Matematika/Lanko ilgis: Skirtumas tarp puslapio versijų
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49 eilutė:
:<math>ds=\sqrt{1+\left(\frac{dy}{dx}\right)^2} dx =\sqrt{1+\left(\frac{\frac{d\rho}{d\theta}\sin\theta+\rho\cos\theta}{\frac{d\rho}{d\theta}\cos\theta-\rho\sin\theta}\right)^2} (\frac{d\rho}{d\theta}\cos\theta-\rho\sin\theta)d\theta =</math>
:<math>=\sqrt{(\frac{d\rho}{d\theta}\cos\theta-\rho\sin\theta)^2+(\frac{d\rho}{d\theta}\sin\theta+\rho\cos\theta)^2}d\theta =</math>
:<math>=\sqrt{\left(\frac{d\rho}{d\theta}\right)^2\cos^2\theta-\rho\frac{d\rho}{d\theta}\sin(\theta)\cos(\theta)+\rho^2\sin^2\theta)^2+(\frac{d\rho}{d\theta}\right)^2\sin^2\theta+\rho\frac{d\rho}{d\theta}\sin(\theta)\cos(\theta)+\rho^2\cos^2\theta)^2}d\theta =</math>
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