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1. Try to prove that: if 19 points are placed in a square with one side length, and any three points are not on a line, then there is at least one triangle with these points as its vertex, and its area is not more than 1 / 18 2. Any five integers, will be able to choose three integers, so that their sum is divided by 3
2. According to the principle of drawers, at least one drawer has two numbers. If the drawer has more than two numbers, three drawers will be taken directly from the drawer. Otherwise, the remaining two drawers have three numbers, 3 = 1 + 2 = 3
Mathematics homework, primary school practical problems
The two trains, fast and slow, depart from a and B at the same time and meet six hours later. It is known that the speed ratio of the two trains is 7:3, and the speed of each train can be calculated. (the distance between the two places is 600 km)
Speed sum = 600 / 6 = 100 km / h
Express speed = 100 × 7 / (7 + 3) = 70 km / h
Idle speed = 100-70 = 30 km / h
How many grams of water is needed to dilute 200 grams of 30% sugar water into 10% sugar water?
200×30%÷10%-200
=60÷10%-200
=600-200
=400g
A, B and C each paid the same amount of money to buy a batch of clothes. When they divided the clothes, a took 1100 sets more than C, and B took 700 sets more than C. when clearing the account, a returned 1800 yuan to C in cash, and B should return how much yuan to C in cash?
1100 + 700 = 1800 sets
1800 △ 3 = 600 sets
A took 1100-600 sets more than the average
B took 700-600 sets more than the average
Party B shall refund to Party C 1800 ／ 500 × 100 = 1800 ／ 5 = 360 yuan
The task of building a canal was assigned to Party A and Party B according to the ratio of 5:4. At the completion of the project, team a actually built 690 meters, which is more than 15% of the assigned task. How many meters is the total length of the canal?
The quilt cover factory originally planned to use 2100 meters of cloth to make large quilt covers, but later changed to make small quilt covers, so that each quilt cover uses 20% less cloth and 60 more small quilt covers?
The task of building a canal is assigned to Party A and Party B according to the ratio of 5:4. When the project is completed, team a has actually built 690 meters, which is more than 15% of the assigned task. What is the total length of the canal? A's original plan is: 690 / (1 + 15%) = 600. The total length is: 600 / 5 * (4 + 5) = 1080 meters
1. It takes 10 hours for Party A to make a batch of parts alone. Party B can only make five sixths of this batch of parts in the same time. Now after Party A and Party B work together for three hours, the rest will be made by Party A. how many more hours?
2. A ship, sailing from port a to port B, travels 96 kilometers in the first three hours. After that, it travels one and six times as much as before. It reaches port B in another two hours. Find out the average speed of the ship
Note: list and answer, and why
1, the efficiency of a is 1 / 10, the efficiency of B is 1 / 10 * 5 / 6 = 1 / 12
Then there is 1 - (1 / 10 + 1 / 12) * 3 = 9 / 20, which is the rest
So the time for a to do is 9 / 20 / (1 / 10) = 4.5 hours
2, distance = 96 + 96 / 3 * 7 / 6 * 2 = 170 and 2 / 3km
Average speed = distance / time = 170 2 / 3 divided by 5 = 34 2 / 15 km / h
The income ratio of Zhang Jia and Li Jia this month is 5:4. When Zhang Jia spent 1200 yuan and Li Jia lost 1000 yuan, the remaining money ratio of the two families is 13:10. How much is the income of Zhang Jia and Li Jia this month?
There are 200 chickens and rabbits. The number of feet of chickens is 160 more than that of rabbits. How many chickens and rabbits are there respectively?
Let's take Zhangjia as the center to find a breakthrough. Let's suppose Zhangjia's monthly income is x yuan. According to "the income ratio of Zhangjia and Lijia is 5:4", we know that Lijia's monthly income is 4 / 5x yuan. After both sides have spent, Lijia's remaining income is (4 / 5x-1000) yuan and Zhangjia's remaining income is (x-1200) yuan, We can know that the money left by the Li family is 10 / 13 of the money left by the Zhang family
Set Zhang's income this month x yuan
4/5x-1000=10/13（x-1200）
4/5x-1000=10/13x-12000/13
4/5x-10/13x=1000-12000/13
2/65x=1000/13
x=2500
So Li's monthly income: 2500 × 4 / 5 = 2000 yuan
A: Zhang's income this month is 2500 yuan, and Li's income this month is 2000 yuan
two
Suppose it's all chickens
There are 400 chicken feet and 0 rabbit feet
A chicken has 400 more feet than a rabbit
Only 160 more in fact
The difference was 400-160 = 240,
After each chicken was replaced with a rabbit, the difference was 4 + 2 = 6
240 △ 6 = 40, which is the number of rabbits
The number of chickens is 200-40 = 160
With X chickens, the number of rabbits is 200-x
2X-4(200-X）=160
6X-800=160
X=160
Therefore, the number of rabbits is 200-160 = 40
Analysis: here the number of chickens is set to x, and because the total number of chickens and rabbits is 200, the number of rabbits is the total number of 200 minus the number of chickens X
And 2x represents the number of chicken feet. Because the chicken has two feet. Similarly, we know that the number of rabbits is 200-x, because rabbits have four feet, so the number of rabbit feet is 4 (200-x)
According to the title, the number of feet of chicken is 160 more than that of rabbit, and the equation 2X-4 (200-x) = 160 is obtained
Xiaohong and Xiaodong can just circle the trunk of a tree 10 times with a 12.56 meter long rope. How many square meters is the cross section of the trunk of this tree?
12.56 ﹣ 10 ﹣ 2 ﹣ 3.14, = 1.256 ﹣ 2 ﹣ 3.14, = 0.2 (m), 3.14 × 0.22, = 3.14 × 0.04, = 0.1256 (M2); a: the cross section of the trunk of this tree is about 0.1256 m2
There is a round piece of iron. A square is dug out in the middle. The area of the square is 5 square centimeters. The radius of the circle is just the length of the diagonal of the square. The area of the circle is larger than that of the square______ Square centimeter
14 × 5 △ 2-5, = 7.85-5, = 2.85 square centimeter
There is a water cup in the sink. The original water depth in the water cup is 6cm, the height of the water cup is 8cm, and the inner diameter of the water cup is 16cm. When the 800 cubic centimeter stone is put into the water cup, the water in the water cup will overflow into the sink. How many milliliters of water will flow into the sink?
Volume of water cup = 16.68 / 2 * (16.68 / 3) *
Water volume in water cup = 3.14 * (16 / 2) * (16 / 2) * 6 = 1205.76 ml
The volume of water flowing into the tank
=Volume of water in water cup + volume of stone - volume of water cup
=1205.76+800-1607.68
=398.08 ml
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