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1. Let QC(x) = x2 + c. Prove that if c < 1/4, there is a unique μ > 1 such that Qc is topologically conjugate to Fμ(x) = μx(1 - x) via a map of the form h(x) = αx+β.
2. A point p is a non-wandering point for f, if, for any open interval J containing p, there exists x E J and n > 0 such that fn(x) E J. Note that we do not require that p itself return to J. Let Ω(f) denote the set of non-wandering points for f.
a. Prove that Ω(f) is a closed set.
b. If Fμ. is the quadratic map with μ > 2 + √5, show that SI(Fμ) = Λ.
c. Identify Ω(Fμ) for each μ satisfying 0 < µ ≤ 3.
The perimeter of a swimming pool is 97m. The width is 2m more than helf of lenght of the pool, find the lenght and the width of the pool?
a recent study of 25 commuters showed that they spent an average of 18.23 on public transportation per week. the
Mathematics-Supply Greater Than Demand- Transportation Model, A company which owns hauling trucks moves materials between three sources (depots) and three destination projects.
simulate 106 outcomes x y wherex r costheta y rsinthetawith theta u0 2pi and r 5 s with s exp1 independently of
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Two tracking stations are on the equator 119 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and a bearing of N 22°E from the eastern station. How far, to the nearest mile, is the balloon from the western ..
Given the explicit solution from part (a), what is the largest possible t-interval on which the explicit solution makes sense?
A dock is 15 feet above the water. Suppose you stand on the edge of the dock and pull a rope attached to a boat at the constant rate of 3 ft/sec. Assuming that the boat remains at water level, at what speed is the boat approaching the dock when it..
Two buses leave towns apart at the same time and travel toward each other. One bus travels slower than the other. If they meet in hours, what is the rate of each bus?
Find the gradient of f(x,y) at (3,2). Compute the directional derivative (triangle u) f(3,2) where u is the unit vector in the direction of v =
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