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# 10 Examples of Inverse Variation

October 4, 2023 written by Rida Mirza

Inverse variation, or inverse proportionality, is a math idea that shows how two things change together, but in opposite ways. When one thing goes up, the other goes down, and when one goes down, the other goes up.

In this article, we will discuss ten examples of inverse variation in mathematics.

## Examples of Inverse Variation

These are 10 examples of inverse variation.

### 1: Kepler’s Third Law

Kepler’s Third Law is an example of inverse variation. Kepler’s Third Law of planetary motion states that the square of the orbital period of a planet is inversely proportional to the cube of its semi-major axis. As a planet moves farther from the sun, its orbital period increases, demonstrating inverse variation.

### 2: Electrical Resistance and Ohm’s Law

Ohm’s Law in electricity describes an inverse relationship between electrical resistance and current flow. When resistance increases, current decreases, and vice versa.

### 3: Boyle’s Law

Boyle’s Law in gas physics demonstrates an inverse variation between the pressure and volume of a gas at constant temperature. As volume increases, pressure decreases, and vice versa.

### 4: Law of Demand

In economics, the Law of Demand illustrates inverse variation. It states that as the price of a product increases, the quantity demanded decreases, and vice versa.

### 5: Similar Triangles

In geometry, similar triangles exhibit inverse variation between their sides. If one side of a similar triangle increases, the corresponding side of the other triangle decreases, maintaining the ratio of similarity.

### 6: Radioactive Decay and Half-Life

Radioactive decay follows inverse variation. The number of radioactive atoms decreases over time, and the half-life of a substance is the time it takes for half of the atoms to decay.

### 7: Laffer Curve

The Laffer Curve in economics illustrates an inverse relationship between tax rates and tax revenue. Tax revenue initially increases as tax rates rise but eventually decreases due to disincentives for economic activity.

### 8: Harmonic Motion

In harmonic motion, the frequency and period are inversely related. As the frequency of oscillation increases, the period decreases, and vice versa.

### 9: Gravitational Force and Inverse Square Law

Newton’s Law of Universal Gravitation demonstrates inverse variation. The gravitational force between two objects decreases as the distance between them increases, following the inverse square law.

### 10: Inverse Square Law of Acoustics

In acoustics, the Inverse Square Law describes the decrease in sound intensity with increasing distance from the source. The intensity is inversely proportional to the square of the distance.

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