SOLUTION: Y varies directly as x and inversely as the square of z. y=8 when x=50 and z=5. Find y when x=20 and z=2.

Algebra ->  Inverses -> SOLUTION: Y varies directly as x and inversely as the square of z. y=8 when x=50 and z=5. Find y when x=20 and z=2.      Log On


   

Question 1084495: Y varies directly as x and inversely as the square of z. y=8 when x=50 and z=5. Find y when x=20 and z=2.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
direct variation is y = kx

indirect variation is y = k/x

direct and indirect combined variation is y = kx/z

in your problem, z is equal to z^2.

it's the same formula except you replace z with z^2.

the direct and indirect combined variation formula becomes y = kx/z^2

y = 8 when x = 50 and z = 5.

formula becomes 8 = 50 * k / 5^2

simplify this to get 8 = 50 * k / 25

simplify further to get 8 = 2 * k

divide both sides of this equation by 2 and solve for k to get k = 4

now that you know the value of k, you can solve the problem.

the problem is find y when x = 20 and z = 2

formula of y = kx / z^2 becomes y = 20*4/4 which becomes y = 20

that's your solution.