Math 1316 t4rsu14. Name: 06/24/2014

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1 Name: 06/24/2014 Math 1316 t4rsu14 1. Given A=52, B= 74, and c=8, use the Law of Sines to solve the triangle for the value of a. Round 2. Given C=116, a=12.9, and c=8.3, use the Law of Sines to solve the triangle (if possible) for the value of b. If two solutions exist, find both. Round 3. Given A=10,b=12, anda=10, use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round 4. A park ranger at point A observes a fire in the direction N 25 36'E. Another ranger at point B, 5 miles due east of A, sites the same fire at N 56 19'W. Determine the distance from point B to the fire. Round answer to two decimal places. 5. Given a=9, b=10, and c=15, use the Law of Cosines to solve the triangle for the value of B. Round 1

2 6. Given A=108, b=9, and c=15, use the Law of Cosines to solve the triangle for the value of a. Round 7. Given a=14, b=12, and c=11, use Heron's Area Formula to find the area of triangle ABC. Round 8. Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N 45 W at 15 miles per hour, and the other travels at a bearing of S 58 W at 17 miles per hour. Approximate the distance between them at noon the same day. Round 9. Find u+ v. u= 4, 1,v= 1,5 10. Find 2u 3v. u=6i, v=j 11. Find the component form of v given its magnitude and the angle it makes with the positive -axis. Magnitude Angle Ä vä= Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 102 miles per hour. If he threw the pitch at an angle of 38 below the horizontal, find the vertical and horizontal components of the velocity.(round your answers to one decimal place.) 2

3 13. The initial and terminal points of vector v are ( 3, 5) and ( 6,6), respectively. Find v in component form. 14. Find the magnitude of vector v. 15. Let w be a vector with initial point ( 4,9) and terminal point ( 7, 3). Write w as a linear combination of the standard unit vectors i and j. 16. Find the dot product of u and v. u= 6,9 v= 2, 7 3

4 17. A force of y= 65 pounds exerted at an angle of 30 above the horizontal is required to slide a table across a floor (see figure). The table is dragged x = 16 feet. Determine the work done in sliding the table. (Note: w=fd, work is forct times distance.) 18. A 875-pound trailer is sitting on an exit ramp inclined at 34 on Highway 35. How much force is required to keep the trailer from rolling back down the exit ramp? Round 19. Find the trigonometric form of i. 20. Find the standard form of the complex number 10 cos( 30 )+isin( 30 ) ˆ. 21. Multiply the complex numbers. Write the answer in trigonometric form. 5 cos 2π 9 +isin 2π ˆ 9 2 cos 3π 7 +isin 3π ˆ Use DeMoivre s Theorem to find the indicated power of the complex number. Write the result in standard form. ( 1+i) Use DeMoivre s Theorem to find the indicated power of the complex number. Write the result in standard form. È 2 cos π 2 +isinπ ÎÍ 2 ˆ 8 4

5 24. Use DeMoivre s theorem to find the indicated roots of the complex number. Fourth roots of 81i 5

6 ID: A Math 1316 t4rsu14 Answer Section 1. b= not possible 3. c=2.04 and miles sq. units miles 9. 5, i 3j , Vertical 62.8 mi h, Horizontal 80.4 mi h. 13. v= 3, ÄvÄ = w= 3i 12j ft-lb pounds cos π 6 +isinπ ˆ i cos 41π i k = 0: 3 cos π 8 +isinπ ˆ 8 k = 1: 3 cos 5π 8 +isin 5π ˆ 8 k = 2: 3 cos 9π 8 +isin 9π ˆ 8 k = 3: 3 cos 13π 13π ˆ +isin 8 8 1