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bio website gplus.to/prosteve037
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seen Jun 22 '13 at 1:54

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accepted Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
Sep
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comment Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
Awesome. Thanks so much for clearing this up for me! :-) You should answer my question so I can +1 you and mark it as the answer haha
Sep
2
comment Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
@Rahul Narain - So in other words the constants of proportionality for each statement hold the "opposite" variable as a factor, correct? (ie. $A = m(C)B$ and $A = n(B)C$)
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Jul
31
comment Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
Thanks for the response! I've been reading up on the Combined Gas Law after seeing this post and have come across multiple times that the constants in each of the laws are actually functions dependent on the other variable. In other words, $T \propto P \space\rightarrow\space T = c_1(V)P$ and $T \propto V \space\rightarrow\space T = c_2(P)V$ Will this always be the case though? Will the constants always depend on each other like they do here?
Jul
27
comment Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
I'm also wondering if there is a geometric intuition behind this, can it be proven using lines and areas?
Jul
27
comment Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
No worries! Thanks for the quick response. Here are the numbers I used $A = 12$, $B = 3$, and $C = 6$. (Thus $k = 4$ and $m = 2$). How would you determine that $\ell = c(4)(2)$? Will $\ell$ always be proportional to $k$ and $m$?
Jul
25
comment Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
Why do you multiply the two terms for $A$ together? And wouldn't $kmBC = A^2$?
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