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Murljashka [212]
3 years ago
11

by what approximate factor is the intensity of an earthquake with the magnitude 5.4 greater than an earthquake with magnitude 5.

3?
Mathematics
2 answers:
erica [24]3 years ago
8 0
1.26 girl im going back from the test and answering all questions
slava [35]3 years ago
3 0

Answer:

The intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3 is about 1.3 times greater.

Step-by-step explanation:

Given : An earthquake with the magnitude 5.4 greater than an earthquake with magnitude 5.3.

To find : By what approximate factor is the intensity of an earthquake of given magnitudes is greater?

Solution :

The equation for the magnitude of an earthquake is given by

M=\log(\frac{I}{I_{0}})

Where, I is the intensity of earthquake and I_0  is constant.

For an earthquake with magnitude 5.4,

5.4= log(\frac{I_{1} }{I_{0} })

Similarly, for an earthquake with magnitude 5.3,

5.3= log(\frac{I_{2} }{I_{0} })

Now, equating both the magnitudes

\frac{log(\frac{I_{1} }{I_{0} })}{log(\frac{I_{2} }{I_{0} })} =\frac{5.4 }{5.3 } \\\\(\frac{I_{1} }{I_{2} })=\frac{10^{5.4} }{10^{5.3} }\\\\(\frac{I_{1} }{I_{2} }) =10^{5.4-5.3}=1.2589\simeq 1.3\\\\I_{1} =1.3I_{2}

The intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3 is about 1.3 times greater.

The factor is 1.3.

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