"Relationships between variables represented by relational expressions" PPT courseware on the relationship between variables

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"Relationships between variables represented by relational expressions" PPT courseware on the relationship between variables

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In the "time for the car to slide down": the height h of the support and the time t for the car to slide down are both changing, and they are both variables.

The time t for the car to slide down changes with the change of the height h of the support.

The height h of the support is the independent variable

The time t for the car to slide down is the dependent variable

The length of the board does not change, it is constant.

y=3x represents the relationship between the area of ​​the triangle and the length of the base of the triangle. It is the relationship between the variable y and the change of x.

Note: The relational expression is another way for us to express the relationship between variables. Using the relational expression, such as y=3x, we can find the value of the corresponding dependent variable based on the value of any independent variable.

As shown in the figure, the height of the cone is 4 cm. When the radius of the base of the cone changes from small to large, the volume of the cone also changes.

(1) In this change process, what are the independent variables and the dependent variables?

The length of the base radius of the cone is the independent variable

The volume of the cone is the dependent variable

(2) If the radius of the base of the cone is r (cm), then the relationship between the volume of the cone V (cm3) and r is:

(3) When the radius of the base changes from 1 cm to 10 cm, the volume of the cone changes from ____ cm3 to ____ cm3.

Cooperation and exchange

Discuss:

Do you know what "low-carbon life" is? "Low-carbon life" refers to a way to minimize the energy consumed in people's lives, thereby reducing carbon, especially carbon dioxide emissions.

Discuss:

(1) The carbon dioxide emissions from household electricity use can be expressed as ___ __ __, where the letters represent ____________.

(2) In the above relationship, for every 1 KW·h increase in power consumption, carbon dioxide emissions increase _______. When electricity consumption increases from 1 KW·h to 100 KW·h, carbon dioxide emissions increase from _______ to _____________.

(3) Xiao Ming’s home consumes approximately 110 KW h of electricity, 20 m3 of natural gas, 5 t of tap water, and 75 L of fuel consumption this month. Please calculate the carbon dioxide emissions of these items.

summary

1. How many methods have we learned so far to express the relationship between independent variables and dependent variables?

Two methods: column table and column relational expression

2. What are the characteristics of lists and column relations expressing the relationship between variables?

Through the column table, the change of the dependent variable as the independent variable changes can be expressed more intuitively.

Using the relationship, we can find the value of the corresponding dependent variable based on the value of an independent variable.

3. What did the students gain from this class?

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"Relationships between variables represented by relational expressions" PPT courseware 4 on the relationship between variables:

"Relationships between variables represented by relational expressions" Relationship between variables PPT courseware 4 Review and thinking In the time experiment of the car sliding down: the height h of the support and the time t for the car sliding down are both changing, and they are both variables. Among them, the time t when the car slides down depends on the support..

"Relationships between variables represented by relational expressions" PPT courseware 3 on the relationship between variables:

"Relationships Between Variables Expressed by Relational Expressions" PPT courseware on the relationship between variables 3 Build a model and explore new knowledge As shown in the figure, the height of BC on the bottom of △ABC is 6 cm. When the vertex C of the triangle moves toward point B along the straight line where the base lies, the area of ​​the triangle changes. ..

"Relationships between variables represented by relational expressions" PPT courseware 2 on the relationship between variables:

"Relationships between variables expressed by relational expressions" Relationship between variables PPT courseware 2 Situation introduction The base of △ABC BC = aThe height of the side of BC is h. If y is used to represent the area of ​​the triangle, then the area y =____________. Determine a What factors determine the area of ​​a triangle?

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Update Time: 2024-07-06

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

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