# Section_ 2.7 Related Rates

Education

16

All Questions

16

Multiple Choice

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True False

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Essay

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Q 1

Assume that x and y are both differentiable functions of t .Find when and for the equation .
A)
B)
C)
D)
E)

Free

Multiple Choice

A

Q 2

Assume that x and y are both differentiable functions of t.Find when and for the equation .
A)
B)
C)
D)
E)

Free

Multiple Choice

D

Q 3

A point is moving along the graph of the function such that centimeters per second.Find when x = 1.
A)
B)
C)
D)
E)

Free

Multiple Choice

E

Q 4

A point is moving along the graph of the function such that centimeters per second.Find when .
A)
B)
C)
D)
E)

Multiple Choice

Q 5

Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second.
A)
B)
C)
D)
E)

Multiple Choice

Q 6

The radius,r,of a circle is increasing at a rate of 3 centimeters per minute.Find the rate of change of area,A,when the radius is 6.
A)
B)
C)
D)
E)

Multiple Choice

Q 7

The radius r of a sphere is increasing at a rate of 9 inches per minute.Find the rate of change of the volume when r = 11 inches.
A) in

^{3}/min B) in^{3}/min C) in^{3}/min D) in^{3}/min E) in^{3}/min Multiple Choice

Q 8

A spherical balloon is inflated with gas at the rate of 900 cubic centimeters per minute.How fast is the radius of the balloon increasing at the instant the radius is 70 centimeters?
A) cm/min
B) cm/min
C) cm/min
D) cm/min
E) cm/min

Multiple Choice

Q 9

All edges of a cube are expanding at a rate of 9 centimeters per second.How fast is the volume changing when each edge is 2 centimeters?
A)486
B)72
C)36
D)108
E)162

Multiple Choice

Q 10

A conical tank (with vertex down)is 20 feet across the top and 18 feet deep.If water is flowing into the tank at a rate of 20 cubic feet per minute,find the rate of change of the depth of the water when the water is 12 feet deep.
A)
B)
C)
D)
E)

Multiple Choice

Q 11

A ladder a = 20 feet long is leaning against the wall of a house (see figure).The base of the ladder is pulled away from the wall at a rate of b = 4 feet per second.How fast is the top of the ladder moving down the wall when its base is 13 feet from the wall? Round your answer to two decimal places.
A)5.00
B)-6.86
C)-3.42
D)6.86
E)-6.00

Multiple Choice

Q 12

A ladder a = 20 feet long is leaning against the wall of a house (see figure).The base of the ladder is pulled away from the wall at a rate of b = 4 feet per second.Consider the triangle formed by the side of the house,the ladder,and the ground.Find the rate at which the area of the triangle is changed when the base of the ladder is 11 feet from the wall.Round your answer to two decimal places.
A)1.48
B)33.41
C)153.81
D)18.92
E)53.68

Multiple Choice

Q 13

A ladder a = 20 feet long is leaning against the wall of a house (see figure).The base of the ladder is pulled away from the wall at a rate of b = 4 feet per second.Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 19 feet from the wall.Round your answer to three decimal places.
A)0.528
B)0.641
C)4.058
D)7.604
E)0.339

Multiple Choice

Q 14

A man 6 feet tall walks at a rate of 10 feet per second away from a light that is 15 feet above the ground (see figure).When he is 13 feet from the base of the light,at what rate is the tip of his shadow moving?
A)
B)50
C)
D)
E)

Multiple Choice

Q 15

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure).When he is 5 feet from the base of the light,at what rate is the length of his shadow changing?
A)
B)
C)
D)
E)

Multiple Choice

Q 16

An airplane is flying in still air with an airspeed of 266 miles per hour.If it is climbing at an angle of 22°,find the rate at which it is gaining altitude.Round your answer to four decimal places.
A)112.4165
B)86.6011
C)120.7615
D)100.7692
E)99.6454

Multiple Choice