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=(10k)/(5) \\ 14=2k \\ k=(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}}=(112)/(2) \\ y=56 \end{gathered}`

Therefore, the value of y is 56.