A quadrilateral whose four corners are right angles is a rectangle.
A quadrilateral with two pairs of right angles is a rectangle.
6. An isosceles right triangle is an isosceles triangle.
7. A figure composed of four line segments must be quadrilateral.
8. The opposite sides of the trapezoid are parallel.
9. Circles and squares with equal perimeters have large areas.
10. The base area and height of a cuboid and a cylinder are equal, and their volumes are equal.
1 1. Any sector can be rolled into a cone.
12. The volume of a cone is 1/3 of that of a cylinder.
13. The line segment passing through the center of the circle is the diameter of the circle.
14. The circumference of the circle is increased by 2? Cm, the radius of the circle increased by 1 cm.
15. The radius of the bottom surface of the cylinder is enlarged by 3 times and the volume is enlarged by 3 times.
Chapter V Application Problems
Section 1 engineering problems
I. Typical examples
1. A project can be completed by team A alone for 20 days. After team A has done it for 8 days, the rest of the work will be completed by team B alone due to other tasks 15 days. Q: How many days does it take for Group B to finish the work alone?
2. A clothing factory wants to produce a batch of clothes. It was originally planned to produce 300 pieces of clothing every day and complete the task in 60 days. In fact, the number of clothes produced every day is 20% more than originally planned. How many days did it actually take to complete the task of making these clothes?
3. The pool has two drainage pipes A and B and a water inlet pipe C. If the pipes A and C are opened at the same time, the pool can be emptied in 20 hours; If tube B and tube C are opened at the same time, the full pool can be emptied in 30 hours; If pipe C is opened separately, the empty pool can be filled within 60 hours. If pipes A, B and C are opened at the same time, how many hours will it take to empty the pool?
4. Three apprentices cooperate to contract a project, which can be completed in eight days. As we all know, it takes the same number of days for a master to do it alone as it takes for two apprentices to cooperate. The number of days required for the cooperation between master and apprentice A is four times that required for disciple B to complete the project alone. Q: How many days does it take for two apprentices to finish this project alone?
A reservoir, with 4 cubic meters of water flowing in every minute. If you turn on five faucets, the pool water will be emptied after two and a half hours; If you turn on 8 faucets, 1 half an hour, the pool water will be emptied. Now turn on the 13 faucet and ask how long it will take to drain the water.
Second, consolidate the practice.
1.Team A and Team B can complete a project in 60 days. If Team A and Team B cooperate in 24 days, Team B can complete the remaining project in 48 days ... Q: How many days does it take for Team A and Team B to complete this project alone?
It takes 20 days for two typists, A and B, to finish a manuscript. After playing together for eight days, B will type the rest of the manuscript alone. If it takes 28 days for A to type this manuscript alone, how many days will it take for B to finish it?
There are many machine parts. It takes 17 days for Party A to do it alone, which is more than 1 day for Party B to do it alone. After 8 days of cooperation, the remaining 420 parts were made by A alone. How many parts is a * * *? A * * * for a few days?
4. The swimming pool is equipped with two water pipes, A and B. Both water pipes are opened at the same time, and the swimming pool is filled 12 hours. If tube A is on for 5 hours and tube B is on for 6 hours, and only the pool is filled, how many hours will it take to fill the pool separately?
5. A project can be completed by Party A alone for 63 days and then by Party B alone for 28 days; If both parties cooperate, it will take 48 days to complete. Now Party A does it alone for 42 days, and then Party B does it alone. How many more days does Party B need to do?
6. Party A needs 65,438+00 hours, Party B needs 65,438+02 hours and Party C needs 65,438+05 hours to move the goods in the warehouse. There are the same warehouses A and B, A starts to move goods in warehouses A and B at the same time, C starts to help A move, and then turns to help B move halfway. Finally, the goods in the two warehouses move at the same time. How long does it take C to help A and B respectively?
Section 2 Travel Issues
Typical example:
1. A car travels from A to B at a speed of 525m per minute, and it is expected to arrive in 40 minutes. However, on the way, the car broke down and was repaired in 5 minutes. If you still need to arrive within the scheduled time, how much faster is the remaining distance per minute?
2. Two cars, A and B, travel in opposite directions from A and B respectively, and meet on the way, 70 kilometers away from A when they meet. After meeting, continue to advance at the original speed, return immediately after reaching the destination, and meet for the second time on the way. At this time, the meeting place is 50 kilometers away from A, and it is known that the time from the first meeting to the second meeting is 4 hours. What is the speed of the two cars?
3. A ship goes back and forth between A and B, sailing smoothly from A to B; It is known that the speed of a ship in still water is 20 kilometers per hour, and it takes 6 hours to get from A to B. The time from B to A is 1.5 times that of A to B. Find the current speed.
The swimming pool is 50 meters long. Party A and Party B start from both ends of the swimming pool, swim to the other end and return immediately. So they swam back and forth for two minutes. It is known that Party A swims 3 meters per second and Party B swims 2 meters per second. How many times have they met in the two minutes since they left?
The circumference of the track of the sports ground is 400 meters. Two athletes, A and B, started from the same direction at the same time. A runs 375 meters per minute, and B runs 325 meters per minute. A How many seconds does it take to surpass Otsuichi Week?
6. A pedestrian and a cyclist walk in the same direction along the same bus route. Cyclists are three times faster than pedestrians. Every 20 minutes, a bus passes pedestrians, and every 40 minutes, a bus passes cyclists. If the bus leaves the departure station at the same time, then every time,
Second, consolidate the exercises:
1.A train has traveled from place A to place B for 2 hours, and it is still 45 kilometers away from place B. It is known that it can complete the journey in 4 hours. How far is the distance between the two places?
Xiaoming walked from home to the King's Family Education Center at a speed of 50 meters per minute for 2 minutes. If so, he will be 8 minutes late for class. Later, he quickened his pace, walking 10 meters more every minute than before, and as a result, he arrived five minutes earlier. Ask for the distance from Xiaoming's home to the king's tutor center?
There is a 400-meter-long circular runway. Party A and Party B run in opposite directions at the same time from a certain point, and meet in 1 minute. If two people run in the same direction, 10 minutes later, and it is known that A is faster than B, find the speed of A and B. ..
On the ascending and descending tracks, two trains face each other. A conductor is 235 meters long, traveling 25 meters per second, and B conductor is 2 15 meters, traveling 20 meters per second. How many seconds does it take for two trains to meet and leave?
5. Captain A180m, traveling 25m per second, and captain B, 385m, traveling 20m per second. If two cars are driving in the same direction and the front of the car is on the same line, how many seconds can car A overtake car B?
6. On a straight highway trunk line, two cyclists start from A and B, which are 500 meters apart. A starts from A and travels 300 meters per minute. B starts from b and travels 200 meters per minute; How long did it take them 5000 meters apart?
7. Party A, Party B and Party C set off by bike at the same time to catch up with the previous pedestrian. They caught up with the pedestrian with 6 points, 9 points and 12 points respectively. It is known that A travels 400 meters per minute, B travels 360 meters per minute, and C travels how many meters per minute?