Chapter 13

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Unformatted text preview: m and thickness 0.5 cm. Explain how you have positioned the coordinate system that you have chosen. (b) Suppose the ball is cut in half. Write inequalities that describe one of the halves. 3 ■ 4, ■ ■ 2) ■ ■ ■ 65. A solid lies above the cone z 31–36 Describe in words the surface whose equation is given. |||| 31. r 3 32. 33. 0 34. 35. ■ 3 ■ ■ ■ ■ ■ oloids z 3 ■ 2 2 ; 66. Use a graphing device to draw the solid enclosed by the parab- 2 36. 3 ■ s x 2 y 2 and below the sphere x y z z. Write a description of the solid in terms of inequalities involving spherical coordinates. 2 ■ ■ ■ ■ x2 y 2 and z 5 x2 y 2. ; 67. Use a graphing device to draw a silo consisting of a cylinder with radius 3 and height 10 surmounted by a hemisphere. 37–48 r2 37. z 39. Identify the surface whose equation is given. |||| 38. r cos 41. r 43. r z 45. 2 sin 2 46. 2 sin 2 47. r 2 2 2 2 cos 44. r cos 2 cos 4 cos 2 2 ■ ■ 2 2z2 4 48. 25 2 6 8 4 1 r ■ sin 42. 2 cos 2 ■ 40. 2 68. The latitude and longitude of a point P in the Northern Hemi- 4 sin ■ ■ ■ ■ ■ 0 ■ ■ ■ sphere are related to spherical coordinates , , as follows. We take the origin to be the center of the Earth and the positive z -axis to pass through the North Pole. The positive x-axis passes through the point where the prime meridian (the meridian through Greenwich, England) intersects the equator. Then the latitude of P is and the longitude is 90 . Find the great-circle distance from Los Ange360 les (lat. 34.06 N, long. 118.25 W) to Montréal (lat. 45.50 N, long. 73.60 W). Take the radius of the Earth to be 3960 mi. (A great circle is the circle of intersection of a sphere and a plane through the center of the sphere.) 5E-13(pp 878-883) ❙❙❙❙ 880 1/18/06 11:46 AM Page 880 CHAPTER 13 VECTORS AND THE GEOMETRY OF SPACE LABORATORY PROJECT ; Families of Surfaces In this project you will discover the interesting shapes that members of families of surfaces can take. You will also see how the shape of the surface evolves as you vary the constants. 1. Use a computer to investigate the family of surfaces ax 2 z by 2 e x2 y2 How does the shape o...
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This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas at Austin.

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