The research of mathematics

The simplest mathematics for solving the organic Junk

Marsigit’s opinion is
A. ABSTRACT
My mathematical Research is about differential equation for predicting and calculating the time to use organic junk especially for solving the flood in Indonesia
B. Introduction
Now many people in the world like everything instantly, the simple example is people will choose to send a message for someone on the other hand both of them is not far. Or maybe by eating noodle like POPMIE etc. And of course it is caused by so many modern technology that person didn’t care about the effect and the impact. We as human just follow the update technology without any thinking deeply. Right?
Let us see that now rainfall decrease, temperature will increase, and rainfall decrease. And we are confused in the condition until air condition cannot make us cool. This is the global warming. As we know that Indonesia, our country got so many disasters from natural cause and human causes. From natural causes for example earthquake, plate electronic, volcanoes, ocean current etc. Then what about human causes? The closest example is flood.
Until now, flood becomes the problem in Indonesia from year to year. And Flood that happened in Indonesia actually caused by us as a human. We cannot keep our country well, we just can make our country dirty and we always ignore about the ways from the government.
Because of it, now I will talk about the organic junk as the solution to reduce flood in our country.Let’s go to see our country that has three areas, that is continental area, air area and archipelago. I don’t know why, Is that because our God angry with us? Or our earth has begun older.
Now, there are so many disasters in our earth, from the wind, earthquake, and the flood. Disaster is when people live in hazardous places like, when a hazardous phenomenon occurs, be it natural or human made, and then when the phenomenon causes a lot of damage, especially where no preventive measure have been taken.
Rubbish have made flood comes indirectly. So, we must do some action to prevent flood in our country starting keep our environment from rubbish. If we ignore the rubbish continually, it will be dangerous for our country especially our life. We can imagine, if flood always comes and there are so many rubbish, it will be not comfortable. There will be so many diseases that happened, so scary right? The government also has the planning to reduce the rubbish because the rubbish will influence our life from our health, our earth until our finance.
And we as the citizen sometimes didn’t care about it; we just claim that the source of the problem of flood is the government. Some of the society assumes that the government just stays in the chair without any action to prevent the flood. Actually the consciousness from the society to participate preventing the flood is very important.
There are so many kind of the way to prevent flood in Indonesia. Generally, we plan some trees to prevent the flood; it is for preventing the water from the rain doesn’t enter to the river directly but defended in the root of the trees. Exactly, it uses for reservoir. Besides that, we can explore some of the dust. Taking the dust in the dust room not in the river or in the way can also reduce the damage of the flood. If the rubbish takes in anywhere, the rubbish can cover the drain of the water and the effect is flood.
One of the ways is keep our country from the organic junk? Why? Actually there is a lot of kind rubbish in our country but the organic junk will help more to help us prevent flood. What is organic junk? Organic junk is rubbish come from any down leaves or any grass that not disturb our environment. We can use them for making compos fertilizer.
Prevention flood with making absorb exploration is the others way for the administration of a town area. DKI Jakarta has applied the responsibility for the citizen to make absorb exploration by Decision Letter Governor No 17 1992. And now we can call it district regulation no 17/1996, the content is the responsibility to make absorb exploration. But everybody didn’t response the statement because of the expensive cost for making absorb exploration. And the result is the flood come year to year.
The government hopes the building of the flood canal in East Jakarta and West Jakarta can reduce the flood in the future. But the building of the flood canal cannot guarantee the flood cannot come. Without any participation from the society widely, the flood will come exactly.Rain is the one of the result of the rubbish. And the other is pollution, and the quality of our life reduces. Why I can say that? Sometimes our society takes the rubbish and they burn the rubbish. Will be the pollution right?
The exactly solution for solving this problem is making the Biopori hole. The form of the hole is a cylinder that made in the land approximately 10 centimeter until 100 centimeter. And the hole is made from the activity by the animal in the land, when they are looking for the food. ( Gamadepok News)
There is the new innovation to prevent the flood. That is the hole of biopori absorption. What is biopori? The hole of biopori absorption is the method of the water absorption to face flood with improving the ability of the land to absorb water. This methods is presented by Dr.Kamir R Brata, he is one of the research from IPB. The procedure to make the hole of biopori absorption is making the hole with diameter 10 centimeter and the depth 80 centimeter firstly. The next step is entering the rubbish into the hole.










