Question

F is inversely proportional to √g
.When f=12, g=64
Work out g when f=16

Answer 1

g = 36

Explanation:

Given f is inversely proportional to
`√(g)` then the equation relating them is

f =
`(k)/(√(g) )` ← k is the constant of proportion

To find k use the condition when f = 12 , g = 64 , then

12 =
`(k)/(√(64) )` =
`(k)/(8)` ( multiply both sides by 8 )

96 = k

f =
`(96)/(√(g) )` ← equation of proportion

When f = 16 , then

16 =
`(96)/(√(g) )` ( multiply both sides by
`√(g)`

16 ×
`√(g)` = 96 ( divide both sides by 16 )

`√(g)` = 6 ( square both sides )

g = 6² = 36

Answer 2

36

Explanation:

f * √g = k

12 * √64 = k

k = ± 96

g = k² / f² = (± 96)² / 16² = 36