1. Two recording devices are set 3,800 feet apart, with th.docx
- 1. 1. Two recording devices are set 3,800 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation? A. 1,857.42 feet B. 1,882.03 feet C. 5,415.26 feet D. 906.67 feet 2. How many asymptotes does a hyperbola have? A. 1 B. 3 C. 2 D. 0 3. Write the following equation in terms of a rotated x′y′- system using θ, the angle of rotation. Write the equation involving x′ and y′ in standard form. xy + 16 = 0; θ = 45°
- 2. A. B. C. D. 4. Find the vertices and locate the foci for the following hyperbola equation: A. B. C. D. 5. Identify the following equation without completing the square: 2x2 – 4x + 3y – 3 = 0 A. circle B. hyperbola C. ellipse D. parabola 6. Find the vertices and locate the foci for the following hyperbola equation: A. vertices: (0, –12), (0, 12) foci: (–13, 0), (13, 0) B. vertices: (–12, 0), (12, 0) foci: (–13, 0), (13, 0) C. vertices: (–12, 0), (12, 0)
- 3. foci: (–5, 0), (5, 0) D. vertices: (–5, 0), (5, 0) foci: (–13, 0), (13, 0) 7. What's the equation of the directrix for the conic section A. x = 2 B. y = 6 C. y = –6 D. x = –3 8. What's the solution set to the following system? A. {(0, 3), (0, –3)} B. {(0, 5), (0, –5)} C. {(3, 0), (–3, 0)} D. {(5, 0), (–5, 0)} 9. Find the focus and directrix of the parabola with the following equation: y2 = 12x A. focus: (0, -3); directrix: y = –3 B. focus: (3, 0); directrix: x = 3 C. focus: (3, 0); directrix: x = –3 D. focus: (0, 3); directrix: y = –3 10. Which graph matches the following equation? A. B. C.
- 4. D. 11. Identify the conic section that the following polar equations represents: A. ellipse B. parabola C. hyperbola D. circle Mark for review (Will be highlighted on the review page)
- 5. 12. Where are the foci for the ellipse A. B. C. D.
- 6. 13. An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers stand 60 inches apart. At a point between the towers and 18 inches along the road from the base of one tower, the cable is 1.44 inches above the roadway. Find the height of the towers. A. 11 in B. 9.5 in C. 9 in D. 8.5 in 14. Identify the following equation without applying a rotation of axes: x2 – 2xy – 2y2 – 3x + 3y + 10 = 0 A. circle B. ellipse C. hyperbola D. parabola 15. Find the standard form of the equation of the ellipse satisfying the following conditions.Major axis vertical with length 18; length of minor axis = 12; center (0, 0) A. B. C.
- 7. D. 16. Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the following parametric equations: A. B. C. D. 17. Find the vertex to the parabola equation: y = x2 & ndash; 4x + 3 A. (2, –1) B. (–2, –1) C. (–1, –2) D. (–1, 2) 18. Use the rotated system to graph the following equation: 7x2 + 2xy + 7y2 = 24 A. B. C. D.
- 8. 19. A batter hits a baseball from 3 feet above home plate along the path x = 69t, y = 3 + 40t – 16t2. How long is the ball in flight, and how far does it travel? A. 0.389s, 26.8' B. 2.573s, 177.5' C. 13.723s, 946.9' D. 0.073s, 5.04' 20. Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the following parametric equations: A. B. C. D. 1. Two recording devices are set 3,800 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?
- 9. A. 1,857.42 feet B. 1,882.03 feet C. 5,415.26 feet D. 906.67 feet 2. How many asymptotes does a hyperbola have? A. 1 B. 3 C. 2 D. 0 3. Write the following equation in terms of a rotated x′y′- system using θ, the angle of rotation. Write the equation involving x′ and y′ in standard form. xy + 16 = 0; θ = 45° A. B. C. D. 4. Find the vertices and locate the foci for the following hyperbola equation: A. B. C. D.
- 10. 5. Identify the following equation without completing the square: 2x2 – 4x + 3y – 3 = 0 A. circle B. hyperbola C. ellipse D. parabola 6. Find the vertices and locate the foci for the following hyperbola equation: A. vertices: (0, –12), (0, 12) foci: (–13, 0), (13, 0) B. vertices: (–12, 0), (12, 0) foci: (–13, 0), (13, 0) C. vertices: (–12, 0), (12, 0) foci: (–5, 0), (5, 0) D. vertices: (–5, 0), (5, 0) foci: (–13, 0), (13, 0) 7. What's the equation of the directrix for the conic section A. x = 2 B. y = 6 C. y = –6 D. x = –3
- 11. 8. What's the solution set to the following system? A. {(0, 3), (0, –3)} B. {(0, 5), (0, –5)} C. {(3, 0), (–3, 0)} D. {(5, 0), (–5, 0)} 9. Find the focus and directrix of the parabola with the following equation: y2 = 12x A. focus: (0, -3); directrix: y = –3 B. focus: (3, 0); directrix: x = 3 C. focus: (3, 0); directrix: x = –3 D. focus: (0, 3); directrix: y = –3 10. Which graph matches the following equation? A. B. C. D. 11. Identify the conic section that the following polar equations represents: A. ellipse B. parabola C. hyperbola D. circle Mark for review (Will be highlighted on the review page)
- 12. 12. Where are the foci for the ellipse
- 13. A. B. C. D. 13. An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers stand 60 inches apart. At a point between the towers and 18 inches along the road from the base of one tower, the cable is 1.44 inches above the roadway. Find the height of the towers. A. 11 in B. 9.5 in C. 9 in D. 8.5 in
- 14. 14. Identify the following equation without applying a rotation of axes: x2 – 2xy – 2y2 – 3x + 3y + 10 = 0 A. circle B. ellipse C. hyperbola D. parabola 15. Find the standard form of the equation of the ellipse satisfying the following conditions.Major axis vertical with length 18; length of minor axis = 12; center (0, 0) A. B. C. D. 16. Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the following parametric equations: A. B. C. D.
- 15. 17. Find the vertex to the parabola equation: y = x2 & ndash; 4x + 3 A. (2, –1) B. (–2, –1) C. (–1, –2) D. (–1, 2) 18. Use the rotated system to graph the following equation: 7x2 + 2xy + 7y2 = 24 A. B. C. D. 19. A batter hits a baseball from 3 feet above home plate along the path x = 69t, y = 3 + 40t – 16t2. How long is the ball in flight, and how far does it travel? A. 0.389s, 26.8' B. 2.573s, 177.5' C. 13.723s, 946.9' D. 0.073s, 5.04' 20. Eliminate the parameter t. Find a rectangular equation for
- 16. the plane curve defined by the following parametric equations: A. B. C. D.