Answer:
d ≈ 5.66
Step-by-step explanation:
given that F varies inversely with d squared, then the equation connecting them is
F = [tex]\frac{k}{d^{2} }[/tex] ← k is the constant of variation
to find k use the condition when F = 8, d = 6
k = Fd² = 8 × 36 = 288, hence
F = [tex]\frac{288}{d^{2} }[/tex]
when F = 9, then
9 = [tex]\frac{288}{d^{2} }[/tex] ← multiply both sides by d²
9d² = 288 ( divide both sides by 9 )
d² = 32 ( take the square root of both sides )
d = ± [tex]\sqrt{32}[/tex], hence
d ≈ 5.66 ← positive value only
