Question 1

Suppose  varies directly as the square of  . If  when  find  when  is 1.
A)2
B)4
C)20
D)10
E)5

Accepted Answer

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Question 2

The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 42 pounds when the spring is stretched 2 inches, find the tension when the spring is stretched three times as far.
A)The tension is 138 pounds.
B)The tension is 126 pounds.
C)The tension is 121 pounds.
D)The tension is 118 pounds.
E)The tension is 252 pounds.

Accepted Answer

Since the tension varies directly with the distance, we can use the formula T=k*d, where k is the constant of proportionality. To find k, we can use the given values:
42 = k*2
k = 21
Now we can use this value of k to find the tension when the spring is stretched three times as far:
T = 21*(3*2)
T = 126
Therefore, the tension is 126 pounds.

Question 3

Suppose  varies directly as the square of  . If  when  find  when  is 4.
A)-5
B)-64
C)-32
D)-40
E)-160

Accepted Answer

The answer of Suppose  varies directly as the square...

Question 4

Assume  varies inversely with the square of  . If  when  find  when  is 3.
A)242
B)81
C)22
D)121
E)18

Accepted Answer

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Question 5

Solve the following proportion.

Accepted Answer

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Question 6

If  varies inversely with  and if  when  find  when  is 21.
A)1
B)7
C)49
D)9
E)441

Accepted Answer

The answer of If  varies inversely with  and...

Question 7

If  varies inversely with  and if  when  find  when  is 32.
A)32
B)8
C)2
D)9
E)7

Accepted Answer

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Question 8

Solve the following proportion.

Accepted Answer

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Question 9

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

Accepted Answer

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Question 10

The amount of money M a woman makes per week varies directly with the number of hours h she works per week. If she works 25 hours and earns $153, how much does she make if she works 30 hours?
A)She makes $196.60.
B)She makes $169.60.
C)She makes $191.60.
D)She makes $183.60.
E)She makes $173.60.

Accepted Answer

We can set up a proportion to solve for the woman's earnings when she works 30 hours:

25 hours/ $153 = 30 hours/ x

Solving for x, we get x = $183.60. Therefore, the woman would make $183.60 if she worked 30 hours, which corresponds to choice D.

Question 11

If  varies directly with  and if  when  find  when  is 11.
A)2.2
B)47
C)55
D)16
E)180

Accepted Answer

The answer of If  varies directly with  and...

Question 12

Assume  varies inversely with the square of  . If  when  find  when  is 6.
A) 
B) 
C) 
D) 
E)

Accepted Answer

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Question 13

If  varies inversely with  and if  when  find  when  is 14.
A) 
B) 
C) 
D) 
E)

Accepted Answer

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Question 14

The resistance  in an electric circuit varies directly with the voltage  . If  when  find  when 
A)R = 40 when V = 160.
B)R = 55 when V = 160.
C)R = 10 when V = 160.
D)R = 25 when V = 160.
E)R = 50 when V = 160.

Accepted Answer

The answer of The resistance  in an electric circuit...

Question 15

If  varies directly with  and if  when  find  when  is 3.
A)-85
B)-13
C)-0.75
D)-10
E)-12

Accepted Answer

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Question 16

If  varies directly with  and if  when  find  when  is 4.
A)-2
B)-289
C)-4
D)-1
E)-6

Accepted Answer

The answer of If  varies directly with  and...

Question 17

If  varies inversely with  and if  when  find  when  is 4.
A)12
B)3
C) 
D) 
E)4

Accepted Answer

When two variables vary inversely, their product is constant. Therefore, we can set up the equation:
11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11 * 11ebfe7e_3468_5814_96cc_a1bad799be68_TBX8806_11 = k
where k is some constant. We are also given that:
11ebfe7e_3468_5815_96cc_55806b9220fa_TBX8806_11 = k/11ebfe7e_3468_5816_96cc_33cc3a77d2fe_TBX8806_11
Plugging in the known values, we can solve for k:
11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11 * 11ebfe7e_3468_5815_96cc_55806b9220fa_TBX8806_11 = k
11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11 * k/11ebfe7e_3468_5816_96cc_33cc3a77d2fe_TBX8806_11 = k
Simplifying:
k = 11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11 * 11ebfe7e_3468_5815_96cc_55806b9220fa_TBX8806_11 = 11ebfe7e_3468_5816_96cc_33cc3a77d2fe_TBX8806_11
Now we can use this constant and the given information to solve for 11ebfe7e_3468_5817_96cc_739e89718751_TBX8806_11:
11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11 * 11ebfe7e_3468_5814_96cc_a1bad799be68_TBX8806_11 = k
11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11 * 4 = k
11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11 * 11ebfe7e_3468_5817_96cc_739e89718751_TBX8806_11 = k/3
11ebfe7e_3468_5817_96cc_739e89718751_TBX8806_11 = (k/3) / 11ebfe7e_3468_3103_96cc_450050ae14a8_TBX8806_11
Simplifying:
11ebfe7e_3468_5817_96cc_739e89718751_TBX8806_11 = 11ebfe7e_3468_5816_96cc_33cc3a77d2fe_TBX8806_11 / 3 = 3

Question 18

Assume  varies inversely with the square of  . If  when  find  when  is 7.
A)49
B)9
C)63
D)18
E)81

Accepted Answer

The answer of Assume  varies inversely with the square...

Question 19

Solve the following proportion.

Accepted Answer

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Question 20

The volume  of a gas varies directly as the temperature  . If  when  find  when  is 90.
A)V is 4 when T is 90.
B)V is 8 when T is 90.
C)V is 7 when T is 90.
D)V is 6 when T is 90.
E)V is 3 when T is 90.

Accepted Answer

The answer of The volume  of a gas varies...

Quiz 7: Rational Expressions

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

The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 42 pounds when the spring is stretched 2 inches, find the tension when the spring is stretched three times as far.

Suppose varies directly as the square of . If when find when is 4.

Assume varies inversely with the square of . If when find when is 3.

Solve the following proportion.

If varies inversely with and if when find when is 21.

If varies inversely with and if when find when is 32.

Solve the following proportion.

If varies directly with and if when find when is 5.

The amount of money M a woman makes per week varies directly with the number of hours h she works per week. If she works 25 hours and earns $153, how much does she make if she works 30 hours?

If varies directly with and if when find when is 11.

Assume varies inversely with the square of . If when find when is 6.

If varies inversely with and if when find when is 14.

The resistance in an electric circuit varies directly with the voltage . If when find when

If varies directly with and if when find when is 3.

If varies directly with and if when find when is 4.

If varies inversely with and if when find when is 4.

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

Solve the following proportion.

The volume of a gas varies directly as the temperature . If when find when is 90.