Provide an appropriate response.The following equations each describe the motion of a particle. For which path is the particle's velocity vector always orthogonal to its acceleration vector?(1) r(t) = t4i + t4j(2) r(t) = cos (7t)i + sin (2t)j(3) r(t) = ti + t3j(4) r(t) = cos (-4t)i + sin (-4t)j
A. Path (2) and Path (4)
B. Path (4)
C. Path (3)
D. Path (1)
Answer: B
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Find the indicated probability. Round your answer to 6 decimal places when necessary.A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 3?
A. 
B. 16
C. 
D. 
Give the domain and range of the relation.
A. range: (-?, ?); domain: (-?, ?) B. range: (-?, 0) ? (0, 4) ? (4, ?); domain: (-?, -5) ? (-5, 0) ? (0, ?) C. range: (-?, 4) ? (4, ?); domain: (-?, -5) ? (-5, ?) D. None of these
Provide an appropriate response.Suppose the time (in minutes) applicants must wait to receive a driver's examination is uniformly distributed with density function f(x) = 
where 0 ? x ? 40 and f(x) = 0 elsewhere. What is the probability that an applicant must wait more than 35 minutes?
Fill in the blank(s) with the appropriate word(s).
Find the volume generated by revolving about the x-axis the region bounded by the following graph.
A. 48? B. 384? C. 640? D. 96?