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On the number axis, an ant starts from the origin and crawls 1 unit length to the right for the first time, then 2 units to the left for the second time, 3 units to the right for the third time, and 4 units to the left for the fourth time, Question: (1) where is the last position of the ant on the number axis? (2) what is the sum of the numbers corresponding to the positions reached after each crawl? (3) how long has the ant crawled
It's OK to have the concept of the number axis. With mathematical induction, the first time 1, the second time, 1-2 = - 1, the third time - 1 + 3 = 2, the fourth time, 2-4 = - 2, the fifth time - 2 + 5 = 3 2009 / 2 = 1004 So at position 1005, 1 + (- 1) + 2 + (- 2) + +1005 = 1005 total distance = 1 + 2 + 3 + +2009=（1...
Paint the surface of a cube with 8cm edges, and then cut them into small cubes with edges of 2cm. What is the number of small cubes with no paint on any surface
(8 / 2) * (8 / 2) * (8 / 2) = 64 (total number of small cubes)
(8 / 2) * (8 / 2) = 16, 16 * 2 = 32 (4 + 4 + 2 + 2) * 2 = 24
32 + 24 = 56 (number of small cubes with painted surface)
64-56 = 8 (number of small cubes without paint surface)
If you don't understand the steps, ask me. The answer must be right
|-0.2 | - (- 3) - (+ 8) | - | - 8-2 + 10 | should have a complete process PS: first change the minus sign into a plus sign! 5.75 - (- 3 / 8) + (- 0.5) - (- 5 / 6) + 4 2 / 3-1 / 8 (42 / 3 is 4 and 2 / 3) If | a | a | = 3, | B | = 1, | C = 5, and | a + B | = a + B, | a + C | = - (a + C), calculate the value of A-B + C |1 / 2-1 | + | 1 / 3-1 / 2 | + | 1 / 4-1 / 3 +. + | 1 / 2010-1 / 2009 |. To get the number (formula)
|-PS: we must change the minus sign into a plus sign first! | - 0.2 | - (+ 8) | - (- 3) - (+ 8) | - 8-2 + 10 | = 0.2-11-0 = -10.85.75 - (- 3 / 8) + (- 0.5) - (- 5 / 6) + 4 4 4 (4): 4.4-11-0 = -10.85.75 - (- 3 / 8) + (- 0.5) - (- 5 / 6) + 4 4 4 4) + (4.5) - (- 5 / 6) + 4 4 4 + 4) + 4.5.5) - (- 5 / 6) + 4 + 4 + 4 + 4 + 4 + 4.5.5) - (- 5 / 6) + 4 + 4 + 4 + 4 + 4.5.5.6 2 / 3-1 / 8 (4 2 / 3 is 4 and 2 / 3)
Help to do a math problem in junior high school According to the demand, a circular paperboard needs to be cut into several sectors by several times. The operation is as follows: in the first cutting, the circular paperboard is divided into four sectors; in the second cutting, one of the fan-shaped surfaces obtained last time is equally divided into four sectors, and then it is carried out according to the method of the second cutting. (1) calculate the total number of sectors after the nth cutting (2) After the 2003 operation, how many fan-shaped cardboard can the original circular cardboard be cut into?
1. (3N + 1)
2. 2003 * 3 + 1 = 6010 (PCS)
(x2 + MX + 8) (x2-3x + n) after opening, what is the value of M + n? (the number next to X is the index, meaning the third power of the sum of squares of x)
The original formula = x ^ 4-3x? + NX? + MX? - 3mx? + mnx + 8x? - 24x + 8N
∵ this equation is opened without terms of X ∵ and X ᙽ 3
∴-3+m=0 8-3m+n=0
∴m=3 n=1
∴m+n=3+1=4
There are 1530t class a goods and 1150t class B goods transported by a certain company in the railway station. Now it is planned to use 50 sections of A, It is known that the freight of each type a carriage is 5000 yuan, and that of each type B carriage is 8000 yuan. 35t of class a goods and 15t of type B goods can be filled with a type a carriage, a type goods of 25t and B goods of 35t can be filled with a B type carriage. According to this requirement, a, B what kind of scheme are there for the number of cars? Please design it and explain which one has the least freight? Let's talk about the method!
