Answer
$\approx 54.86$ lb.
Work Step by Step
If the weight $w$ varies inversely with $d^{2}$, then
there is a nonzero constant $k$ such that
$w=\displaystyle \frac{k}{d^{2}}$
---
If $ w=55$ when $d=3960$,
substituting, we find k:
$55=\displaystyle \frac{k}{3960^{2}}\quad/\times 3960^{2}$
$k=862,488,000$
Thus, we write: $\displaystyle \quad w=\frac{862,488,000}{d^{2}}.$
If $d=3965$,
$w=\displaystyle \frac{862,488,000}{3965^{2}}\approx 54.86$ lb.
