y varies directly as x and inversely as the square of z. y=z when x=63 and z=3. find y when x=50 and z=5

Question

y varies directly as x and inversely as the square of z. y=z when x=63 and z=3. find y when x=50 and z=5

Answer 1

If y varies directly with x then than means y = kx   where k is a constant called the constant of proportion.

If y varies inversely with x then y = k/x ....

 

For this problem y varies directly with x and inversely with z² so...  y = kx/z²

 

We need to find the value of k from the information given.

 

When x = 63 we are told y = z = 3.  Plug that in to find the value of k

 

3 = 63k/3²

3(3²) = 63k

27 = 63k

k = 27/63 = 3/7

 

We now know the value of k so use that information with the new values given...

 

y = kx/z²   y = (3/7)50/5² = 150/7(25) = 6/7