An alcohol solution consists of 6 gallons of pure water and x gallons of alcohol, x > 0. Let f(x) be the ratio of the volume of alcohol to the total volume of liquid. [Note that f(x) is the concentration of the alcohol in the solution.]
(a) Find a possible formula for f(x).
a. F(x) = x/(x+6).
Why did the alcohol go to school?
To get more proof!
Now, let's find the formula for f(x). We know that f(x) is the ratio of the volume of alcohol to the total volume of liquid.
So, the total volume of liquid is 6 gallons of water plus x gallons of alcohol, which is 6 + x gallons.
The volume of alcohol is x gallons.
Therefore, the formula for f(x) is:
f(x) = volume of alcohol / total volume of liquid
f(x) = x / (6 + x)
Voila! There you have it, a possible formula for f(x). Cheers!
To find a possible formula for f(x), we need to find the ratio of the volume of alcohol to the total volume of liquid.
Given that the alcohol solution consists of 6 gallons of pure water and x gallons of alcohol, the total volume of liquid is 6 + x gallons.
Since the concentration of alcohol in the solution is f(x), we can express the volume of alcohol as f(x) times the total volume of liquid.
Therefore, the volume of alcohol is f(x) * (6 + x) gallons.
The ratio of the volume of alcohol to the total volume of liquid is then:
f(x) = (volume of alcohol) / (total volume of liquid)
= (f(x) * (6 + x)) / (6 + x)
So, a possible formula for f(x) is:
f(x) = (f(x) * (6 + x)) / (6 + x)
To find a formula for f(x), we need to determine the ratio of alcohol volume to the total liquid volume.
We are given that the solution consists of 6 gallons of pure water and x gallons of alcohol. The total volume of liquid in the solution is 6 + x gallons.
The volume of alcohol in the solution is x gallons.
Therefore, the ratio of alcohol volume to the total liquid volume, f(x), is given by:
f(x) = x / (6 + x)
So, a possible formula for f(x) is f(x) = x / (6 + x).