math5
Magic Solutions
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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? |
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2. How many asymptotes does a hyperbola have? |
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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° |
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4. Find the vertices and locate the foci for the following hyperbola equation: |
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5. Identify the following equation without completing the square: 2x2 – 4x + 3y – 3 = 0 |
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6. Find the vertices and locate the foci for the following hyperbola equation: |
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8. What's the solution set to the following system? |
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9. Find the focus and directrix of the parabola with the following equation: y2 = 12x |
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10. Which graph matches the following equation? |
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11. Identify the conic section that the following polar equations represents: |
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Mark for review (Will be highlighted on the review page) |
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12. Where are the foci for the ellipse |
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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. |
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14. Identify the following equation without applying a rotation of axes: x2 – 2xy – 2y2 – 3x + 3y + 10 = 0 |
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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) |
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16. Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the following parametric equations:
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17. Find the vertex to the parabola equation: y = x2 & ndash; 4x + 3 |
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18. Use the rotated system to graph the following equation: 7x2 + 2xy + 7y2 = 24 |
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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? |
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20. Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the following parametric equations: |
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