Answer:
[tex]\displaystyle W = \frac{2\,722\,590\, 000}{d^{2}}[/tex]
(Where [tex]W[/tex] refers to the apparent weight in pounds when measured on the surface of the Earth, and [tex]d[/tex] is measured in miles.)
Step-by-step explanation:
Given that [tex]W[/tex] is inversely proportional to the square of [tex]d[/tex], there exists a constant [tex]k[/tex] such that:
[tex]\displaystyle W = \frac{k}{d^{2}}[/tex].
The goal is to find the value of [tex]k[/tex]. Given that [tex]W = 179[/tex] when [tex]d = 3900[/tex]:
[tex]\displaystyle (179) = \frac{k}{(3900)^{2}}[/tex].
Rearrange to obtain:
[tex]\begin{aligned} k &= (179)\, (3900)^{2} \\ &= 2\, 722\, 590\, 000 \end{aligned}[/tex].
Hence, the relation between [tex]W[/tex] and [tex]d[/tex] would be:
[tex]\displaystyle W = \frac{2\,722\,590\, 000}{d^{2}}[/tex].
