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<p><span style="font-family: arial, helvetica, sans-serif; font-size: medium; color: #000000;">Se compra una máquina en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»$«/mo»«mo»#«/mo»«mi»a«/mi»«/math» y su valor se deprecia anualmente «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»$«/mo»«mo»#«/mo»«mi»d«/mi»«/math».</span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium; color: #000000;">Determina una expresión para el valor de la máquina después de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math» años.<br /></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium; color: #000000;">Si el valor de desecho de la maquina es «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»$«/mo»«mo»#«/mo»«mi»b«/mi»«/math», ¿Cuál es la vida útil de la maquina?</span></p> <p> </p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium; color: #ff0000;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium; color: #ff0000;"><strong>Observación:</strong> </span></span><span style="font-family: arial, helvetica, sans-serif; font-size: medium; color: #ff0000;">Si la vida util es 7 años, sólo ingresa 7</span></p>
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<p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">Ya que el valor de la máquina se desprecia</span> <span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»$«/mo»«mo»#«/mo»«mi»d«/mi»«/math» cada año, podemos afirmar que al término del primer año el valor de la máquina será <span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»$«/mo»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»$«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math», al finalizar el segundo año será <span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»$«/mo»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»$«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«/math», y asi sucesivamente.</span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">Está sucesión de valores forman una progresión aritmética cuyo primer termino es <span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math» y diferencia común <span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«/math».</span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">Si queremos determinar una expresión para el valor de la máquina pasados "n" años, lo que realmente debemos determinar es el n-ésimo término de una progresión aritmética. Utilizando el primer término y la diferencia común, tenemos que:</span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»=«/mo»«msub»«mi»a«/mi»«mn»1«/mn»«/msub»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»n«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#183;«/mo»«mi»d«/mi»«/math»</span> </span></span></span></span></span><br /></span></span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">Reemplazando los valores obtenidos:</span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»n«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#183;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»</span> </span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span><br /></span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">Reduciendo términos semejantes finalmente obtenemos:</span></span></span></span></span></p> <p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span>Para saber la vida útil de la máquina debemos considerar el valor de desecho y que valor toma "n" para este valor. Tomando esto en cuenta, realizamos <span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>e igualamos con término general previamente encontrando y despejamos "n".</span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; 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font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; 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font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«mn»3«/mn»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; 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font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/mfrac»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; 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font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">Finalmente obtenemos que la vida útil de la máquina es de <span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;"><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«/math»</span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>años.<br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p> <p style="text-align: left;"> </p> <div style="text-align: center;"> </div>
No, case is unimportant
Yes, case must match
Correct answers
You must provide at least one possible answer. The first matching answer will be used to determine the score and feedback. Click the icon next to the answer field to edit the mathematical properties of the answer and the question.
Answer 1
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">¡Muy bien!</span></p> <p> </p>
Answer 2
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
<p><span style="font-family: arial, helvetica, sans-serif; font-size: medium;">Al parecer cometiste un error, revisa tu desarrollo y consulta a tu profesor si aún te quedan dudas.</span></p> <p> </p>
Answer 3
Answer
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
Settings for multiple tries
Penalty for each incorrect try
100%
50%
33.33333%
25%
20%
10%
0%
Hint 1
Hint text
Hint 2
Hint text
Created / last saved
Created
by
Admin User
on
Thursday, 12 January 2017, 10:03 AM
Last saved
by
Admin User
on
Thursday, 12 January 2017, 10:03 AM
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