A quantity x varies directly with the cube of y and inversely with the square root of z.

Question

A quantity x varies directly with the cube of y and inversely with the square root of z. If x = 571.66666666667 when y = 7 and z = 9, find x when y = 6 and z = 4.

Answer 1

x varies directly with the cube of y and inversely with the square root of z:

 

x = ky³/√z  where k is the constant of proportion

 

571.66666666667 = k(7)³/√9

 

Note.. 571.66666666667 = 571 2/3 = 1715/3

 

1715/3 = 343k/3

 

3(1715/3) = 343k

 

1715 = 343k

 

k = 1715/343 = 5

 

Your equation is:  x = 5y³/√z

 

Now, given values of any 2 variables you can find the value of the 3rd.

Just plug in the 2 given values.

 

y=6, z=4, find x

x = 5(6)³/√4

x = 540