## Problem of the Day #157: EARTHQUAKE!!!
*August 23, 2011*

*Posted by Seungln in : potd , trackback*

A magnitude $6.0$ earthquake struck Virginia today (Aug. 23rd, 2011). (It was actually magnitude $5.9$, but assuming that it’s $6.0$ will make your math easier.) The *relative magnitude* is the magnitude felt by someone within a certain distance from the epicenter (the starting point of the earthquake), and is calculated with the formula

$$\large rm(x) = am \cdot (1 – \log_{10} (1+x^{\frac{3}{19}}))$$

where $rm(x)$ is the relative magnitude, $am$ is the absolute magnitude, and $x$ is the distance from the epicenter to the impact point in miles.

Find the area of the zone within which $rm(x)$ was at least $3.0$, and divide the answer by $\pi mile^2$. The final result will be your answer.

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