Answer:
d ≈ 6.32
Step-by-step explanation:
Given F is inversely proportional to d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of proportion
To find k use the condition when F = 15, d = 4 , then
15 = [tex]\frac{k}{4^2}[/tex] = [tex]\frac{k}{16}[/tex] ( multiply both sides by 16 )
240 = k
F = [tex]\frac{240}{d^2}[/tex] ← equation of proportion
When F = 6 , then
6 = [tex]\frac{240}{d^2}[/tex] ( multiply both sides by d² )
6d² = 240 ( divide both sides by 6 )
d² = 40 ( take positive square root of both sides )
d = [tex]\sqrt{40}[/tex] ≈ 6.32 ( to 2 dec. places )
