Mathematics: Zvaries 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?

The first one is 8x=ythe second one is 4x=y...

Zvaries directly with x4 and inversely with y.

florochoa217

13.03.2022

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

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:

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

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

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