1) Evaluate the mass center for p(x,y,z) A) p(x, y,z) = 4 , solid bounded by z = x² + y² ,z = 4

Q: Let G = {(x, y): 1 ≤ x^2 + y^2 ≤ 16,0 ≤ y ≤ x). Sketch G, and find the coordinates of its centroid.

A:

Q: Find the mass m of the lamina bounded by triagle R with corners are (1,0), (1,1), and (0,1) and with…

A:

Q: Find the mass of a thin shell of density d(x, y, z) = z cut from the upper portion of the sphere x2…

A: According to the given information, it is required to find the mass of a thin shell.

Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

A:

Q: Find the mass of the solid bounded by the xy-plane, yz-plane, xz-plane, and the plane (x/2) + (y/3)…

A:

Q: 2. Find the mass of the solid enclosed by the cone z = Vr² + y² between the planes z = 1 and z = 2…

A: Here, we need to find the mass of the solid enclosed by the cone z=x2+y2 between the planes z=1 and…

Q: Find the mass of the solid bounded by the planes x + z = 1, x – z = –1, y = 0, and the surface y = z…

A: Given, x+z=1x-z=-1y=0y=zAnd the density is,δx,y,z=2y+5 Then the range will be, x→-1+z to 1-zy→0 to…

Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

A:

Q: Find the volume integral of the function f(r, y, 2) = x– y over the parallelepiped with the vertices…

A: By observing the given points we get    0≤x≤3 ,0≤y≤2 and0≤z≤2 and given function is  f(x, y, z) =…

Q: 5) Find the center of mass of the triangular region with vertices (0, 0), (4,0) and (4,1), if p(x,…

A: