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<p><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Una Universidad ha realizado un plan de capacitaciones para sus egresados #g1 y #g2. </span></p> <p> </p> <p><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Las capacitaciones a impartir son: #c1 y #c2.</span></p> <p> </p> <p><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Se sabe que cada uno de los #g1 necesita #h1 horas de #c1 y #h2 horas de #c2 y cada uno de los #g2 necesita #h3 y #h4 horas respectivamente.</span></p> <p> </p> <p><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Sabiendo que se dispone de #h5 horas para #c1 y #h6 horas para #c2 y que se debe hacer uso de todas estas horas, entonces:</span></p> <p> </p> <p><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">a) El número de #g1 que puede realizar las capacitaciónes es: {1:SA:=\#sol1#¡Muy Bien}</span></p> <p> </p> <p><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">b) El número de #g2 que puede realizar las <span style="font-family: arial,helvetica,sans-serif; font-size: medium;">capacitaciónes</span> es: {1:SA:=\#sol2#¡Muy Bien!}</span></p>
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<p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Si consideramos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» e «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math» como:<br /></span></p> <p> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif;"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;"><em><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math»</span></span></em></span><span style="font-size: medium;">: número de #g1</span></span></p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;"><em><span class="nolink"><span class="nolink"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></span></span></em></span>: número de #g2</span></p> <p align="justify"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Como cada uno de los #g1 necesita #h1 horas de #c1 y cada uno de los #g2 necesita #h3 horas de #c1, podemos plantear la primera ecuación de la siguiente forma:</span></p> <p style="text-align: center;" align="justify"> </p> <p style="text-align: center;" align="justify"> </p> <p style="text-align: center;" align="justify"><span class="nolink"><em><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#h1«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»#h3«/mi»«mi»#y«/mi»«mo»=«/mo»«mi»#h5«/mi»«/math»</span></em></span></p> <p align="justify"> </p> <p align="justify"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Donde #h5 es la cantidad de horas que se disponen para #c1</span></p> <p align="justify"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Como cada <span style="font-family: arial,helvetica,sans-serif; font-size: medium;">uno de los</span> #g1 necesita #h2 horas. de #c2 y cada <span style="font-family: arial,helvetica,sans-serif; font-size: medium;">uno de los</span> #g2 necesita #h4 horas de #c2, podemos plantear la segunda ecuación:</span></p> <p align="justify"> </p> <p align="justify"> </p> <p style="text-align: center;" align="justify"><em><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#h2«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»#h4«/mi»«mi»#y«/mi»«mo»=«/mo»«mi»#h6«/mi»«/math»</span></span></em></p> <p align="justify"> </p> <p align="justify"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Donde #h6 es la cantidad de horas que se disponen para #c2</span></p> <p align="justify"> </p> <p align="justify"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">De esta forma, el sistema de ecuaciones es:</span></p> <p align="justify"> </p> <p align="justify"> </p> <p align="center"><em><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#h1«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»#h3«/mi»«mi»#y«/mi»«mo»=«/mo»«mi»#h5«/mi»«/math»</span></em></p> <p align="center"><em><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#h2«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»#h4«/mi»«mi»#y«/mi»«mo»=«/mo»«mi»#h6«/mi»«/math»</span></em></p> <p align="center"> </p> <p align="center"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Para resolver, utilizaremos el Método de Reducción. (recuerda que no es el único método para resolver sistemas de ecuaciones)</span></p> <p align="justify"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Eliminaremos la variable <em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math»</span></span></span></span></span></em>:</span></p> <p align="justify"> </p> <p style="text-align: left; margin-left: 330px;" align="center"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi»#h1«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»#h3«/mi»«mi»#y«/mi»«mo»=«/mo»«mi»#h5«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»/«/mo»«mo»·«/mo»«mo»-«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p style="margin-left: 330px; text-align: left;" align="center"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#h2«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»#h4«/mi»«mi»#y«/mi»«mo»=«/mo»«mi»#h6«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»/«/mo»«mo»·«/mo»«mi»#d2«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p align="center"> </p> <p align="center"> </p> <p align="justify"><span style="font-family: arial,helvetica,sans-serif; font-size: medium;">Luego,</span></p> <p align="justify"> </p> <p align="justify"> </p> <p style="text-align: center;" align="center"> <em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mspace linebreak=¨newline¨/»«mtable columnlines=¨none none solid none¨»«mtr»«mtd»«mo»#«/mo»«mi»h«/mi»«mn»11«/mn»«mo»#«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»h«/mi»«mn»31«/mn»«mo»#«/mo»«mi»y«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»#«/mo»«mi»h«/mi»«mn»51«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»h«/mi»«mn»21«/mn»«mo»#«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»h«/mi»«mn»41«/mn»«mo»#«/mo»«mi»y«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»#«/mo»«mi»h«/mi»«mn»61«/mn»«/mtd»«/mtr»«/mtable»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p align="center"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p align="center"> </p> <p align="center"> </p> <p style="text-align: left;" align="justify"> <span style="font-size: medium;">Sumando ambas ecuaciones:</span></p> <p style="text-align: left;" align="justify"> </p> <p style="text-align: left;" align="justify"> </p> <p style="text-align: center;" align="justify"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»#«/mo»«mi»y«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»y«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p style="margin-left: 330px; text-align: left;" align="justify"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p align="justify"> </p> <p align="justify"> </p> <p align="justify"> <span class="nolink" style="font-size: medium;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Reemplazando este valor en la primera ecuación:</span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p align="justify"> </p> <p align="justify"> </p> <p style="text-align: center;" align="justify"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#h1«/mi»«mi»#x«/mi»«mo»+«/mo»«mi»#h3«/mi»«mo»·«/mo»«mi»#y1«/mi»«mo»=«/mo»«mi»#h5«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p align="justify"> </p> <p align="justify"> </p> <p align="justify"><span class="nolink" style="font-size: medium;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Despejando <em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#x«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em> , obtenemos:</span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p align="justify"> </p> <p style="text-align: center;" align="justify"><em><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#x«/mi»«mo»=«/mo»«mi»#x1«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></em></p> <p align="justify"> </p> <p align="justify"> </p> <p align="justify"><span style="font-size: medium;"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Por lo tanto, el número de #g1 que puede realizar las capacitaciones es #x1, y el número de #g2 que puede realizar las capacitaciones es #y1.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p align="justify"> </p> <p align="justify"> </p> <p align="justify"> </p> <p><strong><span style="font-family: arial,helvetica,sans-serif; font-size: medium; color: #99cc00;">Reporta y/o califica esta pregunta:</span></strong></p> <p align="justify"> </p> <p><span style="font-family: arial,helvetica,sans-serif; font-size: medium; color: #99cc00;">1. Copia este código: <span style="color: #000000;"><strong>EySE. C3. S04. a. LS.</strong></span></span></p> <p align="justify"> </p> <p><span style="font-family: arial,helvetica,sans-serif; font-size: medium; color: #99cc00;">2. Presiona este <span style="text-decoration: underline;"><strong><span style="color: #0000ff;"><a href="https://docs.google.com/forms/d/e/1FAIpQLSejUJfyYOVP4-dMOQ_mWon-7epEMg7Vddq2LNbGnOqwOiOVXQ/viewform" target="_blank"><span style="color: #0000ff; text-decoration: underline;">enlace</span></a></span></strong></span>, pega el código y completa el formulario</span></p> <p> </p> <p align="justify"> </p>
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