 40<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style="font-size: 9pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style=""> </span><span style="font-family: "Arial","sans-serif";"></span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">2<b style="">.</b> <span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">A prestação da casa própria de João consome 30% do seu salário. Se o salário é corrigido com um aumento de 25% e a prestação da casa com um aumento de 20%, a nova percentagem que a prestação passou a consumir do salário do João é </span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) 22,5%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) 24,5%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) 26,8%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">d) 28,8%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style="font-size: 9pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style=""> </span><span style="font-family: "Arial","sans-serif";"></span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style=""> </span><span style="font-size: 9pt; font-family: "Arial","sans-serif";">3<b style="">.</b> <span style=""> </span></span><span style="font-size: 10pt; font-family: "Arial","sans-serif";">A população de uma cidade cresceu 25% em um ano e, no ano seguinte, teve um decrescimento de 25%. Em relação à população inicial da cidade, podemos deduzir corretamente que a população: </span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) aumentou 93,75%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) diminuiu 93,75%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) permaneceu estável<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">d) aumentou 6,25%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">e) diminuiu 6,25%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style="font-size: 9pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style=""> </span><span style=""> </span><span style="font-family: "Arial","sans-serif";"></span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">4<b style="">.</b> </span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">Em uma determinada cidade, o preço da gasolina por litro era de R$ 2,75 e baixou para R$ 2,20. Nesse contexto, o preço da gasolina foi reduzido em: </span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) 15%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) 17%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) 18%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">d) 20%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">e) 25%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style="font-size: 9pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style=""> </span><span style=""> </span><span style="font-family: "Arial","sans-serif";"></span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">5<b style="">.</b> <span style=""> </span><span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">Uma loja de eletrodomésticos publicou o seguinte anúncio:</span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">"Compre uma geladeira por R$ 950,00 para pagamento em 30 dias, ou à vista, com um desconto promocional de 20%". Se um cliente optar pela compra com pagamento em 30 dias, a taxa de juros a ser paga, ao mês, é: </span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) 20%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) 22%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) 25%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">d) 28%<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style="font-size: 9pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style=""> </span><span style="font-family: "Arial","sans-serif";"></span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">6<b style="">.</b> <span style=""> </span><span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">José foi promovido na sua empresa e teve um aumento de 40% no seu salário. Dois meses depois, todos os funcionários da empresa receberam um reajuste de 10%. Qual foi o aumento percentual de José? </span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style="font-size: 9pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style=""> </span><span style="font-family: "Arial","sans-serif";"></span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">7<b style="">.</b> <span style=""> </span><span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">João recebeu um aumento de 10%<span style=""> </span>e com isso seu salário chegou a R$1.320,00. O salário de João antes do aumento era igual a? </span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) R$1.188,00<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) R$1.200,00<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) R$1.220,00<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">d) R$1.310,00<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">e) R$1.452,00<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="line-height: 12pt;"><span style="font-size: 9pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style=""> </span><span style="font-family: "Arial","sans-serif";"></span></p> <p class="MsoNormal" style="line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">8<b style="">.</b> <span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">Pensando em aumentar seus lucros, um lojista aumentou os preços de seus produtos em 25%. Como, a partir desse aumento, as vendas diminuíram, o comerciante decidiu reduzir os novos preços praticados em 25%. Com base nessas informações, é CORRETO afirmar que, após essa redução, as mercadorias dessa loja passaram a: </span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) ter o preço original.<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) ser 5% mais caras.<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) ser 10% mais caras.<span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; line-height: 12pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">d) ser mais baratas.<span style=""> </span></span><span style="font-size: 10pt;"></span></p> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac>PROFESSOR FELLIPE ARRAIShttp://www.blogger.com/profile/08017683679638452640noreply@blogger.com0tag:blogger.com,1999:blog-810340109533890645.post-52862702923635256502011-06-16T20:38:00.000-07:002011-06-16T20:41:50.067-07:00LOGARITMO<!