Section 2.8 Homework

1.  Each side of a square is increasing at a rate of 8 cm/s. At what rate is the area of the square increasing when the area of the square is

?

2.   The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 15 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

3.  A cylindrical tank with radius 7 m is being filled with water at a rate of 3 m3/min. How fast is the height of the water increasing?

4.  The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm?

5.  A plane flying horizontally at an altitude of 1 mi and a speed of 430 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 mi away from the station. (Round your answer to the nearest whole number.)

6.  If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter decreases when the diameter is 8 cm.

7.  A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?

8. At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?

9.  Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing four hours later?

10.   A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.1 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to one decimal place.)

11.  A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 9 m from the dock? (Round your answer to two decimal places.)

12.  At noon, ship A is 70 km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM? (Round your answer to one decimal place.)

13.  A trough is 16 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 9 ft3/min, how fast is the water level rising when the water is 6 inches deep?

14.  Two sides of a triangle have lengths 13 m and 18 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)

1.  Each side of a square is increasing at a rate of 8 cm/s. At what rate is the area of the square increasing when the area of the square is

?

Answer:

$48 c{m}^2/s$