Question

The quantity n varies jointly with the product of z and the square of the sum of x and yWhen n is 18, x = 2, y = 1, and z = 3What is the constant of variation?

Answer 1

The constant of variation is
`(2)/(3)`.

Explanation:

Given : The quantity n varies jointly with the product of z and the square of the sum of x and y When n is 18, x = 2, y = 1, and z = 3.

To find : What is the constant of variation?

Solution :

The quantity n varies jointly with the product of z and the square of the sum of x and y,

i.e.
`n\propto z(x+y)^2`

`n=k* z(x+y)^2`

Where, k is the constant of variation.

Substitute n=18, x = 2, y = 1, and z = 3,

`18=k* 3(2+1)^2\\\\18=k* 3(3)^2\\\\18=k* 3* 9\\\\18=27k\\\\k=(18)/(27)\\\\k=(2)/(3)`

Therefore, the constant of variation is
`(2)/(3)`.