The magnitude, M, of an earthquake is represented by the equation M=23logEE0 where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. In scientific notation rounded to the nearest tenth, what is the amount of energy released by an earthquake with a magnitude of 5.5?

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Physics

29 April, 02:13

The magnitude, M, of an earthquake is represented by the equation M=23logEE0 where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. In scientific notation rounded to the nearest tenth, what is the amount of energy released by an earthquake with a magnitude of 5.5?

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Cesar · Answer 1

The amount of energy released by the earthquake in joules is 4.4*10^12 J.

Explanation:

As, we have given the magnitude,

M = 2/3 Log E/Eo

where E is the amount of energy released by the earthquake in joules and Eo=10^4.4 is the assigned minimal measure released by an earthquake.

As, the magnitude is given which is 5.5 then put it in the above equation,

5.5 = 2/3 Log E/Eo

Log E/Eo = 5.5*3 / 2

Log E/Eo = 8.25

Now, we will find the amount of energy released by an earthquake:

Log E/Eo = 8.25

Taking antilog,

E/Eo = 10^8.25

But Eo is given which is Eo = 10^4.4

E / (10^4.4) = 10^8.25

E = 10^8.25 * 10^4.4

E = 4.4*10^12 J.