Answer:
5.59 times per second.
Step-by-step explanation:
Direct variation is in the form:

Where <em>k</em> is the constant of variation.
Inverse variation is in the form:

In the given problem, the frequency of a vibrating guitar string varies inversely as its length. In other words, using <em>f</em> for frequency and <em>l</em> for length:

We can solve for the constant of variation. We know that the frequency <em>f</em> is 4.3 when the length is 0.65 meters long. Thus:

Solve for <em>k: </em>
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So, our equation becomes:

Then when the length is 0.5 meters, the frequency will be:

Begin solving like you normally would. Add 2.25 to both sides and subtract 9x from both sides to try getting all x values on one side. However, you will find that after subtracting 9x from both sides, all x values go away, and you end with -2.25=1.6. This is not true (-2.25 is not 1.6), so the answer is no solution. There is no value of x which satisfies that equation.
Answer:
9
Step-by-step explanation: