document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980441>Question 980441</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The load that can supported by a rectangular beam varies jointly as the width of the beam and the square of its height, and inversely as the length of the beam. A beam 12 feet long, with a width of 6 inches and a height of 4 inches can support a maxiumum load of 800 pounds. If a similar board has a width of 9 inches and a height of 5 inches, how long must it be to support 1,200 pounds? <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 #601581 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601581\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The condition of this problem means &nbsp;<U>exactly the following</U>:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;The load that can be supported by a rectangular beam <B>is proportional to the width of the beam multiplied by the square of its height \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;and divided by the length of the beam</B>.\r<BR>\n" );
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document.write( "In other words, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%2AH%5E2%29%2FL ALIGN=MIDDLE  ALT=\"%28W%2AH%5E2%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "where &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is the critical load, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W ALIGN=MIDDLE  ALT=\"W\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is the width of the beam, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H ALIGN=MIDDLE  ALT=\"H\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is its height, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the beam&nbsp; and &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the proportionality coefficient which is the constant value for the selected unit system. \r<BR>\n" );
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document.write( "It is how this English is translated to Algebra.\r<BR>\n" );
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document.write( "Therefore, to estimate the critical load, &nbsp;you need to calculate the value of &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%2AH%5E2%29%2FL ALIGN=MIDDLE  ALT=\"%28W%2AH%5E2%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp;&nbsp; for each set of data.\r<BR>\n" );
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document.write( "For the first set you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%2AH%5E2%29%2FL ALIGN=MIDDLE  ALT=\"%28W%2AH%5E2%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A4%5E2%29%2F12 ALIGN=MIDDLE  ALT=\"%286%2A4%5E2%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A16%29%2F12 ALIGN=MIDDLE  ALT=\"%286%2A16%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "For the second set you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28W%2AH%5E2%29%2FL ALIGN=MIDDLE  ALT=\"%28W%2AH%5E2%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A5%5E2%29%2FL ALIGN=MIDDLE  ALT=\"%289%2A5%5E2%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A25%29%2FL ALIGN=MIDDLE  ALT=\"%289%2A25%29%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225%2FL ALIGN=MIDDLE  ALT=\"225%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Now, &nbsp;you have the proportion to find the required <B>L</B>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%5B2%5D%3AF%5B1%5D ALIGN=MIDDLE  ALT=\"F%5B2%5D%3AF%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225%2FL ALIGN=MIDDLE  ALT=\"225%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Substitute here the given critical loads and solve the proportion &nbsp;(the equation)&nbsp; for the unknown &nbsp;<B>L</B>&nbsp; step by step:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1200%2F800 ALIGN=MIDDLE  ALT=\"1200%2F800\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225%2F%288%2AL%29 ALIGN=MIDDLE  ALT=\"225%2F%288%2AL%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225%2F%288%2AL%29 ALIGN=MIDDLE  ALT=\"225%2F%288%2AL%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "3*8*L = 2*225,\r<BR>\n" );
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document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A225%29%2F%283%2A8%29 ALIGN=MIDDLE  ALT=\"%282%2A225%29%2F%283%2A8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500%2F24 ALIGN=MIDDLE  ALT=\"500%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20.833 ft. \r<BR>\n" );
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document.write( "<B>Answer</B>. &nbsp;The beam with the width of &nbsp;9&nbsp; inches and height of &nbsp;5&nbsp; inches must be no longer than &nbsp;20.833 ft &nbsp;to be able to support the load of 1200 pounds.\r<BR>\n" );
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document.write( "<B><U>Couple of notes</U></B>\r<BR>\n" );
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document.write( "1. The formulation of the problem must start with these words:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"The load that can <B><U>be</U></B> supported by a rectangular beam . . . \" \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;instead of \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"The load that can supported by a rectangular beam . . . \"\r<BR>\n" );
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document.write( "2. It doesn't matter in this problem that different dimensions &nbsp;(width, height and length)&nbsp; are presented in different units &nbsp;(feet and inches). \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;What is &nbsp;<U>really important</U>&nbsp; in this context that the &nbsp;<U>corresponding</U>&nbsp; dimensions must be presented in the &nbsp;<U>same units</U>&nbsp; (length and length, &nbsp;width and width, &nbsp;height and height). \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Otherwise you are obliged to make the conversion of dimensions.\r<BR>\n" );
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