Respuesta :
Answer:
Japan : [tex]E=2.8183829313\times 10^{18}[/tex]
California : [tex]E=2.8183829313\times 10^{15}[/tex]
Step-by-step explanation:
The magnitude of an earthquake on the Richter scale can be defined by
[tex]M=\frac{2}{3}\log (E)-3.2[/tex]
where E is the energy of the quake in joules.
Add 3.2 on both sides.
[tex]M+3.2=\frac{2}{3}\log (E)[/tex]
Multiply both sides by 3/2.
[tex]\frac{3}{2}(M+3.2)=\frac{3}{2}\times \frac{2}{3}\log (E)[/tex]
[tex]1.5M+4.8=\log (E)[/tex]
[tex]10^{1.5M+4.8}=E[/tex] [tex][\because \log x=a\Rightarrow x=10^a][/tex]
[tex]E=10^{1.5M+4.8}[/tex] .... (1)
It is given that the 2011 Tohoku earthquake in Japan measured 9.1 on the Richter scale.
Substitute M=9.1 in equation (1).
[tex]E=10^{1.5(9.1)+4.8}[/tex]
[tex]E=10^{18.45}[/tex]
[tex]E=2.8183829313\times 10^{18}[/tex]
Therefore, the energy released by earthquake in japan is [tex]E=2.8183829313\times 10^{18}[/tex].
It is given that the 1999 Hector Mine earthquake in eastern California had a magnitude of 7.1.
Substitute M=7.1 in equation (1).
[tex]E=10^{1.5(7.1)+4.8}[/tex]
[tex]E=10^{15.45}[/tex]
[tex]E=2.8183829313\times 10^{15}[/tex]
Therefore, the energy released by earthquake in California is [tex]E=2.8183829313\times 10^{15}[/tex].
