tag:blogger.com,1999:blog-30429148778850539042024-03-26T00:20:42.090-03:00Bendita MatemáticaInformações matemáticas que considero interessante e compartilho com vocêsProfessor Carlos Binohttp://www.blogger.com/profile/11262624446611323646noreply@blogger.comBlogger79125tag:blogger.com,1999:blog-3042914877885053904.post-24073181534442354032023-04-21T17:35:00.002-03:002023-04-21T17:42:33.435-03:00Demonstração do Teorema Fundamental do Cálculo<h2 style="text-align: justify;">Introdução</h2><div style="text-align: justify;">O Teorema Fundamental do Cálculo (TFC) é uma descoberta importante na história da matemática que une o cálculo diferencial e o cálculo integral, antes considerados ramos independentes. O cálculo diferencial surgiu do problema da tangente, enquanto o cálculo integral surgiu do problema da área, aparentemente não relacionados. O mentor de Newton, Isaac Barrow, percebeu que a derivação e a integração são processos inversos e que esses dois problemas estão estreitamente relacionados. O Teorema Fundamental do Cálculo estabelece a relação precisa entre a derivada e a integral, o que permitiu que Newton e Leibniz desenvolvessem o cálculo como um método sistemático, tornando possível calcular áreas e integrais com mais facilidade e precisão.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Graças ao TFC, o cálculo diferencial e o cálculo integral foram unificados em um único conceito. Newton e Leibniz foram capazes de explorar essa relação e desenvolver o cálculo como um método matemático sistemático. Eles descobriram que o TFC permitia calcular áreas e integrais de maneira mais fácil e precisa, sem a necessidade de calcular limites de somas. Com isso, o cálculo se tornou uma ferramenta essencial para a resolução de problemas matemáticos em uma variedade de áreas, incluindo física, engenharia e economia. A descoberta do Teorema Fundamental do Cálculo é uma das principais realizações da história da matemática e continua a ter um papel fundamental na pesquisa e no ensino da matemática até hoje.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Normalmente, os livros apresentam o TFC em duas partes. A primeira parte do TFC (TFC 1) apresenta a derivada da uma função $g$ definida como $$g(x)=\int_a^x f(t)\; dt$$ onde $f$ é uma função contínua no intervalo de $[a, b]$ e $a\leq x\leq b$. A partir do TFC 1, é possível obter facilmente a segunda parte (TFC 2), que apresenta um método muito mais simples para o cálculo de integrais.</div><div style="text-align: justify;"><br /></div>Apresentaremos a seguir a demonstração do Teorema Fundamental do Cálculo (TFC). No entanto, assumimos que você já possui conhecimento sobre limites, derivadas, a definição de integral e suas propriedades.<h2 style="text-align: justify;">Teorema Fundamental do Cálculo</h2><div style="text-align: justify;"><b>TFC 1</b> - Se $f$ for contínua em $[a, b]$, então a função $g$ definida por </div><div style="text-align: justify;">$$\begin{array}{ccc} \displaystyle g(x)=\int_a^x f(t)\; dt && a\leq x\leq b \end{array}$$</div><div style="text-align: justify;">é contínua em $[a, b]$, é derivável em $(a, b)$ e $g'(x)=f(x)$.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">DEMONSTRAÇÃO</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Da definição de derivada, podemos obter a expressão</div><div style="text-align: justify;">$$g'(x)=\lim_{h\rightarrow 0}\frac{g(x+h)-g(x)}{h}$$</div><div style="text-align: justify;">Para simplificar, vamos considerar que $h>0$. Assim, vamos encontrar a expressão que representa $\frac{g(x+h)-g(x)}{h}$ a partir da definição de $g(x)$ </div><div style="text-align: justify;">$$g(x)=\int_a^x f(t)\; dt\Rightarrow g(x+h)=\int_a^{x+h} f(t)\; dt$$</div><div style="text-align: justify;">Assim, temos que</div>$$\begin{array}{rlr}g(x+h)-g(x) & = \int_a^{x+h} f(t)\; dt-\int_a^x f(t)\; dt & \\<br />& = \int_a^x f(t)\; dt + \int_x^{x+h} f(t)\; dt-\int_a^x f(t)\; dt & \text{; Fizemos:}\int_a^{x+h} f(t)\; dt=\int_a^{x} f(t)\; dt+\int_x^{x+h} f(t)\; dt \\<br />& = \left(\int_a^x f(t)\; dt -\int_a^x f(t)\; dt\right) + \int_x^{x+h} f(t)\; dt & \\<br />\end{array}$$<div>Desta forma,</div><div>$$\label{eq}\begin{equation}g(x+h)-g(x)=\int_x^{x+h} f(t)\; dt\end{equation}$$</div><div><br /></div><div>Dividindo os membros da Equação $\eqref{eq}$ por $h$, temos</div>$$\label{eq1}\begin{equation}\frac{g(x+h)-g(x)}{h}=\frac{1}{h}\int_x^{x+h} f(t)\; dt\end{equation}$$<div><br /></div><div>Pelo Teorema do Valor Extremo, existem $u$ e $v$ pertencentes ao intervalo $[x, x+h]$ tais que $f(u)=m$ e $f(v)=M$, onde $m$ e $M$ são os valores mínimo e máximo absolutos da de $f$ no intervalor $[x, x+h]$. Assim, pelas propriedades das integrais, temos:</div><div><br /></div><div>$$m\cdot (x+h-x)\leq\int_x^{x+h} f(t)\; dt\leq M\cdot (x+h-x)$$</div><div>$$f(u)\cdot h\leq\int_x^{x+h} f(t)\; dt\leq f(v)\cdot h$$</div><div><br /></div><div>Dividindo essa desigualdade por $h$ (lembrando que consideramos $h>0$)</div><div>$$f(u)\leq\frac{1}{h}\int_x^{x+h} f(t)\; dt\leq f(v)$$</div><div><br /></div><div>Usando a Equação $\eqref{eq1}$ para substituir a parte do meio da desigualdade, temos</div><div><br /></div><div>$$\label{eq2}\begin{equation}f(u)\leq\frac{g(x+h)-g(x)}{h}\leq f(v)\end{equation}$$</div><div><br /></div><div>Se tomarmos $h\rightarrow 0$, então $u\rightarrow x$ e $v\rightarrow x$, uma vez que $\{u, v\}\subset [x, x+h]$. Assim</div><div>$$\begin{array}{cccc}\lim_{h\rightarrow 0}f(u)=\lim\limits_{u\rightarrow x}f(u)=f(x) && \lim_{h\rightarrow 0}f(v)=\lim\limits_{v\rightarrow x}f(u)=f(x)\end{array}$$</div><div>pois $f$ é contínua em $x$. Da Desigualdade $\eqref{eq2}$ e do Teorema do Confronto que:</div><div>$$\label{eq3}\begin{equation}g'(x)=\lim\limits_{h\rightarrow 0}\frac{g(x+h)-g(x)}{h}=f(x)\end{equation}$$</div><div><br /></div><div>Se $x=a$ ou $x=b$, então a Equação $\eqref{eq3}$ pode ser interpretada como limites laterais e assim, é possível mostrar que a função $g(x)$ é contínua em $[a, b]$ (tente fazer esta demonstração e coloca nos comentários). Assim, podemos reescreva o TFC 1 como</div><div>$$\label{eq4}\begin{equation}\frac{d}{dx}\int_a^x f(t)\; dt=f(x)\end{equation}$$ quando $f$ for contínua.</div><div style="text-align: right;">$\blacksquare$</div><div><br /></div><div><b>TFC 2</b> - Se $f$ for contínua em $[a, b]$, então</div><div>$$\int_a^b f(x)\; dx=F(b)-F(a)$$</div><div>onde $F$ é qualquer primitiva de $f$, isto é, uma função tal que $F'=f$</div><div><br /></div><div>DEMONSTRAÇÃO</div><div>Sendo $g(x)=\int_a^x f(t)\; dt$ onde $g'(x)=f(x)$, então a função $g$ é uma primitiva de $f$. Assim, o que diferenciaria a $g$ de qualquer outra primitiva $F$ é uma constante $C$ tal forma</div><div>$$F(x)=g(x)+C\Leftrightarrow F'(x)=g'(x)=f(x)$$</div><div><br /></div><div>Se tomarmos $x=a$ e $h=b-a\Rightarrow x+h=a+(b-a)=b$ na Equação $\eqref{eq}$ temos</div><div>$$\int_a^b f(t)dt=g(b)-g(a)$$</div><div><br /></div><div>Se considerarmos qualquer primitiva $F$ de $f$, temos</div><div>$$F(b)-F(a)=[g(b)+C]-[g(a)+C]=g(b)-g(a)=\int_a^b f(t)dt$$</div><div><br /></div><div>Assim, concluímos que</div><div>$$\int_a^b f(x)\; dx=F(b)-F(a)$$</div><div style="text-align: right;">$\blacksquare$</div><div style="text-align: right;"><br /></div><h2 style="text-align: left;">Considerações</h2><div>O TFC pode ser enunciado da seguinte forma</div><div><br /></div><div><b>TFC</b> - Suponha que $f$ seja contínua em $[a, b]$</div><div><ol style="text-align: left;"><li>Se $g(x)=\int_a^x f(t)\; dt$, então $g'(x)=f(x);</li><li>$\int_a^b f(x)\; dx=F(b)-F(a)$, onde $F$ é qualquer primitiva de $f$, ou seja, é qualquer função tal que $F'=f$.</li></ol><div>Como reescrevemos o TFC 1 como $$\frac{d}{dx}\int_a^x f(t)\; dt$$ e como $F'=f$, podemos reescrever o TFC 2 como $$\int_a^b F'(x)\; dx=F(b)-F(a)$$</div></div><div><br /></div><h2 style="text-align: left;">Bibliografia</h2><div>Stewart, James. Cálculo: volume 1. São Paulo: Cengage Learning, 2010.</div><div><br /></div><h3 style="text-align: left;">Nota</h3><div>Parte do texto teve revisão gramatical utilizando a ferramenta ChatGPT, uma ferramenta de inteligência artificial desenvolvida pela OpenAI</div><div><br /></div>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-19175736568014542442022-04-21T20:10:00.001-03:002022-04-21T20:10:53.021-03:00Simulação do lançamento de moeda<p><img align="right" alt="" data-original-height="2065" data-original-width="2675" height="246" src="https://blogger.googleusercontent.com/img/a/AVvXsEgeO3zo-HvkIM2n0gc6k_Y-LjHubnPlWdQ9opPNDO1vbZMWNdMd8ogcnOFP2hkOIecLqn8SGYeOQ8PxcZqF64JVQJpbbVAyBiYCWmAwKQRtQaJINyD4Vn27_oda2sfQzxsmnmlsR1LQ7AwHYsSM-lrvzqglQMTSRgubovKEOfKONsGnaQ4SLFoX5dRRLQ=w320-h246" width="320" /></p><div style="text-align: justify;">Apresento uma simulação de um problema clássico que é a probabilidade de ocorrer um certo número de caras num experimento onde lançamos uma moeda $n$ vezes. </div><p></p><p style="text-align: justify;">O único lançamento de uma moeda é um Ensaio de Bernoulli - pois só há dois resultados possíveis, chamados de sucesso e fracasso, onde a probabilidade de sucesso é $p$ - e esperamos que o resultado seja cara (sucesso).</p><span><a name='more'></a></span><p style="text-align: justify;">Como o experimento consiste em $n$ lançamentos da moeda, com probabilidade de dá cara, em um único lançamento, é $p$ e devemos verificar a quantidade de caras, então estamos diante de um experimento com distribuição binomial. Assim, a probabilidade de dá $k$ caras em $n$ lançamentos é calculado como</p><p style="text-align: justify;">$$P(k)=\binom{n}{k}\cdot p^k \cdot (1-p)^{n-k}$$</p><p style="text-align: left;">Onde $\displaystyle\binom{n}{k}=C_{n, k}=\frac{n!}{k!\cdot (n-k)!}$</p><p style="text-align: justify;">Por exemplo, considerando uma moeda com probabilidade $p=0{,}3$ de dá cara, se você deseja saber a probabilidade de, em 5 lançamentos, obter 3 caras, então</p><p style="text-align: left;">$$P(3)=\binom{5}{3}\cdot 0{,}3^3\cdot (1-0{,}3)^{5-3}=10\cdot 0{,}027\cdot 0{,}49=0{,}1323=13{,}23\%$$</p><p style="text-align: left;">Mas o que significa os $13{,}23\%$ de probabilidade desse experimento? Quer dizer que se o experimento for repetido num grande número de vezes, é esperado que $13{,}23\%$ das vezes haja 3 caras.</p><p style="text-align: left;">Se o experimento for repetido 1000 vezes, por exemplo, esperamos que em $$1000\cdot 0{,}1323\approx 132$$ vezes dê 3 caras.</p><p style="text-align: left;">A seguir, apresento o a simulação do experimento que fiz no GeoGebra. Se tiver interesse em baixar o arquivo, acesse <a href="https://www.geogebra.org/m/khmk4hgv">https://www.geogebra.org/m/khmk4hgv</a></p><script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"
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</script><p style="text-align: left;"><br /></p><p><iframe height="558px" scrolling="no" src="https://www.geogebra.org/material/iframe/id/xhuxgbyd/width/1280/height/558/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/true/ctl/false" style="border: 0px;" title="Simulação do lançamento de uma moeda" width="1280px"> </iframe></p>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-33280002565020296462022-04-08T00:00:00.001-03:002022-04-08T00:28:41.032-03:00Utilizando razão para escolher produtos<img border="1" data-original-height="1648" data-original-width="2102" height="157" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoFk2kTT3Y5y-KflpCKmO13DgdSnq63FonyhtgWD38xHqoO5cQqNPveuvryNuFO-SKok1VNfvY6UiFVfdZ0bunrouqZAfTN3m4isXHyjCSH0-9mXD6t-gCWQfNMzT0pBB-DsS2xWBafW7Wazj6EfjowYMtXBKlC4AuY7ay293hs_cQ7ePc6zooOrStCA/w200-h157/Imagem1.jpg" style="float: left;" width="200" /><p>No supermercado, costumo aplicar razão para comparar produtos que têm quantidade distintas para decidir qual levar. Como considero a aplicação algo simples, acho que por isso nunca me passou pela cabeça em fazer uma postagem abordando o assunto.</p><p>Vou apresentar uma situação que servirá de exemplo de como é simples utilizar a matemática para tomar boas decisões no seu cotidiano. A situação será uma comparação de um mesmo produto que é vendido em embalagens com quantidades diferentes. </p><span><a name='more'></a></span><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script><p>No mercado, o achocolatado de uma mesma marca é vendido em embalagem de 1,2 kg e embalagem de 2 kg com preço R\$ 16,80 e R\$ 25,00, respectivamente.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsXP4837_OkcXpXXitTUuhHLkyJ7hLox7M-3PqH5lyywE6kavIECpXxqCQI0dKQ_jpQN2S3tqEWr45WQQqP89SedBRwUDuF84xJHlp7mYDHm1LOQs_ODaUvb88qTbY2Hn0RWzQr-wuXxavgq9Mtc1OB7EeBouFVfC5P5E1uEzldS5FOPeJMVYVIwdzUA/s2389/Imagem1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2186" data-original-width="2389" height="293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsXP4837_OkcXpXXitTUuhHLkyJ7hLox7M-3PqH5lyywE6kavIECpXxqCQI0dKQ_jpQN2S3tqEWr45WQQqP89SedBRwUDuF84xJHlp7mYDHm1LOQs_ODaUvb88qTbY2Hn0RWzQr-wuXxavgq9Mtc1OB7EeBouFVfC5P5E1uEzldS5FOPeJMVYVIwdzUA/w320-h293/Imagem1.jpg" width="320" /></a></div><p><img border="1" data-original-height="2507" data-original-width="2503" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEYJ0Rw_Zj01Fqhu89w4JZfgMWsA4IszTMh6pR5mPoVeLKu-PuMEoC0A9LohJb_7hbo-Yu4ojidyBzScivRB6B6XBCEOIrQTw8A_pXs2zo3w2Qj_-AWiAUv3ChWt6g2RpLNQbybEZ0ajaUy7PqxDKGvfMGLjOZKdYn6k_uQ6xS5dalpxGzb4_--ql9UQ/w318-h320/Imagem1.jpg" style="float: right;" width="318" />Digamos que estamos na dúvida se levamos 2 pacotes de 1,2 kg ou 1 pacote de 2 kg. Neste caso, precisamos definir algum critério para esta escolha. </p><p>Caso compremos 2 pacotes de 1,2 kg significa que estaríamos dispostos a pagar mais R\$ 8,60 para levar 400 g a mais, em relação ao pacote de 2 kg. Será que vale a pena?</p><p>Ambos os pacotes têm o mesmo produto, o que muda é a quantidade. Desta maneira, um critério que podemos adotar é escolher o pacote que ofereça o menor valor por quilograma.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjbb9QR7IdV_sLe2WmVDyvWKeNHIOk4mOPnNvZ_52Hp1PjcZq0hb95WvwG2QR-1xBXUJIt6kKyYhZAHs9QpNfM4F0tqgLj1_hnmlV_LilaaevwUljz4GqKUixmLRXFbdJn2D9nnvy3PerszikJ3ACXhmZGTiVLN_vS-od2v7syAbyflL5K9HZtIWCnSw/s3291/Imagem1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2587" data-original-width="3291" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjbb9QR7IdV_sLe2WmVDyvWKeNHIOk4mOPnNvZ_52Hp1PjcZq0hb95WvwG2QR-1xBXUJIt6kKyYhZAHs9QpNfM4F0tqgLj1_hnmlV_LilaaevwUljz4GqKUixmLRXFbdJn2D9nnvy3PerszikJ3ACXhmZGTiVLN_vS-od2v7syAbyflL5K9HZtIWCnSw/w400-h315/Imagem1.jpg" width="400" /></a></div><p style="text-align: left;">Pelo critério que adotado, a embalagem de 2 kg apresenta mais vantagem do que a embalagem de 1,2 kg por ter o menor valor por quilograma.</p><p style="text-align: left;">Assim, a aplicação de razão nos ajudou a decidir se valeria apena pagar um valor maior para levar uma quantidade maior do achocolatado.</p><p style="text-align: left;">Você utilizaria outro critério? Comenta aí.</p><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-20147475683425795712022-03-26T16:46:00.003-03:002022-03-26T17:02:30.750-03:00Ilusão de ótica autocinética<p>Já ouviu falar em ilusão de ótica autocinética? Muito provavelmente você já viu uma imagem que a figura estava fixa mas parecia se movimentar. Este fenômeno é chamado de <b>ilusão de ótica autocinética</b>. O vídeo abaixo foi tirado de uma postagem do Facebook de <a href="https://www.facebook.com/gianni.sarcone" target="_blank">Gianni Sarcone</a></p><script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"
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</script><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='390' height='324' src='https://www.blogger.com/video.g?token=AD6v5dxMyE9yknZdDNfdsPE0MEWmo3jG-kHJdOIxMwm_3OeUhFU9hc77SYuwpt0eeYNguUy7OLjNBR9y1FpuvQ0urQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: x-small;">Fonte: <a href="https://www.facebook.com/gianni.sarcone/posts/10209454620520327">https://www.facebook.com/gianni.sarcone/posts/10209454620520327</a></span></div><p style="clear: both; text-align: justify;">No vídeo, as caixas parecem se mover.</p><br /><p><br /></p>
Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-28906729070097016262022-03-07T17:11:00.002-03:002022-03-07T17:11:43.843-03:00Operações com números complexos - Exercícios resolvidos - 2022.1<p>
Resolveremos questões que abordam o conteúdo de operações elementares com
números complexos na forma algébrica (ou forma retangular). Se tiver interesse
em estudar sobre o assunto, recomendo o vídeo a seguir
</p>
<div class="separator" style="clear: both; text-align: center;">
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allowfullscreen=""
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></iframe>
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<br /><span><a name='more'></a></span>
<p><br /></p>
<p><b>1) Sendo $w=2-3i$ e $z=12-5i$, determine $\dfrac{w}{z}$</b></p>
<p style="text-align: center;">
<b
>a) $12+3i$ <span> </span
><span> </span
><span
> b) $\dfrac{3+2i}{5}$ <span> </span
><span> </span><span> c) </span></span
>$\dfrac{3-2i}{13}$ <span> </span
><span> </span
><span> d) </span>$\dfrac{5-2i}{7}$ <span
> </span
><span> </span
><span> e) </span>$\dfrac{1-i}{12}$</b
>
</p>
<p><br /></p>
<p>Assim, temos</p>
<p>$$\dfrac{w}{z}=\dfrac{2-3i}{12-5i}$$</p>
<p>
Vamos multiplicar o numerador e o denominador da fração pelo conjugado do
denominador, ou seja, por $\overline{z}=12+5i$
</p>
<p>
$$\dfrac{w}{z}=\dfrac{2-3i}{12-5i}\cdot\color{Red}{\frac{12+5i}{12+5i}
}=\dfrac{2\cdot 12+2\cdot 5i-3i\cdot 12-3i\cdot
5i}{12^2+5^2}=\dfrac{24+10i-36i-15i^2}{144+25}=$$$$=\dfrac{24-26i-15\cdot
(-1)}{169}=\dfrac{39-26i}{169}=\dfrac{3-2i}{13}$$
</p>
<p style="text-align: center;"><u>Alternativa C</u></p>
<p><br /></p>
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<p><br /></p>
<p><b>2) Sendo $w=2-3i$ determine $w^2$</b></p>
<div style="text-align: center;">
<b
>a) $9+4i$ b)
$-5-12i$ c)
$-2+9i$ d) $4+3i$
e) $4-9i$</b
>
</div>
<p>Temos</p>
<p>
$$w^2=(2-3i)^2=2^2-2\cdot 2\cdot 3i+(3i)^2=4-12i+9i^2=4-12i+9\cdot
(-1)=$$$$=4-12i-9=-5-12i$$
</p>
<p style="text-align: center;"><u>Alternativa B</u></p>
<p><br /></p>
<p>
<b
>3) Sendo $w=2-3i$ e $z=12-5i$, determine
$\dfrac{1}{w}+\dfrac{1}{z}$</b
>
</p>
<p style="text-align: center;">
<b
>a)$\dfrac{38+44i}{169}$<span> </span
><span> </span><span> </span> b)
$\dfrac{14-9i}{7}$ <span> </span><span> </span
><span> c) </span>$\dfrac{2-3i}{13}$<span
> </span
><span> </span
><span> d) </span>$\dfrac{9-14i}{144}$<span
> </span
><span> </span
><span> e) </span>$\dfrac{3+14i}{100}$</b
>
</p>
<p><br /></p>
<p>Temos</p>
<p>
$$\begin{array}{l}\dfrac{1}{w}=\dfrac{1}{2-3i}\color{Red}{\cdot\dfrac{2+3i}{2+3i}}=\dfrac{2+3i}{2^2+3^2}=\dfrac{2+3i}{13}\\
\dfrac{1}{z}=\dfrac{1}{12-5i}\color{Red}{\cdot\dfrac{12+5i}{12+5i}}=\dfrac{12+5i}{12^2+5^2}=\dfrac{12+5i}{169}\end{array}$$
</p>
<p>Assim</p>
<p>
$$\dfrac{1}{w}+\dfrac{1}{z}=\dfrac{2+3i}{13}+\dfrac{12+5i}{169}=\dfrac{13\cdot
(2+3i)+12+5i}{169}=\dfrac{26+39i+12+5i}{169}=\dfrac{38+44i}{169}$$
</p>
<p><br /></p>
<p style="text-align: center;"><u>Alternativa A</u></p>
Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-80492025415406810122022-03-07T15:17:00.000-03:002022-03-07T15:17:16.708-03:00Exercícios resolvidos sobre Modelos de distribuição para variáveis aleatórias discretas - 2022.1<p>Resolveremos alguns exercícios que abordam o conteúdo de modelos distribuição de variáveis aleatórias discretas, especificamente a distribuição binomial e a de Poisson. Caso tenha interesse em estudar sobre o assunto, recomendo que assista o vídeo abaixo.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/Jjbl0wnxtLI" width="320" youtube-src-id="Jjbl0wnxtLI"></iframe></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><b>1) Uma companhia telefônica observa, diariamente, em média, 5 conexões erradas. A probabilidade de observar, hoje, 2 conexões erradas é, aproximadamente:</b><div style="text-align: center;"><b>a) 9% <span> </span><span> </span><span> b) 12% <span> </span><span> </span><span> c) 5% <span> </span><span> </span><span> d) 7% <span> </span><span> </span><span> e) 2%</span></span></span></span></b></div><div><br /></div><div><span><span><span></span></span></span>Observe que cada conexão verificada ou está errada ou não está, sendo assim, cada conexão representa um Ensaio de Bernoulli. Como o número de conexões é indefinida, sendo $X$ o número de conexões erradas e observadas hoje, pode considerar que $X$ tem distribuição Poisson com $\lambda=5$</div><div>$$P(X=2)=\dfrac{e^{-5}\cdot 5^2}{2!}\cong 0,09=9\%$$</div><div style="text-align: center;"><u>Alternativa A</u></div><div style="text-align: center;"><u><br /></u></div><div style="text-align: center;"><u><<script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"
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</script></u></div><div style="text-align: center;"><u><br /></u></div><div><br /></div><div><b>2) Suponha que a probabilidade de pais terem filhos com cabelos castanhos é $\dfrac{1}{3}$. Se uma família tiver 4 crianças a esperança do número de crianças com cabelos castanhos é</b></div><div><p style="text-align: center;"><b>a) $\dfrac{8}{9}$ <span> </span><span> </span><span> b) $\dfrac{5}{4}$ <span> </span><span> </span><span> c) $\dfrac{1}{3}$<span> </span><span> </span><span> d) $\dfrac{4}{3}$<span> </span><span> </span><span> e) $\dfrac{2}{3}$</span></span></span></span></b></p><p><span><span><span><span>Cada criança representa um ensaio de Bernoulli, pois cada uma delas pode ter cabelos castanhos ou não, o que representa apenas dois resultados possíveis. Como estamos contando o número $Y$ de crianças, entre 4, que têm cabelos castanhos, a variável aleatória $Y$ tem distribuição binomial ($Y\sim b(4, 1/3)$). Assim, a esperança de $Y$ é</span></span></span></span></p><p><span><span><span><span>$$E(Y)=4\cdot\dfrac{1}{3}=\dfrac{4}{3}$$</span></span></span></span></p><p style="text-align: center;"><span><span><span><span><u>Alternativa D</u></span></span></span></span></p><p><span><span><span><span><br /></span></span></span></span></p></div>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-9661091425900105132022-02-28T22:35:00.001-03:002022-02-28T22:35:59.936-03:00Conjunto dos números complexos - Lista 1 - 2022.1<p> Resolveremos 3 questões que abordam o conteúdo sobre números complexos. Se tiver o desejo de estudar mais sobre o conteúdo, recomendo que assista os vídeos abaixo</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="205" src="https://www.youtube.com/embed/fDDjX4pDpvw" width="247" youtube-src-id="fDDjX4pDpvw"></iframe> <iframe allowfullscreen="" class="BLOG_video_class" height="205" src="https://www.youtube.com/embed/FYZiC41ZG64" width="246" youtube-src-id="FYZiC41ZG64"></iframe> <iframe allowfullscreen="" class="BLOG_video_class" height="213" src="https://www.youtube.com/embed/FPcITKY1yWY" width="256" youtube-src-id="FPcITKY1yWY"></iframe><br /><br /><br /></div><span><a name='more'></a><b>1) Sendo x um número imaginário, determine as raízes complexas da equação x²-4x+5=0</b></span><div class="separator" style="clear: both; text-align: center;"></div><div><b><span>a) S={i, -i} <span> </span><span> </span><span> </span><span> b) </span></span>S={-4+5i, 5-4i} <span> </span><span> </span><span> </span><span> c) </span>S={-4, 5i} <span> </span><span> </span><span> </span><span> d) </span>S={2+i, 2-i} <span> </span><span> </span><span> </span><span> e) </span>S={1+i, -1+i}</b></div><div><br /></div><div>Vamos utilizar a formula de resolução das equações quadrática para encontrar as raízes da equação $x^2-4x+5=0$</div><div><br /></div><div>Calculando o discriminante $\Delta$:</div><div>$$\begin{array}{ll}\Delta=(-4)^2-4\cdot 1\cdot 5 \\ \Delta=-4\end{array}$$</div><div>Vamos utilizar a fórmula de resolução da equação quadrática</div><div>$$\begin{array}{ll}x=\dfrac{-(-4)\pm\sqrt{-4}}{2\cdot 1} & (\text{Sabemos que }\sqrt{-4}=\sqrt{4\cdot (-1)}=\sqrt{4}\cdot\sqrt{-1}=2i) \\ \\x=\dfrac{4\pm 2i}{2}=2\pm i \\ \\ S=\{2-i, 2+i\}\end{array}$$</div><div><br /></div><div style="text-align: center;"><u>Alternativa D</u></div><div><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script></div><div><br /></div><div><b>2) Marque a alternativa que apresenta a informação correta</b></div><div><b>a) O número 2-9i é real</b></div><div><b>b) O número 3+2i é um imaginário puro</b></div><div><b>c) O número 10i é real</b></div><div><b>d) O número 5 é um imaginário</b></div><div><b>e) O número -2i é um imaginário puro</b></div><div><br /></div><div>F - a) 2-9i é um número imaginário</div><div>F - b) 3+2i é um número imaginário, mas não é imaginário puro</div><div>F - c) 10i é um imaginário puro</div><div>F - d) 5 é um número real</div><div>V - e) -2i é imaginário puro</div><div><br /></div><div style="text-align: center;"><u>Alternativa E</u></div><div><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script></div><div><br /></div><div><b>3) Determine os valores de x e y para que os números (x+y)+3i e 4+(x+2y)i sejam iguais</b></div><div><b>a) x=5 e y=-1 <span> </span><span> </span><span> b) </span>x=3 e y=4 <span> </span><span> </span><span> c) </span>x=7 e y=-3 <span> </span><span> </span><span> d) </span>x=-1 e y=4 <span> </span><span> </span><span> e) </span>x=4 e y=0</b></div><div><br /></div><div>Dois números complexos são iguais se, respectivamente, as partes reais e as partes imaginárias dos números são iguais. No enunciado são apresentados dois números que chamaremos de $z_1$ e $z_2$.</div><div>$$\begin{array}{l}z_1=(x+y)+3i \\ z_2=4+(x+2y)i\end{array}$$</div><div><br /></div><div>Temos</div><div>$$\begin{array}{lcl} Re(z_1)=Re(z_2) & \Leftrightarrow & x+y=4 \\ Im(z_1)=Im(z_2) & \Leftrightarrow & 3=x+2y \end{array}$$</div><div><br /></div><div>Assim, temos o sistema de equações do 1º grau</div><div>$$\left\{\begin{array}{l}x+y=4 \\ x+2y=3 \end{array}\right.$$</div><div>Nas duas equações, podemos determinar $x$ em função de $y$</div><div>$$\left\{\begin{array}{l}x=4-y \\ x=3-2y \end{array}\right.\Rightarrow 4-y=3-2y\Leftrightarrow-y+2y=3-4\Leftrightarrow y=-1$$</div><div><br /></div><div>Vamos encontrar o valor de $x$ substituindo $y$ por $-1$ em $x=4-y$</div><div>$$x=4-(-1)=4+1=5$$</div><div><br /></div><div style="text-align: center;"><u>Alternativa A</u></div>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-10361832629142901912022-02-28T20:10:00.001-03:002022-02-28T20:12:21.942-03:00Sistema de coordenadas e distância entre pontos - Lista 1 - 2022.1<p> Nesta postagem, resolveremos 3 questões relacionadas aos conteúdos sistemas de coordenadas e distância entre pontos. Caso tenha o desejo de estudar sobre o conteúdo, recomendo que assista os vídeos a seguir</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/3YRrpUGdY6o" width="320" youtube-src-id="3YRrpUGdY6o"></iframe></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/sYhNLe-2v9Q" width="320" youtube-src-id="sYhNLe-2v9Q"></iframe></div><br /><span><a name='more'></a></span><div class="separator" style="clear: both; text-align: center;"><br /></div><b>1) O ponto de coordenada (7, 1) é:<br /></b><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/27hKsPI7o9Hm4B0C9gjUkYvyzhyY6asJ1g6bf48g0GGFk-1iU3tYTTenfandd-FmUSxdL5OTa0r1egALk-EykgvsoP9z2K_VNXAFI9tf2o9mt2Ps8fsb8EAseY29K4Y-ZAvv3J3MpszZtAZ8=s796" style="margin-left: 1em; margin-right: 1em;"><b><img border="0" data-original-height="650" data-original-width="796" height="326" src="https://1.bp.blogspot.com/27hKsPI7o9Hm4B0C9gjUkYvyzhyY6asJ1g6bf48g0GGFk-1iU3tYTTenfandd-FmUSxdL5OTa0r1egALk-EykgvsoP9z2K_VNXAFI9tf2o9mt2Ps8fsb8EAseY29K4Y-ZAvv3J3MpszZtAZ8=w400-h326" width="400" /></b></a></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><b>a) A <span> </span><span> </span></b><span><b> b) B <span> </span><span> </span></b><span><b> c) C <span> </span><span> </span></b><span><b> d) D <span> </span><span> </span><span> e) O</span></b></span></span></span><br /><p><br /></p><p>No I Quadrante temos os ponto B(7, 1) e E(4, 6). Sob o eixo das abscissa temos o ponto D(-6, 0). No III Quadrante há o ponto A(-1, -4) e no IV Quadrante, o ponto C(2, -2)</p><p><br /></p><p style="text-align: center;"><u>Alternativa B</u></p><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script><p style="text-align: justify;"><b>2) Dos pontos a seguir, aquele(s) que está(ão) no IV quadrante é(são)</b></p><p style="text-align: justify;"><b>a) F, I, J <span> </span><span> </span></b><span><b> b) A, B, D, E, H <span> </span><span> </span></b><span><b> c) C <span> </span><span> </span><span> d)G</span></b></span></span></p><p style="text-align: justify;"><span><span></span></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/m-v8x-jK3BMHTtGXPHW8mW7PHSKFBhRqkUfLVvZtkld4JdoN5hKDN4deO7IyRJml1RV08ZDtpXzNlJ-dsqDPnSu2fO8xes0KNnzeMkb5aB-fA4xclW-OetfOltXFFoR3lw=s407" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="293" data-original-width="407" height="288" src="https://1.bp.blogspot.com/m-v8x-jK3BMHTtGXPHW8mW7PHSKFBhRqkUfLVvZtkld4JdoN5hKDN4deO7IyRJml1RV08ZDtpXzNlJ-dsqDPnSu2fO8xes0KNnzeMkb5aB-fA4xclW-OetfOltXFFoR3lw=w400-h288" width="400" /></a></div><br /><span>Os pontos pertencentes ao IV Quadrante são aqueles que têm a primeira coordenada positiva e a segunda coordenada negativa que são os pontos F(6, -4), I(3, -3) e J(6, -2).</span><p></p><p style="text-align: justify;"><span><span><span><br /></span></span></span></p><p style="text-align: center;"><span><span><span><u>Alternativa A</u></span></span></span></p><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script><p style="text-align: justify;"><b><span><span><span>3) </span></span></span><span style="text-align: left;">As coordenadas do ponto do eixo das ordenadas equidistante de A(6, 8) e de B(2, 5) é</span></b></p><p style="text-align: justify;"><b><span style="text-align: left;">a) $\left(0,\dfrac{63}{5}\right)$ <span> </span><span> </span><span> b) </span></span><span style="text-align: left;">$\left(0,\dfrac{10}{3}\right)$ <span> </span><span> </span><span> c) </span></span><span style="text-align: left;">$\left(0,\dfrac{71}{6}\right)$ <span> </span><span> </span><span> d) </span></span><span style="text-align: left;">$\left(0,\dfrac{9}{4}\right)$ <span> </span><span> </span><span> e) </span></span><span style="text-align: left;">$\left(0,\dfrac{80}{7}\right)$</span></b></p><p style="text-align: justify;"><span style="text-align: left;"><br /></span></p><p style="text-align: justify;"><span style="text-align: left;">Os pontos pertencentes ao eixo da ordenadas têm a forma $(0, k)$, com $k\in\mathbb{R}$. Sendo $K(0, k)$ um ponto do eixo das ordenadas equidistante dos ponto $A(6, 8)$ e $B(2, 5)$, então, temos</span></p><p style="text-align: justify;"><span style="text-align: left;">$$d(A, K)=d(B, K)$$</span></p><p style="text-align: justify;">Vamos determinar <span style="text-align: left;">$d(A, K)$ e </span><span style="text-align: left;">$d(B, K)$</span></p><p style="text-align: justify;">$$d(A, K)=\sqrt{(0-6)^2+(k-8)^2}=\sqrt{(-6)^2+k^2-2\cdot 8\cdot k+8^2}=\sqrt{k^2-16k+64+36}=\sqrt{k^2-16k+100}$$</p><p style="text-align: justify;">$$ d(B, K)=\sqrt{(0-2)^2+(k-5)^2}=\sqrt{(-2)^2+k^2-2\cdot k\cdot 5+5^2}=\sqrt{k^2-10k+25+4}=\sqrt{k^2-10k+29} $$</p><p style="text-align: justify;">Assim</p><p style="text-align: justify;">$$\sqrt{k^2-16k+100}=\sqrt{k^2-10k+29} $$$$k^2-16k+100=k^2-10k+29$$$$-16k+10k=29-100$$$$-6k=-71$$$$k=\dfrac{71}{6}$$</p><p style="text-align: center;"><u></u></p><div class="separator" style="clear: both; text-align: center;"><u><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiMtlm_ZZ4NpsXsdkLdKN--aBLOwjysfIuFVJdETvLFYjYyRCyAYUlZlSbC2WkzKrrm7WFafPRskrS6_LEOBWv1i-g2LWjbaJDKqlXsAoPRlcoCZomhOXOfamFiIrBDkMqHCVsHTU9o1QuzVssgH2nQzzCgPfrOO7kVe-htEdR7uuMbzCadNN7YIwFlKw" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1314" data-original-width="1080" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEiMtlm_ZZ4NpsXsdkLdKN--aBLOwjysfIuFVJdETvLFYjYyRCyAYUlZlSbC2WkzKrrm7WFafPRskrS6_LEOBWv1i-g2LWjbaJDKqlXsAoPRlcoCZomhOXOfamFiIrBDkMqHCVsHTU9o1QuzVssgH2nQzzCgPfrOO7kVe-htEdR7uuMbzCadNN7YIwFlKw=w328-h400" width="328" /></a></u></div><u><br /><br /></u><p></p><p style="text-align: center;"><u>Alternativa C</u></p>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-53553259108458722142022-02-28T17:02:00.001-03:002022-02-28T17:31:24.332-03:00Variáveis Aleatórias Discretas - Exercício 1<p>Neste postagem, irei apresentar a resolução de 3 questões relacionadas a Variáveis Aleatórias Discretas. Quem tiver interesse em conhecer o conteúdo, assista o vídeo abaixo.</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="331" src="https://www.youtube.com/embed/S0xHUYW5cBY" width="481" youtube-src-id="S0xHUYW5cBY"></iframe></div><br /><span><a name='more'></a></span><p><br /></p><p><b>1) Um casal planeja ter 3 filhos. Sendo M o número de meninas entre os 3 filhos planejados pelo casal, a variância de M é:</b></p><p><b>a) 0,75<span> </span></b><span><b> b) 1,03 <span> </span></b><span><b> c) 1,24 <span> </span></b><span><b> d) 2,37 <span> </span><span> e) 0,41</span></b></span></span></span></p><p><span><span><span><span><br /></span></span></span></span></p><p>Considerando que o casal terá 3 crianças, o espaço amostral $S_1$ é</p><p>$$S_1=\{(AAA), (OAA), (AOA), (AAO), (OOA), (OAO), (AOO), (OOO)\}$$</p><p>Onde $A$ representa uma menina e $O$, menino.</p><p>Sendo $M$ o número de meninas que o casal pode ter, entre as 3 crianças e sendo a probabilidade de nascer uma menina ($P(A)$) igual a probabilidade de nascer um menino ($P(O)$), os valores que $M$ pode assumir são</p><p>$$M=0, 1, 2, 3$$</p><p>As probabilidades de $M$ assumir cada um dos valores estão detalhados na tabela abaixo</p>
<table align="center" border="1">
<thead>
<tr>
<th>i</th>
<th>$M=m_i$</th>
<th>Resultados</th>
<th>$P(M=m_i)$</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td style="text-align: center;">0</td>
<td>$(OOO)$</td>
<td style="text-align: center;">$\dfrac{1}{8}$</td>
</tr>
<tr>
<td>2</td>
<td style="text-align: center;">1</td>
<td>$(AOO), (OAO), (OOA)$</td>
<td style="text-align: center;">$\dfrac{3}{8}$</td>
</tr>
<tr>
<td>3</td>
<td style="text-align: center;">2</td>
<td>$(AAO),(AOA), (OAA)$</td>
<td style="text-align: center;">$\dfrac{3}{8}$</td>
</tr>
<tr>
<td>4</td>
<td style="text-align: center;">3</td>
<td>$(AAA)$</td>
<td style="text-align: center;">$\dfrac{1}{8}$</td>
</tr>
</tbody>
</table>
<p><br /></p><p>Desta forma, a distribuição de probabilidade da variável $M$ é</p>$$<br />\begin{array}{c|c|c|c|c|c}<br />M=m_i & 0 & 1 & 2 & 3 & \text{Total} \\ \hline<br />P(M=m_i) & \dfrac{1}{8} & \dfrac{3}{8} & \dfrac{3}{8} & \dfrac{1}{8} & 1<br />\end{array}<br />$$<p>A variância de $M$ é dada por</p><p>$$Var(M) = E(M^2)-[E(M)]^2$$</p><p>Assim, temos</p><p>$$E(M)=\sum_{i=1}^4 [m_i\cdot P(M=m_i)]=0\cdot\dfrac{1}{8}+1\cdot\dfrac{3}{8}+2\cdot\dfrac{3}{8}+3\cdot\dfrac{1}{8}=\dfrac{12}{8}=1{,}5$$</p><p>$$E(M)=\sum_{i=1}^4 [m_i^2\cdot P(M=m_i)]=0^2\cdot\dfrac{1}{8}+1^2\cdot\dfrac{3}{8}+2^2\cdot\dfrac{3}{8}+3^2\cdot\dfrac{1}{8}=\dfrac{24}{8}=3$$</p><p>Logo</p><p>$$Var(M)=3-1{,}5^2=3-2{,}25=0{,}75$$</p><p style="text-align: center;"><u>Alternativa A</u></p><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script><p style="text-align: center;"><u><br /></u></p><p style="text-align: justify;"><b>2) Uma moeda viciada tem 0,4 de chance de dá cara. Considere o experimento aleatório onde essa moeda é lançada 3 vezes e X é a variável que recebe o número de caras nesse experimento. A esperança de X é:</b></p><p style="text-align: justify;"><b>a) 1,7 <span> </span></b><span><b> b) 3 <span> </span></b><span><b> c) 0,8 <span> </span></b><span><b> d) 1,2 <span> </span><span> e) 2,3</span></b></span></span></span></p><p style="text-align: justify;"><span><span><span><span><br /></span></span></span></span></p><p>Considerando um único lançamento da moeda, então o resultado poderá ser </p>$$<br />\begin{array}{cc} \text{C=cara} & \text{K=coroa} \end{array}<br />$$<p>Desta forma, temos que a probabilidade de um lançamento dá cara é $P(C)=0{,}4$ e probabilidade de um lançamento dá coroa $P(K)=0{,}6$</p><p>O experimento consiste em 3 lançamento dessa moeda e anota o número $X$ de caras. O espaço amostral $S_2$ desse experimento é</p><p>$$S_2=\{(CCC), (KCC), (CKC), (CCK), (KKC), (KCK), (CKK), (KKK)\}$$</p><p>Como cada lançamento é um evento independente, temos</p>$$\begin{array}{l}<br />P(CCC)=0{,}4^3=0{,}064 \\<br />P(KCC)=P(CKC)=P(CCK)=0{,}4^2\cdot 0{,}6=0{,}096 \\<br />P(KKC)=P(KCK)=P(CKK)=0{,}4\cdot 0{,}6^2=0{,}144 \\<br />P(KKK)=0{,}6^3=0{,}216<br />\end{array}$$ <p>Observando o espaço amostral $S_2$ os valores que a variável aleatória $X$ pode assumir são</p><p>$$X=0, 1, 2, 3$$</p><p>Assim, temos</p><p>$$\begin{array}{l}<br />P(X=3)=P(CCC)=0{,}064 \\<br />P(X=2)=P(KCC)+P(CKC)+P(CCK)=3\cdot 0{,}096=0{,}288 \\<br />P(X=1)=P(KKC)+P(KCK)+P(CKK)=3\cdot 0{,}144=0{,}432 \\<br />P(X=0)=P(KKK)=0{,}216<br />\end{array}$$</p><p>Assim, a distribuição de probabilidade de $X$ é</p><p>$$<br />\begin{array}{c|c|c|c|c|c}<br />X=x_i & 0 & 1 & 2 & 3 & \text{Total} \\ \hline<br />P(X=x_i) & 0{,}216 & 0{,}432 & 0{,}288 & 0{,}064 & 1<br />\end{array}<br />$$</p><p>Logo, a esperança de $X$ é</p><p>$$E(X)=\sum_{i=1}^4 [x_i\cdot P(X=x_i)]=0\cdot 0{,}216 + 1\cdot 0{,}432 + 2\cdot 0{,}288 + 3\cdot 0{,}064 = 1{,}2$$</p><p></p><span><div style="text-align: center;"><u>Alternativa D</u></div><div style="text-align: center;"><script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3212046040351734"></script>
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</script></div><div style="text-align: center;"><u><br /></u></div><div style="text-align: center;"><u><br /></u></div><div style="text-align: justify;"><b>3) Numa caixa há 30 peças, das quais 10 são defeituosas. São escolhidas 5 peças ao acaso e sem reposição. Sendo Y o número de peças defeituosas, entre as escolhidas, determine o valor aproximado de P(Y<3)</b></div><div style="text-align: justify;"><b>a) 57,2% <span> </span><span> b) 91,8% <span> </span><span> c) 80,9% <span> </span><span> d) 76,9% <span> </span><span> e) 30%</span></span></span></span></b></div><div style="text-align: justify;"><span><span><span><span><br /></span></span></span></span></div><div style="text-align: justify;">Neste experimento, iremos sortear 5 peças de uma caixa e vamos contar o números $Y$ de peças defeituosas, sabendo que na caixa há 10 peças defeituosas e 20 não defeituosas. Portanto, a probabilidade de sortearmos uma peça defeituosa desta caixa é $$P(D)=\dfrac{10}{30}=\dfrac{1}{3}$$ Então, a probabilidade de sortear uma peça não defeituosa é $$P(\sim D)=1-P(D)=\dfrac{2}{3}$$</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">O espaço amostral $S_3$ deste experimento é grande o que torna inviável descrevê-lo. Assim, utilizaremos técnicas de contagem para obter as informações necessárias para solução do problema. Como serão sorteadas 5 peças, então, os valores que $Y$ podem assumir são</div><div style="text-align: justify;">$$Y=0, 1, 2, 3, 4, 5$$</div><div style="text-align: justify;">Então</div><div style="text-align: justify;">$$P(Y<3)=P(Y=0)+P(Y=1)+P(Y=2)$$</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">O total de maneiras de sortear 5 peças entre as 30 é</div><div style="text-align: justify;">$$n(S_3)=\binom{30}{5}=\dfrac{30!}{5! \cdot (30-5)!}=142\ 506$$</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Para $Y=y_1=0$, deve-se escolher nenhuma peça defeituosa, ou seja, 5 peças defeituosas entre as 20 que estão na caixa. O total de maneiras, $n(Y=0)$, de ocorrer este resultado é </div><div style="text-align: justify;">$$n(Y=0)=\binom{20}{5}=15\ 504$$</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Para $Y=y_2=1$, devemos escolher 1 peça entre as 10 defeituosas e 4 peças entre as 20 não defeituosas. Logo</div><div style="text-align: justify;">$$n(Y=1)=\binom{10}{1}\cdot\binom{20}{4}=10\cdot 4\ 845 = 48\ 450$$</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Seguindo este raciocínio, temos</div><div style="text-align: justify;">$$n(Y=2)=\binom{10}{2}\cdot\binom{20}{3}=45\cdot 1\ 140 = 51\ 300$$</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Assim, </div><div style="text-align: justify;">$$P(Y<3)=P(Y=0)+P(Y=1)+P(Y=2)=\dfrac{n(Y=0)}{n(S_3)}+\dfrac{n(Y=1)}{n(S_3)}+\dfrac{n(Y=2)}{n(S_3)}$$$$P(Y<3)=\dfrac{15\ 504}{142\ 506}+\dfrac{48\ 450}{142\ 506}+\dfrac{51\ 300}{142\ 506}=\dfrac{115\ 254}{142\ 506}\cong 80{,}9\%$$</div><div style="text-align: justify;"><br /></div><div style="text-align: center;"><u>Alternativa C</u></div></span>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-57870934699101468682022-01-27T15:09:00.005-03:002022-01-27T15:09:47.722-03:00Números pitagóricos<p> O Teorema de Pitágoras é uma relação matemática muito conhecida, normalmente estudada nas séries finais do Ensino Fundamental. O enunciado não é complicado de compreender:</p>
<div><span><a name='more'></a></span><span><!--more--></span><table>
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<td><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisZrCe5ygBGB7NSjq4jkFa5g1ooaKJYgc_PTzqbfJ30n-a7h8WJKammnKNrnUtbLfH3PyLGi6aud8-WqaxDAJFfCOiDfGiEqOoZRRpaWskq6g_HESsteBTqpFnf36YehaVNPFe7QEbm1od/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="484" data-original-width="974" height="158" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisZrCe5ygBGB7NSjq4jkFa5g1ooaKJYgc_PTzqbfJ30n-a7h8WJKammnKNrnUtbLfH3PyLGi6aud8-WqaxDAJFfCOiDfGiEqOoZRRpaWskq6g_HESsteBTqpFnf36YehaVNPFe7QEbm1od/w320-h158/image.png" width="320" /></a></div></div><br /></td>
<td><b>TEOREMA DE PITÁGORAS</b>: Considere um triângulo retângulo com catetos medindo $a$ e $b$ e a medida da hipotenusa é $c$. Assim, temos a relação<br />$$a^2+b^2=c^2$$</td>
</tr>
</thead>
</table></div><div>Sendo $a, b$ e $c$ números naturais que satisfazer o Teorema de Pitágoras, então dizemos que $(a, b, c)$ são <b>números pitagóricos</b> ou <b>trinca pitagórica</b> ou <b>terno pitagórico</b>.</div><div><br /></div><div>Um terno pitagórico muito conhecido é $(3, 4, 5)$</div><div>$$3^2+4^2=9+16=25=5^2$$</div><div>Os múltiplos deste terno pitagórico também são ternos pitagóricos, por exemplo $$(6, 8, 10)=2\cdot (3, 4, 5), (15, 20, 25)=5\cdot (3, 4, 5)$$</div><div><br /></div><div>Isso pode ser demonstrado!</div><div><br /></div><div>Seja $(a, b, c)$ um terno pitagórico. Assim, temos $$a^2+b^2=c^2$$</div><div>Sendo $k\in\mathbb{N}$, $(k\cdot a, k\cdot b, k\cdot c)$ também é um terno pitagórico.</div><div>$$(k\cdot a)^2+(k\cdot b)^2=k^2\cdot a^2+k^2\cdot b^2=k^2\cdot (a^2+b^2)=k^2\cdot c^2=(k\cdot c)^2$$ </div><div>Desta maneira, podemos encontrar uma infinidade de ternos pitagóricos que são múltiplos do terno $(3, 4, 5)$, na verdade, existem infinitos ternos pitagóricos que não são múltiplos $(3, 4, 5)$, como $(5, 12, 13)\rightarrow 5^2+12^2=25+144=169=13^2$.</div><div><br /></div><div>Observe que os ternos pitagóricos $(3, 4, 5)$ e $(5, 12, 13)$ são formados por número que são primos entre si, por isso, são identificados como <b>terno pitagórico primitivo</b>. Em seu livro <i>Elementos</i>, Euclides apresentou uma fórmula para identificar os ternos pitagóricos primitivos.</div><div><br /></div><div><b>FÓRMULA DE EUCLIDES</b>: Considere o terno pitagórico $(a, b, c)$ e os números naturais $m$ e $n$, primos entre si, com paridade distinta e $m>n$. Assim, temos</div>$$\begin{array}{l}<br />a=m^2-n^2 \\<br />b=2\cdot m\cdot n \\<br />c=m^2+n^2<br />\end{array}$$<div>Usando as fórmula de Euclides, podemos encontrar qualquer terno pitagórico. A seguir, apresentamos três deles.</div>$$\begin{array}{c|c}<br />\hline<br />(m, n) & (a, b, c) \\ \hline<br />(2, 1) & (3, 4, 5) \\<br />(3, 2) & (5, 12, 13) \\<br />(7, 4) & (33, 56, 65)\\ \hline<br />\end{array}$$<div>Para provarmos que os ternos pitagóricos primitivos são infinitos, vamos utilizar a fórmula de Euclides, tomando $n=1$. Assim, temos</div><div>$$\begin{array}{l}<br />a=m^2-1 \\<br />b=2\cdot m \\<br />c=m^2+1<br />\end{array}$$</div><div>As condições da fórmula de Euclides impõe $m, n$ com paridade distinta, ou seja, um deles deve ser par e o outro ímpar, e $m>n$. Assim, $m$ é par e $m\geq 2$. Vamos considerar um número primo $k$ tal que $m=2k$. Desta forma, temos</div><div>$$\begin{array}{l}<br />a=(2k)^2-1=4k^2-1 \\<br />b=2\cdot (2k)=4k \\<br />c=(2k)^2+1=4k^2+1<br />\end{array}$$</div><div>Veja que $b=4k$ é um número múltiplo de $4$ e de $k$. Os números $a=4k^2-1$ e $c=4k^2+1$ são números ímpares que não são divisíveis por $k$. Desta forma, $(4k^2-1, 4k, 4k^2+1)$ é um terno pitagórico primitivo e como há infinitos números primos, então haverá infinitos ternos pitagóricos primitivos.</div>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com1tag:blogger.com,1999:blog-3042914877885053904.post-40931708775917754382021-10-19T00:09:00.001-03:002021-10-19T00:09:37.239-03:00Meme: Não é um bom tema<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpegztAYN6PlY51bL-Yr7mx6UFJE55xv622c-t9ugJZCFRxXBgIiwEi1VvgMSc2NRQWMNhRDnhuZdhcA1xaiUPSsaBNqO778h9W32COOFAFxX-_A1GmEOMwpSnAf6TDT-1baelONXepbAt/s847/meme.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="847" data-original-width="650" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpegztAYN6PlY51bL-Yr7mx6UFJE55xv622c-t9ugJZCFRxXBgIiwEi1VvgMSc2NRQWMNhRDnhuZdhcA1xaiUPSsaBNqO778h9W32COOFAFxX-_A1GmEOMwpSnAf6TDT-1baelONXepbAt/w493-h640/meme.jpg" width="493" /></a></div><br /><p></p>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-18033872602157348872021-10-18T14:15:00.001-03:002021-10-18T14:19:23.433-03:00Alguns cálculos da Mega-Sena<p style="text-align: left;">Ganhar na Mega-Sena é o sonho de muita gente. Ficar milionário repentinamente não é fácil e esta loteria é a que paga os maiores prêmios, no Brasil. Nesta postagem, não vou dar dicas para ganhar na Mega-Sena - sou um péssimo jogador, pois o máximos que acertei foram 2 números! Mas espero ajudar esclarecendo a forma de encontrar algumas informações sobre a loteria. Vejamos a seguir, as regras da Mega-Sena.<span></span></p><a name='more'></a><p></p><p style="text-align: left;"></p><ul style="text-align: left;"><li>Você faz uma aposta entre 6 e 15 números distintos entre 1 e 60</li><ul><li>Uma aposta de 6 números é chamada de aposta simples</li></ul><li>São sorteados 6 números e ganha prêmios quem acertar 4, 5 ou 6 números</li><ul><li>Cada sorteio é chamado de Concurso</li></ul><li>Os vencedores são classificados em 3 faixas:</li><ul><li>Faixa 3: quem acerta 4 números (quadra)</li><li>Faixa 2: quem acerta 5 números (quina)</li><li>Faixa 1: quem acerta 6 números (sena)</li></ul><li>Cada faixa tem a sua respectiva premiação que é rateada pelo número apostas simples premiadas na própria faixa.</li></ul><div>Atualmente, uma aposta simples custa R\$ 4,50. O valor de uma aposta com $n$ números, onde $7\leq n\leq 15$, é R\$ ($4{,}5\cdot C_{n, 6}$). Veja que $C_{n, 6}$ é o número de combinações de 6 números entre os $n$ escolhidos. Por exemplo, se você vai fazer uma aposta com 9 números, $A_9$:</div><div>$$A_9=C_{9, 6}=\dfrac{9!}{(9-6)!\cdot 6!}=84$$</div><div>é como se estivesse fazendo 84 aposta simples distintas. Por esta razão, o valor da aposta $V_9$ é, em reais</div><div>$$V_9=4{,}5\cdot C_{9,\ 6}=4{,}5\cdot 84=378$$</div><p></p><p style="text-align: left;">No site das <a href="http://loterias.caixa.gov.br/wps/portal/loterias/landing/megasena" target="_blank">Loterias Online da Caixa Econômica há informações dos valores de todas as apostas</a> e a probabilidade de acertar cada uma das faixas de prêmios..</p><div class="content">
<table align="center" border="1px" class="limited table-d" dir="ltr">
<caption style="display: none;">Preços e Probabilidades</caption>
<thead>
<tr>
<th rowspan="2">Quantidade de nº jogados</th>
<th rowspan="2">Valor de aposta</th>
<th colspan="3">Probabilidade de acerto (1 em)</th>
</tr>
<tr>
<th>Sena</th>
<th>Quina</th>
<th>Quadra</th>
</tr>
<tr>
</tr>
</thead>
<tbody>
<tr>
<td>6</td>
<td>4,50</td>
<td>50 063 860</td>
<td>154 518</td>
<td>2 332</td>
</tr>
<tr>
<td>7</td>
<td>31,50</td>
<td>7 151 980</td>
<td>44 981</td>
<td>1 038</td>
</tr>
<tr>
<td>8</td>
<td>126,00</td>
<td>1 787 995</td>
<td>17.192</td>
<td>539</td>
</tr>
<tr>
<td>9</td>
<td>378,00</td>
<td>595 998</td>
<td>7 791</td>
<td>312</td>
</tr>
<tr>
<td>10</td>
<td>945,00</td>
<td>238 399</td>
<td>3 973</td>
<td>195</td>
</tr>
<tr>
<td>11</td>
<td>2 079,00</td>
<td>108 363</td>
<td>2 211</td>
<td>129</td>
</tr>
<tr>
<td>12</td>
<td>4 158,00</td>
<td>54 182</td>
<td>1 317</td>
<td>90</td>
</tr>
<tr>
<td>13</td>
<td>7 722,00</td>
<td>29 175</td>
<td>828</td>
<td>65</td>
</tr>
<tr>
<td>14</td>
<td>13 513,50</td>
<td>16 671</td>
<td>544</td>
<td>48</td>
</tr>
<tr>
<td>15</td>
<td>22 522,50</td>
<td>10 003</td>
<td>370</td>
<td>37</td>
</tr>
</tbody>
</table><p>Para encontrar as probabilidades apresentadas temos que, inicialmente, determinar a probabilidade de acertar a sena com uma aposta simples. O total de maneiras de sortear 6 números entre 60 é</p><p style="text-align: left;">$$C_{60, 6}=50\ 063\ 860$$</p><p style="text-align: left;"></p><p style="text-align: left;">Se você faz uma apostada de simples, $A_6=1$, a probabilidade de acertar a sena, $P_6$, é</p><p style="text-align: left;">$$P_6(A_6) = \dfrac{1}{50\ 063\ 860}$$</p><p style="text-align: left;">O cálculo das probabilidades de outras apostas e faixas é obtida da seguinte forma:</p><p></p><p></p><ul style="text-align: left;"><li>Realiza uma aposta com $n$ números, onde $6\leq n\leq 15$;</li><li>Dos 6 números que são sorteados, é desejado acertar $p$, com $p\in\{4, 5, 6\}$</li></ul><p style="text-align: left;">Então, dos 6 números sorteados, deseja que $p$ deles estejam entre os $n$ números da aposta e os outros $(6-p)$ números estejam entre os $(60-n)$ números que não estão na aposta. Assim, o total de maneiras de fazer uma aposta com $n$ números e acertar $p$, na Mega-Sena, é:</p><p style="text-align: left;">$$C_{n,\ p}\cdot C_{(60-n),\ (6-p)}$$</p><p style="text-align: left;">Por exemplo, deseja-se fazer uma aposta com 10 números e espera-se acertar a quina. Assim, temos $n=10$ e $p=5$. Logo</p><p style="text-align: left;">$$C_{10, 5}\cdot C_{50, 1}=252\cdot 50=12\ 600$$</p><p style="text-align: left;">Portanto, há 12 600 maneiras de acertar a quina com uma aposta de 10 números. Assim a probabilidade de acerta a quina, $P_5$, apostando 10 números, $A_{10}$, é:</p><p style="text-align: left;">$$P_5(A_{10})=\dfrac{C_{10, 5}\cdot C_{50, 1}}{C_{60, 6}}=\dfrac{12\ 600}{50\ 063\ 860}\approx \dfrac{1}{3\ 973}$$</p><p style="text-align: left;">Podemos deduzir que a probabilidade de acerta $p$ números numa aposta de $n$ números é</p><p style="text-align: left;">$$P_p(A_n)=\dfrac{C_{n,\ p}\cdot C_{(60-n),\ (6-p)}}{C_{60, 6}}$$</p><p style="text-align: left;">Outra informação relevante que encontramos na página das Loterias Online é o número de premiações</p></div><p></p><table align="center" border="1px" class="limited table-d" dir="ltr">
<caption style="display: none;">Quantidade de prêmios a receber acertando</caption>
<thead>
<tr>
<th>Apostas</th>
<th colspan="3">6 números</th>
<th colspan="2">5 números</th>
<th>4 números</th>
</tr>
</thead>
<tbody>
<tr>
<td>Quantidade de nº jogados</td>
<td>Sena</td>
<td>Quina</td>
<td>Quadra</td>
<td>Quina</td>
<td>Quadra</td>
<td>Quadra</td>
</tr>
<tr>
<td>6</td>
<td>1</td>
<td>0</td>
<td>0</td>
<td>1</td>
<td>0</td>
<td>1</td>
</tr>
<tr>
<td>7</td>
<td>1</td>
<td>6</td>
<td>0</td>
<td>2</td>
<td>5</td>
<td>3</td>
</tr>
<tr>
<td>8</td>
<td>1</td>
<td>12</td>
<td>15</td>
<td>3</td>
<td>15</td>
<td>6</td>
</tr>
<tr>
<td>9</td>
<td>1</td>
<td>18</td>
<td>45</td>
<td>4</td>
<td>30</td>
<td>10</td>
</tr>
<tr>
<td>10</td>
<td>1</td>
<td>24</td>
<td>90</td>
<td>5</td>
<td>50</td>
<td>15</td>
</tr>
<tr>
<td>11</td>
<td>1</td>
<td>30</td>
<td>150</td>
<td>6</td>
<td>75</td>
<td>21</td>
</tr>
<tr>
<td>12</td>
<td>1</td>
<td>36</td>
<td>225</td>
<td>7</td>
<td>105</td>
<td>28</td>
</tr>
<tr>
<td>13</td>
<td>1</td>
<td>42</td>
<td>315</td>
<td>8</td>
<td>140</td>
<td>36</td>
</tr>
<tr>
<td>14</td>
<td>1</td>
<td>48</td>
<td>420</td>
<td>9</td>
<td>180</td>
<td>45</td>
</tr>
<tr>
<td>15</td>
<td>1</td>
<td>54</td>
<td>540</td>
<td>10</td>
<td>225</td>
<td>55</td>
</tr>
</tbody>
</table><p></p><p style="text-align: left;">Vamos considerar que fizemos uma aposta com 7 números que equivale a $A_7=7$ apostas simples, digamos que os números apostados foram: 01 - 04 - 05 - 30 - 33 - 41- 52. Assim, as 7 combinações possíveis são</p><table align="center">
<thead>
<tr>
<th><span style="font-weight: normal;">Bilhete 1:</span></th>
<th><span style="font-weight: normal;">01</span></th>
<th>04</th>
<th>05</th>
<th>30</th>
<th>33</th>
<th>41</th>
</tr>
</thead>
<tbody>
<tr>
<td>Bilhete 2:</td>
<td>01</td>
<td><b>04</b></td>
<td><b>05</b></td>
<td><b>30</b></td>
<td><b>33</b></td>
<td><b>52</b></td>
</tr>
<tr>
<td>Bilhete 3:</td>
<td>01</td>
<td><b>04</b></td>
<td><b>05</b></td>
<td><b>30</b></td>
<td><b>41</b></td>
<td><b>52</b></td>
</tr>
<tr>
<td>Bilhete 4:</td>
<td>01</td>
<td><b>04</b></td>
<td><b>05</b></td>
<td><b>33</b></td>
<td><b>41</b></td>
<td><b>52</b></td>
</tr>
<tr>
<td>Bilhete 5:</td>
<td>01</td>
<td><b>04</b></td>
<td><b>30</b></td>
<td><b>33</b></td>
<td><b>41</b></td>
<td><b>52</b></td>
</tr>
<tr>
<td>Bilhete 6:</td>
<td>01</td>
<td><b>05</b></td>
<td><b>30</b></td>
<td><b>33</b></td>
<td><b>41</b></td>
<td><b>52</b></td>
</tr>
<tr>
<td>Bilhete 7:</td>
<td><b>04</b></td>
<td><b>05</b></td>
<td><b>30</b></td>
<td><b>33</b></td>
<td><b>41</b></td>
<td><b>52</b></td>
</tr>
</tbody>
</table><p>Vamos supor que os 6 números sorteados foram os mesmos do concurso 1: 04 - 05 - 30 - 33 - 41 - 52. Assim, acertaríamos a sena no Bilhete 7, mas observe que nos demais bilhetes também acertaríamos a quina. Desta forma, com uma aposta de 7 números, acertando a sena, também dá o direito de receber o prêmio de 6 quinas, no mesmo concurso.</p><p>Para generalizar, vamos considerar uma aposta com $n$ números, $6\leq n\leq 15$, onde se acerta $k$ números sorteados, $k\in\{4, 5, 6\}$. Para saber o números de prêmios na sena, quina ou quadra determinamos por</p><table align="center" border="1" style="text-align: center;">
<thead>
<tr>
<th>Sena ($k=6$)</th>
<th>Quina ($k=6,\ 5$)</th>
<th>Quadra ($k=6,\ 5,\ 4$)</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align: center;">1</td>
<td style="text-align: center;">$C_{k, 5}\cdot C_{n-k, 1}$</td>
<td style="text-align: center;">$C_{k, 4}\cdot C_{n-k, 2}$</td>
</tr>
</tbody>
</table><p style="text-align: left;">Se acertar os 6 números, será pago o equivalente a 1 aposta simples, na Faixa 1, independente da quantidade de número da aposta. Por exemplo, se você realiza uma aposta com $n=9$ números e acerta $k=6$. Então o número de prêmios na sena, na quita e na quadra são</p><table align="center" border="1" style="text-align: center;"><thead><tr><th>Sena ($n=9,\ k=6$)</th><th>Quina ($n=9,\ k=6$)</th><th>Quadra ($n=9,\ k=6$)</th></tr></thead><tbody><tr><td>1</td><td>$C_{6, 5}\cdot C_{3, 1}=18$</td><td>$C_{6, 4}\cdot C_{3, 2}=45$</td></tr></tbody></table><p> Assim, no rateio, você receberá 1 prêmio na Faixa 1, 18 prêmios na Faixa 2 e 45 prêmios na Faixa 3.</p><p>Digamos que você fez uma aposta com 10 números, equivalente a $A_{10}=210$ apostas simples e acerta 5 números no sorteio. Assim, temos $n=10$ e $k=5$ </p><table align="center" border="1" style="text-align: center;"><thead><tr><th>Sena ($n=10,\ k=5$)</th><th>Quina ($n=10,\ k=5$)</th><th>Quadra ($n=10,\ k=5$)</th></tr></thead><tbody><tr><td>0</td><td>$C_{5, 5}\cdot C_{5, 1}=5$</td><td>$C_{5, 4}\cdot C_{5, 2}=50$</td></tr></tbody></table><p>Desta forma, você terá direito, no rateio, a 5 premiações na quinta e 50 premiações na quadra.</p><p>Vimos os cálculos das informações apresentadas sobre a Mega-Sena no site das Loterias Online e estes cálculos levam em consideração que todas as combinações possíveis são equiprováveis. Em uma futura postagem, pretendo abordar algumas probabilidades envolvendo dados estatísticos dos concursos.</p><p>Você já acertou a sena, a quina ou a quadra? Coloca nos comentários e diz se você adota alguma estratégia para escolher os números ou se tem alguma história legal pra nos contar envolvendo a Mega-Sena.</p>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-29908854147493550572021-03-05T16:21:00.002-03:002021-10-18T14:15:44.218-03:00Assíntota oblíqua<h4 style="text-align: left;">INTRODUÇÃO</h4><p>Estava preparando uma atividade, com o auxílio do GeoGebra, quando precisei identificar as assíntotas da função</p><p>$$f(x)=\frac{5-x^2}{3+2x}$$</p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPU7a87_SC08k8HcFgBCMfT2Mbo-gYomgAPjzZhCvW6bbkDWpJt0JobEPl8e2WqD4Whf8BSgrdtDdZOg9Wo_RSI4RyrJZGI-rGA9PrChHqI6D5DeN9a-jE9G-wRMYyxwcUnYqwloqmdSJW/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="480" data-original-width="786" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPU7a87_SC08k8HcFgBCMfT2Mbo-gYomgAPjzZhCvW6bbkDWpJt0JobEPl8e2WqD4Whf8BSgrdtDdZOg9Wo_RSI4RyrJZGI-rGA9PrChHqI6D5DeN9a-jE9G-wRMYyxwcUnYqwloqmdSJW/w320-h195/image.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Figura 1</b>: Função $f(x)=\frac{5-x^2}{3+2x}$ com assíntotas $x=-\frac{3}{2}$ e $y=-\frac{x}{2}+\frac{3}{4}$<span><a name='more'></a></span></td></tr></tbody></table><br />Identificar a assíntota vertical $x=-\frac{3}{2}$ não é uma tarefa difícil. Como a função $f$ não está definida em $x=-\frac{3}{2}$, então, verifica-se que<div><br /></div><div>$$\left\{\begin{array}{l}\underset{x\rightarrow-\frac{3}{2}^-}{\lim} f(x) =-\infty \\ \underset{x\rightarrow-\frac{3}{2}^+}{\lim} f(x) =\infty \end{array}\right.$$</div><div><br /><div>Porém, $f(x)\rightarrow -\infty$ quando $x\rightarrow \infty$ e $f(x)\rightarrow \infty$ quando $x\rightarrow -\infty$. Assim, não há assíntotas horizontais, porém, o GeoGebra indica que há uma assíntota oblíqua $y=-\frac{x}{2}+\frac{3}{4}$. Vamos verificar se há pontos em comum entre a curva $f$ e a reta que o <i>software</i> indica como assíntota oblíqua.</div><div><br /></div><div>$$\frac{5-x^2}{3+2x}=-\frac{x}{2}+\frac{3}{4}\Rightarrow 4\cdot (5-x^2) = (3+2x)\cdot (-2x+3)\Rightarrow 20-4x^2=9-4x^2\Rightarrow 20=9$$</div><div><br /></div><div>Desta forma, verificamos que a solução é vazia, assim, não há pontos em comum entre a reta $y=-\frac{x}{2}+\frac{3}{4}$ e a curva $f$. Logo, na Figura 2, região azul não contém pontos da curva $f$.</div><div><p></p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbUmESlVR1CI8olXQSJzsIUffiEUSSWkrd-aXbsyY04pfZyGC7SzuUNHFl25jBFsFMMKLWIlKv0pVPSgdNtvC4cY0e8jGlyx04kyPH21jmUt0lKrKaW1GJO9R3P7Cm51N9pto-bqky9EwW/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="676" data-original-width="786" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbUmESlVR1CI8olXQSJzsIUffiEUSSWkrd-aXbsyY04pfZyGC7SzuUNHFl25jBFsFMMKLWIlKv0pVPSgdNtvC4cY0e8jGlyx04kyPH21jmUt0lKrKaW1GJO9R3P7Cm51N9pto-bqky9EwW/w320-h275/image.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Figura 2</b>: A curva $f$ não possui pontos na região azul</td></tr></tbody></table><br /><p></p><p>Sabemos que é possível que uma curva tenha pontos em comum com suas assíntotas, por isso, se a curva $f$ e a reta $y$ tivessem pontos em comum não poderíamos negar que a reta é uma das assíntotas da curva. Além disso, o fato de não terem pontos em comum, também não confirma que $y$ é uma assíntota da curva. </p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3EX6oyi8H3ygigeEj0wmsllf6uQlz2o0N3Ym1UDcTe2N4s1M3gU2shT7QSWhb3Lt5ZvIlTLs66Qpaz0EGlEG-s9sGTXRhCfcVKY-wnHqzkr9MVJN0W93O1GNUsB7tWJ2O18MjkthR8VPc/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="676" data-original-width="786" height="275" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3EX6oyi8H3ygigeEj0wmsllf6uQlz2o0N3Ym1UDcTe2N4s1M3gU2shT7QSWhb3Lt5ZvIlTLs66Qpaz0EGlEG-s9sGTXRhCfcVKY-wnHqzkr9MVJN0W93O1GNUsB7tWJ2O18MjkthR8VPc/w320-h275/image.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Figura 3</b>: A reta $\overline{PQ}$ não intercepta a curva $f$</td></tr></tbody></table><br /><p></p><p>Por exemplo, na Figura 3, o ponto $P$ pertence a interseção entre as assíntotas e $Q$ é um ponto da região que a curva $f$ não passa. Assim, a reta $\overline{PQ}$ não intercepta a curva $f$, mas também não é uma das assíntota.</p><p><br /></p><h4 style="text-align: left;">DEFINIÇÃO DE ASSÍNTOTA</h4><div><br /></div><div>Dos livros de Cálculo Diferencial e Integral temos a noção de assíntotas verticais e horizontais que são retas cujas curvas se aproximam quando aproximamos $x$ de um número para o qual a função não está definida (no caso de assíntotas verticais) ou quando $x$ tende ao infinito positivo ou negativo (caso das assíntotas horizontais). Vamos observar o gráfico da função $g(x)=\dfrac{e^{x-1}+1}{e^{x-1}-1}$</div><div><br /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFx4Jzq_WpjRp5emoLPAESynvygnb0FZQt-JzIKaWgAkJsAPUekxLiiFl8wekoDVIQh5i9N36dFjg_W9yw0NpbdPHcJxkTpQ9argZaROfs-DcXKjd9WXKG0QVvugDye4O4OaPJ4DF2MBqR/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="818" data-original-width="1016" height="258" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFx4Jzq_WpjRp5emoLPAESynvygnb0FZQt-JzIKaWgAkJsAPUekxLiiFl8wekoDVIQh5i9N36dFjg_W9yw0NpbdPHcJxkTpQ9argZaROfs-DcXKjd9WXKG0QVvugDye4O4OaPJ4DF2MBqR/w320-h258/image.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b>Figura 4</b>: função $g(x)=\dfrac{e^{x-1}+1}{e^{x-1}-1}$ e suas assíntotas<br /><br /></td></tr></tbody></table></div><div>Veja que quando nos distanciamos da origem pela da função $g$ (seja por $x\rightarrow\infty, x\rightarrow-\infty$ ou $x\rightarrow 1$) , o gráfico se aproxima de uma das assíntotas. Desta forma, ao se afastar da origem, a distância entre a função $g$ e sua assíntota mais próxima tende a zero. </div><div>$$\begin{array}{lll}\text{Distância entre }g(x) \text{ e a assintota }a:y=-1: & |g(x)-(-1)|\rightarrow 0, & \text{quando }x\rightarrow -\infty\\\text{Distância entre }g(x) \text{ e a assintota }b:x=1: & |x-1|\rightarrow 0, & \text{quando }x\rightarrow 1\\ \text{Distância entre }g(x) \text{ e a assintota }c:y=1: & |g(x)-1|\rightarrow 0, & \text{quando }x\rightarrow\infty\end{array}$$. </div><div><br /></div><div>Vamos voltar para função $f(x)=\dfrac{5-x^2}{3+2x}$ que tem assíntota vertical <span style="text-align: center;">$x=-\dfrac{3}{2}$ e o GeoGebra indica como assíntota oblíqua $y=-\frac{x}{2}+\frac{3}{4}$ (ver Figura 1).</span></div><div><span style="text-align: center;"><br /></span></div><div><span style="text-align: center;">Podemos facilmente verificar que a distância entre a função $f$ e a reta </span>$x=-\dfrac{3}{2}$ $$\left|x-\left(-\dfrac{3}{2}\right)\right|\rightarrow 0$$ quando $x\rightarrow -\dfrac{3}{2}$.</div><div><br /></div>Para verificar se a distância entre a função $f(x)$ e a reta $y=-\frac{x}{2}+\frac{3}{4}$ tende a 0, vamos considerar pontos genéricos de cada um com mesma abscissa</div>$$(x, f(x)), (x, y) \Leftrightarrow\left(x, \dfrac{5-x^2}{3+2x}\right), \left(x, -\frac{x}{2}+\frac{3}{4}\right)$$</div><div><br /></div><div>Assim, a distância $d$ entre os pontos genéricos é</div><div>$$d=\sqrt{(x-x)^2 + (f(x)-y)^2}=\sqrt{\left(\dfrac{5-x^2}{3+2x}--\frac{x}{2}+\frac{3}{4}\right)^2}=\left|\frac{11}{8x + 12}\right|\rightarrow 0,\text{ quando } x\rightarrow\pm\infty$$</div><div><br /></div><div>Vamos considerar a definição a seguir de assíntota de uma função.</div><div><br /></div><div><b>DEFINIÇÃO 1</b>: A reta $r$ é chamada de assíntota da função $f$ se a distância $d$ entre $r$ e $f$ tender a 0 quando $x\rightarrow\infty, x\rightarrow-\infty$ ou $x\rightarrow a$, quando $f$ não é contínua $a\in\mathbb{R}$. Chamamos $r$ de</div><div><ul style="text-align: left;"><li>assíntota vertical se $r:x=a$;</li><li>assíntota horizontal se $r:y=b$, para $b\in\mathbb{R}$;</li><li>e assíntota oblíqua se $r:mx+q$, para $m,q\in\mathbb{R}$.</li></ul></div><div>Pela Definição 1, a reta $y=-\dfrac{x}{2}+\dfrac{3}{4}$ é assíntota oblíqua da função $f(x)=\dfrac{5-x^2}{3+2x}$.</div><div><br /></div><div>Agora que apresentamos uma definição para assíntotas, vamos mostrar uma forma de identificar as assíntotas de uma função, se existir.</div><div><br /></div><h4 style="text-align: left;">EXISTÊNCIA DE ASSÍNTOTA OBLÍQUA</h4><div><br /></div><div>Vamos considerar uma função $f(x)$ com assíntota $r$. Nos livros de Cálculo Diferencial e Integral é mostrado as formas de encontrar as assíntotas verticais e horizontais, se existirem, de uma função. A saber:</div><div><ul style="text-align: left;"><li>Se $f$ não está definida no número $a\in\mathbb{R}$ e $\underset{x\rightarrow a}{\lim} f(x)=\pm\infty$ então a reta $x=a$ é assíntota vertical de $f$;</li><li>Se $\underset{x\rightarrow-\infty}{\lim}f(x)=a$ ou $\underset{x\rightarrow\infty}{\lim}f(x)=a$ então $y=a$ é assíntota horizontal de $f$.</li></ul><div>Vamos tomar $r:y=mx+q$, desta forma, vamos considerar pontos genéricos de $f$ e $r$, respectivamente, com mesma abscissa</div></div><div>$$(x, f(x)), (x, y)\Leftrightarrow (x, f(x)), (x, mx+q)$$</div><div>Assim, a distância $d$ entre $f$ e $r$ é</div><div>$$d=\sqrt{(x-x)^2+[f(x)-(mx+q)]^2}=|f(x)-(mx+q)|$$</div><div><br /></div><div>Para $x\rightarrow a$, temos</div><div>$$\lim_{x\rightarrow a} d=\lim_{x\rightarrow a}|f(x)-(mx+q)|=|\lim_{x\rightarrow a}f(x) - (m\cdot a+q)|$$</div><div><br /></div><div>Se $f(x)$ for contínua em $a$, então $\underset{x\rightarrow a}{\lim}f(x)=f(a)=k$, assim</div><div>$$\lim_{x\rightarrow a} d=|k-(m\cdot a+q)|=C\geq 0$$</div><div>$C=0$ caso $f$ e $r$ tenha ponto em comum em $x=a$.</div><div><br /></div><div>Se $f(x)$ não é contínua em $a$ e $\underset{x\rightarrow a}{\lim}f(x)=\pm\infty$, temos</div><div>$$\lim_{x\rightarrow a} d=|\lim_{x\rightarrow a}f(x) - (m\cdot a+q)|=\infty$$</div><div><br /></div><div>Assim, provamos que se $\underset{x\rightarrow a}{\lim}f(x)=\pm\infty$ então $f(x)$ se aproxima de uma reta vertical $x=a$. Desta forma, a assíntota só pode ser oblíqua se </div><div>$$\lim_{x\rightarrow-\infty}d=0\text{ ou }\lim_{x\rightarrow\infty}d=0$$</div><div><br /></div><div>Se $\underset{x\rightarrow\infty}{\lim}f(x)=k$ para $$\underset{x\rightarrow\infty}{\lim}d=0\Rightarrow\underset{x\rightarrow\infty}{\lim}(mx+q)=k\Rightarrow m=0, q=k$$ ou seja, a assíntota é horizontal quando $\underset{x\rightarrow\infty}{\lim}f(x)=k$. De forma análoga, podemos mostrar que a assíntota também é horizontal quando $\underset{x\rightarrow-\infty}{\lim}f(x)=k$.</div><div><br /></div><div>Assim, para existir assíntota oblíqua é necessário que $f(x)\rightarrow-\infty$ ou $f(x)\rightarrow\infty$ e a distância $d$ entre $f$ e $r$ deve tender à 0 quando $x\rightarrow-\infty$ ou $x\rightarrow\infty$.</div><div><br /></div><div><b>TEOREMA 1</b>: Uma reta $r:y=mx+q$, com $m\neq 0$, é assíntota oblíqua da função $f(x)$ se, ao menos, um dos limites a seguir existir</div>$$\begin{array}{ccc}<br />\lim_{x\rightarrow-\infty}|f(x)-(mx+q)|=0 &\text{ou}& \lim_{x\rightarrow\infty}|f(x)-(mx+q)|=0<br />\end{array}$$<div><br /></div><div>Sem perda de generalidade, vamos tomar<br /><div>$$\lim_{x\rightarrow\infty}|f(x)-(mx+q)|=0\Rightarrow \lim_{x\rightarrow\infty}(f(x)-mx)-q=0\Rightarrow q=\lim_{x\rightarrow\infty}(f(x)-mx)$$</div><div><br /></div></div><div>Desta forma, pra saber o valor de $q$ precisamos conhecer o valor de $m$. Assim:</div><div>$$\lim_{x\rightarrow\infty}|f(x)-(mx+q)|=0\Rightarrow\lim_{x\rightarrow\infty}\left[\frac{f(x)}{x}-m-\frac{q}{x}\right]=0\Rightarrow m=\lim_{x\rightarrow\infty}\left[\frac{f(x)}{x}-\frac{q}{x}\right]$$</div><div><br /></div><div>Como $\forall q$ temo $\underset{x\rightarrow\infty}{\lim}\dfrac{q}{x}=0$, então</div><div>$$m=\lim_{x\rightarrow\infty}\frac{f(x)}{x}$$</div><div><br /></div><div>Assim, se $|m|=\infty$, então não há assíntota quando $x\rightarrow\pm\infty$, se $m=0$, então a assíntota é horizontal e se $m\in\mathbb{R}^*$ então a assíntota é oblíqua.</div><div><br /></div><h4 style="text-align: left;">EXEMPLO</h4><div><br /></div><div>1) Vamos determinar a assíntota oblíqua da primeira função: $f(x)=\dfrac{5-x^2}{3+2x}$</div><div>$$m=\lim_{x\rightarrow\infty}\frac{f(x)}{x}=\lim_{x\rightarrow\infty}\frac{\frac{5-x^2}{3+2x}}{x}=\lim_{x\rightarrow\infty}\frac{5-x^2}{3x+2x^2}=-\frac{1}{2}$$</div><div>$$q=\lim_{x\rightarrow\infty}(f(x)-mx)=\lim_{x\rightarrow\infty}\left(\frac{5-x^2}{3+2x}+\frac{1}{2}x\right)=\lim_{x\rightarrow\infty}\frac{2\cdot(5-x^2)+(3x+2x^2)}{2\cdot(3+2x)}=\lim_{x\rightarrow\infty}\frac{10+3x}{6+4x}\Rightarrow q=\frac{3}{4}$$</div><div><br /></div><div>Você verá também que $\lim_{x\rightarrow-\infty}\dfrac{f(x)}{x}=-\dfrac{1}{2}$ e $\lim_{x\rightarrow-\infty}(f(x)-mx)=\dfrac{3}{4}$</div><div><br /></div><div>Desta forma, mostramo que a função $f(x)$ tem assíntota oblíqua $y=-\dfrac{x}{2}+\dfrac{3}{4}$, conforme indicado pelo GeoGebra.</div>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-37928314924613745982020-07-16T16:03:00.023-03:002021-10-18T14:16:07.377-03:00Modelagem Matemática na promoção de calças<div>Se você tem interesse Modelagem Matemática, clique no link <a href="https://www.amazon.com.br/gp/search/ref=as_li_qf_sp_sr_tl?ie=UTF8&tag=carlosbino83-20&keywords=Modelagem Matemática&index=aps&camp=1789&creative=9325&linkCode=ur2&linkId=df262dd26e383ac72d561e11a11d48d2" target="_blank">Modelagem Matemática</a><img alt="" border="0" height="1" src="//ir-br.amazon-adsystem.com/e/ir?t=carlosbino83-20&l=ur2&o=33&camp=1789" style="border: none; margin: 0px;" width="1" /> para vê indicação de livros sobre o assunto na Amazon.</div><div><br /></div><div>Garimpando a internet, atrás de questões interessantes em provas de vestibulares e concursos públicos, uma me chamou a atenção e inspirou esta publicação. Trata-se de uma questão do vestibular 2016.1 do IFG, especificamente, a questão 17. Veja a questão:<span><a name='more'></a></span></div><blockquote><div class="separator" style="clear: both;">Uma loja anuncia descontos de acordo com o cartaz abaixo.</div><div class="separator" style="clear: both; text-align: center;"><img alt="" height="378" src="data:image/png;base64,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" width="270" /></div>Sem o desconto, o preço de venda de uma calça é R\$ 100,00. Seu preço de custo é R\$ 50,00. Sabe-se que, nas vendas à crédito e débito, a loja repassa 5% do valor da venda para a agência de cartões. Assinale a resposta <b>correta</b>.