1. Suppose the length of a rectangle is 12 inches and increasing at a rate of 2 inches per hour. At the same time, its width is 20 inches and decreasing at a rate of 5 inches per hour. How fast is its area changing at this moment in time?

2. The area of a circle is increasing at a rate of 30 millimeters per second when its radius is increasing at a rate of 5 millimeters per second. What is the area of the circle?

3. At 9am on November 9th, Jim is 150 miles north of Omaha and travelling south at a rate of 20 miles per hour. At the same time, Marcus is 70 miles east of Omaha and travelling east at a rate of 10 miles per hour. Finally, at the same time, Janet is 50 miles west of Omaha and travelling east at a rate of 15 miles per hour.

(a) How far apart are Jim and Marcus at 9am on November 9th?

(b) Is the distance between Jim and Marcus increasing or decreasing at 9am on November 9th? How quickly?

(c) Is the area of the triangle between Jim, Marcus, and Omaha increasing or decreasing at 9am on November 9th? How quickly?

(d) Is the distance between Jim and Marcus changing more quickly or more slowly than the distance between Marcus and Janet at 9am on November 9th?

4. A 10 meter ladder resting against a wall at a point 8 meters above the ground begins to slide down the wall at a rate of 2 meters per minute. How fast is the bottom of the ladder sliding away from the wall at that time?

5. A potter has a fixed volume of clay in the form of a cylinder. As he rolls the clay, the length of the cylinder, L, increases, while the radius, r, decreases. If the length of the cylinder is increasing at a constant rate of 0.2 cm per second, find the rate at which the radius is changing when the radius is 1.5 cm and the length is 4 cm. Recall that the volume of a cylinder of radius r and height h is given by V = r2h.