Last week on April 23rd,2009 Mr.Marsigit told about mathematical thinking and scientific work in my class. Different mathematician has different definition about science. There is said that science is mathematical thinking, but there is said that science is establish with deductive method contain concept, definition, theorem, axiom, etc. Pure mathematics has characteristic more formal that mathematics is axiomatic mathematics. Before we describe about mathematics, we need strengthen object mathematics. What is mathematical object? Mathematical object is our mind; mathematical object is our idea and abstract and it doesn’t concrete object so we can’t manipulation using our sensory tool. And now, how we get mathematical object? We can get mathematical object from everything being our around.
There are two wise to get mathematical object:
1. We use abstraction
What is abstraction? Abstraction is looking for similarity to get form or simple characteristics to be object of mathematics. For example: “What do you think about the number five?” Every students giving various answer but in English class, the lecture and the students have similar characteristics so they discus about the value of number five. Why? Because this very minute, the lecture explain about English for mathematics so it is abstraction because we just learn several characteristic which we really dispersed.
2. We use idealization
“And what is idealization?” Idealization is straight or don’t taper because straight just for SIROTOL MUSTAQIM. For example, we have plan so it doesn’t really flat because absolutely right just Allah SWT, one other the teacher make question to their student don’t direct so the students must try to solve this problem and then it is called idealization.
And know, what is the characteristic of mathematical thinking? Mathematical thinking has many characteristics among others:
a. Consistent, it means that mathematical thinking must accord with the first requirement. For example we said A so can permanent A.
b. Mathematical logic, it blankets daily logic and formal logic. In mathematical logic contain ma thematic operation, if then statement, relation, etc.
c. There are thesis and antithesis. Thesis is sentence contain rightness but antithesis is opposite from thesis. So, before thesis and antithesis we need write hypothesis which temporary presumption.
Scientific work has standard or criteria inside writing them. Many people do some research or experiment to can write scientific work. A book about Mathematics for Senior High School include inside scientific work. It has systematical among others:
1. Introduction
Introduction contain about background why we write scientific work. Inside it, we can also give some problems to get solution.
2. Discussion
In discussion we said about problems and the solution it. In there, we take in some theory and material others which support it.
3. Conclusion
In this part, we must resume about problem solving in discussion part. We also give recommendation about problems above.
4. Reference
We can get reference from whatever such the books in library, dictionary, internet, etc. References create as source in our scientific work.
If we will write scientific work so we must to know about ethical code scientific work such:
a. Impersonal
It means we forbid to put emotional unsure. For example, we write book about Mathematical for Senior High School and in end page, we write “good luck and success” so we admit personal unsure inside it.
b. Has standard or criteria
It means if we write scientific work must know how arrangement writing, contain inside it is whatever.
c. Objective
Objective has means that suit with topic, so it doesn’t subjective. We write suit our material and it must coherent.
Rabu, 29 April 2009
Rabu, 15 April 2009
Exercise before English Examination
Last week, on 2nd April 2009 Mr. Marsigit gave English examination in my class. I and my friends very surprised because Mr.Marsigit didn’t say anything in before meeting. So we do it during thirty minutes and finally Mr.Marsigit said that it is just exercise to do English examination next week. Immediately, our profile change becomes very happy and we felt relieved.
Exercise I:
1. Explain how to prove that square root of 2 is irrational number!
2. Explain how to show or to indicate that the some angel of triangle is equal to 180 degree!
3. Explain how you are able to get phi!
4. Explain how you are able to find of the area of region foundered by the graph of y equal x square and y equal x plus 2!
5. Explain how you are able to determine the intersection point between the circle x square plus y square equal 20 and y equal x plus 1!
Answer:
1. To prove that the square root of 2 is irrational number so for example we have assumption that the square root of 2 is rational number. It means the square root of 2 equal a over b, which a and b as prime so the square root of 2 equal a over b. a over b can be writing with a equal b times the square root of 2 or a square equal 2 times b square because a square equal 2 times of integer so a square even so a also odd. Example equal 2c so the equation because four c square equal 2b. So, be square even and b also even. But, it's impossible because a and b impossible even because they are relative prime. So, assumption that square root of 2 is rational number is impossible. So, the conclusion that the square root of 2 is irrational number.
