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<div><i>La caja de un camión transportador de granos está siendo llenada con el grano proveniente de un silo a razón de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mfrac»«mrow»«mi»#me«/mi»«/mrow»«mi»#tiempo«/mi»«/mfrac»«/math»</span> .</i></div> <div><i style="font-family: 'times new roman',times,serif; font-size: large;">El grano forma un cono circular recto, cuya altura es constantemente igual a <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#b«/mi»«/math»</span> del radio <span style="text-align: right;">de la bas</span><span style="text-align: right;">e.</span></i></div> <div><i><br></i></div> <div style="text-align: center;"><img title="Arena" alt="Arena" src="http://www.elearning.jmc.usm.cl/file.php/1/RA7_3.3.png" width="397" vspace="0" border="0" hspace="0" height="193"><br></div> <div><br></div> <div><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#pregunta«/mi»«/math»</span></i></div>
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<div><i>Solución:<br><br> <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#enunciado1«/mi»«/math»</span></i></div> <div><i><br></i></div> <div><i><br></i></div> <div style="text-align: center;"><i><img 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" alt="triangulo" title="triangulo" width="243" vspace="0" border="0" hspace="0" height="197"> </i></div> <div style="text-align: justify;"><i>El volumen del cono formado por la arena en un instante <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»t«/mi»«/math»</span>, viene dado por:</i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»V«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«mi»§#960;«/mi»«msup»«mi»R«/mi»«mn»2«/mn»«/msup»«mi»h«/mi»«/math»</span><br></i></div> <div style="text-align: left;"><i>Como <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mo»=«/mo»«mi»#b«/mi»«/math»</span><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mo»§#8658;«/mo»«mi»R«/mi»«mo»=«/mo»«mi»#c«/mi»«/math»</span><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«/math»</span> </i></div> <div style="text-align: justify;"><i>En consecuencia:</i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»V«/mi»«mo»(«/mo»«mi»t«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#e«/mi»«mo»§#183;«/mo»«mi»§#960;«/mi»«mo»§#183;«/mo»«msup»«mi»h«/mi»«mn»3«/mn»«/msup»«/math»</span> (1) con <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mo»=«/mo»«mi»h«/mi»«mo»(«/mo»«mi»t«/mi»«mo»)«/mo»«/math»</span><br></i></div> <div style="text-align: center;"><i>Derivando la expresión (1) respecto a <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»t«/mi»«/math»</span> y buscando <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span> obtenemos:</i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»V«/mi»«mo»(«/mo»«mi»t«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#f«/mi»«mo»§#183;«/mo»«mi»§#960;«/mi»«msup»«mi»h«/mi»«mn»2«/mn»«/msup»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span> (2)</i></div> <div style="text-align: center;"><i><br></i></div> <div style="text-align: justify;"><i>Sabemos que <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»V«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»#a«/mi»«mfrac»«mrow»«mi»#me«/mi»«/mrow»«mi»#tiempo«/mi»«/mfrac»«/math»</span> y <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mo»=«/mo»«mi»#d«/mi»«mi»#m1«/mi»«/math»</span> sustituyendo en (2):</i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mfrac»«mi»#me«/mi»«mi»#tiempo«/mi»«/mfrac»«mo»=«/mo»«mi»#f«/mi»«mo»§#183;«/mo»«mi»§#960;«/mi»«msup»«mfenced»«mrow»«mi»#d«/mi»«mi»#m1«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span><span style="text-align: center;"> </span></i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mfrac»«mi»#me«/mi»«mi»#tiempo«/mi»«/mfrac»«mo»=«/mo»«mi»#f«/mi»«mo»§#183;«/mo»«mi»§#960;«/mi»«mi»#g«/mi»«msup»«mi»#m1«/mi»«mn»2«/mn»«/msup»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span> </i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«mfrac»«mi»#me«/mi»«mi»#tiempo«/mi»«/mfrac»«mo»=«/mo»«mi»#h1«/mi»«mo»§#183;«/mo»«mi»§#960;«/mi»«msup»«mi»#m1«/mi»«mn»2«/mn»«/msup»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span> </i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#i«/mi»«mo»·«/mo»«mi»#a«/mi»«mo»·«/mo»«mfrac»«mn»1«/mn»«mi»§#960;«/mi»«/mfrac»«mfrac»«mn»1«/mn»«msup»«mi»#m1«/mi»«mn»2«/mn»«/msup»«/mfrac»«mfrac»«mrow»«mi»#me«/mi»«/mrow»«mi»#tiempo«/mi»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span> </i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#j«/mi»«mfrac»«mn»1«/mn»«mi»§#960;«/mi»«/mfrac»«mfrac»«mi»#m1«/mi»«mrow»«mi»#tiempo«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span> </i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»#nj«/mi»«mrow»«mi»#dj«/mi»«mo»·«/mo»«mi»§#960;«/mi»«/mrow»«/mfrac»«mfrac»«mi»#m1«/mi»«mrow»«mi»#tiempo«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»</span> </i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»d«/mi»«mi»h«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»t«/mi»«/mrow»«/mfrac»«mo»§#8776;«/mo»«mi»#k«/mi»«mfrac»«mi»#m1«/mi»«mi»#tiempo«/mi»«/mfrac»«/math»</span> </i></div> <div style="text-align: justify;"><i>Que es la velocidad con la que sube el vértice del cono de grano en el instante en que <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mo»=«/mo»«mi»#d«/mi»«mi»#m1«/mi»«/math»</span></i></div> <div style="text-align: left;"><i><br></i></div> <div style="text-align: left;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#enunciado2«/mi»«/math»</span></i></div> <div style="text-align: justify;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#enunciado3«/mi»«/math»</span></i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#enunciado4«/mi»«/math»</span></i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#enunciado5«/mi»«/math»</span></i></div> <div style="text-align: justify;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#enunciado6«/mi»«/math»</span></i></div> <div style="text-align: center;"><i><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#enunciado7«/mi»«/math»</span></i></div> <div style="text-align: justify;"><span style="text-align: start;"><i><br></i></span></div> <div style="text-align: center;"><br></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
#alt1
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>¡Excelente! Sigue así.</i></div>
Choice 2
Answer
#alt2
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>¡Excelente! Sigue así.</i></div>
Choice 3
Answer
#alt3
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>Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</i></div>
Choice 4
Answer
#alt4
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
<i>Revisa el desarrollo para identificar tus errores. ¡Tú puedes!</i>
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
Wednesday, 15 February 2017, 3:41 PM
Last saved
by
Admin User
on
Wednesday, 15 February 2017, 3:41 PM
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