SOLUTION: I really need help with this fast! 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 tha

Question 970554: I really need help with this fast!
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)=________
please explain and thanks in advance.
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39628) (Show Source): You can put this solution on YOUR website!
Already answered. You need to be precise.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The variable z varies jointly with x and y and inversely with the square of t.
z = k*x*y/t^2
------------
Also, z=5 when x=2, y=-3, and t=1/2.
Use these value to solve for "k"::
5 = k*2*-3/(1/2)^2
---
5 = k*-6/4
-6k = 20
-k = 10/3
k = 10/3
-------------------
Equation::
z = (10/3)*x*y/t^2
===============================
Write a function such that f(y)=t when x=-12/(5z)^2 and z=2/5.
---------
(2/5) = (10/3)*(12/25z^2)*y/t^2
----------------
Solve for "y"::::
y = (2/5)t^2/[(8/5z^2]
y = (1/4)(t/z)^2
Cheers,
Stan H.

f(y)=________
======
Cheers,
Stan H.
-----------------
RELATED QUESTIONS
I really need help with this fast! The variable z varies jointly with x and y and... (answered by josgarithmetic)
Find and equation of varitation for the given situation. 1) y varies inversely as the (answered by stanbon)
The variable w varies jointly with y and the square of x and inversely with the square... (answered by Boreal)
Please help me with the following question: Find an equation of variation where y varies (answered by gonzo)
a) y varies jointly as x and w and inversely as the square of z. Find the equation of... (answered by josgarithmetic)
a varible z varies jointly with x and the square of y. if z=5 when x=3 and y=4, find the (answered by stanbon)
A variable z varies jointly with x and the square of y. If z = 6 when x = 4 and y = 3,... (answered by psbhowmick,venugopalramana)
The variable z varies jointly with x and y. Also, z=-75 when x =3 and y=-5. Write an... (answered by stanbon)
When x = 2 and y = 3, z = 42. Write the function that models each of the following... (answered by Theo)