2. To show or to indicate that the some angels of triangle are equal to 180 degree so we can cut all of angel of triangle. Then, we adhere become one so three angel that will configured straight supplementary angel. We also prove it with we draw a line pass one of point angel from triangle which parallel with side in front of it. For example we have triangle ABC and we draw MN line pass point angel B and parallel with AC. Attention that size supplementary angel on B equal size sides of triangle ABC are a degree plus b degree plus c degree equal 180 degree. Every pair angel congruent is pair angel inside opposite on lines parallel.
3. To get phi we must do exercise. We can make a circle has radius of one cm from wire. Then, we wrap wool accord form of that wire. Then, we measure the length of wire with rule. For example, really we get 6 coma 28 it means 6 coma 28 is round of the circle. We know that the round of circle is phi time’s diameter or phi times two times of radius so phi equal round divide two times of radius. So, we can write that 3 coma 14 equal phi times two times of radius. And know phi equal 6 coma 28 divide two equal 3 coma 14.
4. To find of the area of region foundered by the graph of y equal x square and y equal x plus 2 so we must draw of each curve. After draw it, so we look for intersection point between two equations above. So, we get value of x and x as interval of integral to account the area of region it. If, y equal x square and y equal x plus 2 so we can write that x square equal a plus 2 and we get that x square minus x minus two equal zero. So, x minus two in bracket times x plus one in bracket equal zero. So, we get value of x with x equal two and x equal negative one as interval of integral it. Now, we can account the area of region it with integral x plus two minus x square in bracket to x with an equal negative one until x equal two. If we integral the equation so we get half x square plus two x minus one over three x cube with interval x equal negative one until a equal two. So we must substitution x with negative one and two and we get four half. So, the area of region foundered by the graph of y equal x square and y equal x plus two is four half.
5. To determine the intersection point between he circle x square plus y square equal 20 and y equal x plus 1 so we must substitution y equal x plus 1 inside x square plus y square equal 20. And we get x square plus open bracket x plus 1 close bracket square equal 20, so x square plus x square plus two x plus 1 equal 20, so two x square plus two x minus 19 equal zero. To get value of x, we must use the formula abc that x one or x two equal negative b plus minus the root of b square minus four times a times c divide angel negative 4a. So, x one or x two equal negative 2 plus minus the root of 2 square minus 4 times 2 times negative 19 divide negative 4 times 2. After we account it so we get that value of x one equal negative 1 coma 291 or x two equal 1 coma 791.
Exercise II:
1. High line
High line from a triangle is segment line which perpendicular correlates a point angle with a point on side in front of point angle. The theorem high line on hypotenuse a right angle establishes two triangles which uniform and also uniform with right angles.
2. Percentile
Percentile is value which divide batch of data becomes 100 part same.
Formula of percentile:
Pi equal TB Pi plus open bracket (i divide 100) N minus fk divide f P10 close bracket times p.
TB is limit under percentile i
i is number of percentile
N is sum all percentile
f is frequentation class percentile i
fk is frequentation cumulative class percentile i
p is interval class
Exercise to percentile:
Table frequentation and frequentation cumulative score
Score (x) Frequentation (fi) Frequentation cumulative
0-9 3 3
10-19 67 70
20-29 205 275
30-39 245 520
40-49 213 733
50-59 147 880
60-69 77 957
70-79 34 991
80-89 8 999
90-99 1 10000
sum 10000
P10? To get it, so we look for class which contains P10 is we account 10 divide100 in braked N equal 10 divide 100 times 1000 equal 100.
P10 equal 19 coma 5 plus open bracket 100 minus 70 divide 205 close bracket times 10 so we get that P10 equal 20 coma 96.
3. Relation
• Definition of relation is making a pair from element of compilation A to element of compilation B.