<br /><br />a) O lucro na calça é maior se a venda é à vista.<br />b) Tanto na venda à vista quanto no cartão, o lucro é o mesmo.<br />c) Na venda no cartão, o lucro na calça é R\$ 20,00.<br />d) Na venda no cartão, o lucro na calça é R\$ 22,50.<br />e) Na venda no cartão, o lucro na calça é de R\$ 21,25.</blockquote><h4 style="text-align: left;">Resolvendo a questão</h4><div>A questão apresenta uma promoção de venda de calça, onde oferece um desconto sobre o valor de venda (R\$100) dependendo da forma de pagamento. Se for à vista, o desconto será de 40% e se o cliente pagar no cartão, o desconto será de 25%. Também são apresentados os custos da loja com as calças da promoção. Cada calça foi obtida por um preço de R\$50, e a loja paga uma taxa de 5% no valor de venda em cada pagamento realizado no cartão (crédito ou débito).</div><div><br /></div><div>As alternativas se referem ao lucro (L) da loja sobre cada calça que é a diferença entre o valor de venda (V) e o valor de custo (C). $$L=V-C$$</div><div><br /></div><div>Porém, o valor de venda sofre um desconto dependendo da forma de pagamento, a vista ou no cartão. Vamos representar por $V_v$ se a venda for à vista e $V_c$ se a venda for no cartão.</div><div>$$V_v=100\cdot(1-40\%)=60$$ $$V_c=100\cdot(1-25\%)=75$$</div><div><br /></div><div> O mesmo acontece com o valor de custo. Então, vamos representar com $C_v$ o custo para vendas à vista e $C_c$ como o custo para vendas no cartão.</div><div>$$C_v=50$$ $$C_c=50+75\cdot 5\%=50{,}75$$</div><div><br /></div><div>Desta forma, o lucro também vai depender da forma da forma de pagamento. Vamos tomar $L_v$ como lucro por pagamento à vista e $L_c$ o lucro por pagamento no cartão.</div><div>$$L_v=V_v-C_v=60-50=10$$ $$L_c=V_c-C-c=75-53{,}75=21{,}25$$</div><div><br /></div><div>Assim, verificamos que a alternativa correta é a letra E.</div><div><br /></div><h4 style="text-align: left;">Modelando a promoção com lucro fixo e custo dependente do valor de venda</h4><div>Veja que o custo para compras com pagamento à vista é fixo, mas se o pagamento for com cartão o custo vai depende do valor de venda. Será que é possível determinar o valor de venda se fixarmos um lucro?</div><div><br /></div><div>Por exemplo, se desejarmos obter um lucro de R\$15 em cada calça, vamos manter as mesmas condições para o custo com a forma de pagamento sendo cartão, ou seja, custo de R\$50 para obter cada calça e mais o custo de 5% do valor da venda retido pela agência de cartões. Considerando $V$ como o valor de venda, $C$ o valor de custo e $L$ o lucro, temos que</div><div>$$V=C+L$$</div><div>No nosso exemplo, temos $L=15$ e $C=50+0{,}05\cdot V$, ou seja</div><div>$$V=50+0{,}05\cdot V+15\Rightarrow V-0{,}05\cdot V=0{,}95\cdot V=65\Rightarrow V=\frac{65}{0{,}95}\Rightarrow V=68{,}43$$</div><div>Assim $L=V-C\Rightarrow L=68{,}43-50-68{,}43\cdot 0{,}05=18{,}43-3{,}43=15$</div><div><br /></div><div>Com a intenção de generalizar esta situação, vamos considerar que o dono da loja queira obter um lucro fixo $L$ e cada calça (ou qualquer outro produto) tenha um custo fixo de obtenção $c$ e mais um custo variável que é uma taxa $i$ do valor de venda $V$, apresentando um custo total $C=c+i\cdot V$. Essa taxa pode ser a soma de todas as taxas que incidem sobre o $V$, por exemplo, comissão dos vendedores, impostos, taxa de administração do cartão, etc. Com estas informações, podemos determinar uma fórmula para o cálculo do valor de venda $V$</div><div>$$V=L+C\Rightarrow V=L+c+i\cdot V\Rightarrow V-i\cdot V=L+C\Rightarrow$$ $$V=\frac{L+C}{1-i}$$</div><h4 style="text-align: left;">Modelando o valor de venda com custo fixo e lucro dependente do valor de venda</h4><div>Vamos considerar o seguinte contexto, o dono da loja tem um custo fixo $C$, porém, o lucro será uma taxa $t$ do valor de venda $V$. Assim, temos que o lucro $L=t\cdot V$.</div><div>$$V=L+C\Rightarrow V=t\cdot V+C\Rightarrow V-t\cdot V=C\Rightarrow V=\frac{C}{1-t}$$</div><div>Por exemplo, considerando o custo fixo $C=50$ de um produto e desejo de lucro de $t=20\%$ sob o valor de venda $V$, então, o produto deverá ser vendido por</div><div>$$V=\frac{50}{1-0{,}2} =62{,}5$$</div><h4 style="text-align: left;">Custo e lucro dependentes do valor de venda</h4><div>Agora, vamos considerar que o produto tenha um custo fixo $c$ e outro variável que é uma taxa $i$ sob o valor de venda $V$ totalizando $C=c+i\cdot V$. Também vamos considerar que o lucro será uma taxa $t$ sob o valor de venda $V$, ou seja $L=t\cdot V$. Assim, temos</div><div>$$V=L+C\Rightarrow V=t\cdot V+ c+i\cdot V\Rightarrow V-(t+i)\cdot V=c \Rightarrow V=\frac{c}{1-(i+t)}$$</div><div><br /></div><div>Vamos supor que o dono da loja obtenha uma calça por R\$50. Sob o valor de venda, ele tenha que pagar um imposto com taxa de 17% além da comissão de 5% ao vendedor. Ele ainda deseja um lucro de 10% no valor de venda. Vamos determinar o valor de venda da calça que satisfaça as condições?</div><div><br /></div><div>Como custos, temos um valor fixo $c$=50 e duas taxas sob o valor de venda $V$, 17% de imposto e 5% de comissão para o vendedor, assim, temos que $i=17\%+5\%=22\%$. O lucro é uma taxa $t=10\%$ do valor de $V$.</div><div><br /></div><div>Agora, temos condições de determinar o valor de venda $V$ da calça.</div><div>$$V=\frac{c}{1-(i+t)}\Rightarrow V=\frac{50}{1-(0{,}22+0{,}1)}=\frac{50}{1-0{,}32}=\frac{50}{0{,}68}=73{,}53$$</div><h4 style="text-align: left;">Considerações finais</h4><div>Não falamos sobre os descontos que a loja poderia oferecer aos clientes, pois se trata de estratégia de <i>marketing</i> e isso extrapola os objetivos desta publicação. E Deixo como desafio as fórmulas para encontrar o valor de venda caso o lucro fosse calculado sob o valor de custo.</div><div><br /></div><div>Coloca nos comentários o que você achou da postagem e as respostas para o desafio.</div><div><br /></div><div>Até a próxima! </div><div><div>
<table class="tg" style="border-collapse: collapse; border-spacing: 0px;"><thead><tr></tr></thead></table></div></div>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-60873170536681592252020-06-07T15:47:00.001-03:002021-10-18T14:16:30.158-03:00De onde veio R\$ 1,00?No vídeo a seguir, apresentamos um problema muito popular:<br />
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<span><a name='more'></a></span>Fazendo um resumo do problema, vamos considerar que o homem que conta a história se chama Sr. Enzo, então, temos o seguinte:</div>
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Sr. Enzo tomou emprestado R\$ 25,00 com cada uma das suas duas filhas, totalizando R\$ 50,00 de empréstimo. Fez uma compra no valor de R\$ 45,00 que foi pago com o dinheiro emprestado, restando de troco R\$ 5,00. Sr. Enzo ainda emprestou R\$ 3,00 a um amigo que havia encontrado quando voltava pra casa, restando-lhe assim R\$2,00. Com o objetivo de reduzir a dívida com as filhas, Sr. Enzo devolveu R\$ 1,00 a cada uma delas. Assim, Sr. Enzo pensou: </div>
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- Peguei R\$ 24,00 com cada uma das minhas duas filhas, totalizando R\$ 48,00, com mais R\$ 3,00 do meu amigo, dá R\$ 51,00. De onde veio R\$ 1,00? </div>
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Claramente há um erro na conta realizada pelo Sr. Enzo, o problema é descobrir onde está o erro! Considerando que, inicialmente, ele tomou emprestado, com as filhas, R\$ 50,00, vamos vê como o Sr. Enzo gastou o dinheiro:</div>
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<tr><td style="min-width: 60px; text-align: justify;">Descrição da movimentação</td><td style="min-width: 60px; text-align: justify;"> Saldo</td></tr>
<tr><td>Pegou R\$ 50,00 emprestados</td><td>R\$ 50,00 </td></tr>
<tr><td style="min-width: 60px; text-align: justify;">Realizou uma compra de R$ 45,00</td><td style="min-width: 60px; text-align: justify;">R\$ 5,00</td></tr>
<tr><td style="text-align: justify;">Emprestou R\$ 3,00 a um amigo</td><td style="text-align: justify;">R\$ 2,00</td></tr>
<tr><td style="text-align: justify;">Devolveu R\$ 2,00 às filhas</td><td style="text-align: justify;">R\$ 0,00 </td></tr>
</tbody></table>
<div style="text-align: center;">
<br /></div>
<div style="text-align: justify;">
Veja que ele pegou R\$ 50,00 emprestado e gastou os R\$ 50,00. Se olharmos para o que ele deve às filhas, veja que Sr. Enzo recebeu R\$ 50,00 - R\$ 25,00 de cada uma das duas filhas - e a amortizou R\$ 2,00 - devolveu R\$ 1,00 a cada uma das filhas - passando a ter um saldo devedor de R\$ 48,00 - que foi utilizado para realizar uma compra de de R\$ 45,00 e emprestar R\$ 3,00 a um amigo.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Vimos que o Sr. Enzo recebeu um empréstimo das filhas e utilizou o dinheiro para fazer um compra, emprestar um dinheiro a um amigo e amortizar a dívida com as filhas. Mas aonde está o erro nas contas do Sr. Enzo?</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Pra identificar o erro nas contas do Sr. Enzo, é preciso saber que as movimentações que são feitas por ele têm duas naturezas, entrada e saída de dinheiro. Das movimentações realizadas pelo Sr. Enzo, apenas uma pode ser classificada como entrada de dinheiro e as demais representam saída de dinheiro.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<table border="1" bordercolor="#888" cellspacing="0" style="border-collapse: collapse; border-color: rgb(136, 136, 136); border-width: 1px;"><tbody>
<tr><td style="min-width: 60px;"> Entrada</td><td style="min-width: 60px;">Saída </td></tr>
<tr><td style="min-width: 60px;"> Pegou R\$ 50,00 emprestados</td><td style="min-width: 60px;"> Realizou uma compra de R\$ 45,00</td></tr>
<tr><td></td><td> Emprestou R\$ 3,00 a um amigo</td></tr>
<tr><td></td><td> Devolveu R\$ 2,00 às filhas</td></tr>
</tbody></table>
</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
É importante identificar a natureza das movimentações, pois <u>só podemos somar movimentações de mesma natureza e esse é o erro do Sr. Enzo</u>, pois, se descontarmos do empréstimo os R\$ 2,00 que ele devolveu às filhas, de fato, ele recebeu R\$ 48,00 e os R\$ 3,00 que emprestou ao amigo não representa entrada de dinheiro, por isso, não poderia ser somado aos R\$ 48,00 que tomou emprestado.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Se desejarmos considerar todas as movimentações como sendo de mesma natureza, então, as entradas será um número positivo e a saída, negativo. Assim, teremos</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<table border="1" bordercolor="#888" cellspacing="0" style="border-collapse: collapse; border-color: rgb(136, 136, 136); border-width: 1px; text-align: justify;"><tbody>
<tr><td style="min-width: 60px;">Descrição da movimentação</td><td style="min-width: 60px;">Representação</td></tr>
<tr><td>Pegou R\$ 50,00 emprestados</td><td style="text-align: right;">+50,00 </td></tr>
<tr><td style="min-width: 60px;">Realizou uma compra de R$ 45,00</td><td style="min-width: 60px; text-align: right;">-45,00</td></tr>
<tr><td>Emprestou R\$ 3,00 a um amigo</td><td style="text-align: right;">-3,00</td></tr>
<tr><td>Devolveu R\$ 2,00 às filhas</td><td style="text-align: right;">-2,00 </td></tr>
<tr><td style="text-align: right;"> Total</td><td style="text-align: right;">0,00</td></tr>
</tbody></table>
<br /></div>
<div style="text-align: justify;">
Ou seja, no final de todas as movimentações, o Sr. Enzou ficou sem dinheiro!</div>
</div>
<span><!--more--></span><span><!--more--></span><span><!--more--></span>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-57543949867099990502020-01-24T19:04:00.007-03:002021-10-18T14:16:42.572-03:00Qual é a média?<div style="text-align: justify;">
Normalmente, quando vemos um problema que pede a média, imaginamos que seja a média aritmética. Porém, existem contextos cuja a média pode ser outra, como a geométrica ou harmônica. Para saber qual média utilizar, é fundamental identificar a forma de encontrar o acumulado dos valores observados, assim, se as observações fossem substituídas pela média encontrada, o acumulado continua o mesmo. A seguir, veremos exemplos que o contexto mostra que a a média procurada pode ser a aritmética, geométrica ou harmônica.<span><a name='more'></a></span></div>
<h2>
Média Aritmética</h2>
<div>
<div style="text-align: justify;">
A média aritmética dos números reais $$x_1, x_2, \cdots, x_n$$, com $n\in\mathbb{N}$, é $$M_a=\frac{x_1+x_2+\cdots+x_n}{n}$$</div>
<div style="text-align: justify;">
Veja que a média aritmética é igual ao quociente entre a soma dos valores observados e o número de observações. Desta forma, se substituirmos todos os valores observados por $M_a$, a soma seria </div>
</div>
<div>
<div style="text-align: justify;">
$$n\cdot M_a=x_1+x_2+\cdots+x_n$$</div>
</div>
<div>
<div style="text-align: justify;">
Assim, a média aritmética é mais adequada em contextos onde o acumulado dos valores observados é a soma das observações. Veja o exemplo a seguir.</div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
</div>
<div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cdn.pixabay.com/photo/2014/09/07/22/34/car-race-438467_1280.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: justify;"><img border="0" data-original-height="533" data-original-width="800" height="213" src="https://cdn.pixabay.com/photo/2014/09/07/22/34/car-race-438467_1280.jpg" width="320" /></a></div>
<div style="text-align: justify;">
<b>Exemplo $A$</b>: Um piloto dá $5$ voltas em um circuito com os seguintes tempos: $60$ s, $71$ s, $50$ s, $56$ s e $68$ s. Determine a média de tempo das voltas.</div>
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<br /></div>
<div style="text-align: justify;">
Para obtermos o tempo acumulado nas $5$ voltas é necessário somar os tempos de cada volta, assim, de imediato, imaginamos que a média de tempo das voltas é a média aritmética de $60, 71, 50, 56$ e $68$. Assim $$M_a=\dfrac{60+71+50+56+68}{5}=61$$</div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Para o contexto do Exemplo $A$ o número $61$ é adequado, pois, se o piloto tivesse dado $5$ voltas com os tempos de $61$ s, o tempo total (ou tempo acumulado nas $5$ voltas) seria igual a soma dos tempos observados.</div>
<div style="text-align: justify;">
$$60+71+50+56+68=(61-1)+(61+10)+(61-11)+(61-5)+(61+7)=(61+61+61+61+61)+(-1+10-11-5+7)=5\cdot 61+0=305$$</div>
</div>
<div>
<br /></div>
<div>
<h2>
Média Geométrica</h2>
</div>
<div>
<div style="text-align: justify;">
A média Geométrica dos números reais $x_1, x_2, \cdots, x_n$, com $n\in\mathbb{N}$, é </div>
</div>
<div>
<div style="text-align: justify;">
$$M_g=\sqrt[n]{x_1\cdot x_2\cdot{}_\cdots\cdot x_n}$$</div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Assim, a média geométrica é a raíz $n$-ésima do produto dos $n$ valores observados. Ou seja, se substituirmos os números observados pela média geométrica, veremos que $$\left(M_g\right)^n=x_1\cdot x_2\cdot{}_\cdots\cdot x_n$$ Desta forma, a média geométrica e adequada para quando o acumulado das observações é obtido por meio do produto dos valores observados. Veja o exemplo.</div>
</div>
<div>
<a href="https://cdn.pixabay.com/photo/2013/12/12/07/16/analysis-227172_1280.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: justify;"><img border="0" data-original-height="582" data-original-width="800" height="232" src="https://cdn.pixabay.com/photo/2013/12/12/07/16/analysis-227172_1280.jpg" width="320" /></a><br />
<div style="text-align: justify;">
<b style="font-weight: bold;">Exemplo $B$</b>: Os índices de inflação, no Brasil, nós últimos $5$ anos (2015 a 2019) foram $10{,}67\%, 6{,}29\%, 2{,}95\%, 3{,}75\%$ e $4{,}31\%$. Qual a média da inflação anual dos últimos 5 anos?</div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Falou em média, então é média aritmética! Será?</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Vamos lembrar o que representar a inflação.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Se um produto custava em média, no final de 2014, $R\$ 2{,}00$, no final de 2015, considerando que a inflação daquele ano foi $10{,}67\%$, o mesmo produto custava em média <span style="text-align: center;">$$R\$ 2\cdot 1{,}1067\approx R\$ 2{,}21$$ </span>O número $1{,}1067$ é chamado de fator de atualização que foi obtido pela soma $$1+10{,}67\%=1+0{,}1067=1{,}1067$$ Desta forma, os fatores de atualização das inflações de 2015 a 2019 são $1{,}1067, 1{,}0629, 1{,}0295, 1{,}0375$ e $1{,}0431$.</div>
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<div style="text-align: justify;">
<br /></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
Voltando ao produto que custava, em média, $R\$2{,}00$ no final de 2014, se quisermos saber o preço médio deste produto no final de 2016, calculamos <span style="text-align: center;">$$2\cdot 1{,}1067\cdot 1{,}0629=2\cdot 1{,}17631143= 2{,}35262286\approx 2{,}35$$</span></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
Ou seja, o produto custou, em média, em 2016, $R\$ 2{,}35$. O número $1{,}17631143$ é o fator de atualização da inflação acumulada de 2015 a 2016, ou seja, a inflação acumulada dos dois anos é, aproximadamente, $1{,}17631143-1=0{,}17631143\approx 17{,}63\%$. Veja que $17{,}63\% \neq 10{,}67\%+6{,}29\%=16{,}96\%$.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Nessa lógica, o fator de atualização da inflação acumulada do período de 2015 a 2019 é $$1{,}1067\cdot 1{,}0629\cdot 1{,}0295\cdot 1{,}0375\cdot 1{,}0431=1{,}31057753327263625625\approx 1{,}3106$$</div>
