document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43897>Question 43897</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help please!  is L = x H = 6 and W = 8?  I have worked this and not sure I am using correct numbers for height and width... ty so much!\r<BR>\n" );
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document.write( "An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the 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( "a) Find the function V that represents the volume of the box in terms of x.\r<BR>\n" );
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document.write( "b) Graph this function and show the graph over the valid range of the variable x.\r<BR>\n" );
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document.write( "c) 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 #28847 by </B><A HREF=/tutors/aboutme.mpl?userid=adamchapman><B>adamchapman(301)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=adamchapman><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=28847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK, so you start with a flat piece of cardboard with width 6ft and length 8ft.<BR>\n" );
document.write( "If yo draw this out, you can then draw where the xft by xft squares will be cut out. Looking at the cross-shaped web you now have, we can see that the length of the box will be (6-2x)ft, the width will be (8-2x)ft, and the height of the open-topped box will be xft.\r<BR>\n" );
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document.write( "Now to work out the volume we multiply the width by the length and then multiply by the height:<BR>\n" );
document.write( "V=(6-2x)*(8-2x)*(x)<BR>\n" );
document.write( "V=(48-12x-16x+4x^2)*x<BR>\n" );
document.write( "V=4x^3-28x^2+48x\r<BR>\n" );
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document.write( "Here's the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C+200%2C+0%2C+3%2C+0%2C+30%2C+4x%5E3-28x%5E2%2B48x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C+200%2C+0%2C+3%2C+0%2C+30%2C+4x%5E3-28x%5E2%2B48x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note I only drew the graph uo to x=3<BR>\n" );
document.write( "The reason I did this is because if x was any greater than 3, the side of the box with length (6-2x)ft would be less than zero, which is impossible!\r<BR>\n" );
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document.write( "Using the graph, we can see that thethe maximum value occurs when x is about 1.1<BR>\n" );
document.write( "To be exact, V is a maximum of V=24.258 square feet when x=1.131 ft\r<BR>\n" );
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document.write( "I hope this helps.<BR>\n" );
document.write( "If you have any other problems please don't hesitate to contact me at adam.chapman@student.manchester.ac.uk<BR>\n" );
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