"Application of linear functions" PPT courseware 2

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"Application of linear functions" PPT courseware 2

1: Undetermined coefficient method

1. Xiao Ming filled in the following table based on a linear function relationship:

One of the boxes was accidentally covered by ink. Think about it, what was the number originally filled in that box? Explain your reasons.

2. The relationship between the length y (cm) of the spring and the mass x (kg) of the hanging object is a linear function. The image is as shown on the left. Observe the image and answer:

(1) What is the length of the spring when it is not hanging on an object? What else can we know from the picture?

(2) What is the functional relationship between y and x?

(3) When the length of the spring is 24cm, what is the mass of the object hung?

3. As shown in the picture below, two stacks of bowls of the same size are placed neatly on the table. Please answer the following questions based on the data in the picture:

(1) Find the functional relationship between the height y (cm) of bowls neatly placed on the table and the number of bowls x (pieces);

(2) When these two stacks of bowls are placed neatly in one stack, what is the height of the bowls?

2: Piecewise function

1. In order to strengthen citizens’ awareness of water conservation and make rational use of water resources, a certain city stipulates water use standards as follows: when each household’s monthly water consumption does not exceed 6 m3, the water fee is charged at 0.6 yuan/m3. When the quantity exceeds 6 m3, the excess part shall be charged at 1 yuan/m3. Assume that each household's monthly water consumption is x meters 3, and it should pay y yuan.

(1) Write down the functional relationship between y and x when the monthly water consumption per household does not exceed 6 meters 3 and when the monthly water consumption per household exceeds 6 meters 3, and determine whether they are linear functions.

(2) It is known that the water consumption of a certain household in May is m3, find the water bill of this user in May.

2. Teacher Fan started from home and took a taxi to Tongxiang No. 10 Middle School for classes. The taxi charging method is shown in the picture. Please answer the following questions based on the picture:

(1) What is the starting price of a taxi? Within how many distances will only the starting price be charged?

(2) After completing the starting mileage, how much is the fare per kilometer traveled?

(3) Express the relationship between cost y and distance s in an appropriate way.

(4) Teacher Fan spent 41 yuan on the bus fare. Try to find the mileage traveled by Teacher Fan.

13. A company has 12 agricultural vehicles and 6 agricultural vehicles in warehouses A and B respectively. Now it needs to transfer 10 agricultural vehicles to County A and 8 agricultural vehicles to County B. It is known that one agricultural vehicle will be transferred from warehouse A to County A and County B. The freight charges in County B are 40 yuan and 80 yuan respectively; the costs of transporting an agricultural vehicle from warehouse B to County A and County A are 30 yuan and 50 yuan respectively.

(1) Suppose x agricultural vehicles are transferred from warehouse B to county A. Find the functional relationship of the total cost y with respect to x.

(2) Find the transportation plan with the lowest total cost.

14. A chemical factory in our city currently has 290 kilograms of raw material A and 212 kilograms of raw material B. It plans to use these two raw materials to produce a total of 80 pieces of products A and B. To produce one product A requires 5 kilograms of raw material A and raw material B. There are 1.5 kilograms of raw materials, and the production cost is 120 yuan. To produce a product B, 2.5 kilograms of raw materials A and 3.5 kilograms of raw materials B are needed, and the production cost is 200 yuan.

(1) There are several production plans, please design them.

(2) Assume that the total cost of producing two products, A and B, is y yuan, and the number of pieces of one of them is x. Try to write the functional relationship between y and x, and use the properties of the function to explain which of (1) Which production plan has the lowest total cost? What is the lowest cost?

Keywords: Teaching courseware for the application of linear functions, Qingdao edition eighth grade mathematics volume 2 PPT courseware download, eighth grade mathematics slide courseware download, application of linear functions PPT courseware download, .PPT format;

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Update Time: 2024-11-16

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