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Exam 14: Section 4: Multiple Integration

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Find the mass of the lamina bounded by the graphs of the equations Find the mass of the lamina bounded by the graphs of the equations for the density . for the density Find the mass of the lamina bounded by the graphs of the equations for the density . .

Free
(Multiple Choice)
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Question 1
Correct Answer:
Verified

C

Find the mass of the triangular lamina with vertices Find the mass of the triangular lamina with vertices for the density . for the density Find the mass of the triangular lamina with vertices for the density . .

Free
(Multiple Choice)
4.8/5
(34)
Question 2
Correct Answer:
Verified

C

Find the center of mass of the lamina bounded by the graphs of the equations Find the center of mass of the lamina bounded by the graphs of the equations for the density . for the density Find the center of mass of the lamina bounded by the graphs of the equations for the density . .

Free
(Multiple Choice)
4.9/5
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Question 3
Correct Answer:
Verified

B

Determine the location of the horizontal axis 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. 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 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. is 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. where 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. is the y-coordinate of the centroid of the gate, 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. is the moment of inertia of the gate about the line 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. , h is the depth of the centroid below the surface, and A is the area of the gate. 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. 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.

(Multiple Choice)
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Question 4

Find the center of mass of the lamina bounded by the graphs of the equations Find the center of mass of the lamina bounded by the graphs of the equations for the density . for the density Find the center of mass of the lamina bounded by the graphs of the equations for the density . .

(Multiple Choice)
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(25)
Question 5

Find the mass of the lamina bounded by the graphs of the equations Find the mass of the lamina bounded by the graphs of the equations for the density . for the density Find the mass of the lamina bounded by the graphs of the equations for the density . .

(Multiple Choice)
4.9/5
(33)
Question 6

Find the center of mass of the rectangular lamina with vertices Find the center of mass of the rectangular lamina with vertices for the density . for the density Find the center of mass of the rectangular lamina with vertices for the density . .

(Multiple Choice)
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(36)
Question 7

Determine the location of the horizontal axis 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. 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 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. is 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. where 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. is the y-coordinate of the centroid of the gate, 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. is the moment of inertia of the gate about the line 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. , h is the depth of the centroid below the surface, and A is the area of the gate. 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. 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.

(Multiple Choice)
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(33)
Question 8

Set up the double integral required to find the moment of inertia I, about the line 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. of the lamina bounded by the graphs of the equations 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. for the density 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. . Use a computer algebra system to evaluate the double integral.

(Multiple Choice)
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Question 9

Find the mass of the lamina described by the inequalities 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.) given that its density is 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.) . (Hint: Some of the integrals are simpler in polar coordinates.)

(Multiple Choice)
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(31)
Question 10

Find the mass of the triangular lamina with vertices Find the mass of the triangular lamina with vertices for the density . for the density Find the mass of the triangular lamina with vertices for the density . .

(Multiple Choice)
4.9/5
(32)
Question 11

Find the mass of the lamina bounded by the graphs of the equations Find the mass of the lamina bounded by the graphs of the equations for the density . for the density Find the mass of the lamina bounded by the graphs of the equations for the density . .

(Multiple Choice)
4.9/5
(35)
Question 12

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. 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.

(Multiple Choice)
4.9/5
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Question 13

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. 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.

(Multiple Choice)
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Question 14

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. 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.

(Multiple Choice)
4.9/5
(30)
Question 15

Find the mass of the lamina described by the inequalities 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.) given that its density is 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.) . (Hint: Some of the integrals are simpler in polar coordinates.)

(Multiple Choice)
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Question 16

Find the center of mass of the lamina bounded by the graphs of the equations Find the center of mass of the lamina bounded by the graphs of the equations for the density . for the density Find the center of mass of the lamina bounded by the graphs of the equations for the density . .

(Multiple Choice)
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Question 17

Find the center of mass of the rectangular lamina with vertices Find the center of mass of the rectangular lamina with vertices and for the density . and Find the center of mass of the rectangular lamina with vertices and for the density . for the density Find the center of mass of the rectangular lamina with vertices and for the density . .

(Multiple Choice)
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Question 18
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