tag:blogger.com,1999:blog-23678726088554438062024-03-05T13:21:13.472-03:00Licenciatura em MatemáticaMeu objetivo é apenas postar resolução de exercícios e outros assuntos relacionados com o tema matemática. Pretendo ser o mais preciso e objetivo possível.
O que eu faço? Trabalho na iniciativa privada e sou estudante de Mestrado em Matemática, mais precisamente o PROFMAT - Mestrado Profissional em Matemática. Na UFABC.
Obrigado pela visita ao blog.Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.comBlogger86125tag:blogger.com,1999:blog-2367872608855443806.post-64250703119011845072016-02-08T10:10:00.001-02:002016-02-08T10:10:58.601-02:00ExPCEx 2015 - Questão de PolinômiosOlá,<br />
Segue uma questão de polinômios, neste caso de grau 6. Para achar uma das raízes, usamos o teorema das raízes racionais, e vamos fatorando até achar as outras raízes.<br /><br />Seguem o enunciado e a resolução.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqf97kqSebvrK1JLMWpFrUW6KS7IdaQKYsrWquU66dHvOh0f4CUk9dzNp9Q9Uzjpgmb4TV8hQvPc1PvAnbxthIyXmf99jSByH9vR6tyW1-z8pMgfG19YVyFYGIyNAaNnFzOprLr_5H069j/s1600/Clipboard01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="143" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqf97kqSebvrK1JLMWpFrUW6KS7IdaQKYsrWquU66dHvOh0f4CUk9dzNp9Q9Uzjpgmb4TV8hQvPc1PvAnbxthIyXmf99jSByH9vR6tyW1-z8pMgfG19YVyFYGIyNAaNnFzOprLr_5H069j/s640/Clipboard01.jpg" width="640" /></a></div>
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Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com2tag:blogger.com,1999:blog-2367872608855443806.post-43145234927309828752015-09-27T22:37:00.000-03:002015-09-27T22:37:02.483-03:00EsPCEx 2013 - Questão de PA de 2ª OrdemEssa questão foi resolvida usando uma técnica geralmente estudada quando o assunto é progressões aritméticas de 2ª ordem. Não é tema em geral abordado no ensino médio, mas como eu comentei, quem já estudou o assunto não terá problemas. Para quem nunca estudou, é um bom exemplo de aplicação.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil3Bptf4iQ9FfVmarkRFuZc7pwSKN8hIfkru9gXmxC4DYl3nix_otTYY8XeKP-9_31g4JGJ198UAO-ioIP-9BmM8_ULDS2MmCwi1jA-4u4Wo5CzBA7IkDxI0BnhygIjzwdN0RJY6kazP3U/s1600/EsPCEx+2013+-+Quest%25C3%25A3o+de+PA+de+2%25C2%25AA+Ordem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="227" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil3Bptf4iQ9FfVmarkRFuZc7pwSKN8hIfkru9gXmxC4DYl3nix_otTYY8XeKP-9_31g4JGJ198UAO-ioIP-9BmM8_ULDS2MmCwi1jA-4u4Wo5CzBA7IkDxI0BnhygIjzwdN0RJY6kazP3U/s640/EsPCEx+2013+-+Quest%25C3%25A3o+de+PA+de+2%25C2%25AA+Ordem.jpg" width="640" /></a></div>
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Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-50724199747819079002015-09-06T21:16:00.004-03:002015-09-06T21:16:54.266-03:00EsPCEx 2013 - Questão de Complexos<br />
Segue uma questão simples de números complexos.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXZK5L4A3MqJwJCIddkGd5L1zsGW-lqpkhL_bvP2FHZEyf2DvNNzhCqk1IRIH85Mupgs-ITnK-U6Gk3tkWd_Z535NVJi1NjPUpjqqtiVOb11uLEzwaZmMn6GLKLwSuYD-P9xisdA_3Ukmg/s1600/espcex+2013+-+complexos.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="64" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXZK5L4A3MqJwJCIddkGd5L1zsGW-lqpkhL_bvP2FHZEyf2DvNNzhCqk1IRIH85Mupgs-ITnK-U6Gk3tkWd_Z535NVJi1NjPUpjqqtiVOb11uLEzwaZmMn6GLKLwSuYD-P9xisdA_3Ukmg/s640/espcex+2013+-+complexos.jpg" width="640" /></a></div>
