Thank you for the post, but I disagree with your third point. In my opinion Equation III (and all the equations) suffers more from a lack of terms than too many.Originally posted by: kawarimi
Yep all your answers are correct (besides rounding that could make it 1 off), but Equation Ib
should beEquation Ib: 1.7(chapter/episode) ((tied_episode) = (weeks_left) (episode/week)+(85 episodes))
tied_chapter / (1.7 chapter/episode) = (weeks_left) (episode/week)+(85 episodes)
And just to make it less confusing,
in this equation, chapters/episode is just a unit. so a simpler Equation III isEquation III: tied_episode * 1.7 (chapters/episode) = tied_chapter
Equation III: tied_chapter = 1.7 * tied_episode
Let's replace tied_episode with E and tied_chapter with C to make it less confusing (which is why I didn't add these terms in the first place, because I think letters scare off non-mathematicians).
If we added all the terms, it would read:
Equation III: E episodes * 1.7 (chapters / episodes) = C chapters
or
Equation IIIb: C chapters = 1.7E chapters
This is not the same as C = 1.7E, since C = 1.7E implies C chapters = 1.7E episodes and then the units would not cancel out. If you look at the post I link to in my first post, you will find that the original author made mistakes because he fails to accurately handle units.
In high school, my advanced chemistry teacher was a stickler to make sure that we tracked each unit and in college this ability gave me a HUGE advantage on tests. In fact, I think making sure units convert properly is the key to success at applying math skills to science. I am not the brightest of people and definitely not the most dillegent, but I was able to get a couple standard deviations above the mean on many tests just simply because a lot of problems solve themselves if you are anal with your unit conversion. If I posted C = 1.7E, even though in essence that is correct, I feel like I would be setting up some of the young students who read this post to fail in college level math or science.
As for your second point, I agree that your method is more clear than multiplying both sides of equation 1 by 1.7 (chapters / episodes). To do this we would have to modify Equation III still further and write:
Equation IIIc: E episodes = C chapters / 1.7 (chapters / episodes) = C / 1.7 episodes.
Let's do some more math to see how the terms cancel out. It is always fun.=P
Replacing E episodes in Equation Ib like you do we have:
Equation Ib: C chapters / 1.7 (chapters / episodes) = (weeks_left) (episode/week)+(85 episodes)
Multiplying 1.7 (chapters / episodes to both sides we have:
Equation Ibi: C chapters = 1.7weeks_left (episode / week) (chapter / episode) + 1.7 * 85 episodes (chapter / episode)
When we cancel out terms we get Equation Ic.
As for the rounding error. The reason I am not trying too hard with rounding is because the 1.7 constant varies so much during the season. I would say any calculation we make will probably be off by an error of at least three months on either side of the date.
Thanks for the comments.=P
Genin_Dropout