Electric charge is distributed over the disk so that the charge density at (x,y)

ID: 2841315 • Letter: E

Question

Electric charge is distributed over the disk
so that the charge density at (x,y) is coulombs per square meter.
Find the total charge on the disk.

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A plate occupies the rectangle , and the density of the plate at is equal to .

A. What is the total mass?

B. What is the moment about the y-axis?

C. What is the moment about the x-axis?

D. Where is the center of mass? (, )

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A lamina occupies the part of the disk in the first quadrant and the density at each point is given by the function .

A. What is the total mass?

B. What is the moment about the x-axis?

C. What is the moment about the y-axis?

D. Where is the center of mass? (, )

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Evaluate the triple integral

where E is the solid: , , .

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Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables x, y, z) so that

represents the volume of the region in the first octant that is bounded by the 3 coordinate planes and the plane

ly =
uy =
lx =
ux =
lz =
uz =

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Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables x, y, z) so that

represents the volume of the region in the first octant that is inside the paraboloid  and between the planes  and

lx =
ux =
lz =
uz =
ly =
uy =

Find the mass of the rectangular prism , , , with density function .

Your question is not clear , please re-ask after adjusting it.

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