Make y the subject of the formula Z = x\(^2\) + \(\frac{1}{y^3}\)
A. y = \(\frac{1}{(Z - x^2)^3}\) B. y = \(\frac{1}{(Z + x^2)^{\frac{1}{3}}}\) C. y = \(\frac{1}{(Z - x^2)^{\frac{1}{3}}}\) D. y = \(\frac{1}{\sqrt[3]{Z} - \sqrt[3]{x^2}}\)
Correct Answer: C
Explanation
Z = x\(^2\) + \(\frac{1}{y^3}\) Z - x\(^2\) = \(\frac{1}{y^3}\) y\(^3\) = \(\frac{1}{Z - x^2}\) y = \(\sqrt[3]{\frac{1}{Z - x^2}}\) ∴ y = \(\frac{1}{\sqrt[3]{Z - x^2}}\) y = \(\frac{1}{(Z - x^2)^{\frac{1}{3}}}\)
