Question

Find the mass of a thin funnel in the shape of a cone

z =

sqrt | x^{2} + y^{2} |

, 1 ≤ z ≤ 4

if its density function is

ρ(x, y, z) = 7 − z.

Answer #1

comment if you need further clarification on this answer!

Find the mass of a thin funnel in the shape of a cone
z =
x2 + y2
, 1 ≤ z ≤ 3
if its density function is
ρ(x, y, z) = 6 − z.

Find the integral that represents:
The volume of the solid under the cone z = sqrt(x^2 + y^2) and
over the ring 4 ≤ x^2 + y^2 ≤ 25
The volume of the solid under the plane 6x + 4y + z = 12 and
on the disk with boundary x2 + y2 = y.
The area of the smallest region, enclosed by the spiral rθ =
1, the circles r = 1 and r = 3 & the polar...

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)

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

Find the mass of the triangular region with vertices (0, 0), (1,
0), and (0, 5), with density function ρ(x,y)=x2+y2

find the volume between the cone z=sqrt(x^2+y^2) and the sphere
x^2+y^2+z^2=2az, if a=1

The average value of a function f(x, y, z) over a solid region E
is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the
volume of E. For instance, if ρ is a density function, then ρave is
the average density of E. Find the average value of the function
f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid
z = 4 − x2 − y2 and the...

Find the linear approximation of the function f(x, y, z) = sqrt
x2 + y2 + z2 at (3, 6, 6) and use it to approximate the number
sqrt3.01^2 + 5.97^2 + 5.98^2 . (Round your answer to five decimal
places.) f(3.01, 5.97, 5.98)

Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
z =
x2 + y2
and the sphere
x2 + y2 + z2 = 128.

A lamina occupies the first quadrant of the unit disk
(x2+y2≤1x2+y2≤1, x,y≥1x,y≥1). It's density function is
ρ(x,y)=xρ(x,y)=x. Find the center of mass of the lamina.

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