So, I'm back to the regular schedule, at least for a couple weeks. Only one more week until Christmas Break, but that doesn't mean too much for Calculus. We've been assigned a project on optimization, which I have yet to start, and a quiz coming up on Monday. So, basically, we've got more work, probably to make up for the two weeks off later.
So this week was about applying derivatives to more real world situations, namely finding rates of change. After spending a few days on maximizing and minimizing, I suppose it only makes sense that we'd find the things that derivatives are really meant to find, slopes. I've found that these problems aren't bad overall, though, and aside from conical tanks, I often get through relatively quickly. For whatever reason, however, I can't seem to use similar triangles correctly within the context of the problem, but I think that'll be the kind of thing that I'll remember on the quiz just because I forgot it previously. I keep trying to plug in numbers for variables before I really can, and I usually wind up with multiple variables in the end equation and stare dumbfounded at the lack of an obvious solution. Like I said, though, it seems like the kind of thing that I'm going to remember now, if only because I've made the same mistake twice within the span of two, maybe three days.
I think it's probably right for me to address the quiz I was supposed to take last Friday now. It was actually more difficult than I thought, and I wound up spending more time than was probably necessary struggling with negative distances. The third question was the worst by far, and it took me far longer than I'd like to admit to realize that I wasn't actually measuring in time for the majority of the problem. I kept trying to multiply by the rates instead of dividing by them, and that really threw off my answers, hence the aforementioned negative distance. It also didn't help that I attempted to do the quiz while in the same room as QuizBowl practice, and I wound up being just a little more distracted than I thought I'd be. To be fair, though, I saw only four questions and thought that it'd take no more than twenty minutes, when in reality I took a little over an hour total. The final question also proved to be more difficult than it needed to be, mostly due to my own lack of reading comprehension. How was I supposed to know that a semicircle wasn't the same thing as a full circle? Doesn't even make any sense. Anyways, the really dumb thing was that I failed to recognize that the dimensions for the largest four-sided figure in a full circle would be very similar to those in half of that circle. Only after I had painstakingly redone all my work did I realize that I could've used my previous answers to get the final answer in mere seconds. I suppose I would've had to show the proper work regardless, but it would've been just a little easier to solve if I knew the answer beforehand.
Anyways, that's about it. I'm tired and I feel like this was one of the more ramble-y posts I've made (do I say that every time? Because I feel like most of my posts end in this or something similar) and I want to cut myself off before I waste more of your time. For the sake of constancy, next update'll be Friday, so I'll see you then.