= 379. The equation y 0.01 cos(400πt) sin(x) is one possible model for the motion of a stretched string that is 1 foot l

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= 379. The equation y 0.01 cos(400πt) sin(x) is one possible model for the motion of a stretched string that is 1 foot long and that is vibrating 200 times per second. The small number 0.01 is the amplitude (in feet) of the oscillation. Choosing a t-value is equivalent to taking a snapshot of the string, which is defined for x-values from 0 to 1, inclusive (x = 0 is one end of the string and î 1 is the other end). = (a) How far does the center of the string move during one complete vibration? (b) What is the average speed of the center of the string during the interval 0 ≤ t ≤ 0.005? What is the average velocity? (c) Does the center of the string move with constant velocity? With constant speed? (d) Calculate Dty for the center of the string. 1 (e) Calculate Dty for the point on the string where x = 4