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Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-29872275220516982732015-09-06T21:14:00.000-03:002015-09-06T21:14:27.988-03:00EsPCEx 2013 - Questão de InequaçõesPara este tipo de problema existem inúmeras formas diferentes de se resolver. Estou apresentando uma destas formas.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMjGyzFKn4JhAa8LiSaXq7ReTU0GKRtDctFOHbzIkxWNMXqot3thAGiO-armx1iZVpKhCl2dqyIlYzHe_iYD3SVVUztwHDzaiDsTU8oiXZ0s66xCGpf1LafL8eV1GXRvothPWrzMfVnCDf/s1600/espcex+2013+-+inequa%25C3%25A7%25C3%25A3o.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="88" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMjGyzFKn4JhAa8LiSaXq7ReTU0GKRtDctFOHbzIkxWNMXqot3thAGiO-armx1iZVpKhCl2dqyIlYzHe_iYD3SVVUztwHDzaiDsTU8oiXZ0s66xCGpf1LafL8eV1GXRvothPWrzMfVnCDf/s640/espcex+2013+-+inequa%25C3%25A7%25C3%25A3o.jpg" width="640" /></a></div>
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Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-84568083841483356802015-08-14T19:24:00.002-03:002015-08-14T19:24:52.333-03:00FUVEST 2006 Questão de Geometria Plana (Q4)Essa questão causa uma certa estranheza logo no início, por não trazer aparentemente nenhum dado. Com um pouco de reflexão, entretanto, é possível perceber que usando semelhança de triângulos e relações trigonométrica, o resultado sai facilmente.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2cJsW-dgkyiYKDXu7V-Izcl3UtShcySaplW14v39LJaZmjCOT_0xLfGVJnMYMhhBMh2i8bYpHd2gYRv5ahd8ggHBZ1lJ8xn2F_MKefWad96h9rRHwMxqHVuztuLz43oexoiEK3H_P25aB/s1600/q4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2cJsW-dgkyiYKDXu7V-Izcl3UtShcySaplW14v39LJaZmjCOT_0xLfGVJnMYMhhBMh2i8bYpHd2gYRv5ahd8ggHBZ1lJ8xn2F_MKefWad96h9rRHwMxqHVuztuLz43oexoiEK3H_P25aB/s640/q4.jpg" width="640" /></a></div>
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Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-61639073166367630202015-07-29T19:27:00.000-03:002015-07-29T19:27:10.353-03:00Fuvest 2006 - Questão de Geometria PlanaOlá,<br />
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Há outras formas de se resolver esta questão, mas estou apresentando pela lei dos senos e lei dos cossenos.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsyFgH7OZTeZXABU7FN9d1uf9fApU5z2HNVAEwWQbdULaGmS3l1hGTQJ2c909h-mRMQgLc_sImEyzuIxylJMer0iLTZPc4p_w3gKPeSZWD2zNfQZmd0W_YMuK28dLUhM_FOhdSFzQb9tf9/s1600/q5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsyFgH7OZTeZXABU7FN9d1uf9fApU5z2HNVAEwWQbdULaGmS3l1hGTQJ2c909h-mRMQgLc_sImEyzuIxylJMer0iLTZPc4p_w3gKPeSZWD2zNfQZmd0W_YMuK28dLUhM_FOhdSFzQb9tf9/s640/q5.jpg" width="640" /></a></div>
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<iframe allowfullscreen="" frameborder="0" height="390" src="https://www.youtube.com/embed/psWNHUw77Ok" width="640"></iframe> Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-65490882605872339722015-07-22T18:53:00.001-03:002015-07-22T18:57:47.087-03:00EsPCEx 2015 - Questão de ÁlgebraOlá,<br />
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Envolve binômio de Newton. É uma questão bem 'clássica', que exige atenção na manipulação algébrica.<br />
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Segue enunciado:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIwxXQWDDO7e8wTHnsxsyTLbRRwgU4wM6n1yuN-_kptG6o5qo_qNITU1hbFSYoUqu_FZueTbLVkfC3NXHYzdLx87clpjpkJZ8RwfdS4tuly-dh06D10395YaH-9xI2Uf0VE4VadI3fvFEt/s1600/de+%25C3%25A1lgebra.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIwxXQWDDO7e8wTHnsxsyTLbRRwgU4wM6n1yuN-_kptG6o5qo_qNITU1hbFSYoUqu_FZueTbLVkfC3NXHYzdLx87clpjpkJZ8RwfdS4tuly-dh06D10395YaH-9xI2Uf0VE4VadI3fvFEt/s640/de+%25C3%25A1lgebra.jpg" width="640" /></a></div>
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E solução:<br />
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<iframe allowfullscreen="" frameborder="0" height="390" src="https://www.youtube.com/embed/xigPVhevV3k" width="640"></iframe><br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-66082718159775749512015-06-26T19:00:00.001-03:002015-06-26T19:00:59.968-03:00EsPCEx 2015 Questão de Geometria Analítica<br /><br />
Segue mais uma questão do EsPCEx, desta vez uma de Geometria Analítica.<br /><br />
Acho mais interessante usando uma abordagem vetorial, mas neste video a resolvi da forma tradicional.<br /><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEOEUgYZrbuaN9ZaOew-y5VAFCTi26AkJkuDmVq7qmKmbFIbP6-MFycOjWacBqiD6B9vVljAg0_JhftVJv5AoYMs9xOaanhwdjO7y1LpbhikL63U64KBQkUE4hfaSyk54fLVPNmbxvmF1S/s1600/questao+15.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEOEUgYZrbuaN9ZaOew-y5VAFCTi26AkJkuDmVq7qmKmbFIbP6-MFycOjWacBqiD6B9vVljAg0_JhftVJv5AoYMs9xOaanhwdjO7y1LpbhikL63U64KBQkUE4hfaSyk54fLVPNmbxvmF1S/s640/questao+15.jpg" width="640" /></a></div><br /><br />
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<iframe allowfullscreen="" frameborder="0" height="270" src="https://www.youtube.com/embed/A4MpFruTZP4" width="480"></iframe>Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com1tag:blogger.com,1999:blog-2367872608855443806.post-65575001476520980932015-06-07T22:38:00.000-03:002015-06-07T22:38:19.283-03:00EsPCEx 2015 - Questão de Trigonometria e Polinômios Questão que envolve conhecimentos básicos de polinômios e trigonometria.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijfSuiWuc7cyXhsccPF3DHMRqvu_BoIxn1Xbmt0EPZrmpXWMSlhQKFmEgUpX31CuzeZLAiUa-pIlufahawZSqXBP50RJMcs5P1vcYB3w0Rg1p04qq8fASY7OBccGoOQxkSmMZ557d5nWXT/s1600/trigonometria.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijfSuiWuc7cyXhsccPF3DHMRqvu_BoIxn1Xbmt0EPZrmpXWMSlhQKFmEgUpX31CuzeZLAiUa-pIlufahawZSqXBP50RJMcs5P1vcYB3w0Rg1p04qq8fASY7OBccGoOQxkSmMZ557d5nWXT/s640/trigonometria.jpg" width="640" /></a></div>
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Abraços<br />
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Cesar<br />
<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-27393597371451058982015-06-06T09:21:00.001-03:002015-06-06T09:21:23.911-03:00EsPCEx 2015 - Questão de Geometria Espacial e Plana<br /><br />
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Uma questão simples de Geometria Espacial, mas que acaba usando mais <br />
conceitos de Geometria Plana. Basta interpretar corretamente e fazer um <br />
bom desenho.<br /><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxDvmRRLK3_7cMPFhrkdXNtDKiSTcd492U6MKCG6WBWolo0WQ_gXjhREtMFlQHY0RoP0m2aOc-uP1IGzUyXtKNhjAhlNeTJfI0zSdFMMghH9IHHz7Qj2eR7saejdbPjZir1cfYvG0PVjul/s1600/geometria.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="304" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxDvmRRLK3_7cMPFhrkdXNtDKiSTcd492U6MKCG6WBWolo0WQ_gXjhREtMFlQHY0RoP0m2aOc-uP1IGzUyXtKNhjAhlNeTJfI0zSdFMMghH9IHHz7Qj2eR7saejdbPjZir1cfYvG0PVjul/s640/geometria.jpg" width="640" /></a></div><br /><br />
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<iframe allowfullscreen="" frameborder="0" height="270" src="https://www.youtube.com/embed/ZEhvS9EDxGU" width="480"></iframe>Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-88118988245750003452015-05-15T19:29:00.001-03:002015-05-15T22:12:58.827-03:00EsPCEx 2015 Questão de Logaritmos e TrigonometriaUma questão que envolve Trigonometria e Logaritmos. A parte dos logaritmos é meio puxada, o estudante tem que conhecer muito bem as propriedades operatórias. E a parte de trigonometria é mais tranquila.<br />
