Question

You may use k to represent the constant of variation in your working if necessary.

Answer 1

r = 1.6

Explanation:

given r varies directly with m² and inversely as n then the equation relating them is

r =
`(km^2)/(n)` ← k is the constant of variation

to find k use the condition r = 18 when m = 6 and n = 4 , then

18 =
`(k(6)^2)/(4)` =
`(36k)/(4)` ( multiply both sides by 4 to clear the fraction )

72 = 36k ( divide both sides by 36 )

2 = k

r =
`(2m^2)/(n)` ← equation of variation

when m = 2 and n = 5 , then

r =
`(2(2)^2)/(5)` =
`(2(4))/(5)` =
`(8)/(5)` = 1.6