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

Verified step by step guidance

1. Identify the type of variation described. Since h varies inversely as t, this means that h is inversely proportional to t.
2. Recall the general form of an inverse variation equation: \(h = \frac{k}{t}\), where \(k\) is the constant of variation.
3. Write the variation equation using the given variables: \(h = \frac{k}{t}\).
4. Understand that \(k\) is a constant that can be determined if specific values of \(h\) and \(t\) are given, but for now, it remains as \(k\) in the equation.
5. This equation expresses the relationship where as \(t\) increases, \(h\) decreases proportionally, and vice versa.

Key Concepts

Inverse Variation

Inverse variation describes a relationship where one variable increases as the other decreases, such that their product is constant. Mathematically, if h varies inversely as t, then h × t = k, where k is a constant.

Constant of Variation

The constant of variation, denoted as k, is a fixed value that relates two variables in a variation equation. In inverse variation, k equals the product of the two variables, remaining unchanged regardless of their individual values.

Writing Variation Equations

To write a variation equation, identify the type of variation (direct or inverse) and express the relationship using the constant of variation. For inverse variation, the equation takes the form h = k / t, clearly showing how h depends on t.