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 = \(\frac{1}{\sqrt[3]{Z} - \sqrt[3]{x^2}}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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 = \(\frac{1}{(Z - x^2)^{\frac{1}{3}}}\)
Source: Myschool Past Questions Archive (Record #31893)