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1 A street with two lanes, each 10 wide goes through a semicircuar tunnel with radius 12 t. How high is the tunnel at the edge of each lane? C 673 D 68IR A 6538 8 663t 2 An archaeologist found the remains of an ancient wheel which she then placed on a grid If an arc of the wheel passes through A(-7,0). B(-14) and C7,0) locate the center of the wheel C2-) A (0.-3) B (1-4) 3. A single-lane street 10 ft wide goes through a semiaroular tunnel with radus 9t How high is the tunnel at the edge of each lane? 6.03 643 A C740 8. 9.10 In 198

1 A street with two lanes, each 10 wide goes through a semicircuar tunnel with radius 12 t. How high is the tunnel at the edge of each lane? C 673 D 68IR A 6538 8 663t 2 An archaeologist found the remains of an ancient wheel which she then placed on a grid If an arc of the wheel passes through A(-7,0). B(-14) and C7,0) locate the center of the wheel C2-) A (0.-3) B (1-4) 3. A single-lane street 10 ft wide goes through a semiaroular tunnel with radus 9t How high is the tunnel at the edge of each lane? 6.03 643 A C740 8. 9.10 In 198

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. A street with two lanes, each 10 t wide. goes through a semicrcular tunnel with radius 12 ft. How high is the tunnel at the edge of each lane? A 653 B. 2 An archaeologist found the remains of an ancient wheel which she then placed on a grid. If an arc of the wheel passes through A(-7,0). B(-3,4) and C(7,0), locate the center of the wheel A. C. 6.73 6.63 ft D. 683 t (0.-3) B. C. (2-3) (1.-6) D. A-1) 3. A single-lane street 10 ft wide goes through a semicroular tunnel with radius 9t How high is the tunnel at the edge of each lane? A. 8. 4. In 1986, a nuclear reactor exploded at a power plant about 110 kilometers north and 15 klometers west of Kiev At first, officials evacuated people within 30 kilometers of the power plant. Write an equation to represent the boundary of the evacuated region d the origin of the coordinate system is at Kiev A. 6.03 t C. 7.48 t 6.43ft 9.10 t (x+ 15) +(y - 110)900 B. (r+ 110) + (y - 15)30 C. (x- 15) + (y+ 110 900 D (x- 15) + (y +110- 30 5 A Ferris wheel is elevated im above the ground. When a car reaches the highest point on the ferris wheet, its altitude from ground level is 31 m. How far away from the center, horizontally, is the car when it is at an altitude of 25 m? A. 12 m C. D. 14 m B. 6. A satelite dish has a shape called a paraboloid, where each cross-section is a parabola Since radio signals (parallel to the axis) will bounce off the surface of the dish to the focus the receiver should be placed at the focus. How far should the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the vertex? 13 m 15 m A. C. 3.10 ft 212 D. 4 t 7. The cable of a suspension bridge hangs in the shape of a parabola. The towers supporting the cable are 400 ft apart and 150 ft high. If the cable, at its lowest, is 30 f above the bridge at its midpoint, how high is the cable 50 ft away (horizontally) from ether tower? A. 62.10 50 t C. 8821 t B. D. 975 ft
Transcribed Image Text:1. A street with two lanes, each 10 t wide. goes through a semicrcular tunnel with radius 12 ft. How high is the tunnel at the edge of each lane? A 653 B. 2 An archaeologist found the remains of an ancient wheel which she then placed on a grid. If an arc of the wheel passes through A(-7,0). B(-3,4) and C(7,0), locate the center of the wheel A. C. 6.73 6.63 ft D. 683 t (0.-3) B. C. (2-3) (1.-6) D. A-1) 3. A single-lane street 10 ft wide goes through a semicroular tunnel with radius 9t How high is the tunnel at the edge of each lane? A. 8. 4. In 1986, a nuclear reactor exploded at a power plant about 110 kilometers north and 15 klometers west of Kiev At first, officials evacuated people within 30 kilometers of the power plant. Write an equation to represent the boundary of the evacuated region d the origin of the coordinate system is at Kiev A. 6.03 t C. 7.48 t 6.43ft 9.10 t (x+ 15) +(y - 110)900 B. (r+ 110) + (y - 15)30 C. (x- 15) + (y+ 110 900 D (x- 15) + (y +110- 30 5 A Ferris wheel is elevated im above the ground. When a car reaches the highest point on the ferris wheet, its altitude from ground level is 31 m. How far away from the center, horizontally, is the car when it is at an altitude of 25 m? A. 12 m C. D. 14 m B. 6. A satelite dish has a shape called a paraboloid, where each cross-section is a parabola Since radio signals (parallel to the axis) will bounce off the surface of the dish to the focus the receiver should be placed at the focus. How far should the receiver be from the vertex, if the dish is 12 ft across, and 4.5 ft deep at the vertex? 13 m 15 m A. C. 3.10 ft 212 D. 4 t 7. The cable of a suspension bridge hangs in the shape of a parabola. The towers supporting the cable are 400 ft apart and 150 ft high. If the cable, at its lowest, is 30 f above the bridge at its midpoint, how high is the cable 50 ft away (horizontally) from ether tower? A. 62.10 50 t C. 8821 t B. D. 975 ft
8. A satelite dish in the shape of a paraboloid is 10 ft across, and 4 t deep at its vertex How far is the receiver from the vertex if it is placed at the focus? A. 0.12 n B. 3.33 ft C. 156t D. 5.12 t 9. The arch of a bridge is in the shape of a semiellipse, with its major axis at the water level. Suppose the arch is 20 t high in the middle, and 120 f across its major axds How high above the water level is the arch, at a point 20 t from the center (horizontally)? A 18.76 t C. 19.76 B. 18. 86 ft D. 19.86 ft 10. The orbit of a planet has the shape of an elipse, and on one of the foc is the star around which it evolves. The planet is dosest to the star when it is at one vertex. It is the farthest from the star when it is at the other vertex. Suppose the closest and farthest distances of the planet from this star are 420 million kilometers and 580 million kilometers, respectively. Find the equation of the ellipse in the standard form with center at the origin and the star at thex-axis Assume all units are in millions of kilometers A. 255 500 240 600 B. 250 600 240 600 C. 250 000 3D1 243 600 y D. 243 600 250 600 11. In an ellipse, sound or light coming from one focus is reflected to the other focus. In a whispering gallery, a person can hear another person whisper from across the room f the two people are standing at the foci. The whispering gallery at the Museum of Science and Industry in Chicago has an elliptical cross section that is 13.5 t by 47 t. Write an equation to model this ellipse. Assume that the center is at the ongin and the major axis is horizontal A. (금) (등) B. D. 31 12 Consider question #11, how far apart are tthe points at which two people should stand to hear each other whisper? 3337 B. A. C. 44.37 t 4237 t D. 45.37t ODULES
Transcribed Image Text:8. A satelite dish in the shape of a paraboloid is 10 ft across, and 4 t deep at its vertex How far is the receiver from the vertex if it is placed at the focus? A. 0.12 n B. 3.33 ft C. 156t D. 5.12 t 9. The arch of a bridge is in the shape of a semiellipse, with its major axis at the water level. Suppose the arch is 20 t high in the middle, and 120 f across its major axds How high above the water level is the arch, at a point 20 t from the center (horizontally)? A 18.76 t C. 19.76 B. 18. 86 ft D. 19.86 ft 10. The orbit of a planet has the shape of an elipse, and on one of the foc is the star around which it evolves. The planet is dosest to the star when it is at one vertex. It is the farthest from the star when it is at the other vertex. Suppose the closest and farthest distances of the planet from this star are 420 million kilometers and 580 million kilometers, respectively. Find the equation of the ellipse in the standard form with center at the origin and the star at thex-axis Assume all units are in millions of kilometers A. 255 500 240 600 B. 250 600 240 600 C. 250 000 3D1 243 600 y D. 243 600 250 600 11. In an ellipse, sound or light coming from one focus is reflected to the other focus. In a whispering gallery, a person can hear another person whisper from across the room f the two people are standing at the foci. The whispering gallery at the Museum of Science and Industry in Chicago has an elliptical cross section that is 13.5 t by 47 t. Write an equation to model this ellipse. Assume that the center is at the ongin and the major axis is horizontal A. (금) (등) B. D. 31 12 Consider question #11, how far apart are tthe points at which two people should stand to hear each other whisper? 3337 B. A. C. 44.37 t 4237 t D. 45.37t ODULES
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