Solving Variation Problems Solutions

• When solving variation problems, it is important to remember that the    constant    of variation is not always provided. 

• How you solve the problem depends on:
 
  •    the given information and    
  •    what is asked.    

Note

Setting up the problem and using substitution are good options for getting started.

Example 3

If y varies directly as ${\mathit{x}}^{\mathbf{2}}\mathbf{,}$ and $\mathit{y}\mathbf{=}\mathbf{–}\mathbf{8}$ when $\mathit{x}\mathbf{=}\mathbf{4}\mathbf{,}$ find y when $\mathit{x}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{2}\mathbf{.}$

Example 4

With stringed instruments, the length, l, of a string varies inversely as the frequency, f, of its vibrations. When the length of a string is 40 centimeters, it vibrates at a frequency of 180 cycles per second. Determine the length of a string with a frequency of 300 cycles per second.