If x varies inversely as the cube root of y and x = 1 when y = 8, find y when x = 3
A. \(\frac{1}{3}\)
B. \(\frac{2}{3}\)
C. \(\frac{8}{27}\)
D. \(\frac{4}{9}\)
Correct Answer: C
Explanation
\(x \propto \frac{1}{\sqrt[3]{y}} \implies x = \frac{k}{\sqrt[3]{y}}\)
When y = 8, x = 1
\(1 = \frac{k}{\sqrt[3]{8}} \implies 1 = \frac{k}{2}\)
\(k = 2\)
\(\therefore x = \frac{2}{\sqrt[3]{y}}\)
When x = 3,
\(3 = \frac{2}{\sqrt[3]{y}} \implies \sqrt[3]{y} = \frac{2}{3}\)
\(y = (\frac{2}{3})^{3} = \frac{8}{27}\)
