Question

the weight W of an object varies inversly as the square of the distance d from the center of the earth. at sea level (3978m from the center of the earth), an astrongest weighs 136 lb. find her weight when she is 414 mi. the surface of the earth and the space craft is not in motion?

Answer 1

Because the weight varies inversely as the square of the distance, you should have that
\[ \frac{W_2}{W_1} = \left(\frac{R_1}{R_2}\right)^2\]
so
\[W_2 = \left(\frac{R_1}{R_2}\right)^2 W_2\]
Here,
\[R_1 = 3978 \space mi\]
\[R_2 = R_1 + 414 mi = 3978 mi + 414 mi = 4392 mi \]
\[W_1 = 136 lbs\]
As a side note, the abbreviation for miles is mi, not m. m is the abbreviation for meters.

Answer 2

Eek. That second equation should be
\[W_2 = \left(\frac{R_1}{R_2}\right)^2 W_1\]