• Domain relation R from A to B is subset compilation from A while range E is subset compilation from B. Example A={1,2,3,4,5} and B={a,b,c,d}
Relation R= {(1,b), (3,b), (4,c), (4,d)}
Domain from relation R from A to B={1,3,4}
Range from relation R from A to B={b,c,d}
• Kind of relation
a. Reflective relation
Relation R called reflective relation if to every a element S, (a,a) element R is every element S is related with their self. Example relation R inside G is same and uniform relation
b. Symmetry relation
Relation R called symmetry relation if to every a,b element S (a,b) element R so (b,a) element R. Example G is parallel relation.
c. Transitive relation
Relation R called transitive relation if to every a,b element S if (a,b) element R and (b,c) element R. Example Q is relation minus from.
d. Equivalent relation
Relation R called equivalent relation if relations R are reflective relation, symmetry relation, and transitive relation.
Exercise I:
1. Explain how to prove that square root of 2 is irrational number!
2. Explain how to show or to indicate that the some angel of triangle is equal to 180 degree!
3. Explain how you are able to get phi!
4. Explain how you are able to find of the area of region foundered by the graph of y equal x square and y equal x plus 2!
5. Explain how you are able to determine the intersection point between the circle x square plus y square equal 20 and y equal x plus 1!
Answer:
1. To prove that the square root of 2 is irrational number so for example we have assumption that the square root of 2 is rational number. It means the square root of 2 equal a over b, which a and b as prime so the square root of 2 equal a over b. a over b can be writing with a equal b times the square root of 2 or a square equal 2 times b square because a square equal 2 times of integer so a square even so a also odd. Example equal 2c so the equation because four c square equal 2b. So, be square even and b also even. But, it's impossible because a and b impossible even because they are relative prime. So, assumption that square root of 2 is rational number is impossible. So, the conclusion that the square root of 2 is irrational number.
2. To show or to indicate that the some angels of triangle are equal to 180 degree so we can cut all of angel of triangle. Then, we adhere become one so three angel that will configured straight supplementary angel. We also prove it with we draw a line pass one of point angel from triangle which parallel with side in front of it. For example we have triangle ABC and we draw MN line pass point angel B and parallel with AC. Attention that size supplementary angel on B equal size sides of triangle ABC are a degree plus b degree plus c degree equal 180 degree. Every pair angel congruent is pair angel inside opposite on lines parallel.
3. To get phi we must do exercise. We can make a circle has radius of one cm from wire. Then, we wrap wool accord form of that wire. Then, we measure the length of wire with rule. For example, really we get 6 coma 28 it means 6 coma 28 is round of the circle. We know that the round of circle is phi time’s diameter or phi times two times of radius so phi equal round divide two times of radius. So, we can write that 3 coma 14 equal phi times two times of radius. And know phi equal 6 coma 28 divide two equal 3 coma 14.
4. To find of the area of region foundered by the graph of y equal x square and y equal x plus 2 so we must draw of each curve. After draw it, so we look for intersection point between two equations above. So, we get value of x and x as interval of integral to account the area of region it. If, y equal x square and y equal x plus 2 so we can write that x square equal a plus 2 and we get that x square minus x minus two equal zero. So, x minus two in bracket times x plus one in bracket equal zero. So, we get value of x with x equal two and x equal negative one as interval of integral it. Now, we can account the area of region it with integral x plus two minus x square in bracket to x with an equal negative one until x equal two. If we integral the equation so we get half x square plus two x minus one over three x cube with interval x equal negative one until a equal two. So we must substitution x with negative one and two and we get four half. So, the area of region foundered by the graph of y equal x square and y equal x plus two is four half.
5. To determine the intersection point between he circle x square plus y square equal 20 and y equal x plus 1 so we must substitution y equal x plus 1 inside x square plus y square equal 20. And we get x square plus open bracket x plus 1 close bracket square equal 20, so x square plus x square plus two x plus 1 equal 20, so two x square plus two x minus 19 equal zero. To get value of x, we must use the formula abc that x one or x two equal negative b plus minus the root of b square minus four times a times c divide angel negative 4a. So, x one or x two equal negative 2 plus minus the root of 2 square minus 4 times 2 times negative 19 divide negative 4 times 2. After we account it so we get that value of x one equal negative 1 coma 291 or x two equal 1 coma 791.
Exercise II:
1. High line
High line from a triangle is segment line which perpendicular correlates a point angle with a point on side in front of point angle. The theorem high line on hypotenuse a right angle establishes two triangles which uniform and also uniform with right angles.
