document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160326>Question 160326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118266 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=118266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^3<BR>\n" );
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document.write( "Let the side of the removed squares = x<BR>\n" );
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document.write( "The dimension of the box will be: (24-2x) by (30-2x) by x (height)<BR>\n" );
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document.write( "A volume equation, L * W * H<BR>\n" );
document.write( "(24-2x) * (30-2x) * x  = 1040<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "(720 - 48x - 60x + 4x^2) * x = 1040<BR>\n" );
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document.write( "Multiply by x;<BR>\n" );
document.write( "720x - 108x^2 + 4x^3 = 1040<BR>\n" );
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document.write( "4x^3 - 108x^2 + 720x - 1040 = 0<BR>\n" );
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document.write( "Simplify; divide by 4:<BR>\n" );
document.write( "x^3 - 27x + 180x - 260 = 0<BR>\n" );
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document.write( "Graphing this would be one way to solve this<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+8%2C+-50%2C+200%2C+x%5E3-27x%5E2%2B180x-260%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-50%2C+200%2C+x%5E3-27x%5E2%2B180x-260%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x = 2 cm would work<BR>\n" );
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document.write( "L: 30-4 = 26 cm<BR>\n" );
document.write( "W: 24-4 = 20 cm<BR>\n" );
document.write( "H: 2 cm<BR>\n" );
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document.write( "Check the volume<BR>\n" );
document.write( "(26*20*2 = 1040<BR>\n" );
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document.write( "You can see there is another solution on the graph: x ~ 7.4<BR>\n" );
document.write( "The dimensions for that would be<BR>\n" );
document.write( "L: 30-14.8 = 15.2<BR>\n" );
document.write( "W: 24-14.8 = 9.2<BR>\n" );
document.write( "H: 7.4 cm<BR>\n" );
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document.write( "Check vol with this: 15.2*9.2*7.4 = 1035.8 (because not an integer)<BR>\n" );
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