document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=842373>Question 842373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a wire that is 65 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?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #507621 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=507621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have a wire that is 65 cm long.<BR>\n" );
document.write( " You wish to cut it into two pieces.<BR>\n" );
document.write( "One piece will be bent into the shape of a square. <BR>\n" );
document.write( "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( "perimeter + circumference = 65<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ax%29 ALIGN=MIDDLE  ALT=\"2pi%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = circumference of the circle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2865-%282%2Api%2Ax%29%29 ALIGN=MIDDLE  ALT=\"%2865-%282%2Api%2Ax%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = perimeter of the square<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2865-%282%2Api%2Ax%29%29%2F4 ALIGN=MIDDLE  ALT=\"%2865-%282%2Api%2Ax%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = one 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%2865-%282%2Api%2Ax%29%29%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28%2865-%282%2Api%2Ax%29%29%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area of the square<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%2Ax%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the total area<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2865-%282%2Api%2Ax%29%29%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28%2865-%282%2Api%2Ax%29%29%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-3%2C+10%2C+-100%2C+300%2C+%28%2865-%282%2Api%2Ax%29%29%2F4%29%5E2%2B%28pi%2Ax%5E2%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "minimum area occurs when x = 4.55<BR>\n" );
document.write( "C = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2A4.55 ALIGN=MIDDLE  ALT=\"2%2Api%2A4.55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " C = 28.6 is the circumference with minimum area\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );