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<p align="justify"><i><font size="4" face="times new roman,times,serif">La funciĆ³n <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"><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">Ā«math xmlns=ĀØhttp://www.w3.org/1998/Math/MathMLĀØĀ»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«/mathĀ»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> es #cr si y sĆ³lo si:</font></i></p>
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<div align="justify"><font size="4"><i><font face="times new roman,times,serif">SoluciĆ³n</font><font face="times new roman,times,serif">:</font></i></font></div><font size="4" face="times new roman,times,serif"><i> <div align="justify"><br /></div></i></font><font face="times new roman, times, serif"> <div style="text-align: left; " align="justify"><i><font size="4">Recordemos que la funciĆ³n <span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«/mathĀ»</span> serĆ” #cr si:</font></i></div> <div style="text-align: left; " align="justify"><i style="text-align: center; "><span class="nolink"><span class="nolink"><font size="4"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#desĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mathĀ»</span></span></span></span></font></span></span></i></div> <div style="text-align: left; " align="justify"><i style="text-align: center; "><font size="4">Entonces, necesitamos calcular <span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span></font></i></div> <div style="text-align: left; " align="justify"><i style="text-align: center; "><font size="4"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«moĀ»Ā§#8658;Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#dfĀ«/miĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></font></i></div></font><i style="font-family: 'times new roman', times, serif; font-size: large; "> <div style="text-align: center; " align="justify"><br /></div></i> <div style="text-align: left; " align="justify"><i style="font-family: 'times new roman', times, serif; font-size: large; "><font size="4">Por lo tanto, debemos encontrar la soluciĆ³n de la siguiente inecuaciĆ³n:</font></i></div> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: center; " align="justify"><font size="4" face="times new roman, times, serif"><i><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«miĀ»#dfĀ«/miĀ»Ā«miĀ»#desĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mathĀ»</span></span></span></span></span></span> </i></font></div> <div style="text-align: left; " align="justify"><font size="4" face="times new roman, times, serif"><i>Para esto debemosĀ encontrar los </i><b style="font-style: italic; ">puntos crĆticos </b><span style="font-style: italic; ">de</span></font><b style="font-style: italic; font-family: 'times new roman', times, serif; font-size: large; "> </b><i style="text-align: center; font-family: 'times new roman', times, serif; font-size: large; "><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span><font size="4">, que se obtienen</font></span></i></div> <div style="text-align: left; " align="justify"><font size="4" face="times new roman, times, serif"><span style="font-style: italic; ">resolviendo la siguiente ecuaciĆ³n de segundo grado:</span></font></div> <div style="text-align: center; " align="justify"><font size="4" face="times new roman, times, serif"><span style="font-style: italic; "><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#dfĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mathĀ»</span></span></span></span></span></span></span></font></div> <div style="text-align: left; " align="justify"><font size="4" face="times new roman, times, serif"><span style="font-style: italic; ">Para resolverla utilizamos la fĆ³rmula:</span></font></div><font size="4" face="times new roman, times, serif"><span style="font-style: italic; "> <div style="text-align: left; " align="justify"><br /></div></span></font> <div style="text-align: center; " align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mtable columnalign="left" rowspacing="0"Ā»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»aĀ«/miĀ»Ā«msupĀ»Ā«miĀ»xĀ«/miĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msupĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»bĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»cĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8658;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«moĀ»-Ā«/moĀ»Ā«miĀ»bĀ«/miĀ»Ā«moĀ»Ā±Ā«/moĀ»Ā«msqrtĀ»Ā«mrowĀ»Ā«msupĀ»Ā«miĀ»bĀ«/miĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msupĀ»Ā«moĀ»-Ā«/moĀ»Ā«mnĀ»4Ā«/mnĀ»Ā«miĀ»aĀ«/miĀ»Ā«miĀ»cĀ«/miĀ»Ā«/mrowĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«miĀ»aĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtd/Ā»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></div> <div style="text-align: center; " align="justify"><em><font size="4" face="Times New Roman">AsĆ, de</font></em>Ā <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#dfĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span><font size="4" face="times new roman,times,serif"><em>obtenemos los parĆ”metros:</em></font></span></div><span class="nolink"></span> <div style="text-align: center; " align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«miĀ»aĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#apĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»,Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»bĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#bpĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»,Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»cĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#cĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></div> <div style="text-align: left; " align="justify"><span style="font-style: italic; font-family: 'times new roman', times, serif; font-size: large; "><font size="4">Reemplazando estos valores en la fĆ³rmula obtenemos:</font></span></div><span style="font-style: italic; font-family: 'times new roman', times, serif; font-size: large; "> <div style="text-align: center; " align="justify"><br /></div></span> <div style="text-align: center; " align="justify"><i><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mtable columnalign="left" rowspacing="0"Ā»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«moĀ»-Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#bpĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā±Ā«/moĀ»Ā«msqrtĀ»Ā«mrowĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#bpĀ«/miĀ»Ā«msupĀ»Ā«moĀ»)Ā«/moĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msupĀ»Ā«moĀ»-Ā«/moĀ»Ā«mnĀ»4Ā«/mnĀ»Ā«moĀ»Ā·Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#apĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā·Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#cĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mrowĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«moĀ»Ā·Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»#apĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»#mbpĀ«/miĀ»Ā«moĀ»Ā±Ā«/moĀ»Ā«msqrtĀ»Ā«miĀ»#discĀ«/miĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«miĀ»#deĀ«/miĀ»Ā«/mfracĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfenced close="" open="{"Ā»Ā«mtableĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«msubĀ»Ā«miĀ»xĀ«/miĀ»Ā«mnĀ»1Ā«/mnĀ»Ā«/msubĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»#mbpĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«msqrtĀ»Ā«miĀ»#discĀ«/miĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«miĀ»#deĀ«/miĀ»Ā«/mfracĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#r6Ā«/miĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtdĀ»Ā«msubĀ»Ā«miĀ»xĀ«/miĀ»Ā«mnĀ»2Ā«/mnĀ»Ā«/msubĀ»Ā«moĀ»=Ā«/moĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»#mbpĀ«/miĀ»Ā«moĀ»-Ā«/moĀ»Ā«msqrtĀ»Ā«miĀ»#discĀ«/miĀ»Ā«/msqrtĀ»Ā«/mrowĀ»Ā«miĀ»#deĀ«/miĀ»Ā«/mfracĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#r4Ā«/miĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mfencedĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></i> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: left; " align="justify"><i style="font-family: 'times new roman', times, serif; font-size: large; "><font size="4">Por lo tanto, podemos escribir la inecuaciĆ³n de la siguiente manera:</font></i></div><i style="font-family: 'times new roman', times, serif; font-size: large; "> <div style="text-align: left; " align="justify"><br /></div></i> <div style="text-align: center; " align="justify"><font size="4" face="times new roman, times, serif"><i><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mtable columnalign="left" rowspacing="0"Ā»Ā«mtrĀ»Ā«mtdĀ»Ā«mfracĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»fĀ«/miĀ»Ā«/mrowĀ»Ā«mrowĀ»Ā«miĀ»dĀ«/miĀ»Ā«miĀ»xĀ«/miĀ»Ā«/mrowĀ»Ā«/mfracĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»#p1Ā«/miĀ»Ā«miĀ»#opr4Ā«/miĀ»Ā«miĀ»#p2Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»+Ā«/moĀ»Ā«miĀ»#p3Ā«/miĀ»Ā«miĀ»#opr6Ā«/miĀ»Ā«miĀ»#p4Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»#desĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mtdĀ»Ā«/mtrĀ»Ā«mtrĀ»Ā«mtd/Ā»Ā«/mtrĀ»Ā«/mtableĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></i></font> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: left; " align="justify"><font size="4" face="times new roman, times, serif"><i>Para que este producto sea #des 0 se debe cumplir que ambos factores sean de #comentario signo, es decir:</i></font></div><font size="4" face="times new roman, times, serif"><i> <div style="text-align: center; " align="justify"><br /></div></i></font><font size="4" face="times new roman, times, serif"> <div style="text-align: center; " align="justify"><br /></div></font> <div style="text-align: center; " align="justify"><font size="4" face="times new roman, times, serif"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mfenced close="]" open="["Ā»Ā«mrowĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s1Ā«/miĀ»Ā«miĀ»#opr4Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des1Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s2Ā«/miĀ»Ā«miĀ»#opr6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des2Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mrowĀ»Ā«/mfencedĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></font> <div style="text-align: center; " align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«miĀ»#opĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></div> <div style="text-align: center; " align="justify"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«mfenced close="]" open="["Ā»Ā«mrowĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s1Ā«/miĀ»Ā«miĀ»#opr4Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des3Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#s2Ā«/miĀ»Ā«miĀ»#opr6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«miĀ»#des4Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«mnĀ»0Ā«/mnĀ»Ā«/mrowĀ»Ā«/mfencedĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></div> <div style="text-align: left; " align="justify"><i style="font-family: 'times new roman', times, serif; font-size: large; "><font size="4">Resolviendo cada inecuaciĆ³n:</font></i></div><span style="font-family: 'times new roman', times, serif; font-size: large; "> <div style="text-align: center; " align="justify"><br /></div></span> <div style="text-align: center; " align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large; "><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des1Ā«/miĀ»Ā«miĀ»#r4Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des2Ā«/miĀ»Ā«miĀ»#r6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»#opĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des3Ā«/miĀ»Ā«miĀ»#r4Ā«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§#8743;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«miĀ»#des4Ā«/miĀ»Ā«miĀ»#r6Ā«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></span> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: