Question

Find the center of mass of a thin plate of constant density δ covering the given region.

The region bounded by the parabola y=3x-6x^2 and the line and the line y=-3x

The center of mass is (_,_)

Type an Ordered Pair

Answer #1

Find the center of mass of a thin plate covering the region
bounded below by the parabola y=x^2 and above by the line y=x if
the plate's density at the point (x,y) is δ(x)=13x.
The center of mass is (x̄,ȳ) = (_,_)
Type an Ordered Pair. Simplify your answer.

Find the center of mass of a thin plate covering the region
between the x-axis and the curve y=20/x^2,
5 less than or equal to x less than or equal to 8, if the
plate's density at a point (x,y) is delta(x)=2x^2
The center of the mass is (x,y)= _____

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function, if D is bounded by the
parabola y=4-x^2 and the y-axis. p(x,y)=y

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function, if D is bounded by the
parabola y=4-x^2 and the x-axis. p(x,y)=y

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.

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.

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.

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function ρ. where D is the
triangular region enclosed by the lines x = 0, y = x, and 2x + y =
6 and ρ(x, y) = 6x 2 .

Find the mass and center of mass of the lamina that occupies the
region D and has the given density function ρ.
D is bounded by the parabolas y = x2 and x =
y2; ρ(x, y) = 19 sqt(x)

A thin plate covers the triangular region of the xy-plane with
vertices (0,0), (1,1), and (−1,1). (Coordinates measured in
cm.)
(a) Find the mass of the plate if its density at (x,y) is
sin(y^2) kg/cm^2 .
(b) Find the mass of the plate if its density at (x,y) is
sin(x^2) kg/cm^2 .

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