document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201030>Question 201030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> not sure if in right area but can someone help me with this problem\r<BR>\n" );
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document.write( "An open box is to be constructed from a piece of cardboard that is 30in. by 30in. by cutting a square out of each corner and folding up the sides.  What are the dimensions of the box that will yield the maximum volume?\r<BR>\n" );
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document.write( "so confused<BR>\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151274 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=151274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An open box is to be constructed from a piece of cardboard that is 30in. by 30in. by cutting a square out of each corner and folding up the sides. What are the dimensions of the box that will yield the maximum volume? <BR>\n" );
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document.write( "Draw the 30 by 30 piece.<BR>\n" );
document.write( "Draw a square in each of the four corners.<BR>\n" );
document.write( "Let the dimensions of each square be \"x\" by \"x\".<BR>\n" );
document.write( "Imagine cutting out those four squares and folding<BR>\n" );
document.write( "up the remaining flaps to make a box with no top.<BR>\n" );
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document.write( "The base is \"30-2x\" by \"30-2x\" and the height is \"x\".<BR>\n" );
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document.write( "The volume is as follows:<BR>\n" );
document.write( "V = x(30-2x)^2<BR>\n" );
document.write( "V(x) = 900x - 120x^2 + 4x^3<BR>\n" );
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document.write( "Take the derivative and set it equal to zero:<BR>\n" );
document.write( "V'(x) = 900 - 240x + 12x^2 = 0<BR>\n" );
document.write( "Sove for \"x\":<BR>\n" );
document.write( "2x^2 - 40x + 150 = 0<BR>\n" );
document.write( "(x-15)(2x-10)= 0<BR>\n" );
document.write( "x = 15 or x = 5<BR>\n" );
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document.write( "x = 15 gives you a minumum volume of zero.<BR>\n" );
document.write( "x = 5 gives you a maximum volume of 5*20 = 100<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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