[tex]1) \\ Notatie: \\ \alpha =\;\text{masura unghiului cautat} \\ L_{cerc} =2\pi R = 2\pi * 9=18\pi \;cm \\ \frac{ \alpha}{360} = \frac{3\pi}{18\pi} \\ \\ \alpha=\frac{360*3\pi}{18\pi} =\frac{360*3}{18}= \frac{360}{6}=\boxed{60^o}[/tex]
[tex]2) \\ 4 x^{2} + y^{2} = 4(3x+2y)-25 \\ 4 x^{2} + y^{2} = 12x+8y-25 \\ 4 x^{2} + y^{2} - 12x-8y+25=0 \\ 4 x^{2} - 12x + y^{2}-8y+25= 0 \\ 4 x^{2} - 12x + y^{2}-8y+9+16= 0 \\ (4x^{2} - 12x + 9)+ (y^{2}- 8y+16)= 0 \\ (2x-3)^2+ (y-4)^2=0 \\ 2x-3=0 \;\;\;=\ \textgreater \ x = \frac{3}{2} \;\;\; (radacina \;dubla) \\ y-4=0\;\;\; =\ \textgreater \ \;\;\;y=4\;\;\; (radacina \;dubla) \\ m_g = \sqrt{xy} =\sqrt{\frac{3}{2}*4}= \sqrt{3*2}= \boxed{\sqrt{6}} [/tex]
