(Solved): Given the following systems, determine whether or not they are; (i) time-invariant, (ii) BIBO stab ...

Given the following systems, determine whether or not they are; (i) time-invariant, (ii) BIBO stable, (iii) causal, and/or (iv) memoryless. Use formal mathematical proofs to support your answers. (a) \( y(t)=\cos (x(t)+2 t) \) (b) \( y(t)=[x(t+1)]^{2} \)