Calculus 1: Related Rates Problems

A 10 by 6 foot rectangular swimming pool is being filled. Find the rate at which the height of the water rises if the hose is pouring at $20 \frac{{ft}^3}{hour}$

Find the rate of change of the height of the water level if the hose is pouring $2 \frac{{ft}^3}{m}$

A man is walking away from a lamp at $5 \frac{ft}{s}$

a. Find the rate at which the tip of his shadow is changing

b. Find the rate at which the length of his shadow is changing

A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole?

A cylindrical water tank with a radius of 4 meters is being filled with water at a constant rate of 2 cubic meters per minute. Find the rate at which the water level is rising when the water is 3 meters deep.

Use the function $f(x) = -x^2 + 3x + 10$ to answer the following: a. On the interval [2,6], what is the average rate of change?

b. On the interval (2,6), when does the instantaneous rate of change equal the average rate of change?