Answer:
d ≈ 10.80
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 variation
To find k use the condition F = 14, d = 5 , then
14 = [tex]\frac{k}{5^2}[/tex] = [tex]\frac{k}{25}[/tex] ( multiply both sides by 25 )
350 = k
F = [tex]\frac{350}{d^2}[/tex] ← equation of variation
when F = 3 , then
3 = [tex]\frac{350}{d^2}[/tex] ( multiply both sides by d² )
3d² = 350 ( divide both sides by 3 )
d² = [tex]\frac{350}{3}[/tex] ( take square root of both sides )
d = [tex]\sqrt{\frac{350}{3} }[/tex] ≈ 10.80 ( positive value to 2 dec. places )
