Question

Please, I could really use some help.

Z is directly proportional to x and inversely proportional to y^2.

a. if Z=10 when x=2 and y =1, what is z when x= 4 and y =3.

b. if y doubles by what factor must x change in order for z to remain the same ?

I need help with part B please.

Answer 1

Z= k x / y^2 but you have to find k from the Z, x, y combination given.

After that, plug values into the equation you found and you are done.

Answer 2

The equation is in the form of

\[\Large Z = \frac{kx}{y^2}\]

Answer 3

Since y doubles, you replace y with 2y and simplify to get

\[\Large Z = \frac{kx}{y^2}\]

\[\Large Z = \frac{kx}{(2y)^2}\]

\[\Large Z = \frac{kx}{4y^2}\]

Answer 4

To force the right side in the third line to turn back into the right side of the 1st line, you must replace x with 4x (so the 4's divide and cancel out)

So that means x must quadruple