document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583241>Question 583241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An industrial rain gutter is constructed by folding the edges of a sheet of metal<BR>\n" );
document.write( "20 inches wide so that the cross section of the gutter is a rectangle. How much edge<BR>\n" );
document.write( "should be folded up on each side to maximize the area of the cross section?\r<BR>\n" );
document.write( "\n" );
document.write( "im the picture it shows that it has 3 divisions the 2 sides and the base<BR>\n" );
document.write( " <BR>\n" );
document.write( "its problen two in this websiter<BR>\n" );
document.write( "http://math.arizona.edu/~cjewell/112/homework/Homework13.pdf  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372446 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=372446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An industrial rain gutter is constructed by folding the edges of a sheet of metal<BR>\n" );
document.write( "20 inches wide so that the cross section of the gutter is a rectangle.<BR>\n" );
document.write( " How much edge should be folded up on each side to maximize the area of the cross section?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "End would look something like this |__|<BR>\n" );
document.write( "Let the vertical sides = s<BR>\n" );
document.write( "Let the horizontal = b<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2s + b = 20 inches<BR>\n" );
document.write( "b = (20-2s)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "Area = s * b <BR>\n" );
document.write( "replace b with (20-2s)<BR>\n" );
document.write( "A = s(20-2s)<BR>\n" );
document.write( "A = -2s^2 + 20s<BR>\n" );
document.write( "This is a quadratic equation, we can find max area by finding the axis of symmetry. Formula: x = -b/(2a)<BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-20%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"%28-20%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = +5 inches on each side will give the max area<BR>\n" );
document.write( ":  <BR>\n" );
document.write( "Find the area<BR>\n" );
document.write( "b = 20 - 2(5)<BR>\n" );
document.write( "b = 10 is the base<BR>\n" );
document.write( "A = 5 * 10<BR>\n" );
document.write( "A = 50 sq/in is max area\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );