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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
Under this section we're going to go back and revisit the concept of modeling only now we're going to look at this in light of the fact as we now understand how to solve systems of
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Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2 2 linear systems of ODE. (1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems are topologi
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