document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999931>Question 999931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wire, 130 cm long, is cut into two pieces. One piece is bent to form a square of side x cm and the other piece is bent to form a circle of radius r cm. The total area of the square and the circle is A cm^2.\r<BR>\n" );
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document.write( "(a) show that A= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28%26%23960%3B%2B4%29x%B2%29+-+%28260x%29+%2B+4225%29%2F+%26%23960%3B ALIGN=MIDDLE  ALT=\"%28%28%28%26%23960%3B%2B4%29x%B2%29+-+%28260x%29+%2B+4225%29%2F+%26%23960%3B\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if the formula plot doesn't work, this is the formula:<BR>\n" );
document.write( " (((&#960;+4)x²) - (260x) + 4225)/ &#960;\r<BR>\n" );
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document.write( "(b) given that x and r can vary, find the value of x for which a has a stationary value\r<BR>\n" );
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document.write( "thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617497 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=617497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The contribution of length from the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B1%5D=4x ALIGN=MIDDLE  ALT=\"L%5B1%5D=4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The contribution of length from the circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B2%5D=2pi%2Ar ALIGN=MIDDLE  ALT=\"L%5B2%5D=2pi%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B1%5D%2BL%5B2%5D=130 ALIGN=MIDDLE  ALT=\"L%5B1%5D%2BL%5B2%5D=130\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2pi%2Ar=130 ALIGN=MIDDLE  ALT=\"4x%2B2pi%2Ar=130\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bpi%2Ar=65 ALIGN=MIDDLE  ALT=\"2x%2Bpi%2Ar=65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For the square,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bs%5D=x%5E2 ALIGN=MIDDLE  ALT=\"A%5Bs%5D=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the circle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A%5Bc%5D=pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5Bs%5D%2BA%5Bc%5D ALIGN=MIDDLE  ALT=\"A=A%5Bs%5D%2BA%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%5E2%2Bpi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=x%5E2%2Bpi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the length above,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar=65-2x ALIGN=MIDDLE  ALT=\"pi%2Ar=65-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%2865-2x%29%2Fpi ALIGN=MIDDLE  ALT=\"r=%2865-2x%29%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%5E2r%5E2=%2865-2x%29%5E2 ALIGN=MIDDLE  ALT=\"pi%5E2r%5E2=%2865-2x%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=pi%5E2r%5E2=4x%5E2-260x%2B4225 ALIGN=MIDDLE  ALT=\"pi%5E2r%5E2=4x%5E2-260x%2B4225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2=%284x%5E2-260x%2B4225%29%2Fpi ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2=%284x%5E2-260x%2B4225%29%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into the area formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%5E2%2B%284x%5E2-260x%2B4225%29%2Fpi ALIGN=MIDDLE  ALT=\"A=x%5E2%2B%284x%5E2-260x%2B4225%29%2Fpi\"   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%2Ax%5E2%29%2Fpi%2B%284x%5E2-260x%2B4225%29%2Fpi ALIGN=MIDDLE  ALT=\"A=%28pi%2Ax%5E2%29%2Fpi%2B%284x%5E2-260x%2B4225%29%2Fpi\"   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%29x%5E2-260x%2B4225%29%2Fpi ALIGN=MIDDLE  ALT=\"A=%28%284%2Bpi%29x%5E2-260x%2B4225%29%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Stationary value is where the derivative of A with respect to x equals zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%284%2Bpi%29x-260=0 ALIGN=MIDDLE  ALT=\"2%284%2Bpi%29x-260=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=260%2F%282%284%2Bpi%29%29 ALIGN=MIDDLE  ALT=\"x=260%2F%282%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=x=130%2F%284%2Bpi%29 ALIGN=MIDDLE  ALT=\"x=130%2F%284%2Bpi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );