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.
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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) (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.
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