Question

y varies jointly as a and B and inversely as the square root of C. Y=14 when a= 5, B = 2 and c=25.Find Y when a=4, B=4, c= 4.

Answer 1

First, let's write the expression described by the problem.

$y=\frac{k(ab)}{\sqrt[]{c}}$

Then, we use the given magnitudes to find k (the constant of proportionality).

$\begin{gathered} 14=\frac{k(5\cdot2)}{\sqrt[]{25}} \\ 14=\frac{10k}{5} \\ 14=2k \\ k=\frac{14}{2} \\ k=7 \end{gathered}$

The constant of proportionality is 7.

Then, we use k value to find y with a = 4, b = 4, and c = 4.

$\begin{gathered} y=\frac{7(4\cdot4)}{\sqrt[]{4}}=\frac{112}{2} \\ y=56 \end{gathered}$

Therefore, the value of y is 56.