left; " align="justify"><i style="font-family: 'times new roman', times, serif; font-size: large; "><font size="4">Escribiendo como intervalos:</font></i></div><i style="font-family: 'times new roman', times, serif; font-size: large; "> <div style="text-align: center; " align="justify"></div></i> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: center; " align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large; "><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«moĀ»(Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in1Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in2Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»Ā§#8745;Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in3Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in4Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«miĀ»#cjĀ«/miĀ»Ā«moĀ»Ā§nbsp;Ā«/moĀ»Ā«moĀ»(Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in5Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in6Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»Ā§#8745;Ā«/moĀ»Ā«moĀ»]Ā«/moĀ»Ā«miĀ»#in7Ā«/miĀ»Ā«moĀ»,Ā«/moĀ»Ā«miĀ»#in8Ā«/miĀ»Ā«moĀ»[Ā«/moĀ»Ā«moĀ»)Ā«/moĀ»Ā«/mathĀ»</span></span></span></span></span></span><br /></span><span style="font-family: 'times new roman', times, serif; font-size: large; "> <div style="text-align: center; " align="justify"><br /></div></span> <div style="text-align: left; " align="justify"><span style="font-family: 'times new roman', times, serif; font-size: large; "><i><font size="4">Resolviendo, obtenemos</font>:</i></span></div><span style="font-family: 'times new roman', times, serif; font-size: large; "><em></em></span> <div style="text-align: left; " align="justify"><br /></div> <div style="text-align: center; " align="justify"> <table style="text-align: center; " border="1" width="100%"><tbody> <tr> <td valign="top" width="100%"><i style="text-align: center; font-family: 'times new roman', times, serif; font-size: large; ">x#pert#r1#r2#r3#r4#r5#r6#r7</i> </td> </tr></tbody> </table></div> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: left; " align="justify"><font size="4" face="times new roman,times,serif"><i>Observemos el grĆ”fico de <span class="nolink">Ā«math xmlns="http://www.w3.org/1998/Math/MathML"Ā»Ā«miĀ»fĀ«/miĀ»Ā«moĀ»(Ā«/moĀ»Ā«miĀ»xĀ«/miĀ»Ā«moĀ»)Ā«/moĀ»Ā«moĀ»=Ā«/moĀ»Ā«miĀ»#fĀ«/miĀ»Ā«/mathĀ»</span></i></font><br /></div> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: center; " align="justify"><br /></div> <div style="text-align: center; " align="justify">#t1</div> <div style="text-align: center; " align="justify"><font face="times new roman,times,serif"><font size="4"><i>Si observas el grĆ”fico, en rojo estĆ” marcada la parte #cr, que coincide con el resultado obtenido.</i><br /></font></font></div></div></div></div></div></div>
One or multiple answers?
Multiple answers allowed
One answer only
Shuffle the choices?
Number the choices?
a., b., c., ...
A., B., C., ...
1., 2., 3., ...
i., ii., iii., ...
I., II., III., ...
No numbering
WIRIS variables
Algorithm
Choice 1
Answer
#x1#pert#r1#r2#r3#r4#r5#r6#r7
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%
-5%
-10%
-11.11111%
-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
<div style="text-align: left; " align="left"><font size="4"><i><font face="times new roman,times,serif">Ā”Excelente!</font> </i></font></div>
Choice 2
Answer
#x1#pert#w1#w2#w3#w4#w5#w6#w7
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%
-5%
-10%
-11.11111%
-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
<div style="text-align: left; "><i><font size="4"></font></i></div> <div style="text-align: left; " align="left"><i><font size="4" face="times new roman,times,serif">Revisa el desarrollo para identificar tus errores.</font></i></div>
Choice 3
Answer
#x1#pert#q1#q2#q3#q4#q5
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%
-5%
-10%
-11.11111%
-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
<div style="text-align: left; "><i><font size="4"> <div style="text-align: left; "><i><font size="4" face="times new roman,times,serif">Revisa el desarrollo para identificar tus errores.</font></i></div></font></i></div>
Choice 4
Answer
#x1#pert#k1#k2#k3#k4#k5
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%
-5%
-10%
-11.11111%
-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
<div style="text-align: left; "><i><font size="4"> <div style="text-align: left; "><i><font size="4" face="times new roman,times,serif">Revisa el desarrollo para identificar tus errores.</font></i></div></font></i></div>
Choice 5
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%
-5%
-10%
-11.11111%
-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
Choice 6
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%
-5%
-10%
-11.11111%
-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
Choice 7
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%
-5%
-10%
-11.11111%
-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
Combined feedback
For any correct response
For any partially correct response
Options
Show the number of correct responses once the question has finished
For any incorrect response
Settings for multiple tries
Penalty for each incorrect try
100%
50%
33.33333%
25%
20%
10%
0%
Hint 1
Hint text
Options
Clear incorrect responses
Show the number of correct responses
Hint 2
Hint text
Options
Clear incorrect responses
Show the number of correct responses
Created / last saved
Created
by
Admin User
on
Friday, 23 August 2013, 3:10 PM
Last saved
by
Admin User
on
Friday, 23 August 2013, 3:10 PM
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