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

Answer:

$z=\frac{63}{4}$

Step-by-step 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

$y = \frac{k}{x}$

In this case we know that:

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

We write this as:

$z = k\frac{x ^ 4}{y}$

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

So we use this information to find the constant k

$3 = k\frac{2 ^ 4}{4}$

$3 = k\frac{16}{4}$

$3 = 4k$

$k = \frac{3}{4}$

So the equation is:

$z = \frac{3}{4}\frac{x ^ 4}{y}$

Finally when x = 4 and y = 9 then:

$z = \frac{3}{4}\frac{4 ^ 4}{9}$

$z = \frac{3}{4}\frac{4 ^ 4}{9}$

$z=\frac{63}{4}$