Set a = {x | x ^ 2 - [2A + (a ^ 2 + 1)] x + 2A (a ^ 2 + 1) ≤ 0}, B = {x | (X-2) [x - (3a + 1)] ≤ 0}, when the real number a is a value, a is included in B

Set a = {x | x ^ 2 - [2A + (a ^ 2 + 1)] x + 2A (a ^ 2 + 1) ≤ 0}, B = {x | (X-2) [x - (3a + 1)] ≤ 0}, when the real number a is a value, a is included in B

For any real number a, since 2A

Let the fixed point P in the complex plane correspond to the complex number P = a + bi, and the moving point Z correspond to the complex number Z = x + Yi, and all of ε belong to R ^ +, satisfying the inequality | z-p|

Because z-p. is the distance from Z to P. that is, P is the center of the circle and E is the radius of the circle
Not including the circle, of course

Find the rule 1 49 [
Find the rule
☆= □＝

16 36

How to prove that there are infinitely many prime numbers?
There are infinitely many prime numbers, which is a well-known proposition of disprovement. However, how to prove it?

Suppose that the prime number is finite, suppose that there are only finite n prime numbers, and the largest prime number is p
Let Q be the product of all prime numbers plus 1, then q = (2 * 3 * 5 *...) *P) + 1 is not a prime
Then, Q can be divided into 2, 3 Integral division of numbers in, P
And Q is determined by these two, three Any division of P will result in 1, which contradicts it
So prime numbers are infinite
If Q can be divided by a number less than Q, there are two cases: prime numbers less than Q or composite numbers less than Q. prime numbers less than Q are also included in 2,3,5 If it can be divided by a composite number m less than Q, then the composite number m can be divided into two smaller prime numbers. Let m = s * t, then s

Sin α - sin β = one third of cos α + cos β = one half of COS (α + β)

sinα-sinβ=1/3 (1)cosα+cosβ=1/2 (2)(1)²+(2)²sin²α+sin²β-2sinαsinβ+cos²α+cos²β+cosαcosβ=1/9+1/42+2(cosαcosβ-sinαsinβ)=13/362+2cos(α+β)=13/36cos(α+β)=-59...

2011 primary school sixth grade winter vacation homework mathematics problem solving
Practical questions:
1. When a batch of parts is processed, the ratio of the number of completed parts to the total number of parts is 1:3. If another 15 parts are processed, the number of completed parts is the same as the number of remaining parts. How many parts are there in this batch?
2. Mr. Wang used some money to buy prizes for his students. If he bought only 8 pens, he could buy 16 exercise books. If he bought 5 pens, how many exercise books could he buy with the rest of the money?
3. Party A and Party B each bring a bundle of telephone lines to install the telephone for the user. After they come back, they communicate with each other about their work
A said, "I used half of a bundle and there are 50 meters left."
B said, "I used 25 meters more than you, but only 40% of the bundle is left."
Please calculate how many meters of telephone line each of them has according to their conversation?
4. A batch of rice was transported to the disaster area. Four trucks were used to transport two fifths of this batch of rice. On average, what percentage of this batch of rice was transported by each truck? How many trucks will the rest of the rice be transported?
Fill in the blanks:
1. The volume of water formed by ice has been reduced by one eleventh, and () is regarded as the unit of "1"
2. Storybooks are one fifth more than science and technology books. Storybooks are ()% of science and technology books, and science and technology books are () less than storybooks
640 ml = () l (filling fraction) = () min when 1 / 4

1、 1/2-1/4=1/4
15÷1/4=60
There are 60 parts in this batch
2. 8:16 = 1:2 a pen is equivalent to two notebooks
5x2 = 10 5 pens is equivalent to 10 notebooks
16-10 = 6. The rest of Mr. Wang's money can buy 6 exercise books
3. A said, "I used half of a bundle, and there are 50 meters left." a took 50x2 = 100 meters
B said: "I used 25 meters more than you. B used 50 + 25 = 75 meters
But only 40% of the bundle is left. "B used 1-40% = 60%
B took 75 ／ 60% = 125 meters
4、2/5÷4=2/20=1/10
On average, one tenth of this batch of rice is transported by each truck
1-2/5=3/5
3/5÷1/10=6
The rest of the rice has to be transported by six trucks
1. The volume of water formed by ice has been reduced by one eleventh, which is the unit of "1"
2. Storybooks are one fifth more than science and technology books. Storybooks are (120)%, and science and technology books are (one sixth) less than storybooks
3.640 ml = (16 / 25) l (filling fraction) = (75) min when 1 / 4

1 + 1 + 1 + 3 + 100 + 200-134 + 456789 - | =?

1+1+1+3+100+200-134+456789=456960

Integers include natural numbers,

Yes!
The range of integers is larger than that of natural numbers

3, 4, 7, 12, 19, 31, (), 81
1 ,1 ,2 ,3 ,5 ,（ ） ,13 ,（ ）,34.
1/3 ,4/3 ,7/3 ,（ ） ,（ ）,（ ）.
16 ,8 ,14 ,7 ,12 ,6 ,（ ）,（ ）...

1 , 1 , 2 , 3 , 5 , （8 ） ,13 ,（ 21 ）, 34.
1/3 ,4/3 ,7/3 ,（10/3 ） ,（ 13/3 ）,（16/3 ）.
16 ,8 ,14 ,7 ,12 ,6 ,（ 10 ）,（ 5）...

The sum of four consecutive natural numbers is a three digit number between 400 and 440, and the sum can be divisible by 9. It is necessary to find the four consecutive natural numbers______ 、______ 、______ 、______ ．

According to the above analysis, only 414 numbers can be divided by 9 between 400 and 440. Let the minimum natural number be X. according to the meaning of the question, we get x + X + 1 + X + 2 + X + 3 = 414, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 4x + 6 = 414, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 4x = 414-6, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 408 △ 4, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 102, x + 1 = 102 + 1 = 103, x + 2 = 102 + 2 = 104, x + 3 = 102 + 3 = 105. A: these four continuous natural numbers are 102103104105. So the answer is: 102103104105