2. In the real-world, humans hear sound as an analog signal. This means the signal is a continuous waveform, which is completely processable by human ears. However, machines 'hear' sound a little
differently, as they process sound digitally, which is a discrete waveform.
When sound is recorded or transmitted electronically, the continuous (analog) waveform is sampled to
convert it to a discrete (digital) sequence. Sampling is the process of reducing a continuous-time
signal to a discrete-time signal. As the sampling rate increases, the sound quality of the recording or
transmission will improve.
The graphs below represent two different samples of a pure tone. Sample 1 is taken 8 times per unit
of time. Sample 2 is taken 16 times per unit of time.
I
Sample 1:

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24