MA 154 Exam 3 Spring 2008 This exam covers Section 7.4 starting with Question #35, and all of Sections 7.6, 8.1, 8.2, 8.3 and 8.4 11. Given 4,5 and 7,8 find 3 2ab ab==−− A. 2,5 B. 22, 5−− C. 2,31− D. 26, 1− E. None of the above 2. Determine the value of m such that the two vectors are orthogonal. 2 8 and 16 5amij b ij=+ =− A. 1.25− B. 5 C. 1.25 D. 5− E. None of the above. 3. Approximate the solutions to four decimal places in the interval [)0,π. 210cos 4cos 5 0xx−−= A. 0.3630,2.1351 B. 0.9348, 0.5348− C. 1.0065,2.7786 D. 0.6848, 0.8002− E. None of the aboveMA 154 Exam 3 Spring 2008 This exam covers Section 7.4 starting with Question #35, and all of Sections 7.6, 8.1, 8.2, 8.3 and 8.4 24. If a projectile is fired from ground level with an initial velocity v ft/sec and at an angle of θ degrees with the horizontal, the range R of the projectile is given by: 2sin cos16vRθθ= If v = 92 ft/sec, approximate the angles, to the nearest tenth of a degree, that result in a range of 162 feet. A. 19.7 ,70.3°° B. 18.9 ,71.1°° C. 20.1 ,69.9°° D. 21.2 ,68.8°° E. None of the above. 5. Find the solutions of the equation that are in the interval [)0,2π. ()()sin 2 sin 0tt+= A. 50, , ,33πππ B. 324,,,22 3 3ππππ C. 240, , ,33πππ D. 35,,,2233πππ π E. None of the above.MA 154 Exam 3 Spring 2008 This exam covers Section 7.4 starting with Question #35, and all of Sections 7.6, 8.1, 8.2, 8.3 and 8.4 36. Find the exact value of the expression. 1cos cos3π−⎡⎤⎛⎞−⎜⎟⎢⎥⎝⎠⎣⎦ A. 3π B. 23π C. 43π D. 3π− E. None of the above. 7. Write the expression as an algebraic expression in x for x > 0. 1sin 2tan3x−⎡⎤⎛⎞⎜⎟⎢⎥⎝⎠⎣⎦ A. 2669xxx++ B. 2623xx− C. 2299xx− D. 269xx+ E. None of the above.MA 154 Exam 3 Spring 2008 This exam covers Section 7.4 starting with Question #35, and all of Sections 7.6, 8.1, 8.2, 8.3 and 8.4 48. Which of the following equations most closely resembles the graph of the function? A. ()1sinyx−= B. ()11sin 22yx−= C. 12sin2xy−⎛⎞=⎜⎟⎝⎠ D. 11sin22xy−⎛⎞=⎜⎟⎝⎠ E. ()12sin 2yx−= 9. Which of the following best describes the length of side b? A. Between 40 and 41 B. Between 39 and 40 C. Between 38 and 39 D. Between 41 and 42 E. None of the above 10. Find the smallest positive angle between vectors 3, 8 and 7,12−− − , to the nearest whole degree. A. 51º B. 120º C. 60º D. 129º E. None of the above -1 - 1/2 0 1/2 1π π− 49° 12 34 bMA 154 Exam 3 Spring 2008 This exam covers Section 7.4 starting with Question #35, and all of Sections 7.6, 8.1, 8.2, 8.3 and 8.4 511. From point P along a level path the angle of elevation of the top of a tree is 34°. From a point 50 meters closer to the tree, and along a line connecting the base of the tree and point P, the angle of elevation of the top of the same tree is 49°. What is the height of the tree to the nearest tenth of a meter? A. 60.4 meters B. 81.5 meters C. 89. 6 meters D. 73.8 meters E. None of the above 12. Which of the following best describes the measure of angle γ? A. Between 80° and 81° B. Between 24° and 25° C. Between 20° and 21° D. Between 84° and 85° E. Between 42° and 43° 13. Which of the following is a unit vector in the opposite direction as 512aij=− +. A. 512ij−+ B. 51213 13ij− C. 5 12ij− D. 51213 13ij−+ E. None of the above 37° 12 γ 29MA 154 Exam 3 Spring 2008 This exam covers Section 7.4 starting with Question #35, and all of Sections 7.6, 8.1, 8.2, 8.3 and 8.4 614. Distance between automobiles. Two automobiles leave a city at the same time and travel along straight highways that differ in direction by 80°. If their speeds are 60 mi/hr and 45 mi/hr, respectively, approximately, to the nearest tenth of a mile, how far apart are the cars at the end of 25 minutes? A. 34.5 miles B. 68.5 miles C. 36.5 miles D. 48.5 miles E. None of the above 15. An airplane, with airspeed of 200 miles per hour, is flying in the direction 60º and a 55 mile per hour wind is blowing directly from the west. What is the ground speed of the airplane rounded to the nearest mile per hour? A. 249 mph B. 154 mph C. 232 mph D. 179 mph E. None of the aboveMA 154 Exam 3 Spring 2008 This exam covers Section 7.4 starting with Question #35, and all of Sections 7.6, 8.1, 8.2, 8.3 and 8.4 7Exam 3 Answers Question Answer Form A Green 1. 26, 1− D 2. 1.25 C 3. 0.3630,2.1351 A 4. 18.9 ,71.1°° B 5. 240, , ,33πππ C 6. 3π A 7. 269xx+ D 8. ()12sin 2yx−= E 9. b=40.6 A 10. 129º D 11. 81.5 meters B 12. 20.4 C 13. 51213 13ij− B 14. 28.5 miles E 15. 249 mph