Problem 42 - Algebra and Trigonometry

Question

What does it mean if two quantities vary inversely?

Step-by-Step Solution

Answer

Inverse variation or inverse proportionality means that as one quantity increases, the other decreases at a rate that keeps their product constant.

Step 1: Defining Inverse Variation

Inverse variation, also known as inverse proportionality, is a concept in mathematics that describes a relationship between two variables where their product is constant.

Step 2: Explanation With Formula

If one variable is a and the other variable is b, we say that a and b are inversely proportional if \( a \times b = k \), where k is a constant. This means that as a increases, b decreases in such a way that their product always remains the same.

Step 3: Real Life Example

For instance, the speed needed to travel a certain distance and the time it takes to travel at that speed are inversely proportional. The faster you go (increase speed), the less time it will take (decrease time), but the product (distance) remains the same.