Inverse Variation
As the price of an item increases, its sales decrease. This is an example of inverse variation. An inverse variation problem has one constant of variation, but is divided instead of multiplied.
Practical Problem: Threshold Weight
Direct variation is used in a practical problem to find the threshold weight for men of different heights.
Practical Problem: The Amount of Weight a Shelf Can Hold
The amount of weight a shelf can hold varies with the length, width, and thickness of the board. Finding how much weight a specific board can hold combines direct, joint, and inverse variation and is illustrated here.
Practical Problem: The Speed of Two Pulleys
A practical problem involving the speeds of two pulleys of different diameters is solved using inverse variation.
Joint Variation
Joint variation is when the constant of variation applies to two values. The interest paid on a loan, for examples, varies jointly with the interest rate and the amount borrowed.
Combining Direct, Joint, and Inverse Variation in a Problem
A problem combining direct, joint, and inverse variation is demonstrated and solved.
Variation Problems
A variation problem always involves two sets of information and two formulas. To solve a variation problem, a general formula is written from the variation statement. A specific formula can then be written with the constant of variation.