# 2.7

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1. Each side of a square is increasing at a rate of 2 cm/s. At what rate is the area of the square increasing when the area of the square is 25 cm^2?
2. The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 13 cm and the width is 9 cm, how fast is the area of the rectangle increasing?
3. A cylindrical tank with a radius 5 m is being filled with water at rate of 2 m^3/min. How fast is the height of the water increasing?
4. The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm?
5. Suppose y = sqrt(2x + 1), where x and y are functions of t.
6. If a snowball melts so that its surface area decreases at a rate of 2 cm^2/min, find the rate at which the diameter decreases when the diameter is 12 cm.
7. A street light mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?
8. A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks away from the spotlight toward the building at a speed of 2.3 m/s, how fast is the length of his shadow on the building decreases when he is 4m from the building? (Round your answer to one decimal place.)
9. Water is leaking out of an inverted conical tank at a rate of 7,000 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2m, find the rate at which water is being pumped into the tank. (Round your answer to the nearest integer.)
10. Two sides of a triangle are 4m and 5m in length and the angle between them is increasing at a rate of 0.06 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is pi/3 rad.