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February 1st, 2015, 12:31 AM   #11
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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.
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February 1st, 2015, 09:56 AM   #12
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Quote:
Originally Posted by unistu View Post
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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