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Chapter 2: Problem 42

What does it mean if two quantities vary inversely?

Short Answer

Expert verified
When two quantities vary inversely, it means as one quantity increases, the other decreases such that their product is constant. This relationship can be expressed as \(xy = k\) where \(k\) is a constant.

Step by step solution

01

Define Inverse Variation

Inverse variation describes how one quantity changes in relation to another. In inverse variation, as one quantity increases, the other decreases. This is also sometimes called an inverse proportion.
02

Illustrate Relationship

In mathematical terms, if two quantities \(x\) and \(y\) vary inversely, their product is a constant. This can be expressed as \(xy = k\), where \(k\) is a constant.
03

Example

As an example of inversely related quantities, consider the relationship between speed and time taken for a journey. If you travel at a faster speed, the time it takes to reach your destination decreases. Hence, they are inversely related

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