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 )