Using k as the constant of variation, write a variation equation for each situation. h varies inversely as t.

Key Concepts

Inverse Variation

Inverse variation describes a relationship where one variable increases while the other decreases, maintaining a constant product. Mathematically, if h varies inversely as t, it can be expressed as h = k/t, where k is a non-zero constant. This means that as t increases, h decreases proportionally, and vice versa.

Constant of Variation

The constant of variation, denoted as k, is a specific value that represents the product of the two variables in an inverse variation relationship. In the equation h = k/t, k remains constant regardless of the values of h and t. Understanding this constant is crucial for solving problems involving inverse variation, as it allows for the prediction of one variable based on the other.

Variation Equation

A variation equation is a mathematical expression that describes how one quantity changes in relation to another. In the context of inverse variation, the equation h = k/t serves as the variation equation, illustrating the relationship between h and t. Recognizing how to formulate and manipulate variation equations is essential for solving real-world problems that involve proportional relationships.