document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203019>Question 1203019</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a problem with questions relating to variation as the sum of two parts.<BR>\n" );
document.write( "Here is a worked example.<BR>\n" );
document.write( "A quantity, p, is the sum of two terms, one of which is constant while the other varies inversely as the square of q.<BR>\n" );
document.write( "When q = 1, p=-1;<BR>\n" );
document.write( "when q = 2, p=2;<BR>\n" );
document.write( "find the positive value of q when p=2.75<BR>\n" );
document.write( "If a and b are constants, p=a+b/q2;<BR>\n" );
document.write( "q = 1, p= -1<BR>\n" );
document.write( "-1 = a +b/12;<BR>\n" );
document.write( "therefore -1 = a+b (equation 1)<BR>\n" );
document.write( "when q = 2, p=2<BR>\n" );
document.write( "2 = a+b/22<BR>\n" );
document.write( "2=a+b/4<BR>\n" );
document.write( "8 = 4a+b (equation 2)<BR>\n" );
document.write( "Subtracting equation 1 from 2 gives<BR>\n" );
document.write( "9=3a<BR>\n" );
document.write( "so a =3<BR>\n" );
document.write( "Substituting a = 3 into equation 1 we get<BR>\n" );
document.write( "-1 = 3+b<BR>\n" );
document.write( "b=-4<BR>\n" );
document.write( "so p=3-4/q2<BR>\n" );
document.write( "so when p = 2.75, 2.75 = 3-4/q2<BR>\n" );
document.write( "4/q2 = ¼<BR>\n" );
document.write( "q2 = 16<BR>\n" );
document.write( "q=+/- 4 and we want the positive value so q = 4<BR>\n" );
document.write( "I have tried to apply the same approach to the following problem:<BR>\n" );
document.write( "A quantity C is the sum of two parts.  The first part varies directly as the cube of t;<BR>\n" );
document.write( "the second part varies inversely as the square of t.<BR>\n" );
document.write( "C = 74, t = 1<BR>\n" );
document.write( "C = 34, t = 2<BR>\n" );
document.write( "Find C when t = 3<BR>\n" );
document.write( "I wrote C = a3 +b/t2<BR>\n" );
document.write( "74 = a3+b/12<BR>\n" );
document.write( "74 = a3 +b (equation 1).\r<BR>\n" );
document.write( "\n" );
document.write( "34 = a3+b/22<BR>\n" );
document.write( "34 = a3+b/4<BR>\n" );
document.write( "136 = 4a3+b (equation 2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract equation 1 from 2<BR>\n" );
document.write( "136 = 4a3+b<BR>\n" );
document.write( "74 = a3 +b<BR>\n" );
document.write( "This gives 62 = 3a3<BR>\n" );
document.write( "a3 = 20.67<BR>\n" );
document.write( "a = 2.74\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting into the first equation<BR>\n" );
document.write( "74 = 20.67 + b/12<BR>\n" );
document.write( "74 = 20.67+b<BR>\n" );
document.write( "b=53.33\r<BR>\n" );
document.write( "\n" );
document.write( "To find C when t = 3<BR>\n" );
document.write( "C = a3+b/t2<BR>\n" );
document.write( "C = 20.67 + 53.33/9<BR>\n" );
document.write( "9C = 186.03+53.33<BR>\n" );
document.write( "9C = 239.36<BR>\n" );
document.write( "C = 25.6 but the answer is 62.<BR>\n" );
document.write( "Where have I gone wrong?\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838252 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You are doing most of the work right; but your equation for C in the new problem is not what you intended.<br><BR>\n" );
document.write( "NOTE: For readability, use \"^\" (shift-6) to denote an exponent -- e.g. \"q^2\" and \"t^3\" instead of \"q2\" and \"t3\".  (It might be that you were using some other special character to represent and exponent, and that special character doesn't show up at all.)<br><BR>\n" );
document.write( "In the new problem, you wrote<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=a%5E3%2Bb%2Ft%5E2 ALIGN=MIDDLE  ALT=\"C=a%5E3%2Bb%2Ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "But what you meant was<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=at%5E3%2Bb%2Ft%5E2 ALIGN=MIDDLE  ALT=\"C=at%5E3%2Bb%2Ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Fix that and solve the problem using the methods you show and you will get the correct answer of 62.<br><BR>\n" );
document.write( "I'll go ahead and finish solving the problem; but you will get more benefit if you finish it yourself and compare your work and final answer to mine.<br><BR>\n" );
document.write( "t=1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=74=a%2Bb ALIGN=MIDDLE  ALT=\"74=a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t=2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=34=8a%2Bb%2F4 ALIGN=MIDDLE  ALT=\"34=8a%2Bb%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136=32a%2Bb ALIGN=MIDDLE  ALT=\"136=32a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=62=31a ALIGN=MIDDLE  ALT=\"62=31a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=74=2%2Bb ALIGN=MIDDLE  ALT=\"74=2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=72 ALIGN=MIDDLE  ALT=\"b=72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2t%5E3%2B72%2Ft%5E2 ALIGN=MIDDLE  ALT=\"C=2t%5E3%2B72%2Ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When t=3...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2%2827%29%2B72%2F9=54%2B8=62 ALIGN=MIDDLE  ALT=\"C=2%2827%29%2B72%2F9=54%2B8=62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );