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>
<em />
<em />
<em />
So, our equation becomes:

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

Answer:
250 nickles
Step-by-step explanation:
Nickles and dimes are coins with different currency values. One nickel(N) is equal to 5 cents while one dime(D) is equal to 10 cents. The ratio of nickel:dime is 5:7, to put into the equation it will be:
N/D= 5/7
7N=5D ---> 1st equation
There are 350 dimes, the equation will be:
D=350 ----> 2nd equation
We can find out the number of nickels by substitute the 2nd equation into the first. The calculation will be
7N=5D
N= 5D/7
N=5(350)/7
N= 250
Answer:

Step-by-step explanation:
Here is a problem with the concept of properties of the exponent.
We are given
and we have to find the value of 5x.
Now,
{Since we are given that
}
⇒
{Since we can write
}
⇒
{Since we know the formula of exponent as
}
(Answer)
Rewrite 9 1/6 divided by 5/6 as follows:
55 6
---- * -----
6 5
Reducing this produces the desired quotient, 11.