<div style="text-align: justify;">
Assim, a inflação acumulada no período de 2015 a 2019 é $$1{,}3106-1=0{,}3106=31{,}06\%$$ Veja que $$31{,}06\%\neq 10{,}67\%+6{,}29\%+2{,}95\%+3{,}75\%+4{,}31\%=27{,}97\%$$</div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
Se tivermos uma média dos fatores de atualização anual de 2015 a 2019, poderemos determinar a média da inflação anual do período. Porém, a média dos fatores de atualização não pode ser a média aritmética, pois, ja vimos que o acumulado dos fatores de atualização não é obtido através da soma dos fatores de atualização observados, mas pelo produto das observações. Neste contexto, a média que procuramos é a média geométrica dos fatores de atualização.</div>
<div style="text-align: justify;">
$$M_g=\sqrt[5]{1{,}1067\cdot 1{,}0629\cdot 1{,}0295\cdot 1{,}0375\cdot 1{,}0431}\approx 1{,}05558$$</div>
<div style="text-align: justify;">
Com este resultado, podemos determinar, aproximadamente, a média da inflação anual</div>
<div style="text-align: justify;">
$$1{,}05558-1=0{,}05558=5{,}558\%$$</div>
<div style="text-align: justify;">
Assim, se substituirmos as inflações observadas no período de 2015 a 2019 por $5{,}558\%$ a inflação acumulada será, aproximadamente, a mesma da inflação acumulada do quinquênio.</div>
<div style="text-align: justify;">
$$1{,}05558^5-1\approx 31{,}06\%\approx 1{,}1067\cdot 1{,}0629\cdot 1{,}0295\cdot 1{,}0375\cdot 1{,}0431-1$$</div>
<h2>
Média Harmônica</h2>
<div>
<div style="text-align: justify;">
A média harmônica dos números reais $x_1, x_2, \cdots, x_n$, com $n\in\mathbb{N}$, é $$ M_h=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+\cdots +\frac{1}{x_n}}$$</div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
</div>
<div>
<div style="text-align: justify;">
A média harmônica é o inverso da média aritmética dos inversos dos valores observados. Se substituirmos os valores observados pela média harmônica, teremos$$\frac{n}{M_h}=\frac{1}{x_1}+\frac{1}{x_2}+\cdots +\frac{1}{x_n}$$ Assim, verificamos que o acumulado das observações é obtido por meio da soma dos inversos das observações. Utilizamo a média harmônica em situações que envolvem grandezas inversamente proporcionais. Vejamos alguns exemplos.</div>
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<div style="text-align: justify;">
<br /></div>
</div>
<div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://images.pexels.com/photos/2291071/pexels-photo-2291071.jpeg?auto=compress&cs=tinysrgb&dpr=2&h=650&w=940" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: justify;"><img border="0" data-original-height="800" data-original-width="599" height="320" src="https://images.pexels.com/photos/2291071/pexels-photo-2291071.jpeg?auto=compress&cs=tinysrgb&dpr=2&h=650&w=940" width="239" /></a></div>
<div style="text-align: justify;">
<b>Exemplo $C$</b>: Ao voltar pra casa, Pedro dirigiu o primeiro terço do caminho com velocidade de $80 km/h$, o segundo terço, devido a má conservação do trecho, a velocidade foi de $60 km/h$ e o último terço do caminho com velocidade de $120 km/h$. Qual a velocidade média que Pedro percorreu o caminho pra casa?</div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Mais uma vez, poderíamos cair na tentação de calcular a média aritmética. Então, vamos provar que a velocidade média, neste caso, é a média harmônica das velocidades.</div>
<div style="text-align: justify;">
<br /></div>
O problema não informa o comprimento do caminho percorrido, porém, é informado que foi aplicado velocidades constantes em cada terço do caminho. Diremos que o primeiro terço foi percorrido com velocidade $v_1$ no tempo $t_1$, o segundo terço teve velocidade $v_2$ no tempo $t_2$ e o terceiro terço do caminho foi percorrido com velocidade $v_3$ no tempo $t_3$. Digamos que todo o caminho teve comprimento $3d$, assim, cada terço teve distância $d$. Então, temos: $$v_1=\dfrac{d}{t_1}, v_2=\dfrac{d}{t_2}, v_3=\dfrac{d}{t_3}$$ Considere que todo o caminho foi percorrido a uma velocidade média $v$ num tempo $t=t_1+t_2+t_3$. Assim, temos:$$<br />
<br />
v=\frac{3d}{t}\Rightarrow 3d=vt \Rightarrow 3d=v(t_1+t_2+t_3)<br />$$ Observe que $t_1=\dfrac{d}{v_1}$, $t_2=\dfrac{d}{v_2}$ e $t_3=\dfrac{d}{v_3}$. Logo $$<br />
<br />
3d=v\left(\frac{d}{v_1}+\frac{d}{v_2}+\frac{d}{v_3}\right)\Rightarrow v\left(\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}\right)=3 \Rightarrow v=\frac{3}{\dfrac{1}{v_1}+\dfrac{1}{v_2}+\dfrac{1}{v_3}}<br />
<br />
$$ Sendo $v_1=80$, $v_2=60$ e $v_3=120$, a velocidade média que Pedro percorreu todo o caminho foi é a média harmônica das velocidades que ele aplicou em cada terço: $$<br />
<br />
v=\frac{3}{\dfrac{1}{80}+\dfrac{1}{60}+\dfrac{1}{120}}=80 km/h<br />
<br />
$$ Desta forma, se Pedro tivesse percorrido todo o caminho a uma velocidade constante de $80 km/h$, levaria o mesmo tempo para percorrer o trajeto da forma que fez no problema. $$<br />
<br />
t=\frac{d}{80}+\frac{d}{60}+\frac{d}{120}=\frac{3d+4d+2d}{240}=\frac{9d}{240}=\frac{3d}{80}<br />
<br />
$$<a href="https://cdn.pixabay.com/photo/2019/09/07/20/48/faucet-4459689_1280.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="522" data-original-width="800" height="209" src="https://cdn.pixabay.com/photo/2019/09/07/20/48/faucet-4459689_1280.jpg" width="320" /></a><br />
<div style="text-align: justify;">
<b>Exemplo $D$</b>: Numa casa há três torneiras que levam $48$ minutos, $80$ minutos e $120$ minutos, respectivamente, para encher uma caixa d'água. Qual a média de tempo das três torneiras para encher a caixa d'água?</div>
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<br />
<div style="text-align: justify;">
Como o volume da caixa d'água é a mesma para qualquer torneira, então, o acumulado das observações seria encher a caixa d'águas com as três torneiras, desta forma, a vazão de cada uma iria se junta.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Vamos considerar que uma torneira tenha vazão $v_1$ que enche uma caixa d'água em $48$ min, as outras torneiras terá vazão $v_2$ e $v_3$ que enchem a caixa d'água em $80$ min e $120$ min, respectivamente, assim </div>
$$v_1=\dfrac{1}{48}, v_2=\dfrac{1}{80}, v_3=\dfrac{1}{120}<br />$$<span style="text-align: justify;">Considere $v$ a vazão das três torneiras juntas, assim </span><br />
<div style="text-align: justify;">
$$v=v_1+v_2+v_3=\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}=\dfrac{1}{24}$$</div>
<div style="text-align: justify;">
<br /></div>
<div>
<div style="text-align: justify;">
A vazão das três torneiras juntas é $1$ caixa d'água em $24$ min. Se quisermos calcular a vazão média das torneiras ($v_m$), como a vazão total (vazão acumulada) é a soma das vazões das três torneiras, então, devemos calcular a média aritmética</div>
<div style="text-align: justify;">
$$v_m=\dfrac{\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}}{3}=\dfrac{1}{72}$$</div>
</div>
<div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
A vazão média é $1$ caixa d'água em $72$ minutos, quer dizer que o tempo médio para encher a torneira é o inverso da vazão média, que é a média aritmética das vazões, ou seja, o tempo médio das torneiras é a média harmônica dos tempos observados.</div>
<div style="text-align: justify;">
$$M_h=\dfrac{3}{\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}}=72$$</div>
</div>
</div>
</div>
</div>
Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-34808118692075470862019-09-02T22:32:00.000-03:002020-01-28T22:18:56.577-03:00GEOMETRIA HIPERBÓLICA: Determinando o h-centro de uma h-circunferência no Disco de Poincaré<div style="text-align: justify;">
<h2>
Introdução</h2>
Veremos uma forma de determinar o h-centro de uma h-circunferência, no modelo de Disco de Poincaré.</div>
<a href="https://www.blogger.com/null" name="more"></a><br />
<h2>
Construção</h2>
<div style="text-align: justify;">
Na <a href="http://www.benditamatematica.com/2018/01/determinando-o-h-centro-de-uma-h.html#construcao1">Construção 1</a>, o círculo $c$, com centro em $O$ e raio $r>0$, será o plano hiperbólico $\mathbb{H}$, os pontos $A,B\in\mathbb{H}$ são o centro e um ponto, respectivamente, da circunferência $d$, no plano euclidiano, desta forma, $d$ também é uma h-circunferência. Os pontos $A$ e $B$ podem ser movidos. Clique no botão Voltar e Avançar para acompanhar os passos para determinar o h-ponto $O_d$, h-centro de $d$.</div>
<div style="text-align: justify;">
<br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><iframe height="570px" name="construcao1" scrolling="no" src="https://www.geogebra.org/material/iframe/id/XfNZQy5X/width/394/height/570/border/888888/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/true/ctl/false" style="border: 0px;" title="Determinando o centro hiperbólico de uma circunferência hiperbólica" width="394px"> </iframe></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://ggbm.at/n7ZrCGd7" target="_blank">Construção 1</a></td></tr>
</tbody></table>
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Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-13473283196720716412019-08-18T15:23:00.001-03:002020-01-26T22:40:11.596-03:00Relacionando números complexos e matrizes $2\times 2$Apresentamos uma relação entre o conjunto dos números complexos e o conjunto das matrizes quadradas de ordem 2. Com a intenção de sermos objetivos, não faremos uma explanação formal sobre os complexos e as matrizes, apresentaremos apenas alguns conceitos para comprovar a relação entre os conjuntos.<br />
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<h3>
Definição e forma algébrica de um número complexo</h3>
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O conjunto dos números complexos, indicado por $\mathbb{C}$, é formado por números que têm a forma $z=a+bi$, com $a,b\in\mathbb{R}$ e $i=\sqrt{-1}$, assim, $i^2=-1$.<br />
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Todo número complexo $z=a+bi$ tem o seu <i>conjugado</i>, indicado por $\overline{z}$, que é um número complexo na forma $\overline{z}=a-bi$.<br />
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Considerando os números complexos $z_1=a+bi$ e $z_2=c+di$, definimos duas operações em $\mathbb{C}$:<br />
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<ul>
<li><b>SOMA</b>: $z_1+z_2=(a+c)+(b+d)i$</li>
<li><b>MULTIPLICAÇÃO</b>: $z_1\cdot z_2=(a\cdot c-b\cdot d)+(a\cdot d+ b\cdot c)i$</li>
</ul>
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Em caso particular do produto entre um número complexo $z=a+bi$ e seu conjugado $\overline{z}=a-bi$ é $$z\cdot\overline{z}=a^2+b^2$$.</div>
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<h3>
Relação entre $\mathbb{C}$ e $\mathbb{M}_2$</h3>
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Vamos indicar por $\mathbb{M}_2$ o conjunto das matrizes quadradas de ordem 2, ou seja, se $A\in\mathbb{M}_2$, então $A$ tem a forma:</div>
<div>
$$A=\begin{pmatrix} a & b\\ c & d \end{pmatrix}, \text{ com } a,b,c,d\in\mathbb{R}$$<br />
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Considerando as operações com matrizes, é possível provar que a matriz $I_2=\begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix}$ desempenha a mesma função em $\mathbb{M}_2$ que o número $1$ em $\mathbb{C}$. Considerando a $A=\begin{pmatrix} 0 & 1\\ -1 & 0 \end{pmatrix}$, é possível ver que $A^2=-I_2$, desta forma, verifica-se que a matriz $A$ desempenha a mesma função, em $\mathbb{M}_2$, que o número imaginário $i$, em $\mathbb{C}$. Desta forma, dados $a,b\in\mathbb{R}$ temos que a matriz $$Z=a\cdot\begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix}+b\cdot\begin{pmatrix} 0 & 1\\ -1 & 0 \end{pmatrix}=\begin{pmatrix} a & b\\ -b & a \end{pmatrix}$$ pode ser associada ao número complexo $z=a+bi$.<br />
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Assim, podemos estabelecer uma função bijetiva $\Psi:\mathbb{C}\rightarrow\mathbb{M}_2$ tal que $$\Psi(a+bi)=\begin{pmatrix} a & b\\ -b & a \end{pmatrix}$$ com $a,b\in\mathbb{R}$.<br />
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Portanto, considerando os números complexos $z_1=a+bi$ e $z_2=c+di$, podemos definir as operações:<br />
<br />
<ul>
<li><b>ADIÇÃO</b>: $\Psi(z_1+z_2)=\Psi(z_1)+\Psi(z_2)=\begin{pmatrix} a+c & b+d\\ -(b+d) & a+c \end{pmatrix}$</li>
<li><b>MULTIPLICAÇÃO</b>: $\Psi(z_1\cdot z_2)=\Psi(z_1)\cdot\Psi(z_2)=\begin{pmatrix} ac-bd & ad+bc\\ -(ad+bc) & ac-bd \end{pmatrix}$</li>
</ul>
</div>
Temos ainda que $$\Psi(z_1\cdot\overline{z_1})=\begin{pmatrix} a^2+b^2 & 0\\ 0 & a^2+b^2 \end{pmatrix}$$<br />
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<h3>
Conclusão</h3>
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Esta postagem é um recorte de um artigo publicado na Revista Eletrônica da Matemática. Caso queira se aprofundar neste conteúdo, clique na referência abaixo para ter acesso ao artigo completo.</div>
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<h3>
Referência</h3>
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<a href="https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3351" target="_blank">BEMM, Laerte; CAETANO, Douglas Monteiro. Geometria no conjunto das matrizes. <b>Revista Eletrônica da Matemática</b>, Bento Gonçalves, Rs, v. 2, n. 5, p.158-176, jul. 2019. Semestral. Disponível em: <https: article="" index.php="" periodicos.ifrs.edu.br="" view="">. Acesso em: 18 ago. 2019.</https:></a>Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-72826561009775713642019-07-24T23:30:00.001-03:002019-07-24T23:30:38.003-03:00O prazer da estatística<div class="separator" style="clear: both; text-align: center;">
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<br />Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-43912386270710909072018-01-16T00:34:00.000-03:002020-01-28T22:18:22.097-03:00GEOMETRIA HIPERBÓLICA: Um pouco mais sobre h-circunferências no Disco de Poincaré<div style="text-align: justify;">
Na postagem <a href="http://www.benditamatematica.com/2017/10/circunferencia-hiperbolica-no-disco-de.html" target="_blank">Circunferência hiperbólica no Disco de Poincaré</a> é mostrado que uma h-circunferência também é uma circunferência euclidiana, porém o centro euclidiano (centro) e o centro hiperbólico (h-centro) não coincidem, exceto se as h-circunferências e o Disco de Poincaré são concêntricos.</div>
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Nesta postagem, apresentaremos algumas relações entre o plano hiperbólico, h-circunferências e h-eixo de simetria.</div>
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<a href="https://www.blogger.com/null" name="more"></a>Na <a href="http://www.benditamatematica.com/2018/01/um-pouco-mais-sobre-h-circunferencias.html#figura1">Figura 1</a>, as circunferências $c=\mathcal{C}\left(O,r\right)$ e $e=\mathcal{C}\left(O_e,s\right)$, com $r,s\in\mathbb{R}^*_+$, são ortogonais, sendo que $c$ representa o plano hiperbólico $\mathbb{H}$ (Disco de Poincaré) e $e$ é uma circunferência que gera a h-reta $h$.<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVO4k0k1LSZNoZRtZlmJsyiEqUBgEaXkri0b8n8BLmFZ3vvceyGNClnWcKkU-s8EVbNBQM2v4IZAjSCkNEaSjH1JWuwy3aiV9C_r7bTuwl3Jda1BKzOctB_Bp_y39wPc03_rPmoDW_qbcl/s1600/h-circunfer%25C3%25AAncia.png" imageanchor="1" name="figura1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="998" data-original-width="1442" height="442" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVO4k0k1LSZNoZRtZlmJsyiEqUBgEaXkri0b8n8BLmFZ3vvceyGNClnWcKkU-s8EVbNBQM2v4IZAjSCkNEaSjH1JWuwy3aiV9C_r7bTuwl3Jda1BKzOctB_Bp_y39wPc03_rPmoDW_qbcl/s640/h-circunfer%25C3%25AAncia.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Figura 1</b></td></tr>
</tbody></table>
<span style="text-align: justify;">Temos ainda que $d$ é uma h-circunferência com h-centro em $O$, $d'$ é um h-circunferência com h-centro $O'$ e centro $O_{d'}$. As h-circunferências $d$ e $d'$ são simétricas em relação ao h-eixo $h$, portanto, temos que $O$ e $O'$ são simétricos em relação a $h$.</span><br />
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<a href="https://www.blogger.com/null" name="relacao1"></a><b>Relação 1</b> - No plano euclidiano, os pontos $O, O_{d'}$ e $O'$ são colineares</div>
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DEMONSTRAÇÃO<br />
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<div style="text-align: justify;">
No plano $\mathbb{H}$, como $O$ e $O'$ são simétricos em relação à $h$, então, no plano euclidiano, $O$ e $O'$ são inversos em relação à circunferência $e$, então, $O, O'$ e $O_e$ são colineares.</div>
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<div style="text-align: justify;">
Para prova que o ponto $O_{d'}$ pertence à reta $\overline{OO_e}$, vamos considerar as retas $i$ e $j$, tangentes a $d$ em $D$ e $E$, respectivamente, e interceptam-se no ponto $O_e$, ver <a href="http://www.benditamatematica.com/2018/01/um-pouco-mais-sobre-h-circunferencias.html#figura2">Figura 2</a>.</div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtRUw41CDe5G4NoD9fWG09CQ0bvMG0CiWQ8fgIrimdhu6Ca-b6zRDhSeTR752Es0ur92Xn45KaAbabdT6RjVCoKQiStHLuzWPPLjuXWJHH3kSTn-H0gaCV_ZjWm1QujdoaCxRUcxc2auzZ/s1600/h-circunfer%25C3%25AAncia.png" imageanchor="1" name="figura2" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="999" data-original-width="1448" height="440" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtRUw41CDe5G4NoD9fWG09CQ0bvMG0CiWQ8fgIrimdhu6Ca-b6zRDhSeTR752Es0ur92Xn45KaAbabdT6RjVCoKQiStHLuzWPPLjuXWJHH3kSTn-H0gaCV_ZjWm1QujdoaCxRUcxc2auzZ/s640/h-circunfer%25C3%25AAncia.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b>Figura 2</b></td></tr>
