SOLUTION: Find an equation of variation in which y varies jointly as x and the square root of z and inversely as w, and y=1 when x=5, z=4 and w=20. Absolutely stumped, any help would be g

Algebra ->  Rational-functions -> SOLUTION: Find an equation of variation in which y varies jointly as x and the square root of z and inversely as w, and y=1 when x=5, z=4 and w=20. Absolutely stumped, any help would be g      Log On


   

Question 1034273: Find an equation of variation in which y varies jointly as x and the square root of z and inversely as w, and y=1 when x=5, z=4 and w=20.
Absolutely stumped, any help would be greatly appreciated. Thank you
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The description is transformed literally the way described.

y=k%5B1%5Dx%2Asqrt%28z%29 and y=k%5B2%5D%281%2Fw%29, but put together as described, y=kx%2Asqrt%28z%29%2Fw.

Solve the formula for k, and use the given data to evaluate k.

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find an equation of variation in which y varies jointly as x and the square root of z and inversely as w, and y=1 when x=5, z=4 and w=20.
Absolutely stumped, any help would be greatly appreciated. Thank you
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The first statement says that 

y = %28k%2Ax%2Asqrt%28z%29%29%2Fw     (1)

with the coefficient of proportionality k = const, constant.

You need to find this coefficient.

The second statement says that

1 = %28k%2A1%2Asqrt%284%29%29%2F20     (2)

after substitution (plugging in) the values y=1, x=1, z=4 and w=20 into (1).

You can rewrite (2) in the form 

1 = %28k%2A1%2A2%29%2F20 = k%2F10     (2')  

and get k = 10.

Now the formula (1) becomes 

y = %2810%2Ax%2Asqrt%28z%29%29%2Fw     (1')

It is exactly what they want from you:

You are expected to write the formula mathematically, based on the word description, and find the proportionality coefficient.