An earthquake occurs in city P. An expert finds that the magnitude of the earthquake (M) on the Richter scale of a place x km from city P is given by M=Ae^-0.007x, where A is a constant. The magnitude of an earthquake in city Q, which is 100 km from city P, is measured to be 4 on the Richter scale.
(a)Find the magnitude of the earthquake in city P on the Richter scale.
(b)Estimate the area of the region centered at P where the magnitude of the earthquake is 7 or above on the Richter scale. (Give your answer correct to the nearest 100 km^2)
F.4 AMaths
2010-05-01 6:16 am
回答 (2)
2010-05-01 7:49 am
✔ 最佳答案
a. Put M = 4, x = 1004 = Ae^(-0.007)(100), A = 8.055
So, the magnitude of earthquake at P = 8.055e^(-0.007x)
b. Put M = 7,
7 = 8.055e^(-0.007x)
Radius of the area, x = 20.05 km
As the seismic wave spread out uniformly, so the area, A
= pix^2
= pi(20.05)^2
= 1300 km^2 (to the nearest km^2)
參考: Physics king
2010-05-06 12:00 am
收錄日期: 2021-04-19 22:09:04
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https://hk.answers.yahoo.com/question/index?qid=20100430000051KK01589