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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 constant, the air pressure P (kPa) inside 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.
(1) Write the expression of this function.
(2) When the gas volume is 1m3, what is the pressure?
(3) When the air pressure inside the balloon is greater than 192 kPa, the balloon will explode. To be safe, what size should the balloon be?
List analytical expressions of inverse proportional functions for practical problems
(1) To list the functional relationship expressions in practical problems, you should first analyze clearly the fractions that should be satisfied between each variable, that is, the relationship between variables in practical problems - establish an inverse proportional function model - solve practical problems
(2) When formulating functional relationships in practical problems, the value range of the independent variables must be indicated after the relationship.
Self-test questions
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:
2. As shown in the figure, the image of the direct proportional function y=k1x and the image of the inverse proportional function y=k1/x intersect at two points A and B. The coordinates of point A are (√3, 2√3).
(1) Write the expressions of these two functions respectively.
(2) Can you find the coordinates of point B? How did you ask for it?
(3) If the coordinate of point C is (–4, 0). Find the area of △BOC.
(4) Try to find point D on the coordinate axis so that △AOD≌△BOC.
practice practice
The drainage pipe of a certain reservoir can drain 8m3 per hour, and the entire pond can be emptied in 6 hours.
⑴What is the volume of the reservoir? ____________
⑵If you add a drainage pipe. Let the hourly drainage volume reach Q (m3), then how will the time t (h) required to drain the full pool of water change? __________
⑶Write the relationship between t and Q. ____________
⑷If you plan to drain a full pool of water within 5 hours, then the drainage volume per hour should be at least ____________.
⑸It is known that the drainage pipe can be up to 12m3 per hour, so at least __________h can drain all the water in the pond.
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"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 6:
"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 6 Example 1 A gas company in a city wants to build a cylindrical gas storage room with a volume of 103 underground. (1) The bottom area S (unit: m2) of the storage room and its depth d (Unit: m) What kind of function is related to...
"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 5:
"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 5 What are the properties of the graph of the inverse proportional function? The inverse proportional function y=k/x is composed of two curves. When k0, the two curves are located in the ________quadrant, and in each In a quadrant, y depends on the _________ of x..
"Practical Problems and Inverse Proportional Functions" Inverse Proportional Function PPT Courseware 4:
"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?