AN84 Answers: Chapter 11 4. x y 1 6 3 2 ( ) ( ) + = − y x 9 5 V 5 (21, 3) F 5 (21, 4.5) (24, 4.5) (2, 4.5) D: y 5 1.5 5. x y 7 16 1 2 2 + = y x 5 5 V2 5 (0, 24) F2 F1 V1 5 (0, 4) (!7, 0) (2!7, 0) 6. y x 2 4 2 8 1 2 2 ( ) ( ) − − − = y x 8 8 V2 5 (2, 0) V1 5 (2, 4) (2 2 2!2, 2) (2 1 2 !2, 2) (2 1 !10, 5) F2 F1 (2, 2) 7. Hyperbola 8. Ellipse 9. Parabola 10. x y2 1. 2 2 ′ + ′ = This is the equation of an ellipse with center at 0, 0 ( ) in the x y -plane. ′ ′ The vertices are at 1, 0 ( ) − and 1, 0 ( ) in the x y -plane. ′ ′ y x 5 5 2 1 y9 x9 11. Hyperbola; x y 2 3 1 2 2 ( ) + − = 12. y x 1 2 3 = − + y x 5 45 (1, 0) (10, 21) (25, 22) (22, 1) 13. The microphone should be located 2 3 ft from the base of the reflector, along its axis of symmetry. Cumulative Review (page 752) 1. x h 6 5 3 − + − 2. 5, 1 3 , 2 { } − − 3. x x 3 2 { } − ≤ ≤ or 3, 2 [ ] − 4. (a) Domain: , ; ( ) −∞∞ range: 2, ( )∞ (b) y x log 2 ; 3( ) = − domain: 2, ; ( )∞ range: , ( ) −∞∞ 5. (a) 18 { } (b) 2, 18 ( ] 6. (a) y x2 2 = − (b) x y 2 4 2 2 ( ) − + = (c) x y 9 4 1 2 2 + = (d) y x 2 1 2 ( ) = − (e) y x 3 1 2 2 − = (f) y 4x = 7. k k 12 , θ π π = ± is any integer; k k 5 12 , θ π π = ± is any integer 8. 6 θ π = 9. r 8 sinθ = y x 10 10 10. x x k k 3 4 , isaninteger π π { } ≠ ± 11. 22.5 { }° 12. y x 5 5 2 = + CHAPTER 11 Systems of Equations and Inequalities 11.1 Assess Your Understanding (page 765) 3. F 4. consistent; independent 5. 3, 2 ( ) − 6. consistent; dependent 7. b 8. a 9. 2 2 1 5 5 2 2 1 8 ( ) ( ) ⋅ − − = ⋅ + − = ⎧ ⎨ ⎪⎪ ⎩⎪⎪ 11. 3 2 4 1 2 4 1 2 2 3 1 2 1 2 ⋅ − ⋅ = ⋅ − ⋅ =− ⎧ ⎨ ⎪⎪ ⎪⎪⎪ ⎩ ⎪⎪ ⎪⎪ ⎪ 13. 4 1 3 1 2 4 1 3 − = ⋅ + = ⎧ ⎨ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪ 15. 3 1 3 1 2 2 4 1 1 2 0 2 1 3 2 8 ( ) ( ) ( ) ⋅ + − + ⋅ = − − − = − − ⋅ = − ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ 17. ( ) ( ) ( ) ⋅ + − + ⋅ = − − + = ⋅ − − − ⋅ = ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ 3 2 3 2 2 2 4 2 3 2 2 10 5222 32 8 19. x y 6, 2; 6, 2 ( ) = = y 10 x 10 (6, 2) x 2 y 5 4 x 1 y 5 8 21. x y 3, 6; 3, 6 ( ) = = − − y 10 x 10 2x 1 3y 5 212 5x 2 y 5 21 (3, 26) 23. x y 8, 4; 8, 4 ( ) = = − − y 10 x 10 3x 5 24 x 1 2y 5 0 (8, 24) 25. x y 1 3 , 1 6 ; 1 3 , 1 6 ( ) = = − − y 1 x1 , 1 3 1 6 2 3x 2 6y 5 2 5x 1 4y 5 1 27. Inconsistent y 2 x 2 2x 1 y 5 1 4x 1 2y 5 3 29. x y 3 2 , 3; 3 2 , 3 ( ) = = , 3 3 2 y 5 x 5 2x 2 y 5 0 4x 1 2y 5 12 31. x y x y y , 4 2, isanyrealnumber, {( ) } = − or x y y x x , 4 2 , isanyrealnumber { } ( ) = − 33. x y 1, 1; 1, 1 ( ) = = 35. x y 3 2 , 1; 3 2 , 1 ( ) = = 37. x y 4, 3; 4, 3 ( ) = = 39. x y 2 3 , 5 6 ; 2 3 , 5 6 ( ) = = − − 41. x y 1 5 , 1 3 ; 1 5 , 1 3 ( ) = = 43. x y z 6, 3, 1; 6,3, 1 ( ) = = = − − 45. x y z 2, 1, 1; 2, 1,1 ( ) = = − = − 47. Inconsistent 49. x y z x z y z z , , 5 2, 4 3; isanyrealnumber ( ) { } = − = − 51. Inconsistent 53. x y z 1, 3, 2; 1,3, 2 ( ) = = = − − 55. x y z 3, 1 2 , 1; 3, 1 2 , 1 ( ) = − = = − 57. Length 30 ft; width 15 ft 59. 27 Starlink, 34 others
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