LAST ASSIGNMENT

CIRCLE

The last meet with Dr. Marsigit as my lecture for English II, He give me task to explain to my friend about topic of mathematic. I choice circle, and my partner is Ambar Puspita who ever called Tata. I do it in my house at Saturday, January 10, 2009.

First I explain the definition of circle. A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are the same distance from a given point called the center. The common distance of the points of a circle from its center is called its radius. A diameter is a line segment whose endpoints lie on the circle and which passes through the centre of the circle. The length of a diameter is twice the length of the radius. The ratio of a circle's circumference to its diameter is π (pi), a constant that takes the same value (approximately 3.1416) for all circles or use pi 22/ 7 for the radius that have factor of 7. Thus the length of the circumference is πd, or 2πr, where d is diameter and r is radius. And the area of circle is πr^2.

The area and circumference of circle earn symbol with

A = πr^2 or A = (πd^2)/ 4

C = πd or C = 2πr

With: A: area or circle r: radius pi: 22/ 7 or 3.14

C: circumference d: diameter (2r)

For the example : A circle with 7 in radius. How is the area of its?

Solution: A= πr^2 we use pi= 22/ 7 because the radius of circle is 7 have factor 1 and 7. So the area = (22/ 7 )*7*7 = (22*49)/ 7= 22*7( the denominator and numerator devided by 7)= 154

We get the solution, so the area of circle is 154.

Until here Tata understand what I explain to her just often she confuse with my pronunciation that not yet fluently. Then I give her an exercise, she did it easily because topic of circle is easy to understand and have learned at elementary school. With this task we learn English together because we explaining each other. She take cube to explained to me, she do it well. We like this task because we can explore our English in math and learn how to be teacher when explain some topic next.

Source:

http://en.wikipedia.org/wiki/Circle

Task of Math Blog

Communication of Math in Blog

Blog is like our diary, our daily book but it can be read by everybody, because blog is one of application in web that can be access by everybody in everywhere. So we must be polite if want to fill blog. We must use standard language and write formally. Blog can be use to communicate people around the world. Blog can be used in our lesson too. To increase our communication with lecture we can use blog. That blog can be used to shown our assignment with follow lecture’s blog. It can watering down lesson in the class, more effective and efficient. We can exploiting blog to increase our level English or mathematic, we can sharing with other blogger. With blog we going to global world, global communication. So we should develop our blog to communication its with mathematic as our lesson. Mathematic is exact knowledge, so basically mathematic lesson is same around the world just the development that different. From that we use blog to increase study mathematic and communicate mathematic with other. We can get advantage from this because more fluently than other if we more develop and study.

Task of Communication

Communication in English

Today English become an International Language. All people in the world use English for communication global, to communicate to other people that live in different country. Communications often interpreted as talk to other people, speak that can be understand each other. Communication global that use English generating some problem in language is called language illness. The differences of culture providing differences of pronunciation that can resulting intersection. So also the differences of individual intelegency. According to Dr.Marsigit in his lesson the problem for individual intelegency there are two levels. Lowest level and highest level. Lowest level are material communication used in informal communication and normative communication that interconnected with feeling, about bad, good, wrong, or true some language listened. Highest level are formularize communication used to talk and write formally like write in blog and spiritual communication about implementation of religion, believe in God, like praying to God.

To develop our communication in English, we should be more active. Like active in the class lesson and our daily activity. Don’t be afraid to do wrong, in exercise do wrong is usual. More important to develop our skill with exercise to speak English in our life.

ENGLISH MATH VIDEO TASK

Name : Noviana Serawati
NIM : 07305144030 Day, date : Monday, Des 01, 2008
Prodi : Math NR 07 Time :
E – mail : english.sera@gmail.com

English task on Tuesday, November 25, 2008
Class E room 204
Video 1
PRE CALCULUS

-- Graph of a rational function
Can have discontinuities has a polynomial in the denominator
Example:
f(x) = (x+3) /(x-1)
Is called Off Limit,when x = 1 subtitued to function f the denominator can be 0.
f(1) = 1+3/1-1
f(1) = 4/0
that’s impossible, the graph will shown break and discontinuity function.Bad choice.
When x = 0,

f(0) = 0+3 /0-1
f(0) = 3 /-1
f(0) = -3
That’s possible, not all rational function will give 0 in denominator and can be 0.

-- Break 2 ways in rational function:
1. Missing point is a loophole
Example:
y = (x^2+2x-3) / x-1
if x = 1 subtitued to function f
y = (1^2+2.1-3) /1-1
= 0/0
That’s not allowed, missing removable singularity when x leads to
The right way to solve that function with factor and simplify.
y = (x^2+2x-3) / x-1
y = (x-1)(x+3) / x-1
y = x + 3
Insert 1 to y = x + 3
y = 1 + 3 = 4 that’s no problem.
2. Zero in denominator
Example :
in function f(x) =(x+3) /(x-1) and insert 1.


Video 2
LIMIT by INSPECTION
1. x goes to positive or negative infinity
2. Limit involved a polynomial devided by a polynomial

Example 1:
Lim (x^3+7) /(x^2-x-6)
x--~
( polynomial over by polynomial with limit x approach infinity )
To solving limit above :
- looking the power of x in the numerator and denominator
- must be dividing f by polynomial if power of x in numerator highest than in denominator, limit can be positive or negative infinity
example above power of x in numerator highest than in denominator.

Example 2:
Lim (x+3) /(x^2-1)
x--~

Its mean power of x in denominator highest than in numerator, that limit will equal to 0.
Example 3 :
Lim (7x^3+x^2+1) / (3x^3+4)
x--~
That’s limit have same of power of x in denominator and in numerator, so the solution of that’s limit is same of the coefficient from the highest power of x in denominator and in numerator it self. The solution can be:
= Lim (7x^3+x^2+1) / (3x^3+4) = 7/3
x--~


Video 3
PROBLEM SOLVING ABOUT GRAPH MATH

-- The graph , if the function is difined by h(x)= g(2x)+ 2.What is the value of h(-1)?
Solution:
The fungtions is h(x)= g(2x)+ 2. If h(-1) is mean when x = -1, we substituted this to the functions
h(x)= g(2x)+ 2
h(-1)= g(2.0)+ 2
= g (-2) + 2
g(-2) is mean g when ,if we look the graph of y=g (x) we get g(-2)= 1 because x= -2 and y= 1
So h(-1)= g(-2)+ 2
= 1 + 2
= 3
We get the value of is 3.

-- Let the function f be defined by f(x)= 2x- 7 . If 4f(p)=24 ,What is the value of f(2p)?
Solution:
The function is f(x)= 2x- 7
The value of f(2p) is mean f when x= 2p ,we have 4f(p)= 24 because each space between have factors 4. So we can over by 4 and we get f(p)= 6
f(p)= 6 its mean f when x= p equal to 6, we can substituted this value to the function f(x)= 2x- 7 we get f(p)= 2p- 7= 6
2p = 13
p = 6,5
So we can get f(2p) If p = 6,5 so 2p = 13 is mean f when x=13 we subtitued this value to the function f(x)= 2x- 7
f(13)= 2.13- 7
= 26 - 7
= 19
We get the value of f(2p) is 19.

v In the xy coordinate x= y^2- 16 intersects line at (0,p) and (7,t) .What is the greatest possible value of the slope of l?
The function x= y^2- 16 intersects line at (0,p) and (7,t) .The formula of slope is m= (y2- y1) / x2- x1 the coordinate of l are (0,p) and (7,t) . thats mean x1= 0, y1= p, x2= 7, y2= t we subtitued thus to the m
m = (y2- y1) / x2- x1
= t- 0 / 7- p
= t / 7- p
We get the greatest possible value of the slope l is t / 7- p


Video 4
INVERS FUNCTION

Notation by : F(x,y) = 0
Function y = f (x) is called VLT and x = g (y) is called HLT

-- Function x = g(y) : invertible
Example:
1. Line function y = 4x – 3 and y = x
y = 4x – 3
x = 4x – 3
3 = 3x
x = 1
Subtuted x = 1 in y = 4x – 3
y =4 - 3 = 1
So, line function y = 4x – 3 and y = x intersect in (1,1)

4x – 3 = y
4x = y + 3
x = 1/4(y + 3)
x = 1/4 y + 3/4 and y = 1/4 x + 3/4

in invers function the line be write:
f(x) = 4x - 3
g(x) = 1/4 x + 3/4
f(g(x)) = 4(1/4 x + 3/4) -3
= x + 3 – 3
= x
g(f(x)) = 1/4(4x – 3) + 3/4
= x - 3/4 + 3/4
= x
From the operation above will get the conclusion :
g = f^-1
f(g(x)) = g(f^-1 (x)) = x
g(x) = f^-1 (f(x)) = x

2. Line function y= (x-2) /(x+3)
y(x+3) = x- 2
yx+ 3y = x- 2
(y-1)x = -2-3y
x= (-2- 3y) / (y- 1)
and
y= (-2- 3x) / (x-1)