Answer:
199.9 lb
Step-by-step explanation:
Let w = weight and d = distance from the center of the earth.
If y varies inversely with x, the standard form of the equation is
y = k/x
Here, the weight varies inversely with the square of the distance, so the form of the equation is
w = k/d^2
We can find k, the constant of proportionality, by using the given information. At the earth's surface, the distance from the center of the earth is 3960 miles, and the weight of the man is 200 lb.
w = 200; d = 3960
w = k/d^2
200 = k/(3960^2)
k = 200 * 3960^2
k = 3.136 * 10^9
The equation is
w = (3.13632 * 10^9)/d^2
When the man is 1 mile above the surface of the earth, the distance to the center of the earth is 3960 miles + 1 mile = 3961 miles
w = (3.13632 * 10^9)/(3961^2)
w = 199.9
Answer: 199.9 lb
