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Use a change of variables to find the volume of the solid region lying below the surface Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places. A) B) C) D) E) and above the plane region R: region bounded by the parallelogram with vertices Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places. A) B) C) D) E) . Round your answer to two decimal places.


A) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places. A) B) C) D) E)
B) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places. A) B) C) D) E)
C) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places. A) B) C) D) E)
D) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places. A) B) C) D) E)
E) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places. A) B) C) D) E)

Correct Answer

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Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below. Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below. A) B) C) D) E)


A) Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below. A) B) C) D) E)
B) Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below. A) B) C) D) E)
C) Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below. A) B) C) D) E)
D) Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below. A) B) C) D) E)
E) Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below. A) B) C) D) E)

Correct Answer

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Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder . A) B) C) D) E) but outside the cylinder Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder . A) B) C) D) E) .


A) Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder . A) B) C) D) E)
B) Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder . A) B) C) D) E)
C) Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder . A) B) C) D) E)
D) Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder . A) B) C) D) E)
E) Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder . A) B) C) D) E)

Correct Answer

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Evaluate the following iterated integral. Evaluate the following iterated integral. A) B) C) D) E)


A) Evaluate the following iterated integral. A) B) C) D) E)
B) Evaluate the following iterated integral. A) B) C) D) E)
C) Evaluate the following iterated integral. A) B) C) D) E)
D) Evaluate the following iterated integral. A) B) C) D) E)
E) Evaluate the following iterated integral. A) B) C) D) E)

Correct Answer

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Use a change of variables to find the volume of the solid region lying below the surface Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the graphs of (Hint: Let .) Round your answer to two decimal places. A) 5.13 B) 21.35 C) 3.56 D) 5.13. E) 42.70 and above the plane region R: region bounded by the graphs of Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the graphs of (Hint: Let .) Round your answer to two decimal places. A) 5.13 B) 21.35 C) 3.56 D) 5.13. E) 42.70 (Hint: Let Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the graphs of (Hint: Let .) Round your answer to two decimal places. A) 5.13 B) 21.35 C) 3.56 D) 5.13. E) 42.70 .) Round your answer to two decimal places.


A) 5.13
B) 21.35
C) 3.56
D) 5.13.
E) 42.70

Correct Answer

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Find the mass of the lamina described by the inequalities Find the mass of the lamina described by the inequalities and , given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) A) B) C) D) E) and Find the mass of the lamina described by the inequalities and , 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 Find the mass of the lamina described by the inequalities and , given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) A) B) C) D) E) . (Hint: Some of the integrals are simpler in polar coordinates.)


A) Find the mass of the lamina described by the inequalities and , given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) A) B) C) D) E)
B) Find the mass of the lamina described by the inequalities and , given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) A) B) C) D) E)
C) Find the mass of the lamina described by the inequalities and , given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) A) B) C) D) E)
D) Find the mass of the lamina described by the inequalities and , given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) A) B) C) D) E)
E) Find the mass of the lamina described by the inequalities and , given that its density is . (Hint: Some of the integrals are simpler in polar coordinates.) A) B) C) D) E)

Correct Answer

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A

Evaluate the double integral below. Evaluate the double integral below. A) B) 0 C) D) E)


A) Evaluate the double integral below. A) B) 0 C) D) E)
B) 0
C) Evaluate the double integral below. A) B) 0 C) D) E)
D) Evaluate the double integral below. A) B) 0 C) D) E)
E) Evaluate the double integral below. A) B) 0 C) D) E)

Correct Answer

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Set up a triple integral that gives the moment of inertia about the Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below. ​ ​ A) ​ ​ B) ​ ​ C) ​ ​ D) ​ ​ E) ​ ​ -axis of the solid region Q of density given below. ​ Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below. ​ ​ A) ​ ​ B) ​ ​ C) ​ ​ D) ​ ​ E) ​ ​ ​


A) Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below. ​ ​ A) ​ ​ B) ​ ​ C) ​ ​ D) ​ ​ E) ​ ​ ​
​
B) Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below. ​ ​ A) ​ ​ B) ​ ​ C) ​ ​ D) ​ ​ E) ​ ​ ​
​
C) Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below. ​ ​ A) ​ ​ B) ​ ​ C) ​ ​ D) ​ ​ E) ​ ​ ​
​
D) Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below. ​ ​ A) ​ ​ B) ​ ​ C) ​ ​ D) ​ ​ E) ​ ​ ​
​
E) Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below. ​ ​ A) ​ ​ B) ​ ​ C) ​ ​ D) ​ ​ E) ​ ​ ​
​

Correct Answer

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Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E)


A) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E)
B) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E)
C) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E)
D) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E)
E) Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R. A) B) C) D) E)

Correct Answer

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Evaluate the iterated integral Evaluate the iterated integral by switching the order of integration. Round your to three decimal places. ​ A) 0.056 B) 0.076 C) 36.056 D) 4.056 E) 3.056 by switching the order of integration. Round your to three decimal places. ​


A) 0.056
B) 0.076
C) 36.056
D) 4.056
E) 3.056

Correct Answer

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A

Use a change of variables to find the volume of the solid region lying below the surface Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices . A) B) C) D) E) and above the plane region R: region bounded by the square with vertices Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices . A) B) C) D) E) .


A) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices . A) B) C) D) E)
B) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices . A) B) C) D) E)
C) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices . A) B) C) D) E)
D) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices . A) B) C) D) E)
E) Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices . A) B) C) D) E)

Correct Answer

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Find the mass of the triangular lamina with vertices Find the mass of the triangular lamina with vertices for the density . ​ A) 11,337,408k B) 22,674,826k C) 11,337,398k D) 11,337,413k E) 22,674,816k for the density Find the mass of the triangular lamina with vertices for the density . ​ A) 11,337,408k B) 22,674,826k C) 11,337,398k D) 11,337,413k E) 22,674,816k . ​


A) 11,337,408k
B) 22,674,826k
C) 11,337,398k
D) 11,337,413k
E) 22,674,816k

Correct Answer

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Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations and in the first octant. A) 273,375 B) 30,375 C) 182,250 D) 91,125 E) 60,750 and Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations and in the first octant. A) 273,375 B) 30,375 C) 182,250 D) 91,125 E) 60,750 in the first octant.


A) 273,375
B) 30,375
C) 182,250
D) 91,125
E) 60,750

Correct Answer

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Use cylindrical coordinates to find the volume of the solid inside both Use cylindrical coordinates to find the volume of the solid inside both and . ​ A) ​ B) ​ C) D) E) and Use cylindrical coordinates to find the volume of the solid inside both and . ​ A) ​ B) ​ C) D) E) . ​


A) Use cylindrical coordinates to find the volume of the solid inside both and . ​ A) ​ B) ​ C) D) E) ​
B) Use cylindrical coordinates to find the volume of the solid inside both and . ​ A) ​ B) ​ C) D) E) ​
C) Use cylindrical coordinates to find the volume of the solid inside both and . ​ A) ​ B) ​ C) D) E)
D) Use cylindrical coordinates to find the volume of the solid inside both and . ​ A) ​ B) ​ C) D) E)
E) Use cylindrical coordinates to find the volume of the solid inside both and . ​ A) ​ B) ​ C) D) E)

Correct Answer

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Use an iterated integral to find the area of the region shown in the figure below. Use an iterated integral to find the area of the region shown in the figure below. A) B) C) D) E)


A) Use an iterated integral to find the area of the region shown in the figure below. A) B) C) D) E)
B) Use an iterated integral to find the area of the region shown in the figure below. A) B) C) D) E)
C) Use an iterated integral to find the area of the region shown in the figure below. A) B) C) D) E)
D) Use an iterated integral to find the area of the region shown in the figure below. A) B) C) D) E)
E) Use an iterated integral to find the area of the region shown in the figure below. A) B) C) D) E)

Correct Answer

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Write a double integral that represents the surface area of Write a double integral that represents the surface area of over the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​ A) B) C) D) E) over the region R: triangle with vertices Write a double integral that represents the surface area of over the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​ A) B) C) D) E) . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​


A) Write a double integral that represents the surface area of over the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​ A) B) C) D) E)
B) Write a double integral that represents the surface area of over the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​ A) B) C) D) E)
C) Write a double integral that represents the surface area of over the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​ A) B) C) D) E)
D) Write a double integral that represents the surface area of over the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​ A) B) C) D) E)
E) Write a double integral that represents the surface area of over the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. ​ A) B) C) D) E)

Correct Answer

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B

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 . ​ A) B) C) D) E) for the density Find the center of mass of the lamina bounded by the graphs of the equations for the density . ​ A) B) C) D) E) . ​


A) Find the center of mass of the lamina bounded by the graphs of the equations for the density . ​ A) B) C) D) E)
B) Find the center of mass of the lamina bounded by the graphs of the equations for the density . ​ A) B) C) D) E)
C) Find the center of mass of the lamina bounded by the graphs of the equations for the density . ​ A) B) C) D) E)
D) Find the center of mass of the lamina bounded by the graphs of the equations for the density . ​ A) B) C) D) E)
E) Find the center of mass of the lamina bounded by the graphs of the equations for the density . ​ A) B) C) D) E)

Correct Answer

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Use a triple integral to find the volume of the solid bounded by the graphs of the equations Use a triple integral to find the volume of the solid bounded by the graphs of the equations . A) B) C) D) E) .


A) Use a triple integral to find the volume of the solid bounded by the graphs of the equations . A) B) C) D) E)
B) Use a triple integral to find the volume of the solid bounded by the graphs of the equations . A) B) C) D) E)
C) Use a triple integral to find the volume of the solid bounded by the graphs of the equations . A) B) C) D) E)
D) Use a triple integral to find the volume of the solid bounded by the graphs of the equations . A) B) C) D) E)
E) Use a triple integral to find the volume of the solid bounded by the graphs of the equations . A) B) C) D) E)

Correct Answer

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Evaluate the iterated integral Evaluate the iterated integral . A) B) C) D) E) .


A) Evaluate the iterated integral . A) B) C) D) E)
B) Evaluate the iterated integral . A) B) C) D) E)
C) Evaluate the iterated integral . A) B) C) D) E)
D) Evaluate the iterated integral . A) B) C) D) E)
E) Evaluate the iterated integral . A) B) C) D) E)

Correct Answer

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Use a double integral to find the volume of the indicated solid. Use a double integral to find the volume of the indicated solid. A) 16 B) 9 C) 4 D) 20 E) 6


A) 16
B) 9
C) 4
D) 20
E) 6

Correct Answer

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