Answer the following questions. Use Equation Editor when writing mathematical expressions or equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. You must show your work and/or justify your answer on ALL problems (even if it isn’t requested or the problem seems simple).

Hint: Pay attention to the units of measure. You may have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for your conversions.

1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation:w=Cr^-2 , where C is a constant, and r is the distance in miles that the object is from the center of Earth.

a. Solve the equation w=Cr^-2 for r. Show all work. (Hint: We are not looking for a value. We are solving for r in terms of the other variables. Remember to simplify your answer, including rationalizing the denominator if needed.) (6 pts)

b. Suppose that an object is 150 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the Earth.) Show all work. (6 pts)

c. Use the value of C you found in the previous question to determine how much the object would weigh in the following locations. (Hint: feet must first be converted to miles in part i and ii). Show all work.

i. Dark Valley (184 feet below sea level). (6 pts)

ii. The top of Mount Molehill (22,340 feet above sea level). (6 pts)

2. The equation gives the distance D= 1.2√h, D, in miles that a person can see to the horizon from a height, h, in feet.

a. Solve this equation for h. Show all work. (Hint: We are not looking for a value. We are solving for h in terms of the other variables. Remember to simplify your answer.) (6 pts)

b. Tall’s Peak is 13,225 feet in elevation. How far can you see to the horizon from the top of Tall’s Peak? Show all work. (5 pts)

c. From the top of Tall’s Peak, can you see a park that is about 104 miles away? Explain your answer and show all work. (5 pts)


Please remember to show all work and use Equation Editor to maximize your score.

All work should be in your own original words.

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