Write each formula as an English phrase using the word varies or proportional. C=2πr, where C is the circumference of a circle of radius r.

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Identify the formula given: \( C = 2\pi r \).

Recognize that \( C \) represents the circumference of a circle and \( r \) represents the radius.

Understand that the formula shows a direct relationship between the circumference and the radius.

Express the relationship in words: The circumference \( C \) varies directly with the radius \( r \).

Alternatively, you can say: The circumference \( C \) is proportional to the radius \( r \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Circumference of a Circle

The circumference of a circle is the distance around it, calculated using the formula C = 2πr, where C represents the circumference and r is the radius. This relationship shows how the circumference is directly related to the radius, meaning that as the radius increases, the circumference also increases.

Direct Variation

Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. In the context of the formula C = 2πr, the circumference varies directly with the radius, indicating that if the radius doubles, the circumference also doubles, maintaining a constant ratio.

Proportional Relationships

Proportional relationships occur when two quantities maintain a constant ratio or relationship to each other. In this case, the circumference of a circle is proportional to its radius, meaning that for any circle, the ratio of the circumference to the radius is always the same, specifically 2π.

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