document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118048>Question 118048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> FIND THE CONSTANT OF VARIATION K.\r<BR>\n" );
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document.write( "m varies directly with n: m = 144 when n = 8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86103 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By saying that m varies directly with n, the problem is telling you that if n increases, then<BR>\n" );
document.write( "m must increase also in proportion to the increase in n.<BR>\n" );
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document.write( "This being the case we can write the equation:<BR>\n" );
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document.write( "m = Kn<BR>\n" );
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document.write( "Notice that if n doubles, then m will double also. If n triples, then m will triple also.<BR>\n" );
document.write( "And so on. In other words, m is varying directly in proportion to the variation in n.<BR>\n" );
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document.write( "The problem then tells you that m = 144 when n = 8. Substitute these two values into the<BR>\n" );
document.write( "equation and you get:<BR>\n" );
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document.write( "144 = K(8)<BR>\n" );
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document.write( "Solve for K (the constant of variation) by dividing both sides of this equation by 8 and<BR>\n" );
document.write( "you get:<BR>\n" );
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document.write( "K = 144/8 = 18<BR>\n" );
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document.write( "So the constant of variation is 18 and the equation becomes:<BR>\n" );
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document.write( "m = 18n<BR>\n" );
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document.write( "If n = 1 then m = 18. If n doubles to 2, then m = 18*2 = 36 so m has doubled also. If <BR>\n" );
document.write( "n triples to 3, then m = 18*3 = 54, and that is 3 times the 18 that m was when n was only 1.<BR>\n" );
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document.write( "Finally, when n = 8 then m = 18*8 = 144, just as the problem said it should be.<BR>\n" );
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document.write( "Hope this helps you to understand the meaning of the constant of variation and how to find<BR>\n" );
document.write( "it when you are told that direct variation is involved.<BR>\n" );
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