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

Answer:

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

$\begin{gathered} 10=\frac{k}{\sqrt[4]{81}} \\ \implies10=\frac{k}{3} \\ \text{Cross multipl}y \\ k=10\times3 \\ k=30 \end{gathered}$

Substitute k=30 into the equation of variation.

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

When x=29.

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

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