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" 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.<iframe allowfullscreen="" frameborder="0" height="344" src="https://www.youtube.com/embed/3n5Jn6dKQHg" width="459"></iframe>Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com3tag:blogger.com,1999:blog-2367872608855443806.post-77196793361320167742015-04-11T12:38:00.001-03:002015-04-11T12:39:37.320-03:00EsPCEx 2015 Questão de Função Quadrática<br />
Questão do EsPCEx 2015 que também envolve modelagem matemática, pois uma equação deve ser montada e um ponto de máximo deve ser determinado.<br />
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Segue o enunciado e a resolução em video:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirt-loB0FQE1xWoCB1_Fn-A9HEhgt6NjmbmjHndWabVBxKuwY14eFPgHHiUxBpkA7vs4AVTrUdeahUDCU8_VBs7t1eBXbfVSwKKCWIdWJl2wAPorBL8YIg7VL5195bxxPoWm2il8MNpKK4/s1600/EspCEx+2015+-+04.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirt-loB0FQE1xWoCB1_Fn-A9HEhgt6NjmbmjHndWabVBxKuwY14eFPgHHiUxBpkA7vs4AVTrUdeahUDCU8_VBs7t1eBXbfVSwKKCWIdWJl2wAPorBL8YIg7VL5195bxxPoWm2il8MNpKK4/s1600/EspCEx+2015+-+04.jpg" height="316" width="640" /></a></div>
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<iframe allowfullscreen="" frameborder="0" height="270" src="https://www.youtube.com/embed/rBtkKBHVCIY" width="480"></iframe>Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-72837364044840831342015-04-10T21:50:00.000-03:002015-04-10T21:50:16.956-03:00EsPCEx 2015 - Questão de Probabilidade Olá, segue mais uma questão da prova do EsPCEx, desta vez uma questão de probabilidade.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Hu1jIyDflBo6Avv_-kn_3BVjI6j7R1v49tOaMcb97x-IKlPfRcd5yiaNPwmiDLQHhoyCwLOskqPLdql-7Y-a6UWiZ7FHOD9434mhM6JZ0nwjX-P40m6ybkERXc_UOLOyW4FOzgygtrua/s1600/EspCEx+2015+-+16.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Hu1jIyDflBo6Avv_-kn_3BVjI6j7R1v49tOaMcb97x-IKlPfRcd5yiaNPwmiDLQHhoyCwLOskqPLdql-7Y-a6UWiZ7FHOD9434mhM6JZ0nwjX-P40m6ybkERXc_UOLOyW4FOzgygtrua/s1600/EspCEx+2015+-+16.jpg" height="320" width="640" /></a></div>
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Solução no video:<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/9c2ruJhOSBg?feature=player_detailpage" width="640"></iframe><br />
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Abraços<br />
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Cesar<br />
<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-44906878831200713882015-03-20T19:18:00.001-03:002015-03-20T19:18:57.445-03:00 EsPCEx 2015 - Questão de TrigonometriaOlá, segue enunciado e resolução de uma questão de trigonometria do vestibular EsPCEx 2014/2015.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgABxOND8maW53F9gaOD3cnnwMBAueibNxq_B6LORyKMFQHFfyqsrUPPc7fcuGRR54CxMx4PJVzMvWeqQ3LWg8QzrzUONe2XnZauj1ZPZ5m302Y6dk9BLfS4W8JkcVsijk8z86ILpT2CY0J/s1600/questao+4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgABxOND8maW53F9gaOD3cnnwMBAueibNxq_B6LORyKMFQHFfyqsrUPPc7fcuGRR54CxMx4PJVzMvWeqQ3LWg8QzrzUONe2XnZauj1ZPZ5m302Y6dk9BLfS4W8JkcVsijk8z86ILpT2CY0J/s1600/questao+4.jpg" height="290" width="640" /></a></div>
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/gxAFG0JOaM8?feature=player_detailpage" width="640"></iframe><br />
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Abraços<br />
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Cesar<br />
<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com2tag:blogger.com,1999:blog-2367872608855443806.post-418845748433407982015-03-18T20:33:00.000-03:002015-03-18T20:33:21.371-03:00FUVEST 2015 - Trigonometria e Complexos - Questão 4 item cOlá, agora o item c) do problema abaixo. Os itens a) e b) foram feitos em outros videos.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhKJcW-nbcCfqFjrWPnEsO_oJqKDmj4aQWClQNaaNcVLJxil_pB-mfGyW2XhgQ1HmQoZtZA1VG5Pc5kdBpTK-1LNdcP86Nd-w8k4pvczlW_Y5Pq4Vn3MdW4nuRnKx4pg4u1EQUjuy1TRvo/s1600/4b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhKJcW-nbcCfqFjrWPnEsO_oJqKDmj4aQWClQNaaNcVLJxil_pB-mfGyW2XhgQ1HmQoZtZA1VG5Pc5kdBpTK-1LNdcP86Nd-w8k4pvczlW_Y5Pq4Vn3MdW4nuRnKx4pg4u1EQUjuy1TRvo/s1600/4b.jpg" height="204" width="640" /></a></div>
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A a resolução em video:<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/9pGrqh_wcHA?feature=player_detailpage" width="640"></iframe><br />
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Abraços<br />
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CesarCesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-8763104782972123022015-03-12T16:00:00.001-03:002015-03-12T16:01:00.090-03:00FUVEST 2015 - Trigonometria e Complexos - Questão 4 item bOlá,<br />
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Agora segue o enunciado a resolução em video do item b, que depende o item a.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBDbYd2hGY77cDPGNdvBNFcDO8XNSSVUbP5AF59p6rto2qGb2174Zjz9aTT3mUgC2NAOhWpIYgyr0eoftcHpUGuAjqkVRdI_j1DoGvAwL8Z6ydOXPSSQ_X3w4H4cSrXN56HOlL85rqpyNL/s1600/4b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBDbYd2hGY77cDPGNdvBNFcDO8XNSSVUbP5AF59p6rto2qGb2174Zjz9aTT3mUgC2NAOhWpIYgyr0eoftcHpUGuAjqkVRdI_j1DoGvAwL8Z6ydOXPSSQ_X3w4H4cSrXN56HOlL85rqpyNL/s1600/4b.jpg" height="207" width="640" /></a></div>
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Segue a solução em video.<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/LvHhqf6esg4?feature=player_detailpage" width="640"></iframe><br />
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Abraços<br />
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Cesar<br />
<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-72849010340950960832015-03-12T15:56:00.001-03:002015-03-12T15:56:21.887-03:00FUVEST 2015 - Trigonometria e ComplexosOlá,<br />
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Segue o enunciado da questão 4 da FUVEST 2015, 2ª fase. A questão tem 3 itens, estou resolvendo-a em tres videos diferentes porque considero-a longa e um pouco complicada para o pessoal de ensino médio.<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSCNFFOn6yQDIftckKg5B3LRTQo_XUzljD8Mg629qEqZjxTxTmhkRSy2FUqmzG4UNx-wmxI1bm8IbnjhaULYU1CZXZ8k5xm5Sq17-ceylON160ElCywoXlJUTavPGwMVZm6y3cgz6huaa5/s1600/4b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSCNFFOn6yQDIftckKg5B3LRTQo_XUzljD8Mg629qEqZjxTxTmhkRSy2FUqmzG4UNx-wmxI1bm8IbnjhaULYU1CZXZ8k5xm5Sq17-ceylON160ElCywoXlJUTavPGwMVZm6y3cgz6huaa5/s1600/4b.jpg" height="207" width="640" /></a></div>
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Segue em video a solução do item a, com sugestão para quem quiser tentar resolver.<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/c3-jMswEMv4?feature=player_detailpage" width="640"></iframe><br />
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Abraços<br />
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Cesar<br />
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<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-74065042588546630092014-11-27T22:43:00.001-02:002014-11-27T22:43:21.213-02:00ITA 1973 - Problema de Função Exponencial Olá,<br />
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Segue agora um problema do vestibular do ITA de 1973, sobre função exponencial. É muito interessante esta função pois ela modela diversos fenômenos naturais e este aqui é um exemplo. O problema não é de fato difícil; o segredo é saber interpretar o texto e possuir habilidade de manipulação de expressões que envolvem expoentes.<br />
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Segue o enunciado e a resolução.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHzhIjmm5osCVQXsmoT06m1Ej7oi8_6KiySYE8XI563OCdzm1T9nO0CcECKs-2AEmu38DqKabdS_DTV3nYlzIWg2YT0J1AhmFIt8b2fEuSvkBfXMfCID9C9YMMcfHJtDzJDRtF63Dkrr1g/s1600/ITA+1973.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHzhIjmm5osCVQXsmoT06m1Ej7oi8_6KiySYE8XI563OCdzm1T9nO0CcECKs-2AEmu38DqKabdS_DTV3nYlzIWg2YT0J1AhmFIt8b2fEuSvkBfXMfCID9C9YMMcfHJtDzJDRtF63Dkrr1g/s1600/ITA+1973.jpg" height="260" width="640" /> </a></div>
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Abraços</div>
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Cesar </div>
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<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com1tag:blogger.com,1999:blog-2367872608855443806.post-79807946811751142922014-10-30T17:48:00.000-02:002014-10-30T17:51:32.269-02:00ITA 1992 - Problema de Geometria AnalíticaSegue a resolução de um problema de Geometria Analítica do exame do ITA de 1992. Apesar da dificuldade tradicional do exame, essa questão não é tão difícil, eu acredito que possa ser feita por bons alunos do Ensino Médio.<br />
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O enunciado é:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4QH7DFJXGCLWBMia5O7PKyZLZ8Ym6I_YyPu1Nvnkh7ASFVtYEvkwTum7SrTMNbM4CWjDH7LN9Y16FCqlk_Dq-LvB9HCmOmynuj9TKz_3x1qUARg5cJANYi_Z3frpXnsWH5RlC6TeCl01B/s1600/Clipboard01.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4QH7DFJXGCLWBMia5O7PKyZLZ8Ym6I_YyPu1Nvnkh7ASFVtYEvkwTum7SrTMNbM4CWjDH7LN9Y16FCqlk_Dq-LvB9HCmOmynuj9TKz_3x1qUARg5cJANYi_Z3frpXnsWH5RlC6TeCl01B/s1600/Clipboard01.jpg" height="238" width="640" /></a></div>
<span id="goog_1131043384"></span><span id="goog_1131043385"></span><br />
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<div style="text-align: justify;">
<span id="goog_1131043384">E a resolução segue no video abaixo:</span></div>
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<span id="goog_1131043384"><iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/ihYHl6YLzFQ?feature=player_detailpage" width="640"></iframe></span><br />
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<span id="goog_1131043384">Abraços</span><br />
<span id="goog_1131043384">Cesar </span><span id="goog_1131043385"></span>Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-72781664045112006042014-09-19T20:20:00.001-03:002014-09-19T20:20:03.424-03:00PROFMAT - Aritmética (MA 14) Exercício 3.1.19 d (Divisibilidade)Olá,<br />
Segue uma resolução de um problema de Aritmética do Profmat. Está no livro "Elementos de Aritmética" de A. Hefez, o livro-texto da disciplina MA14-Aritmética.<br />
