"Application of Inverse Proportional Function" Inverse Proportional Function PPT Courseware 2

Description

"Application of Inverse Proportional Function" Inverse Proportional Function PPT Courseware 2

learning target

1. Experience the process of analyzing the relationship between two variables in practical problems, establishing a function model, and then solving the problem;

2. Understand the connection between mathematics and real life, enhance application awareness, and improve the ability to use algebraic methods to solve problems.

New course introduction

1. Properties of the inverse proportional function: The graph of the inverse proportional function y=k/x, when k>0, the graph is located in the first and third quadrants. In each quadrant, the value of y decreases as x increases. ; When k<0, the image is located in the second and fourth quadrants, and the value of y increases with the increase of x.

2. The two branches of the hyperbola approach the coordinate axis but cannot intersect with the coordinate axis.

3. The graph of the inverse proportional function is a centrally symmetrical graph with the origin as the center of symmetry.

4. Pick any point on the graph of the inverse proportional function y=k/x, and draw the vertical line (or parallel line) of the coordinate axis and the S rectangle = lKl enclosed by the coordinate axis.

(1) Use an algebraic expression containing S to express p. Is p the inverse proportional function of S? Why?

From p=F/S, we get p=600/S

p is the inverse proportional function of S, because given a value of S, there is a unique p value corresponding to it. According to the function definition, p is the inverse proportional function of S.

(2) When the area of ​​the board is 0.2m2, what is the pressure?

When S=0.2m2,

p＝600/0.2＝3000(Pa)．

When the area of ​​the board is 0.2m2, the pressure is 3000Pa.

Track training

1. 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?

Analysis: The volume of the reservoir is: 8×6=48(m³).

(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?

Analysis: At this time the required time t(h) will be reduced.

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

Analysis: The functional relationship between t and Q is: t=48/Q.

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

Analysis: When t=5h, Q=48/5=9.6m³. So the drainage volume per hour is at least 9.6m³.

(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 pond?

Analysis: When Q=12(m³), t=48/12=4(h). Therefore, it takes at least 4 hours to drain the full pool of water.

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Update Time: 2024-10-20

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