Question

F is inversely proportional to d^2.

When F = 15, d = 4
Work out d (positive value rounded to 2 DP) when F = 6

Answer 1

d ≈ 6.32

Explanation:

Given F is inversely proportional to d² then the equation relating them is

F =
`(k)/(d^2)` ← k is the constant of proportion

To find k use the condition when F = 15, d = 4 , then

15 =
`(k)/(4^2)` =
`(k)/(16)` ( multiply both sides by 16 )

240 = k

F =
`(240)/(d^2)` ← equation of proportion

When F = 6 , then

6 =
`(240)/(d^2)` ( multiply both sides by d² )

6d² = 240 ( divide both sides by 6 )

d² = 40 ( take positive square root of both sides )

d =
`√(40)` ≈ 6.32 ( to 2 dec. places )