Change of wired rifle microphones to a radio microphone system within a musical theatre

Please help me with this problem. If you can please supply any diagrams for this problem. The theatre's concerns when changing of wired rifle microphones to a radio microphone system are: on propagation related problems within the theatre and the positioning of transmit and receive antennas and "space diversity" reception. Please help me!!!

[3.6]If the Fourier transform of the signal v(t)? The minimum sampling rate for the signal?

If the Fourier transform of the signal v(t)? The minimum sampling rate for the signal? Attached pdf file. ================================================ OTA: Please take this problem only if you can show step by step problem solving. Thank you

[7] A voltage V is a function of time, t, and is given by V(t) = Xcoswt +YSinwt?

A voltage V is a function of time, t, and is given by V(t) = Xcoswt +YSinwt? Attached pdf file. ============================================ OTA: please take only if you can show step by step problem solving. thank you.

[8]To recover the baseband signal, m(t), from the amplitude-modulated signal?

To recover the baseband signal, m(t), from the amplitude-modulated signal? Attached pdf file. ============================================ OTA: please take this problem only if you can show step by step problem solving. thank you.

[9]The autocorrection function of this waveform, R(x), is given by?

The autocorrection function of this waveform, R(x), is given by? Attached pdf file. ====================================== OTA: please take this problem only if you can show step by step problem solving. thank you.