Prefinal Exam Flashcards
Given the parts of an oblique spherical triangle: A = 121°, B = 29°, and a = 136°. Compute side c.
127.41°
Find the product of the complex number 3cis (π/3) and its conjugate.
9
Find the work done by a constant force F = 2i + 4j if its point of application to a block moves from P1(1, 1) to P2(4, 6). Assume that |F| is measured in newtons and |d| is measured in meters.
26 J
Given the vector 4i + 3j - 6k. Find the angle that the vector makes with the y-axis.
67.41°
Find the distance from Rio de Janeiro (22°54’ S, 43°10’ W) to Sydney (33°52’ S, 151°12’ E), in NM.
7, 297
A spherical triangle has an angle C = 90° and sides a = 50° and c = 80°. Find the value of b in degrees.
74.33°
Find the value of x in the equation: ( x + yi ) ( 1 - 2i ) = 7 - 4i.
3
Evaluate: ( 1 - i )⁷.
8 + 8i
Find the angle between the 2 vectors < 2, 2, -1 > and < 5, -3, 2 >.
84°
An airplane flew from Sydney ( 151°12’ E, 33°52’ S ) on a course N 40° W and maintaining a uniform altitude. What is its distance in nautical miles from Sydney when it crosses the equator?
2,473.20 NM
Evaluate: i⁴³ - i^-10
1 - i
A ship sails from New York ( 40°43’ N, 74° W ) to Cape of Good Hope ( 34°21’ S, 18°13’ E ). Find its course when it crosses the equator.
S 52° 54’ E
Find the torque at the origin if a constant force F = 2i + 5j - 3k is applied at a point ( 3, 4, 2 ). F is in newton and in m.
26.5 N/m
Find the value of x if the vectors A = 2i + 4j - 6k and B = xi - 2j + 3k are parallel.
-1
Find the absolute value of the complex number 3 + 4i.
5
