document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255965>Question 255965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please explain to me how to do this??\r<BR>\n" );
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document.write( "Mr. Greene has 8.5-by-11 in. cardboard sheets. As a class project, Mr. Greene asked each of his students to make an open-top box under these conditions:<BR>\n" );
document.write( "I) Each box must be made by cutting small squares from each corner of a cardboard sheet.<BR>\n" );
document.write( "II) The box must have a volume of 48 in^3.<BR>\n" );
document.write( "III) The amount of cardboard waste must be minimized.<BR>\n" );
document.write( "What is the approximate side length for the small squares that would be cut from the cardboard sheet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188423 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=188423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mr. Greene has 8.5-by-11 in. cardboard sheets. As a class project,<BR>\n" );
document.write( " Mr. Greene asked each of his students to make an open-top box under these conditions:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I) Each box must be made by cutting small squares from each corner of a cardboard sheet.<BR>\n" );
document.write( "II) The box must have a volume of 48 in^3.<BR>\n" );
document.write( "III) The amount of cardboard waste must be minimized.<BR>\n" );
document.write( "What is the approximate side length for the small squares that would be cut from the cardboard sheet?<BR>\n" );
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document.write( "Draw a rectangle representing the 8.5 by 11 in sheet. Cut out a small square in each corner, label the side of the square as x.<BR>\n" );
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document.write( "Visualize bending the sides up to form an open box; it will be apparent that<BR>\n" );
document.write( "Box dimensions will be:<BR>\n" );
document.write( "(11-2x) = box length<BR>\n" );
document.write( "(8.5-2x) = box width<BR>\n" );
document.write( "x = box height<BR>\n" );
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document.write( "Vol: height * Length * width<BR>\n" );
document.write( "x*(11-2x)*(8.5-2x) = 48<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "x(93.5 - 22x - 17x + 4x^2) = 48<BR>\n" );
document.write( "x(93.5 - 39x + 4x^2) = 48<BR>\n" );
document.write( "93.5x - 39x^2 + 4x^3 - 48 = 0<BR>\n" );
document.write( "The equation<BR>\n" );
document.write( "4x^3 - 39x^2 + 93.5x - 48 = 0<BR>\n" );
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document.write( "Now the easiest way, is to plot this equation on a graphing calc<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-20%2C+30%2C+4x%5E3-39x%5E2%2B93.5x-48%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-20%2C+30%2C+4x%5E3-39x%5E2%2B93.5x-48%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note we have 3 solutions for x, the last one x=6+ is not valid but<BR>\n" );
document.write( "x = .7 and = 2.7 are, however, the removed square would be \"waste\" therefore<BR>\n" );
document.write( "x = .7 would be the smallest square, that would be the choice<BR>\n" );
document.write( " </SPAN>\n" );
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