document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174983>Question 174983</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132031248/algebrahomeworkh>california algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 56. Tonya wants to make a metal tray by cutting four identical square corner pieces from a rectangular metal sheet. Then she will bend the sides up to make an open tray.\r<BR>\n" );
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document.write( "a. Let the length of each side of the removed squares be x in. Express the volume of the box as a polynomial function of x.\r<BR>\n" );
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document.write( "b. Find the dimensions of a tray that would have a 384-in. to the 3rd power capacity.\r<BR>\n" );
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document.write( "rectangle diagram with length 20in. and width 16in. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130061 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 56. Tonya wants to make a metal tray by cutting four identical square corner pieces from a rectangular metal sheet. Then she will bend the sides up to make an open tray. <BR>\n" );
document.write( "a. Let the length of each side of the removed squares be x in. Express the volume of the box as a polynomial function of x. <BR>\n" );
document.write( "L = length<BR>\n" );
document.write( "W = width<BR>\n" );
document.write( "Vol = (L-2x)*(W-2x)*x<BR>\n" );
document.write( "V = (WL - 2x*(W+L) + 4x^2)*x<BR>\n" );
document.write( "V = 4x^3 - 2x^2(W+L) + WLx<BR>\n" );
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document.write( "b. Find the dimensions of a tray that would have a 384-in. to the 3rd power capacity. <BR>\n" );
document.write( "rectangle diagram with length 20in. and width 16in.<BR>\n" );
document.write( "Do you mean to start with a sheet 20 by 16?<BR>\n" );
document.write( "384 = 4x^3 - 2x^2*(16+20) +320x<BR>\n" );
document.write( "384 = 4x^3 - 72x^2 +320x<BR>\n" );
document.write( "x^3 - 18x^2 + 80x - 96 = 0<BR>\n" );
document.write( "x = 2, 4 or 12 inches<BR>\n" );
document.write( "12 won't work, since cutting 12\" from 2 corners totals 24\", more than the size of the sheet.<BR>\n" );
document.write( "So either 2 or 4 inches will produce a tray of 384 cubic inches.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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