Electric charge is distributed over the disk so that the charge density at (x,y) is coulombs per square meter. Find the total charge on the
disk.

450.819

The work

2.

Find the mass of the rectangular region with density function .

1

The work

3.

Find the mass of the triangular region with vertices (0, 0), (1, 0), and (0, 4), with density function
.

17/3

The work

4.

A lamina occupies the part of the rectangle
0 &le x &le 6, 0 &le y &le 4 and the density at each point is given by the function .

A. What is the total mass?

B. Where is the center of mass?
( , )

A) 744

B) ( 3.581, 2.2151)

The work

5.

A lamina occupies the region inside the circle
but outside the circle
.
The density at each point is inversely proportional to its distance from the orgin.

Where is the center of mass?
( , )

( 0, 3.794)

The work

6.

A lamina occupies the part of the disk in the
first quadrant and the density at each point is given by the function .

A. What is the total mass?

B. What is the moment about the x-axis?

C. What is the moment about the y-axis?
D. Where is the center of mass?
(, )

E. What is the moment of inertia about the origin?

A. Total mass: 245.437
B. 625
C. 625
D. Center of mass:
( 2.546, 2.546)
E. 4090.62

The work

7.

You are getting married and your dearest relative has baked you a cake which
fills the volume between the two planes, z = 0 and z = 1x + 7y + c, and inside the cylinder . You are to cut it in half by
making two vertical slices from the center outward. Suppose one of the slices
is at &theta = 0 and the other is at &theta = &psi .

What is the limit, ?

&pi

The work

8.

A lamp has two bulbs, each of a type with an average lifetime of 3 hours. The
probability density function for the lifetime of a bulb is .
What is the probability that both of the bulbs will fail within 2 hours?