Solve the variation problems in Exercises 93

Name: Problem 96, Chapter 3: Precalculus
Uploaded: 2020-06-14T21:33:44-08:00
Duration: 2 min 44 s
Channel: Michael Dunne
Description: Solve the variation problems in Exercises 93–98. The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker?

Solve the variation problems in Exercises 93–98. The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker?

Solve the variation problems in Exercises 93–98.
The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker?

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Key Concepts

Inverse Variation

An inverse variation describes a relationship between two variables in which one variable increases as the other decreases such that their product remains constant. In algebra, this is typically expressed as y = k/x, where k is a constant. This concept is important when understanding how one quantity affects another in a reciprocal manner.

Inverse Square Relationship

An inverse square relationship is a specific type of inverse variation where a quantity is inversely proportional to the square of another variable. This means that if the independent variable (such as distance) is doubled, the resulting quantity (like intensity or loudness) becomes one-fourth of its initial value. This concept is widely used in physics to describe phenomena such as light, sound, and gravitational forces.

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