Questions: Write an equation describing the relationship of the given variables. y varies inversely as the cube root of x and when x=125, y=3.

Transcript text: Write an equation describing the relationship of the given variables. $y$ varies inversely as the cube root of $x$ and when $x=125, y=3$. \[ y= \] $\square$

Solution

Solution Steps

Step 1: Determine the constant of proportionality $k$

To find the constant of proportionality $k$, we substitute the given values of $x = 125$ and $y = 3$ into the equation $y = \frac{k}{\sqrt[3]{x}}$. Solving for $k$, we get $k = y \times \sqrt[3]{x} = 3 \times 5 = 15$.

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

With $k = 15$, the specific equation that describes the relationship between $y$ and $x$ is $y = \frac{15}{\sqrt[3]{x}}$.