Question 1

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 150 pounds 4,000 miles from the center of the Earth, how much will he weigh at a distance of 5,000 miles from the center of the Earth? F = __________ pounds

Accepted Answer

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

Question 2

If  varies inversely with  and if  when  find  when  is  .  = __________

Accepted Answer

The answer of If  varies inversely with  and...

Question 3

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

Accepted Answer

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

Question 4

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 5,000 miles from the center of the Earth?

Accepted Answer

The weight of a body varies inversely with the square of the distance from the center of the Earth, so $F = k/d^2$, where $k$ is a constant. Given $F = 600$ pounds at $d = 2000$ miles, we can find $k = 600 \times 2000^2$. At $d = 5000$ miles, the weight $F = k/5000^2$. Substituting the value of $k$ from the first condition, $F = (600 \times 2000^2) / 5000^2 = 96$ pounds.

Question 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 10 hours and earns $143, how much does she make if she works 15 hours? M = $__________

Accepted Answer

The answer of The amount of money M a woman...

Question 6

If  varies directly with  and if  when  find  when  is 15.  = __________

Accepted Answer

The answer of If  varies directly with  and...

Question 7

The volume  of a gas varies directly as the temperature  . If  when  find  when  is 480.  = __________

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

If  varies directly with  and if  when  find  when  is  .  = __________

Accepted Answer

The answer of If  varies directly with  and...

Question 12

If  varies inversely with  and if  when  find  when  is 10.  = __________

Accepted Answer

The answer of If  varies inversely with  and...

Question 13

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

Accepted Answer

The answer of If  varies directly with  and...

Question 14

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

Accepted Answer

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

Question 15

If  varies inversely with  and if  when  find  when  is 48.  = __________

Accepted Answer

The answer of If  varies inversely with  and...

Question 16

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?

Accepted Answer

Using the formula for inverse variation, we have:

P1 × V1 = P2 × V2

where P1 and V1 are the pressure and volume of the first container, and P2 and V2 are the pressure and volume of the second container.

Substituting the given values, we have:

50 × 4 = P2 × 10

Simplifying, we get:

200 = 10P2

Dividing both sides by 10, we get:

P2 = 20

Therefore, the pressure on a container whose volume is 10 cubic feet is 20 pounds per square inch.

Question 17

The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 41 pounds when the spring is stretched 7 inches, find the tension when the spring is stretched twice as far. __________ pounds

Accepted Answer

The answer of The tension t in a spring varies...

Question 18

If  varies inversely with  and if  when  find  when  is 10.

Accepted Answer

The answer of If  varies inversely with  and...

Question 19

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? __________ pounds per square inch

Accepted Answer

The answer of The pressure exerted by a gas on...

Question 20

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

Accepted Answer

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

Quiz 7: Rational Expressions

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 150 pounds 4,000 miles from the center of the Earth, how much will he weigh at a distance of 5,000 miles from the center of the Earth? F = __________ pounds

If varies inversely with and if when find when is . = __________

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

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 5,000 miles from the center of the Earth?

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 10 hours and earns $143, how much does she make if she works 15 hours? M = $__________

If varies directly with and if when find when is 15. = __________

The volume of a gas varies directly as the temperature . If when find when is 480. = __________

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

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

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

If varies directly with and if when find when is . = __________

If varies inversely with and if when find when is 10. = __________

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

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

If varies inversely with and if when find when is 48. = __________

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?

The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 41 pounds when the spring is stretched 7 inches, find the tension when the spring is stretched twice as far. __________ pounds

If varies inversely with and if when find when is 10.

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