Question

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

Answer 1

Answer:

5.59 times per second.

Step-by-step explanation:

Direct variation is in the form:

$y=kx$

Where k 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 f for frequency and l for length:

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

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

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

Solve for k:

$k=4.3(0.65)=2.795$

So, our equation becomes:

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

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

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