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Chapter 2: Problem 44

Explain what is meant by joint variation. Give an example with your explanation.

Short Answer

Expert verified
Joint variation means a quantity varies directly or inversely with the product of two or more other quantities. For example, a car's fuel efficiency varies directly with speed and terrain condition.

Step by step solution

01

Definition

Joint variation (also known as combined variation) is a variation where a quantity is directly or inversely proportional to the multiplication or division of two or more other quantities. Joint variation uses the combined variation identity y = kxz (where y is the dependent variable which varies directly as x and z, and k is the constant of variation).
02

Direct Variation

In direct variation, as one quantity increases, the other quantity also increases, or as one decreases, the other also decreases. This is normally represented as y = kx, where k is the constant of direct variation.
03

Inverse Variation

In inverse variation, as one quantity increases, the other quantity decreases. This is usually represented as y = k/x, or yx = k, where k is the constant of inverse variation.
04

Example

To illustrate, let's consider the example of a car's fuel efficiency. If a car is driven at a steady speed on a flat terrain (speed and terrain being x and z), the fuel efficiency (y) varies directly with those two factors. If either the speed increases or the terrain becomes more uneven, then the car's fuel efficiency will decrease. Similarly, if the speed decreases or the terrain becomes less uneven, the fuel efficiency improves. Hence, in this situation, the car's fuel efficiency shows joint variation with speed and terrain.

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