Question

F is inversely proportional to d^2.

When F = 5, d = 9
Work out d (positive value rounded to 2 DP) when F = 3

Answer 1

11.62

Explanation:

F is inversely proportional to d^2, so

`F=(k)/(d^2)`

for some constant k. To find k plug in given values for F and d.

`5=(k)/(9^2)\\5=(k)/(81)\\k=405`

Now you can find d for F = 3.

`3=(405)/(d^2)\\\\3d^2=405\\\\d^2=135\\d=√(135)\approx 11.62`

Answer 2

11.6

Explanation:

F = k/ d^2

where k = proportionality constant

k = Fd^2

k = 5 * 9^2

k = 5*81 = 405

d = (K/F)^1/2

d = (405/3)^1/2

d = 11.62 =11.6