MA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 1 1. Find the exact value of the expression. 12sin sin3π−       A. 3π B. 23π C. 3π− D. 43π E. None of the above 2. Approximate the solutions of the equation, to four decimals, in the interval,2 2π π −  . 25sin sin 2 0x x− − = A. 0.7373, 0.9633− B. 0.5708, 0.8335− C. 0.4820, 1.4245− D. 0.5403, 0.7403− E. None of the aboveMA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 2 3. Find the exact value of the expression. 1cos 2sin5x−       A. 210 225x x− B. 5 25x− C. 22 2525x x− D. 225 225x− E. None of the above 4. There are two distinct triangles possible with a side a = 12.0 cm, side b = 17.0 cm, and angle38α= °. Find the perimeter of both triangles to the nearest tenth of a cm. A. 50.0 ,39.6cm cm B. 52.7 , 44.8cm cm C. 48.3 ,36.5cm cm D. 49.1 ,37.4cm cm E. None of the aboveMA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 3 5. Height of a hot-air balloon. The angles of elevation of a balloon from two points A and B on level ground are A = 22°20' and B = 41°20', respectively. The points A and B are 8.8 miles apart and the balloon is between the points, in the same vertical plane. Approximate, to the nearest tenth, the height of the balloon above the ground. A. 2.5miles B. 3.1miles C. 3.3miles D. 2.7miles E. None of the above 6. The lengths of the sides of a triangle are 20, 21, and 31. To the nearest degree, find the measure of the largest angle in the triangle. A. 82° B. 102° C. 98° D. 78° E. None of the aboveMA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 4 7. Distance between ships. A ship leaves port at 1:40 p.m. and travels S33°E at the rate of 24 mi/hr. Another ship leaves the same port at 1:40 p.m. and travels S20°W at 9 mi/hr. Approximate, to the nearest tenth of a mile, how far apart the ships are at 3:00 p.m.? A. 27.5miles B. 26.6miles C. 28.3miles D. 29.4miles E. None of the above 8. Given vectors2 5 and 3 ,a i j b i j= − + = −find 4 5a b+ A. 6 14i j+ B. 4 20i j+ C. 5 25i j+ D. 8 12i j+ E. None of the above 9. Find the vector that has 5 times the magnitude and is in the same direction as5, 12−. A. 25, 60− B. 25 60,13 13− C. 5 12,13 13− D. 121,5− E. None of the aboveMA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 5 10. The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate, to the nearest tenth, the magnitude of the resultant vector. (a) 5.5 kg, 111° (b) 2.7 kg, 210° A. 6.5kg B. 6.1kg C. 5.3kg D. 5.7kg E. None of the above 11. An airplane with airspeed of 350 mi/hr is flying in the direction 76°, and a 50 mi/hr wind is blowing in the direction of 100°. Approximate, to the nearest degree, the plane’s true course. A. 81° B. 79° C. 82° D. 78° E. None of the aboveMA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 6 12. Determine m such that the two vectors are orthogonal. 3 4 , 9a mi j b i j= + = + A. 12m= − B. 34m= C. 12m= D. 34m−= E. None of the above 13. Find a function in x that satisfies the following conditions. A. ( )()( )( )27 52 4xf xx x− +=− + B. ( )()( )( )10 52 4xf xx x−=+ − C. ( )()( )( )27 52 4xf xx x−=+ − D. ( )()( )( )10 52 4xf xx x− +=− + E. None of the above Vertical asymptotes: x = 2, x = 4− Horizontal Asymptote: y = 0 x-intercept: 5,− f(1) = 12MA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 7 For Questions 14 and 15, use the function: ( )223 42 15x xf xx x+=+ − 14. What is the horizontal asymptote? A. 0y= B. 3y= C. There is no horizontal asymptote D. 415y−= E. None of the above 15. What are the vertical asymptotes? A. 5, 3x x= = − B. 40,3x x−= = C. 5, 3x x= − = D. 40,3x x= = E. None of the aboveMA 15400 Exam 3 Spring 2010 Covers all of Section 7.6, 8.1, 8.2, 8.3, 8.4, and all of 4.5 8 Exam 3 Answers Question Answers 1. 3π A 2. 0.5708, 0.8335− B 3. 225 225x− D 4. 48.3 , 36.5cm cm C 5. 2.5miles A 6. 98° C 7. 26.6miles B 8. 7 15i j+ E 9. 25, 60− A 10. 5.7kg D 11. 79° B 12. 12m= − A 13. ( )()( )( )10 52 4xf xx x− +=− + D 14. 3y= B 15. 5, 3x x= − =