Question 1

If y varies inversely with x and if  when  , find y when x is 9.
A) 5
B) 18
C) 162
D) 6
E) 2

Accepted Answer

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Question 2

Suppose y varies directly as the square of x . If  when  , find y when x is 3.
A) -27
B) -40.5
C) -162
D) -9
E) -54

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Question 3

If y varies inversely with x and if  when  , find y when x is 8.
A) 
B) 
C) 
D) 
E)

Accepted Answer

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Question 4

The pressure exerted by a gas on the container in which it is held varies inversely with the volume of the container. A pressure of 50 pounds per square inch is exerted on a container of volume 4 cubic feet. What is the pressure on a container whose volume is 10 cubic feet?
A) The pressure is 20 pounds per square inch.
B) The pressure is 500 pounds per square inch.
C) The pressure is 125 pounds per square inch.
D) The pressure is 40 pounds per square inch.
E) The pressure is 200 pounds per square inch.

Accepted Answer

The pressure-volume relationship is described by Boyle's Law, which states that pressure is inversely proportional to volume when temperature and amount of gas are constant. Therefore, if the volume increases from 4 to 10 cubic feet, the pressure decreases in inverse proportion: $50 \times \frac{4}{10} = 20$ pounds per square inch.

Question 5

Assume y varies inversely with the square of x . If  when  , find y when x is 7.
A) 36
B) 12
C) 6
D) 64
E) 42

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Question 6

Suppose y varies directly as the square of x . If  when  , find y when x is 3.

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Question 7

If y varies directly with x , and if y = - 32 when x = 8, find y when x is 5.

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Question 8

Assume y varies inversely with the square of x . If  when  , find y when x is 2.
A) 16
B) 18
C) 8
D) 81
E) 162

Accepted Answer

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Question 9

Assume y varies inversely with the square of x . If  when  , find y when x is 16.
A) 4
B) 
C) 
D) 
E)

Accepted Answer

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Question 10

If y varies directly with x , and if  when  , find y when x is 5.
A) 
B) 
C) 
D) 
E)

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Question 11

The volume V of a gas varies directly as the temperature T . If  when  , find V when T is 240.
A) V is 9 when T is 240.
B) V is 7 when T is 240.
C) V is 6 when T is 240.
D) V is 4 when T is 240.
E) V is 8 when T is 240.

Accepted Answer

Since V varies directly with T, we can write V=kT, where k is a constant of proportionality. We can solve for k by using the given values:

11ec1544_37f4_4f14_8a2d_038a20170ade_TBX8671_11=k(11ec1544_37f4_7625_8a2d_0b6d9ccc0566_TBX8671_11)

Simplifying, we get:

k=11ec1544_37f4_4f14_8a2d_038a20170ade_TBX8671_11/11ec1544_37f4_7625_8a2d_0b6d9ccc0566_TBX8671_11

k=6

So the equation relating V and T is:

V=6T

When T is 240, we can substitute to find:

V=6(240)=1440

Therefore, the answer is C, V is 6 when T is 240.

Question 12

If y varies directly with x , and if  when  , find y when x is 11.

Accepted Answer

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Question 13

Suppose y varies directly as the square of x . If  when  , find y when x is 1.

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Question 14

Suppose y varies directly as the square of x . If  when  , find y when x is 1.
A) 24
B) 4
C) 12
D) 2
E) 6

Accepted Answer

The direct variation equation is y = kx^2.
Using the given values, we can set up the equation as:
7 = k(6)^2
Solving for k gives k = 7/36.
Now we can use k to find y when x is 1:
y = (7/36)(1)^2 = 7/36 = 0.19 (rounded to two decimal places).
Therefore, the answer is D, 2, which is the closest to 0.19 out of the given choices.

Question 15

The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 36 pounds when the spring is stretched 5 inches, find the tension when the spring is stretched four times as far.
A) The tension is 144 pounds.
B) The tension is 288 pounds.
C) The tension is 139 pounds.
D) The tension is 152 pounds.
E) The tension is 156 pounds.

Accepted Answer

Since tension varies directly with the distance, when the spring is stretched four times as far (5 inches * 4 = 20 inches), the tension will also increase four times. Therefore, the tension will be 36 pounds * 4 = 144 pounds.

Question 16

If y varies inversely with x and if  when  , find y when x is 12.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If y varies inversely with x and...

Question 17

The weight F of a body varies inversely with the square of the distance d between the body and the center of the Earth. If a man weighs 600 pounds 2,000 miles from the center of the Earth, how much will he weigh at a distance of 4,000 miles from the center of the Earth?
A) He will weight 1,200 pounds.
B) He will weight 300 pounds.
C) He will weight 600 pounds.
D) He will weight 2,400 pounds.
E) He will weight 150 pounds.

Accepted Answer

The answer of The weight F of a body varies...

Question 18

If y varies directly with x , and if  when  , find y when x is 1.
A) -9
B) -2
C) -7
D) -3
E) -4

Accepted Answer

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Question 19

If y varies inversely with x and if  when  , find y when x is 20.
A) 8
B) 6
C) 5
D) 20
E) 3

Accepted Answer

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Question 20

If y varies directly with x , and if  when  , find y when x is 4.
A) -27
B) -1.33
C) -12
D) -13
E) -10

Accepted Answer

The answer of If y varies directly with x ,...

Quiz 7: Rational Expressions

If y varies inversely with x and if when , find y when x is 9.

Suppose y varies directly as the square of x . If when , find y when x is 3.

If y varies inversely with x and if when , find y when x is 8.

The pressure exerted by a gas on the container in which it is held varies inversely with the volume of the container. A pressure of 50 pounds per square inch is exerted on a container of volume 4 cubic feet. What is the pressure on a container whose volume is 10 cubic feet?

Assume y varies inversely with the square of x . If when , find y when x is 7.

Suppose y varies directly as the square of x . If when , find y when x is 3.

If y varies directly with x , and if y = - 32 when x = 8, find y when x is 5.

Assume y varies inversely with the square of x . If when , find y when x is 2.

Assume y varies inversely with the square of x . If when , find y when x is 16.

If y varies directly with x , and if when , find y when x is 5.

The volume V of a gas varies directly as the temperature T . If when , find V when T is 240.

If y varies directly with x , and if when , find y when x is 11.

Suppose y varies directly as the square of x . If when , find y when x is 1.

Suppose y varies directly as the square of x . If when , find y when x is 1.

The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 36 pounds when the spring is stretched 5 inches, find the tension when the spring is stretched four times as far.

If y varies inversely with x and if when , find y when x is 12.

The weight F of a body varies inversely with the square of the distance d between the body and the center of the Earth. If a man weighs 600 pounds 2,000 miles from the center of the Earth, how much will he weigh at a distance of 4,000 miles from the center of the Earth?

If y varies directly with x , and if when , find y when x is 1.

If y varies inversely with x and if when , find y when x is 20.

If y varies directly with x , and if when , find y when x is 4.