2. Percentile
Percentile is value which divide batch of data becomes 100 part same.
Formula of percentile:
Pi equal TB Pi plus open bracket (i divide 100) N minus fk divide f P10 close bracket times p.
TB is limit under percentile i
i is number of percentile
N is sum all percentile
f is frequentation class percentile i
fk is frequentation cumulative class percentile i
p is interval class
Exercise to percentile:
Table frequentation and frequentation cumulative score
Score (x) Frequentation (fi) Frequentation cumulative
0-9 3 3
10-19 67 70
20-29 205 275
30-39 245 520
40-49 213 733
50-59 147 880
60-69 77 957
70-79 34 991
80-89 8 999
90-99 1 10000
sum 10000
P10? To get it, so we look for class which contains P10 is we account 10 divide100 in braked N equal 10 divide 100 times 1000 equal 100.
P10 equal 19 coma 5 plus open bracket 100 minus 70 divide 205 close bracket times 10 so we get that P10 equal 20 coma 96.
3. Relation
• Definition of relation is making a pair from element of compilation A to element of compilation B.
• Domain relation R from A to B is subset compilation from A while range E is subset compilation from B. Example A={1,2,3,4,5} and B={a,b,c,d}
Relation R= {(1,b), (3,b), (4,c), (4,d)}
Domain from relation R from A to B={1,3,4}
Range from relation R from A to B={b,c,d}
• Kind of relation
a. Reflective relation
Relation R called reflective relation if to every a element S, (a,a) element R is every element S is related with their self. Example relation R inside G is same and uniform relation
b. Symmetry relation
Relation R called symmetry relation if to every a,b element S (a,b) element R so (b,a) element R. Example G is parallel relation.
c. Transitive relation
Relation R called transitive relation if to every a,b element S if (a,b) element R and (b,c) element R. Example Q is relation minus from.
d. Equivalent relation
Relation R called equivalent relation if relations R are reflective relation, symmetry relation, and transitive relation.
Rabu, 01 April 2009
Reflection in Video
On 19th April 2009 Mr.Marsigit show with my class several video. The video very interesting because gives me motivation. I very heart burning with one people in video besides he is a child. But, I get knowledge that I must believe with myself and I don’t saw something from one different away.
In first video, show how the teacher gives motivation to their students. The teacher tells about W. Shakespeare who writes some interesting story. He tells the story very loudly thus his sound reverberates. Several students listen with him but several students busy with themselves activity for example writes something. Several students very admired with that story because the story waken spirit. Suddenly, the teacher jump on the table, he likes orator who give high spirit. He don’t afraid with his act and he advertise with his student don’t afraid to have a dream or have an ambition. Why the teachers speak it? Because, all this time the students just study oriented. They don’t have skill in outside. Consequently, the students must listen with their breast and the teacher gives freedom to them. The students must find themselves. Possible, we think the teacher stand on the table is one of mistake but let’s we don’t saw from it. We don’t have consider and look at something in different way. If we know something, we must look in the other way. The teacher demands their students to stand on the table likes him. Listen it, the students hurry up do it. In last video, two students stand on the table. They are very happy because they have freedom from their teacher.
In second video, I saw that there is a son stand on the stage and many audiences on his round. In there, he speaks very loudly and makes audiences admired with him. His speak like adult, and his every pronunciation have a meaning. The audiences very surprised with all his gesture. A son gives motivation to audiences so they believe with themselves. He said that “You believe me? You must believe that next week, I still stand on this stage.” Environment very noisy and make audiences give applause more and more loudly and their sound more and more jarring. A son runs to surround stage to give a motivation with audiences. The audience come from various reach, child, and adult, old, young. I become heart burning with him, why tendering like him very brave to speak in front of many people. He is very trust and he is very believed with himself. All of the audiences very enjoy with him. From this video, I get one of knowledge that we must believe with our ability so we don’t doubt with our work. A son in video has a high spirit to give motivation with the audiences.
In third video, there are two collage students song “what you know about math?” They have a high spirit to study about mathematics. I think, mathematics are integral, limit, trigonometry, curve, differential, exponent, and numerical. Really, in my opinion about mathematics is very a little. Because I think, mathematics just a lesson in my class but mathematics becomes breathes all of science. In the video, I look everything use mathematics. It means all the time I don’t understand about mathematics. I still have to study about mathematics. It isn’t just lesson but a knowledge which very important to all people in their life. If there are someone say mathematics just arithmetic is blunder. At last video, two collage students said that they know all about mathematics.
In fourth video, show how to solve differential equation. We will solve differential equation and integral equation. How to solve the differential or integral equation? There are some steps to solve it:
First, we must find y = f(x), satisfies the equation for values x and y.
How to solve ∫ (4x²) dx?
Try to get dependent variable, y all by it self. To solve that equation,
First we write = 4x² then we multiply the both segment with dx so acquirement that
dx (dy/dx) = (4x²) dx
We write with:∫ dy = ∫ (4x²) dx
To solve it, we must know formula of integral that ∫ x square n dx = x square (n+1) divide n+1
So ∫ 4x² = 4/3 x cubic
In fifth video, there is a teacher explain how to solve a linear equation so the students can be understand. So, I will try to solve several equations as the teacher.
1. X – 5 = 3
We can solve a linear equation above with add 5 on each segment, so in left segment just acquirement value from X. So, the equation can be writing with:
X – 5 = 3
X– 5+5 = 3+5
X = 8
Therefore, the solution from X min 5=3 is X = 8.
2. 7 = 4a – 1
Such as number one, we can solve a linear equation above with add 1 on both segment, so in right segment only acquirement value from a. So, the equation can be writing with:
7 = 4a min 1
7+1 = 4a min 1+1
8 = 4a
a = 2
Therefore, the solution from 7 = 4a-1 is a = 2.
3. 2/3 y = 8
We can solve this linear equation such as both the equation above but we don’t add numerically but we must multiply both segments with 3/2 and can acquirement value of y. So, the equation can be writing with:
2/3 y = 8
(2/3 y) times (3/2) = 8 times 3/2
y = 24/2
y = 12
Therefore, the solution from 2/3 y = 8 is y = 12.
Three examples above are very simple, so let’s we solve a linear equation more complex than above. There is several equation and we must solve it.
1. 5 min 2X = 3X+1
Because there is coefficient X on the both segment so we must delete one of them. For example we will delete negative 2X and 1 so we must add 2X and negative 1 on the both segment and acquirement value of X. So, the equation can be writing with:
5─2X+2X─1 = 3X+2X+1─1
4 = 5X
So get value of X, we must multiply the both segment with 1/5 and can be writing that:
4 times 1/5 = 5X times 1/5
X = 4/5
Therefore, the solution from 5─2X = 3X+1 is X = 4/5.
2. 3─5(2m─5) = ─2
To solve the equation above, we must multiply 5 with something on bracket so we get that:
3─10m+25 = ─2
─10m+28 = ─2
─10m = ─30 , to get value of m so we must divide the both segment with ─10 and can be writing with:
─10m/─10 = ─30/─10
m = 3
Therefore, the solution from 3─5(2m─5)= ─2 is m = 3.
3. (1/2y+1/4) = (1/3y+5/4)
We can solve the equation with multiply the both segment with KPK from 2, 3, and 4 but KPK of them is 12. We can write the equation with:
(1/2y+1/4) = (1/3y+5/4)
12(1/2y+1/4) = 12(1/3y+5/4)
6y+3 = 4y+15
2y = 12
y = 6
Therefore, the solution from (1/2y+1/4) = (1/3y+5/4) is y = 6.
4. 0,35a─0,2 = 0,15a+0,1
We can solve the equation with multiply the both segment 100 because number in behind of coma is two number. So, we can write the solution with:
0,35a─0,2 = 0,15a+0,1
100(0,35a─0,2) = 100(0,15a+0,1)
35a─20 = 15a+10
20a = 30
a = 3/2
Therefore, the solution of 0,35a─0,2 = 0,15a+0,1 is a = 3/2.
In sixth video, There is a teacher explains about logarithm. We know that there are many formula bases about logarithm and now I will try explaining about it.
I. log base x A equal B this form have same meaning or equivalent with X square B equal A, so we can write the both form with log base x A equal B equivalent X square b equal A.
Let’s we prove the equation above with multiply the both segment with C so can be writing with:
Log base x A equal B equivalent X square b equal A
C (log base x A)equal BC equivalent (X square b) square c equal A square c
C log base x A equal BC equivalent X square b times c equal A square c
Log base x A square c equal BC equivalent log base x A square equal BC
From explanation above, we can saw that log base A = B equivalent with X square b= A.
II. Log base x A + log base x B = log base x AB
To prove the equation above, we can use that:
If log base x A = k so X square k = A and can be writing with:
Log base x A = k so X square k = A
If log base x B = m so X square m = B and can be writing with:
Log base x B = m so X square m = B
If log base x A/B = n so X square n = A/B
= X square k divide X square m
= X square k minus m
We know that n = k-m so the equation is true. So we get equation that
log base x A+ log base x B = log base x AB
Really, many formulas to logarithm, but in the video just explain two formulas. If multiplication be addition so division is diminution, that statement can be writing with:
Log base x A plus log base x B = log base x AB so log base x A min log base x B = log base x A/B
In first video, show how the teacher gives motivation to their students. The teacher tells about W. Shakespeare who writes some interesting story. He tells the story very loudly thus his sound reverberates. Several students listen with him but several students busy with themselves activity for example writes something. Several students very admired with that story because the story waken spirit. Suddenly, the teacher jump on the table, he likes orator who give high spirit. He don’t afraid with his act and he advertise with his student don’t afraid to have a dream or have an ambition. Why the teachers speak it? Because, all this time the students just study oriented. They don’t have skill in outside. Consequently, the students must listen with their breast and the teacher gives freedom to them. The students must find themselves. Possible, we think the teacher stand on the table is one of mistake but let’s we don’t saw from it. We don’t have consider and look at something in different way. If we know something, we must look in the other way. The teacher demands their students to stand on the table likes him. Listen it, the students hurry up do it. In last video, two students stand on the table. They are very happy because they have freedom from their teacher.
In second video, I saw that there is a son stand on the stage and many audiences on his round. In there, he speaks very loudly and makes audiences admired with him. His speak like adult, and his every pronunciation have a meaning. The audiences very surprised with all his gesture. A son gives motivation to audiences so they believe with themselves. He said that “You believe me? You must believe that next week, I still stand on this stage.” Environment very noisy and make audiences give applause more and more loudly and their sound more and more jarring. A son runs to surround stage to give a motivation with audiences. The audience come from various reach, child, and adult, old, young. I become heart burning with him, why tendering like him very brave to speak in front of many people. He is very trust and he is very believed with himself. All of the audiences very enjoy with him. From this video, I get one of knowledge that we must believe with our ability so we don’t doubt with our work. A son in video has a high spirit to give motivation with the audiences.
In third video, there are two collage students song “what you know about math?” They have a high spirit to study about mathematics. I think, mathematics are integral, limit, trigonometry, curve, differential, exponent, and numerical. Really, in my opinion about mathematics is very a little. Because I think, mathematics just a lesson in my class but mathematics becomes breathes all of science. In the video, I look everything use mathematics. It means all the time I don’t understand about mathematics. I still have to study about mathematics. It isn’t just lesson but a knowledge which very important to all people in their life. If there are someone say mathematics just arithmetic is blunder. At last video, two collage students said that they know all about mathematics.
In fourth video, show how to solve differential equation. We will solve differential equation and integral equation. How to solve the differential or integral equation? There are some steps to solve it:
First, we must find y = f(x), satisfies the equation for values x and y.
How to solve ∫ (4x²) dx?
Try to get dependent variable, y all by it self. To solve that equation,
First we write = 4x² then we multiply the both segment with dx so acquirement that
dx (dy/dx) = (4x²) dx
We write with:∫ dy = ∫ (4x²) dx
To solve it, we must know formula of integral that ∫ x square n dx = x square (n+1) divide n+1
So ∫ 4x² = 4/3 x cubic
In fifth video, there is a teacher explain how to solve a linear equation so the students can be understand. So, I will try to solve several equations as the teacher.
1. X – 5 = 3
We can solve a linear equation above with add 5 on each segment, so in left segment just acquirement value from X. So, the equation can be writing with:
X – 5 = 3
X– 5+5 = 3+5
X = 8
Therefore, the solution from X min 5=3 is X = 8.
2. 7 = 4a – 1
Such as number one, we can solve a linear equation above with add 1 on both segment, so in right segment only acquirement value from a. So, the equation can be writing with:
7 = 4a min 1
7+1 = 4a min 1+1
8 = 4a
a = 2
Therefore, the solution from 7 = 4a-1 is a = 2.
3. 2/3 y = 8
We can solve this linear equation such as both the equation above but we don’t add numerically but we must multiply both segments with 3/2 and can acquirement value of y. So, the equation can be writing with:
2/3 y = 8
(2/3 y) times (3/2) = 8 times 3/2
y = 24/2
y = 12
Therefore, the solution from 2/3 y = 8 is y = 12.
Three examples above are very simple, so let’s we solve a linear equation more complex than above. There is several equation and we must solve it.
1. 5 min 2X = 3X+1
Because there is coefficient X on the both segment so we must delete one of them. For example we will delete negative 2X and 1 so we must add 2X and negative 1 on the both segment and acquirement value of X. So, the equation can be writing with:
5─2X+2X─1 = 3X+2X+1─1
4 = 5X
So get value of X, we must multiply the both segment with 1/5 and can be writing that:
4 times 1/5 = 5X times 1/5
X = 4/5
Therefore, the solution from 5─2X = 3X+1 is X = 4/5.
2. 3─5(2m─5) = ─2
To solve the equation above, we must multiply 5 with something on bracket so we get that:
3─10m+25 = ─2
─10m+28 = ─2
─10m = ─30 , to get value of m so we must divide the both segment with ─10 and can be writing with:
─10m/─10 = ─30/─10
m = 3
Therefore, the solution from 3─5(2m─5)= ─2 is m = 3.
3. (1/2y+1/4) = (1/3y+5/4)
We can solve the equation with multiply the both segment with KPK from 2, 3, and 4 but KPK of them is 12. We can write the equation with:
(1/2y+1/4) = (1/3y+5/4)
12(1/2y+1/4) = 12(1/3y+5/4)
6y+3 = 4y+15
2y = 12
y = 6
Therefore, the solution from (1/2y+1/4) = (1/3y+5/4) is y = 6.
4. 0,35a─0,2 = 0,15a+0,1
We can solve the equation with multiply the both segment 100 because number in behind of coma is two number. So, we can write the solution with:
0,35a─0,2 = 0,15a+0,1
100(0,35a─0,2) = 100(0,15a+0,1)
35a─20 = 15a+10
20a = 30
a = 3/2
Therefore, the solution of 0,35a─0,2 = 0,15a+0,1 is a = 3/2.
In sixth video, There is a teacher explains about logarithm. We know that there are many formula bases about logarithm and now I will try explaining about it.
I. log base x A equal B this form have same meaning or equivalent with X square B equal A, so we can write the both form with log base x A equal B equivalent X square b equal A.
Let’s we prove the equation above with multiply the both segment with C so can be writing with:
Log base x A equal B equivalent X square b equal A
C (log base x A)equal BC equivalent (X square b) square c equal A square c
C log base x A equal BC equivalent X square b times c equal A square c
Log base x A square c equal BC equivalent log base x A square equal BC
From explanation above, we can saw that log base A = B equivalent with X square b= A.
II. Log base x A + log base x B = log base x AB
To prove the equation above, we can use that:
If log base x A = k so X square k = A and can be writing with:
Log base x A = k so X square k = A
If log base x B = m so X square m = B and can be writing with:
Log base x B = m so X square m = B
If log base x A/B = n so X square n = A/B
= X square k divide X square m
= X square k minus m
We know that n = k-m so the equation is true. So we get equation that
log base x A+ log base x B = log base x AB
Really, many formulas to logarithm, but in the video just explain two formulas. If multiplication be addition so division is diminution, that statement can be writing with:
Log base x A plus log base x B = log base x AB so log base x A min log base x B = log base x A/B
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