1. Warm Up 1. 2. 3.

2. Day two

3. Write the following statements mathematically John’s height is changing at the rate of 3 in./year The volume of a cone is decreasing by 2 in 3 /min. The radius of a circle in increasing at 4 ft. per hour

4. A rectangle has length l and width w. Write an equation to represent the rate of change of the perimeter. What is the rate of change of the perimeter if the length is increasing at 2 inches /min. and the width is decreasing 3 inches/min.?

5. Write an equation to represent the rate of change of the area. If the length is decreasing at 2 inches/min. and the width is increasing 1.5 inches/min., What is the rate of change of the area when the length is 10 and the width is 4? A rectangle has length l and width w.

6. Air is being pumped into a spherical balloon at the rate of 4.5 cubic inches per minute. Find the rate of change of the radius when the radius is 2 inches.

7. A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a constant rate of 1.2 feet per second. When the radius is 4 feet, at what rate is the total area of the disturbed water changing?

8. All edges of a cube are expanding at the rate of 5 cm/sec. How fast is the surface area changing when the length of each edge is 12 cm?

9. A piece of ice in the shape of a cube melts uniformly so that its volume decreases at 3 cm 3 /sec. How fast is its surface area decreasing when the edge of the cube is 5 cm.?

10. The volume of a sphere is increasing at a rate of 12 cubic feet per second. When the volume of the sphere is 972π cubic feet, how fast, in square feet per second, is the surface area increasing?

11. A 20 ft long ladder is leaning against a wall and sliding toward the floor. If the foot of the ladder is sliding away from the base of the wall at a rate of 10 ft/sec, a) how fast is the top of the ladder sliding down the wall when the top of the ladder is 12 ft. from the ground?

12. A 20 ft long ladder is leaning against a wall and sliding toward the floor. If the foot of the ladder is sliding away from the base of the wall at a rate of 10 ft/sec, b) find the rate at which the angle between the ladder and the wall is changing when the top of the ladder is 12 ft. from the ground?

13. Darth Vader's spaceship is approaching the origin along the positive y-axis at 50 km/sec. Meanwhile his daughter Ella's spaceship is moving away from the origin along the positive x-axis at 80 km/sec. When Darth is at y = 1200 km and Ella is at x = 500 km, is the distance between them increasing or decreasing? At what rate?

14. A girl 4 feet tall walks at a rate of 1.5 ft/sec away from a light that is 10 feet above the ground. At what rate is the length of her shadow changing when she is 8 feet from the base of the light?

15. Suppose senior board decided to throw a graduation bash and the coca cola is flowing freely from the bottom of a giant cone-shaped barrel which is 12 feet deep and 6 feet in radius at the top. If the coke is disappearing at a rate of 6 cubic feet per hour, at what rate is the depth of the coke in the tank going down when the depth is 4 feet?

16. A student is using a straw to drink from a conical paper cup at a rate of 3 cubic centimeters a second. If the height of the cup is 10 cm. and the diameter of its opening is 6 cm., how fast is the level of the liquid falling when the depth of the liquid is 5 cm?