Hey all, it's been a long time since I last posted on this blog. A lot of things have happened since then. I'm now in Canada and yes, it is home to one of the biggest game development companies that I want to work on.. Vancouver, Canada is the home of Electronic Arts!! By moving in this country, I got a whole new shot at this whole journey. But nothing comes without a high price though. I got separated with my friends, my pets, my cousins, my hometown, and most of all, my ever dearest love. It was very hard at first but I was able to cope up after few weeks of doing nothing but watch cartoons :) I guess this is how life really is. You just have to know how to deal with those ups and downs and be happy with it.
Anyway, I actually had a shot at working at EA as a game tester but I turned down (that's right!!) the position since during that time, I was already enrolled at this certain course that I took at BCIT. What the hell were you thinking?! you might say. Well, it's hard for me to explain but I knew that with all of the free time that I will have for not working, I will have all the time in the world to further improve myself and target a more higher level position in the company. Right now, I just don't feel that my skills are enough to move me up the hierarchy so I decided to just wait (and be a bum) and gain as much knowledge as I can before I enter the industry.
Okay, enough about that. During the last few months, I've been working like hell on this pre-calculus book that I bought during a library sale. After I finished this other C++ book, I decided that its time to move on to more theories and less application (after all, how am I gonna program if I don't know what I'm gonna program). And so, its back to 4th year high school for me.. revisiting those topics that talk about radicals, polynomials, exponentiations, fractions, quadratics, etc. and I really try to answer all of the questions at the end of the chapter at the end of the book (that's like 140 questions per chapter!!) so that this time, it sticks to my brain for good!! And what's more interesting is that I try to find out how these polynomials are applied to the real world. It's really very interesting to learn how some of the real world problems that deal with numbers can be expressed as equations (I know we've been doing a lot of these during high school but I wasn't paying attention back then on how important these stuffs really are!!). It's truly impressive that by solving these equations, you get a concrete and valid answer out of the problem that seemed very impossible to solve just by looking at it!! Here's a very simple example:
Mowing on a garden lawn having an area of 5 feet requires Jim 2 hours to finish and 3 hours to finish for Jen. If Jim and Jen were to work together, how long will it take for the said lawn to be mowed?
We can express Jim and Jen's work in terms of a fraction of work that they can do per hour. Hence:
Jim can mow 5/2 feet of the garden in 1 hour (2.5 feet per hour)
and Jen can mow 5/3 feet of the garden in the same hour (1.67 square feet per hour)
Finally, we can express their combined work rate as 5/x
Remember, what we expressed here is how much work can be done in an hour. An x variable is needed since we do not know yet how many hours is needed for the both of them to mow the entire lawn. Also, we assume here that they both worked throughout the duration and that they worked on a consistent basis (that is, 2.5 feet per hour for Jim and 1.67 feet per hour for Jen).
Equating the problem, we have:
Jim's work rate + Jen's work rate = Combined work rate
5/3 + 5/4 = 5/x
Solving for x, we have:
x = (4)(3)(5) / (20 + 15)
x = 12 / 7
Hence, if Jim and Jen works together to mow the 5 feet lawn, it will take them 12 / 7 hours or 1 and 5/12 hours to finish - a lot more quicker than working alone.
So how do we check if our answer is correct? Simple. We just solve for equality. Hence:
We know that:
x = 12/7
And the working equation was :
5/3 + 5/4 = 5/x
By the virtue of substitution, we have:
5/3 + 5/4 = 5/(12/7)
Solving for both the left hand side (LHS) and right hand side (RHS) of the equation, we have:
35 / 12 = 35 / 12
Hence, this clearly shows that we have an equality and that our solution is correct!
You see, this is just one of the amazing things math can do. Without the knowledge on how to translate those into equations, we might have not arrived in the proper answer or even if we did, it would have took us a lot of time using ubiquitous methods.
There are a lot of things that I really have to learn in that area. Right now, I'm on section 1.6, page 67 of the book and there are a lot of problems whose complexity far exceeds the one that I just wrote down. Perhaps the real key to this one is really understanding what the problem is all about and knowing how you would express them algebraically. Well, I guess that's it for now. I need to get some sleep now as it is already 7 minutes past 5 in the morning :) (I really need to change my sleeping habits).
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