y varies directly as x and inversely as the square of z. y=20 when x =80 and z=4. Find y when x=56 and z=2

Question

y varies directly as x and inversely as the square of z. y=20 when x =80 and z=4. Find y when x=56 and z=2

Answer 1

 

y = k*x/z^2 for some fixed number constant k

 

20 = k(80/4^2) = k(80/16) = 5k

 

k = 20/5 = 4

 

The function is  y = 4*x/z^2

 

Then y = 4*56/2^2 = 4*56/4 = 56