The quantity y varies directly with the square of x and inversely with z. when x is 9 and z is 27. y is 6. what is the constant of
variation

2

Step-by-step explanation:

Varies directly means we multiply to the constant, where as inversely means we divide the constant.

So we have

"y varies directly with the square of x and inversely with z".

This means x^2 will be on top and z will be on bottom.

Like this:

We are given x=9,z=27, and y=6.  This will allow us to find k.

k is constant no matter what (x,y,z) we have.

Divide both sides by 3:

So the constant of variation is 2.