Question 1

Solve the problem. Round your answer, if appropriate.
-A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. At what rate is the length of his shadow changing when he is 30 ft away from the lamppost? (Do not round your answer)

Accepted Answer

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Question 2

Solve the problem. Round your answer, if appropriate. -Boyle's law states that if the temperature of a gas remains constant, then PV = c, where , , and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 13 in. ³/sec, at what rate is P increasing when P = 70 lb/in.² and V = 30 in.³? (Do not round your answer.)

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Question 3

Solve the problem. Round your answer, if appropriate.
-Electrical systems are governed by Ohm's law, which states that V = IR, where V = voltage, I = current, and R = resistance. If the current in an electrical system is decreasing at a rate of 5 A/s while the voltage remains constant at 22 V, at what rate is the resistance increasing (in /sec) when the current is 40 A? (Do not round your answer.)

Accepted Answer

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Question 4

Solve the problem. Round your answer, if appropriate. -The volume of a sphere is increasing at a rate of 2 cm³/sec. Find the rate of change of its surface area when its volume is cm³. (Do not round your answer.)

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Question 5

Solve the problem. Round your answer, if appropriate. -The volume of a rectangular box with a square base remains constant at 1100 cm³ as the area of the base increases at a rate of 10 ²/sec. Find the rate at which the height of the box is decreasing when each side of the base is 15 cm long. (Do not round your answer.)

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Question 6

Solve the problem. Round your answer, if appropriate.
-The radius of a right circular cylinder is increasing at the rate of  , while the height is decreasing at the rate of  . At what rate is the volume of the cylinder changing when the radius is 6 in. and the height is 12 in.?

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Question 7

Solve the problem. Round your answer, if appropriate.
-An inverted conical water tank with a height of 12 ft and a radius of 3 ft is drained through a hole in the vertex. If the water level drops at a rate of 1 ft/min, at what rate is water (in  /min) draining from the tank when the water depth is 8 ft? (Hint: Use similar triangles.)

Accepted Answer

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Quiz 3: Derivatives

Solve the problem. Round your answer, if appropriate. -A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. At what rate is the length of his shadow changing when he is 30 ft away from the lamppost? (Do not round your answer)

Solve the problem. Round your answer, if appropriate. -The volume of a sphere is increasing at a rate of 2 cm3/sec. Find the rate of change of its surface area when its volume is cm3. (Do not round your answer.)

Solve the problem. Round your answer, if appropriate. -The radius of a right circular cylinder is increasing at the rate of , while the height is decreasing at the rate of . At what rate is the volume of the cylinder changing when the radius is 6 in. and the height is 12 in.?