document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041677>Question 1041677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a window has the form of a rectangle surrounded by a semi circle if perimeter is 40 units.find its dimensions so that the area of window is maximum </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656643 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=656643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume the window is X wide and Y long.<BR>\n" );
document.write( "So then the perimeter of the window would be.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=X%2B2Y%2B%28pi%2F2%29%2AX ALIGN=MIDDLE  ALT=\"P=X%2B2Y%2B%28pi%2F2%29%2AX\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bpi%2F2%29X%2B2Y=40 ALIGN=MIDDLE  ALT=\"%281%2Bpi%2F2%29X%2B2Y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the area of the window would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=XY%2B%28pi%2F2%29%28X%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"A=XY%2B%28pi%2F2%29%28X%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=XY%2B%28pi%2F8%29X%5E2 ALIGN=MIDDLE  ALT=\"A=XY%2B%28pi%2F8%29X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From eq. 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2Y=40-%281%2Bpi%2F2%29X ALIGN=MIDDLE  ALT=\"2Y=40-%281%2Bpi%2F2%29X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20-%28%281%2Bpi%2F2%29%2F2%29X ALIGN=MIDDLE  ALT=\"Y=20-%28%281%2Bpi%2F2%29%2F2%29X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20-%281%2F2%2Bpi%2F4%29X ALIGN=MIDDLE  ALT=\"Y=20-%281%2F2%2Bpi%2F4%29X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's just call the constant in front of X, B, just for better readability.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20-BX ALIGN=MIDDLE  ALT=\"Y=20-BX\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then substituting into 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=X%2820-BX%29%2B%28pi%2F8%29X%5E2 ALIGN=MIDDLE  ALT=\"A=X%2820-BX%29%2B%28pi%2F8%29X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=20X-BX%5E2%2B%28pi%2F8%29X%5E2 ALIGN=MIDDLE  ALT=\"A=20X-BX%5E2%2B%28pi%2F8%29X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28pi%2F8-B%29X%5E2%2B20X ALIGN=MIDDLE  ALT=\"A=%28pi%2F8-B%29X%5E2%2B20X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28pi%2F8-1%2F2-pi%2F4%29X%5E2%2B20X ALIGN=MIDDLE  ALT=\"A=%28pi%2F8-1%2F2-pi%2F4%29X%5E2%2B20X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28-pi%2F8-1%2F2%29X%5E2%2B20X ALIGN=MIDDLE  ALT=\"A=%28-pi%2F8-1%2F2%29X%5E2%2B20X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-%28%284%2Bpi%29%2F8%29X%5E2%2B20X ALIGN=MIDDLE  ALT=\"A=-%28%284%2Bpi%29%2F8%29X%5E2%2B20X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Once again, let's use a constant, C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=CX%5E2%2B20X ALIGN=MIDDLE  ALT=\"A=CX%5E2%2B20X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Convert to vertex form to find the vertex and maximum area.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=C%28X%5E2%2B%2820%2FC%29X%29 ALIGN=MIDDLE  ALT=\"A=C%28X%5E2%2B%2820%2FC%29X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=C%28X%5E2%2B%2820%2FC%29X%2B%2810%2FC%29%5E2%29-C%2810%2FC%29%5E2 ALIGN=MIDDLE  ALT=\"A=C%28X%5E2%2B%2820%2FC%29X%2B%2810%2FC%29%5E2%29-C%2810%2FC%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=A=C%28X%2B10%2FC%29%5E2-100%2FC ALIGN=MIDDLE  ALT=\"A=C%28X%2B10%2FC%29%5E2-100%2FC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-%28%284%2Bpi%29%2F8%29%28X-80%2F%284%2Bpi%29%29%2B800%2F%284%2Bpi%29 ALIGN=MIDDLE  ALT=\"A=-%28%284%2Bpi%29%2F8%29%28X-80%2F%284%2Bpi%29%29%2B800%2F%284%2Bpi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the maximum area of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bmax%5D=800%2F%284%2Bpi%29 ALIGN=MIDDLE  ALT=\"A%5Bmax%5D=800%2F%284%2Bpi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "occurs when,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28X=80%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"highlight%28X=80%2F%284%2Bpi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20-%281%2F2%2Bpi%2F4%29%2880%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"Y=20-%281%2F2%2Bpi%2F4%29%2880%2F%284%2Bpi%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=Y=20-%28%282%2Bpi%29%2F4%29%2880%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"Y=20-%28%282%2Bpi%29%2F4%29%2880%2F%284%2Bpi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20-%28%282%2Bpi%29%2F%284%2Bpi%29%29%2A20 ALIGN=MIDDLE  ALT=\"Y=20-%28%282%2Bpi%29%2F%284%2Bpi%29%29%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20%281-%282%2Bpi%29%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"Y=20%281-%282%2Bpi%29%2F%284%2Bpi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20%28%284%2Bpi%29%2F%284%2Bpi%29-%282%2Bpi%29%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"Y=20%28%284%2Bpi%29%2F%284%2Bpi%29-%282%2Bpi%29%2F%284%2Bpi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20%28%284%2Bpi-2-pi%29%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"Y=20%28%284%2Bpi-2-pi%29%2F%284%2Bpi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=20%282%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"Y=20%282%2F%284%2Bpi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28Y=40%2F%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"highlight%28Y=40%2F%284%2Bpi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );