For #9, will I always get the right answer if I take the volume (32), divide it by the pressure (4), and multiply it by the rate (2)?

Question

anonymous · Answer

attachment

anonymous · Answer

Because I get the right answer doing that with this problem...

kinggeorge · Answer

I don't think so. I'm pretty sure that's an artifact of $2^2=4$. Or something similar.

anonymous · Answer

what do you mean?

kinggeorge · Answer

Well, if we do the actual problem out, we get that $c=128$. Then, we have that $$dV=-\;{128 \over P^2} dP$$We know that $dP =2$ and $P=4$. Solving, we find that $dV =-16$.

So really, it seems like it's because everything is just a power of two.

anonymous · Answer

i see

kinggeorge · Answer

For a counterexample, let $V=40$. Then we get that $dV =-35/2$ using the method I wrote out. Using your hypothetical method, we get that it would be $-20$.

anonymous · Answer

haha i like creating my own ways to solve things.