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

Answer 1

Since y varies directly with the square root of x and inversely with z, then the equation that relates x, y and z has the form:

$y=k\cdot\frac{x^2}{z}$

To find the value of the constant of proportionality k, substitute the given values of x, y and z:

$\begin{gathered} 27=k\cdot\frac{9^2}{6} \\ \Rightarrow27=k\cdot\frac{81}{6} \\ \Rightarrow k=\frac{6\cdot27}{81} \\ \Rightarrow k=2 \end{gathered}$

Therefore, the value of the constant of proportionality, is:

$2$