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VMariaS [17]
3 years ago
14

Could someone please help me? Thank you and explain the work because I don’t get this

Mathematics
1 answer:
lesya [120]3 years ago
5 0

Answer:

5.59 times per second.

Step-by-step explanation:

Direct variation is in the form:

y=kx

Where <em>k</em> is the constant of variation.

Inverse variation is in the form:

\displaystyle y=\frac{k}{x}

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:

\displaystyle f=\frac{k}{\ell}

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:

\displaystyle 4.3=\frac{k}{0.65}

Solve for <em>k: </em>

<em />k=4.3(0.65)=2.795<em />

<em />

So, our equation becomes:

\displaystyle f=\frac{2.795}{\ell}

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

\displaystyle f=\frac{2.795}{.5}=5.59\text{ times per second.}

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