Goal Use inverse variation and joint variation models Warmup Simplify Inverse Variation 2 variables x and y vary inversely if k is called the constant of variation Example 1 Tell whether x and y show direct variation inverse variation or neither ID: 486332
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Slide1
9.1 Inverse and Joint Variation
Goal: Use inverse variation and joint variation models.Slide2
Warm-up
Simplify:Slide3
Inverse Variation
2 variables, x and y, vary inversely if:
k is called the constant of variation.Slide4
Example 1
Tell whether x and y show direct variation, inverse variation, or neither:
Inverse Variation
Direct Variation
NeitherSlide5
Example 2
Write an equation that relates x and y such that x and y vary inversely and y = 15 when x =⅓.
This is the inverse equation.Slide6
Example 3
The driving time between two specific locations varies inversely with the average driving speed. The driving distance between Chicago and Minneapolis is about 400 miles.
Write an inverse variation model.
Describe how driving time and driving speed are related.
What is the value of k in this situation?
As the rate r increases, the driving time decreases.
The value of k is 400, which is the total distance traveled.Slide7
Example 4
A
50
100
120
150h24
12108
The table compares the area A of the bottom of a rectangular carton (in square inches) with the height h for four cartons that have the same volume. Does this data show inverse variation? If so, find a model for the relationship between A and h.
So, yes the data shows inverse variation.Slide8
Types of Variation
Joint variation occurs when a quantity varies directly as the product of two or more other quantities. For example, if
z =
kxy
, then z varies jointly with x and y.
Types of Variation
In each equation, k is a constant and k ≠ 0.
Relationship
Equationy varies directly with x y varies inversely with x z varies jointly with x and yy varies inversely with the squareof x
z varies directly with y and inverselywith xSlide9
Example 5
The amount of light
E
(measured in
lux) provided by a 50-watt light bulb varies inversely with the square of the distance d (in meters) from the bulb. At a distance of 1 meter, the amount of lux
E is 53.2a. Write an equation relating E and d.
b. What is the amount of light 3 meters from the bulb?Slide10
Assignment
pp. 469-471
20-50 even
56-68 even