Question

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​

Answer 1

Answer:

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:

$y=k\frac{x^2}{z}$

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.

$6=k\frac{9^2}{27}$

$6=k\frac{81}{27}$

$6=k(3)$

Divide both sides by 3:

$2=k$

So the constant of variation is 2.

Answer 2

Answer:

The constant of variation is 2.

Step-by-step explanation:

If y is directly influenced by x², it means that the function of y will be multiplied with x². with y being inversely influenced by z, it means that the function will be divided by z. The entire function can be written as being multiplied by an unknown factor, a:

$y=a\frac{x^{2} }{z}$

Replacing the known values of x, y and z, the unknown factor, a can be calculated:

$6=a*\frac{9^{2}}{27}\\6=a*\frac{81}{27}\\6=a*3\\a=2$

The constant of variation is 2.