document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203465>Question 203465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> having trouble setting this up can someone help please\r<BR>\n" );
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document.write( "A rectangular box with no top (pictured above) is to contain 2250 cubic inches of volume. Find the dimensions of the box that will minimize the surface area. The length (l) of the base is three times the width (w).\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153540 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=153540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular box with no top (pictured above) is to contain 2250 cubic inches of volume. <BR>\n" );
document.write( "Find the dimensions of the box that will minimize the surface area. <BR>\n" );
document.write( "The length (l) of the base is three times the width (w).<BR>\n" );
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document.write( "But what about the height of the box? Is it the same as the width,<BR>\n" );
document.write( " or do we have to find it? (h), assuming this is the case:<BR>\n" );
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document.write( "l * w * h = 2250 cu/inches<BR>\n" );
document.write( "Let w = x, then we can write it:<BR>\n" );
document.write( "3x * x * h = 2250<BR>\n" );
document.write( "3x^2 * h = 2250<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2250%2F%283x%5E2%29 ALIGN=MIDDLE  ALT=\"2250%2F%283x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "reduce fraction<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2Fx%5E2 ALIGN=MIDDLE  ALT=\"750%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height of the box<BR>\n" );
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document.write( "Surface area for box without a top<BR>\n" );
document.write( "S.A. = (l*w) + 2(l*h) + 2(w*h)<BR>\n" );
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document.write( "Substitute 3x for l and x for w<BR>\n" );
document.write( "S.A. = 3x*x + 2(3x*h) + 2(x*h)<BR>\n" );
document.write( "S.A = 3x^2 + 6hx + 2hx<BR>\n" );
document.write( "S.A = 3x^2 + 8hx<BR>\n" );
document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2Fx%5E2 ALIGN=MIDDLE  ALT=\"750%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for h<BR>\n" );
document.write( "S.A = 3x^2 + 8(x*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2Fx%5E2 ALIGN=MIDDLE  ALT=\"750%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "S.A = 3x^2 + 8(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2Fx ALIGN=MIDDLE  ALT=\"750%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "S.A = 3x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6000%2Fx ALIGN=MIDDLE  ALT=\"6000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Graph this equation and find the min surface area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+20%2C+-500%2C+2000%2C+3x%5E2+%2B+%286000%2Fx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+20%2C+-500%2C+2000%2C+3x%5E2+%2B+%286000%2Fx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On a Ti-83, it says, min S.A. at x = 10, which is 900 sq/in, as indicated here.<BR>\n" );
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document.write( "find h:<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2Fx%5E2 ALIGN=MIDDLE  ALT=\"750%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2F100 ALIGN=MIDDLE  ALT=\"750%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 7.5<BR>\n" );
document.write( "Then l= 30, w=10, h=7.5; the dimensions of the box<BR>\n" );
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document.write( "Check volume: 30 * 10 * 7.5 = 2250<BR>\n" );
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document.write( "Did this make sense?  </SPAN>\n" );
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