document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73411>Question 73411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) 	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 the folding up the flaps. Let x denote the length of each side of the square to be cut out.<BR>\n" );
document.write( "a) 	Find the function V that represents the volume of the box in terms of x.<BR>\n" );
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document.write( "b) 	Graph this function and show the graph over the valid range of the variable x..<BR>\n" );
document.write( "Show Graph here\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?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52543 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=52543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  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 the folding up the flaps. Let x denote the length of each side of the square to be cut out.<BR>\n" );
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document.write( "A few things we know<BR>\n" );
document.write( "The length = (8 - 2x)<BR>\n" );
document.write( "The width: = (6 - 2x)<BR>\n" );
document.write( "The height = x<BR>\n" );
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document.write( "a) Find the function V that represents the volume of the box in terms of x.<BR>\n" );
document.write( "Answer<BR>\n" );
document.write( "V(x) = (8-2x) * (6-2x) * x<BR>\n" );
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document.write( "V(x) = (48 - 16x - 12x + 4x^2) * x<BR>\n" );
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document.write( "V(x) = x(4x^2 - 28x + 48)<BR>\n" );
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document.write( "V(x) = 4x^3 - 28x^2 + 48x<BR>\n" );
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document.write( "b) Graph this function and show the graph over the valid range of the variable x..<BR>\n" );
document.write( "Show Graph here<BR>\n" );
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document.write( "When you plot this. Plot every 1/4 ft: x = .25, .5, .75. 1.00, <BR>\n" );
document.write( "Then plot every 1/10 ft: 1.1, 1.2, 1.3 1.4, 1.5,<BR>\n" );
document.write( "Then plot every 1/4 ft: 1.75, 2.00 etc<BR>\n" );
document.write( "This will give you a close value for the max.<BR>\n" );
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document.write( "c) Using the graph, what is the value of x that will produce the maximum volume?<BR>\n" );
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document.write( "Answer: It looks like x is slightly greater than 1 ft, say 1.1 ft and the actual volume is about 24 cu ft </SPAN>\n" );
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