A particle moves so that r(t) = (3 cos t + 3t sin t)i + (3 sint – 3t cos t)j+ (2t² )k. Find the distance traveled by the particle from t = 0 to t = 67.

Find d cos Z dz

The number W (in thousands) of scenic and sightseeing transportation workers employed in a certain country during 2014 can be modeled by W = 31.176 + 8.541 sin(0.568t - 2.595) where t is the time (in months), with t = 1 corresponding to January. Find the average number of scenic and sightseeing transportation workers, in thousands, during the first quarter (0 ≤ t ≤ 3), the second quarter (3 ≤ t ≤ 6), and the entire year (0 ≤ t ≤ 12). (Round your answers to three decimal places.) (a) the first quarter (0 ≤ t ≤ 3) thousand workers (b) the second quarter (3 ≤ t ≤ 6) thousand workers (c) the entire year (0 ≤ t ≤ 12) thousand workers

A f(t) = 5 cos 100+ +) = 5 cos(10 +7) Find its amplitude, frequency, and period. B. Sketch g(t)=e* sin (27).