Question

Write an equation that describes the following relationship: y varies inversely as the cube root of x and when x=64, y=2

Answer 1

Since y varies inversely as the cube root of x then:

$\begin{gathered} y=\frac{k}{\sqrt[3]{x}}, \\ \text{where k is the constant of proportionality.} \end{gathered}$

Now, to determine the value of k, we use the fact that when x=64, y=2:

$2=\frac{k}{\sqrt[3]{64}}.$

Solving the above equation for k we get:

$\begin{gathered} \frac{k}{\sqrt[3]{64}}\times\sqrt[3]{64}=2\times\sqrt[3]{64}, \\ k=2\sqrt[3]{64}, \\ k=2\cdot4=8. \end{gathered}$

Therefore:

$y=\frac{8}{\sqrt[3]{x}}\text{.}$

Answer:

$y=\frac{8}{\sqrt[3]{x}}\text{.}$