"Application of Inverse Proportional Function" Inverse Proportional Function PPT Courseware 3

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"Application of Inverse Proportional Function" Inverse Proportional Function PPT Courseware 3

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1.What is an inverse proportional function?

Generally, a function of the form y=k/x (k is a constant, k≠0) is called an inverse proportional function.

2. What is the graph of the inverse proportional function? It is a hyperbola

3. What are the properties of the graph of the inverse proportional function y=k/x?

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When k>0, the two curves are located in the first and third quadrants respectively. In each quadrant, y decreases as x increases;

When k<0, the two curves are located in the second and fourth quadrants respectively. In each quadrant, y increases with the increase of x.

Question exploration

When the pressure of people and wooden boards on the wetland is constant, how will the pressure P (Pa) of people and wooden boards on the ground change as the area S (m2) of the wooden boards changes?

If the total pressure of the man and the wooden board on the wetland ground is 600N, then (1) use an algebraic expression containing S to express P. Is P an inverse proportional function of S? Why?

Solution: p=600/s(s>0)P is the inverse proportional function of S.

Do it

1. The voltage of the battery is a fixed value. When using this power supply, the functional relationship between the current I (A) and the resistance R (Ω) is as shown in the figure.

(1) What is the voltage of the battery? Can you write an expression for this function?

Solution: Because the relationship between current I and voltage U is IR=U (U is a fixed value), substitute the coordinates (9,4) of point A on the image to get U=36. Therefore, the voltage of the battery U= 36V.

(2) If the current of an electrical appliance powered by a battery must not exceed 10A, then within what range should the variable resistance of the electrical appliance be controlled?

Solution: When I≤10A, the solution is R≥3.6(Ω). Therefore, the variable resistance should be no less than 3.6Ω.

practice

The drainage pipe of a certain reservoir drains 8m³ per hour, and the entire pond can be emptied in 6 hours.

(1) What is the volume of the reservoir?

(2) If a drainage pipe is added so that the drainage volume per hour reaches Q (m³), how will the time t (h) required to drain the full pool of water change?

(3) Write the functional relationship between t and Q;

(4) If a full pool of water is to be drained within 5 hours, what is the minimum drainage volume per hour?

(5) It is known that the maximum drainage volume of the drainage pipe is 12m³ per hour, so how long does it take to drain the entire pool?

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"Application of Inverse Proportional Functions" PPT courseware:

"Application of Inverse Proportional Functions" PPT courseware uses the knowledge of inverse proportional functions to solve practical problems. The general idea can be roughly divided into the following two steps: (1) Carefully review the question and establish the inverse proportional function ________; (2) Based on the known conditions, find the solution from a variable ______________..

"Applications of Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 2:

"Applications of Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 2 Learning Objectives 1. Experience the process of analyzing the relationship between two variables in practical problems and establishing a function model, and then solve the problem; 2. Understand the connection between mathematics and real life, and enhance application Consciousness, mention...

"Applications of Inverse Proportional Functions" PPT courseware of inverse proportional functions:

"Application of Inverse Proportional Function" Inverse Proportional Function PPT Courseware Application of Inverse Proportional Function The application of inverse proportion function is to use the knowledge of inverse proportion function to solve practical problems and geometric problems related to inverse proportion function. Through the established relationship of inverse proportion function,...

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Update Time: 2024-10-13

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