Solving a Puzzling Equation: A Homework Statement

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Homework Statement



Hi .

I found this in my textbook. I want to know how they got to the answer. I really don't know how they got it.

\frac{\frac{x}{2}}{0.40-\frac{x}{2}}= 6.8 x 10-2
x= 0.0272 - 0.068x
x= 0.025

Homework Equations


N/A


The Attempt at a Solution


i just don't know where to start or how to solve this.
 
Last edited:
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Multiply both sides by 0.4-x/2
 
rootX said:
Multiply both sides by 0.4-x/2
thanks...cant believe the solution was so simple...sometimes the easiest things become so mind boggling
 
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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