Dr. Watt MATH 16600 Chapter 8 Test #3 Name: __________________________
Each problem is worth 10 points.
1. Find the length of the curve y = x 3/2 , from
( 0,0 )
to (1/ 4, 1/ 8 ) .
2. Find the arc length of the curve 3x = 2 ( y −1) 2 , 2 ≤ y ≤ 5 .
3
3. Find the area of the surface obtained by rotating the curve y = 2x, 0 ≤ x ≤ 1 , about
the x-axis.
4. Find the center of mass of the system
m1 = 2, P1 = (5,1), m2 = 3, P2 = (3,−2), and m3 = 5, P3 = (−2, 4).
5. Find the centroid of the region bounded by y = sin 2x, y = 0, x=0, and x = π2
6. A swimming pool 5m wide, 10m long, and 3m deep is filled with seawater of density
1030 kg / m3 . Find the hydrostatic force on one end of the pool (i.e., one of the 5m x 3m
ends). The gravitational constant is 9.8 m / s2 . Do not forget to give the units on the final
answer.
7. A tank is completely filled with water of density 1,000 kg / m3 . The end of the tank is
vertical and has the shape of a semicircle, the lower half of a circle, with radius 10m.
Find the hydrostatic force against the end of the tank. The gravitational constant is
9.8 m / s2 . Do not forget to give the units on the final answer.
8. The demand function for a certain commodity is p(x) = 5 −
x
. Find the consumer's
10
surplus when the sales level is 30 units.
t
9. An animal population is increasing at a rate of 200 + e per year (where t is measured
in years). By how much does the animal population increase between the fourth and
tenth years?
10. (NO LONGER COVERED IN COURSE) The mean length of angelfish is 6.25 in
with a standard deviation of .75 in. Assuming the length of fish is a normal distribution,
find the percent of angelfish greater than 8 in long.