document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134762>Question 1134762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Norman window is constructed by adjoining a semicircle to the top of ab ordinary rectangular window. The perimeter of the window is 12 feet. The diameter of a circle and the length of a rectangle are x， the width is y.<BR>\n" );
document.write( "1) Write the area A of the window as a function of x.<BR>\n" );
document.write( "2) What dimensions will produce a window of maximum area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752244 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:<BR>\n" );
document.write( " The perimeter of the window is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. The diameter of a circle and the length of a rectangle are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the width is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "1) Write the area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the window as a function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The perimeter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+2y+%2B+x+%2B1%2F2%282pi%2Ar%29+ ALIGN=MIDDLE  ALT=\"P+=+2y+%2B+x+%2B1%2F2%282pi%2Ar%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=P=+2y+%2B+x+%2B+pi%28x%2F2%29 ALIGN=MIDDLE  ALT=\"P=+2y+%2B+x+%2B+pi%28x%2F2%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=P=+2y+%2B%281+%2Bpi%2F2%29x ALIGN=MIDDLE  ALT=\"P=+2y+%2B%281+%2Bpi%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .......given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+12 ALIGN=MIDDLE  ALT=\"P=+12\"   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=12=+2y+%2B%281+%2Bpi%2F2%29x ALIGN=MIDDLE  ALT=\"12=+2y+%2B%281+%2Bpi%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=2y+=12-%281+%2Bpi%2F2%29x ALIGN=MIDDLE  ALT=\"2y+=12-%281+%2Bpi%2F2%29x\"   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+=6-%28%282+%2Bpi%29x%2F2%29%2F2 ALIGN=MIDDLE  ALT=\"y+=6-%28%282+%2Bpi%29x%2F2%29%2F2\"   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+=6-%28%282+%2Bpi%29x%29%2F4 ALIGN=MIDDLE  ALT=\"y+=6-%28%282+%2Bpi%29x%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We find an equation for maximum area.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+xy+%2B%281%2F2%29pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A+=+xy+%2B%281%2F2%29pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x%2F2 ALIGN=MIDDLE  ALT=\"r=x%2F2\"   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=A+=+xy+%2B%281%2F2%29pi%2A%28x%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"A+=+xy+%2B%281%2F2%29pi%2A%28x%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+xy+%2B%281%2F2%29pi%2A%28x%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"A+=+xy+%2B%281%2F2%29pi%2A%28x%5E2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+xy+%2B%281%2F8%29pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\"A+=+xy+%2B%281%2F8%29pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute in for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+x%286-%28%282+%2Bpi%29x%29%2F4%29+%2B%281%2F8%29pi%2Ax%5E2+ ALIGN=MIDDLE  ALT=\"A+=+x%286-%28%282+%2Bpi%29x%29%2F4%29+%2B%281%2F8%29pi%2Ax%5E2+\"   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=A+=+6x-%281%2F4%29%282+%2Bpi%29x%5E2+%2B%281%2F8%29pi%2Ax%5E2+ ALIGN=MIDDLE  ALT=\"A+=+6x-%281%2F4%29%282+%2Bpi%29x%5E2+%2B%281%2F8%29pi%2Ax%5E2+\"   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=A+=+-%28pi%2Ax%5E2%29%2F8+-+x%5E2%2F2+%2B+6x ALIGN=MIDDLE  ALT=\"A+=+-%28pi%2Ax%5E2%29%2F8+-+x%5E2%2F2+%2B+6x\"   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=A+=+-%281%2F8%29+%284+%2B+pi%29+x%5E2%2B+6x ALIGN=MIDDLE  ALT=\"A+=+-%281%2F8%29+%284+%2B+pi%29+x%5E2%2B+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the window as a function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2) What dimensions will produce a window of maximum area?\r<BR>\n" );
document.write( "\n" );
document.write( "Next compute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx ALIGN=MIDDLE  ALT=\"dA%2Fdx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Set it equal to zero and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=dA%2Fdx+=+2%28-1%2F8%29%284+%2B+pi%29x%2B6 ALIGN=MIDDLE  ALT=\"dA%2Fdx+=+2%28-1%2F8%29%284+%2B+pi%29x%2B6\"   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=dA%2Fdx+=+-%281%2F4%29+%284+%2B+pi%29x%2B6 ALIGN=MIDDLE  ALT=\"dA%2Fdx+=+-%281%2F4%29+%284+%2B+pi%29x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "set =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F4%29+%284+%2B+pi%29x%2B6=0 ALIGN=MIDDLE  ALT=\"-%281%2F4%29+%284+%2B+pi%29x%2B6=0\"   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=%281%2F4%29+%284+%2B+pi%29x=6 ALIGN=MIDDLE  ALT=\"%281%2F4%29+%284+%2B+pi%29x=6\"   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=+%284+%2B+pi%29x=6%2F%281%2F4%29 ALIGN=MIDDLE  ALT=\"+%284+%2B+pi%29x=6%2F%281%2F4%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=%284+%2B+pi%29x=24 ALIGN=MIDDLE  ALT=\"%284+%2B+pi%29x=24\"   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=x=24%2F%284+%2B+pi%29 ALIGN=MIDDLE  ALT=\"x=24%2F%284+%2B+pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24%2F%284+%2B+3.14%29+ ALIGN=MIDDLE  ALT=\"x=24%2F%284+%2B+3.14%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=x=24%2F7.14 ALIGN=MIDDLE  ALT=\"x=24%2F7.14\"   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=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >≈ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.35ft ALIGN=MIDDLE  ALT=\"3.35ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3.35ft%2F2=1.675 ALIGN=MIDDLE  ALT=\"r=3.35ft%2F2=1.675\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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+=%286-%282+%2Bpi%29x%29%2F4 ALIGN=MIDDLE  ALT=\"y+=%286-%282+%2Bpi%29x%29%2F4\"   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+=%286-%282+%2B3.14%293.35%29%2F4 ALIGN=MIDDLE  ALT=\"y+=%286-%282+%2B3.14%293.35%29%2F4\"   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+=%286-5.14%2A3.35%29%2F4 ALIGN=MIDDLE  ALT=\"y+=%286-5.14%2A3.35%29%2F4\"   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+=6-%285.14%2A3.35%29%2F4 ALIGN=MIDDLE  ALT=\"y+=6-%285.14%2A3.35%29%2F4\"   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 ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ≈ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.7ft ALIGN=MIDDLE  ALT=\"1.7ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "dimensions that will produce a window of maximum area are:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >≈ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.35ft ALIGN=MIDDLE  ALT=\"3.35ft\"   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=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >≈<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.675 ALIGN=MIDDLE  ALT=\"1.675\"   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 ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ≈ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.7ft ALIGN=MIDDLE  ALT=\"1.7ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "check the perimeter first then see what would be maximum area\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=+2y+%2B%281+%2Bpi%2F2%29x ALIGN=MIDDLE  ALT=\"12=+2y+%2B%281+%2Bpi%2F2%29x\"   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=12=+2%2A1.7+%2B%281+%2B3.14%2F2%293.35 ALIGN=MIDDLE  ALT=\"12=+2%2A1.7+%2B%281+%2B3.14%2F2%293.35\"   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=12=+2%2A1.7+%2B%28%282+%2B3.14%29%2F2%293.35 ALIGN=MIDDLE  ALT=\"12=+2%2A1.7+%2B%28%282+%2B3.14%29%2F2%293.35\"   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=12=+2%2A1.7+%2B%285.14%2A3.35%29%2F2 ALIGN=MIDDLE  ALT=\"12=+2%2A1.7+%2B%285.14%2A3.35%29%2F2\"   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=12=+3.4+%2B8.6095 ALIGN=MIDDLE  ALT=\"12=+3.4+%2B8.6095\"   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=12=+12.0095 ALIGN=MIDDLE  ALT=\"12=+12.0095\"   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=12=+12 ALIGN=MIDDLE  ALT=\"12=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> true\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now find maximum area\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+xy+%2B%281%2F8%29pi%2Ax%5E2+ ALIGN=MIDDLE  ALT=\"A+=+xy+%2B%281%2F8%29pi%2Ax%5E2+\"   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=A+=+3.35%2A1.7+%2B%281%2F8%293.14%2A%283.35%29%5E2 ALIGN=MIDDLE  ALT=\"A+=+3.35%2A1.7+%2B%281%2F8%293.14%2A%283.35%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+5.695+%2B%281%2F8%293.14%2A11.2225 ALIGN=MIDDLE  ALT=\"A+=+5.695+%2B%281%2F8%293.14%2A11.2225\"   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=A+=+5.695+%2B4.40483125 ALIGN=MIDDLE  ALT=\"A+=+5.695+%2B4.40483125\"   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=A+=+5.695+%2B4.40483125 ALIGN=MIDDLE  ALT=\"A+=+5.695+%2B4.40483125\"   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=A+=10.0998 ALIGN=MIDDLE  ALT=\"A+=10.0998\"   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=A+ ALIGN=MIDDLE  ALT=\"A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >≈ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10ft%5E2 ALIGN=MIDDLE  ALT=\"10ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );