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2 31. x² + y² = 4, z = -1

2 31. x² + y² = 4, z = -1

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 22CT
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le with ver- tices A(1, 2, 3), B(-2, 0, 5), and C(4, 1, 5). (A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.) 22. Find an equation of a sphere if one of its diameters has end- points (5, 4, 3) and (1, 6, -9). far vila 23. Find equations of the spheres with center (2, -3, 6) that touch (a) the xy-plane, (b) the yz-plane, (c) the xz-plane. 24. Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant. 3 25-38 Describe in words the region of R³ represented by the equation(s) or inequality. 25. x = 5 27. y < 8 29. 0≤ z ≤ 6 31. x² + y² = 4, z = -1 2 33. x² + y² + z² = 4 LY 35. 1 ≤ x² + y² + z² ≤ 5 37. x² + z² ≤ 9 of Coug 26. y = -2 28. z > -1 30. y² = 4 32. x² + y² = 4 34. x² + y² + z² ≤ 4 36. x = Z 38. x² + y² + z² > 2z 39-42 Write inequalities to describe the region. 39. The region between the yz-plane and the vertical plane x = 5 44 4
Transcribed Image Text:le with ver- tices A(1, 2, 3), B(-2, 0, 5), and C(4, 1, 5). (A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.) 22. Find an equation of a sphere if one of its diameters has end- points (5, 4, 3) and (1, 6, -9). far vila 23. Find equations of the spheres with center (2, -3, 6) that touch (a) the xy-plane, (b) the yz-plane, (c) the xz-plane. 24. Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant. 3 25-38 Describe in words the region of R³ represented by the equation(s) or inequality. 25. x = 5 27. y < 8 29. 0≤ z ≤ 6 31. x² + y² = 4, z = -1 2 33. x² + y² + z² = 4 LY 35. 1 ≤ x² + y² + z² ≤ 5 37. x² + z² ≤ 9 of Coug 26. y = -2 28. z > -1 30. y² = 4 32. x² + y² = 4 34. x² + y² + z² ≤ 4 36. x = Z 38. x² + y² + z² > 2z 39-42 Write inequalities to describe the region. 39. The region between the yz-plane and the vertical plane x = 5 44 4
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