Question

____INVERSE PROPORTION_____

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F is inversely proportional to d squared
When F=8 d=6

Work out d (positive value rounded to 2 DP) when F=9

Answer 1

d ≈ 5.66

Explanation:

given that F varies inversely with d squared, then the equation connecting them is

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

to find k use the condition when F = 8, d = 6

k = Fd² = 8 × 36 = 288, hence

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

when F = 9, then

9 =
`(288)/(d^(2) )` ← multiply both sides by d²

9d² = 288 ( divide both sides by 9 )

d² = 32 ( take the square root of both sides )

d = ±
`√(32)`, hence

d ≈ 5.66 ← positive value only