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Minggu, 17 Maret 2013

Mathematics


      Reflection Of Video

     What You Know About Math (Knowing Math)
What you know about math
what you know about math
what you know about math
hey, don’t you know i represent math league when i add shorty subtract
freshman backpack where i holdin’ all my work at
what you know about math
what you know about math
what you know about math
i know all about math
answer’s 44 it’s real easy cus it’s sig figs
you got 45 your answers high you rounded too big
what you know about math
what you know about math
what you know about math
i know all about math
ti-80 silver edition know i’m shinin’ dog
extra memory on the back to do my natural log
you know we multiply while memorizing pi
take limits to the sky be sure to simplify
graphing utility it’s trigonomety 100 our math b
don’t you cheat off me
distance is rate times time
the sign graph ain’t no line
exponential decline
but your score can’t beat mine
we’re memorizing rate for our math league states
against the math league greats
not gettin many dates
i got to find a mate but girls just playa hate and always make me wait
can’t even integrate
don’t you know i represent math league when i add shorty subtract
freshman backpack where i holdin’ all my work at
what you know about math
what you know about math
what you know about math
i know all about math
That song tell about the contents of mathematics, there are limit, trigonometry, phi, etc. The song is told that the answer to the question is 44, because 44 is an easy and significant figures . And if you  answer 45 , it’s your answers high you rounded too big.  Also talked about memorizing log ln (x) and given that pi is 3. 1415. 92,653,589,732. This song also talks about the limit of lim (x) approaches infinity, which is the same as simplifying.  the way to count distance is rate times time. The sign graph ain’t no line, exponential decline.  tell also when following math league, their score is higher, because they are memorizing rate for our math league states.

VIDEO 2
English Golden X Section C

In algebra, we will meet with an equation, for example is ax=b. A an b are constant and x is a variable. If we given 4x= 12, we can know that 4 is a and 12 is b.  We have to find a solution for x. A solution is a value that when subtititued in place of a variable, makes an equation true. The solution set is the set of all solution. Let us find the solution of 4x = 12. First, we divide both sides by 4, so we find that
4x/4 = 12/4
The number 4 on the left are cancelled out and left x= 12/4. Twelve divided by four equals three, so we find that x=3. the solution of this equation is three.
The other example is 7x = 63. We can find a solution in the same way. First, we divide both sides by 7, so we find that
7x/7=63/7.
The number 7 on the left are cancelled out and left x= 63/7. Sixty-three divided by seven is nine. So the solution of x is 9.
            The more complex equations in algebra is
ax+b=c
A, b, and c is constant and x is variable. For example is 5x+3 = 18. Number three is a substract, so we must reduce each segment with three. We find that five x plus three minus three equals eighteen minus three. So five x equals fifteen.  Then ,both sides divided by five, finally we get x = 3. The solution of this equation is 3
5x +3-3=18-3
5x= 15
x= 15/5
x=3

VIDEO 3
FUNCTION
Function is an algebratic statment that provides a link between two or more variables.  For example
1.  y= 2x
If you know y, you will know the solution of x variable. From the equations above, if we pick x=2 we will find that y is 10.
2. y= 3x + 4
Variable y must be itself. so y^2, 1/y, and √y are not allowed in this equation. A function is a codependent relationship between x's. Function is a relation in wich each element of one set paired with one. Relation is a numerial expression.  Relation is divided in two part, equations and inequalities.  The example of equation is 1+3=4. The example of inequalities is 8>5. Number is also divided into two, spesific numbers and nonspesific numbers. Non spesific numbers is variable, foe examples are  x and y.
The variable relations is express contain variables.  In equation y= 3x+4, if we subtitute x = 1, we will find that y is 7.
Function of x
The function of x is symbolized by f(x)=y  . For example:
y= 3x+4   ,  (3x +4) is y. so we can write it as
y= f(x) = 3x+4                (y is equal s f(x) equals three x plus four)
the writing in the standard form is f(x) = 3x+4. If a function is not written in standard form, then we have to change it in the standard form.
The symbols a function of x is not only written as f (x), but can also be written with other symbols such as g (x) and h (x) . For example:
f(x)= 2x+1                             (f( x) equals two x plus one)
g(x)= x^2-3x+2                     (g(x) equals x squared minus 3 x plus two)
h(x)= 2                                  (h(x) equals two)
The variable x of all equations is same. if we pick x equals five we will find that:
f(x)= 2(5)+1= 11                              (f(x) equals two multiplied by five plus one equals eleven)
g(x)= (5)^2-3(5)+2=  12                 (h(x) equals Five squared minus three multiplied by five   plus two equals tweleve)
h(x)= 2                                            (h(x)= 2, because it isn’t have variable)
      
VIDEO 4
Degree
The ilustration of degree is when we look at the clockwise turn around from the initial position (terminal), and return to the starting position. Measures (360 ̊), three hundred sixty degrees.  It’s make a circle and 360 ̊ is full circle. So one degree is equal to 1/360 ̊ of full revolution and eleven degree is 11/ 360 ̊ of full revolution.



                          90 ̊
Ninety degree is a quarter of full revolution. We can call it right angle. And one hundred eighty degree is called stright angle.
To measure angles we use  degrees and the radian. The radian uses radius of circle to figure out measurement of an angle. It’s important learn to convert radian to degrees and degrees to radian. one full revolution is equal to 2∏ radian.
            We gave the equation
            360= 2  radian                (divide both sides by 2)
            360 ̊/2 = 2  radian/ 2     , we find that
            180̊ =  radian                 (divide both sides by 180 ̊)
            180 ̊/ 180 ̊=  radian/ 180 ̊ ,    The number of 180 ̊ on the left are cancelled out and left      1/ 180 ̊ =  radian
This is an example the convert from degree to radian:
            Convert 120 ̊to radian
            give number in degres, 1/ 180 ̊            =  radian
            the next step is
            1 ̊ =  radian/ 180 ̊     (multiply both sides by 120)
120x 1 ̊ =120 x  radian/ 180 ̊           
120 ̊= 2  radian/3
The answer is 120 ̊= 2  radian/3
                
Convert from radian to degree:
convert 11  radians/12 into degrees
lets follow this steps:
given number of radians
1 radians = 180 ̊/                      (multiply both sides by 11 /12)
Remember:  can’t do something to one side without doing something on the other side
11 /12 x 1 radians = 180 ̊/  x 11 /12  (simplify)
11 /12 radians = 180 ̊/ 1 x 11/ 12   finally we find that
11 /12 radians = 165 ̊
Theanswer is 165 ̊.     

VIDEO 5
INTEGER

Integer is whole numbers and their negatives. Whole numbers are not fractions or decimals. one are whole number. Five, one hundred thirty four, and two milions are also whole numbers. Whole numbers can’t be negatives. Integers can be positive, negative, or zero.
The examples of whole numbers are 0, 1, 2, 4. and it’s can’t be decimals or fractions. The examples of negative whole numbers are -1, -2, -5 and it’s also can’t be decimals or fractions.
            We can see the integer in a number line. Number line is a vertical and horizontal line. It’s marked of even intervals or units. It’s similar to thermometer that have units of numbers. When moving to the right and up the line, the number became greater. And when moving to the left and down from  the line,  the number  became smaller. So that, the numbers above of zero or to the right of zero is positive. And the numbers bellow  or to the left of zero is negative. Negative number is the number that have minus sign in front, for exampe is  (-5).
            integers are arranged in digits. Digits are divided into 0-9. Every number is in certain digits. This is an example of naming digits:
45, 678, 324, if it is identified from the rear, we know that four is “units place”, two is in “tens place”, three is in “hundred place”, eight is in “thousands”, seven is in “tenthousand” of digits, six is in “hundred thousand “, five is in “Milions” of digits, and than four is “ten milions” of digits.

VIDEO VI
Trigonometry function
Trigonometry function is the relations of different sides of a triangle with respect to an angle. With trig. function, you only need to know the values of the sides, to find measure of an angle. There are six trig. function, the sine, cosine, tangent, cosecant, secant, and cotangent. The six basic of trig. function are define by sides of triangle and angle being measured.
SIN Ө = OPP/ HYP                      CSC Ө= HYP/OPP
COS Ө= ADJ/HYP                         SEC Ө= HYP/ADJ
TAN Ө= OPP/ADJ                        COT Ө= ADJ/OPP
Look at this:
HYP
ADJ
OPP
 







To help us remember the formula, we can abbreviate it as “SOH CAH TOA”.
In the first word we find that:
 S= sine
 O= opposite
H= hypotenuse
In the second word we find that:
C= Cosine
A= Adjecent
H= Hypotenuse
In the third word we find that:
T= Tangent
O= opposite
A= A djecent




VIDEO V11
Geometry_Quadrilaterals and Their Secret Informat

Quadrilateral is 4 sided polygon. Which includes quadrilateral is rectangle, parallelogram, square, rhombus, and trapezoid.



                      
           

Rectangle is a quadrilateral with four right angles. Because it have four right angles, it’s opposite sides are parellel. The adjacent sides are perpendicular to one and other. If the width of the two-sided rectangular are tilted, we will get the form of a parallelogram.
 



Parallelogram is a quadrilateral that has opposite sides parallel. It also have two congruent pairs of supplementary angles.




Square is a rectangle that all four sides are congruent. So the square have 4 right angles, parallel sides, and congruent sides.
C
B
D
A
Square is a form of rhombus. A rhombus is quadrilateral with four congruent and parallel sides. like one cactus two cacti, we might call one rhombus two rhombai. 



Trapezoid is a quadrilateral with only one pair of parallel sides. In this trapezoid, segment AB and CD is parallel.
The conclusion is:
Parallelogram’s have the opposite sides that parallel, so rectangle, square, rhombus, and trapezoid are parallelogram, but the parallelogram is not the rectangle, square, rhombus, and trapezoid.
If we talk about parallelogram, we will discuss about parallel line and triangle theorems used with other shapes.
Theorem:
The opposite sides of a parallelogram are congruent.
C
D
B
A
given ABCD  is parallelogram. Prove: AB̅ || CD


                                                        

No
Statement
Reason
1
ABCD is parallelogram
1.      we given it from the information.
2
Draw diagonal BD̅
2.      Two point/ One line. Now we have 2 triangle ABD dan DCB
3
We show that AB̅‖CD̅ ; AD̅‖CB̅
3.      It’s the definition of parellelogram
4
 <1=<2 ; <3=<4
4  alt. interior angle theorem
5
BD̅ congruent BD̅
5 reflexive prop.
6
Angle- side – angle postulate
6       ABD Congruent     CDB
7
AB̅=CD̅ ; DA̅=BD̅
7  CPCTC


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