document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=706282>Question 706282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey guys, this question is related to applications of calculus (I couldn't find the section.<BR>\n" );
document.write( "So, the question is as follows:\r<BR>\n" );
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document.write( "A rectangular block, the length of whose base is twice the width has a total surface area of 300cm^2. Find the dimensions of the block if it is of maximum volume. \r<BR>\n" );
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document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435095 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=435095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x length, y width, z height.<BR>\n" );
document.write( "volume of the box would be xyz.\r<BR>\n" );
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document.write( "x=2y as given, so volume is 2*y*y*z or volume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=2y%5E2z. ALIGN=MIDDLE  ALT=\"v=2y%5E2z.\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Surface area was given as 300 cubic units.   Accounting for the lengths measurements,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2Ay%2Ay%2B2yz%2B2%2Ay%2A2%2Az=300 ALIGN=MIDDLE  ALT=\"2%2A2%2Ay%2Ay%2B2yz%2B2%2Ay%2A2%2Az=300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4y^2+2yz+4yz=300<BR>\n" );
document.write( "...and few more steps...<BR>\n" );
document.write( "z=(300-4y^2)/(2y+4y)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%282%2F3%29%2875-y%5E2%29%2Fy ALIGN=MIDDLE  ALT=\"z=%282%2F3%29%2875-y%5E2%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Back to the volume formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=2y%5E2%28z%29 ALIGN=MIDDLE  ALT=\"v=2y%5E2%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "v=2y^2(2/3)(75-y^2)/y<BR>\n" );
document.write( "v=...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=100y-%284%2F3%29y%5E3 ALIGN=MIDDLE  ALT=\"v=100y-%284%2F3%29y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----Taking derivative of formula in this form may be easiest.\r<BR>\n" );
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document.write( "The task to do now is the maximize v as a function of width y.   Differentiate v with respect to y.<BR>\n" );
document.write( "You then simply calculate x from knowing how x and y were given.  Then you may need to use the z formula found above to caclulate z. </SPAN>\n" );
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