Two waves are simultaneously passing through a string and their equations are: $y_1 = A_1 \sin k(x - vt)$, $y_2 = A_2 \sin k(x - vt + x_0)$. Given amplitudes $A_1 = 12\text{ mm}$ and $A_2 = 5\text{ mm}$, $x_0 = 3.5\text{ cm}$ and wave number $k = 6.28\text{ cm}^{-1}$. The amplitude of resulting wave will be $\_\_\_\_$ mm.