Graded Related Rates Assignment PDF

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Graded Homework Due 11/07/2017 1. Suppose a closed rectangular box has a length that is changing at a rate of 1 m/s, a width that is changing at a rate of -2 m/s and a height that is changing at a rate of 1 m/s. When the length is 4 meters, the width is 3 meters and the height is 2 meters, a. Find the rate at which the volume is changing. b. Find the rate at which the surface area is changing. c. Find the rate at which the diagonal length is changing.  Volume V lwh , Surface Area SA  2lw  2lh  2hw ,  2 2 2  Diagonal Length  S  l  w  h

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2. A 13-ft ladder is leaning against a house when its base starts to slide away (see the figure below). By the time the base is 12ft from the house, the base is moving at the rate of 5 ft/sec. a. How fast is the top of the ladder sliding down the wall? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing? c. At what rate is the angle  between the ladder and the ground changing?

3. Waters drains from the conical tank shown in the figure below at the rate of 5 ft 3 / min .

a. What is the relation between the variables h and r in the figure below? b. How fast is the water level dropping when h 6 ft ?

4. The figure below shows a boat 1 km off-shore, sweeping the shore with a d  0.6 rad / sec. How fast is the searchlight. The light turns at a rate of, dt

light moving along the shore when it reaches point A?

1 V  r 2 h 3 and the Lateral Surface of a cone is 5. The volume of a cone is

A  r r 2  h 2 a. Write an equation that represent how fast the volume is changing if r is a constant. b. Write an equation that represent how fast the volume is changing if h is a constant c. Write an equation that represent how fast the volume is changing if r and h are not constants. d. Write an equation that represent how fast the lateral surface area is changing if r and h are not constants....