document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=757984>Question 757984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rain gutter is made from sheets of aluminum that are\r<BR>\n" );
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document.write( "12 inches wide by turning up the edges to form right angles.\r<BR>\n" );
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document.write( "Determine the depth of the gutter that will maximize its\r<BR>\n" );
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document.write( "cross-sectional area and allow the greatest amount of water to flow.\r<BR>\n" );
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document.write( "What is the maximum cross-sectional area?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461165 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=461165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rain gutter is made from sheets of aluminum that are <BR>\n" );
document.write( "12 inches wide by turning up the edges to form right angles. <BR>\n" );
document.write( "Determine the depth of the gutter that will maximize its <BR>\n" );
document.write( "cross-sectional area and allow the greatest amount of water to flow.<BR>\n" );
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document.write( "Let the height be \"x\"<BR>\n" );
document.write( "Then base is 12-2x<BR>\n" );
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document.write( "Area = x(12-2x) = -2x^2 + 12x<BR>\n" );
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document.write( "Maximum of this parabola occurs when x = -b/(2a) = -12/(-4) = 3<BR>\n" );
document.write( "That is the depth of gutter.<BR>\n" );
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document.write( "That cross-section area is x(12-x) = 3*9 = 27 sq in.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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