# Math

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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: , where C is a constant, and r is the distance that the object is from the center of the earth.

a. Solve the equation r^-2 = wC^-1 for r. Solve the equation for C. Solve the equation for w.

b. Suppose that an object is 350 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is approximately 4,000 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

i. 1,100 feet below sea level (for example, near the bottom of the ocean)

ii. 21,500 feet above sea level (for example, on the top of a high mountain)

• Math -

r^-2 = wC^-1
or
1/r^2 = w/C
C = wr^2 or w = C/r^2

b) if w=350 and r = 4000(5280)
C = 350(4000*5280)^2

c) i) if r = 40005280) -1100 = 21118900
w = C/r^2 = 350.036

ii, use r = 4000(5280) + 21500
to get w = 349.29