Now I'll give you the idea to solve the first problem, and the following problems will depend on your performance!
Assuming that the walking time of people is X, the distance from the mountain to the bottom is f(x), and the distance from the mountain to the bottom is g(x), then
F(x) is a monotonically increasing function, g(x) is a monotonically decreasing function, and another function h(x)=f(x)-g(x) is a monotonically increasing function and continuous.
If there is h(0)0, it is proved by the zero theorem that h(x)=0 must exist in the interval where X belongs to [0,9]. 3. My classmate offered a reward of 100 for this question. Please search for help in mathematics and mathematical modeling, and send the answer to the email address 799472980@qq. Thank you.
1.a Company departs from Yamashita Hotel at 8:00 in the morning, goes up the mountain along a path, reaches the top of the mountain at 5:00 in the afternoon, and checks in. At 8:00 am the next day, go down the mountain along the original road and return to the hotel at 5:00 pm. A second said that A must pass through the same place in the route at the same time in two days. Why?
2. As shown in the figure, a cylindrical tube with a diameter of is wound with wide strips of cloth, and the strips are required not to overlap. What is the angle between the cloth strip and the pipe axis? If the length of the pipeline is known, how long cloth strip is needed (the influence of both ends can be considered)? What if the pipe is of other shapes (such as hexagon, ellipse, etc.)? )?
3. Establish a production, sales and storage mode that does not allow out of stock. Let the output rate remain unchanged and the sales rate remain unchanged. In each production cycle T, the first period () is production and sales at the same time, and the later period () is sales and non-production, and the graph of storage capacity is drawn. Let the preparation cost of each production be, the storage cost of each product per unit time be, and determine the optimal production cycle with the minimum total cost as the goal. Discuss the peaceful situation.
4. A company mixed four kinds of liquid raw materials (A, B, C and D) with different sulfur content to produce two kinds of products (A and B). According to the requirements of production technology, raw materials A, B and D must be poured into a mixing tank for mixing, and then the mixed liquid and raw material C are mixed to produce A and B respectively. It is known that the sulfur contents of raw materials A, B, C and D are 3 1 and 2 1(%) respectively, and the purchase prices are 6 16, 10 and 15 (thousand yuan/ton) respectively; The sulfur content of products A and B shall not exceed 2.5 and 1.5(%) respectively, and the price shall be 9 15 (thousand yuan/ton) respectively. According to market information, the supply of raw materials A, B and C is not limited, and the supply of raw material D is up to 50 tons; The market demand of products A and B is 100 tons and 200 tons respectively. How to arrange production?
5. Using analytic hierarchy process to solve a practical problem can refer to the following questions:
Schools choose excellent students or classes, try to give some standards and build a hierarchical structure model. It can be divided into two situations: relative evaluation and absolute evaluation.
When you buy a personal computer, you should consider factors such as function and price, and how to make a decision.
Establish a hierarchical structure model of college graduates' choice of volunteers.
Your hometown is going to raise money to run a small farm, isn't it raising pigs, chickens, ducks and rabbits? ...