<PRE><B>Question 190888</B>
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If the load weight is jointly proportional to the width and the square of the depth and inversely proportional to the beam length, then you can write the relationship thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ L = \frac{kwd^2}{l}]



Where  &lt;i&gt;&lt;b&gt;L&lt;/b&gt;&lt;/i&gt; is the load weight, &lt;i&gt;&lt;b&gt;w&lt;/b&gt;&lt;/i&gt; is the beam width, &lt;i&gt;&lt;b&gt;d&lt;/b&gt;&lt;/i&gt; is the beam depth, &lt;i&gt;&lt;b&gt;l&lt;/b&gt;&lt;/i&gt; is the beam length, and &lt;i&gt;&lt;b&gt;k&lt;/b&gt;&lt;/i&gt; is the constant of proportionality.


If something is proportional it goes in the numerator -- it is proportional to &lt;i&gt;&lt;b&gt;w&lt;/b&gt;&lt;/i&gt; and *[tex \LARGE d^2], so both go in the numerator.  If it is inversely proportional, it goes in the denominator, like our &lt;i&gt;&lt;b&gt;l&lt;/b&gt;&lt;/i&gt;.  And finally, you have to put in a constant of proportionality.  It doesn&#39;t matter where that goes except that it is generally computationally easier if you leave it in the numerator.


Since you didn&#39;t give the beam length, what we need to do is to calculate a value for *[tex \LARGE \frac{k}{l}] given that &lt;i&gt;&lt;b&gt;w&lt;/b&gt;&lt;/i&gt; = 3 cm, &lt;i&gt;&lt;b&gt;d&lt;/b&gt;&lt;/i&gt; = 5 cm, and &lt;i&gt;&lt;b&gt;L&lt;/b&gt;&lt;/i&gt; = 630 kg.  So substitute the values:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 630 = \frac{k(3)(5)^2}{l} = \frac{75k}{l}]


And then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{k}{l} = \frac{630}{75} = 8.4]


Now re-write your proportion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ L = 8.4\,\cdot\,wd^2]


And substitute the new values for &lt;i&gt;&lt;b&gt;w&lt;/b&gt;&lt;/i&gt; and &lt;i&gt;&lt;b&gt;d&lt;/b&gt;&lt;/i&gt;, namely 5 and 3 respectively.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ L = 8.4\,\cdot\,(5)(3)^2 = 8.4\,\cdot\,45 = 378\text{ kg}]




John
*[tex \LARGE e^{i\pi} + 1 = 0]
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