Use spherical coordinates to find the mo- ment of inertia of the solid homogeneous hemisphere of radius 1 and density 3 about a diameter of its base. 1. I = 47

Q: 3.22 Convert the coordinates of the following points Cartesian to cylindrical and spherical…

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Q: Use spherical coordinates. Evaluate III. (x² + y2) dv, where E lies between the spheres x² + y² + z²…

A: Evaluate the triple integrals conversion yo spherical co-ordinates

Q: Convert the point (x, y, z) = ( – 4, – 5, – 5) to cylindrical coordinates. Give answers either as…

A: Co ordinates in cartesian form , (x,y,z) = (-4,-5,-5)

Q: Given the function Y(0) = S4 Use the Laplace Transform table to convert this function into f(t).

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Q: lies between the cylinders x2 + y² = 4 and x² + y? 2 2 6 above the xy-plane and below the plane z =…

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Q: Evaluate the integral by changing to spherical coordinates. (x³ + xy² + æz²) dz dy dæ

A: The limits of integration are  -1-x2-y2≤z≤1-x2-y2, 0≤y≤1-x2 and -1≤x≤0 It is one-fourth of the unit…

Q: Ĉ the given curve is rotated around the y-axis Find the area of the resulting surface y = I 9 2 "² I…

A: The given curve is:y=14x2-12ln x ;           4≤x≤5

Q: Determine the moment of inertia about the x-axis and the polar radius of gyration about point O for…

A: From the given information to find:

Q: Use spherical coordinates. Evaluate (6 – x2 - y?) dv, where H is the solid hemisphere x2 + y² + z² <…

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Q: (c) Evaluate zdz dy dr using spherical coordinates.

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: Verify that dV = p sin o dp de dy when using spherical coordinates. %3D

A: We have to represent a differential element.