document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87115>Question 87115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me?\r<BR>\n" );
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document.write( "I am working on a problem.  The problem is :<BR>\n" );
document.write( "   From a 12cm by12cm piece of cardboard, square corners are cut out so that the sides can be folded up to make a box.  Express the volume of the box as a function of the length, x, in centimeters, of a cut-out- square and determine a reasonable domain for this function.  \r<BR>\n" );
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document.write( "So far I have a table that looks like :  ( the lines separate the columns <BR>\n" );
document.write( "length -  volume<BR>\n" );
document.write( "20   -     0<BR>\n" );
document.write( "10    -    100<BR>\n" );
document.write( "8      -   128<BR>\n" );
document.write( "6       -  108<BR>\n" );
document.write( "4        - 64<BR>\n" );
document.write( "2         -20<BR>\n" );
document.write( "0         -0\r<BR>\n" );
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document.write( "The instructor says that I am on the right track, but I need to find out how the length and the volume relate to each other.  I know that the domain is {10,8, 6, 4,2}.  If you could help me figure out the equation it would be helpful, I don't see patterns well.  <BR>\n" );
document.write( "THANK YOU<BR>\n" );
document.write( "Amanda\r<BR>\n" );
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document.write( "PS  I need to turn it in by tomorrow  thank you again </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63069 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=63069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From a 12cm by 12cm piece of cardboard, square corners are cut out so that the sides can be folded up to make a box. Express the volume of the box as a function of the length, x, in centimeters, of a cut-out- square and determine a reasonable domain for this function. <BR>\n" );
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document.write( "Let an edge of the cutout square be x.<BR>\n" );
document.write( "After sides are folded up the bottom of box is a 12-2x by 12-2x square.<BR>\n" );
document.write( "The height of the box is x.<BR>\n" );
document.write( "Volume = length*width*height<BR>\n" );
document.write( "Volume = (12-2x)(12-2x)x<BR>\n" );
document.write( "Volume = 4x(6-x)^2<BR>\n" );
document.write( "Volume = 4x[36-12x+x^2)<BR>\n" );
document.write( "Volume = 4x^3-48x+144x<BR>\n" );
document.write( "Domain: Since the base is 12-2x by 12-2x a reasonable domain would be 0 < x < 12<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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