The area of a rectangle is 6 times of the root sign 2 square centimeter. One side of the rectangle is 2 / 1 of the root sign 3 square centimeter. What is the length of the other side

The area of a rectangle is 6 times of the root sign 2 square centimeter. One side of the rectangle is 2 / 1 of the root sign 3 square centimeter. What is the length of the other side

Four times root six. Also, please note that the side length is centimeter

It is proved that the sum of the product of four consecutive integers plus one is just the square of an odd number

It is proved that the sum of the product of four continuous natural numbers plus one is the square of an odd number
Let four numbers be a, a + 1, a + 2 and a + 3 respectively
Because a * (a + 1) (a + 2) (a + 3) + 1
=a(a+3)(a+2)(a+1)+1
=(a^+3a)(a^+3a+2)+1
=(a^+3a)^+2(a^+3a)+1
=(a^+3a+1)^
So the sum of the product of four continuous natural numbers plus one is the square of a number
And because a ^ + 3A + 1 = a * (a + 3) + 1 and a * (a + 3) is even,
So a ^ + 3A + 1 is odd
So the sum of the product of four continuous natural numbers plus one is the square of an odd number

There is a 2-meter-long lever with a 24 N object at the left end and a 40 n object at the right end. To balance the lever, how far should the fulcrum be from the left end? If you add 8 N to each end of the object, which side should the fulcrum move to balance? How much?

Let the distance between the fulcrum and the left end be L1, then L2 = l-l1 = 2m-l1, from the lever balance condition, f1l1 = f2l2, that is: 24N × L1 = 40n × (2m-l1), then L1 = 1.25m; from the lever balance condition, F1 'L1' = F2 'L2', that is: (24N + 8N) × L1 '= (40n + 8N) × (2m-l1'), then L1 '= 1.2m

For a circle and a square of equal circumference, the area of the circle must be larger than that of the square______ (judge right or wrong)

Suppose that the circumference of both the circle and the square is 16, then the radius of the circle is 16 △ π △ 2 = 8 π, the area is: π × (8 π) 2 = 64 π≈ 20.38, the side length of the square is 16 △ 4 = 4, and the area is 4 × 4 = 16; so the area of the circle is larger than that of the square, so the answer is: correct

Prove that 11.1211.1 is also a composite number
"." stands for n ones

The same proof as the previous question
11.1211.1
=11... 100... 0 + 11... 1 (n + 1 ones, n zeros)
=11...1×100...0+11...1
=11... 1 × 100... 01 (n + 1 1 n-1 0)
It's a sum

School name score
1、 Fill in the blanks
1、（ ）÷25 =（ ）×38 =111 ÷（ ）=3
2. 2.05kg = () kg () g = () g
3. 15% of a is equal to 25% of B, then B is () of a, and a is () more than B
4. Mr. Li's monthly salary after retirement is 1780 yuan. According to the regulations, the part over 800 yuan has to pay 5% personal income adjustment tax. Mr. Li's actual salary is () yuan
5. The length of a wire is 13 meters plus 13 meters. The wire is () meters long
6. The bottom area and height of a cylinder and a cone are equal. Given that the volume of a cone is 7.8 cubic meters, then the volume of a cylinder is ()
7. It is only required to indicate the quantity, and it is better to draw a statistical chart
8. Xiao Ming bought a bottle of toothpaste with a net weight of 45 cubic centimeters. The diameter of the circular exit of the toothpaste is 6 mm. He brushes his teeth once in the morning and once in the evening, and the length of the toothpaste extruded each time is about 20 mm. It is estimated that this bottle of toothpaste can last () days
9. A school number each student, set the end with 1 for boys and 2 for girls: 0331231 means "No.23 of class 1, grade 3, who entered in 2003, is a boy". Then, 0521162 means that the student is No.23 of class () of grade () who entered in () and is ()
10. Here is a statistical chart of a patient's temperature record
① The nurse takes the patient's temperature every () hours
② The maximum temperature of the patient is () degrees centigrade, and the minimum temperature is () degrees centigrade
③ The temperature at 6 pm on June 2 is ()
④ The body temperature dropped the fastest in () time and was stable in () time
）
1－(16 ＋17 )×2 33.6÷8＋33.6÷87 1.25×615 ＋3.8÷45
24÷(13 ＋34 －16 ) 17115 ÷16 4.2×0.36＋42×6.4%
3. Find the unknown X. (6 points)
48÷13 －0.4X=4 0.5X＋2X=1115 0.3:X=411
4-column calculation. (4 points)
(1) 25% of a number is equal to the sum of 14 and 16
(2) 14% of number a is equal to 30% of number B. number a is 48. What's number B?
5. Complete the following questions as required. (6 points)
(1) Turn 213:1.5 into the simplest integer ratio (2) decompose 714 into prime factor
(3) Find the least common multiple of 12, 30 and 36
6. It is known that the area of a right triangle is 5 square centimeters, so we can find the area of a circle
5、 On the right is a statistical chart of the number of days required for three persons to complete a project alone. (6 points)
(1) How many days can party A and Party B cooperate in this project?
(2) How many more days will it take for Party A to do the first six days and Party C to do the rest of the work?
(8 points for 5 questions, 5 points for each other, 28 points in total)
1. To build a canal, we have built a total length of 37 kilometers. Now it is 3 kilometers away from the midpoint. How long is the water?
2. Li Qiang read a story book. On the first day, he read 25 pages. On the second day, he read 14 pages of the book. There are 62 pages left. So what page should Li Qiang start reading on the third day?
3. Look at the diagram
4. The distance between a and B is 648 kilometers. A and B travel from two places at the same time. A travels 80 kilometers per hour. A's speed is 45 times that of B. how many hours do they meet?
5. A family of three adults and four children travel to a certain place. The charge standard of travel agency a is: if you buy four full tickets, the rest of you will get half price discount; the charge standard of travel agency B is: family travel is group ticket, 75% discount of the original price. The original price of both travel agencies is 100 yuan per person
(1) Which travel agency does the family choose cost less?
If you join their family tour, which travel agency do you suggest you should go to?
(1) The ratio of a number

6、 Use your math knowledge to solve math problems
1. 37 + 3 = 40m 40x2 = 80m
2.（62+25）*（1-14%）=101
101X14%=11 11+25=36

If the height of a cylinder is increased by 3 cm, the side area will be increased by 18.84 square cm. What is the bottom area of the cylinder______ ．

The radius of this cylinder is: 18.84 △ 3 △ 3.14 △ 2 = 1 (CM), the bottom area of this cylinder is: 3.14 × 12 = 3.14 (square cm); answer: the bottom area of this cylinder is 3.14 square cm. So the answer is: 3.14 square cm

What's the way to see the past with superluminal speed?
Well, if there are two beams of light shooting at each other, then the relative speed of these two beams is twice the speed of light. There is also superluminal speed. How can we go back to the past? Space time machine? It's impossible. In a word, no matter how fast the speed is, we won't go back to the past or reach the future. The reason is a bit troublesome, but it's right

It's not to go back to the past, but to see the past. For example, if you were doing something a day ago, now you are chasing at the speed of super light to catch up with the light you emitted when you did that thing a day ago, you can see the scene of a day ago. So, going back to the past, you just catch up with the light you emitted from the past

A physics problem about the balance of two forces,
In fact, Xiaohong's experiment is not very rigorous, because the small card also has gravity. Does this have an impact on the experimental conclusion? Why?
Hook code, small card
It's a very common device to explore the balance of two forces

If suspended in the air, gravity in the vertical direction will make the force in the horizontal direction not in a straight line, making the experiment into a three force balance. Horizontally placed on the table, because the paper is too thin, using the spring force measuring time will make the paper suspended, affecting the experiment
Here's the idea

The side length of a square is increased by 5 cm and its area is increased by 185 square cm. Find the side length of the original square

Let the side length of the original square be x, then the side length of the current square is x + 5
Then x * x + 185 = (x + 5) ^ 2
x=16
The side length of the original square is 16cm