Question

F varies inversely as the square of d. When d=2, f = 6. Find d when f is 1.5

Answer 1

d = 4

Explanation:

Given f varies inversely as d² then the equation relating them is

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

To find k use the condition when d = 2, f = 6 , then

6 =
`(k)/(2^2)` =
`(k)/(4)` ( multiply both sides by 4 )

24 = k

f =
`(24)/(d^2)` ← equation of variation

When f = 1.5 , then

1.5 =
`(24)/(d^2)` ( multiply both sides by d² )

1.5d² = 24 ( divide both sides by 1.5 )

d² = 16 ( take the square root of both sides )

d =
`√(16)` = 4