document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550154>Question 550154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume of a car, V, is directly proportional to the square of its length, l. Calculate the percentage increase in V when l is doubled.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358489 by </B><A HREF=/tutors/aboutme.mpl?userid=TutorDelphia><B>TutorDelphia(193)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TutorDelphia><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=TutorDelphia><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=358489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> direct proportion's formula is y=kx. In this case y=V and x=length squared<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=k%2Al%5E2 ALIGN=MIDDLE  ALT=\"V=k%2Al%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's say the length was 10 and k was 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=1%2A%28l0%29%5E2 ALIGN=MIDDLE  ALT=\"V=1%2A%28l0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=1%2A100 ALIGN=MIDDLE  ALT=\"v=1%2A100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "vs <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=1%2A%2820%29%5E2 ALIGN=MIDDLE  ALT=\"v=1%2A%2820%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "v=1*400\r<BR>\n" );
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document.write( "400 is a 300% increase using the formula new minus old over old or (400-100)/100=3=300%\r<BR>\n" );
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document.write( "Now let's do the general case. Percent increase is new minus old over old\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=k%2Al%5E2 ALIGN=MIDDLE  ALT=\"V=k%2Al%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "vs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=k%2A%282l%29%5E2 ALIGN=MIDDLE  ALT=\"V=k%2A%282l%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=k%2A4%28l%5E2%29 ALIGN=MIDDLE  ALT=\"V=k%2A4%28l%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "new minus old over old:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2A4%28l%5E2%29-k%2A%28l%5E2%29%29%2F%28k%2A%28l%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28k%2A4%28l%5E2%29-k%2A%28l%5E2%29%29%2F%28k%2A%28l%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2A3%28l%5E2%29%2F%28k%2A%28l%5E2%29%29 ALIGN=MIDDLE  ALT=\"k%2A3%28l%5E2%29%2F%28k%2A%28l%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The k and l^2 cancel out and we are left with 3 which is equal to 300%<BR>\n" );
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