Pythagoras verification theorems

 At this time, I want to recount the experiences I describe a mathematical concept with my friend, and by utilizing the existing literature. Ads on saturday 10th january 2009. 11:10 hours at the residence daughter Riau RW Monginsidi street No.10 Jetis, Yogyakarta with Dian sukrianingrum as patner me. Here is a story. 
On that day I tried to discuss pythagoras theorm with my friends. First, I explain about how the pythagoras theorm found. I use a square image and help the triangle to prove theorems phytagoras. Made up a square ABCD and EFGH. Wide area square EFGH = c2, while the broad square ABCD is: (a + b) (a + b) = a ^ 2 + 2 ab + b ^ 2 
Wide areas of the triangle-triangle EFGH corral the size of the same, namely: 1 / 2 ab. If the triangle is knowledgeable fourth note, it is: 4 * 1 / 2 * ab. So that the broad square EFGH = broad square ABCD-4 * L. Triangle encircle the square EFGH. 
C ^ 2 = (a * ^ 2 +2 ab + b ^ 2) -2 * ab 
C ^ 2 = a ^ 2 + b ^ 2 
In addition, can also prove theorems phytagoras drawing a triangle with the carpenter's square and the square, which was then painted a line parallel to the field. Then cut the square in the carpenter's square on the field square on the hypotenusa. So that the square on the carpenter's square will cover the right side in the field square hypotenusa.
 When I do an experiment to find theorem Pythagoras image through the media, my friends are interested to participate to try it out. So that's me so early in the tense, I finally feel tense shade. In an experiment that I do, can note that the square is the long sides of a triangle is hypotenusa carpenter's square with the broad number of areas square of the length of the sides is carpenter's square is the triangle. The conclusion is known as the next theorems Pythagoras. Pythagoras's theorems can further be defined as follows. "For each triangle carpenter's square, square long hypotenusa apply equal amount of square length of the right side." 
If ABC is triangular carpenter's square with a long hypotenusa, b and c, while the length of the right side then apply a ^ 2 = b ^ 2 + c ^ 2. 
As the concept of the application. I give an application of theorems of Pythagoras up space. 
Finally, I finished the job in explaining. It's very roomy. In making this material from the book I summary mathematical theorems of Pythagoras and of the theorems phytagoras. I explained, there is no difficulty for my friend to understand what I've described. Because that is what I've described this in fact is not strange for my friends.

assigment 3

The Blog for The Development of Mathematics

Currently, the Internet is not foreign to us again. With the Internet, make it easy for us to communicate globally. The impact caused the internet with either positive or negative depending on how we treat it, whether for the purposes of good or ugly. 
On the internet, we can perform various activities. For example, browsing, chat, download, or just add our perspective. As in our efforts to communicate globally, in this case in order to develop the global mathematics, one of which is to take advantage of the blog. Blog is a place of communication via the Internet that can be used by anyone without the need to issue a lot of money and effort . We live access via the Internet anytime and anywhere. 
In the process of learning mathematics at this time have used blogs as a medium for online learning. So that they can make good lecture for students and lecturers. If the lecturers are not present in the lecture , the blog can be used as a means of informal lectures. We can also learn about how to manage your blog properly, so the blog is worth reading. In addition to using the blog as a medium of learning, can also take advantage of the video that mathematics can be downloaded for free via the Internet. So that we can learn English as well as mathematics through the video. Live how we manage and develop the existing facilities is to improve the learning of mathematics in the lectures.

Assignments 2

Kinds of levels communication

When the English language offers a cultural aspect as we have the local intelligences that are social acumen, emotional intelligences, and spiritual intelligences. If we are faced with 2 different things, then we must choose which of benefit to us. 
Communication is important. In daily life, anywhere, anytime, with anyone and we always communicate. For example, in the school activities of communication is very important. Communication between teachers with the students, students with students, teachers with teachers. 
There are 4 kinds of levels of communication, among others:
1. materials communication . This communication is the most basic communication-communication    among the others. For example, when we cook be towards our communication devices Cooks. 
2. formal communication . This is how we communicate formally. For example, if we write a scientific paper, write an article. 
3.normative communication. This communication is used when we want to think about things. 
4.spiritual communication. This communication is the most high, the communication between human beings with the gods.
where the position of the English? 
English can be used for spiritual communication, formal, normative, or material. The English language can also be used to communicate in daily life. To be able to speak English effectively, we must become active. Because if not, then we will have trouble. 
Conclusion, if we want to speak English effectively, then we must be active, not passive.

Assignments 1

Video 1
Pre-calculus: Graph of A Rational Function

       We start by graph of rational function. which can have discontinuities. Why? Because has a polynomial in denominator.
Example:
If f(x) = (x + 2)/(x-2)
When x =1, the function becomes
f(1)=3/0
With zero is denominator, for this function choice x=1 is bad idea. This resulted in the break in function graph. For example,
f(x)= (x + 2)/(x-2)
When insert 0 for x. so,
f(0)=0+2/0-1
f(0)=-2
So, point in the graph is (0,-2). Next we try, insert 1 for x. so,
f(1)=3/0. 0 is denominator.
That is you know, is impossible. So, x value that may be entered when x is equal to zero function.
Pictures on the graph if the function f(x) = (x+2)/(x-1), with x=1 then the graph will not be through the line x=1. So, the rational function don't always work this way. Check the graph. f(x)=1/(x^2+1). When insert -1 for x so,
f(-1)=1/((-1)^2+1)
f(-1)= ½. But the graph is not broken. So, not all rational function give zero in denominator.
        Polynomials for graph smooth unbroken curve. There is no value for the function, will lead to break in the function. for example,
y= (x^2-x-6)/(x-3). when insert 3 for x, so y =0/0. That not possible, not feasible and not allowed. Another way is, with factor top and bottom the rational function and simplify. The above examples are, y= (x^2-x-6)/(x-3). With factor polynomial,
y=((x-3)(x+2))/(x-3). Will become more simple so that, y = x +2. When insert 3 for x, is not bad.

Video 2
Limit By Inspection
 
        Determining limit by inspection, there are two conditions. First, x goes to positive or negative infinity. Second, limit involves a polynomial divided by a polynomial. For example,
Limit (x^3+4)/(x^2+x+1) as x approaches infinity.
This problem are two conditions where: first, polynomial over polynomial and second, x approaches infinity. The key to determining limits by inspection is in looking at power of x in the numerator and the denominator. Remember, to apply these rules, must be dividing by polynomials and x has to be approaching infinity. Another first shortcut rule if the highest power of x is greater in numerator, and limit is positive or negative infinity. Last looking the example,
Limit (x^3+4)/(x^2+x+1) as x approaches infinity.
Highest power of x in numerator 3 and greater highest power of x in denominator 2. The limit can be positive or negative infinity since all the numbers are positive and x is going to positive infinity, the limit is positive infinity. If you can’ tell if the answer is positive or negative infinity you can substitution a large number for x and see if you end up with a positive or negative number, whatever sign you get is the sign of infinity for the limit.
Now, the second shortcut rule.
If the highest power of x is in the denominator and the limits is zero.
Example,
Limit (x^2+3)/(x^3+1) as x approaches infinity.
Hence, highest power of x in numerator 2 last highest power of x in denominator 3. Then value the limit equal to zero.
Now, last shortcut rule.
This rule use when highest power of x in numerator is same as highest power of x in denominator. Limit is x positive and negative infinity is just the quotient of the coefficients of the two highest powers. For example,
Limit (4x^3+x^2+1)/(x^3+4) as x approaches infinity.
Then, as highest power in both nominator and denominator is 3. According in this rule then means limit is just the coefficients of x cubic’s over each other. The coefficient x^3 in nominator is 4 and coefficient x^3 in denominator is 3. So, limit =4/3.


Video 3
Solusing Problem Graph Math 1

         First problems, the figure above shows the graph of y=g(x). if the function h is defined by h(x)=g(2x)+2. What is the value of h(1)?
Solution:
h(x)=g(2x)+2, when subtitud h(1) for this function then
h(1)=g(2x)+2. we can see the graph, for g(2) then g(2)=1. hence,
h(1)=1+2
h(1)=3
          Second problems, let function f be defined by f(x)= x+1. If two f(p) =20, what is the value of f (3p)?
Solution:
When f(3p), what is f when x=3p
When f(x)=x+1 and 
2f(p) =20. so,
f(p) =10. when f(x) insert p, then
f(p) =p+1=10
p =9
When x =3p, then insert p=9
x =3*9
x =27
So, x =27. later then, insert x =27 for the function.
f(27) =27+1
F(27)=28
           Last problems, in the xy-coordinate plane, the graph x =y^2-4. Intersect line l at (0,p) and (5,t). what is the greathest possible value the slope of l ?
Solution:
Search greatest m, where x =y^2-4 and intersect line l.
x one is 0 and x two is 5. Then y one is p and y two is t.
Then, slope in the graph is line l=m=(y two – y one)/( x two - x one).
So, slope m =(t–p)/5.


Video 4
Invers Function

      An inverse function uniquely identifies the input x of another function based only on its output y, for all y is a member of Y. A function is invertible if and only if this rule defines a function. Not all functions have an inverse. For this rule to be applicable, each element y is a member of Y must correspond to exactly one element x is a member of  X.
f(x,y)=0 and function y =f(x).
No 1. one function x =g(x) at y =y(x), v intersect t and x =g(y), h intersect t.
For example, line y =2x-1 and line y =x have the point. So, to find the point we are the substitution y =x at function y =2x-1. so established,
x=2x-1
1+x=2
x=1, then
2x-1=y
2x=y+1
x=1/2(y+1)
x=1/2y+1/2
x=1/2y+1/2 we can change to y =1/2x+1/2.
The function f(x) =2 x and g(x) =1/2 x +1/2. So, 
f(g(x)) =2 sometimes -1. Sometime is 1/2x-1/2. So,
f(g(x)) = x. 
g(f(x)) =1/2 sometime +1/2. Sometime is x -1. So,
g(f(x)) = x. 
So, is the conclusion g =f invers.
f(g(x)) =(f invers(x))=x and g(f(x) =f invers(f(x)) =x.
Line y = (x -1)/(x +1), the graphics will not be the same with the 2x and x is the same as the one, but one line will go through point (1, 0) and (0, 1/2). So,
y(x+2) =x-1
xy+2y =x-1
xy-x =-1-2y
(y-1)x =-1-2y
x =-1-2y/y-1
We can be change to y =-1-2x/x-1.
When x =0, y =-1. When y =0, x =-1/2. And when x =1, y =-2.