document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856837>Question 856837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a total of 1700 square centimeters of material is to be used to make a box with a square base and an open top, find the largest possible volume of such a box.\r<BR>\n" );
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document.write( "The box is drawn 3-D with no top, the right face and front face of the box has an x and along the left corner is the h.\r<BR>\n" );
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document.write( "Could you help me?\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Ashley Dodson </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516158 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=516158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The square base makes this a simpler problem than if no side were square.\r<BR>\n" );
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document.write( "x = side of base edge<BR>\n" );
document.write( "y = height\r<BR>\n" );
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document.write( "AREA ACCOUNTING FOR 1700 SQUARE CM<BR>\n" );
document.write( "The base area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and there are FOUR surfaces of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy ALIGN=MIDDLE  ALT=\"xy\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4xy ALIGN=MIDDLE  ALT=\"4xy\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Altogether, the area equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%284xy%2Bx%5E2=1700%29 ALIGN=MIDDLE  ALT=\"highlight_green%284xy%2Bx%5E2=1700%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "VOLUME FORMULA<BR>\n" );
document.write( "v for volume, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28v=%28x%5E2%29y%29 ALIGN=MIDDLE  ALT=\"highlight_green%28v=%28x%5E2%29y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Can you understand that analysis?<BR>\n" );
document.write( "Can you continue from there yourself?<BR>\n" );
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document.write( "After almost completing the solution myself, the problem question is either for College Algebra or for first semester of Calculus.  If for College Algebra, you might use a graphing calculator to find the maximum point.  If Calculus, then you would differentiate v against x, solve for x if the derivative is zero, and that will be the x value for maximum volume, v.  The process should bring you to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2F%28dx%29%29v=425-%283%2F4%29x%5E2=0 ALIGN=MIDDLE  ALT=\"%28d%2F%28dx%29%29v=425-%283%2F4%29x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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