REFLECTION OF VIDEOS

VIDEO I
DEAD POET SOCIETY
In this first video, I can see there are so many unique things that appeared from the story. This video told us about a teacher is a class that teaching his student in different way. He wants to make his students having a lot of courage and spirits to face everything in this world.
Firstly, the teacher told about Shakespeare who write something interesting and it make the other people enjoy with it. Sometimes, the teacher also gives some examples about the dialogue in drama. He looks so happy when all of his students in that class interested with what that he said to them.
The teacher also gives some beautiful words to his students. He said that we must always look at thing from the different ways because if we can see for example if we see the problem from different way, exactly we got the solving problem from it. And the second motivation is the teacher want to build the self confidence to his students. He shows that he can get a great spirit when he believes that his self can do it.
The teacher move up to the table in front of the class and the students see him with a lot of curiosity, but at that time the teacher said with the load voice, he said that if we want to get the self confidence, we must has an assumptions that we are the greatest person and we can do everything that we should do. So, after this section, the teacher asks the student to also climb the table one by one. He wants to gives a good motivation to his students to always having the self confidence and always having a good spirits to face every problem.


VIDEO II
THE GREAT SHOW
In the second video, I can see there is a show that shows a child who has a great spirit and he also told a beautiful poem. The poem was said about the spirit, the motivation, the trust, and everything in feels mathematics. We must not only learn mathematics by calculating and remembering the role and formulas, but something deeper from it’s that is we also must know the essentials meaning and the usage the mathematics in our life.
The child makes all of audience in that show was very interested with what that he said. So much applauses and shouts sent to the child. He said his poem by confident and it makes the audiences exactly knows what’s the meaning inside the poem.
The poem can makes the audience get the spirit to love mathematics from the heart. Because of we believe in mathematics so we can be the good mathematicians. So, thank to the child, you can successfully makes the other people believe in their selves that they can do it.


VIDEO III
WHAT’S YOU KOW ABOUT MATH?
In this third video, we can see there are two or may be more than two people singing the rap music and the song tells us about mathematics. In that video, we can see the people who sings that song is the great people who having a big spirit and motivations to find the way how to learn mathematics. Sometimes mathematics makes some people feels confuse and they thing m mathematics is difficult. But, the reality we want or not, we must learn it because mathematics is the most important science in our life.
There are a lot of problems in mathematics because when we want to learn it there’s something too hard to understand the role and formulas. So, in that song, the singers want to help us in study mathematics, and we can learn mathematics by simple way. First, we must having a big spirit to learn it, and the next way is we must try to write some formulas to some papers and put it in the wall of the class or may be our room.
We also sometimes can use the calculator and find there are some unique formulas. And from the song too, we must applied the mathematics to our life if we want to learn it. The trigonometry, logic, integral, exponent, and etc are the material that we must know in mathematics. So make it come true in our life. And finally we can say “I know all about math!”


VIDEO IV
SOLVING THE DIFFERENTIAL EQUATION
In this video, we can learn how to solve the problem in differential equation. For example is:
We want to solve this problem Dy/Dx = 4 x^(2 )
To solve it, we must do, first integrate it (Dy/Dx = 4 x^(2 )) so we can get this formula: ∫▒1 dy= ∫▒〖4x^2 〗 dx
And from this integrating system from whole equation we can get:
y = 4/3 x^(3 )+ C ( y equal four third times x cubic plus c), with C is constant
If we want to know the curve, we must represent it to curve from this equation.

VIDEO V
SOLVING ALGEBRAIC PROBLEMS
We can see the way how to solve some algebraic problems from this video.
For example =
x – 5 = 3 ( x minus five equal 3)
To can solve it, (solve here is we can get the value of x), the steps are:

By adding the right side and left side with 5.
X – 5 +5 = 3+5 (x minus five plus five equal three plus five)
And we can calculate it.
X minus five plus five is equal x + 0 that is x, and in the right side, is three plus five equal eight. So, we can get
X= 8

7 = 4a – 1 ( seven equal four a minus one)
If we want to solve it, that is to get the value of a, we must firstly adding the right and the left side of that problem by 1, we do it to make the right side is only 4a. So, the problem being :
7 + 1= 4a (seven plus one equal four a)
So we can calculate it 8 = 4a
From it, we can see that a is two, it’s come from a = 8/4 =2 (a equal eight fourth equal two)

2/3 x = 8 ( two third x equal eight)
If we want to solve it, first way is we must times the right and the left side by 3/2 (three second) because we want to get the value of x as a variable. So, the pattern is:
3/2 .2/3 x = 3/2 . 8 (three second times two third x equal three second times eight) So, we can get x = 12

The next problem is 5 – 2x = 3x + 1 (five minus two x equal three x plus one)

The first way to can solve it is adding the left and right side by minus 3x, so the pattern will be:
5 – 2x - 3x = 3x + 1 - 3x
(Five minus 2x minus 3x equal five minus 5x, and 3x plus one minus 3x is equal one).
5 – 5x = 1
The second way is by adding the right and left side by minus 5.
– 5x – 5 = 1 – 5 (five minus five equal one minus five)
-5x = - 4 (negative five x equal negative four)
So, the next trick if we want to find the value of x as a variable, we must dividing the whole equation by negative five ( -5 )
(-5)/(-5) x = (-4)/(-5) (negative five over negative five times x equal negative four over negative five)
So, x is 4/5 (four fifth)

3 – 5(2m – 5) = -2 (three minus five times open bracket two m minus five close bracket equal negative two)
To finish that equation, we must first make this equation being
3 – 10m + 25 = -2 (three minus ten m plus twenty five equal negative two)
And the next is calculating and it being:
-10m + 28 = -2 (negative ten m plus twenty eight equal negative two)
If we want to find the value of m, with the same system like the numbers before, we must adding the whole equation by negative 28
-10m + 28 -28 = -2 -28 (negative ten m plus twenty eight minus twenty eight equal negative two minus twenty eight)
-10m = -30 (negative ten m equal negative thirty)
And we can find the value of m is 3, by dividing the whole equation by negative 10.

