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Find the center of mass of a homogeneous solid bounded by the paraboloid and

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Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane .

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Use the transformation to evaluate the integral , where R is the region bounded by the ellipse .

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Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3.

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Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane .

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Use a triple integral to find the volume of the solid bounded by and the planes and .

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Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas .

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Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and

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Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid.

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Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places. R is the parallelogram bounded by the lines .

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Use spherical coordinates to find the volume of the solid that lies within the sphere above the xy-plane and below the cone . Round the answer to two decimal places.

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Use the given transformation to evaluate the integral. , where R is the square with vertices (0, 0), (4, 6), (6, ), (10, 2) and

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Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius and density 1 about a diameter of its base.

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Use spherical coordinates.Evaluate , where is the ball with center the origin and radius .

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