Name: 
 

03-04 - Related Rates



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

Consider the following relationship exists between y and x over time, t :

mc001-1.jpg

Determine mc001-2.jpg  at the moment that  mc001-3.jpg,   mc001-4.jpg, and   mc001-5.jpg

a.
mc001-6.jpg
d.
mc001-9.jpg
b.
mc001-7.jpg
e.
mc001-10.jpg
c.
mc001-8.jpg
f.
mc001-11.jpg
 

 2. 

A fish aquarium in the shape of a rectangular prism cracked near the bottom of the tank.  Water is pouring out at a rate of  mc002-1.jpg. The dimensions of the aquarium tank are:

mc002-2.jpg


What is the rate at which the water level is decreasing?
mc002-3.jpg
a.
mc002-4.jpg
d.
mc002-7.jpg
b.
mc002-5.jpg
e.
mc002-8.jpg
c.
mc002-6.jpg
f.
mc002-9.jpg
 

 3. 

A 12 foot ladder is leaning against a wall and top of the ladder begins to slide down the wall.  Let the height the ladder reaches up the wall be the variable x in feet and the distance the foot of the ladder is horizontally away from the bottom of the wall be the variable y in feet.

At the moment the value of  x = 10 feet, the velocity of the top of the ladder is falling at is mc003-1.jpg.  Determine the approximate speed at which the foot of the ladder is moving (i.e. find mc003-2.jpg).
mc003-3.jpg
a.
mc003-4.jpg
d.
mc003-7.jpg
b.
mc003-5.jpg
e.
mc003-8.jpg
c.
mc003-6.jpg
f.
mc003-9.jpg
 

 4. 

A consumer researcher noticed that a particular brand of soap is roughly a rectangular prism and reduced in size as it was used in a specific ratio of  height, length, and width to respectively mc004-1.jpg. If this ratio remains consistent and the volume of the bar of soap is decreasing at a rate of mc004-2.jpg, determine the rate at which the height is decreasing when the bar of soap has the dimensions
mc004-3.jpg.
mc004-4.jpg
a.
mc004-5.jpg
d.
mc004-8.jpg
b.
mc004-6.jpg
e.
mc004-9.jpg
c.
mc004-7.jpg
f.
mc004-10.jpg
 

 5. 

A sink is approximately the shape of a hemisphere with a diameter of 32 cm, as shown in the diagram, and is filling from the bottom up.  The volume of the water can be described as a function of the height of the water using the function:
mc005-1.jpg
If the faucet is filling the sink at a rate of mc005-2.jpg, how fast is the level of water rising when the height is 6 cm?
mc005-3.jpg
a.
mc005-4.jpg
d.
mc005-7.jpg
b.
mc005-5.jpg
e.
mc005-8.jpg
c.
mc005-6.jpg
f.
mc005-9.jpg
 

 6. 

Water is being pumped in to a trough at 3 ft3/min. The trough is a triangular prism that is 10 feet long. The ends or bases of the trough are isosceles triangles. The isosceles triangles have a base of 6 feet and 4 feet high as shown in the diagram.


How fast is the height of the water level rising when the water is 3 feet high?
mc006-1.jpg
a.
mc006-2.jpg
d.
mc006-5.jpg
b.
mc006-3.jpg
e.
mc006-6.jpg
c.
mc006-4.jpg
f.
mc006-7.jpg
 



 
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