Question

An earthquake with a rating of 6 is considered a major earthquake that can cause damage over a large area.

What is the value of x when the Richter scale rating is 6? Round your answer to the nearest hundredth.

Answer 1

Explanation:

The formula for calculating the magnitude of an earthquake using the Richter scale is:

M = log10(A) - log10(A0)

where M is the magnitude, A is the amplitude of the earthquake, and A0 is a reference amplitude. The reference amplitude is 1 micron at a distance of 100 km from the epicenter.

For a major earthquake with a rating of 6, we can assume that the amplitude is 1 meter (or 1,000,000 microns), since the Richter scale is logarithmic. Substituting these values into the formula, we get:

6 = log10(1000000) - log10(1)

Simplifying:

6 = 6 - 0

Therefore, x = 1 meter, rounded to the nearest hundredth.