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 February 1st, 2015, 12:31 AM #11 Member   Joined: Dec 2014 From: Queensland Posts: 59 Thanks: 2 the course im in is an itroductory course to engineering mathmatics. I havent been informed of the consant k of proportionality. My question was You are to mill a beam from a cylindrical wooden log. The strength S of a beam is proportional to its width (w) and to the square of its depth (d). What is the width and depth of the strongest beam that can be cut from a 300 mm diameter wooden log? from this i get $$S=wd^{2}$$ and the $$w=300^{2}-w^{2}$$ was also $$w=\sqrt{90000}-\sqrt{30000}$$ $$S$$ is proportional to $$wd^{2}$$ is it not from the statement? meaning $$S=wd^{2}$$. can $$k$$ be $$1$$? so am i wrong? we havent been tought the constant of proprotionality as i thought s was proportional to w*d^2. am i wrong? Last edited by unistu; February 1st, 2015 at 01:05 AM.
February 1st, 2015, 09:56 AM   #12
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 Originally Posted by unistu the course im in is an itroductory course to engineering mathmatics. I havent been informed of the consant k of proportionality. My question was You are to mill a beam from a cylindrical wooden log. The strength S of a beam is proportional to its width (w) and to the square of its depth (d). What is the width and depth of the strongest beam that can be cut from a 300 mm diameter wooden log? from this i get $$S=wd^{2}$$
Not quite -- it's S = kwd^2 for some constant k. It will turn out that it doesn't matter what k is, though, so you'd get the same answer then if you assumed k = 1.

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