The function of the innovation is:
1. Improving the ability of the water absorption
The hole of biopori absorption is also made in the surface of the land and the land is covered by semen. Basically, buildings have an absorption area about 20 – 40 % square but caused the narrow area it will be impossible to make this innovation. The biopori’s hole can solve this problem, by making the biopori hole so maybe we can say that 41 times the area of the absorption without any construction biopori hole.
2. Changing the rubbish into the compos fertilizer
If we enter the organic rubbish in the biopori hole, it will be very useful for the root of plant and the animal in the land like worm. As we know that there are two kind of rubbish. There are organic rubbish and inorganic rubbish. And the percentage of organic rubbish is about 80 %. So the consistency biopori hole can reduce the problem that caused by organic rubbish. And finally organic rubbish will produce compos fertilizer could taken in the next period. Maybe it will be very useful for the person who lke planting some of plant, for example flower.
We can make the biopori hole in our house, the biopori hole can made in above rain canal near our home, office or school etc. ( Organisasi.org.2008)
Using amount the rubbish as the sample that enter in the hole and the next the rubbish will explored in the land, the rate of the rubbish that enter and exit is quite enough, and also the hole have the arbitrary volume can arranged a mathematical model. Before we arrange the mathematical model, e need the knowledge about the mathematical model. Model is a description a object that arranged with a destination. (R.Rent Nagle: 1994)
Actually an action is not always describe and present in mathematical formula but the other way we can present as a copied in physically. (B. Susanta: 1989)
Generally the model is arranged for predicting an object and also imitating the behavior of the object that observed. (Djoko Luknanto: 2003)
This model is arranged to observing hole and determining the connection between the most frequently of the rubbish, the decomposer, the rate and the volume in the time for explore the organic junk. After the function of the most frequently rubbish can be predicted so we can know the function of the tare and also the function of the time for exploring the rubbish. This is used for doing the observation without object and doing the prediction the next time. And we must arrange the entire variable for explain the mathematical model clearly.
This model is the same with the model on the increasing the population. Like the model about the population of protozoa. If the model f the protozoa’s population, we assume that the amount of the food and the other element for supporting their life, their life normally, and there is not the victim. For arranging the model, we need an assumption. This model is called Malthus model. (Polking: 2006)
Like explain before, the model of the protozoa’s population, we need any assumption so the rate of the population proportionally. This is resulted enough; cause if the assumption is given so will be difficult for finishing. (James Stewart: 2006)
For finishing the solution so we need the simplest solution easily, we must do something:
1. Assume that all the enter thing in the hole, I means organic junk must be the same. ( all the thing is the organic junk ) and all the thing need the same time for doing the exploration.
2. All of the decomposer is the same index so just one notation for the decomposer, although there is a lot of kind of the decomposer.
3. Making the link between the variables simple. It means that we must assume the rate of the rubbish and the decomposer is ,;’’’’’’’’’’’’’’’’’’’’’’

After the assumption is quite enough we can make the formula for this problem in the mathematical model. This is the variable :
: The frequently of the rubbish
: the frequently of the decomposer
: the rate enter and leave the system
: the volume of the biopori hole

We can apply this formula with differential equation. For example x is the notation of R in the function of t and the derivative as the rate of x in the time. .
This is the same with the simple mathematical model for boning and the ending life of the citizen, we must add more assumption. That is not the immigration or emigration in the population. If we convert the mathematical model in the biopori model in mathematics we must assume that there is not the rubbish is proportionally. (Edwards: 2005)
For example is the rate of that enter the system. And is the rate of that leave the system. So e can rite the equation in the model that enters and leave. Look at the picture.

This is the mathematical model
(1)
(Shepley L.Ross; 1984)
From the equation we can substitute R as the function of x because both of them as the symbolic amount the rubbish as the function of t. And we can find the rat of the rubbish ( )
(2)
The rate of the entering rubbish is the notation of ( ) and the notation of OUT is as the outing the rubbish. hkvhkivhkjvkljvl
(3)
This is the model of The rate when the outing the rubbish
(4)
Substitute the equation of (3) and (4) to the equation of (2) we can get
(5)
After the entire variable substitute in the equation and we are ready with the mathematical model so we must use the connection with mathematics. It means that we choose differential equation as the mathematical model for solving and getting the best solution. One of the applications of the differential equation is the arrangement of the rate equation. (Golberg: 1998)
The Equation of (5) is the first linier differential equation and e can finish our problem to the differential equation, that is:
(6)
(William E. Boyce: 1997)
Because of and is the name of the function. And also is the variable so we can change in to differential equation with decreasing both of the with ) so
(7)
The simplest calculation, we can change to we can obtain
(8)
The equation of (5) is not exact equation so that will be difficult for getting the solution. If we want to finish and solve the equation we must change the form of the equation will be an exact equation. And we need the factoring of integration for getting the solution easily. And the exact equation is the supplication between the factoring of the integration and the unusual of the equation. And for getting the factoring of the integration we can use the formula of the first differential equation. Look at the formula
(9)
We must choose the factoring of integration is not zero
(10)
(Rusmanto Rahardi: 2003)
The other world
(11)
We can get
(12)
(Blanchard:1998)
And the factoring integration of is
(13)

