Question

Write an equation describing the relationship of the given variables. y varies inversely with the cube root of x. When x=27 then y=5. Find y when x=125.The value for y is:Answer

Answer 1

Let us begin by representing the relationship using mathematical symbols

`y\text{ }\alpha\text{ }\frac{1}{\sqrt[3]{x}}`

Hence, we can write:

`y\text{ = }\frac{k}{\sqrt[3]{x}}`

Where k is the constant of proportionality

When x = 27 and y =5, we have the equation representing the relationship to be:

`\begin{gathered} 5\text{ = }\frac{k}{\sqrt[3]{27}} \\ k\text{ = 5 }*\text{ 3} \\ k\text{ = 15} \\ \\ y\text{ = }\frac{15}{\sqrt[3]{x}} \end{gathered}`

We are required to find y when x = 125

When we substitute the value of x into the equation above, we have the value of y to be:

`\begin{gathered} y\text{ = }\frac{15}{\sqrt[3]{125}} \\ y\text{ = 3} \end{gathered}`

Answer:

The value of y is 3