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?

Respuesta :

Answer:

4.5*10^12

Explanation:

5.5=2/3log(E/10^4.4)

8.25=log(E10^4.4)

10^8.25=E/10^4.4

E=10^4.4*10^8.25

E=10^12*4.5

Magnitude is an earthquake's greatest commonly used measure of size. It is a measure of the size of the source for just an earthquake. so, it is identical regardless of how or where you perceive it, and the further calculation can be defined as follows:

Given formula:

[tex]\to\bold{ magnitude\ M = \frac{2}{3} \log \frac{E}{E_0}}[/tex]

The minimum measure released by such an earthquake shall be allocated to where E is the amount of power released in Joules and [tex]\bold{ E_0=10^{4.4}}[/tex].

As 5.5, then put in the above equation this same magnitude is given:

[tex]\to\bold{ magnitude\ M = \frac{2}{3} \log \frac{E}{E_0}}[/tex]

                       [tex]\bold{5.5= \frac{2}{3} \log(\frac{E}{10^{4.4}})}\\\\ \bold{8.25=\log( \frac{E}{10^{4.4}})} \\\\ \bold{10^{8.25}=\frac{E}{10^{4.4}}}\\\\ \bold{E=10^{4.4}\times 10^{8.25}}\\\\ \bold{E= 4.5 \times 10^{12} }[/tex]

Therefore the final answer is "[tex]\bold{ 4.5 \times 10^{12} }[/tex]".

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