"The relationship between variables represented by relational expressions" The relationship between variables PPT courseware 2

Description

"The relationship between variables represented by relational expressions" The relationship between variables PPT courseware 2

Situation import

The base BC of △ABC= a, and the height on BC is h. If y is used to represent the area of ​​the triangle,

Then the area y =____________.

What are the factors that determine the area of ​​a triangle?

base and height of triangle

Explore new knowledge

Self-study guide one

1. Complete the question: As shown in the picture, the height of △ABC on the bottom side BC is 6 cm. When the vertex C of the triangle moves toward B along the straight line where the base lies, how does the area of ​​the triangle change?

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

(2) If the length of the base BC of the triangle is x (cm), then the area y (cm2) of the triangle can be expressed as y=3x.

relational expression

1. When a relational expression is used to express the relationship between a dependent variable and an independent variable, an algebraic expression containing the independent variable (expressed by a letter) is usually used to express the dependent variable (also expressed by a letter). Such a mathematical formula (equation) is called relational expression.

2. The writing method of relational expression is different from that of equation. The dependent variable must be written separately on the left side of the equal sign.

practice

1. Cut off equal-sized squares from the four corners of a rectangle with a length of 20cm and a width of 10cm. If the side length of the cut-off square is x cm and the area of ​​the shaded part is y (cm2), then y The relationship with x is y=200 - 4x2.

2. The diameter of the base of the cylinder is 6cm. When the height h (cm) of the cylinder changes from large to small, the volume V (cm3) of the cylinder changes accordingly. Then the relationship between V and h is___________

3. The height of the cone is 4 and the radius of the base is r. Then the volume V of the cone can be expressed as_______.

Variant

The radius of the base of the cone is 2cm, and the height varies from small to large.

(1) In this change process, the independent variable is _________ and the dependent variable is _________.

(2) If the height of the cone is h (cm), then the relationship between the volume of the cone V (cm3) and h is _________.

(3) When the height changes from 1cm to 10cm, the volume of the cone changes from _____cm3 to _____cm3

Practice in class

1. At a certain place on the earth, the relationship between temperature T (℃) and height d (m) can be approximately expressed. According to this relationship, when the values ​​of d are 200, 400, 600, 800, and 1000 respectively, calculate Corresponding T value, and present the results in a table.

2. Following (2) in "Discussion", can you talk about the changes in carbon dioxide emissions from household tap water as the tonnage of tap water used changes?

practice

There is a square with a side length of 3 cm. If the side length increases, its area also changes.

(1) If the side length increases by x cm, the relationship between its area y (cm2) and x is _______________

(2) When x changes from 3cm to 7cm, its area y changes from ________cm2 to ________cm2

Drills in class

1. The class plans to purchase table tennis balls for 50 yuan. The relationship between the total number n (pieces) purchased and the unit price a (yuan) is ( )

A. an=50 B.a=50/n C.n=50/a D. None of the above writings are standardized

2. Teacher Zhang leads x students to visit a certain zoo. It is known that adult tickets are 10 yuan each and student tickets are 5 yuan each. Assume that the total cost of tickets is y yuan, then y=5x+10

3. After a candle with an original length of 20cm is lit, the relationship between its remaining length y (cm) and burning time x (minutes) is as follows:

Then the relationship between the remaining length y (cm) and the burning time x (minutes) is y=20-x/10. It is estimated that this candle can burn up to 200 minutes.

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

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"Relationships between variables represented by relational expressions" PPT courseware 3 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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Update Time: 2024-09-13

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