document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983709>Question 983709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identical squares are cut from each corner of an 8 inch by 11.5 inch rectangular piece of cardboard.The sides are folded up to make a box with no top .If the volume of the resulting box is 63.75 cubic inches,how long is the edge of each square that is cut off ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604508 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=604508\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> u, edge of each identical cut-out square<BR>\n" );
document.write( "w, width of rectangular cardboard<BR>\n" );
document.write( "L, length of cardboard<BR>\n" );
document.write( "v, volume of the open-top box\r<BR>\n" );
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document.write( "The box is u tall and the base is  (w-2u)(L-2u).<BR>\n" );
document.write( "The volume is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%28w-2u%29%28L-2u%29%2Au=v%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%28w-2u%29%28L-2u%29%2Au=v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Solve for u.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28wL-2uL-2uw%2B4u%5E2%29u=v ALIGN=MIDDLE  ALT=\"%28wL-2uL-2uw%2B4u%5E2%29u=v\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4u%5E3-2Lu%5E2-2wu%5E2%2BwLu-v=0 ALIGN=MIDDLE  ALT=\"4u%5E3-2Lu%5E2-2wu%5E2%2BwLu-v=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%284u%5E3-%282L%2B2w%29u%5E2%2BwLu-v=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%284u%5E3-%282L%2B2w%29u%5E2%2BwLu-v=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----Now we need to plug-in the known values for the cubic equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4u%5E3-39u%5E2%2B92u-63.75=0 ALIGN=MIDDLE  ALT=\"4u%5E3-39u%5E2%2B92u-63.75=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Integers are preferred so multiply by 4...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2816u%5E4-156u%5E2%2B368u-255=0%29 ALIGN=MIDDLE  ALT=\"cross%2816u%5E4-156u%5E2%2B368u-255=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---possibly wrong - did not work-\r<BR>\n" );
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document.write( "The roots (if Rational Roots Theorem)  we want must be positive but certainly much less than 8.  Most sensible to first check for 1 and 3  (both are factors of 255).\r<BR>\n" );
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document.write( "I used a graphing tool. <BR>\n" );
document.write( "...   graph shows roots at u=1.5 and u=1.6. </SPAN>\n" );
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