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0.8t 25. x = cos 8t, y = sin 8t, z = e08r, t≥ 0 е

0.8t 25. x = cos 8t, y = sin 8t, z = e08r, t≥ 0 е

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 27RE
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17-20 Find a vector equation and parametric equations for the line segment that joins P to Q. 17. P(2, 0, 0), Q(6, 2,-2) 19. P(0, -1, 1), (1,3,4) 21-26 Match the parametric equations with the graphs (labeled I-VI). Give reasons for your choices. II I III V 18. P(-1, 2, -2), Q(-3, 5, 1) 20. P(a, b, c), Q(u, v, w) A y Dessigorafg IV VI XOA gyben ZĄ finit y 2.8 2.8 31. At sect 32. At v the 33-37 U equation points th 33. r(t) 34. r(t) 35. r(t) 36. r(t) 37. r(t) 38. Grap y = proj 39. Grap Expl a cor 40. Grap
Transcribed Image Text:17-20 Find a vector equation and parametric equations for the line segment that joins P to Q. 17. P(2, 0, 0), Q(6, 2,-2) 19. P(0, -1, 1), (1,3,4) 21-26 Match the parametric equations with the graphs (labeled I-VI). Give reasons for your choices. II I III V 18. P(-1, 2, -2), Q(-3, 5, 1) 20. P(a, b, c), Q(u, v, w) A y Dessigorafg IV VI XOA gyben ZĄ finit y 2.8 2.8 31. At sect 32. At v the 33-37 U equation points th 33. r(t) 34. r(t) 35. r(t) 36. r(t) 37. r(t) 38. Grap y = proj 39. Grap Expl a cor 40. Grap
te t) ate e 21. x = t cos t, y=t, z = t sin t, t≥ 0 22. x = cos t, y = sin t, z = 1/(1 + f²) 23. x = t, y = 1/(1 + t²), z = f² 24. x = 25. x = 26. x = cos t, y = sin t, z = cos 2t cos 8t, y = sin 8t, z = e0.81, t≥0 cos²t, y = sin²t, z = t 27. Show that the curve with parametric equations .x = t cos y = t sin t, z = t lies on the cone z² = x² + y², and use t fact to help sketch the curve. 28. Show that the curve with parametric equations x = sin !, sin't is the curve of intersection of the sur z = x² and x² + y² = 1. Use this fact to help sketch the c y = cost, z = 29. Find three different surfaces that contain the curve r(t) = 2ti + e'j + e²¹ k. 30. Find three different surfaces that contain the curve r(t) = t² i + In tj + (1/t) k. 31. At what points does the curve sect the paraboloid z = x² + y²? 2 32. At what points does the helix r(t) = (sin t, cost, t) inter r(t) = ti+(21-12) kim
Transcribed Image Text:te t) ate e 21. x = t cos t, y=t, z = t sin t, t≥ 0 22. x = cos t, y = sin t, z = 1/(1 + f²) 23. x = t, y = 1/(1 + t²), z = f² 24. x = 25. x = 26. x = cos t, y = sin t, z = cos 2t cos 8t, y = sin 8t, z = e0.81, t≥0 cos²t, y = sin²t, z = t 27. Show that the curve with parametric equations .x = t cos y = t sin t, z = t lies on the cone z² = x² + y², and use t fact to help sketch the curve. 28. Show that the curve with parametric equations x = sin !, sin't is the curve of intersection of the sur z = x² and x² + y² = 1. Use this fact to help sketch the c y = cost, z = 29. Find three different surfaces that contain the curve r(t) = 2ti + e'j + e²¹ k. 30. Find three different surfaces that contain the curve r(t) = t² i + In tj + (1/t) k. 31. At what points does the curve sect the paraboloid z = x² + y²? 2 32. At what points does the helix r(t) = (sin t, cost, t) inter r(t) = ti+(21-12) kim
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