If the number of A-type cargo box is x, then the number of B-type cargo box is (50-x). 35x + 25 (50-x) ≥ 153015x + 35 (50-x) ≥ 1150, the solution is: 28 ≤ x ≤ 30. ∵ x is a positive integer,
The purchase price of a product is 3000 yuan, and the price is 4500 yuan. The store requires that the profit of the product is not less than 5%, and the minimum discount is () A. 20% off B. 70% off C. 5% off D. 5% off
The discount for this product is X
From the meaning of the title: 4500 × x
10-3000=0.05×3000
X = 7
Therefore, B
It's from Beijing Normal University Press! The first volume of mathematics book, 242 pages of 12.13.14.15.16 questions (all using equations) No books, 12. There is a cube billet with edge length of 0.6m. If you want to forge it into a rectangular steel with a cross section of 0.008 m, how high is the steel forged? 13. A company sold 12200 pairs of shoes a and B last year. This year, the sales volume of type a shoes was 6% more than that of last year, and the sales volume of type B shoes decreased by 5% compared with last year. The total sales volume of two kinds of shoes increased by 50 pairs. How many pairs of shoes were sold last year? 14. There is a bamboo pole and a rope. The rope is 0.5 meters longer than the bamboo pole. After the rope is folded in half, it is 0.5 meters shorter than the bamboo pole. How many meters are the length of this bamboo pole and this rope? 15. During the Spring Festival, Xiao Ming and Xiao Ying went to see Mr. Li, who gave them sugar in a special way. Mr. Li first took Xiaoming a piece, then gave him one seventh of the sugar box, then gave Xiaoying two pieces, and then gave her the remaining one seventh of the sugar box? 16. It takes 26 seconds for the train to pass through a 256 meter long tunnel (i.e. from the front entrance to the rear exit), and the train passes through the 96 meter long tunnel in 16 seconds. Calculate the length of the train
12. 0.6×0.6×0.6÷0.008=27
13. Suppose a sold x pairs last year and B sold 12200-x pairs
X(1+6%)+(12200-X)(1-5%)=12200+50
X=6000
14. Set rope length x and bamboo pole length x-0.5
X÷2+0.5=X-0.5
X=2
15. Let x
1 + (X - 1) × 1/7 = 2 + （{X - [1 + (X - 1) × 1/7] -2 } × 1/7）
X= 36
16. Let the length be x and the speed a
26X=256+A
16X=96+A
10X=160
X=16
I hope LZ can understand how it came out
A math problem in junior high school Xiaoming and Xiaogang set out from a to B according to the same route. It is known that Xiao Ming's speed is 80 meters per minute, and Xiao Gang walks 120 meters per minute. (1) if Xiao Ming starts five minutes later, Xiao Gang starts at the same time, so they both arrive at place B. the distance between a and B remains the same. (2) the distance between the two places remains unchanged, and if they start at the same time, Xiaogang will immediately go back to pick up Xiaoming after arriving at place B, Ask them when they will meet
(1) If the time from point a to point B is t, then 80 * (T + 5) = 120 * t, then t = 10 minutes, the distance is equal to 10 * 120 = 1200 meters. (2) when Xiaogang arrives at point B, Xiaoming has already walked 800 meters, and there is still 400 meters left
Fill a 40 cm diameter and 60 cm high cylindrical bucket full of water into another cylindrical bucket with a radius of 30 cm. What is the height of the water at this time?
Let this be the height X
20*20*60=30*30*x
24000=900x
x=3/80
RELATED INFORMATIONS
- 1. The Beijing Tianjin Intercity Railway will be put into operation on August 1, 2008. It is estimated that the one-way direct operation time of high-speed train between Beijing and Tianjin will be half an hour. In a test run, the running time of the test train from Beijing to Tianjin is 6 minutes longer than the expected time, and the travel time from Tianjin to Beijing is the same as the expected time The average driving speed is 40 kilometers per hour. What is the average speed from Beijing to Tianjin during the test run?
- 2. The answer to the latest test paper of compulsory education curriculum standard experimental textbook published by people's Education Press I am a teacher, I want to let students read early at the end of the term!
- 3. If the rational number a is greater than the rational number B, then () A. The absolute value of a is greater than that of B B. The absolute value of a is less than that of B C. The opposite number of a is greater than that of B D. The opposite number of a is less than that of B
- 4. 2005x－2007y＝2003 2004x－2006y＝2002 x. How much y
- 5. Junior high school mathematics book Volume 1, page 24 exercise (in the inquiry below) 4 problem formula Plus answer!
- 6. Exploration on the expansion of 94 pages in the experimental textbook of compulsory education curriculum standard
- 7. Why is Pythagorean theorem the first mathematical theorem discovered by human beings? When I studied the Pythagorean theorem, I felt that the discovery of this theorem was not simple. Why do many countries say that the Pythagorean theorem is the earliest mathematical theorem they know. Is this accidental or
- 8. Chapter nine arithmetic problems The water surface of a pool is 10 feet square. In the center, there is a reed which is one foot higher than the water surface. If you pull it vertically to the bank, its top just reaches the surface of the bank. Ask the water depth and the length of the reed
- 9. Zuchongzhi also wrote a book called‘
- 10. Find some English stories. Do me a favor. On Wednesday, I have to Hope is some fairy tales in English
- 11. 1.（10-11）×（11-12）×（12-13）×… ×（99-100）=_____ . 2. - 1 - (- 5 and 1 / 2) × (+ 3 / 11) [main process] 3.2 / 3 × (- 1 / 2) - (- 1 and 1 / 2) × (- 1 and 1 / 3) [main process] 4. Simple calculation: 15 × (- 3 / 5 + 1 / 3) - 24 × (5 / 12-7 / 8) [main process] 5. Using a simple method to calculate: - 8 × (- 13 and 7 / 12) - (- 5) × (- 13 and 7 / 12) + 4 × (- 13 and 7 / 12) [main process] 6. Two kinds of operations are defined as follows: + 0means "+ there is a circle outside" × "means" × there is a circle outside ". For any two rational numbers a, B has: a + ○ B = a + B-2, a ×0b = a · B-2. Find the value of - 4 × (6 + ○ 8)
- 12. According to the book classification of Xinhua Bookstore, understand the classification of society
- 13. Xiaoming and Xiaogang go to the library to borrow books. Xiaoming goes once every nine days and Xiaogang goes once every six days. If they meet in the library on February 2, what day will they meet again in the library?
- 14. On June 1, I went to Xinhua Bookstore to buy a book. Walking into the bookstore, it was like walking into the sea of books. I crowded into the crowd and bought a copy of "youth composition guide". I was very happy. At this time, a young pioneer ran over and saw that he was very anxious. He also wanted to buy the book, but the odd number had been sold out. I gave my book to him, and the sales assistant and aunt saw this scene, Laugh. (enlarge it into a composition of more than 400 words) On June 1, I went to Xinhua Bookstore to buy a book. Walking into the bookstore, it was like walking into a sea of books. I crowded into the crowd and bought a copy of "youth composition guide". I was very happy. At this time, a young pioneer ran over and saw that he was very anxious. He wanted to buy the book, but the book was sold out. I gave my book to him, and the shop assistant and aunt saw this scene, Laugh. (according to the above story content, please expand reasonable imagination, and write things in detail. If you can't write more than 400 words, you can also make an outline)!
- 15. Use the solution of one variable linear equation According to the plan, one third of a highway can be completed in 18 days. If the work efficiency is improved by one fifth after four days of work, how many days can we finish half of it?
- 16. It can only have power, bracket, fraction, decimal, positive and negative numbers~ No letters! Only 25 questions are enough! There are addition, subtraction, multiplication and division~
- 17. Stores a and B sell the same goods at the same price, and they offer different preferential schemes. The goods purchased at point a are charged at 90% of the original price. After purchasing 100 yuan of goods in store B, the goods purchased again are charged at 80% of the original price. How can customers choose the shop to get more preferential treatment?
- 18. Mother bought 2 kg of apple and 2 kg of pear, and paid 52 yuan in total. The unit price of pear is 14 yuan / kg. How much is the apple per kilogram? Mr. Li bought two sets of books and paid a total of 22 yuan. The number of copies of the two sets of books was the same, and the unit prices were 2.5 yuan / copy and 3 yuan / copy, respectively. How many copies of each series were there? All of them were solved by solving the equation
- 19. If mother goes to the fruit store to buy apples, if it costs 4.5 yuan per kilogram, she can buy 4 kilograms. If her mother costs 5 yuan per kilogram of apples, how many kilograms can she buy? Answer in two ways
- 20. Xiao Ming paid 20.1 yuan for 3 kg pear and 3 kg apple, while Xiao Fang paid 15.1 yuan for 1 kg pear and 3 kg apple?