Question

In a river basin a station A was in operative during a storm, while stations B,C,D and E, surrounding A were in operation, recording 74 mm,88 mm,71 mm and Xmm of monthly rainfall. The coordinates of the stations in km are A(0,0),B(9,6),C(12,−9),D(−11,−6) and E(−7,7). Estimate the missing monthly rainfall of station A by the inverse distance method. Where X is the last two digits of your Registration #

Answer 1

80.04 mm

Step-by-step explanation:

X = 85mm.

AB² = 117, AC² = 135, AD² = 157. AE = 7√2.

Sum of inverse squares = 0.03253.

coefficient of rainfall at B = 1/117 ÷ 0.03253

contribution of rainfall at B towards A:

74 ×( 1÷117 )÷ 0.03253 mm = 19.44 mm

contribution of rainfall at C towards A:

88 ×( 1÷135 )÷ 0.03253 mm = 20.04 mm.

contribution of rainfall at D towards A:

71 ×( 1÷157 )÷ 0.03253 mm = 13.90 mm.

contribution of rainfall at E towards A:

85 ×( 1÷98 )÷ 0.03253 mm = 26.66 mm.

Estimate of the rainfall at A: summing the above four contributions to the estimate

= 80.04 mm.

formula= Xi × 1/d_i² /( Sum of all 1/d_i²)