We need to find two relations, and use them to find the value of y when z = 15.
We will see that the value of y in that case is 4,860.
We know that <u>y varies inversely with the square of x</u>, also <u>y is also proportional to the cube of z</u>
Then we can write:
y = k/x^2
y = c*z^3
We also know that:
When x = 3, y = 80.
Replacing that in the first equation to find the value of k:
80 = k/3^2
80 = k/9
80*9 = k = 720
We also know that when x = 2, z = 5
From the first relation we have:
y = 720/2^2 = 720/4 = 180
Now we replace this in the equation of y and z:
y = c*z^3
180 = c*5^3
180 = c*125
180/125 = c = 1.44
Now we need to calculate y when z = 15, then we just need to replace z by 15 in the equation for y and z:
y = 1.44*(15)^3 = 4,860.
If you want to learn more, you can read:
brainly.com/question/2548537
