The wavelength, W, of a wave varies inversely as its frequency, F. A wave with a frequency of 500 kHz has a length of 158 meters. What is the frequency of a wave with a length of 282 meters? Round your answer to the nearest tenth.

The equation of variation is $LaTeX: \displaystyle W = \frac{k}{F}$ . Substituting gives $LaTeX: \displaystyle W = \frac{k}{500}$ and solving for $LaTeX: \displaystyle k$ gives $LaTeX: \displaystyle 79000$ . This gives the variation equation $LaTeX: \displaystyle W = \frac{79000}{F}$ . Using the given wave length gives the equation $LaTeX: \displaystyle 282 = \frac{79000}{F}$ . Solving for $LaTeX: \displaystyle F$ gives $LaTeX: \displaystyle F = \frac{79000}{282}=280.1$ meters.