Question

Determine the centroid, C(x̅, y̅, z̅), of the solid formed in the first octant bounded by y = 4 − x^2 and x − z = 0.

Answer #1

Determine the centroid C(x,y,z) of the solid formed in
the first octant bounded by z+y-16=0 and x^2=16-y.

B is the solid occupying the region of the space in the first
octant and bounded by the paraboloid z = x2 + y2- 1 and the planes
z = 0, z = 1, x = 0 and y = 0. The density of B is proportional to
the distance at the plane of (x, y).
Determine the coordinates of the mass centre of solid B.

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.

a) Sketch the solid in the first octant bounded by:
z = x^2 + y^2 and x^2 + y^2 = 1,
b) Given
the volume density which is proportional to the distance from the
xz-plane, set up integrals
for finding the
mass of the solid using cylindrical
coordinates, and spherical coordinates.
c) Evaluate one of these to find the mass.

a. Let S be the solid region first octant bounded by the
coordinate planes and the planes x=3, y=3, and z=4 (including
points on the surface of the region). Sketch, or describe the shape
of the solid region E consisting of all points that are at most 1
unit of distance from some point in S. Also, find the volume of
E.
b. Write an equation that describes the set of all points that
are equidistant from the origin and...

1. Determine the centroid of the area bounded by the y − axis,
the x − axis, and the curve x^2 + y − 4 = 0.

4. Consider the solid bounded by the paraboloid x^2+ y^2 + z = 9
as well as by the planes y = 3x and z = 0 in the first octant.
(a) Graph the integration domain D.
(b) Calculate the volume of the solid with a double
integral.

Question 2
D is the region in the first octant bounded by: z = 1 −
x2 and z = ( y − 1 )2
Sketch the domain D.
Then, integrate f (x, y, z) over the domain in 6 ways: orderings of
dx, dy, dz.

Find the centroid using the circular disc method: The
volume formed by revolving about Oy the area in the first quadrant
bounded by y^2 = 4ax, y=0, x=a.

Calculate the mass of the solid E in the first octant
inside the cone z = (1/s) sqrt(x^2 + y^2) in the sphere of radius
10 whose density is given by δ (x, y , z) = 36(x^2) + 36(y^2) +
36(z^2).
please help

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