document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205455>Question 1205455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the fact that the load a beam with a rectangular cross section can support is jointly proportional to the beam's width and the square of its depth and inversely proportional to its length.<BR>\n" );
document.write( "A beam 3 cm wide and 5 cm deep can support a load of 630 kg. What load can it support when turned on its side? </SPAN>\n" );
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document.write( "The given information gives us the following equation:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=load=%28%28k%29%28width%29%28depth%5E2%29%29%2Flength ALIGN=MIDDLE  ALT=\"load=%28%28k%29%28width%29%28depth%5E2%29%29%2Flength\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where k is a constant of proportionality.<br><BR>\n" );
document.write( "We are given the load that can be supported for a given width and depth.  But we are not given the length, so we can't determine the constant of proportionality.<br><BR>\n" );
document.write( "But to solve the problem we don't have to know the value of k.   k is some constant, and in this problem the length is a constant.  So the difference in the load that can be supported is due to putting the bean on its side -- i.e., switching the width and depth.<br><BR>\n" );
document.write( "For the load of 630kg, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28width%29%28depth%5E2%29=%283%29%285%5E2%29=75 ALIGN=MIDDLE  ALT=\"%28width%29%28depth%5E2%29=%283%29%285%5E2%29=75\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "When the beam is turned on its side, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28width%29%28depth%5E2%29=%285%29%283%5E2%29=45 ALIGN=MIDDLE  ALT=\"%28width%29%28depth%5E2%29=%285%29%283%5E2%29=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "So the load that can be supported when the beam is turned on its side is 45/75 = 3/5 of the load it can support in the given configuration.<br><BR>\n" );
document.write( "630*(3/5)=378<br><BR>\n" );
document.write( "ANSWER: 378kg<br><BR>\n" );
document.write( " </SPAN>\n" );
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