1/2 x + 1/4 = 1/3 x + 5/4 (a half x plus a quarter equal one third x plus five fourth)
To can find the value of x, we can do:
First is times the whole equation by 12, it because 12 is the GCD of 2, 3, and 4 from that equation. So, the equation being
12 (1/2 x + 1/4) = 12 (1/3 x +5/4) (twelve times open bracket a half x plus a quarter close bracket equal twelve open bracket one third x plus five fourth close bracket)
6x + 3 = 4x + 15 (six x plus three equal four x plus fifteen)
To continue our work is we can move the 4x from the right side to the left side to make it gather with the 6x, and the next, we can calculate it easily. And we also can move the 3 from left side to the right side to make we can easily calculate it to find the value of x. So, the pattern of that equation will be:
6x – 4x = 15 – 3 (six x minus four x equal fifteen minus three)
2x = 12 (two x equal twelve)
And we can see here if x is 12/2 (twelve over two) = 6

T he next algebraic problem is :
0.35x – 0.2 = 0.15x – 0.1 (oh point three five x minus oh point two equal oh point one five x minus oh point one)
To can find the value of x, we can start the way to answer it by times the whole equation by 100 (one hundred) to make it easily to calculate. So the pattern will be:
100 (0.35x – 0.2) = 100 (0.15x – 0.1) (one hundred times open bracket oh point three five x minus oh point two close bracket equal one hundred times open bracket oh point one five minus oh point one close bracket)
35x – 20 = 15x – 10 (thirty five x minus twenty equal fifteen x minus ten)
With the same way from the upper number, we can see that it being:
35x – 15x = -10 + 20 (thirty five x minus fifteen x equal negative ten plus twenty)
and we just calculate it
20x = 10 (twenty x equal ten)
So, we can find the value of x is a half, it from 10/20 (ten over twenty) = 1/2 (a half)
From the examples, we can learn about the basic way to solve the algebraic problem, it is very important because the basic system is very usable in our process to learn mathematics. So, I wish it can give us some knowledge.

VIDEO VI
LAW OF LOGARITHM
In this video, we showed about some proof from the theorems in logarithm, it will be so important to us because we as the student who learn mathematics.
The first thing that explained here was about the basic principle in logarithm. That is about the pattern of logarithm.
If we have a number with the pattern like this, for example x to the b equals a
x^b = a, we can explain it into the logarithm pattern and it being
〖log〗_x a = b (read: log with the base x from a equals b)
The next are about some law of logarithm with the way how to can find it.
〖log〗_x AB= 〖log〗_xA + 〖log〗_xB (log base x A times B equal log base x A plus log base x B)
If we want to know how to can get that law is we must study this proof:
Assumptions:
〖log〗_xA = L (log base x A equal L) means 〖 x〗^L = A (x to the power of L equal A)
〖log〗_xB = M (log base x B equal M) means x^M = B (x to the power of M equal B)
〖log〗_x AB = N (log base x A times B equal N) means x^N = AB (x to the power of N equal A times B)
From these assumptions, we know that:
〖log〗_x AB = N ⇒ x^N = AB (x to the power of N equal A times B)
x^N = 〖 x〗^L. x^M (x to the power of N equal x to the power of L times x to the power of M)
x^N = x^(L+M) (x to the power of N equal x to the power of L plus M)
So, we can conclude that N = L + M (N equal L plus M)
And from it we can see that 〖log〗_x AB = 〖log〗_xA + 〖log〗_xB (log base x A times B equal log base x A plus log base x B) is true.

〖log〗_x A/B = 〖log〗_xA - 〖log〗_xB (log base x A over B equal log base x A minus log base x B)
With the same way like at number 1 above, we can see how to can get that law. So, let’s we start it.
Assumptions:
〖log〗_xA = L (log base x A equal L) means〖 x〗^L = A ( x to the power of L equal A)
〖log〗_xB = M (log base x B equal M) means x^M = B (x to the power of M equal B)
〖log〗_x A/B = N (log base x A over B equal N) means x^N= A/B (x to the power of N equal A over B)
From these assumptions, we can get:
〖log〗_x A/B = N ⇒ x^N= A/B (x to the power of N equal A over B)
x^N = 〖 x〗^L/(〖 x〗^M ) (x to the power of N equal x to the power of L
over x to the power of M)
x^N = x^(L-M) (x to the power of N equal x to the power of L minus M)
So, we can conclude that: N = L – M ( N equal L minus M)
And from it we can see that 〖log〗_x A/B = 〖log〗_xA - 〖log〗_xB (log base x A over B equal log base x A minus log base x B) is true.
That’s all about that I gave from watching the video I until VI, I hope it will be usable to us and I’m so sorry if there are so many mistakes. And I will very happy if some people want to correct my work.