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

2

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(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(9^2)/(27)`

`6=k(81)/(27)`

`6=k(3)`

Divide both sides by 3:

`2=k`

So the constant of variation is 2.

Answer 2

The constant of variation is 2.

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(x^(2) )/(z)`

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

`6=a*(9^(2))/(27)\\6=a*(81)/(27)\\6=a*3\\a=2`

The constant of variation is 2.