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Exam 7: Section 6: Applications of Integration

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Set up and evaluate integrals for finding moment about the x-axis for the region bounded by the graphs of the equations. (Assume Set up and evaluate integrals for finding moment about the x-axis for the region bounded by the graphs of the equations. (Assume .) .) Set up and evaluate integrals for finding moment about the x-axis for the region bounded by the graphs of the equations. (Assume .)

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Question 1
Correct Answer:
Verified

A

Find the center of mass of the point masses lying on the x-axis. Find the center of mass of the point masses lying on the x-axis.

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Question 2
Correct Answer:
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E

Consider a beam of length Consider a beam of length feet with a fulcrum x feet from one end as shown in the figure. Two objects weighing 36 pounds and 108 pounds are placed at opposite ends of the beam. Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is equilibrium. feet with a fulcrum x feet from one end as shown in the figure. Two objects weighing 36 pounds and 108 pounds are placed at opposite ends of the beam. Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is equilibrium. Consider a beam of length feet with a fulcrum x feet from one end as shown in the figure. Two objects weighing 36 pounds and 108 pounds are placed at opposite ends of the beam. Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is equilibrium.

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Question 3
Correct Answer:
Verified

D

Set up and evaluate integrals for finding the moment about the y-axis for the region bounded by the graphs of the equations. (Assume Set up and evaluate integrals for finding the moment about the y-axis for the region bounded by the graphs of the equations. (Assume .) . .) Set up and evaluate integrals for finding the moment about the y-axis for the region bounded by the graphs of the equations. (Assume .) . .

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Question 4

Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses.

(Multiple Choice)
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Question 5

Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses.

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Question 6

Use the Theorem of Pappus to find the volume of the solid formed by revolving the region bounded by the graphs of Use the Theorem of Pappus to find the volume of the solid formed by revolving the region bounded by the graphs of about the x-axis. Round your answer to two decimal places. about the x-axis. Round your answer to two decimal places.

(Multiple Choice)
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Question 7

Find the center of mass of the point masses lying on the x-axis. Find the center of mass of the point masses lying on the x-axis.

(Multiple Choice)
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(38)
Question 8

Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses. Find the center of mass of the given system of point masses.

(Multiple Choice)
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Question 9

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

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Question 10

Find Mx, My, and Find M<sub>x</sub>, M<sub>y</sub>, and for the lamina of uniform density bounded by the graphs of the equations . for the lamina of uniform density Find M<sub>x</sub>, M<sub>y</sub>, and for the lamina of uniform density bounded by the graphs of the equations . bounded by the graphs of the equations Find M<sub>x</sub>, M<sub>y</sub>, and for the lamina of uniform density bounded by the graphs of the equations . .

(Multiple Choice)
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Question 11

Consider a beam of length Consider a beam of length feet with a fulcrum x feet from one end as shown in the figure. In order to move a 550-pound object, a person weighing 214 pounds wants to balance it on the beam. Find x (the distance between the person and the fulcrum) such that the system is equilibrium. Round your answer to two decimal places. feet with a fulcrum x feet from one end as shown in the figure. In order to move a 550-pound object, a person weighing 214 pounds wants to balance it on the beam. Find x (the distance between the person and the fulcrum) such that the system is equilibrium. Round your answer to two decimal places. Consider a beam of length feet with a fulcrum x feet from one end as shown in the figure. In order to move a 550-pound object, a person weighing 214 pounds wants to balance it on the beam. Find x (the distance between the person and the fulcrum) such that the system is equilibrium. Round your answer to two decimal places.

(Multiple Choice)
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Question 12

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

(Multiple Choice)
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Question 13

Find the volume of the solid generated by rotating the circle Find the volume of the solid generated by rotating the circle about the y-axis. about the y-axis.

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Question 14

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

(Multiple Choice)
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Question 15

Find the center of mass of the point masses lying on the x-axis. Find the center of mass of the point masses lying on the x-axis.

(Multiple Choice)
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Question 16

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

(Multiple Choice)
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Question 17

Find Mx, My, and Find M<sub>x</sub>, M<sub>y</sub>, and for the lamina of uniform density bounded by the graphs of the equations . for the lamina of uniform density Find M<sub>x</sub>, M<sub>y</sub>, and for the lamina of uniform density bounded by the graphs of the equations . bounded by the graphs of the equations Find M<sub>x</sub>, M<sub>y</sub>, and for the lamina of uniform density bounded by the graphs of the equations . .

(Multiple Choice)
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Question 18

Find the volume of the solid generated by rotating the circle Find the volume of the solid generated by rotating the circle about the x-axis. about the x-axis.

(Multiple Choice)
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Question 19
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