The variable z varies jointly with x and y and inversely with the square of t. Also, z=5 when x=2, y=-3, and t=1/2. Write a function such that f(y)=t when x=(-12)/(5z)^2 and z=2/5.
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+33653
z= kxy/t^2
5 = k*2*(-3)/(1/4). Hence k = -5/24
z = -(5/24)xy/t^2
When x = -12/(5z)^2 then z = -(5/24)(-12)y/(5zt)^2 or z^3 = y/(10t^2)
With z = 2/5 we have 8/125 = y/(10t^2) so that t = (5/4)y^(1/2)
Hence if f(y) = (5/4)y^(1/2) then f(y) = t when the above conditions hold.
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