alpha 273degree v 426 Find the vertical component of v A 1

alpha = 273degree, |v| = 426; Find the vertical component of v. A) 195.4 B) 183.2 C) 378.6 D) 574 13) alpha = 533degree, |v| = 21.6; Find the horizontal component of v. A) 12.9 B) 17.3 C) 4.4 D) 30.2 14) C = 121.6degree a = 4.9 km b = 9.9 km A) c = 13.1 km, A = 18.8degree, B = 39.6degree B) No triangle satisfies the given conditions. C) c = 18.9km, A = 16.8degree, B = 41.6degree D) c = 16 km, A = 20.8degree, B = 37.6degree Find all real numbers in the interval [0,2pi) that satisfy the equation. 15) tanx + secx = 1 A) {5pi/4} B) {0} C) No solution D) {pi/4} Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. 16) squareroot3(cos 315 + i sin 315)/squareroot6(cos 45 + i sin 45) A) squareroot2/2 B) squareroot2/2+squareroot2/2i C) -squareroot2/2i D) -squareroot2/2-squareroot2/2i Determine whether the vectors are parallel, perpendicular, or neither. 17) v=(2,3), w = (3, -2) A) perpendicular B) parallel C) neither Two forces of 320 N and 220 N (newtons) act on an object. The angle between the forces is 15degree. Find the magnitude of the resultant and the angle that it makes with the larger force. A) 535 N, 6degree B) 4 N, 6degree C) 537N,6degree D) 536N,6degree Two forces of 250 N and 60 N (newtons) act on an object at right angles. Find the magnitude of the sultant and the angle that it makes with the larger force. A) 257N, 77degree B) 257 N,13degree C) 257 N,3degree D) 66,100 N, 13degree

Solution

12) |v| = 426

alpha = 27.3 deg

vertical component = |v| cos alpha

= 426 cos 27.3 = 378.55

13) |v| = 21.6

alpha = 53.3 deg

horizontal component = |v| sin alpha

= 21.6 sin 53.3

= 17.32

14 ) C = 121.6 deg

a = 4.9 km

b = 9.9 km

applying cosine rule

c^2 = a^2 + b^2 - 2ab cos C

c^2 = 4.9^2 + 9.9^2 - 2(4.9)(9.9) cos 121.6

c^2 = 172.85

c = 13.14

applying sine rule

a / sin A = c / sin C

4.9 / sin A = 13.14 / sin 121.6

sin A = 4.9 / 15.42

A = 18.52 deg

B = 180 - ( 18.52 + 121.6 ) = 39.88

option A is correct