document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=47150>Question 47150</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078608619/algebrahomeworkh>advanced mathematical concepts precalculus with applications </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> an 18inch by 20 inch sheet of cardboard is cut and folded to make a box for the great pecan company<BR>\n" );
document.write( "1.Write a polynomial function to model the volume of the box<BR>\n" );
document.write( "2.Graph the function <BR>\n" );
document.write( "3.The company wants the box to have a volume of 224 cubic inches.Write an equation to model this situation.<BR>\n" );
document.write( "4.Find a positive integer for x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31226 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=31226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To make a box from a 18 by 20 inch piece of cardboard, you would need to cut the corners from the piece.  Let's say that you cut an x by x square from each corner of the given piece of cardboard so that you could then fold the sides up to form an open box. The volume of the resulting box can be expressed by the following polynomial function of x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%2818-2x%29%2820-2x%29 ALIGN=MIDDLE  ALT=\"V+=+x%2818-2x%29%2820-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+360x-36x%5E2-40x%5E2%2B4x%5E3 ALIGN=MIDDLE  ALT=\"V+=+360x-36x%5E2-40x%5E2%2B4x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+4x%5E3-76x%5E2%2B360x ALIGN=MIDDLE  ALT=\"V+=+4x%5E3-76x%5E2%2B360x\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the polynomial function.\r<BR>\n" );
document.write( "\n" );
document.write( "The graph looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C15%2C-20%2C500%2C4x%5E3-76x%5E2%2B360x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C15%2C-20%2C500%2C4x%5E3-76x%5E2%2B360x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "If the volume is to equal 224 cubic inches, the equation would be:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3-76x%5E2%2B360x+=+224 ALIGN=MIDDLE  ALT=\"4x%5E3-76x%5E2%2B360x+=+224\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 224 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3-76x%5E2%2B360x-224+=+0 ALIGN=MIDDLE  ALT=\"4x%5E3-76x%5E2%2B360x-224+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify by dividing through by 4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-19x%5E2%2B90x-56+=+0 ALIGN=MIDDLE  ALT=\"x%5E3-19x%5E2%2B90x-56+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x \r<BR>\n" );
document.write( "\n" );
document.write( "The 3 solutions are:<BR>\n" );
document.write( "x = 0.73<BR>\n" );
document.write( "x = 6.53<BR>\n" );
document.write( "x = 11.74\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );