English translation

***It's a 15-year-old boy. He used to be a problem boy. But after talking to his mother, he changed his life. He didn't bring any trouble to his mother any more__________________ -Martin's life has become more difficult. His mother has no ability to pay for his education

English translation
New goals

How did I learn to learn English
Last year, I had a hard time in English class. First of all, when the teacher gave a lecture, it was difficult for me to understand her meaning. At first, she spoke too fast, I couldn't understand every word. Later, I realized that it doesn't matter if you don't understand every word. I also dare not speak in class, because I think my classmates may laugh at me. I often can't make complete sentences, I began to watch English TV programs. It helped me a lot. I think more listening practice is one of the secrets of becoming an excellent language learner. I found another difficult thing is English grammar. So I decided to take a lot of grammar notes in every class. Then I began to write some original sentences with the grammar I was learning. The help it brought me was amazing Now I like learning English, and I got an a this term. I left a deep impression on the teacher

The function f (x) defined on (- 1,1) satisfies f (x) - f (y) = f [(X-Y) / (1-xy)]. When x belongs to (- 1,0), f (x) > 0,
If a = f (1 / 5) + F (1 / 11), B = f (0), C = f (the - 2 power of E), then the size relation of a, B, V is

Let x = y = 0, then f (0) - f (0) = f (0) so, f (0) = 0, let x = 0, y = x, then f (0) - f (x) = f (- x), that is, f (- x) = - f (x). So, the function f (x) is odd on (- 1,1), because when x belongs to (- 1,0), f (x) > 0. So, when x belongs to (0,1), f (x) C > A. so, the size relation of a, B, C is a

Calculate the absolute value DX of definite integral ∫ 0 ^ 21-x

∫(0,2) |1-x| dx
=∫(0,1) |1-x| dx+∫(1,2) |1-x| dx
=∫(0,1) (1-x) dx+∫(1,2) (x-1) dx
=(x-x²/2)|(0,1)+(x²/2-x)|(1,2)
=1

Which three identical numbers multiply by two?

Under the cubic root, 2, that is 2 ^ (1 / 3), that is 1 / 3 of 2
This number is about 1.2599210498948731647272106072782

It's better to list the formula to me!
The first reduction is to evaluate (- x) 2 · x-x (- x) 2 + x2 · (- x2) + 1, where x is the reciprocal of the smallest prime number

X is 1 / 2
You wrote Those two are squares, right
It should be this
x3-x3-x4+1=1-x4
Bring in x = 1 / 2
The result is 15 / 16

Use 1,2,3,4,5 to form the natural number without repeating number, from small to large order: 1,2,3,4,5,12 54321. The number 206 is

There are five digits in the composition
There are 5 * 4 = 20 2 digits in the composition
There are 5 * 4 * 3 = 60 three digits
There are 5 * 4 * 3 * 2 = 120 of the four digits
So the 206 th is the smallest 5-digit
twelve thousand three hundred and forty-five

Let the domain of function fn be positive, f (1) = 1, f (M + n) = FM + FN + Mn, and find the analytic expression of FN

Let m = 1, then f (n + 1) = f (1) + F (n) + N, the recurrence formula F (n + 1) - f (n) = 1 + n is obtained,
The final answer can be obtained by superposition

1. When a satisfies what condition, the solution of the equation 3x + a = X-7 about X is negative?
2. If the solution set of inequality 4x-3a ＞ - 1 is the same as that of inequality 3x ＞ 2x + 2, please determine the value of A~

1 .3x+a=x-7
2x=-a-7-7
2.3x＞2x+2
x>2
4x-3a＞-1
x>1/4(3a-1)=2
a=3

What is the center of a triangle

1. The center of gravity is the intersection of three middle lines. The three middle lines of a triangle intersect at a point. The distance from this point to the vertex is twice the distance from it to the midpoint of the opposite side;
2. Perpendicularity: the intersection of the three heights of a triangle;
3. Heart: the intersection of the bisectors of the three interior angles is the abbreviation of the center of the inscribed circle of the triangle;
4. Outer center: the intersection of three vertical lines, which is the abbreviation of the center of circumscribed circle of triangle;
5. Side center: the intersection of an inner bisector and other two outer bisectors. There are three. It is short for the center of the side tangent circle of a triangle
If and only if a triangle is an equilateral triangle, the center of an equilateral triangle consists of four centers

English translation