Kyy010203 發問於 科學及數學數學 · 1 十年前

F.4 AMaths

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)

2 個解答

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  • 1 十年前
    最愛解答

    a. Put M = 4, x = 100

    4 = 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)

    資料來源: Physics king
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