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Evaluate the triple integral.Round your answer to one decimal place. Evaluate the triple integral.Round your answer to one decimal place.

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Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , and Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , ,and having the mass density Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) ,


A) Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , , Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) ,
B) Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , , Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) ,
C) Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , , Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) ,
D) Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) , , Find the mass and the center of mass of the lamina occupying the region R,where R is the triangular region with vertices and ,and having the mass density A) , B) , C) , D) ,

E) B) and C)
F) A) and D)

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Find the volume under Find the volume under and above the region bounded by and . A) B) C) D) E) and above the region bounded by Find the volume under and above the region bounded by and . A) B) C) D) E) and Find the volume under and above the region bounded by and . A) B) C) D) E) .


A) Find the volume under and above the region bounded by and . A) B) C) D) E)
B) Find the volume under and above the region bounded by and . A) B) C) D) E)
C) Find the volume under and above the region bounded by and . A) B) C) D) E)
D) Find the volume under and above the region bounded by and . A) B) C) D) E)
E) Find the volume under and above the region bounded by and . A) B) C) D) E)

F) All of the above
G) A) and B)

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Sketch the solid whose volume is given by the iterated integral Sketch the solid whose volume is given by the iterated integral

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The double integral The double integral ,where ,gives the volume of a solid.Describe the solid. ,where The double integral ,where ,gives the volume of a solid.Describe the solid. ,gives the volume of a solid.Describe the solid.

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The wedge bounded ab...

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Evaluate the integral by reversing the order of integration. Evaluate the integral by reversing the order of integration.

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Evaluate the double integral by first identifying it as the volume of a solid. Evaluate the double integral by first identifying it as the volume of a solid. A) B) C) D) E)


A) Evaluate the double integral by first identifying it as the volume of a solid. A) B) C) D) E)
B) Evaluate the double integral by first identifying it as the volume of a solid. A) B) C) D) E)
C) Evaluate the double integral by first identifying it as the volume of a solid. A) B) C) D) E)
D) Evaluate the double integral by first identifying it as the volume of a solid. A) B) C) D) E)
E) Evaluate the double integral by first identifying it as the volume of a solid. A) B) C) D) E)

F) A) and B)
G) A) and E)

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Use polar coordinates to find the volume of the solid bounded by the paraboloid Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . A) B) C) D) E) and the plane Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . A) B) C) D) E) .


A) Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . A) B) C) D) E)
B) Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . A) B) C) D) E)
C) Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . A) B) C) D) E)
D) Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . A) B) C) D) E)
E) Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . A) B) C) D) E)

F) A) and C)
G) None of the above

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Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes. A) B) C) D) E) None of these if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes. A) B) C) D) E) None of these ,and that the sides are along the positive axes.


A) Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes. A) B) C) D) E) None of these
B) Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes. A) B) C) D) E) None of these
C) Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes. A) B) C) D) E) None of these
D) Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at ,and that the sides are along the positive axes. A) B) C) D) E) None of these
E) None of these

F) All of the above
G) D) and E)

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Use cylindrical coordinates to evaluate Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D) where T is the solid bounded by the cylinder Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D) and the planes Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D) and Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D)


A) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D)
B) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D)
C) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D)
D) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D) Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and A) B) C) D)

E) B) and D)
F) B) and C)

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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.


A) 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. A) k B) k C) k D) k k 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. A) k B) k C) k D) k
B) 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. A) k B) k C) k D) k k 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. A) k B) k C) k D) k
C) 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. A) k B) k C) k D) k k 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. A) k B) k C) k D) k
D) 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. A) k B) k C) k D) k k 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. A) k B) k C) k D) k

E) B) and D)
F) C) and D)

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Use polar coordinates to evaluate. Use polar coordinates to evaluate.

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Identify the surface with equation Identify the surface with equation

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Upper half of a righ...

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Evaluate the double integral. Evaluate the double integral. is bounded by the circle with center the origin and radius 36. Evaluate the double integral. is bounded by the circle with center the origin and radius 36. is bounded by the circle with center the origin and radius 36.

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Use a double integral to find the area of the region R where R is bounded by the circle Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D)


A) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D)
B) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D)
C) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D)
D) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D) Use a double integral to find the area of the region R where R is bounded by the circle A) B) C) D)

E) C) and D)
F) All of the above

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Calculate the iterated integral. Calculate the iterated integral. A) B) C) 8 D) E) None of these


A) Calculate the iterated integral. A) B) C) 8 D) E) None of these
B) Calculate the iterated integral. A) B) C) 8 D) E) None of these
C) 8
D) Calculate the iterated integral. A) B) C) 8 D) E) None of these
E) None of these

F) C) and D)
G) B) and C)

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Find the Jacobian of the transformation. Find the Jacobian of the transformation. A) B) C) D) E)


A) Find the Jacobian of the transformation. A) B) C) D) E)
B) Find the Jacobian of the transformation. A) B) C) D) E)
C) Find the Jacobian of the transformation. A) B) C) D) E)
D) Find the Jacobian of the transformation. A) B) C) D) E)
E) Find the Jacobian of the transformation. A) B) C) D) E)

F) A) and C)
G) A) and E)

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Use polar coordinates to find the volume of the sphere of radius 3 .Round to two decimal places.


A) Use polar coordinates to find the volume of the sphere of radius 3 .Round to two decimal places. A) B) C) D) E)
B) Use polar coordinates to find the volume of the sphere of radius 3 .Round to two decimal places. A) B) C) D) E)
C) Use polar coordinates to find the volume of the sphere of radius 3 .Round to two decimal places. A) B) C) D) E)
D) Use polar coordinates to find the volume of the sphere of radius 3 .Round to two decimal places. A) B) C) D) E)
E) Use polar coordinates to find the volume of the sphere of radius 3 .Round to two decimal places. A) B) C) D) E)

F) B) and C)
G) B) and D)

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Evaluate Evaluate where D is the figure bounded by and . where D is the figure bounded by Evaluate where D is the figure bounded by and . and Evaluate where D is the figure bounded by and . .

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Calculate the double integral.Round your answer to two decimal places. Calculate the double integral.Round your answer to two decimal places.

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