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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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  1. 29 April, 02:37
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    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.
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