"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 5

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"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 5

What are the properties of the graph of an inverse proportional function?

The inverse proportional function y=k/x is composed of two curves. When k>0, the two curves are located in the ________quadrant respectively. In each quadrant, y changes with the _____________ of x;

When k<0, the two curves are located in the __________ quadrant respectively. In each quadrant, y varies with x.

Example 3

Xiaowei wants to use a sled bar to move a big rock. It is known that the resistance and resistance arm remain unchanged, which are 1200 Newtons and 0.5 meters respectively.

(1) What is the functional relationship between power F and power arm L?

(2) When the power arm is 1.5 meters, what is the minimum force required to pry the stone?

(3) 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?

Learn something:

In electricity, the output power P (watts) of an electrical appliance, the voltage U (volts) at both ends and the resistance R (ohms) of the electrical appliance have the following relationship: PR=U2

think:

1. The above relationship can be written as P=U²/R

2. The above relationship can be written as R=U²/P

Consolidation exercises

The voltage of the battery is a constant value. When using the 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?

(2) Please write the expression of this function.

(3) If the current limit of the electrical appliance using the battery as power supply does not exceed 10A, then within what range should the variable resistance of the electrical appliance be controlled?

Solution: (3) Substituting I=10 into I=36/R, we get: R=3.6

The results can be seen that if the current is 10A, the resistance of the electrical appliance should be 3.6Ω. If the current does not exceed 10A, the resistance of the electrical appliance should be no less than 3.6Ω, that is (R≥3.6)

The picture on the right depicts an image of a car driving at a constant speed on a highway. Answer the following questions based on the information provided by the image.

(1) What is the total length of this highway?

(2) Please write the functional expression between speed v and time t.

(3) How many hours does it take a car to reach its destination at the slowest time? If we arrive in less than 3 hours, what speed should the car go at?

(4) What is the slowest speed of the car? How many hours does it take to travel the entire distance by car?

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"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 4 Exploration Activity 1: The municipal gas company wants to build a cylindrical gas storage room with a volume of 104m3 underground. (1) The bottom area S (unit: m2) of the storage room and its depth What kind of function does d (unit: m) have?

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"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 3 The balloon is filled with a certain mass of gas. When the temperature remains unchanged, the air pressure P (kPa) in the balloon is an inverse proportional function of the balloon volume V. When the balloon volume is 0.8m3, the air pressure inside the balloon is 120 kPa..

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Update Time: 2024-10-04

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