</tbody></table>
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<div style="text-align: justify;">
Deste modo, a reta $\overline{OO_e}$ é bissetriz do ângulo $\angle DO_eE$ (ver nos comentários a justificativa desta conclusão). </div>
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<div style="text-align: justify;">
Tomando $e$ como uma circunferência de inversão, conforme o <a href="http://www.benditamatematica.com/2016/09/inversao-de-reta-em-relacao.html#teorema1" target="_blank">Teorema 1 - Inversão de reta em relação à circunferência</a>, como as retas $i$ e $j$ passam pelo centro de inversão, então, suas respectivas inversões são as próprias retas $i$ e $j$. Temos ainda que se $D'$ e $E'$ são os inversos dos pontos $D$ e $E$, respectivamente $$\left(D\in d\cap i,E\in d\cap j\right)\Rightarrow \left(D'\in d'\cap i, E'\in d'\cap j\right)$$</div>
</div>
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<div style="text-align: justify;">
Além disso, como $i$ e $j$ interceptam $d$ em um único ponto, cada um, então, cada reta intercepta $d'$ em um único ponto. Assim, as retas $i$ e $j$ são tangentes a $d'$ em $D'$ e $E'$, respectivamente. Portanto, o centro de $d'$, ponto $O_{d'}$, também pertence à bissetriz do ângulo $\angle DO_eE$, ou seja $$O_{d'}\in\overline{OO_e}$$ Assim, os pontos $O, O_{d'}$ e $O'$ são colineares.</div>
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$\square$</div>
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<div style="text-align: justify;">
<a href="https://www.blogger.com/null" name="relacao2"></a><b>Relação 2</b> - Os pontos $O'$ e $O_e$ são inversos em relação a $c$</div>
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DEMONSTRAÇÃO</div>
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<br /></div>
<div style="text-align: justify;">
Sendo $c$ e $e$ circunferências ortogonais, então, o inversos de $e$ em relação a $c$ é a própria circunferência $e$ (ver <a href="http://www.benditamatematica.com/2016/10/inversao-de-circunferencia-em-relacao.html" target="_blank">Inversão de circunferência em relação a outra circunferência</a>). Como $O$ é o centro de $c$ e $O'$ é o inverso de $O$ em relação a $e$, pelo <a href="http://www.benditamatematica.com/2017/01/centro-do-inverso-de-uma-circunferencia.html#teorema1" target="_blank">Teorema 1-Centro do inverso de uma circunferência que não passa pelo centro de inversão</a>, o inversos de $O'$ em relação a $c$ é $O_e$.</div>
<div style="text-align: right;">
$\square$</div>
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Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com1tag:blogger.com,1999:blog-3042914877885053904.post-75561943637635801452017-10-13T14:25:00.000-03:002020-01-28T22:18:12.679-03:00GEOMETRIA HIPERBÓLICA: Circunferência hiperbólica no Disco de Poincaré<div>
Nesta postagem, mostraremos que uma h-circunferência é igual a uma circunferência no plano euclidiano, porém, o h-centro é distinto do centro e o modo de medir o raio também é diferente. Para melhor compreensão desta postagem, sugerimos a leitura das seguintes postagens: <a href="http://www.benditamatematica.com/2016/10/inversao-de-circunferencia-em-relacao.html" target="_blank">Inversão de circunferência em relação a outra circunferência</a> e <a href="http://www.benditamatematica.com/2017/01/isometria-no-disco-de-poincare-reflexao.html" target="_blank">Isometria no Disco de Poincaré: Reflexão em torno de uma h-reta</a>. Assim, vamos construir uma h-circunferência a partir da <a href="http://www.benditamatematica.com/2017/01/isometria-no-disco-de-poincare-reflexao.html#definicao3" target="_blank">Definição 3 - Isometria no Disco de Poincaré: Reflexão em torno de uma h-reta</a> transcrita a seguir:<br />
<blockquote class="tr_bq">
Dado um h-ponto $C$ e uma h-distância $\rho$, definiremos a circunferência hiperbólica $\lambda$, ou h-circunferência, com h-centro em $C$ e h-raio $\rho$ o conjunto dos h-pontos que estão a uma h-distância $\rho$ do h-ponto $C$<br />
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<div style="text-align: justify;">
Seja $P$ um h-ponto tal que $\rho=d_h(O,P)$ e seja $P_0\in\mathbb{H}$ um ponto genérico tal que $P$ e $P_0$ são equidistantes de $O$, no plano euclidiano, ver <a href="http://www.benditamatematica.com/2017/10/circunferencia-hiperbolica-no-disco-de.html#figura1">Figura 1</a>.</div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpSFNDcmdPEVsA8qcj-DMljyKnXljLJize8pyHWfO2ZtdZ-oP7qlhgmcJvgA9IJW2bFdZQEIJk-qbncU92eDV8udngkbaSsWneE2qxARvfZFq_56T_kPF8ynhBcTJXtxl5Hmsnp0e0EC5d/s1600/h-circunfer%25C3%25AAncia1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" class="post" data-original-height="883" data-original-width="836" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpSFNDcmdPEVsA8qcj-DMljyKnXljLJize8pyHWfO2ZtdZ-oP7qlhgmcJvgA9IJW2bFdZQEIJk-qbncU92eDV8udngkbaSsWneE2qxARvfZFq_56T_kPF8ynhBcTJXtxl5Hmsnp0e0EC5d/s200/h-circunfer%25C3%25AAncia1.png" width="187" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.blogger.com/null" name="figura1"></a>Figura 1</b></td></tr>
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<div style="text-align: justify;">
Sendo $Z_1$ e $Z_3$ pontos ideais da h-reta $\overline{OP_0}$ e $Z_2$ e $Z_4$ pontos ideais da h-reta $\overline{OP}$. Temos:</div>
<div style="text-align: justify;">
$$\begin{matrix} d_h(O,P_0)=\left|\ln\dfrac{\overline{Z_3P_0}\cdot\overline{Z_1O}}{\overline{Z_1P_0}\cdot\overline{Z_3O}}\right|\\ \rho=d_h(O,P)=\left|\ln\dfrac{\overline{Z_4P}\cdot\overline{Z_2O}}{\overline{Z_2P}\cdot\overline{Z_4O}}\right| \end{matrix}$$</div>
<div style="text-align: justify;">
Como, no plano euclidiano, os pontos $P,P_0$ são equidistantes do $O$, então</div>
<div style="text-align: justify;">
$$\begin{matrix} \overline{Z_1P_0}\cong\overline{Z_2P}\\ \overline{Z_3P_0}\cong\overline{Z_4P}\\ \end{matrix}$$</div>
<div style="text-align: justify;">
E ainda temos que $Z_1,Z_2,Z_3,Z_4$ são equidistantes de $O$, desta forma, teremos $d_h(O,P_0)=\rho$<br />
<div style="text-align: right;">
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</div>
<div style="text-align: justify;">
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7XsGBU6G7I7Xqml3OJdXsJHuRZBN5MZat1xyEKnw34lfWkzbjINKEA9C7uHg5LqIaQnhDokjCJzK4phsNJFVUW_V5kfv5DnH6mi9nlqSLXuL8XIdngI4I4WECuqAVc-mEwRzstbubcJRA/s1600/h-circunfer%25C3%25AAncia2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="819" data-original-width="810" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7XsGBU6G7I7Xqml3OJdXsJHuRZBN5MZat1xyEKnw34lfWkzbjINKEA9C7uHg5LqIaQnhDokjCJzK4phsNJFVUW_V5kfv5DnH6mi9nlqSLXuL8XIdngI4I4WECuqAVc-mEwRzstbubcJRA/s200/h-circunfer%25C3%25AAncia2.png" width="197" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.blogger.com/null" name="figura2"></a>Figura 2</b></td></tr>
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No plano euclidiano, sabemos que o lugar geométrico de todos os pontos que estão a uma distância $\overline{OP}$ do ponto $O$ é a circunferência $\lambda$, que tem centro no ponto $O$ e raio $\overline{OP}$. Considerando ainda o plano euclidiano, sendo $P$ e $P_0$ equidistante de $O$, verificamos que $P$ e $P_0$ são também equidistantes de $O$ no plano hiperbólico, assim, vemos que o lugar geométrico do h-ponto $P_0$ é a circunferência $\lambda$. Como todos os h-pontos de $\lambda$ são equidistantes de $O$, pela <a href="http://www.benditamatematica.com/2017/01/isometria-no-disco-de-poincare-reflexao.html#definicao3" style="text-align: start;" target="_blank">Definição 3 - Isometria no Disco de Poincaré: Reflexão em torno de uma h-reta</a>, $\lambda$ é uma h-circunferência com h-centro $O$ e h-raio $\overline{OP}$. Podemos generalizar para toda h-circunferência, com h-centro em $O$ e que passa por um h-ponto $P\neq O$ é uma circunferência euclidiana com centro no ponto $O$ e raio $\overline{OP}$, ver <a href="http://www.benditamatematica.com/2017/10/circunferencia-hiperbolica-no-disco-de.html#figura2">Figura 2</a>.<br />
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Vimos que se o h-centro de uma h-circunferência $\lambda$ for o h-ponto $O$, então, $\lambda$ é uma circunferência euclidiana, vamos mostrar a seguir que qualquer h-circunferência com h-centro diferente de $O$ é uma circunferência euclidiana.<br />
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Considere $r$ como um h-eixo de simetria arbitrário (ver <a href="http://www.benditamatematica.com/2017/01/isometria-no-disco-de-poincare-reflexao.html#definicao2" target="_blank">Definição 2 - Isometria no Disco de Poincaré: Reflexão em torno de uma h-reta</a>). Se $O\in r$, então, $r$ é um diâmetro de $\alpha$ gerado por uma reta $r_0$. Deste modo, a reflexão da circunferência $\lambda$ em torno da h-reta $r$ será, no plano euclidiano, o simétrico da circunferência $\lambda$ em relação à reta $r_0$, que denominaremos por $\lambda'$. Como $r_0$ passa pelo centro de $\lambda$, então, $\lambda$ será simétrica a si mesmo, ou seja, $\lambda'=\lambda$, portanto, no plano hiperbólico, o simétrico da h-circunferência $\lambda$ em torno de um h-eixo $r$ que passa por seu centro $O$ será a própria h-circunferência $\lambda$, ver <a href="http://www.benditamatematica.com/2017/10/circunferencia-hiperbolica-no-disco-de.html#figura3">Figura 3</a>.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAmCxonmSBSZUcLjzvlPg14f56GvVSc4r1-JKF_K7avJjzY1qOhQqcuCA3Qy4Z7aJPMFwoV0DfJFCowpGn-M8MUZtOeX9BCw_FlETC9H6UVKVKtMOyqSAniKPhFOjtYL_XvootUURNP-Bx/s1600/h-circunfer%25C3%25AAncia3.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="819" data-original-width="810" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAmCxonmSBSZUcLjzvlPg14f56GvVSc4r1-JKF_K7avJjzY1qOhQqcuCA3Qy4Z7aJPMFwoV0DfJFCowpGn-M8MUZtOeX9BCw_FlETC9H6UVKVKtMOyqSAniKPhFOjtYL_XvootUURNP-Bx/s200/h-circunfer%25C3%25AAncia3.png" width="197" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.blogger.com/null" name="figura3"></a>Figura 3</b></td></tr>
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Se $O\notin r$, ou seja, $r$ é uma h-reta gerada por uma circunferência $r_a$, então, o simétrico da h-circunferência $\lambda$ em relação à $r$, denominaremos por $\lambda'$, será, no plano euclidiano, o inverso de $\lambda$ em relação à circunferência $r_a$. De acordo com o <a href="http://www.benditamatematica.com/2016/10/inversao-de-circunferencia-em-relacao.html#teorema1" target="_blank">Teorema 1 - Inversão de circunferência em relação a outra circunferência</a>, o inverso de $\lambda$ em relação à $r_a$ será outra circunferência, $\lambda'$, ver <a href="http://www.benditamatematica.com/2017/10/circunferencia-hiperbolica-no-disco-de.html#figura4">Figura 4</a>. Sendo $O'$ o simétrico de $O$ em relação à h-reta $r$, o <a href="http://www.benditamatematica.com/2017/01/isometria-no-disco-de-poincare-reflexao.html#teorema1" target="_blank">Teorema 1 - Isometria no Disco de Poincaré: Reflexão em torno de uma h-reta</a> diz que a reflexão em torno de uma h-reta é uma isometria, ou seja, é uma aplicação que conserva distância e ângulo, então, como $O$ é um h-ponto que está a uma distância $\rho$ de qualquer ponto de $\lambda$, então $O'$ está a uma distância $\rho$ de qualquer ponto de $\lambda'$, portanto, a h-circunferência $\lambda'$ tem centro no ponto $O'$ e raio $\rho$.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg60oEDWypKRWOSU6bjJ6-X43TZiDh6It31Y15LeXVPkUy3QEJhNv5NFsXLowwZ-ngcA0t-ggRyIaua8bvTx2b5ljzUMdtvzaKe9Nfd0rQftUhAQ5cvIXtgJXCZKmoh5ky-BRNaoOrMl3vI/s1600/h-circunfer%25C3%25AAncia4.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="819" data-original-width="1145" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg60oEDWypKRWOSU6bjJ6-X43TZiDh6It31Y15LeXVPkUy3QEJhNv5NFsXLowwZ-ngcA0t-ggRyIaua8bvTx2b5ljzUMdtvzaKe9Nfd0rQftUhAQ5cvIXtgJXCZKmoh5ky-BRNaoOrMl3vI/s320/h-circunfer%25C3%25AAncia4.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.blogger.com/null" name="figura4"></a>Figura 4</b></td></tr>
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Pela arbitrariedade na escolha da h-reta $r$ podemos generalizar que as circunferências hiperbólicas também são circunferências euclidianas, porém, o centro euclidiano não coincide com o centro hiperbólico a não ser que $O$ seja o h-centro.<br />
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Na <a href="http://www.benditamatematica.com/2017/10/circunferencia-hiperbolica-no-disco-de.html#construcao1">Construção 1</a>, feita no Geogebra, a h-circunferências $\lambda$ tem h-centro em $O$ e $A$ é um h-ponto de $\lambda$, onde $\rho=\overline{OA}$. Temos ainda que $r$ é um h-eixo de simetria, como pontos ideais $Z_1$ e $Z_2$, $\lambda'$ e $O'$ são os simétricos de $\lambda$ e $O$ em torno de $r$, respectivamente, o h-ponto $Q$ pertence a $\lambda'$ e o ponto $E$ é o centro euclidiano de $\lambda'$. Os pontos na cor amarela podem ser movidos.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><iframe height="427px" scrolling="no" src="https://www.geogebra.org/material/iframe/id/SxXsH3SW/width/432/height/427/border/888888/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/true/ctl/false" style="border: 0px;" title="Circunferências Hiperbólica no Disco de Poincaré" width="432px"> </iframe></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><a href="https://ggbm.at/PrWm9CdE" name="construcao1" target="_blank"><b>Construção 1</b></a><br />
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Observe que, em $\lambda'$, no plano euclidiano, $\overline{EQ}$ é o raio enquanto que, no plano hiperbólico, $\overline{O'Q}=\rho$ é o h-raio. </div>
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Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-49557085323632238492017-10-09T12:26:00.000-03:002020-01-26T22:40:33.475-03:00Aplicação da matemática para tomar uma decisão<div style="text-align: justify;">
Já deve ter se deparado, num supermercado, onde, por exemplo, você quer comprar um chocolate em pó e verifica-se o mesmo produto vendido em embalagens de $400\text{g}$ e $1{,}3\text{kg}$ com os seguintes preços:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7mBQUol3232r0gKrYW2JBQ_kk_P_-YkrkiTCJhQC2Kx07faZP18MF2D44MTiPgD8phyN0mqM4vo6diRiD0DpRlkHls1Iq4aL8CUzr0z_ImM97_n6YGqCtBlqRBQsxESasLbswjcGGbtOx/s1600/pre%25C3%25A7os.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="377" data-original-width="626" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7mBQUol3232r0gKrYW2JBQ_kk_P_-YkrkiTCJhQC2Kx07faZP18MF2D44MTiPgD8phyN0mqM4vo6diRiD0DpRlkHls1Iq4aL8CUzr0z_ImM97_n6YGqCtBlqRBQsxESasLbswjcGGbtOx/s320/pre%25C3%25A7os.jpg" width="320" /></a></div>
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Que critério você utilizaria para fazer uma das seguintes escolhas para comprar o achocolatado: Leva três latas de $400\text{g}$ ou um pacote de $1{,}3\text{kg}$?<br />
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Este problema é aberto e não tem uma única resposta certa, já que cada um iria aplicar o seu critério, mas, vamos mostrar duas formas de aplicar a matemática para decidir entre uma embalagem de $1{,}3\text{kg}$ ou três embalagens de $400\text{g}$.</div>
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SITUAÇÃO 1: vamos considerar que há uma necessidade de economizar o máximo possível, então, três embalagens de $400\text{g}$ é equivalente a $1200\text{g}=1{,}2\text{kg}$ onde você irá pagar $$\text{R}\$(3\cdot 4{,}50)=\text{R}\$13{,}50$$ que é menor do que $\text{R}\$14{,}30$ que é o preço do achocolatado da embalagem de $1{,}3\text{kg}$. Nesta situação, a melhor escolha é comprar três latas de $400\text{g}$ de achocolatado. Desta forma, você deixaria de levar $100\text{g}$ de achocolatado, mas isso não é problemas, porque estará economizando $\text{R}\$0,80$ é isso é o mais importante, observando o critério adotado!<br />
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SITUAÇÃO 2: vamos considerar que você queira levar o mais vantajoso, ou seja, se pudéssemos colocar as duas ofertas em embalagens de mesma quantidade e com valor de venda proporcional ao preço de cada oferta, o mais vantajoso seria a mais barata. Assim, devemos colocar as quantidades de cada embalagem numa mesma unidade de medida, por exemplo $400\text{g}=0{,}4\text{kg}$. Em seguida, vamos dividir o preço pela quantidade, em $\text{kg}$, e encontrar o valor de $1\text{kg}$ do achocolatado em cada oferta. Assim, vamos tomar como <b>oferta 1</b> o preço do achocolatado na embalagem de $1{,}3\text{kg}$, e <b>oferta 2</b> o preço do achocolatado na embalagem de $400\text{g}=0{,}4\text{kg}$<br />
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$$\begin{array}{dclcl}<br />
\text{oferta 1} & = & \dfrac{\text{R\$}14{,}30}{1{,}3\text{kg}} & = & \text{R\$}11{,}00/\text{kg} \\<br />
\text{oferta 2} & = & \dfrac{\text{R\$}4{,}50}{0{,}4\text{kg}} & = & \text{R\$}11{,}25/\text{kg}<br />
\end{array}$$</div>
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Desta forma, verificamos que o achocolatado da oferta 1, na embalagem de $1{,}3\text{kg}$, é mais vantajoso que o achocolatado da oferta 2, na embalagem de $400\text{g}$.<br />
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Veja que estes cálculos, embora simples, são trabalhosos para fazer mentalmente, desta forma, sugiro que leve uma calculadora (pode ser a do celular) sempre que for ao mercado. Que critério você iria adotar para escolher entre as duas ofertas? Deixe seus comentários.</div>
Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-14233882284723135832017-09-08T14:45:00.000-03:002017-09-08T14:45:54.767-03:00Elipse como sendo o lugar geométrico dos centros das circunferências tangentes a uma circunferência $d$, com centro $C$ e raio $r$, e que passa por um ponto $F\neq C$ interno à $d$Nesta postagem, vamos responder a seguinte pergunta: <b>Qual o lugar geométrico dos centros das circunferências tangentes a uma circunferência $d$, com centro $C$ e raio $r$, e que passa por um ponto $F\neq C$ interno à $d$?</b> Na postagem <a href="http://www.benditamatematica.com/2017/07/associando-pontos-da-circunferencia-uma.html" target="_blank">Associando pontos da circunferência a uma elipse ou hipérbole</a>, apresenta uma construção que sugere que a resposta da nossa pergunta é uma elipse. Assim, vamos provar a nossa tese.<br />
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A definição mais usual da elipse é a seguinte:<br />
Sejam $F_1$ e $F_2$ dois pontos distintos e uma distância $a \in \mathbb{R}_+$. A elipse de focos $F_1$ e $F_2$ é o lugar geométrico do ponto $P$ tal que soma das distâncias entre $P$ e os focos é igual a $2a$.<br />
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<tr><td class="tr-caption" style="text-align: center;">Figura 1</td></tr>
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Na Figura 1, temos uma elipse cujos elementos são:<br />
Focos $F_1$ e $F_2$;<br />
Vértices $A_1$, $A_2$, $B_1$ e $B_2$;<br />
Centro $C$;<br />
Eixo maior $\overline{A_1A_2}=2a$;<br />
Eixo menos $\overline{B_1B_2}=2b$;<br />
Distância focal $\overline{F_1F_2}=2c$.<br />
$a^2=b^2+c^2$<br />
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Seja $d$ uma circunferência com centro em $C$ e raio $r$ e considere um ponto $F\neq C$ interno a $d$. Sendo $P_1 \in d$ e $P$ um ponto equidistante de $P_1$ e $F$, pela arbitrariedade na escolha do ponto $P_1$, na Figura 2, apresentamos o lugar geométrico do ponto $P$, denominado por $c$.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgqKqpmfUKNiPUjtcIAFwg8i-aTfNivTAgqlJcCSLf-kY3e5YoYnvQl2uLyTfR9GQCWW0EMgF7jRAbc9r6EgGmz2Wrp3QAp_GS-OgwYkeYSalbtyQ5Yf1vOCDlM6KjlwNGlvY-dFpVoPJL/s1600/Figura7.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="662" data-original-width="780" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgqKqpmfUKNiPUjtcIAFwg8i-aTfNivTAgqlJcCSLf-kY3e5YoYnvQl2uLyTfR9GQCWW0EMgF7jRAbc9r6EgGmz2Wrp3QAp_GS-OgwYkeYSalbtyQ5Yf1vOCDlM6KjlwNGlvY-dFpVoPJL/s320/Figura7.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 2</td></tr>
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Assim, temos $r=\overline{CP_1}$, vamos tomar $m\in\mathbb{R}$ tal que $$\begin{equation}\label{eq1}m=\overline{FP}=\overline{PP_1}\end{equation}$$. Deste modo, temos $$\begin{equation}\label{eq2}\overline{CP}=r-m\end{equation}$$<br />
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Portanto, a soma das distâncias do ponto $P$ aos pontos $C$ e $F$, respectivamente, é $$\begin{equation}\label{eq3}d(P,C)+d(P,F)=\overline{CP}+\overline{PF}=(r-m)+m=r\end{equation}$$<br />
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Assim, mostramos que $c$ é uma elipse de focos $C$ e $F$.<br />
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Observe a Figura 3, O ponto $M$ é ponto médio do segmento $\overline{CF}$, como $C$ e $F$ são focos da elipse $c$, então $M$ é centro de $c$. A reta $f$ é determinada pelos pontos $C$ e $F$; os pontos $X_1$ e $X_2$ pertencem a interseção entre $f$ e a circunferência $d$; $A_1$ é ponto médio de $F$ e $X_1$ e $A_2$ é ponto médio de $F$ e $X_2$, logo, $A_1,A_2\in c$; a reta $g$ é perpendicular à $f$ e passa por $M$ (ou seja, $g$ é a mediatriz de $\overline{CF}$); e os pontos $B_1$ e $B_2$ pertencem a interseção entre $g$ e $c$.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgi9j_r8AqyCvBzVaZzanI4Nzlqcp5zzkWOFpfSJsn5OZaP29l-8a9d7uYlHJsmAz_JYSS9IFq9tEBwDJHXpohScY0wzHu7OXP_78RSp8oHIfmBEImTq3n12pu2q1tgGGVqufFjkhePldAS/s1600/fig1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="655" data-original-width="671" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgi9j_r8AqyCvBzVaZzanI4Nzlqcp5zzkWOFpfSJsn5OZaP29l-8a9d7uYlHJsmAz_JYSS9IFq9tEBwDJHXpohScY0wzHu7OXP_78RSp8oHIfmBEImTq3n12pu2q1tgGGVqufFjkhePldAS/s320/fig1.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figura 3</td></tr>
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Tomando $\overline{FX_2}=2x$, para $x\in\mathbb{R}$, então $$\begin{equation}\label{eq4}\overline{CF}=r-2x\Rightarrow\overline{CM}=\overline{MF}=\dfrac{r-2x}{2}\end{equation}$$<br />
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Temos ainda que $$\overline{X_1F}=\overline{X_1C}+\overline{CF}=2r-2x$$ também podemos escrever $\overline{X_1F}$ como $$\overline{X_1F}=2\cdot\left(\overline{A_1C}+\overline{CF}\right)$$ assim, teremos $$2\cdot\left(\overline{A_1C}+\overline{CF}\right)=2r-2x\Rightarrow\overline{A_1C}+\overline{CF}=r-x\Rightarrow\overline{A_1C}+r-2x=r-x\Rightarrow\overline{A_1C}=x$$<br />
logo $\overline{A_1C}=\overline{A_2F}$.<br />
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Como $A_1$ e $A_2$ são pontos de $c$ e de $f=\overline{CF}$, então, o segmento $\overline{A_1A_2}$ é o eixo maior de $c$ e temos $$\overline{A_1A_2}=x+r-2x+x=r$$<br />
Como $B_1,B_2$ são pontos da reta $g$ que é perpendicular ao eixo maior e passa pelo centro $M$ da elipse $c$, então $\overline{B_1B_2}$ é o eixo menor de $c$, assim, temos a relação $$\begin{equation}\label{eq5}\overline{B_1F}^2=\overline{MB_1}^2+\overline{MF}^2\end{equation}$$<br />
Sabendo que $\overline{B_1C}+\overline{B_1F}=r$ e que $g$ é mediatriz do segmento $\overline{CF}$, podemos concluir que $$\begin{equation}\label{eq6}\overline{B_1F}=\dfrac{r}{2}\end{equation}$$<br />
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Aplicando $\ref{eq4},\ref{eq6}$ em $\ref{eq5}$ temos<br />
$$\left(\dfrac{r}{2}\right)^2=\overline{B_1M}^2+\left(\dfrac{r-2x}{2}\right)^2\Rightarrow\overline{B_1M}=\dfrac{\sqrt{x\left(2r-x\right)}}{2}$$<br />
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Assim, concluímos que o lugar geométrico dos centros das circunferências tangentes a uma circunferência $d=\mathcal{C}(C,r)$ e que passa por um ponto $F$ interno à $d$ é a elipse $c$ com focos em $C$ e $F$, com eixo maior medindo $r$ e eixo menor medindo $\dfrac{\sqrt{x\left(2r-x\right)}}{2}$, onde $x$ é a distância de um dos focos e o extremo mais próximo do eixo maior.Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-91297205467277261832017-07-17T23:14:00.000-03:002017-07-17T23:14:28.067-03:00Utilizando uma circunferência para construir uma hipérbole<div style="text-align: justify;">
Vamos fazer um estudo sobre a hipérbole que pode ser obtida a partida da construção da postagem no link <a href="http://www.benditamatematica.com/2017/07/associando-pontos-da-circunferencia-uma.html">http://www.benditamatematica.com/2017/07/associando-pontos-da-circunferencia-uma.html</a>.<br />
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A definição mais usual para hipérbole é</div>
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<i>Sejam $F_1$ e $F_2$ dois pontos distintos do planos e $2c$ é a distância entre eles. A hipérbole é o lugar geométrico do ponto $P$ tal que a diferença das distância entre $P$ e cada um dos focos é $2a$, com $0 < a < c$ </i></div>
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Na Construção 1, vamos considerar que a circunferência $d$ tem raio $p$, ou seja, $\overline{CP_1}=p$, a distância entre $P_1$ e $P$ será $m$, como $P$ é equidistante de $P_1$ e $F$, então, $\overline{P_1P}=\overline{PF}=m$, ver Figura 1.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyOQ7dPZgec-6uLRWKwU-8Rp7f01KeSOR7bX-9pwOUA4fg9x6YtfDfZ8ABLeNu4x8AyStKNg7FhVUf01tyUH1MOEvKTnOX0fPPVnThRI1VLB3Bu9DGPwWJVrTbHAGLHuNyDJ7JiyOboQEb/s1600/Figura1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="704" data-original-width="1531" height="183" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyOQ7dPZgec-6uLRWKwU-8Rp7f01KeSOR7bX-9pwOUA4fg9x6YtfDfZ8ABLeNu4x8AyStKNg7FhVUf01tyUH1MOEvKTnOX0fPPVnThRI1VLB3Bu9DGPwWJVrTbHAGLHuNyDJ7JiyOboQEb/s400/Figura1.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Figura 1</td></tr>
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Assim, temos:</div>
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$$\left\{\begin{array}{l}<br />
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\overline{CP}=p+m \\<br />
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\overline{PF}=m<br />
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\end{array}\right.\Rightarrow \left|\overline{CP}-\overline{PF}\right|=\left|p+m-m\right|=p$$<br />
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Deste modo, verificamos que quando $F$ é externo a $d$, o lugar geométrico de $P$ é uma hipérbole com foco $C$ e $F$. Na Figura 2, os pontos $A_1$ e $A_2$ são os vértices da parábola, assim $\overline{A_1A_2}$ é o eixo focal, $A_1$ é associado ao ponto $A'_1$ e $A_2$ é associado ao ponto $A'_2$. Sendo $p$ o raio de $d$ e $n$ a distância entre $A_2$ e $F$, vamos determinar a medida $2a$ do eixo focal.</div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOOv_AEWzY1LIMonIsCHp6U8VCzoNKgGPFuXMEX5CV6QreHNPqu_IF2Nnc8xLM8t3vXU8AkjOfsio9EhReBFjj4WGA_CsKxZYU7j1jitoBzhG9-Wt93I0AOqz2_J4laj4NHzBAyy40na14/s1600/figura2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="704" data-original-width="1531" height="183" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOOv_AEWzY1LIMonIsCHp6U8VCzoNKgGPFuXMEX5CV6QreHNPqu_IF2Nnc8xLM8t3vXU8AkjOfsio9EhReBFjj4WGA_CsKxZYU7j1jitoBzhG9-Wt93I0AOqz2_J4laj4NHzBAyy40na14/s400/figura2.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Figura 2</td></tr>
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A distância entre $A_1$ e $F$ é</div>
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$$d(A'_1,F)=2p+2n$$</div>
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Como $A_1$ é ponto médio de $A'_1$ e $F$, então</div>
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$$d(A_1,F)=\frac{d(A'_1,F)}{2}=\frac{2p+2n}{2}=p+n$$</div>
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Veremos que a distância entre os vértices da hipérbole é igual ao raio da circunferência $d$</div>
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$$d(A_1,A_2)=d(A_1,F)-d(A_2,F)=p+n-n=p$$</div>
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Como $A_2$ é o ponto médio entre $A'_2$ e $F$, então, a distância, 2c, entre os focos $C$ e $F$ é</div>
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$$d(C,F)=d(C,A'_2)+d(A'_2,F)=p+2n$$</div>
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Na Figura 3, $M$ é o centro da hipérbole e $\overline{B_1B_2}$ é o eixo não focal. Então, $\overline{MA_2}=\dfrac{p}{2}$ e $\overline{B_1A_2}=\dfrac{p+2n}{2}$. Vamos determina a medida $2b$ do eixo não focal utilizando a relação</div>
$$c^2=a^2+b^2\Rightarrow\left( \dfrac{p+2n}{2} \right)^2=\left( \dfrac{p}{2} \right)^2+b^2 \Rightarrow b=\dfrac{\sqrt{n\left( 2p+n \right)}}{2}\Rightarrow \overline{B_1B_2}=2b=\sqrt{n\left( 2p+n \right)}$$<br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihPGehZtP4S1X_vEHe5huBsm9bvsOAG-BmUu7gAc8R7OzY4MsCPHCc8Teug495rxRAhP6EXRehPVCiGNAUnQvrM2egWPJGZZJ2vakdaGtrU-g82Wf_P8AEeSb27TNtc1CQkA1To1Udnbnt/s1600/figura3.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="853" data-original-width="1171" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihPGehZtP4S1X_vEHe5huBsm9bvsOAG-BmUu7gAc8R7OzY4MsCPHCc8Teug495rxRAhP6EXRehPVCiGNAUnQvrM2egWPJGZZJ2vakdaGtrU-g82Wf_P8AEeSb27TNtc1CQkA1To1Udnbnt/s320/figura3.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Figura 3</td></tr>
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Sejam as reta $t_1$ e $t_2$ tangentes à circunferência $d$ nos pontos $P_1$ e $P_2$, respectivamente, e passam por $F$. Neste caso, não há circunferência que tangencie $d$ em $P_1$ ou $P_2$ e passe por $F$. Desta forma, vamos mostrar que as mediatrizes de $\overline{P_1F}$ e $\overline{P_2F}$ são as assíntotas da parábola.</div>
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Sabemos que as assíntotas têm coeficientes angulares $\dfrac{b}{a}$ e $-\dfrac{b}{a}$ e passa pelo centro da hipérbole. Assim, considere a Figura 4.</div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVZ-Jc7TfBLYAbtbTP-RwaawRdu4f11vU7NjiX5xa9tghy8omZn0TpCGy0PEUlhbnIKg3QrNbe9oT_4WQ1USo2reAMU2rq66WnvAqLx0hYc5NKsOEPRQV2-M3E-KHMP87y4fq9qQe5_mZY/s1600/figura4.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="853" data-original-width="1171" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVZ-Jc7TfBLYAbtbTP-RwaawRdu4f11vU7NjiX5xa9tghy8omZn0TpCGy0PEUlhbnIKg3QrNbe9oT_4WQ1USo2reAMU2rq66WnvAqLx0hYc5NKsOEPRQV2-M3E-KHMP87y4fq9qQe5_mZY/s320/figura4.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Figura 4</td></tr>
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A circunferência $e$ tem centro em $M$ e raio $c=\overline{MF}=\dfrac{p+2n}{2}$, $P_1$ pertence a interseção de $d$ e $e$ e $t_1=\overline{P_1F}$. </div>
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O triângulo $\triangle CP_1F$ é retângulo em $P_1$, pois $C\widehat{P_1}F=90^\circ$ porque é o ângulo do arco capaz da diagonal de $e$. Como $\overline{CP_1}=2a$ e $\overline{CF}=2c$, então $\overline{P_1F}=2b=\sqrt{n\left( 20+n \right)}$, por causa da relação $c^2=a^2+b^2$. Então, temos $$tg \left(C\widehat{P_1}F\right)=\frac{2b}{2a}=\frac{b}{a}=\frac{2\sqrt{n\left( 20+n \right)}}{p}$$</div>
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A mediatriz $s$ de $P_1$ e $F$ é perpendicular a $\overline{P_1F}$, então, $s // \overline{CP_1}$ e, como $M$ é equidistante de $P_1$ e $F$, então $s$ passa por $M$, logo $s$ é assíntota da hipérbole. De forma análoga, podemos mostrar que a mediatriz entre entre $F$ e $P_2$, o outro ponto de interseção entre $d$ e $e$, é a outra assíntota da parábola, ver Figura 5.</div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCUbl2inr5aYTAHpu928cz7qM0kjc8WBZ1VNb2b5V9Rvy8WLr99jTnSgWkiR6UH_Mw9icumX6xk6Y-RmNjlzBKV5_GJNoJ_cjNxHQRFbSohStLZwHZPQm_T1EFcSdv6UpmQJNQKEj6hdW5/s1600/figura5.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="853" data-original-width="1171" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCUbl2inr5aYTAHpu928cz7qM0kjc8WBZ1VNb2b5V9Rvy8WLr99jTnSgWkiR6UH_Mw9icumX6xk6Y-RmNjlzBKV5_GJNoJ_cjNxHQRFbSohStLZwHZPQm_T1EFcSdv6UpmQJNQKEj6hdW5/s320/figura5.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Figura 5</td></tr>
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Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0tag:blogger.com,1999:blog-3042914877885053904.post-84605064657365306292017-07-16T21:21:00.001-03:002020-01-26T22:40:59.302-03:00Associando pontos da circunferência a uma elipse ou hipérbole<div style="text-align: justify;">
Na Revista do Professor de Matemática Nº 66 tem um artigo com o título <a href="http://rpm.org.br/cdrpm/66/8.html" target="_blank">Obtendo as cônicas com dobraduras</a> que apresenta construções, que podem ser feitas no software de Geometria Dinâmica. Segue os passos da construção que fiz no Geogebra, os comandos apresentados em cada um dos passos deverão ser colocados no Campo Entrada, no Geogebra.<br />
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<li style="text-align: justify;">Coloque três pontos distintos $C,F$ e $R$;</li>
<li style="text-align: justify;">Insira o comando "d=Círculo(C, R)", criando assim a circunferência $d$ com centro em $C$ e raio $\overline{CR}$;</li>
<li style="text-align: justify;">Coloque o ponto $P_1$ na circunferência $d$ utilizando o comando "P_1=Ponto(d)";</li>
<li style="text-align: justify;">Trace a reta $r=\overline{CP_1}$ com o comando "r=reta(C,P_1)";</li>
<li style="text-align: justify;">Trace a mediatriz $s$ dos pontos $P-1$ e $F$ com o comando "s=Mediatriz(P_1, F)";</li>
<li style="text-align: justify;">Marque o ponto $P\in r\cap s$ utilizando o comando "P=Interseção(r, s)".</li>
<li style="text-align: justify;">Identifique o lugar geométrico $c$ do ponto $P$ através do comando "c=LugarGeométrico(P, P_1)".</li>
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A seguir, apresentamos a construção feita no Geogebra</div>
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<iframe height="216px" scrolling="no" src="https://www.geogebra.org/material/iframe/id/YadkkDHM/width/467/height/216/border/888888/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/true/ctl/false" style="border: 0px;" title="Associando pontos de uma circunferência a uma elipse ou hipérbole" width="467px"> </iframe></div>
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<b><span style="font-size: x-small;"><a href="https://ggbm.at/SWnReRkF" target="_blank">Construção 1</a></span></b></div>
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Na Construção 1, mova o ponto $C$ para alterar a posição da circunferência $d$, movendo o ponto $R$ alterará o raio de $d$, movendo o ponto $F$ alterá a cônica e movendo o ponto $P_1$, moverá o ponto $P$.</div>
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Observe que se o ponto $F$ é externo à circunferência $d$, então, o lugar geométrico de $P$ sugere ser uma hipérbole com focos $C$ e $F$; e se $F$ é interno à $d$ e distinto de $C$, a construção sugere que o lugar geométrico de $P$ é uma elipse com focos $C$ e $F$.</div>
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Carlos Binohttp://www.blogger.com/profile/13206865729097389825noreply@blogger.com0