Question

The Richter scale is a way of converting seismographic readings into numbers that provide easy reference for measuring the magnitude M of an earthquake. Scientists don't rely on it, but it is still the scale reported in the media whenever an earthquake occurs. All earthquakes are compared to a zero-level earthquake whose seismographic reading measures 0.001 millimeter at a distance of 100 kilometers from the epicenter. An earthquake whose seismographic reading measures millimeters has magnitude M(z) given by M(c) = log(z/To) where To is the reading of the zero-level earthquake at the same distance from its epicenter. The intensity of an earthquake is defined as the ratio of z to To. What is the magnitude of an earthquake whose seismographic reading is 0.1 millimeter at a distance of 100 kilometers from its epicenter? What is its intensity? The San Francisco earthquake of 1906 measured 8.3 on the Richter scale. How did the intensity of that earthquake compare to a more recent (May 2008) earthquake in China which measured 7.9 on the Richter scale?

          The Richter scale is a way of converting seismographic readings into numbers that provide easy reference for measuring the magnitude M of an earthquake. Scientists don't rely on it, but it is still the scale reported in the media whenever an earthquake occurs. All earthquakes are compared to a zero-level earthquake whose seismographic reading measures 0.001 millimeter at a distance of 100 kilometers from the epicenter. An earthquake whose seismographic reading measures millimeters has magnitude M(z) given by
M(c) = log(z/To)
where To is the reading of the zero-level earthquake at the same distance from its epicenter.
The intensity of an earthquake is defined as the ratio of z to To.
What is the magnitude of an earthquake whose seismographic reading is 0.1 millimeter at a distance of 100 kilometers from its epicenter? What is its intensity? The San Francisco earthquake of 1906 measured 8.3 on the Richter scale. How did the intensity of that earthquake compare to a more recent (May 2008) earthquake in China which measured 7.9 on the Richter scale?

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Added by Alexander H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman K

07/05/2022

Step 1

1 millimeter at a distance of 100 kilometers from its epicenter, we use the formula M(c) = log(z/To), where z = 0.1 and To = 0.001. Plugging in the values, we get M(c) = log(0.1/0.001) = log(100) = 2. Show more…

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The Richter scale is a way of converting seismographic readings into numbers that provide easy reference for measuring the magnitude M of an earthquake. Scientists don't rely on it, but it is still the scale reported in the media whenever an earthquake occurs. All earthquakes are compared to a zero-level earthquake whose seismographic reading measures 0.001 millimeter at a distance of 100 kilometers from the epicenter. An earthquake whose seismographic reading measures millimeters has magnitude M(z) given by M(c) = log(z/To) where To is the reading of the zero-level earthquake at the same distance from its epicenter. The intensity of an earthquake is defined as the ratio of z to To. What is the magnitude of an earthquake whose seismographic reading is 0.1 millimeter at a distance of 100 kilometers from its epicenter? What is its intensity? The San Francisco earthquake of 1906 measured 8.3 on the Richter scale. How did the intensity of that earthquake compare to a more recent (May 2008) earthquake in China which measured 7.9 on the Richter scale?

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00:01 The question named the ritter -wit scale is a way of converting seismographic readings into numbers that provide easy reference for measuring the magnitude m of an earthquake.

00:08 The question that allows the whole text of this question is, what is the magnitude of an earthquake whose seismographic reading is 0 .1mm distance of 100 kilometers from its epicenter, that is part a.

00:23 Part b is what is the intensity, the san francisco earthquake of 19 .06 measured 8 .300 scale.

00:30 And the option of question c is, how did the intensity of that earthquake compared to more recent earthquake in china, which measured 7 .9 on the richer scale.

00:39 Coming to the solutions, one by one, we know that mx is equal to log x upon x not.

00:52 The x not is equal to 0 .001 which m that is at 100 kilometer epicenter epi center okay so it is zero level earthquake it is zero level earthquake coming to the question number one question number one is we have to find out the intensity of the earthquake.

01:33 We have the formula mx is equal to log keeping the values of in the given formula 1 log 0 .1 divided by 0 .0 .01 so we get it as m x is equal to log 100.

01:55 The value of log 100 is 2 now i is equal to x divided by x x not which is equal to 0 .1 divided by 0 .001 which is equal to 100.

02:13 So the intensity of earthquake.

02:19 So the magnitude of earthquake is, so the magnitude of earthquake is 2 and the intensity is 100.

02:42 Now coming to answer number b, that is question number b.

02:46 M.

02:46 Mishin number b is asking what is the intensity the san francisco earthquake of 1906 measured 8 .3 on the richer scale.

02:52 Now the san francisco magnitude was san francisco earthquake is equal to 8 .3.

03:10 So according to the formula 8 .3 is equal to log x divided by 0 .001.

03:19 X is equal to 0 .001 .10 raised to the power 8 .3, multiplied by 10 ways to the power 8 .3...

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