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Get Full Access to Linear Algebra With Applications - 8 Edition - Chapter 3.5 - Problem 2
Get Full Access to Linear Algebra With Applications - 8 Edition - Chapter 3.5 - Problem 2

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# The populations of U.S. cities, suburbs, and nonmetro areas in 2012 are described by the ISBN: 9781449679545 435

## Solution for problem 2 Chapter 3.5

Linear Algebra with Applications | 8th Edition

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Problem 2

The populations of U.S. cities, suburbs, and nonmetro areas in 2012 are described by the following vector Xo (in units of one million), and the populations in the following years are given by a Markov chain with the transition matrix P. (See Exercise 7, Section 2.8.) Determine the long-term predictions for the populations of these regions, assuming no change in their total population. (This model is a refinement of the model of the previous exercise in that the metro areas are broken down into city and suburbia.) Initial populations Xo = [ li ::urb 52 nonmetro (from) city suburb nonmetro (to) [ 0.% 0.01 O.ot5] city p = 0.03 0.98 0.005 suburb 0.01 0.01 0.98 nonmetro

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Trigonometry Section 2.4 and 2.5 Cos(a-b) = cosacosb + sinasinb Cos(a+b) = cosacosb – sinasinb Sin(a-b) = sinacosb - cosasinb Sin(a+b) = sinacosb + cosasinb tana−tanb Tan(a-b) =1+tanatanb tana+tanb Tan(a+b) = 1−tanatanb Here is an example problem: 7π 7π 2π π Find the Exact value ofn12 (hint: 12= 3− 4 ) 2π π 2π π 2π π sin(3 − 4)=sin 3 cos4−cos 3 sin4 Plug in the values ¿ √3 √2 − −1 √2 ( 2 ( 2 ( 2 ( 2 Derive reference angles ¿ √6−− √ Multiply 4 4 √ √ 2 4 Combine (this is the finished form of the problem

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##### ISBN: 9781449679545

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