document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=425090>Question 425090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)You are designing a rain gutter made from a piece of sheet metal 1 foot by 5 feet.  The gutter will be formed by turning up two sides.  You want the gutter to have the greatest volume possible.  <BR>\n" );
document.write( "a.How much should you turn up?\r<BR>\n" );
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document.write( "b.What is the maximum volume? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296144 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=296144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are designing a rain gutter made from a piece of sheet metal 1 foot by 5 feet.<BR>\n" );
document.write( " The gutter will be formed by turning up two sides.<BR>\n" );
document.write( " You want the gutter to have the greatest volume possible.<BR>\n" );
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document.write( "a.How much should you turn up? <BR>\n" );
document.write( "Change the width of the sheet metal to 12 inches<BR>\n" );
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document.write( "The end of the gutter sort of looks like this x|__|x<BR>\n" );
document.write( "x = the height of the gutter, (the amt turned up)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "12 - 2x = the width of the gutter<BR>\n" );
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document.write( "Greatest volume with be determined by the greatest cross section area<BR>\n" );
document.write( "A = x(12-2x)<BR>\n" );
document.write( "A = -2x^2 + 12x<BR>\n" );
document.write( "Find the axis of symmetry to find the height with the greatest area<BR>\n" );
document.write( "x = -b/(2a); in this equation a=-2, b=12<BR>\n" );
document.write( "x = -12/(2*-2)<BR>\n" );
document.write( "x = 3 inches is the height for the greatest cross sectional area<BR>\n" );
document.write( "then<BR>\n" );
document.write( "12 - 2(3) = 6 inches is the width of the gutter<BR>\n" );
document.write( "3 * 6 = 18 sq inches is the cross sectional area<BR>\n" );
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document.write( "b. What is the maximum volume?<BR>\n" );
document.write( "18 *5(12) = 1080 cu/inches<BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1080%2F12%5E3 ALIGN=MIDDLE  ALT=\"1080%2F12%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .625 cu ft </SPAN>\n" );
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