We can substitute the equation of (9) to the equation of (13), so we can get
(14)
Finishing the equation of (14) we can get
(15)
Multiplying the equation of (8) with the equation of (15) we can get
(16)
By the general method of the first differential equation we can change the equation of (16) will be
(17)
By integration the equation of (18) we can get
(18)
Dividing again the equation of (18) with the factoring of integration (15) we can get
(19)
The equation of (19) is the solution or hard solution of the problem. For getting the Constanta we substitute when = 0, so we can get the equation
(20)
Finishing the equation of (20), we can get
(21)
After knowing the value of the Constanta we can find the value details from the solution that is by substituting the Constanta in the hard solution and we can obtain
(22)
The next procedure we can find the function of t if we assume that there is not decomposer we can looking for the function of t so the result is
(23)
The next again we can find the function of t with divided the equation of (23) with we will get
(24)
For finding the value of t we can change will be the coefficient with the logarithm theorem natural (Dale Verberg:2001)
(25)
We can get
(26)
Dividing the equation of (26) with , we can get
(27)
We can observe the mathematical model with some of data so we can conclude that the amount of the decomposer didn’t more that the amount of the rubbish. Because if the amount of the decomposer more that the amount of the rubbish the calculation of the time will be negative. In fact as e know that the times is positive.
There is not the false model but there is the model less than relevancy from the problem. There is not perfect model; it is just approach the solution. The perfect solution and the perfect model just come from Our God. Thanks.
C. Conclusion
We can convert the problem in our country with differential equation but the next action is depending on ourselves. Because keeping our environment is one of our duties.
D. REFERENCE
Blanchard, Paul, Robert L. Pevaney dan Glen R. Hall. Differential Equation, Brooks/Cole Publishing Company, New York: 1998
Boyce, William E. dan Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc: 1997
Bronson, Richard. Schaum Outlines of Differential Equation, Mc Grawhill, New York: 1993
Edwards, C. Hendry dan David E.Penney. Differential Equation & Linear Algebra. Pearson, Georgia: 2005
Golberg, Jack dan Mark C. Potter. Differential Equations: A System Aproached. Prentire Hall. Sidney: 1998
Hofmann, Laurenced dan Gerald L. Bradley. Calculus for Bussines, economics and the Social and Life Sciences. Mc Garw Hill, Boston:2000
Polking John, albert Bogges, dan David Arnold. Differential Equation. Pearson. New Jersey: 2006
Rahardi, Rustanto, Herman Hudodo dan Imam Supeno. JICA: Common Textbook Persamaan Differensial Biasa. JICA, Malang: 2003
Ross, Shepley L, Differential Equations, John Wiley & Sons, Inc: 1984
Stewart, James. Calculus, Concepts & Context 3: Metric Function.Thomson, Belmont (USA):2006
Susanta, B. dan Bambang Soejiono, Materi Pokok Model Matematik, Karunika, Jakarta:1989
Verberg, Dale dan Edwin J.Purcell. Kalkulus Differensial, Interaksara:2001
Nagle, R.Rent dan Edwarb B. Saff, Fundamentals of Differential Equations and Boundary Value Problems, Addison-Wesley Publish: 1994
Lubang Resapan Biopori.http://gamadepok news.com. pada tanggal 29 Oktober 2009
Luknanto, Djoko. 2003. Model Matematika, Bahan Kuliah Hidraulika Komputasi. http://luk.staff.ugm.ac.id/hidkom/pdf/ModelMatematik.pdf pada tanggal 2 November 2009
Organisasi. 2008. Pengertian Biopori & Cara Membuat Lubang Resapan Biopori Air (LRB) Pada Lingkungan Sekitar Kita. http://organisasi.org/pengertian-biopori-cara-membuat-lubang-resapan-biopori-air-lrb-pada-lingkungan-sekitar-kita pada tanggal 1 Desember 2009
Wikipedia. Biopori. http://id.wikipedia.org/wiki/Biopori. pada tanggal 1 November 2009

1. There is four ball in the flat plane and for all the ball must be connected or touch each other. If the radius of the ball have the same value, 2 cm. Determine the high of the pile ball!
Answer:
Given from the question four balls must be connected so we can graph like the picture above:





So for finding the high of the pile ball we can describe that the triangle that we can look actually is a pyramid if in the plane room. This is the description:
The distance between center points also has the same value, 2 cm + 2 cm + 4 cm.
So the pyramid has the same distance for every side is 4 cm. For example, between A and B there is E. So for finding the high of the pyramid we can calculate ABE triangle. But we must know the length of BE side before. Look at the procedure above;

(BC)2 = (BE)2 + (EC)2
(4 )2 = (BE)2 + (2)2
(BE)2 = 16 – 4
(BE)2 =12
BE =2 √3
So we can see that BCD triangle is an equilateral triangle. If AO side is the altitude for ABE triangle therefore O is bisector of BE side. So, the length of OB side and OE are the same too that is OB + OE = BE then OB = OE = √3.
Look the ABE triangle above, where O point is between A and E point.


A


B O E
AB2 = AO2 + OB2
16 = AO2 + (√3)2
AO2 =16 – 3
AO = √13
Now, we can know the high of the pile ball (4 + √13) cm

2. The experiment holds on USAID, University in Australia. Research says that 70 % people believe that drug is not useful. According to the research, how much the probability at least three from five people who taken randomly say that drug is not useful.
Answer:
Using binomial leaflet the theory says that: if ‘p’ as a succeed so there is a ‘q’ as a failure. Then because p + q =1, q = 1 – p.
If we bring the question above to the binomial leaflet we can stimulate into:
70 % is the probability for p so p = 70 % = 0,7
Then q = 1 – p = 1 – 0,7 = 0,3
If at least three from five taken randomly, we can calculate the probability of person that says drug is not useful with binomial leaflet. B ( x, n, p ) = C53 (0.07)3 (0.03)2
And the result is 0,3087

3. Find the solution of the differential equation above
dy / dx = - (3x2y + y2 ) / ( 2x3 +3xy )
“Cannot be solved”



4. What is the plane equation for z = x2 + y2 in (1, 1, 2)?
Answer:
We can substitute z with f (x,y) because z is the function in x and y. To know what are the plane equation we must calculate the derivative based x and the derivative based y from the function.
F (x,y) = x2 + y2
∂f (x,y) / ∂x = 2x
∂f (x,y) / ∂y = 2y then write the vector coordinate ◊f(x,y) = 2xi + 2yj
From the question given that the plane equation in (1, 1, 2)
So ◊f(1,1) = 2i + 2j
There is the formula z –zo = ◊f (xo,yo) (x-xo, y-yo)
Z = f(1,1) + ◊f(1,1) (x-1,y-1)
Z = 2x + 2y +2


5. Find the minimum or maximum value from the function a(x) = l x – 1 l ; I = [0,3]
Answer:
For knowing the maximum and minimum value of a(x) = l x – 1 l in I = [0,3]
We must know the function has the stationer point, singular point and the end point.
1. Find the dot point from the interval. The interval [0,3] indicate 0≤ x ≥ 3, then substitute 0 and 3 into a(x) = l x – 1 l becomes a(0) = 1, a(3) = 2.
2. Find the first derivative or stationer point and we get a’(x) = 1, then substitute to the function will get a(1) = 0
3. Find the singular point but in this sample a(x) didn’t have singular point.
After that we can conclude that o as the minimum value and 2 as a maximum value and (1, 0) is the minimum point (3,2) is the maximum point for the [0,3] as interval of that function.


The Question is come from WIDHATUL MILLLA ( 08305141012 ), and will be finished by ANDINI SETIARI ( 08305141017 )

REVIEW
CONTENT
There are 5 chapters in this book. All of them are used to learn mathematics for Junior High School. The materials divided into 2 units that are:
Chapter:
1. Similarly
2. Three dimensional curved surfaces shapes
3. Statistic and probability
4. Exponents and Routs
5. Number sequence and series
We think that the content of this book is enough complete. There is a previous in every chapter that make the readers now what will they learn in this chapter. All of the chapters are arranged by some subtitle. It is complete with definitions, example problem (can also gives problem solving), some exercises and evaluations. Besides the exercises of every subtitle, there are exercises in the end of every chapter that content of solving mathematics problems. Exactly it is suitable with the material of this chapter. There are 20 multiple choices problems and 5 essays. In the end of every unit, there is an evaluation. This book is also be completed with “final evaluation” at the last part of this book. Student must solve 30 multiple choice problems and 10 essays.
Generally, this book is very good and interest for student. It content is suitable to the curriculum of studying n Junior High School. At this moment in Indonesia (suitable to KTSP). The problems in the exercises and the evaluations are realistic problems. We can find the problems in our daily activities. So, it makes the student can imagine and solve the problem easily.
This book is excellence because it is use a bilingual book. So, there are two languages (Indonesian and English) in one book. Every Indonesian page translates to English page directly. It is very useful, because after reading this book, students not only improve their mathematics skill and knowledge but also develop their English. We think this book is suitable to some schools that pioneer their school to be world class school in Indonesia.
Over all, the content of this book is complete enough and very simple to use. Not too difficult to understand all of the mathematics content of this book. The point plus of this book is about its bilingual. So we recommended this book to all of the student year IX. We hope it can help to learn mathematics be easier.
Problem
In our Opinion, the questions that included in this book already organized with the curriculum standard. The type of the questions is so variety, there are from the low level questions until the high level questions. And it can for knowing the level of understanding by every student. The questions which have provided are related to daily life. So, the students can know the meaning from each questions and the relation between the problems with our daily life.
The questions in this book can improve the creativity of the students which is already done the questions because most of the questions are high quality. In the end of the sub themes also provided sample questions with their solution. And it make the students can understand the themes more, really.
In this book is also provided sample exercises. Then, in the end of the themes is provided competition test. It can know the understood of the student with this theme. And in every mid semester, this book is provided mid semester test.
Beside it, this book is completed with the evaluation and the evaluation is located in the end of the semester. So the student can really understand the themes. The form of the questions is check point and essay. But in the exercises part is only essay. Then in the competition test, mid semester test and semester test are check point and essay. Because of the questions are so variety we think that the student will be happy to study this book. Unfortunately, this book isn’t completed with the final answer.
INTEREST
This book is interest enough to read especially for student who have an ideal to become a mathematician and an English expert all at once, in order to you don’t made mathematic source of misfortune. The third grade student of junior high school and full of challenge teacher need to understand the content of this book. Because in the midst of image that mathematic make don’t fell up for studying, need to look for a solution in order to can escaped from the disease mentioned above. Infraction of this book, the writer gives power of attraction that is:
1. Many colors that make us no sleepy and bored when we read or study this book.
2. We can easier to figure out with the picture.
3. Bilingual in order to later mathematic and English are balanced in our life
4. The writer has written many books. This is the fourth book that I know.
5. Succeeded to tell every day event that straight related with mathematic.
What we need to noted, the material was translated into English was not just translated without draft. If we keep follow the statements in every chapter of this book till the references, we find that the material with Indonesian in left page and material with English in right page. This book writer is also to pay attention grammar focus in order to can to be analyzed by public. Reading in detail about the student must finish up a new problem trickily, and I’m very interested in doing it or reading about other people doing it. Inclination up till now only orientation to Cambridge curriculum and the output to bring about lameness properly evaluated. Strategy with to maximize potency human resources was made compulsory.
Apparently this book certainly isn’t finish yet in the sense the step of mathematician and an English expert all at once in Indonesia still keep here. We are the next generation!



INFORMAtion
We can get many kind of information from this book. Beside can increasing our knowledge of mathematics (lesson), it cans also increasing our knowledge of some concept of mathematics in our real life. Some of the information is:
 In chapter I: When a part of sunshine is blocked by a certain object their will a shadow of the body compare our shadow and the tower shadow besides. By comparing our shadow and tower shadow we can measure the height of the shadow. We can use the concept of similarity to measure.
 In chapter II: If the building has a circle form with the similar diameter on every floor, then the sides of the buildings should be informing of curve. If the tortuous sides of the building are to be layered by glasses, so that the area of needed glasses could be get by using the concept of three dimensional curved surfaces shape.
 In chapter III: Rain is one of the natural phenomena on the earth. The highest average of rain density can be found in Cherrapunji, Bangladesh. The height of that region is 1.290 m above the sea level and average rain density is 1.270 cm so that it is called the wettest points on the earth. While the lowest average of rain density can be found in Atacama Desert, Chili. It has 0, 01 cm average of rain density so that it is called the driest point on the earth. Hence, the p probability of the rain in Atacama Desert is very low; moreover the area several place in Atacama Desert that has never been rained 400 th for predicting the rain density we can use the concept of statistic and probability.
 In chapter IV: If someone jumps from a high with original velocity is zero, then it is called free fall movement. The relation between the velocity and height of the man from the ground is formulated by V = where V is the velocity, g is the gravitation at the place, and h is the height from the ground. The form is one of the examples of roots that we can learn in chapter IV.
 In chapter V: When a ball fallen from a certain height on the flat ground, the ball will bounce back but with the lower height from its initial height. If the comparisons between the ball height at this moment and the ball height before outs constant, so we can calculate the height of the ball from the time it was fallen until it’s stopped using the geometric series.

Before..I wanna say thanks you to Dian Tri Handayani because without her assignment I cannot improve my English about mathematics. 1. What is Jangka in English? Jangka in English is pair of compasses. I wanna give the example image of jangka. Look at this




2. What s bilangan genap and bilangan ganjil in English? Bilangan genap is even number and for example 2, 4, 6, 8, 10 etc. If in the calculus, we can find what a kind of number detailly. Maybe with curve or line in cartesius koordinate. And then bilangan ganjil is odd number, this is an all of number except an even number. For example 1, 3, 5, 7, 9. etc.

3. What is Luas Bangun in English? we can say area fot the meaning of luas bangun.
The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers.
• Area of a Square
If l is the side-length of a square, the area of the square is l2 or l × l.
Example:
What is the area of a square having side-length 3.4?
The area is the square of the side-length, which is 3.4 × 3.4 = 11.56.
• Area of a Rectangle
The area of a rectangle is the product of its width and length.
Example:
What is the area of a rectangle having a length of 6 and a width of 2.2?
The area is the product of these two side-lengths, which is 6 × 2.2 = 13.2.
• Area of a Parallelogram
The area of a parallelogram is b × h, where b is the length of the base of the parallelogram, and h is the corresponding height.
Example:
What is the area of a parallelogram having a base of 20 and a corresponding height of 7?
The area is the product of a base and its corresponding height, which is 20 × 7 = 140.
• Area of a Trapezoid
If a and b are the lengths of the two parallel bases of a trapezoid, and h is its height, the area of the trapezoid is
1/2 × h × (a + b) .
The figure formed is a parallelogram having an area of h × (a + b), which is twice the area of one of the trapezoids.
Example:
What is the area of a trapezoid having bases 12 and 8 and a height of 5?
Using the formula for the area of a trapezoid, we see that the area is
1/2 × 5 × (12 + 8) = 1/2 × 5 × 20 = 1/2 × 100 = 50.
• Area of a Triangle
Consider a triangle with base length b and height h.
The area of the triangle is 1/2 × b × h.
The figure formed is a parallelogram with base length b and height h, and has area b × ×h.
This area is twice that of the triangle, so the triangle has area 1/2 × b × h.
Example:
What is the area of the triangle below having a base of length 5.2 and a height of 4.2?
The area of a triangle is half the product of its base and height, which is 1/2 ×5.2 × 4.2 = 2.6 × 4.2 = 10.92..

Area of a Circle

The area of a circle is Pi × r2 or Pi × r × r, where r is the length of its radius. Pi is a number that is approximately 3.14159.
Example:

What is the area of a circle having a radius of 4.2 cm, to the nearest tenth of a square cm? Using an approximation of 3.14159 for Pi, and the fact that the area of a circle is Pi × r2, the area of this circle is Pi × 4.22 3.14159 × 4.22 =55.41…square cm, which is 55.4 square cm when rounded to the nearest tenth.


4. What is keliling bangun in English?
Round about form...

5. What is nilai ekstrim in English? nilai estrim is ekstrim value

We can know about it in calculus. If in calculus, we can know nilai tertinggi or the the top of curve with ekstrim value.

6. What is nilai mutlak in English?

Nilai mutlak is absolute value. We can know about it also in calculus for example the absolute value from -1 is 1 While if in matlab, we can write "abs" so we can know the absolute value directly.

7. What is Integral tentu in English? Integral tentu in English is a certain integral.

8. What is Integral tak tentu? Integral tak tentu in English is a uncertain integral

For example....
Power of x.
xn dx = x(n+1) / (n+1) + C
(n -1) Proof
1/x dx = ln|x| + C

Exponential / Logarithmic
ex dx = ex + C
Proof
bx dx = bx / ln(b) + C
Proof, Tip!

ln(x) dx = x ln(x) - x + C
Proof

Trigonometric
sin x dx = -cos x + C
Proof
csc x dx = - ln|CSC x + cot x| + C
Proof

COs x dx = sin x + C
Proof
sec x dx = ln|sec x + tan x| + C
Proof

tan x dx = -ln|COs x| + C
Proof
cot x dx = ln|sin x| + C
Proof

Trigonometric Result
COs x dx = sin x + C
Proof
CSC x cot x dx = - CSC x + C
Proof

sin x dx = COs x + C
Proof
sec x tan x dx = sec x + C
Proof

sec2 x dx = tan x + C
Proof
csc2 x dx = - cot x + C
Proof

Inverse Trigonometric
arcsin x dx = x arcsin x + (1-x2) + C

arccsc x dx = x arccos x - (1-x2) + C

arctan x dx = x arctan x - (1/2) ln(1+x2) + C

Inverse Trigonometric Result

dx
________________________________________
(1 - x2)
= arcsin x + C


dx
________________________________________
x (x2 - 1)
= arcsec|x| + C


dx
________________________________________1 + x2 = arctan x + C

Useful Identities
arccos x = /2 - arcsin x
(-1 <= x <= 1)
arccsc x = /2 - arcsec x
(|x| >= 1)
arccot x = /2 - arctan x
(for all x)

Hyperbolic
sinh x dx = cosh x + C
Proof
csch x dx = ln |tanh(x/2)| + C
Proof

cosh x dx = sinh x + C
Proof
sech x dx = arctan (sinh x) + C
tanh x dx = ln (cosh x) + C
Proof
coth x dx = ln |sinh x| + C
Proof


9. What is kuadrat in English?kuadrat in English is qudrate...
Fo example the quadrate of 4 is 16

10. What is lebih besar atau sama dengan in English?lebih besar ata sama dengan in English is bigger or equal..( >= )
11. What is akar in English?
Akar in English is root. Root in matematika is the antonym of quadrate. For example the root of 16 is 4. And the root n Biologi is the part of tree.
12. What is sumbu simetri inEnglish?Sumbu simetri in English is which of simetrims.
13. What is koordinat kartesius in English? Coordinate cartesius..
14. What is logika and himpunan? mix ang logical is himpunan dan logika..
This is one of subbab which studied in logical.
DISJUNGSI, CONJUNTION, IMPLICATION, BIIMPLIKASI AND
NEGASINYA
Occasionally, we are required to make a statement or menegasikan new indicate disavowal of the statement above, using perakit "Not" or "no". In addition, they must combine the two statements or
using more perakit "or", "and", "If ... then ....", and "if ...And only if .... ", known in mathematics as a conjunction, disjungsi, the implicationsand biimplikasi. This section will discuss these perakit-perakit
1.Negasi
If p is the "East Java capital of Surabaya.", Then negasi or from ingkaranstatement p is the p: "Singapore is not the capital of East Java." or"It is not true that the East Java capital of Surabaya.".
From the above examples seem clear that p is a correct statement of value Surabaya because in fact the capital of East Java.

2. Conjunction
Conjunction is a compound statement that uses perakit "and".
For example, Adi following statement:
"Fahmi eating rice and drinking coffee."The statement ekivalen with single following two statements: "Fahmi eatrice. "and" Fahmi drinking coffee. "
In the process of learning in the classroom, give the opportunity for students toask themselves, in which case the above statement Adi valuable correct and valuable in the case where one of four in the following cases,
namely:
(1) Fahmi the right to eat rice and he also drank coffee,
(2) Fahmi eat rice, but it does not
drinking coffee,
(3) Fahmi did not eat rice, but he drank coffee, and (4) does not Fahmi
eating rice and he does not drink coffee.:

In the first case, Fahmi is correct to eat rice and he also drank coffee. In cases like this, you probably will not say Adi earlier statement valuable one. The reason, according to earlier statements Adi with reality. In the case of second, Fahmi eat rice, but he does not drink coffee. In this case, of course you will that compound statement earlier Adi valuable because even if one Fahmi have to eat rice, but he does not drink coffee, as stated Adi.
Analogoushence, in the third case, Fahmi not eating rice, although he is drinking coffee. As the two earlier cases, you will read that statement compound Adi. Mentioned as a valuable Fahmi did not eat rice as stated Adi. Fahmi that eating rice and drinking coffee. Finally, the fourth case, not Fahmi eating rice and he does not drink coffee. In this case you will read that Adi compound statement before any value because there is no congruence between the expressed by the fact that indeed.
3. Disjungsi
Disjungsi is a compound statement that uses perakit "or".
For example, Adi following statement: "Fahmi eat rice or drink coffee." Now,to ask yourself, in which case the above statement will be Adi correct value in the following four cases, namely:
(1) Fahmi is correct to eat rice and he also drank coffee,
(2) Fahmi eat rice, but he does not drink coffee,
(3) Fahmi do not eat rice, but he drank coffee, and
(4) Fahmi did not eat rice and it does not drinking coffee.
In the first case, Fahmi is correct to eat rice and he also drank coffee. In cases like this, you probably will not say Adi earlier statement valuable one, as Adi earlier statement in accordance with reality. In the case of second, Fahmi eat rice, but he does not drink coffee. In this case, of course you will that compound statement earlier Adi value is correct because Fahmi correct eating rice, although he does not drink coffee, as stated Adi.
While in the third case, Fahmi not eat rice, but he drank coffee. As the two earlier cases, you will read that statement compound Adi correct value before because Fahmi not even eat rice, but he is drinking coffeeas stated Adi. Finally, the fourth case, not eating Fahmirice, and he does not drink coffee. In this case you will read that statementAdi valuable compound earlier because no one conformity between the stated with the fact that indeed. He says Fahmi eat rice or drink coffee, but the fact is, Fahmi not do so.
4. Implications
Suppose there are two statements p and q. Often come to the attention of scientists and is matematikawan show or prove that, if the p value will lead to correct q value is also true. To achieve these desires,diletakkanlah word "If" statement before the first ago placed the word "then" in statements between the first and second statements, so that a statement obtained compound called implications, conditional statements, conditional orhypothetical with notation "⇒" like this:
p ⇒ q
The above notation can be read with:
1) If p then q,
2) q if p,
3) p is a sufficient condition for q, or
4) q is a necessary condition for p.
Implication p ⇒ q is a compound of the most difficult to understand theSMU students. To help students understand the complex implications, and Mr. and Mrs. Teacher can start the learning process with berceritera
Adi says that the plural of the following:
If rainy days then I (Adi) bring an umbrella.In this case dimisalkan:
p: Day rain.
q: Adi bring an umbrella.
Give the opportunity for students to think, in the case where a statement Adi earlier will be valuable right or wrong for the following four cases, namely:
(1) Day really Adi rain and really bring an umbrella,
(2) Day really rain but Adi does not carry an umbrella,
(3) Day does not rain but Adi bring an umbrella, and
(4) Day Adi does not rain and no umbrella.

In the case of the first day really rainy and Adi really bring an umbrellaas he reveal. How it may be stated in a lie this case? Thus clear that both components equally valuable true that statement has caused compound (implications) that Adi was stated earlier will be valued properly. In the second case, that day really rain but not Adi bring an umbrella as he should do as dinyatakannya, how Adi earlier statements may be properly assessed? With other components of value p, but not properly followed by the components of q should also correct value, will cause the compound statement (implications) that Adi stated earlier will be worth one.
Finally, for the third and fourth cases, where the day does not rain, of course You will not be called compound statements (implications) as Adi the statement is wrong, because it states that Adi is just something that is going to happen he will bring an umbrella if rain days.
5. Biimplikasi
Biimplikasi or bikondisional compound statement is a statement from the two p and q with the dinotasikan p ⇔ q value equal to (p ⇒ q) ∧ (q ⇒ p) so it can be read: "p if and only if q" or "p if and only if q."
Thus biimplikasi clear that the two statements p and q will only true value if the second statement tunggalnya worth the same. Biimplikasi example:
1.Triangle is a triangular carpenter's square if and only if the broad square in the
hipotenusanya with the same amount of square-wide on both sides of the square the other.

15. What is tegak lurus in English? Tegak lurus is upright..
16. What is kesebangunan? Kesebangunan is construction
17. What is jajar genjang? Jajar genjang is parallelogram
18. What is Belah Ketupat?Belah ketupat is a form like a square but a little different
19. What is barisan dan deretan? Barisan dan Deretan is formation and row
There is two kind of Formation and row in mathematics. That is Aritmatics and Geometry.
1. Aritmatics
Line arithmetic
U 1, U 2, U 3, U ....... n-1, U n is called the line arithmetic, if
U 2 - U 1 = U 3 - U 2 = .... = U n - U n-1 = constant
This difference is also called (b) = b = U n - U n-1
Tribe to line arithmetic n-a, a + b, a +2 b, ......... , A + (n-1) b
U 1, U 2, U 3 ............., U n
The formula to-n:
U n = a + (n-1) b = bn + (ab) ® Fu ngsi linier in n
Arithmetic progression
a + (a + b) + (a +2 b) +. . . . . . + (A + (n-1) b) called the arithmetic progression.
a = beginning of the race
b = different
n = many tribes
U n = a + (n - 1) b is-n to tribe
N the number of tribes
Sn = 1 / 2 n (a + U n)
= 1 / 2 n [2a + (n-1) b]
= 1/2bn ² + (a - 1/2b) n ® quadratic function (in n)
Description:
Difference between the two tribes that sequence is fixed (b = n S ")
Rows of arithmetic will be increased if b> 0
Arithmetic will be down the line if b <0
Valid relations U n = S n - S n-1, or Un = S n '- 1 / 2 S n "
If the number of odd tribe, the tribe of the
U t = 1 / 2 (U 1 + U n) = 1 / 2 (U 2 + U n-1) ff.
S n = 1 / 2 n (a + U n) = t ® U NU t = Sn / n
If three numbers form a line arithmetic, to facilitate calculation of the number-eg the number that is a - b, a, a + b
2. Geometry

Line geometry
U 1, U 2, U 3, U ......., n-1, U n is called the line geometry, if
U 1 / U 2 = U 3 / U 2 = .... = U n / U n-1 = constant
This constant is called a comparison / ratio (r)
Ratio r = U n / U n-1
Tribe to n-line geometry
a, ar, ar ², ....... ar n-1
U 1, U 2, U 3 ,......, U n
Tribe to n U n = ar n-1 ® exponential function (in n)
Array geometry
a + ar ² + ....... + Ar n-1 called array geometry
a = beginning of the race
r = ratio
n = many tribes
N the number of tribes
Sn = a (r n -1) / r-1, if r> 1
= A (1-r n) / 1-r, if r <1 ® exponential function (in n)
Description:
The ratio between the two tribes that sequence is still
Line geometry will be increased, if applicable for each n
U n> U n-1
Line geometry will be down, if applicable for each n
U n
Alternately up and down, if r <0
Valid relations U n = S n - S n-1
If the number of odd tribe, the tribe of the
Ut = 1 Xu Ö U Ö U n = 2 n-1 Xu ff.
If three numbers form a line geometry, to facilitate the calculation, eg the number-number is the a / r, a, ar
Array geometry BERHINGGA TAK
Array geometry is not berhingga's Answer
U 1 + U 2 + U 3 + ..............................
¥
å Un = a + ar + ar ² .........................
n = 1
where n ® ¥ and -1 <1 so that r n ® 0
By using the formula the number of array geometry obtained:
Amount not berhingga ¥ S = a / (1-r)
Array geometry is not convergent berhingga will (have any number of) for -1 <1
Note:
a + ar + ar 2 + ar 3 + ar 4 + ....... ..........
The number of tribes in the odd position
a + ar 2 + ar 4 + ....... odd S = a / (1-r ²)
The number of tribes in the whole
a + ar 3 + ar + 5 ...... even S = ar / 1-r ²
Obtained the relationship: S even / odd S = r
USE
Calculation TUNGGAL INTEREST (Interest is calculated based on the initial capital)
M 0, M 1, M 2, M n .............,
M 1 = M 0 + P/100 (1) M 0 = (1 + P/100 (1)) M 0
M 2 = M 0 + P/100 (2) M 0 = (1 + P/100 (2)) M 0
M n = M 0 + P/100 (n) ® M 0 M n = (1 + P/100 (n)) M 0
Calculation BUNGA compound (Interest is calculated based on the capital last)
M 0, M 1, M 2, M n ..........,
M 1 = M 0 + P/100. M 0 = (1 + P/100) M 0
M 2 = (1 + P/100) M 0 + P/100 (1 + P/100) M 0 = (1 + P/100) (1 + P/100) M 0
= (1 + P/100) 0 M ²
Mn = (1 + P/100) n M 0
Description:
M 0 = initial capital
M n = n the period after the Capital
p = Percent per period or interest rate
n = Number of
Note:
Compound interest formula can also be used for plant growth, the development of bacteria (p> 0) and also for shortening the engine, radio active material shedding (p <0).

Introduction to English 1

Before, I want to tell about me. My name is Widhatul Milla, usually my friend called me meela. Now, I', a student of Mathematics Programs at Yogyakarta State University.


February 17,2009 is the first time I get an English lesson, and when I am in the second grade of my college. Because not in the first grade yet.Do you know who lecturer that teaches us in the class of RegulerMathematics 2008? Mr. Marsigit is the name of my English university-level instructor . He is very friendly and humorist. He come from Purbalingga, and he have gone in the many country for something that important like International seminar etc.


In first meeting, I get some new knowledge from Mr.Marsigit. He told about " How to communicate Mathematics in English? ". There are many ways to become a success. This is not only success for mathematics but all of our dreams. Let me to know about it..

• Actually that before We must have a good behaviour or a good attitude. And after that we must develop our competen. And the first we must have a high spirit and motivation. Without a spirit we will nt reach our dreams and we can't do everything maximall. An we also need a high motivation, we can get themotivation from many people who arond us. Maybe like our parent, our friend, our lecturer etc. The most important is make a good perception in our life and we always pray to God. You must believe that without it we can't be easier.
  

• Tallent, Experience and knowledge, they are a something that help us to develop our competen.And to learn a knowledge, we must have a tool or a equipment. For example a some strategi like study regularly. And don forget to improve our English. The way to improve our English and the one of the many ways is try speak English a day and a day. And if we are a student of mathematics the way to learn mathematics by try some question, try to finish many kinds of questions.

• The third I want to ask you How to communicate mathematics in English? Before we have to know what a communicate is. Communicate is to hear, to comment, to talk, to write, to understand, to discuss, to translate and to reflect. By it, we can do what must we do.We will have many experience such as international conference and debate.

• Use our knowledge to others, our live will be valuable if we can use our knowledge to others. So don't be a stingy people , we must share our knowledge to others.

• Have a good role in International networking, so Mr.Marsigit give an assignment to make blog and becoming th follower her in the her blog.

February 24 2009 is the second section for learning English with our English lecturer.

Mathematic it self, there are many sources that we can access. If we want contribute and improve the University especially UNY we can access Blog UNY. What is the blog site? UNY.co.id. And Mr. Marsigit said that he expected that we will become conduldate of student. We must have a responsibility.

Mathematics is not isolated, who write the difine of matematics?
He say that allof person can define what the meaning of matematics. Coming from a good attitude, high motivation or spirit, good understanding of mathematics, mathematics is very simple. And he said "Guest your partner, family to speaking English. What is the way?
The way is with looking at TV Program, writing down by Compoter, ictionary or website.

Prof.Katagiri ( Tokyo, Japan) said that If you talking about mathematics, we can talk about mathematics thinking; that is

1. Math attitude
2. Math method
3. Math content

Three component related each other.

Without way, we cannot study mahematics our math will not be good except we havea doog attitude on it. But a good attitude, math beyond me so we never reach mathematics completely. How to be come a mathematican? We need a method, this is by getting experience.

We cannot get mathematics content without mathematics method although we have a good attitude.

And,,actually mathematics is
part our live, ourself and also our mind or our thinking.

maturelife

Introduction English1( MATHR08)

My name is Widhatul Milla...
I am come from Solo full of love