Question

y varies inversely as the fourth root of x and when x = 81, y = 10. What would be y when x=29. Round your answer to two decimal places.

Answer 1

y=12.93

Explanation:

If y varies inversely as the fourth root of x, then we have:

`y\propto\frac{1}{\sqrt[4]{x}}`

Introducing the constant of variation, k, we have the equation:

`y=\frac{k}{\sqrt[4]{x}}`

When x = 81, y = 10

`\begin{gathered} 10=\frac{k}{\sqrt[4]{81}} \\ \implies10=(k)/(3) \\ \text{Cross multipl}y \\ k=10*3 \\ k=30 \end{gathered}`

Substitute k=30 into the equation of variation.

`y=\frac{30}{\sqrt[4]{x}}`

When x=29.

`\begin{gathered} y=\frac{30}{\sqrt[4]{29}}=(30)/(2.3206)=12.926 \\ y\approx12.93 \end{gathered}`

The value of y when x=29 is 12.93 (correct to 2 decimal places).