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Deck 14: Section 4: Multiple Integration
ملء الشاشة (f)
سؤال
Set up the double integral required to find the moment of inertia I, about the line 
of the lamina bounded by the graphs of the equations 
for the density 
. Use a computer algebra system to evaluate the double integral.
A)
B)
C)
D)
E)
of the lamina bounded by the graphs of the equations for the density . Use a computer algebra system to evaluate the double integral.A)
B)
C)
D)
E)
سؤال
Find the mass of the lamina described by the inequalities 
given that its density is 
. (Hint: Some of the integrals are simpler in polar coordinates.)
A)
B)
C)
D)
E)
given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)A)
B)
C)
D)
E)
سؤال
Set up and evaluate a double integral required to find the moment of inertia, I, about the given line, of the lamina bounded by the graphs of the following equations. Use a computer algebra system to evaluate the double integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the location of the horizontal axis 
for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for 
is 
where 
is the y-coordinate of the centroid of the gate, 
is the moment of inertia of the gate about the line 
, h is the depth of the centroid below the surface, and A is the area of the gate. 
A)
B)
C)
D)
E)
for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for is where is the y-coordinate of the centroid of the gate, is the moment of inertia of the gate about the line , h is the depth of the centroid below the surface, and A is the area of the gate. A)
B)
C)
D)
E)
سؤال
Find the center of mass of the lamina bounded by the graphs of the equations 
for the density 
.
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
سؤال
Find the center of mass of the rectangular lamina with vertices 
for the density 
.
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
سؤال
Find the mass of the lamina bounded by the graphs of the equations 
for the density 
.
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
سؤال
Find the center of mass of the rectangular lamina with vertices 
and 
for the density 
.
A)
B)
C)
D)
E)
and for the density .A)
B)
C)
D)
E)
سؤال
Find the mass and moments of inertia of the lamina, with given density, bounded by the graphs of the equations given below and use them to find the radii of gyration about the axes. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the location of the horizontal axis 
for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for 
is 
where 
is the y-coordinate of the centroid of the gate, 
is the moment of inertia of the gate about the line 
, h is the depth of the centroid below the surface, and A is the area of the gate. 
A)
B)
C)
D)
E)
for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for is where is the y-coordinate of the centroid of the gate, is the moment of inertia of the gate about the line , h is the depth of the centroid below the surface, and A is the area of the gate. A)
B)
C)
D)
E)
سؤال
Find the mass of the lamina bounded by the graphs of the equations 
for the density 
.
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
سؤال
Find the mass of the triangular lamina with vertices 
for the density 
.
A) 401k
B) 809k
C) 800k
D) 400k
E) 805k
for the density .A) 401k
B) 809k
C) 800k
D) 400k
E) 805k
سؤال
Find the center of mass of the lamina bounded by the graphs of the equations 
for the density 
.
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
سؤال
Find the center of mass of the lamina bounded by the graphs of the equations 
for the density 
.
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
سؤال
Find the mass of the triangular lamina with vertices 
for the density 
.
A) 139,968k
B) 279,946k
C) 139,958k
D) 139,973k
E) 279,936k
for the density .A) 139,968k
B) 279,946k
C) 139,958k
D) 139,973k
E) 279,936k
سؤال
Find the mass and moments of inertia of the lamina, of given density, bounded by the graphs of the equations given below and use them to find the radii of gyration about the axes. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the mass of the lamina described by the inequalities 
given that its density is 
. (Hint: Some of the integrals are simpler in polar coordinates.)
A) 768
B) 128
C) 512
D) 256
E) 392
given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)A) 768
B) 128
C) 512
D) 256
E) 392
سؤال
Find the mass of the lamina bounded by the graphs of the equations 
for the density 
.
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
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العب
ملء الشاشة (f)
Deck 14: Section 4: Multiple Integration
1
Set up the double integral required to find the moment of inertia I, about the line of the lamina bounded by the graphs of the equations for the density . Use a computer algebra system to evaluate the double integral.
A)
B)
C)
D)
E)
of the lamina bounded by the graphs of the equations for the density . Use a computer algebra system to evaluate the double integral.A)
B)
C)
D)
E)
2
Find the mass of the lamina described by the inequalities given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)
A)
B)
C)
D)
E)
given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)A)
B)
C)
D)
E)
3
Set up and evaluate a double integral required to find the moment of inertia, I, about the given line, of the lamina bounded by the graphs of the following equations. Use a computer algebra system to evaluate the double integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Determine the location of the horizontal axis for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for is where is the y-coordinate of the centroid of the gate, is the moment of inertia of the gate about the line , h is the depth of the centroid below the surface, and A is the area of the gate.
A)
B)
C)
D)
E)
for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for is where is the y-coordinate of the centroid of the gate, is the moment of inertia of the gate about the line , h is the depth of the centroid below the surface, and A is the area of the gate. A)
B)
C)
D)
E)
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5
Find the center of mass of the lamina bounded by the graphs of the equations for the density .
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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6
Find the center of mass of the rectangular lamina with vertices for the density .
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
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7
Find the mass of the lamina bounded by the graphs of the equations for the density .
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
فتح الحزمة
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8
Find the center of mass of the rectangular lamina with vertices and for the density .
A)
B)
C)
D)
E)
and for the density .A)
B)
C)
D)
E)
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9
Find the mass and moments of inertia of the lamina, with given density, bounded by the graphs of the equations given below and use them to find the radii of gyration about the axes.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Determine the location of the horizontal axis for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for is where is the y-coordinate of the centroid of the gate, is the moment of inertia of the gate about the line , h is the depth of the centroid below the surface, and A is the area of the gate.
A)
B)
C)
D)
E)
for figure (b) at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure (a)). The model for is where is the y-coordinate of the centroid of the gate, is the moment of inertia of the gate about the line , h is the depth of the centroid below the surface, and A is the area of the gate. A)
B)
C)
D)
E)
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k this deck
11
Find the mass of the lamina bounded by the graphs of the equations for the density .
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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12
Find the mass of the triangular lamina with vertices for the density .
A) 401k
B) 809k
C) 800k
D) 400k
E) 805k
for the density .A) 401k
B) 809k
C) 800k
D) 400k
E) 805k
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13
Find the center of mass of the lamina bounded by the graphs of the equations for the density .
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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14
Find the center of mass of the lamina bounded by the graphs of the equations for the density .
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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15
Find the mass of the triangular lamina with vertices for the density .
A) 139,968k
B) 279,946k
C) 139,958k
D) 139,973k
E) 279,936k
for the density .A) 139,968k
B) 279,946k
C) 139,958k
D) 139,973k
E) 279,936k
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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16
Find the mass and moments of inertia of the lamina, of given density, bounded by the graphs of the equations given below and use them to find the radii of gyration about the axes.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
فتح الحزمة
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17
Find the mass of the lamina described by the inequalities given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)
A) 768
B) 128
C) 512
D) 256
E) 392
given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.)A) 768
B) 128
C) 512
D) 256
E) 392
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افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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18
Find the mass of the lamina bounded by the graphs of the equations for the density .
A)
B)
C)
D)
E)
for the density .A)
B)
C)
D)
E)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 18 في هذه المجموعة.
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