document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218034>Question 218034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dalton has a closed rectangular box with a square base at least 10 inches long have a surface area of 900 square inches.  what dimensions will give the box a maximum volume? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164363 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=164363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Dalton has a closed rectangular box with a square base at least 10 inches long<BR>\n" );
document.write( " have a surface area of 900 square inches.<BR>\n" );
document.write( " what dimensions will give the box a maximum volume?<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Let x = the side of the square base<BR>\n" );
document.write( "Actually the maximum is when the box is a perfect cube, therefore<BR>\n" );
document.write( "let x = the height of the box also<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Surface area equation, find h:<BR>\n" );
document.write( "6x^2 = 900<BR>\n" );
document.write( "simplify divide by 6<BR>\n" );
document.write( "x^2 = 150<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28150%29 ALIGN=MIDDLE  ALT=\"sqrt%28150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 12.247\"<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Max vol: 12.247 by 12.247 by 12.247, and 12.247^3 = 1836.9 cu/in<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can prove this: <BR>\n" );
document.write( "let the height = h, <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Surface area equation, find h:<BR>\n" );
document.write( "2x^2 + 4xh = 900<BR>\n" );
document.write( "simplify divide by 2<BR>\n" );
document.write( "x^2 + 2xh = 450<BR>\n" );
document.write( "2xh = -x^2 + 450<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%5E2+%2B+450%29%2F%282x%29 ALIGN=MIDDLE  ALT=\"%28-x%5E2+%2B+450%29%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Volume equation<BR>\n" );
document.write( "V = x^2 * h<BR>\n" );
document.write( "Replace h<BR>\n" );
document.write( "V = x^2(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%5E2+%2B+450%29%2F%282x%29 ALIGN=MIDDLE  ALT=\"%28-x%5E2+%2B+450%29%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "V = x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%5E2+%2B+450%29%2F2 ALIGN=MIDDLE  ALT=\"%28-x%5E2+%2B+450%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "V = x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%5E3+%2B+450x%29%2F2 ALIGN=MIDDLE  ALT=\"%28-x%5E3+%2B+450x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " <BR>\n" );
document.write( "Graph this equation y=V<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+30%2C+-1000%2C+2000%2C+%28-x%5E3%2B450x%29%2F2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+30%2C+-1000%2C+2000%2C+%28-x%5E3%2B450x%29%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Shows max volume when x is a little over 12\"; vol is about 1800 cu/in\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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