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# Liberty MATH 114 Homework 3 Answers Complete Solutions

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### Question 1

Graph the direct variation equation.

y=7x

### Question 2

The distance d you bike varies directly with the amount of time t you bike. Suppose you bike 13.8 mi in 1.25 h. What is an equation that relates d and t? What is the graph of the equation?

Write an equation that relates d and t. Choose the correct answer below.

### Question 3

For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.

Write an equation for the direct variation. Select the correct choice and fill in any answer boxes in your choice below.

### Question 4

For the data in the table below, does y vary directly with x? If it does, write an equation for the direct variation.

### Question 5

Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then graph the equation.

### Question 6

Translate the sentence into an equation.

S varies directly as t.

Choose the correct answer below.

### Question 7

Translate the equation into a sentence by using the phrase “varies directly” or “varies inversely.”

L=kt

### Question 8

Find an equation that meets the conditions p varies inversely as d, and p=9 when d=6.

## STATUS

### Question 9

If y varies directly as x, and y=15 when x=5, find y when x=7.

### Question 10

If G varies inversely as r, and G=12 when r=4, find G when r=6.

### Question 11

The cost of tuition at a certain college varies directly as the number of credit hours taken. For the academic year 2005-2006, the cost of 15 credit hours was $1440. What did 13 credit hours cost?

### Question 12

The distance that an object falls varies directly as the square of the time the object is in motion. If an object falls for 3 seconds, it will fall 144.9 feet. To estimate the height of a cliff, a person drops a stone at the edge of the cliff and measures how long it takes for the stone to reach the base. If it takes 3.8 seconds, what is the height of the cliff?

### Question 13

The weight (in pounds) w=f(d) of an object varies inversely as the square of its distance (in thousands of miles) d from the center of Earth.

a. An astronaut weighs 250 pounds at sea level (about 4 thousand miles from Earth’s center). Find an equation of f.nothing

b. How much would the astronaut weigh at 1 thousand miles above Earth’s surface?

c. At what distance from the center of Earth would the astronaut weigh 1 pound?

d. Estimate how much the astronaut would weigh on the surface of the Moon. The Moon is a mean distance of about 239 thousand miles from Earth.

Has model breakdown occurred?

e. Without finding an equation, discuss how an equation of a model for a 240-pound astronaut would compare with the equation you found in part (a). Discuss how the variation constants would compare.

### Question 14

The intensity (in watts per square meter, W/m2) I=f(d) of a television signal varies inversely as the square of the distance d (in kilometers) from the transmitter. The intensity of a television signal is 50 W/m2 at a distance of 2.5 km. Complete parts (a) through (d) below.

a. Find an equation of f.

b. Find f(1), f(2), f(3), and f(4). What do they mean in this situation?

What do these values mean in this situation?