Question

Find the center mass of the solid bounded by planes x+y+z=1, x=0 y=0, and z=0, assuming a mass density of ρ(x,y,z)=7sqrt(z)

Xcm

Ycm

Z cm

Answer #1

Find the center of the mass of a solid of constant density that
is bounded by the
parabolic cylinder x=y^2 and the planes z=0 , z=x and x=2 when
the density is ρ.

3. Use double integrals to find the center of mass, (xcm, ycm),
of a lamina with density function ρ = x bounded by y = x^2 , x = 0
and y = 1.

Find the center of mass of a solid of constant density that is
bounded by the cylinder x^2 + y^2 = 4, the paraboloid surface z =
x^2 + y^2 and the x-y plane.

Let D be the solid in the first octant bounded by the planes
z=0,y=0, and y=x and the cylinder 4x2+z2=4.
Write the triple integral in all 6 ways.

Find the volume of the solid bounded by the cylinder x^2+y^2=9
and the planes z=-10 and 1=2x+3y-z

Find the center of mass of the region bounded by the paraboloid
x^2 + y^2 − 2 = z and the plane x + y + z = 1 assuming the region
has uniform density 8.

Find the mass and center of mass of the lamina bounded by the
graphs of the equations for the given density.
y = 7x, y = 7x3, x ≥
0, y ≥ 0, ρ = kxy

Find the integral that represents the volume of the solid
bounded by the planes y = 0, z = 0, y = x and 6x + 2y + 3z = 6
using double integrals.

Find the integral that represents the volume of the solid
bounded by the planes y = 0, z = 0, y = x, and 6x + 2y + 3z = 6. No
need to solve the integral.

A solid is described along with its density function. Find the
center of mass of the solid using cylindrical coordinates:
The upper half of the unit ball, bounded between z = 0 and z =
√(1 − x^2 − y^2) , with density function δ(x, y,z) = 1.

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