Math 1337
Quiz #8 (Sec. 2.7)
Name: ___________________________________________________
Please show all work on this page.
1. A point moves along the curve y = 2x2 – 1 in such a way that the y value is decreasing at the rate
3
of 2 units per second. At what rate is x changing when x =
?
2
2. A right triangle has one leg with constant length 8 cm. The length of the other leg is decreasing at 3
cm/sec. Find the rate of change of the hypotenuse when the variable leg is 6 cm.
3. How rapidly will the fluid level inside a vertical cylindrical tank drop if we pump the fluid out at the rate
of 300 liters per minute? V = r2h.
4. Water runs into a conical tank at the rate of 9 ft3/min. The tank stands point down and has a height of 10
feet and a base radius of 5 feet. How fast is the water level rising when the water is 6 feet deep?
1
V  r 2 h
3
5. A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius, r, of
the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what
rate is the total area of the disturbed water changing? A = r2
6. A 13-foot ladder is leaning against a house when its base starts to slide away. By the time the base is
12 feet from the house, the base of the ladder is moving at the rate of 5 ft/sec.
a. How fast is the top of the ladder sliding down the wall at that time? x2 + y2 = c2
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing at that time.
1
A  bh
2