In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter H(f) is shown in Figure (b). If it is desired that the output signal z(t) = 10x(t), the maximum value of W (in Hz) should be strictly less than ___________________________

The waveform of a periodic signal x(t) is shown in the figure.

A signal g(t) is defined by $$g(t) = x\left( {{{t - 1} \over 2}} \right)$$.

The average power of g(t) is___________________________.

If $$\log_x\left(\frac57\right)=\frac{-1}3$$, then the value of x is

Operators $$\square$$,◊,$$\rightarrow$$ are defined by : a $$\square$$ b = $$\frac{a-b}{a+b}$$; a ◊ b = $$\frac{a+b}{a-b}$$; a $$\rightarrow$$ b = ab. Find the value of (66 $$\square$$ 6) $$\rightarrow$$ (66 ◊ 6).