Question

If y varies jointly as the cube of x, w, and the square of z, what is the effect on w when x, y, and z are doubled?

Answer 1

`w` decreases by a factor of 16.

That is, `w_"new" = 1/16w`

Explanation:

Based on this description, we can create the following equation:

`y = kx^3wz^2`

Where `k` is a constant which doesn't really matter for this particular problem.

The problem asks what happens to `w` when the other variables are doubled, so let's solve for `w` to see what it is originally.

`y = kx^3wz^2`

`y/(kx^3z^2)=w`

Now, the problem asks us to double everything except `w` and see what happens.

`((2y))/(k(2x)^3(2z)^2)=w_"new"`

`(2y)/(k(8x^3)(4z^2))=w_"new"`

`2/(8*4)(y/(kx^3z^2))=w_"new"`

`1/16(y/(kx^3z^2))=w_"new"`

`1/16w = w_"new"`

So `w` decreases by a factor of 16 when the other 3 variables are doubled.

Final Answer