Task of English II

I.Title : Pre Calculus
Sub title : Graphs of a rational function
We can have discontinuity polynomial in denominator.
For example : ,
if , we get undefinition
if we get (0,)
We know that not all rational function will give zero in the denominator. But a rational function can be zero in the denominator.
There are 2 ways of break, they are :
i). Missing point is a loophole . we can see from the factor top and bottom.
For example : we can simplified it become
y=(x+6)
but, if we choose x=4, we can get
ii). X approaches zero inthe denominator.
II.Determining limits by inspection.
There are two rules, e.g. :
X goes to positive or negative infinity
Limits involves a polynomial divided by a polynomial
The tips are :
Looking the power of x in the numerator and the denominator.
The polynomial must be divided by a polynomial
If the power of the numaretor is higher than the denominator, so the limits is positive or negative infinity.
For example :
, the example means that a polynomial over polynomial and x approaches infinity. The highest power of x in numerator is 3, and the highest power of x in denominator is 2.
, the example has same power of the numerator and the denominator, so we can solve the question by divide the coefficient of of the numerator and the denominator. So,
III. Solving problem about graph math
There is a function , if the function h is defined by
Answer :
= 1+2
= 3
Let the function f be defined by , if
Answer : we can analog with a function f when
f(x)=x+1→2f(p)=20
f(p)=10
if x=p, we get f(p)=p+1
10=p+1
9=p
p=9 →x=9
x=3p
x=27
So,
In the xy-coordinate plane, the graph of intersects line at and what is the greatest possible value of slope of line ?
Answer :
Line :
=
0
5
p
t

A POint, Line, and Plane on Space

A Point, Line, and Plane on Space
Analysis and Model
There are three original element in goemetry, they are point, line, and plane. The third element are undefined element.
A point can be imagined look like a position on space. A point hasn’t length and thick. Trace of needle puncture or track of pencil tip can be assumption as a model of a point. A point can be representatived by a dot which given named by a capital letter.
A line can be assumption as a set of point in a infinite long row, and it haven’t width. A line can be representatived by a rope of thread be sprawled.
A plane can be assumption as a set of point in a infinite tightly row and it haven’t width.
C
D
E
B
A
α
F
Picture 1
On picture 1, α-plane contain A, B, C, and D points. We can say that the fourth points located on α-plane. and on α-plane. Based on picture.1 we can say that :
B ∈ α → means B-point on α-plane
C ∈ → means C-point on
∈ α → means on α-plane
= -plane, etc.
The position of point, line, and plane on space
The position of two points
Definition : two coincide points means two same points.
A
B
Picture.2
The position of point and line
Definition : colinear points are points on a line.
C
A
g
h
B
D
Picture.2
Based on picture.3, we can see that A and B are two colinear points, because both of them on h-line. Reciprocally, C and D are two colinear points, because they are on g-line. But A and C are not colinear points because they are not in a line.
The position of point and plane
A point can be located on a plane or not. If A-point on α-plane, we can say that α-plane through A-point or A-point on α-plane.
Axiom : any three points on at least one plane
any three non-colinear points accurately on one plane
Definition : coplanar
Coplanar points if and only if there is a plane which hold them.
P
Q
α
R
S
Picture.3
Based on picture.4, we can see that P, Q, and R are non-colinear points, however they are on one plane, it is α-plane. So, we can say that P, Q, and R re the third coplanar points. While, S-points is not on α-plane. Therefore, P, Q, R, and S are non-coplanar points.
The Position of two lines
Two lines can be assumption on a plane or not. If two lines are on a plane, they may intersect at one point or parallel. If two lines are not on a plane, we can say that they are cross each other.
Definition : ( Parallel and cross-lines)
Two different lines are parallel if and only if they are coplanar and they don’t intersect at a point.
Two different lines are cross each other if and only if they are coplanar.
D
gefinition : if there ar two different lines intersect at a point, so they are precise on a plane.
k
m
h
Q
R
n
P
Picture.4
α
Based on picture.5 : h, k, and m-lines are coplanar because they are on a plane, it is α-plane. h and k are parallel lines and they are on a plane. k and m are intersect at Q-point and they are on a plane. Likewise, h and m intersect at P-point and they are on a plane. n is not on α-plane. g-line pierces α-plane precise at a point, it is R-point. We also can say that g-line is not on α-plane. but m-line is on α-plane. therefore g and m are cross-lines. G-line is not on α-plabe but k is on α-plane. Therefore g and k are cross-lines.
The position of line and plane
I
g
gf there are a line and a plane, there are some possibility, such as the line pierces the plane, the line is parallel with the plane, or the line is on the plane.
h
R
α
α
Picture.5
Picture.6
g
α
Picture.7
Based on picture.5, g-line pierces α-plane. g-line and α-plane are interset each other if they have precise a league point. g-line pierces α-plane precise at a point, it is R-point. so we can say that R is intersection point of g-line and α-plane.
Based on picture.6, g-line is not on α-plane and h-line is on α-plane. g and h are parallel. So we can say that g-line is parallel with α-plane. g-line and α-plane are parallel if they are not coalesce at any point.
Based on picture.7, whole of g-line is on α-plane. means all points of g-line are on α-plane.
The position of two planes
If there are two planes, so there are two possibility, such as they will intersect or they are parallel each other.
β
(α,β)
α
α
β
Picture.8
Picture.9
Picture.8 : α and β are intersect each other if they are coalesce precise at a line. The coalition line is named by intersection line of α and β-planes. So, we can say that (α,β)-line is a set of all points which on α-plane and β-plane.
Picture.9 : α and β are parallel, if they don’t coalesce at any point.
T
she position of three planes
s
P
α
α
γ
β
β
γ
s
Picture.10
Picture.11
α
γ
β
Picture.12
α
β
γ
α
β
γ
Picture.13
Picture.14
Picture.10 : γ-plane intersect s-line precises at a point, it is P-point.
Picture.11 : γ-plane contain all parts of s-line. It means that α, β, and γ-planes are intersect at a line, it is s-line.
Picture.12 : γ-plane is parallel with s-line. s-line is intersection point of α-plane and β-plane, and s-line is parallel with γ-plane, so (α,γ)-line and (β,γ)-plane are parallel with s-line. so, s-line ∥ (α,β)-line ∥ (β,γ)-line.
Picture.13 : γ-plane is intersect α-plane. α∥β, so γ-plane is intersect β-plane. so, (α,γ)-line ∥ (β,γ)-line.
Picture.14 : γ ∥ α, because α ∥ β and γ ∥ α, so γ ∥ β. We can concluse that α-plane ∥ β-plane ∥ γ-plane.
E
G
Hxercises.
E
F
C
D
A
B
Picture.15
Answer these questions based on information of picture.15 !
1). Coplanar lines such as :
a.
b.
c.
d.
answer : c
2). The plane which parallel with BCGF-plane is :
a. ABFE-plane
b. ADHE-plane
c. ABCD-plane
d. EFGH-plane
answer : b
The discussion has been hold in Diyani Arif Setyorini’s rent house at Gejayan Street after we got the lectures, on Thursday, 18 December 20008 about 4 p.m.. I’ve used a literature of first semester, its title is “Suplemen Bahan Kuliah Ilmu Ukur Analitik Ruang“. Bluffy, she took my papers, then read it. She could conceived all parts of the material. Without I explained to her, she could answered two questions correctly. According to me, she has good imagination to ‘make sketches’ of each condition. So, she hasn’t got difficulties.

Intensive Language Via Blog

Intensive Language Via Blog
The outline of the lecture on 23 December 2008 are :
The problems that become our challenges are :
Language purvey different aspects
We have local culture, such as local intelligent like emotional and spiritual matters.
Language can give negative effect, such as misconception of using culture
But, now we also get new challenge, it is about conscience.
There are some levels of communication, namely :
The lowest level of communication are material communication (about noun-matter, such as reaction of chemistry or send letter to someone) and normative communication.
The highest level of communication are formulize communication (such as have a dialogue at a meeting or write our opinion at the blog) and spiritual communication ( such as implementation of our religion, like get praying everyday).
There are more chances for active learner of English to develop their life skill, like leadership, enterpreneur, art, etc.
Communication is one of social phenomena which everybody gets it. One of its influence is psychology.
There are some kinds of unhealthy communication which can destroy the meaning of language, such as active vocal.

Blog

The task : Re-explain what Mr. Dr. Marsigit said at the English lecture II on Monday, 23 December 2008
Based on my literatures that I’ve looked for in the internet (source : http://www.wikipedia.com/), the definition of blog is a blog (a contraction of the term "Web log") is a Web site, usually maintained by an individual with regular entries of commentary, descriptions of events, or other material such as graphics or video. Entries are commonly displayed in reverse-chronological order. We can share many ideas, feeling, and more, even our privacy. Blog can load our ideas via text (verbal), image, video (sound, music). We can update our profile or informations at the blog every minutes we want. Likewise, we could ask many thing to another people at discussion group, such as what is the relationships between applied-english and mathematics (about non exact-knowledges), what is chemistry structure of etanol (about exact-knowledges), how is the florescence of currency (about economic), what is superior seed of soybean which could product best granule and give many profits for the farmer (about agriculture), and another sectors.
Initially, we should know what is the history of English as a second language and as an official language throughout the world, especially in Commonwealth countries and in many international organizations, and English is the third largest language by number of native speakers, after Mandarin Chinese and Spanish. However, when combining native and non-native speakers, English is probably the most commonly spoken language in the world. English is a West Germanic language that originated from the Anglo-Frisian and Lower Saxon dialects brought to Britain by Germanic settlers and Roman auxiliary troops from various parts of what is now northwest Germany and the Northern Netherlands. One of these German tribes were the Angles, who may have come from Angeln, and Bede wrote that their whole nation came to Britain, leaving their former land empty. The names 'England' (or 'Aenglaland') and English are derived from the name of this tribe. (source : http://www.wikipedia.com/). Predigested that through blog, we can share many thoughts about what is the ways to propose the ability of mathematics and english. Even, we suggested to ask foreigner who have english as the major language.
For enhance our knowledge, I would like to explain some conveniences of learning english, such as :
We have more avenues to achieve jobs, because english is a requirement in number of fields, occupations, and professions, though at basic level.
We can get more knowledges accidentally, when we get a route-trip and we see some pamphlet or brochure in english at the streets, we’ll know what their matter.
We can continue further our education abroad indeed english as its lingua franca in the lectures and they’ll serve literatures in English.
We’ll get much of update-international news every minutes, from internet, radio, television, etc.
As a student like me, I could give some suggestions to everyone who wants be active learner of English, such as :
We can translate lot of English literature to each native language, from that we would enhance our vocabulary.
Try to reveal our opinion in each discussions, though with one or less than 3 person in a discussion group.
We often look for some literatures from internet, newspaper, or books that contents some interest topics, so we could read them vehemently.
We can involve in some activites which explore our capability in learning English, like in Safel-UKM (Unit Kegiatan Mahasiswa) of Yogyakarta State University, or another English courses.
We can listen English News at radio or watch English News at television to practice our listening of English.
One of most substantial feature in communication of English is we must wise when we have a talk, with whom we make the dialogue, where and when we hold it. We must distinguish of some kinds dialogues. Precedent, we must be polite when we have a dialogue with our parents, teachers or lecturers; we could have pleasure talk with friends or classmates; and we must be formal when we get an occasion in a meeting, court and plenum.

Blog

A KITE
The definition of a kite is quadrilateral which one of the diagonal coincide with pivot diagonal another.
For example : the description of the picture
A
D B
C picture 1
If ABCD is a kite, then :
AB AD
BC DC
AC and BD is diagonal a kite. Diagonal AC and diagonal BC intersect at O.
<>Example : Look at the picture 1
AC = 10 , AO = 4 , DC = 8
Find DO !
Answer :
AC = AO + OC
10 = 4 + OC
OC = 6
To find OD we use the Pythagoras theorem because < COD is a right angle.
OD2 + OC2 = DC2
OD2 = DC2 – OC2
OD =
=
=
=
= 2
Exercise :
Look at the picture 2 A
AC = 15
AD = 6
DC = 12 D B
Find DO !
C