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"The relationship between variables represented by relational expressions" The relationship between variables PPT courseware 3
Build models and explore new knowledge
As shown in the figure, the height of △ABC on the bottom side BC 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.
(1) In this change process, what are the independent variables and dependent variables?
The independent variable is the length of side BC and the dependent variable is the area of ΔABC.
(3) If the length of the base of the triangle is x (cm), then the area of the triangle y (cm2) can be expressed as y=3x.
(4) When the base length changes from 12 cm to 3 cm, the area of the triangle changes from 36 cm2 to 9 cm2
Relationships are another way we can compare relationships between variables.
Note: A relation is an equation; the dependent variable is usually written on the left side of the equal sign, and the algebraic expression containing the independent variable is written on the right side of the equal sign.
Using the relational expression, such as y=3x, the value of the dependent variable can be calculated based on the value of any independent variable that meets the conditions.
Do it and apply new knowledge
1. As shown in the figure, the radius of the base of the cone is 2 cm. When the height of the cone changes from small to large, the volume of the cone also changes accordingly.
(1) In this change process, what are the independent variables and dependent variables?
The independent variable is the height of the cone and the dependent variable is the volume of the cone.
(2) If the height of the cone is h (cm), then the relationship between the volume of the cone V (cm3) and h is v=4/3πh.
(3) When the height changes from 1 cm to 10 cm, the volume of the cone changes from 4/3π cm3 to 40/3π cm3
2. 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 accordingly.
(1) In this change process, what are the independent variables and dependent variables?
The independent variable is the radius of the base of the cone, and the dependent variable is the volume of the cone.
(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 base radius changes from 1 cm to 10 cm, the volume of the cone changes from 4/3π cm3 to 400/3π cm3.
practice
As shown in the picture: the width of the rectangle is 8cm, the length is x cm, and the perimeter is y cm.
⑴. Write the relationship between y and x;
⑵. When x=10cm, what is the value of y equal to in cm?
⑶. When y=40cm, what is the value of x equal to in cm?
Enlightenment and reflection
1 What did you learn from this lesson?
2 This lesson mainly explores the variable relationships in graphics
3 Use relational expressions to express the relationship between variables
4. Ability to find relevant numerical values based on relational expressions
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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 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?
"Relationships between variables represented by relational expressions" PPT courseware on the relationship between variables:
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