QUESTION 1 A. Gravel is being dumped from a conveyor belt at a rate of 10...

QUESTION 1

A. Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 11 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V= 1/3 pi r^2h. When the pile is 11 feet high, its height is increasing at _______ feet per minute.

B.A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 50 ft from the base of the pole? ______ft/sec How fast is the length of her shadow increasing? ______ft/sec

C. Water is leaking out of an inverted conical tank at a rate of 0.0087 m^3/min. At the same time water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 6 meters. If the water level is rising at a rate 0.19 m/min when the height of the water is 4.5 meters, find the rate at which water is being pumped into the tank. Water is being pumped in at _____m^3/min.

D. The tip of a 27 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 2 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 10 feet away from the base of the ball?

E. A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2cm/min. At what rate is the volume of the snowball decreasing when the diameter is 17cm? (Answer is positive number)

Expert Solution

milcah answered 3 years ago

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