Question

If y varies directly with the square root of x and inversely with z, what is the constant of proportionality if y = 27 when x= 9 and z = 6? A 13.5 B 18 C 54 D 2

Answer 1

C) 54

1) In this combined variation, let's write out the given relationship:

Considering that y varies directly with the square root of x and inversely with z.

Now we can find k, the constant of proportionality:

`\begin{gathered} y=\frac{k\sqrt[]{x}}{z} \\ 27=\frac{k\sqrt[]{9}}{6} \\ k\sqrt[]{9}=6\cdot27 \\ k\sqrt[]{9}=162 \\ 3k=162 \\ (3k)/(3)=(162)/(3) \\ k=54 \end{gathered}`

2) Note that since this is a combined variation we need to write it as a unique equation.

3) Hence, the answer is C) 54