document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=531437>Question 531437</A>: <I><SPAN STYLE=\"word-break: break-all;\">   ______8______          <BR>\n" );
document.write( "  |_|x             <BR>\n" );
document.write( "  |x<BR>\n" );
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document.write( "13|<BR>\n" );
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document.write( "  |_|__________ \r<BR>\n" );
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document.write( "This is a paper that is cut from EACH side in small squares when you fold it is a rectangular prism with no top, 13 is the lenght and 8 is the width. it did'nt let me draw the other half but it is a FULL rectangle and all four sides of the corners a cube is cut out and that is X.  What is the value of X and Maximum volume of it and could you show work too my Teacher said use a TI calculator if you can and i dont have one and she said that it was going to be a parabola it would be great if you could help me thanks!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350462 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=350462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a paper that is cut from EACH side in small squares when you fold it is a rectangular prism with no top, 13 is the lenght and 8 is the width. it did'nt let me draw the other half but it is a FULL rectangle and all four sides of the corners a cube is cut out and that is X. What is the value of X and Maximum volume of it and could you show work too my Teacher said use a TI calculator if you can and i dont have one and she said that it was going to be a parabola it would be great if you could help me thanks! <BR>\n" );
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document.write( "Draw a rectangle with length=13 and width=8<BR>\n" );
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document.write( "Draw a square at each corner of the rectangle (in the rectangle)<BR>\n" );
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document.write( "Draw the rectangle that connects the squares<BR>\n" );
document.write( "with width = 8-2x and length = 13-2x<BR>\n" );
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document.write( "If you cut out those squares and fold up the four sides<BR>\n" );
document.write( "you will have a rectangular prism with height = x and<BR>\n" );
document.write( "base = 8-2x by 13-2x<BR>\n" );
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document.write( "Volume = x(8-2x)(13-2x) = (4x^3 - 42x^2 + 104x)<BR>\n" );
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document.write( "To find the maximum volume find the derivative:<BR>\n" );
document.write( "V'(x) = 12x^2-84x+104<BR>\n" );
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document.write( "Solve 12x^2-84x+104 = 0<BR>\n" );
document.write( "3x^2 - 21x + 26 = 0 <BR>\n" );
document.write( "Solve using the Quadratic Formula:<BR>\n" );
document.write( "x = [21 +- sqrt(21^2 - 4*3*26)]/6<BR>\n" );
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document.write( "x = [ 21 +- sqrt(129)]/2<BR>\n" );
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document.write( "Positive solution:<BR>\n" );
document.write( "x = [21 + 11.36]/2<BR>\n" );
document.write( "x = 16.18<BR>\n" );
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document.write( "Find the Maximum Volume<BR>\n" );
document.write( "V(x) = (4x^3 - 42x^2 + 104x)<BR>\n" );
document.write( "V(16.18) = 4*16.18^3 - 42*16.18^2 + 104*16.18 = 7630.6 cu. units<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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