Solving a System of Equations in Linear Algebra

kasse
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In a city there are four one-way streets that cross each other like this:

http://www.badongo.com/pic/1751680

The number of cars that pass every hour is shown.

Show that x=(x1,x2,x3,x4) satisfies a system on the form

Ax=b
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I really have no clue what to to here.
 
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There are cars coming in, and coming out of each direction. The difference (out - in) is the number of cars that take a turn into another segment. Similar to a Markov problem.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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