The speed of the boat against the stream is calculated as:
u - v = 5 (km/hr)
Substitute the value of \( u \):
7 - v = 5
Solving for \( v \):
v = 7 - 5 v = 2 km/hr
Thus, the speed of the stream is 2 km/hr, which matches option (b).
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.