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<p>Considerando-se os vetores «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»a«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«/math»(#a, #b, #c) e «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»b«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«/math»(#d, #e, #f), calcule o vetor que é dado por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»c«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mover»«mi»a«/mi»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«mi»k«/mi»«mo»§#183;«/mo»«mover»«mi»b«/mi»«mo»§#8640;«/mo»«/mover»«/math», de forma que o módulo de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»c«/mi»«mo»§#8640;«/mo»«/mover»«/math» seja o menor possível.</p> <p>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»k«/mi»«/math» é uma constante.</p>
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<p style="text-align: justify;">O vetor «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»c«/mi»«mo»§#8640;«/mo»«/mover»«/math» é dado por:</p> <p style="text-align: justify;"> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»c«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»+«/mo»«mi»k«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math».</p> <p style="text-align: justify;">A norma euclidiana (ou módulo) do vetor «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»c«/mi»«mo»§#8594;«/mo»«/mover»«/math» é dada por :</p> <p style="text-align: center;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨||¨ close=¨||¨»«mover»«mi»c«/mi»«mo»§#8640;«/mo»«/mover»«/mfenced»«mo»=«/mo»«msup»«mfenced»«mrow»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi»n«/mi»«/munderover»«msup»«mfenced open=¨|¨ close=¨|¨»«msub»«mi»c«/mi»«mi»i«/mi»«/msub»«/mfenced»«mn»2«/mn»«/msup»«/mrow»«/mfenced»«mrow»«mn»1«/mn»«mo»/«/mo»«mn»2«/mn»«/mrow»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»w«/mi»«/math».</p> <p style="text-align: justify;">Fazendo-se «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»w«/mi»«mo»=«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi»n«/mi»«/munderover»«msup»«mfenced open=¨|¨ close=¨|¨»«msub»«mi»c«/mi»«mi»i«/mi»«/msub»«/mfenced»«mn»2«/mn»«/msup»«/math», teremos:</p> <p style="text-align: center;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»w«/mi»«mo»=«/mo»«msup»«mfenced open=¨||¨ close=¨||¨»«mover»«mi»c«/mi»«mo»§#8594;«/mo»«/mover»«/mfenced»«mn»2«/mn»«/msup»«mo».«/mo»«/math»</p> <p>O vetor «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»c«/mi»«mo»§#8640;«/mo»«/mover»«/math» terá um módulo mínimo quando (considerando-se o valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»k«/mi»«/math») a derivada «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»d«/mo»«mi»w«/mi»«/mrow»«mrow»«mo»d«/mo»«mi»k«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»0«/mn»«/math», portanto:</p> <p style="text-align: center;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»d«/mo»«mi»w«/mi»«/mrow»«mrow»«mo»d«/mo»«mi»k«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mo»#«/mo»«mi»w«/mi»«mo»=«/mo»«mn»0«/mn»«mo».«/mo»«/math»</p> <p style="text-align: justify;">Solucionando-se a equação em «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»k«/mi»«/math», nós acharemos que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»y«/mi»«/math» (Obs.: consideraremos apenas a parte real da solução).</p> <p style="text-align: justify;">Você pode chegar a essa solução usando o comando do Matlab:</p> <p style="text-align: center;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mi»v«/mi»«mi»e«/mi»«mo»(«/mo»«mo»`«/mo»«mo»#«/mo»«mi»w«/mi»«mo»=«/mo»«mn»0«/mn»«mo»`«/mo»«mo»)«/mo»«/math»</p> <p style="text-align: justify;"> </p> <p style="text-align: justify;">Dai:</p> <p style="text-align: center;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»c«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»+«/mo»«mi»k«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mi»x«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mi»y«/mi»«mo»;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»z«/mi»«mi»z«/mi»«mo»)«/mo»«/math»</p>
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Algorithm
Choice 1
Answer
<p><span>(#xx; #yy; #zz)</span></p>
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<p><span>(#xe1; #ye1; #ze1)</span></p>
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<p><span>(#xe2; #ye2; #ze2)</span></p>
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Choice 4
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<p><span>(#xe3; #ye3; #ze3)</span></p>
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Choice 5
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<p>Nenhuma das respostas esta correta</p>
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Feedback
Combined feedback
For any correct response
<p>Sua resposta está correta.</p>
For any partially correct response
<p>Sua resposta está parcialmente correta.</p>
Options
Show the number of correct responses once the question has finished
For any incorrect response
<p>Sua resposta está incorreta.</p>
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Hint 1
Hint text
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Hint 2
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Clear incorrect responses
Show the number of correct responses
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Tuesday, 17 September 2013, 4:24 PM
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Tuesday, 17 September 2013, 4:24 PM
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