# Algebra

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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 that the object is from the center of Earth.

a. Solve the equation w=Cr^-2 for C.

b. Suppose that an object is 500 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.)

c. Use the value of C you found in the previous question to determine how much the object would weigh in

i. Death Valley (382 feet below sea level).

ii. the top of Mount McKinley (30,320 feet above sea level).

(Round answers to the nearest hundredth ).

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

a. Solve this equation for h.

b. Long’s Peak in Rocky Mountain National Park, is 15,345 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? (Round the answer to the nearest hundredth). Can you see Cheyenne, Wyoming (about 92 miles away)? Explain your answer.