9.1 inverse and joint variation

9.1 Inverse and Joint Variation:

9.1 Inverse and Joint Variation Goal: Use inverse variation and joint variation models.

Warm-up:

Warm-up Simplify:

Inverse Variation:

Inverse Variation 2 variables, x and y, vary inversely if: k is called the constant of variation.

Example 1:

Example 1 Tell whether x and y show direct variation, inverse variation, or neither: Inverse Variation Direct Variation Neither

Example 2:

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.

Example 3:

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.

Example 4:

Example 4 A 50 100 120 150 h 24 12 10 8 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.

Types of Variation:

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 Equation y varies directly with x y varies inversely with x z varies jointly with x and y y varies inversely with the square of x z varies directly with y and inversely with x

Example 5:

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 53.2 a. Write an equation relating E and d . b. What is the amount of light 3 meters from the bulb?

Assignment:

Assignment pp. 469-471 20-68 even