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What d'you learn at school today?


Crimson

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I didn't learn a whole lot today. I didn't even learn a lot on Friday, asides from watching a video about Neslon Mandela, which neglected to mention that he was a dirty communist. :eww: (I'm making fun of how American schools teach us to not like Commies.)

 

Anyways, what I learned today? Let's see...

  • In my A+ computer class we only watched a 10 minute video on, well I don't even remember. Asides from that, I just played Team Fortress 2 the rest of the hour.
  • In my Game Maker class I made it so that my Jet's special weapon to use against the boss (I made my Godzilla) is a Bass Cannon.
  • In English we played Charades. My teacher's reasoning for this was so that we'd look stupid, as we have to give speeches on Wednesday. If we look stupid now, then maybe we won't feel as stupid on Wednesday apparently.
  • In Economics, I pretty much slept the whole hour. We learned about recessions, and depressions, and such.
  • In Science, my partner worked on fortifying our Toothpick bridge.
  • In Study hall, I just read The Fault in our Stars the entire hour. It's a great book!
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I don't go back to school until next week, but I did go back to my old high school to teach some kids how to set up a sound system for the concert they're putting on. So that was pretty fun.

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I learned something in AP Calculus AB class today that I found to be particularly fascinating - the formal definition of the natural logarithmic function, which involved the use of an accumulation function.
 
The natural logarithmic function is a special kind of logarithm. It is a logarithm with base e, which is Euler's number. Similar to ?, it is an irrational number with an infinite number of non-repeating decimals. It has tremendous use in mathematical applications involving exponential growth, such as compound interest or population growth. 
 
Euler's number is formally defined analytically as the following:

img-2205541-1-8d7fd8270549fd0f682d81d1cd
 
A logarithm, in general, is an exponent. Logarithms can be used to determine to what number, or exponent, a specified base must be raised to in order to result in the specified value. 
 
A logarithm takes the following general form:
 
img-2205541-2-mdyDj5.png
 
Such that:
 
img-2205541-3-VdQm5L.png

The natural logarithm is a special kind of logarithm in which b = e. In other words, it is a logarithm with a base of Euler's number, and is written as the following:
 
img-2205541-4-OjNdk5.png
 
 
The natural logarithm shows up frequently in Calculus. For example, the antiderivative of the reciprocal function f(x) = 1 / x is equal to the natural logarithm of the absolute value of x plus C, F(x) = ln|x| + C, where C is the arbitrary constant of integration. Conversely, the derivative of F(x) = ln|x| + C is equal to the reciprocal function, f(x) = 1 / x. The antiderivative of the natural logarithmic function can be ascertained through utilization of the integration by parts formula, and is equal to F(x) = x*ln|x| - x + C.
 
Following from its algebraic definition, ln(x) = y can be interpreted as the following: to what power y must e be raised to in order to equal x?
 
However, the formal mathematical definition of ln(x) can be stated using a concept known as accumulation functions from Calculus. An accumulation function is a function defined by the definite integral of a different function, in which the upper limit of integration varies:
 
img-2205332-1-MBuzvS.png
 
 
The natural logarithmic function is formally defined by the following accumulation function:
 
img-2205541-6-256136fe0a6931d60d70717afd
 
One of the things that I love the most about Calculus is that it allows you to begin to understand the basics of the foundational concepts behind topics you learned about in previous mathematics classes.

Edited by SCS
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I learned that you should never trust your friend with a pen and sleep a lot. Also, don't put the clumsy person close to the edge.

 

Well, I *actually* learned some stuff. I learned some more random science and math. We did WW1 research today. That's about it.

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  • 3 weeks later...

I have no class on fridays, cause college :lol:

So i'll do thursday instead. In my Design II class, we're turning paintings into 3-D paintings. Basically, we take several layers of hard foam boards and cut them out into shapes and layer them on top of each other so that they give the picture dimension. Then, we paint it just like the picture. Here's the painting i chose to recreate, made by Tamara Lempicka :D I'm turning it 3-D, yall. Its gonna be great

 

 

 

lempicka043.jpg

 

 

Edited by crazitaco
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I learned about how dangerous the mines are in Bolivia, and this one particular one named the Devil's Mine. There were these two boys that were forced to work there so that they could get money for what they need to survive and go to school, they worshipped both the Devil and God because in the mines; it was believed that if you didn't make some sort of offering to the Devil, he would kill you with the explosions in the mine. They had to sacrifice llamas so that they would live... It was an intense documentary...

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I learned that 1. My CPU in my laptop @ 1.8GHz running Circuit maker under WINE is at least 16 percent faster at calculating the sim than a 3 GHz Pentium 4 doing the same calculations under windows 7.

 

2. Circuit maker is rubbish.

 

3. Sputnik was rubbish even for its time. All sputnik did was turn a radio transmitter on and off. Explorer had instrumentation on board.

 

Today was mostly labs so nothing new was really taught.

 

And something I've learned from a textbook completely unrelated to school is that comb filtering consists of an audio source and competing reflections that result in peaks and nulls in the audio spectrum. Moving your head even an inch while listening to a loud speaker can have a drastic affect on audio fidelity. I also learned that the speakers you use are more often than not the most damaging device in the playback system.

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