Question

____INVERSE PROPORTION_____

Answer 1

Answer:

d ≈ 5.66

Step-by-step explanation:

given that F varies inversely with d squared, then the equation connecting them is

F = $\frac{k}{d^{2} }$ ← k is the constant of variation

to find k use the condition when F = 8, d = 6

k = Fd² = 8 × 36 = 288, hence

F = $\frac{288}{d^{2} }$

when F = 9, then

9 = $\frac{288}{d^{2} }$ ← multiply both sides by d²

9d² = 288 ( divide both sides by 9 )

d² = 32 ( take the square root of both sides )

d = ± $\sqrt{32}$, hence

d ≈ 5.66 ← positive value only