Math

CalculusQ&A Libraryhe Richter scale is used to measure the intensity of earthquakes. The Richter scale rating of an earthquake is given by the formula R = (2/3)(log(E)-11.8) where E is the energy released by the earthquake (measured in ergs†). a) The San Francisco earthquake of 1906 is estimated to have registered R = 7.9 on the Richter scale. How many ergs of energy were released? (Round the significand, or coefficient of the scientific notation to three decimal places.) ____x10^23ergs b) The Japan earthquake of 2011 registered 9.0 on the Richter scale. Compare the two: The energy released in the 1906 earthquake was what percentage of the energy released in the 2011 quake? (Round your answer to two decimal places.) c) Solve the equation given above for E in terms of R. d)Use the result of part (c) to find the ratio of two earthquakes registering R1 and R2 on the Richter scale, assuming they release E1 and E2 ergs of energy, respectively. (Simplify your answer completely. Enter your answer in terms of R1 and R2 only.) e)If one earthquake registers 2 points more on the Richter scale than another, then it releases _____ times the amount of energy.Start your trial now! First week only $4.99!*arrow_forward*

Question

he Richter scale is used to measure the intensity of earthquakes. The Richter scale rating of an earthquake is given by the formula

R = (2/3)(log(E)-11.8)

where *E* is the energy released by the earthquake (measured in ergs†).

a) The San Francisco earthquake of 1906 is estimated to have registered R = 7.9 on the Richter scale. How many ergs of energy were released? (Round the significand, or coefficient of the scientific notation to three decimal places.)

____x10^23ergs

b) The Japan earthquake of 2011 registered 9.0 on the Richter scale. Compare the two: The energy released in the 1906 earthquake was what percentage of the energy released in the 2011 quake? (Round your answer to two decimal places.)

c) Solve the equation given above for *E* in terms of *R*.

d)Use the result of part (c) to find the ratio of two earthquakes registering *R*_{1} and *R*_{2} on the Richter scale, assuming they release *E*_{1} and *E*_{2} ergs of energy, respectively. (Simplify your answer completely. Enter your answer in terms of *R*_{1} and *R*_{2} only.)

e)If one earthquake registers 2 points more on the Richter scale than another, then it releases _____ times the amount of energy.

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