document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=267042>Question 267042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Packaging. A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Equal-sized squares x inches on a side will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular box.<BR>\n" );
document.write( "A) Express the volume of the box V(x) in terms of x.<BR>\n" );
document.write( "B) What is the domain of the function V ( determined by the physical restrictions)?<BR>\n" );
document.write( "C) Complete table<BR>\n" );
document.write( "Volume<BR>\n" );
document.write( "X         V (x)<BR>\n" );
document.write( "1<BR>\n" );
document.write( "2<BR>\n" );
document.write( "3<BR>\n" );
document.write( "D) Plot the points in part (C) and sketch a graph of the volume function through these points. (c) a graphing utility can be used as an aid. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196068 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=196068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) Express the volume of the box V(x) in terms of x.<BR>\n" );
document.write( "answer - - > <BR>\n" );
document.write( "length = 12 - 2x<BR>\n" );
document.write( "width = 8-2x<BR>\n" );
document.write( "height = x<BR>\n" );
document.write( "V(x) = (12-2x)(8-2x)(x)<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "B) What is the domain of the function V ( determined by the physical restrictions)?<BR>\n" );
document.write( "domain of the length: 0 <= x <= 6<BR>\n" );
document.write( "domain of the width: 0 <= x <= 4<BR>\n" );
document.write( "Of these two: 0 <= x < = 4 <BR>\n" );
document.write( "--------<BR>\n" );
document.write( "C) Complete table<BR>\n" );
document.write( "Volume<BR>\n" );
document.write( "X . . . . . . . . .  V (x)<BR>\n" );
document.write( "1 . . . . . . . . .  60<BR>\n" );
document.write( "2 . . . . . . . . .  64<BR>\n" );
document.write( "3 . . . . . . . . .  36<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "D) Plot the points in part (C) and sketch a graph of the volume function through these points. (c) a graphing utility can be used as an aid.<BR>\n" );
document.write( "here is a graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+10%2C+-10%2C+100%2C+%2812-2x%29%288-2x%29%28x%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+10%2C+-10%2C+100%2C+%2812-2x%29%288-2x%29%28x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );