Questions: Write an equation describing the relationship of the given variables. y varies inversely as the cube root of x and when x=8, y=7.

Transcript text: Write an equation describing the relationship of the given variables. $y$ varies inversely as the cube root of $x$ and when $x=8, y=7$.

Solution

Solution Steps

Step 1: Determine the constant of proportionality $k$

To find the constant of proportionality $k$, we substitute the given values of $x = 8$ and $y = 7$ into the equation $y = \frac{k}{\sqrt[3]{x}}$. Solving for $k$, we get $k = y \times \sqrt[3]{x} = 7 \times 2 = 14$.

Step 2: Use $k$ to find the specific equation

With $k = 14$, the specific equation that describes the relationship between $y$ and $x$ is $y = \frac{14}{\sqrt[3]{x}}$.