Matematika/Evoliutė ir evolventė: Skirtumas tarp puslapio versijų

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:<math>y'=\frac{y_t'}{x_t'}; \quad y''=\frac{ y_t'' x_t' - y_t' x_t''}{x_t'^3}.</math>
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:<math>\alpha=x-\frac{\frac{y_t'}{x_t'}(1+(\frac{y_t'}{x_t'})^2)}{\frac{ y_t'' x_t' - y_t' x_t''}{x_t'^3}}=x-\frac{y_t'}{x_t'}(1+(\frac{y_t'}{x_t'})^2)\cdot \frac{ x_t'^3}{ y_t'' x_t' - y_t' x_t''}=x-\frac{y_t'}{x_t'}\cdot\frac{(x_t')^2+(y_t')^2}{(x_t')^2}\cdot \frac{ x_t'^3}{ y_t'' x_t' - y_t' x_t''}=x-\frac{y'(x'^2+y'^2)}{ y'' x' - y' x''}, \quad (7')</math>
:<math>\beta=y+\frac{1+(\frac{y_t'}{x_t'})^2}{\frac{ y_t'' x_t' - y_t' x_t''}{x_t'^3}}=y+\frac{x'(x'^2+y'^2)}{ y'' x' - y' x''}. \quad (7')</math>
 
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