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Question 1185524: Solve each of the following problems.
1. Find the Harmonic mean between 1/2 and 1/10
2. Determine the harmonic mean between x and y
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a reference.
https://www.mathsisfun.com/numbers/harmonic-mean.html
the basic procedure is:
find the reciprocals of the numbers involved.
find the average of those reciprocals.
take the reciprocal of that.
that's your harmonic mean.
in your problem.
the numbers are 1/2 and 1/20.
their reciprocals are 2 and 20.
the average of those reciprocals is 22/2 = 11
the reciprocal of that is 1/11.
that's your harmonic mean.
it's decimal equivalent is .090909091 when rounded to 9 decimal points.
the harmonic mean of x and y is as shown below.
the reciprocal of x and y is 1/x and 1/y.
the sum of 1/x and 1/y is 1/x + 1/y.
1/x * y/y = y/xy.
1/y * x/x = x/xy.
their sum is (x + y) / xy.
their average is (x + y) / xy * 1/2 = (x + y) / 2xy.
the reciprocal of their average is 2xy / (x + y).
that's your harmonic mean of x and y.
as an example, if x = 3 and y = 5, then their harmonic mean would be equal to:
(2*3*5)/(3+5) = 30/8 = 3.75.
if you looked for their harmonic mean directly, you would:
take the reciprocal of each of those numbers = 1/3 and 1/5.
add them up to get 1/3 + 1/5 = 5/15 + 3/15 = 8/15
divide that by the number of numbers = 2 to get (8/15)/2 = 8/30
take the reciprocal of that to get 30/8 which is equal to 3.75.
the solutions to your questions are:
the harmonic mean of 1/2 and 1/20 is equal to 1/11.
the harmonic mean of x and y is 2xy/(x+y).
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