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Which of the following describe this formula correctly: $S = 2\pi rh$

1.S is jointly proportional to radius and height

2.S is directly proportional to radius and height or

3.S varies directly with radius and height.

I am leaning towards choice 3 but I am not 100% positive.

This is stuff on variation that might help. k is a constant

"S varies as x" means S = kx

"S varies jointly as x and y" means S = kxy

"S varies as x + y" means S = k(x + y)

"S varies inversely as x" means S = k/x
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How are the adverbs "jointly" and "directly" defined in your book? – J. M. May 9 '11 at 15:28
I think directly means a constant is being multiplied with 1 variable, jointly means a constant is being multiplied with more than 1 variable. see edit. – Matt May 9 '11 at 15:36
So, why did you choose the third as opposed to, say, the first? – J. M. May 9 '11 at 15:36
Ah, because I didn't realize 2pi(r) wasn't a constant. 2pi would be k and radius and height would be variables so thinking about it that way, the first choice seems best. – Matt May 9 '11 at 15:41
I would go with the first choice as well. – El'endia Starman May 9 '11 at 16:37
up vote 1 down vote accepted

The verb "describe" in the question is in the plural. That would seem to imply that any number of answers can be selected. As Chris noted in the comments, all three sentences are OK (assuming an appropriate definition of the terms used).

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