"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 6

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"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 6

Example 1 A gas company in a certain city wants to build a cylindrical gas storage room with a volume of 103 underground.

(1) What is the functional relationship between the bottom area S (unit: m2) of the storage room and its depth d (unit: m)?

(2) The company decides to set the bottom area S of the storage room to 500m2. How deep should the construction team dig down during construction?

(3) When the construction team dug 15m underground according to the plan in (2), they encountered hard rock. In order to save construction funds, the company temporarily changed the plan and changed the depth of the storage room to 15m accordingly. How much should the floor area of ​​the storage room be changed to meet the needs? (Accurate to 0.01m2)

Example 2: Dock workers loaded cargo onto a ship at a rate of 30 tons per day, and it took exactly 8 days to complete the loading.

(1) The ship starts unloading after arriving at its destination. What is the functional relationship between the unloading speed v (unit: tons/day) and the unloading time t (unit: days)?

(2) Due to an emergency, the cargo on the ship must be unloaded within no more than 5 days. So on average, how many tons of cargo must be unloaded every day?

Analysis: According to the loading speed  loading time = the total amount of cargo, the total amount of cargo loaded on the ship can be calculated: and then according to the unloading speed = the total amount of cargo unloading time, the functional analytical expression of v and t is obtained.

Solution: (1) Suppose the total amount of cargo on the ship is k tons, then according to the known conditions:

k=30×8=240

Therefore, the functional analytical expression of v and t is

v=240/t

Example 3 Xiaowei wants to use a crowbar to move a big stone. It is known that the resistance and resistance arm remain unchanged at 1200 Newtons and 0.5 meters respectively.

(1) What is the functional relationship between power F and power arm l? When the power arm is 1.5 meters, what is the minimum force required to move the stone?

(2) If you want the power F to not exceed half of the force in question (1), how much longer must the power arm be at least?

Analysis: Lever Law: If the distance between two objects and the fulcrum is inversely proportional to their weight, then the lever is balanced.

Resistance × resistance arm = power × power arm

Thinking questions

1. A school’s science and technology team conducted a field trip and encountered a muddy wetland more than ten meters wide. In order to pass through the wetland safely and quickly, they laid a number of wooden boards along the route to construct a temporary passage, thus successfully completing the task.

(1) Can you understand the reason for doing this?

(2) If the total pressure exerted by the man and the wooden board on the wetland ground is 600 N, then how to express P (pressure) using an algebraic expression containing S (the area of ​​the wooden board)?

(3) When the area S of the board is 0.2m2, how big is the pressure P?

(4) When the pressure is 6000Pa, what is the area of ​​the board?

2. In a closed circuit, the function graph between current I (A) and resistance R (Ω) is as shown below. Answer the following questions:

(1) Write the functional relationship between the current I (A) and the resistance R (Ω) in the circuit.

(2) If the resistance of an electrical appliance is 5 Ω and the maximum current allowed to pass through it is 1 A, will it burn out if the electrical appliance is connected to this closed circuit? Try to explain it through calculation.

3. As shown in the figure, a brick wall with a length of 80 m is used and a fence is used to form a rectangular garden against the wall. The planned area of ​​the garden is 180 m2. Let the length of the side of the garden parallel to the direction of the wall be x (m). The other side adjacent to it is y (m).

(1) Find the functional relationship expression of y with respect to x and the value range of the independent variable x;

(2) Draw the graph of this function;

(3) If the length of one side of the enclosed garden parallel to the wall is required to be no less than 2/3 of the wall length, find the value range of the length of the other side adjacent to it.

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Update Time: 2024-10-03

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