The quantity y is partly constant and partly varies inversely as the square of z.when y =6, z =2 and when y =4.5, z= 4. Find the relationship between y and z and find y when z = 10
Let's denote the constant part of y as k. So, we have:
y = k * (1/z^2)
Using the given values when y = 6 and z = 2, we can solve for k:
6 = k * (1/2^2)
6 = k * (1/4)
k = 24
Now, we can substitute the value of k into the equation to get:
y = 24 * (1/z^2)
Using the given values when y = 4.5 and z = 4, we can find the relationship between y and z:
4.5 = 24 * (1/4^2)
4.5 = 24 * (1/16)
4.5 = 24/16
4.5 = 1.5
So, our relationship between y and z is:
y = 1.5
Now, we can find y when z = 10:
y = 1.5 * (1/10^2)
y = 1.5 * (1/100)
y = 1.5/100
y = 0.015