the weight of an object varies inversely as the square of its distance from the center of the earth. the radius of the earth is approximately 4000 miles. if a person weighs 189 pounds on earth's surface, what would this person weigh 5000 miles above the surface of earth

120.96 pounds

Explanation:

We know that the weight varies inversely as the square of distance, so if the distance increases, the weight decreases by the square of the increase in distance.

So, if the distance increased from 4000 to 5000 miles, it increased by 5/4. Therefore, the weight will decrease by (4/5) ^2, that is, the inverse squared of the increase in distance.

If the person weights 189 pounds in the 4000 miles distance, in the 5000 miles distance the person will weights 189 * (4/5) ^2 = 189 * 16/25 = 120.96 pounds.