Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Consider the following relationship exists between y and x over
time, t :  Determine  at the
moment that  ,  , and
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2.
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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
 . The dimensions of the aquarium tank are:
What
is the rate at which the water level is decreasing? | | | |
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3.
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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  . Determine the approximate speed at which the foot of the ladder is moving (i.e.
find  ). | | | |
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4.
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5.
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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:
If the faucet is
filling the sink at a rate of  , how fast is the level of water rising when the
height is 6 cm? | | | |
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6.
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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? | | | |
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