document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149561>Question 1149561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a rectangular piece of cardboard with perimeter 10 inches, three parallel and equally spaced creases are made. The cardboard is then folded along the creases to make a rectangular box with open ends. Letting x represent the distance (in inches) between the creases, use a graphing calculator to find the value of x that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770895 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  On a rectangular piece of cardboard with perimeter 10 inches, three parallel and equally spaced creases are made.<BR>\n" );
document.write( " The cardboard is then folded along the creases to make a rectangular box with open ends.<BR>\n" );
document.write( " Letting x represent the distance (in inches) between the creases, use a graphing calculator to find the value of x that maximizes the volume enclosed by this box.<BR>\n" );
document.write( " Then give the maximum volume. Round your responses to two decimal places.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let L = the length of the cardboard<BR>\n" );
document.write( "let x = dist between creases<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2L + 8x = 10<BR>\n" );
document.write( "simplify divide by 2<BR>\n" );
document.write( "L + 4x = 5<BR>\n" );
document.write( "L = (5-4x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Volume<BR>\n" );
document.write( "V = x^2 * L<BR>\n" );
document.write( "Replace L with (5-4x)<BR>\n" );
document.write( "V = x^2(5-4x)<BR>\n" );
document.write( "V = -4x^3 + 5x^2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graph this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1%2C+4%2C+-1%2C+4%2C+-4x%5E3%2B5x%5E2%2C+1.16%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1%2C+4%2C+-1%2C+4%2C+-4x%5E3%2B5x%5E2%2C+1.16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Max volume when x = .83 inches<BR>\n" );
document.write( "Find the volume<BR>\n" );
document.write( "V = -4(.83^3) + 5(.83^2)<BR>\n" );
document.write( "V = -2.29 + 3.45<BR>\n" );
document.write( "V =  1.16 cu/in is the max volume (green line)<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );