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?

Question

asked Feb 23, 2020 231k views

2 Answers

Amrro · Answer 1 · 2020-02-29T15:47:52+0000

Answer:

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=(63)/(4)