Answer:
A
Step-by-step explanation:
let r represent rate and d distance.
Given that r varies directly as d² then the equation relating them is
r = kd² ← k is the constant of variation
To find k use the condition r = 4 when d = 15, then
4 = k × 15² = 225k ( divide both sides by 225 )
k = [tex]\frac{4}{225}[/tex]
r = [tex]\frac{4}{225}[/tex] d² ← equation of variation
When r = 9, then
9 = [tex]\frac{4}{225}[/tex]d² ( multiply both sides by 225 )
2025 = 4d² ( divide both sides by 4 )
506.25 = d² ( take the square root of both sides )
d = [tex]\sqrt{506.25}[/tex] = 22.5 = 22 [tex]\frac{1}{2}[/tex] → A
