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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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I need help with 1 and 2 thank you so much!!
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Let's look at the Richter scale, a logarithmic function that is used to measure the magnitude of
earthquakes. The magnitude of an earthquake is related to how much energy is released by the
quake. Instruments called seismographs detect movement in the earth; the smallest movement
that can be detected shows on a seismograph as a wave with amplitude Ao.
A- the measure of the amplitude of the earthquake wave
Ao – the amplitude of the smallest detectable wave (or standard wave)
From this you can find R, the Richter scale measure of the magnitude of the earthquake using the
formula:
R = log
The intensity of an earthquake will typically measure between 2 and 10 on the Richter scale. Any
earthquakes registering below a 5 are fairly minor; they may shake the ground a bit, but are
seldom strong enough to cause much damage. Earthquakes with a Richter rating of between 5
and 7.9 are much more severe, and any quake above an 8 is likely to cause massive damage.
(The highest rating ever recorded for an earthquake is 9.5 during the 1960 Valdivia earthquake in
Chile.)
1. Use the logarithm properties to solve this equation for Ao.
2. We want to compare two earthquakes. Using the equation you got in part A, plug in A1
and Ri for earthquake 1 and do the same for earthquake 2 with A2 and R2. Since both of
these equations are equal to Ao, you can set them equal to each other. Do this and then
solve for R2-R1.
3. Earthquake 1 registered 7.0 on the Richter scale. Earthquake 2 was 3 times stronger than
Earthquake 1. What did Earthquake 2 register on the Richter scale?
4. Earthquake 1 measured a 7.0 on the Richter scale. Earthquake 2 registered 5.3. How much
more intense was Earthquake 1?"
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Let's look at the Richter scale, a logarithmic function that is used to measure the magnitude of
earthquakes. The magnitude of an earthquake is related to how much energy is released by the
quake. Instruments called seismographs detect movement in the earth; the smallest movement
that can be detected shows on a seismograph as a wave with amplitude Ao.
A- the measure of the amplitude of the earthquake wave
Ao – the amplitude of the smallest detectable wave (or standard wave)
From this you can find R, the Richter scale measure of the magnitude of the earthquake using the
formula:
R = log
The intensity of an earthquake will typically measure between 2 and 10 on the Richter scale. Any
earthquakes registering below a 5 are fairly minor; they may shake the ground a bit, but are
seldom strong enough to cause much damage. Earthquakes with a Richter rating of between 5
and 7.9 are much more severe, and any quake above an 8 is likely to cause massive damage.
(The highest rating ever recorded for an earthquake is 9.5 during the 1960 Valdivia earthquake in
Chile.)
1. Use the logarithm properties to solve this equation for Ao.
2. We want to compare two earthquakes. Using the equation you got in part A, plug in A1
and Ri for earthquake 1 and do the same for earthquake 2 with A2 and R2. Since both of
these equations are equal to Ao, you can set them equal to each other. Do this and then
solve for R2-R1.
3. Earthquake 1 registered 7.0 on the Richter scale. Earthquake 2 was 3 times stronger than
Earthquake 1. What did Earthquake 2 register on the Richter scale?
4. Earthquake 1 measured a 7.0 on the Richter scale. Earthquake 2 registered 5.3. How much
more intense was Earthquake 1?
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