Tricky question..

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• Jan 12th 2009, 04:48 PM
AlgebraicallyChallenged
Tricky question..
Evening Forum I have a interesting word problem..

What's the difference between saying "The thicker a beam is, the stronger it is." and saying "The strength of a beam varies directly as its thickness."?

any comments ?
• Jan 12th 2009, 04:56 PM
Mush
Quote:

Originally Posted by AlgebraicallyChallenged
Evening Forum I have a interesting word problem..

What's the difference between saying "The thicker a beam is, the stronger it is." and saying "The strength of a beam varies directly as its thickness."?

any comments ?

Well "The thicker a beam is, the stronger it is" is very vague. It doesn't express the relationship between thickness and strength very precisely. For example, does it mean exponentially proportional? Increasing the thickness a LITTLE may increase the strength A LOT. This is exponential proportionality.

However, the 2nd statement is a statement of direct proportionality. If strength = S, and thickness = T, then the 2nd statement says $S = kT$ where k is some constant! This means that if you change S, then T change proportionally!

So all in all. The first statement does not specify how proportionally one variable changes to another, but the 2nd statement does!