Question

Z varies directly with x4 and inversely with y.

When x = 2 and y = 4, z = 3.
What is the value of z when x = 4 and y = 9?

Answer 1

z=(kx)/y
3=(k*2)/4
3=k/2
k=6
***
z=6x/y
***
z=6*4/9
z=8/3

Answer 2

`z=(63)/(4)`

Explanation:

When two variables vary in a directly proportional way, it means that when one variable grows, the other also grows.

This is represented by the following equation

`y = kx`

Where k is the constant of proportionality

When two variables vary in an inversely proportional way, it means that when one variable grows, the other decreases.

This is represented by the following equation

`y = (k)/(x)`

In this case we know that:

z varies directly with
`x^4` and inversely with y.

We write this as:

`z = k(x ^ 4)/(y)`

We know that When
`x = 2` and
`y = 4,\ z = 3`.

So we use this information to find the constant k

`3 = k(2 ^ 4)/(4)`

`3 = k(16)/(4)`

`3 = 4k`

`k = (3)/(4)`

So the equation is:

`z = (3)/(4)(x ^ 4)/(y)`

Finally when x = 4 and y = 9 then:

`z = (3)/(4)(4 ^ 4)/(9)`

`z = (3)/(4)(4 ^ 4)/(9)`

`z=(63)/(4)`