--[if gte mso 9]><xml> <o:officedocumentsettings> <o:allowpng/> <o:targetscreensize>1024x768</o:TargetScreenSize> </o:OfficeDocumentSettings> </xml><![endif]--><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:trackmoves/> <w:trackformatting/> <w:hyphenationzone>21</w:HyphenationZone> <w:punctuationkerning/> <w:validateagainstschemas/> <w:saveifxmlinvalid>false</w:SaveIfXMLInvalid> <w:ignoremixedcontent>false</w:IgnoreMixedContent> <w:alwaysshowplaceholdertext>false</w:AlwaysShowPlaceholderText> <w:donotpromoteqf/> 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</w:LatentStyles> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} </style> <![endif]--> <p class="MsoNormal" style="margin-bottom: 2pt; line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">1<b style="">.</b> (Ufg)<span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">A teoria da cronologia do carbono, utilizada para determinar a idade de fósseis, baseia-se no fato de que o isótopo do carbono 14 (C-14) é produzido na atmosfera pela ação de radiações cósmicas no nitrogênio e que a quantidade de C-14 na atmosfera é a mesma que está presente nos organismos vivos. Quando um organismo morre, a absorção de C-14, através da respiração ou alimentação, cessa, e a quantidade de C-14 presente no fóssil é dada pela função C(t) = C<sub>0</sub>10<sup>nt</sup>, onde t é dado em anos a partir da morte do organismo, C<sub>0</sub> é a quantidade de C-14 para t = 0 e n é uma constante. Sabe-se que 5 600 anos após a morte, a quantidade de C-14 presente no organismo é a metade da quantidade inicial (quando t = 0).</span></p> <p class="MsoNormal" style="margin-bottom: 2pt; line-height: 105%;"><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">No momento em que um fóssil foi descoberto, a quantidade de C-14 medida foi de C<sub>0</sub>/32. 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mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} </style> <![endif]--> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></p><p class="MsoNormal" style="margin-bottom: 2pt; line-height: 105%;"><span style="font-size: 9pt; line-height: 105%; font-family: "Arial","sans-serif";">2<b style="">.</b> (Ufsm)<span style=""> </span></span><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";">Os projetos sociais que visam melhorar a qualidade de vida de certa cidade são realizados segundo a previsão populacional para a época de implementação. Sabe-se que a população da cidade aumenta de acordo com a lei P(t) = 2000 . 10<sup>t</sup>, onde t é o tempo em anos e P(t) é o total de habitantes após t anos. Para atender uma população de 160000 habitantes, adotando log 2 = a, o projeto deverá estar pronto num total de anos igual a </span><span style="font-size: 11pt; line-height: 105%;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) </span><span style="font-size: 10pt; font-family: "Arial","sans-serif";">3a + 1 </span><span style="font-size: 10pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) </span><span style="font-size: 10pt; font-family: "Arial","sans-serif";">3a </span><span style="font-size: 10pt; font-family: "Arial","sans-serif";"><span style=""> </span></span><span style="font-size: 10pt;"></span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: 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mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} </style> <![endif]--> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></p><p class="MsoNormal" style=""><span style="font-size: 9pt; font-family: "Arial","sans-serif";">3<b style="">.</b> (Ufjf)<span style=""> </span></span><span style="font-size: 10pt; font-family: "Arial","sans-serif";">Uma pessoa aplicou uma quantia inicial em um determinado fundo de investimento. Suponha que a função <i>F</i>, que fornece o valor, em reais, que essa pessoa possui investido em relação ao tempo <i>t</i>, seja dada por:</span></p><p class="MsoNormal" style=""><span style="font-size: 10pt; font-family: "Arial","sans-serif";"> F(t) = 100(1,2)<sup>t</sup>.</span></p> <p class="MsoNormal" style=""><span style="font-size: 10pt; font-family: "Arial","sans-serif";">O tempo <i>t</i>, em meses, é contado a partir do instante do investimento inicial.</span></p> <p class="MsoNormal" style=""><span style="font-size: 10pt; font-family: "Arial","sans-serif";">a) </span><span style="font-size: 10pt; font-family: "Arial","sans-serif";">Qual foi a quantia inicial aplicada?</span></p> <p class="MsoNormal" style=""><span style="font-size: 10pt; font-family: "Arial","sans-serif";">b) </span><span style="font-size: 10pt; font-family: "Arial","sans-serif";">Quanto essa pessoa teria no fundo de investimento após 3 meses da aplicação inicial?</span></p> <p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt;"><span style="font-size: 10pt; font-family: "Arial","sans-serif";">c) </span><span style="font-size: 10pt; font-family: "Arial","sans-serif";">Utilizando os valores aproximados log<sub>10</sub> 2 = 0,3 e log<sub>10</sub> 3 = 0,48, quantos meses, a partir do instante do investimento inicial, seriam necessários para que essa pessoa possuísse, no fundo de investimento, uma quantia igual a R$ 2.700,00?<br /></span></p><p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; font-weight: bold; color: rgb(255, 0, 0);">GABARITO</p><p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; font-weight: bold; color: rgb(255, 0, 0);">1) 28 mil</p><p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; font-weight: bold; color: rgb(255, 0, 0);">2) A</p><p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; font-weight: bold; color: rgb(255, 0, 0);">3)</p><p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; font-weight: bold; color: rgb(255, 0, 0);">A) 100 reais.</p><p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt; font-weight: bold; color: rgb(255, 0, 0);">B) 172,8 reais.</p><p class="MsoNormal" style="margin-left: 11.35pt; text-indent: -11.35pt;"><span style="font-weight: bold; color: rgb(255, 0, 0);">C) 18 meses.</span><br /><span style="font-size: 10pt; font-family: "Arial","sans-serif";"></span><span style="font-size: 11pt;"></span></p> <p class="MsoNormal" style="margin-bottom: 2pt; line-height: 105%;"><br /><span style="font-size: 10pt; line-height: 105%; font-family: "Arial","sans-serif";"></span><span style="font-size: 11pt; line-height: 105%;"></span></p> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac>PROFESSOR FELLIPE ARRAIShttp://www.blogger.com/profile/08017683679638452640noreply@blogger.com0