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<i><font size="4" face="times new roman,times,serif">Determinar el o los intervalos donde la función <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math»</span></span></span></span></span></span></span></span> </span></span>es <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#c«/mi»«/math»</span></span></span></span></span></span></span></span></span></span>:</font></i>
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<div><font size="4"><i><font face="times new roman,times,serif">Solución</font><font face="times new roman,times,serif">:</font></i></font></div><br /> <div align="justify"><em><font size="4" face="Times New Roman"></font></em></div> <div align="justify"><em><font size="4" face="Times New Roman"></font></em></div> <div align="justify"><em><font size="4" face="Times New Roman"></font></em></div> <div align="justify"></div> <div align="justify"><em><font size="4" face="Times New Roman"></font></em></div><font face="times new roman,times,serif"><i> <div align="justify"><font size="4"></font></div> <div align="justify"><font size="4">Para resolver, debemos recordar lo siguiente:<br /><br /></font></div> <div align="justify"><font size="4"></font></div> <div align="justify"><font size="4"></font></div> <div align="justify"><font size="4"></font></div> <div align="justify"><font size="4"></font></div> <div align="justify"> <p align="justify"><em><font size="4">Sea <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span> una función derivable en su dominio:</font></em></p> <p align="justify"><em><font size="4">- Si <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">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»#h«/mi»«mo»§nbsp;«/mo»«mn»0«/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> en <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">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»]«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»[«/mo»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>, se tiene que <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span> es #c en </span></span></span></font></em><font face="times new roman,times,serif"><i><em><font size="4"><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">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»]«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»[«/mo»«/math»</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></font></em></i></font></p></div> <div align="justify"></div> <div align="justify"></div></i></font><font size="4" face="times new roman,times,serif"><i> <div align="justify"><font face="times new roman, times, serif"><i><font size="4"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">Por lo tanto, nuestra función <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math»</span> será <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#c«/mi»«/math»</span> si </span></span></span></span></font></i></font><font face="times new roman, times, serif"><i><font size="4"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"> <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»#h«/mi»«/math»</span></span></span></span></span></span></span></span></span></span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mn»0«/mn»«/math»</span></font></i></font></div> <div align="justify"><font size="4" face="times new roman, times, serif"><i>Para obtener <span style="text-align: center; "></span><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/math»</span></span></span></span></span></span></span></span></span></span> utilizamos la regla de la derivada del cuociente (división) de funciones:</i></font></div><font size="4" face="times new roman, times, serif"><i> <div><br /></div></i></font> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mfrac»«mrow»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»·«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»·«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«msup»«mfenced»«mrow»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»</span></span></span></span></span></span></span></span></span></span><br /></i></font></div> <div><font size="4" face="times new roman, times, serif"><i>Si <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f1«/mi»«/math»</span></span></span></span></span></span></span></span></span></span> y <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f2«/mi»«/math»</span></span></span></span></span></span></span></span></span></span>, reemplazamos en nuestra fórmula:</i></font></div> <div><font size="4" face="times new roman, times, serif"><i><br /></i></font></div> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mfenced»«mi»#f«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#f1«/mi»«mo»)«/mo»«mo»·«/mo»«mo»(«/mo»«mi»#f2«/mi»«mo»)«/mo»«mo»-«/mo»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»(«/mo»«mi»#f2«/mi»«mo»)«/mo»«mo»·«/mo»«mo»(«/mo»«mi»#f1«/mi»«mo»)«/mo»«/mrow»«msup»«mfenced»«mi»#f2«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»</span></span></span></span></span></span></span></span></span></span></i></font></div> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mfrac»«mrow»«mo»(«/mo»«mi»#f11«/mi»«mo»)«/mo»«mo»·«/mo»«mo»(«/mo»«mi»#f2«/mi»«mo»)«/mo»«mo»-«/mo»«mo»(«/mo»«mi»#f22«/mi»«mo»)«/mo»«mo»(«/mo»«mi»#f1«/mi»«mo»)«/mo»«/mrow»«msup»«mfenced»«mi»#f2«/mi»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»</span></span></span></span></span></span></span></span></span></span></i></font></div> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mfrac»«mrow»«mi»#g1«/mi»«/mrow»«msup»«mfenced»«mrow»«mi»#f2«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»</span></span></span></span></span></span></span></span></span></span><br /></i></font></div> <div><font size="4" face="times new roman, times, serif"><i>Por lo tanto,</i></font></div> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»#g1«/mi»«/mrow»«msup»«mfenced»«mrow»«mi»#f2«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/math»</span></span></span></span></span></span></span></span></span></span></i></font></div> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"></span></span></span></span></span></span></span></span></i></font></div> <div><font size="4" face="times new roman, times, serif"><i>Ahora, notemos que <span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«msup»«mfenced»«mrow»«mi»#f2«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»</span></span></span></span></span></span></span></span></span></span> siempre es mayor que <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mn»0«/mn»«/math»</span> <br />o sea, <br /></i></font></div> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mrow»«mi»#g1«/mi»«/mrow»«msup»«mfenced»«mrow»«mi»#f2«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mi»#h«/mi»«/math»</span></span></span></span></span></span></span></span></span></span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mn»0«/mn»«/math»</span></i></font></div> <div><font size="4" face="times new roman, times, serif"><i>si: </i></font></div> <div style="text-align: center; "><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"><span class="nolink"><span class="nolink"><span class="nolink"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#g1«/mi»«mi»#h«/mi»«/math»</span></span></span></span></span></span></span></span></span></span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mn»0«/mn»«/math»</span></i></font></div> <div><font size="4" face="times new roman, times, serif"><i>Resolviendo la inecuación tenemos que</i></font></div> <div><font size="4" face="times new roman, times, serif"><i><br /></i></font></div> <div style="text-align: center; "><font size="4" face="times new roman, times, serif"><i><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«mo»§#8712;«/mo»«mi»#n1«/mi»«mi»#k1«/mi»«mi»#kk«/mi»«mi»#k2«/mi»«mi»#n2«/mi»«mi»#n5«/mi»«mi»#n3«/mi»«mi»#k3«/mi»«mi»#kk2«/mi»«mi»#k4«/mi»«mi»#n4«/mi»«/math»</span></i></font></div> <div><font size="4" face="times new roman, times, serif"><i>En consecuencia, <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math»</span> es <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#c«/mi»«/math»</span> cuando:</i></font></div> <div><font size="4" face="times new roman, times, serif"><i><br /></i></font></div> <div style="text-align: center; "><font size="4" face="times new roman, times, serif"><i><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«mo»§#8712;«/mo»«mi»#n1«/mi»«mi»#k1«/mi»«mi»#kk«/mi»«mi»#k2«/mi»«mi»#n2«/mi»«mi»#n5«/mi»«mi»#n3«/mi»«mi»#k3«/mi»«mi»#kk2«/mi»«mi»#k4«/mi»«mi»#n4«/mi»«/math»</span></i></font></div> <div style="text-align: left; "><font size="4" face="times new roman, times, serif"><i><br />Como podemos apreciar en la gráfica, <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»h«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math»</span> es #c en el tramo de color rojo.</i></font></div> <div style="text-align: left; "><font size="4" face="times new roman, times, serif"><i><br /></i></font></div> <div style="text-align: center; ">#g6</div></i></font>
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WIRIS variables
Algorithm
Choice 1
Answer
#n1#k1#kk#k2#n2#n5#n3#k3#kk2#k4#n4
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
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16.66667%
14.28571%
12.5%
11.11111%
10%
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Feedback
<p align="justify"><span style="text-align: justify; font-style: italic; font-family: 'times new roman', times, serif; font-size: large; "><font size="4">¡Muy Bien! Sigue asÃ.</font></span> </p>
Choice 2
Answer
#n11#k11#kkk#k22#n22#n55#n33#k33#kkk2#k44#n44
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
25%
20%
16.66667%
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12.5%
11.11111%
10%
5%
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Feedback
<font style="font-style: italic; font-family: 'times new roman', times, serif; " size="4">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</font>
Choice 3
Answer
#par1#valor1#com1#valor2#par2
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%
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-14.28571%
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Feedback
<font style="font-style: italic; font-family: 'times new roman', times, serif; " size="4">Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</font>
Choice 4
Answer
#par11#valor11#com11#valor22#par22
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%
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-12.5%
-14.28571%
-16.66667%
-20%
-25%
-30%
-33.33333%
-40%
-50%
-60%
-66.66667%
-70%
-75%
-80%
-83.33333%
-90%
-100%
Feedback
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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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