Question

If r varies directly as p and inversely as q2, and r = 27 when p =3 and q = 2, find r when p = 2 and q= 3

k = ______r = ______

Answer 1

k = 36 and r = 8

Explanation:

Given that r varies directly as p and inversely as q² then the equation relating them is

r =
`(kp)/(q^2)` ← k is the constant of variation

To find k use the condition r = 27 when p 3 and q = 2, thus

27 =
`(3k)/(4)` ( multiply both sides by 4 )

108 = 3k ( divide both sides by 3 )

k = 36

r =
`(36p)/(q^2)` ← equation of variation

When p = 2 and q = 3, then

r =
`(36(2))/(3^2)` =
`(72)/(9)` = 8