document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=503532>Question 503532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a wire that is 53 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minium?<BR>\n" );
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 #339364 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have a wire that is 53 cm long. You wish to cut it into two pieces.<BR>\n" );
document.write( " One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle.<BR>\n" );
document.write( " Let A represent the total area of the square and the circle.<BR>\n" );
document.write( " What is the circumference of the circle when A is a minimum?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = circumference of the circle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(53-x) = the perimeter of the square<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2853-x%29%2F4 ALIGN=MIDDLE  ALT=\"%2853-x%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the side of the square<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2853-x%29%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28%2853-x%29%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area of the square<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the area of the circle using the circumference<BR>\n" );
document.write( "find the radius (r)<BR>\n" );
document.write( "2*pi*r = x<BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%282%2Api%29 ALIGN=MIDDLE  ALT=\"x%2F%282%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6.28 ALIGN=MIDDLE  ALT=\"x%2F6.28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the area of the circle<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replace r with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6.28 ALIGN=MIDDLE  ALT=\"x%2F6.28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F6.28%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2F6.28%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F39.48%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F39.48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel pi into 39.48<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F12.566 ALIGN=MIDDLE  ALT=\"x%5E2%2F12.566\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Total area of circle and square<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F12.566 ALIGN=MIDDLE  ALT=\"x%5E2%2F12.566\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2853-x%29%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28%2853-x%29%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F12.566 ALIGN=MIDDLE  ALT=\"x%5E2%2F12.566\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282809-106x%2Bx%5E2%29%2F16%29 ALIGN=MIDDLE  ALT=\"%28%282809-106x%2Bx%5E2%29%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "convert these fractions to decimal coefficients<BR>\n" );
document.write( "A(x) = .0796x^2 + .0625x^2 - 6.625x + 175.5625<BR>\n" );
document.write( "A(x) = .1421x^2 - 6.625x + 175.5625<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the axis of symmetry of this quadratic equation (min area)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-6.625%29%29%2F%282%2A.1421%29 ALIGN=MIDDLE  ALT=\"%28-%28-6.625%29%29%2F%282%2A.1421%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.625%2F.2842 ALIGN=MIDDLE  ALT=\"6.625%2F.2842\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 23.31 cm is the circumference when they have min area<BR>\n" );
document.write( " </SPAN>\n" );
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