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O enunciado é:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgikt8LtqswAB-3Cs33CRBFThGxC_hd4kyElbt3TNGJ-3cs3VaEGUOXxz_Ri8-WzAA1pVMfVwDeDZGeKbGACCaAGEO6Iw3eIQshSAsqyhIRl2d2mzlc1st8U_PgL9hU_vhbluUGUREELDRJ/s1600/quest%C3%A3o.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgikt8LtqswAB-3Cs33CRBFThGxC_hd4kyElbt3TNGJ-3cs3VaEGUOXxz_Ri8-WzAA1pVMfVwDeDZGeKbGACCaAGEO6Iw3eIQshSAsqyhIRl2d2mzlc1st8U_PgL9hU_vhbluUGUREELDRJ/s1600/quest%C3%A3o.jpg" height="127" width="320" /></a></div>
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Bom, segue agora a resolução:<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/UKCN93mzPiM?feature=player_detailpage" width="640"></iframe><br />
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Um abraço,<br />
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Cesar<br />
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Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-76845553822739332532014-07-30T18:42:00.003-03:002014-07-30T18:42:42.975-03:00Probabilidades - FUVEST 2005 - 2ª Fase Segue uma questão sobre cálculo de probabilidade, da Fuvest 2005, 2ª fase. Entendo ser uma questão simples, mas deve-se ter cuidado com a interpretação. O maior problema é o cálculo combinatório.<br />
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Enunciado:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUVCfdFTsYlPkn_642s6sWXPBfvMFhFOQyKt36FUzbdlInmTjJO-plgGWNDXBk7XDC3xiePFhUnbhM1WcRXmkX58vY6qqJX38hrEczbekisVh_S8DgDmV8tjLrdByEs6zoqNXc25TIs7hL/s1600/q10.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUVCfdFTsYlPkn_642s6sWXPBfvMFhFOQyKt36FUzbdlInmTjJO-plgGWNDXBk7XDC3xiePFhUnbhM1WcRXmkX58vY6qqJX38hrEczbekisVh_S8DgDmV8tjLrdByEs6zoqNXc25TIs7hL/s1600/q10.jpg" height="85" width="640" /></a></div>
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Solução:<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/FmpxRkPz5Do?feature=player_detailpage" width="640"></iframe><br />
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Abraços<br />
CesarCesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-29528449128899704192014-07-10T19:31:00.002-03:002014-07-10T19:31:53.602-03:00Questão de Funções Quadráticas - UNICAMP 2014Segue nesse post uma questão sobre funções quadráticas do vestibular Unicamp 2014. Questão simples, mas deve ajudar o pessoal que estuda para vestibulares. Segue o enunciado e o video em seguida.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidnyp7WetfWJCGnitEjSOl5ARl6SAt5BQHdZcx2-CvbhPAu0pXcpsEs93cIocDWogmSbYy99vEly6ggKsOuYD4P4qx63rCW3pTkY7AyHJfTNaimNzgtwkI1LHCXlzLjLlAarsrdA0GSsji/s1600/questao.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidnyp7WetfWJCGnitEjSOl5ARl6SAt5BQHdZcx2-CvbhPAu0pXcpsEs93cIocDWogmSbYy99vEly6ggKsOuYD4P4qx63rCW3pTkY7AyHJfTNaimNzgtwkI1LHCXlzLjLlAarsrdA0GSsji/s1600/questao.jpg" height="210" width="640" /></a></div>
<span id="goog_1622095165"></span><span id="goog_1622095166"></span><br />
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<span id="goog_1622095165"><iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/j78UAVlKtIg?feature=player_detailpage" width="640"></iframe></span><br />
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<span id="goog_1622095165">Cesar </span><span id="goog_1622095166"></span>Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-39088807458635781292014-04-04T20:16:00.002-03:002014-04-04T20:16:46.596-03:00Questão de Geometria UNICAMP 2014Segue uma questão de Geometria Plana do vestibular da Unicamp 2014. O item a era trivial, mas o item b pede que o candidato prove a veracidade de uma proposição - algo bem interessante de se fazer.<br />
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Eis a questão:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP8n6wskKAV_f-0YyMsGVsP5XHJTrlGLlNz-QGjZ1vFlFAsGIsjJ1S-MM7JM3q5sMdzmRX5K_-g6BzkghyM6USbxK02VH_Wr7CXJqbniLCpj1yc-LUnNK2rrkLAd_abWSrP66tpEufag9Y/s1600/Unicamp+2014+17.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP8n6wskKAV_f-0YyMsGVsP5XHJTrlGLlNz-QGjZ1vFlFAsGIsjJ1S-MM7JM3q5sMdzmRX5K_-g6BzkghyM6USbxK02VH_Wr7CXJqbniLCpj1yc-LUnNK2rrkLAd_abWSrP66tpEufag9Y/s1600/Unicamp+2014+17.jpg" height="387" width="640" /></a></div>
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E aqui a resolução em video:<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/wzlE6SeN_GI?feature=player_detailpage" width="640"></iframe><br />
<br />
Abraços<br />
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Cesar<br />
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<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-27166358669231895852014-03-23T23:04:00.001-03:002014-03-23T23:04:09.483-03:00Questão de Probabilidade - UNICAMP 2014Olá,<br />
Segue uma questão de probabilidade bem simples, mas que encerra uma pequena sutileza: como precificar o valor de uma aposta em loteria? Tirei do vestibular da UNICAMP 2014.<br />
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Eis o enunciado:<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNgrJXBUQNz5ULxzYP1gO84wCtCN22HFgvYRr45TsLqULMuSLKEq9T8fC7rKyc2F0MNJm6smqP-FeMFABe6_DsLEI7uBjYbZg1MnwaPEUeyV1whl8oJPSvIGO4tsjxzgX0JFOS4LB9Maq3/s1600/Quest%C3%A3o+16+UNICAMP+2014.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNgrJXBUQNz5ULxzYP1gO84wCtCN22HFgvYRr45TsLqULMuSLKEq9T8fC7rKyc2F0MNJm6smqP-FeMFABe6_DsLEI7uBjYbZg1MnwaPEUeyV1whl8oJPSvIGO4tsjxzgX0JFOS4LB9Maq3/s1600/Quest%C3%A3o+16+UNICAMP+2014.jpg" height="174" width="640" /></a></div>
E a resolução em video:<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/ywv06HSMytA?feature=player_detailpage" width="640"></iframe><br />
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Abraços<br />
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Cesar<br />
<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0tag:blogger.com,1999:blog-2367872608855443806.post-68969786716408634182014-03-10T22:19:00.001-03:002014-03-10T22:22:19.215-03:00Matemática UNICAMP 2014 2ª Fase - Questão 14Segue a resolução desta questão com os devidos comentários.<br />
Uma questão sem grandes dificuldades, basta conhecer o conceito de média aritmética.<br />
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Enunciado:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmcAbNwrgqtbOHRfnVsSs2DPyg4MZwP3U1K4nSABiC3-h-Wgh198JBCzvGGTMZ25qNZRW80vzZ61oyqIOoFCgSPQg2hjNTXASd-Oa2JzOvK926T72qkDqGgLj4KOubDEJFv_I7S2kfDWt3/s1600/figura.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmcAbNwrgqtbOHRfnVsSs2DPyg4MZwP3U1K4nSABiC3-h-Wgh198JBCzvGGTMZ25qNZRW80vzZ61oyqIOoFCgSPQg2hjNTXASd-Oa2JzOvK926T72qkDqGgLj4KOubDEJFv_I7S2kfDWt3/s1600/figura.jpg" height="196" width="640" /></a></div>
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Video:<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/i3u3NoHOzAg?feature=player_detailpage" width="640"></iframe><br />
<br />
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Cesar<br />
<br />Cesar Rosahttp://www.blogger.com/profile/09835787427535506287noreply@blogger.com0