Question

Let a be directly proportional to m and n^2, and inversely proportional to y^3. If a=4 when m=9, n=4, and y=2, find a when m=7, n=3, and y=5.

a=? (Type an integer or a simplified fraction.)

Answer 1

4

Explanation:

Step 1

Let a be directly proportional to m and n^2

a
`\alpha` m(n)²

a = km(n)²

Step 2

Let a be inversely proportional to y^3

a
`\alpha`
`(1)/(y^(3) )`

a =
`(k)/(y^(3) )`

Step 3

Plug values in the equation to find k

4 = k (9)(4)²/2³

4 = k 144 / 8

4 = 18k

k = 4/18

k = 2/9

Step 4

find a

a = (2/9)(9)(4)²/2³

= 32 / 8

= 4