Question

Suppose r varies directly with the square of m and inversely as s. If r= 12 when m = 6 and s=4, find r when m = 4 and s 10

please show work​

Answer 1

`r=(32)/(15)`

Explanation:

If r varies directly with the square of m and inversely as s,

then
`r=(km^2)/(s)` where k is some constant

Given r = 12 when m = 6 and s = 4:

`r=(km^2)/(s)`

⇒
`12=(k6^2)/(4)`

⇒
`(12*4)/(6^2) =k`

⇒ k =
`(4)/(3)`

Therefore, substituting the found value of k into the original equation:
`r=(4m^2)/(3s)`

Find r when m = 4 and s = 10:

`r=(4m^2)/(3s)`

⇒
`r=(4*4^2)/(3*10)`

⇒
`r=(32)/(15)`