document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185524>Question 1185524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following problems.\r<BR>\n" );
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document.write( "1. Find the Harmonic mean between 1/2 and 1/10<BR>\n" );
document.write( "2. Determine the harmonic mean between x and y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816360 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/numbers/harmonic-mean.html\" target = \"_blank\">https://www.mathsisfun.com/numbers/harmonic-mean.html</a>\r<BR>\n" );
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document.write( "the basic procedure is:\r<BR>\n" );
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document.write( "find the reciprocals of the numbers involved.\r<BR>\n" );
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document.write( "find the average of those reciprocals.\r<BR>\n" );
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document.write( "take the reciprocal of that.\r<BR>\n" );
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document.write( "that's your harmonic mean.\r<BR>\n" );
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document.write( "in your problem.\r<BR>\n" );
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document.write( "the numbers are 1/2 and 1/20.\r<BR>\n" );
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document.write( "their reciprocals are 2 and 20.\r<BR>\n" );
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document.write( "the average of those reciprocals is 22/2 = 11\r<BR>\n" );
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document.write( "the reciprocal of that is 1/11.\r<BR>\n" );
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document.write( "that's your harmonic mean.\r<BR>\n" );
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document.write( "it's decimal equivalent is .090909091 when rounded to 9 decimal points.\r<BR>\n" );
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document.write( "the harmonic mean of x and y is as shown below.\r<BR>\n" );
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document.write( "the reciprocal of x and y is 1/x and 1/y.\r<BR>\n" );
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document.write( "the sum of 1/x and 1/y is 1/x + 1/y.\r<BR>\n" );
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document.write( "1/x * y/y = y/xy.\r<BR>\n" );
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document.write( "1/y * x/x = x/xy.\r<BR>\n" );
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document.write( "their sum is (x + y) / xy.\r<BR>\n" );
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document.write( "their average is (x + y) / xy * 1/2 = (x + y) / 2xy.\r<BR>\n" );
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document.write( "the reciprocal of their average is 2xy / (x + y).\r<BR>\n" );
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document.write( "that's your harmonic mean of x and y.\r<BR>\n" );
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document.write( "as an example, if x = 3 and y = 5, then their harmonic mean would be equal to:\r<BR>\n" );
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document.write( "(2*3*5)/(3+5) = 30/8 = 3.75.\r<BR>\n" );
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document.write( "if you looked for their harmonic mean directly, you would:\r<BR>\n" );
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document.write( "take the reciprocal of each of those numbers = 1/3 and 1/5.\r<BR>\n" );
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document.write( "add them up to get 1/3 + 1/5 = 5/15 + 3/15 = 8/15\r<BR>\n" );
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document.write( "divide that by the number of numbers = 2 to get (8/15)/2 = 8/30\r<BR>\n" );
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document.write( "take the reciprocal of that to get 30/8 which is equal to 3.75.\r<BR>\n" );
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document.write( "the solutions to your questions are:\r<BR>\n" );
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document.write( "the harmonic mean of 1/2 and 1/20 is equal to 1/11.\r<BR>\n" );
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document.write( "the harmonic mean of x and y is 2xy/(x+y).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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