please help with this problem!!!!!
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.
f(y)=________ ????????
+33653 1. z(x,y,t) = k*x*y/t where k is a constant
We know that 5 = k*2*(-3)/(1/2) or 5 = -12k so k = -5/12
Hence z(x,y,t) = -5xy/(12t)
2. When x = -12/(5z)^2 we have z = -5*(-12)/(5z)^2*y/(12t) or z = y/(5z^2*t) or t = y/(5z^3)
Since z = 2/5 then t = y/(5*2^3/5^3) or t = 25y/8
3. Since f(y) = t we must have f(y) = 25y/8
(check the algebra - I did this quickly!)
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