document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082919>Question 1082919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open crate will be constructed from 12 by 12 (inches) piece of wooden plywood by cutting away squares of equal size from four corners and folding up the sides. Determine the size of the cutout that maximizes the volume of the box. Find the length, width, and volume of the crate.<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 #697017 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=697017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> v for the volume:<BR>\n" );
document.write( "x, the size of edge length of the cutout corner\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x%28144-48x%2B4x%5E2%29 ALIGN=MIDDLE  ALT=\"v=x%28144-48x%2B4x%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=v=4x%5E3-48x%5E2%2B144x ALIGN=MIDDLE  ALT=\"v=4x%5E3-48x%5E2%2B144x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdx=12x%5E2-96x%2B144=0 ALIGN=MIDDLE  ALT=\"dv%2Fdx=12x%5E2-96x%2B144=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-24x%2B36=0 ALIGN=MIDDLE  ALT=\"3x%5E2-24x%2B36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "discriminant,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%5E2-4%2A3%2A36=144=12%5E2 ALIGN=MIDDLE  ALT=\"24%5E2-4%2A3%2A36=144=12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2824%2B-+12%29%2F6 ALIGN=MIDDLE  ALT=\"x=%2824%2B-+12%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28cross%28x=6%29%2Cor%2Chighlight%28x=2%29%29 ALIGN=MIDDLE  ALT=\"system%28cross%28x=6%29%2Cor%2Chighlight%28x=2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Length and width each is  8 inches.<BR>\n" );
document.write( "Volume is 128 cubic inches. </SPAN>\n" );
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