document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83177>Question 83177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> All day I've tried to get this word problem completed and I have no clue.  Can you help me?\r<BR>\n" );
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document.write( "An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps.  Let x denote the length of each side of the square to be cut out.\r<BR>\n" );
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document.write( "Questions:\r<BR>\n" );
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document.write( "Find the function V that represents the volume of the box in terms of x.<BR>\n" );
document.write( "Graph this function and show the graph over the valid range of the variable x.<BR>\n" );
document.write( "Using the graph, what is the value of x that will produce the maximum volume? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59694 by </B><A HREF=/tutors/aboutme.mpl?userid=Mona27><B>Mona27(45)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mona27><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=59694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you can imagine the cardboard 6 feet by 8 feet, and you're cutting squares of side x from each corner.<BR>\n" );
document.write( "The length of the box would be 8-2x, and the width would be 6-2x, and the height is x.<BR>\n" );
document.write( "So the volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=x%288-2x%29%286-2x%29 ALIGN=MIDDLE  ALT=\"V=x%288-2x%29%286-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The relevant range of values of x are from 0 to 3, since you can't have the cut-out squares having a larger side than half the width of the original rectangular cardboard..<BR>\n" );
document.write( "The graph looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1%2C+3%2C+-2%2C+30%2Cx%2A%288-2x%29%2A%286-2x%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1%2C+3%2C+-2%2C+30%2Cx%2A%288-2x%29%2A%286-2x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "And the value of x which will give the maximum volume is approximately 1.13 </SPAN>\n" );
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