VIDEOS OF MATHEMATICS

Video 1
“Do You Believe?”
In the first video there is an explanation about trusting someone. In this video, there is a children who orating and give some questions for audience, like : Do you believe in me? Do you believe in me? over and over again. He said that he can be believed and don`t underestimating him. He said that he can do anything and also can be anything. Then all in the room give applause for his oration.
Not only adult people can make a change in this world but also moppet can do that. So we must believe everyone, belong children. The important matter is we also need to believe in ourself.

Video 2
“What You Know about Math”
There are a lot of knowledges in mathematics. In this video there are two people who singing a song about mathematics. In the song, they explain about mathematics and some items in mathematics, like significant figures, graphic, trigonometry, exponent, calculator, phi, ln x, etc.

Video 3
“English Solving Problem“
There are some questions :
1. If the function h(x)=g(2x)+2, what the value of h(1)?
Answer:
h(x)=g(2x)+2
h(1)=g(2x1)+2 g(2x1) = 1
h(1)=3

2. The graph of f(x) = x + 1 if 2f(p) = 20. What the value of f(3p)?
Answer:
2f(p) = 20
f(p) = 10
f(x) = x + 1
We substitution p to f(x) = x + 1, become f(p) = p + 1
f(p) = p + 1 = 10
p = 10 – 1 = 9
f(3p)????
3p = 3(9) = 27
f(x) = x + 1
f(3p) = 3p + 1 = 27 + 1 = 28
So the value of f(3p) equals 28

3. In the xy-coordinate plane, the graph of x equals y square minus four intersects line l at (0, p) and (5, t). What is the greatest possible value of the slope of graph?
x equals y square minus four
Line l: m equals ytwo minus yone all over xtwo minus xone
Equals t minus p all over five minus 0

Video 4
“Properties of Logarithms”
Log x to the base b equals y similar with b to the power of y equals x
Log x to the base ten equals log x
Log x to the base e equals ln x (natural logarithm)
Example :
1. Log one hundred to the base ten equals x
Ten to the power of x equals one hundred
Ten to the power of two equals one hundred
x equals two
2. Log x to the base two equals three
Two to the power of three equals x
eight equals x
So log eight to the base two equals three
3. Log one forty nine to the base seven equals x
Seven to the power of x equals one forty nine
Seven to the power of x equals one seven to the power of two
Seven to the power of x equals seven to the power of negative two
x equals negative two

Log M times N to the base b equals log M to the base b plus log N to the base b
Log M over N to the base b equals log M to the base b minus log N to the base b
Log x to the power of n to the base b equals n log x to the base b
Expand:
Log x square times y plus one in bracket all over z to the power of three to the base three
Equals log x square times y plus one in bracket to the base three minus log z to the power of three to the base three
Equals log x square to the base three plus log y plus one in bracket to the base three minus log z to the power of three to the base three
Equals two times log x to the base three plus log y plus one in bracket to the base three minus three times log z to the base three

Video 5
“Graph of A Rational Function”
Graphs of a rational function
Let the function f be defined by f(x) equals x plus two all over x minus one, if x equals one
We can substitute one to that function
So, f(x) equals one plus two all over one minus one
And we get that denominator equals zero
We know that if the denominator equals zero, so the result can’t be definitioned. Because the denominator of a rational function can’t be zero.
Example:
y equals x square minus x minus six all over x minus three, if x equals three
Answer:
1. Substitute three to that function
y equals three square minus three minus six all over three minus three
Then, we get that denominator equals zero
We know that if the denominator is zero, so the result can’t be definitioned.
2. Factored the function
y equals x square minus x minus six all over x minus three
y equals x minus three in bracket times x plus two in bracket all over x minus three
y equals x plus two
y equals three plus two
y equals five
With use the second way, we can get the answer of the function.

Video 6
“Trigonometry“
Trigonometry’s story is right triangle. Relationship between the sides to the angles. So, let’s make a right triangle. The angles we call theta. The side of line is 3, 4, and 5 in the hypotenuse.
Sin theta equals?
To solve those problem, we must use the trick in order to we can solve : soh cah toa
It means :
soh: sin is opposite over hypotenuse
cah: cos is adjust over hypotenuse
toa: tan is opposite over adjust
So, sin theta equals 4 as opposite over 5 as hypotenuse.
Cos theta equals 3 as adjust over 5 as hypotenuse.
Then let see, one left. Tan theta equals 4 as opposite over 3 as adjust
Then, we named the other angle is x.
So, tan x is also opposite over adjust, tan x equals 3 as opposite over 4 as adjust. It means that tan x is inverse of tan theta.