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Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot. If α , β be the elevations of the top of the tower from these stations, prove that its inclination ? is given by cot ? = b cot α - a cot β/b-a .
Ans: Let AE = x, BE = h
Tan φ =BE/AE =h/x
x= h x (1/tan φ)
x = h cot φ ---------------1
tan α =BE/CE = h /a + x
a + x = h cot α
x= h cot α - a --------------2
tan β = BE/DE = h/b + x
b+x = h cot β
x = h cot β - b ---------------3
from 1 and 2
h cot φ = h cot α - a
h ( cot φ + cot α ) = a
h = a /- cot φ + cot α -------------4
from 1 and 3
h cot φ = h cot β - b
h ( cot φ - cot β) = b
h= b/- cot φ + cot β
from 4 and 5
a/- cot φ + cot α = b/- cot φ + cot β
a (cot β - cot φ ) = b ( cot α - cot φ )
- a cot φ + b cot φ = b cot α - a cot β
(b - a) cot φ = b cot α - a cot β
cot φ = b cot α - a cot β/b - a
In a frequency distribution mode is 7.88, mean is 8.32 find the median. (Ans: 8.17) Ans: Mode = 3 median - 2 mean 7.88 = 3 median - 2 x 8.32 7.88 +16.64 = 3 median
Steps for Radio test Assume we have the series ∑a n Define, Then, a. If L b. If L>1 the series is divergent. c. If L = 1 the series might be divergent, this i
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a statisics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. find the probability that a given class pe
4856+12334
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