Question 1185524
here's a reference.


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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).