Monday, April 2, 2012, I get
chance to look some videos about mathematics. The videos tell us about angle,
degree and radian, multiplying exponent, everyday mathematics multi division
math and quadratic form. In this time, I will try to resume all the video.
First, the video tell us about
Angle. I’m sure all about you know what is angle? Angle is scale rotation a
line segment from one point base to other position. Beside that in the wake two
dimension that uniform, angle can defined as space between two line straight
segment that intersect.
·
positive angle, if an angle is generated by
a-counter clockwise rotation.
·
negative angle, if an angle is generated by a
clockwise rotation.
We can use graph in x , y to
measure the angle. In euclidean geometry, the measures of the interior angles
of a triangle add up to π radians, or 180°, or 1/2 turn; the measures of the
interior angles of a simple quadrilateral add up to 2π radians, or 360°, or 1
turn. In general, the measures of the interior angles of a simple polygon with
n sides add up to [(n − 2) × π] radians, or [(n − 2) × 180]°, or (2n − 4) right
angles, or (n/2 − 1) turn. Angle have some special angle, such us 0˚, 30˚, 45˚,
60˚, 90˚. It is important to memorize special angle.
The second video is about degree
and radian. Degree is one full counterclockwise rotation of terminal side
angle.
1˚ = 1/360 of full revolution
90˚ = ¼ of full revolution, and
it is called right angle
180˚=1/2 of full revolution, and
it is called straight angle
360˚ = full circle
Radians is angle unit field that
a symbol with “rad”. One radian or 1 rad is magnitude angle that formed by two
the radius of the circle of radius 1 meter and form an arc along the well 1
meter. Radian have relation with degree.
360˚ = 1 full revolution
1 full revolution = 2π radians
1˚ =…radian, 1 radian=…˚
360˚ = 2π radian
360˚/2 = 2π/2 radian
180˚= π radian
180˚/180 = π/180 radian
1˚= π/180 radian
1 radian = 180/π radian
The next video tell us about
exponent. Exponent is a repeated multiplication. Exponent can be write x y, but
exponent can also write with sign as follow ^, ex 3^5 that is 35. x
is cardinal number and y is exponent. The example to 35, 3 is cardinal number
and number 5 is exponent. To calculate 35 we must multiply 5 times to number 3.
What is said equation can with this step : 3 rank 5 equal to 243.
Rule I
Some both base and multiply base
anbn = (ab)n
Example : 35x45= (3.4)5=125
Before learn the next rules, it
will be important if we know that
Raise to second power is square,
and raise to third power is cube.
Rule II
Divide instead multiply
an/bn= (a/b)n
example : 63/23 = (6/2)3 = 3x3x3
Rule III
Base number base power
(an)m =an.m
Example: (23)2=82
Rule IV
Differential exponent, same
number base
an+am = a(n+m)
example : 2.3x2.5 = 2(3+5)
Rule V
an/am = a(n-m)
Example : 45/43 = 4(5-3)=42
Then, the next video is Everyday
Mathematics Multi Division Math, it is about some method to multiply and
division.
Standard algorithm for
multiplying
26×31= …
It can be solved by different methods
First method, (20×31) +
(5×31)+(1×31) = 620 + 155 + 31=806
Then, products method
26×31 = 1×6 + 1×20+30×6+30×20=
806
Lathice Method
26×31= …
26×31=806
Standard algorithm for division
By long division 133 : 6 =22 R.1
or 22 1/6
This division can be solved by
different method
First method
133:6=…
6×10=60
6×20=120
6×1=6
6×21=126
6×1=6
6×22=132
6×22+1=133
so, 133:6 = 22 R.1
Division Algorithms Questions
method
133:6= …
6×10=60
6×10=60
6×1=6
6×1=6
(10+10+1+1)=22
So, 133:6 = 22 R.1
The last video is about
Quadratic Equation
(3x-1)(x+2) = 3x2+6x-x-2 =
3x2+5x-2 (it is basic quadratic form)
y=3x2+5x-2
Standard quadratic form :
y=ax2+bx+c
Linear equation
y=mx+b
m is slope and y b is
y-intercept
Rate of change for quadratic
equation is not constant
Slope changing over times
y=100-16x
at x=0 → y=100
at x=1→y=100-16=84
at x=2→ y=100-2.16=68
different point → different
slope.
