document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=322321>Question 322321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle is inscribed inside the semi-circle y=square root of 100-x^2. what are the dimensions of the rectangle with maximum area? include a diagram </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #230778 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=230778\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a rectangle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW ALIGN=MIDDLE  ALT=\"A=L%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2x ALIGN=MIDDLE  ALT=\"L=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=y ALIGN=MIDDLE  ALT=\"W=y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2xy ALIGN=MIDDLE  ALT=\"A=2xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28100-x%5E2%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28100-x%5E2%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=2x%2Asqrt%28100-x%5E2%29 ALIGN=MIDDLE  ALT=\"A=2x%2Asqrt%28100-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now area is only a function of x.<BR>\n" );
document.write( "Differentiate with respect to x to find the maximum.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=2x%2A%281%2F2%29%28100-x%5E2%29%5E%28-1%2F2%29%28-2x%29%2Bsqrt%28100-x%5E2%29%282%29 ALIGN=MIDDLE  ALT=\"dA%2Fdx=2x%2A%281%2F2%29%28100-x%5E2%29%5E%28-1%2F2%29%28-2x%29%2Bsqrt%28100-x%5E2%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=2sqrt%28100-x%5E2%29-2x%5E2%2Fsqrt%28100-x%5E2%29 ALIGN=MIDDLE  ALT=\"dA%2Fdx=2sqrt%28100-x%5E2%29-2x%5E2%2Fsqrt%28100-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set the derivative equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28100-x%5E2%29-2x%5E2%2Fsqrt%28100-x%5E2%29=0 ALIGN=MIDDLE  ALT=\"2sqrt%28100-x%5E2%29-2x%5E2%2Fsqrt%28100-x%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28100-x%5E2%29=2x%5E2%2Fsqrt%28100-x%5E2%29 ALIGN=MIDDLE  ALT=\"2sqrt%28100-x%5E2%29=2x%5E2%2Fsqrt%28100-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-x%5E2=x%5E2 ALIGN=MIDDLE  ALT=\"100-x%5E2=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=100 ALIGN=MIDDLE  ALT=\"2x%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=50 ALIGN=MIDDLE  ALT=\"x%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2850%29=5sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2850%29=5sqrt%282%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=sqrt%28100-50%29=5sqrt%282%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28100-50%29=5sqrt%282%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=2%285sqrt%282%29%29%2A5sqrt%282%29 ALIGN=MIDDLE  ALT=\"A=2%285sqrt%282%29%29%2A5sqrt%282%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=100 ALIGN=MIDDLE  ALT=\"A=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-12%2C12%2C-12%2C12%2Cgrid%281%29%2Cline%28-7%2C0%2C-7%2C7.07%29%2Cline%28-7%2C7.07%2C7%2C7.07%29%2Cline%287%2C7.07%2C7%2C0%29%2Cgraph%28300%2C300%2C-12%2C12%2C-12%2C12%2Csqrt%28100-x%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );