Students from Class A and Class B go to the park at the same time. The walking speed of Class A is 4 kilometers per hour, and that of Class B is 3 kilometers per hour. The school has a car with a speed of 48 kilometers per hour, which can just carry a class of students. In order to make these two classes arrive in the shortest time, what is the walking distance ratio between Class A and Class B students?
2.
There are four teams, A, B, C and D, participating in the football round robin. Every two teams play a game. The winner will get 3 points and the loser will get 0 points. If the game is tied, both teams will get 1 point. Now A, B and C get 7 points, 1 point and 6 points respectively. It is known that A and B are tied, so Ding got () points.
4.
5. Write a two-digit number 62 first, then write the sum of these two numbers at the right end of 62 as 8 to get 628, then write the sum of the last two digits 2 and 8 as 10 to get 628 10, and use the above method to get a 2006-bit integer: 628 1065438+.
6. The wise old man visited Xiaoming's grade, and Xiaoming said that there were more than 100 students in their grade. The old man asked the students to line up in a row of three, and as a result, there was one more person, five more people, two more people, seven more people and one more person. The old man said, I know the number of people in your grade should be ().
7.
8. The sum of100 nonzero natural numbers is equal to 2006, so their greatest common divisor is ().
Second, answering the following questions requires a short process. (Each question 10, ***40)
9. As shown in Figure 4, the diameter Ab of circle O is perpendicular to CD, and AB = 10 cm. Draw an arc AEB with c as the center and CA as the radius. Find the area of crescent-shaped ADBEA (shaded part)?
10. The crawling speed ratio of A, B and C is 8: 6: 5. They crawl in the same direction from the same point along a circle at the same time, and stop crawling when they return to the starting point at the same time for the first time. How many times has Ant A caught up with Ant Otsuichi? (including the end time).
1 1. As shown in Figure 5, ABCD is a rectangle, BC = 6 cm, AB = 10 cm, and AC and BD are diagonal lines. How many cubic centimeters does the shadow part sweep when the solid rotates around CD? (π takes 3. 14)
12. Fold a long line in half, then fold it in half, * * * 10 times to get a bunch of lines. Cut this bundle of wires into 10 with scissors. Q: How many pieces of different lengths can you get?
13, a, b and c are natural numbers with two digits. The digits of A and B are 7 and 5 respectively, and the decimal digit of C is 1. If they satisfy the equation
Ab+c=2005, then a+b+c= ()
14. The length-width ratio of rectangular container is 4: 3: 2. 0.9 yuan per square meter if the container surface is painted with first-class paint. If the second-class paint is used, the cost per square meter can be reduced to 0.4 yuan, and a container can save 6.5 yuan, so the total surface area of the container is () square meters and the volume is () cubic meters.
15. In the figure, ABCD is a rectangle, and E and F are the midpoint of AB and DA respectively.
G is the intersection of BF and DE, and the area of quadrilateral BCDG is 40 square centimeters.
Then the area of ABCD is () square centimeters.
There are 2, 3, 4, 5, 6, 7, 8, 9, 10 and1* *10 natural numbers. Choose seven numbers from this 10 number to form any three of these seven numbers.
From the number 10, you can choose at most () numbers, which are pairwise coprime.
17. As shown in the figure, BD and CF divide the rectangular ABCD into four pieces, red.
The triangle area is 4 square centimeters, and the yellow triangle area is 8 square meters.
Square centimeters, then the area of the green quadrangle is () square centimeters.
18. Terminal A is upstream of Terminal B. The "2005" remote control model starts from Terminal A and sails back and forth between the two terminals. It is known that the speed of a model plane in still water is 200 meters per minute, and the current speed is 40 meters per minute. Twenty minutes after take-off, the model plane is located 960 meters downstream of Terminal A and flies to Terminal B. Then the distance between Pier A and Pier B is () meters.
19, a rectangle, 6 cm long and 4 cm wide. After cutting off the largest square on this rectangle, the maximum circumference of the remaining part is () cm.
20.A and B set out from A and B, which are 520 meters apart, and walked in opposite directions at the same time. A's speed is 30 meters per minute. 10 minutes later, the speed of B is (