If \(y \propto \frac{1}{\sqrt{x}}\) and x = 16 when y = 2, find x when y = 24
-
\(\frac{1}{9}\)
- \(\frac{1}{6}\)
- \(\frac{1}{3}\)
- \(\frac{2}{3}\)
The correct answer is: A
Explanation
\(y \propto \frac{1}{\sqrt{x}}\)
\(y = \frac{k}{\sqrt{x}}\)
When x = 16, y = 2.
\(2 = \frac{k}{\sqrt{16}} \implies 2 = \frac{k}{4}\)
\(k = 8\)
\(y = \frac{8}{\sqrt{x}}\)
When y = 24,
\(24 = \frac{8}{\sqrt{x}}\)
\(\sqrt{x} = \frac{8}{24} = \frac{1}{3}\)
\(\therefore x = (\frac{1}{3})^2\)
\(x = \frac{1}{9}\)