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Butterfly : r7(t) = (6 cos (; t),6 sin (Ft),t+1) %3D Wasp : r¿(t) = (t² – 9, –2t² + 12,3t² – 23) 5. Use the given formulas to determine the following : (a) Describe the paths of the butterfly and the wasp (you do not have to sketch). (b)Verify that the butterfly and wasp collide at t = 3 , and determine the angle at (c) Find the speeds of both the butterfly and the wasp when they collide.

Butterfly : r7(t) = (6 cos (; t),6 sin (Ft),t+1) %3D Wasp : r¿(t) = (t² – 9, –2t² + 12,3t² – 23) 5. Use the given formulas to determine the following : (a) Describe the paths of the butterfly and the wasp (you do not have to sketch). (b)Verify that the butterfly and wasp collide at t = 3 , and determine the angle at (c) Find the speeds of both the butterfly and the wasp when they collide.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For problems #5 and #6, we consider the trajectories of a butterfly and a wasp (with time t in seconds and displacement in inches): Butterfly: ri(t) = (6 cos (t),6 sin (t),t+ 1) Wasp : r(t) = (t? – 9, –2t² + 12,3t? – 23) 5. Use the given formulas to determine the following : (a) Describe the paths of the butterfly and the wasp (you do not have to sketch). (b)Verify that the butterfly and wasp collide at t = 3, and determine the angle at (c) Find the speeds of both the butterfly and the wasp when they collide. 6. Using only the velocity and speed functions of the butterfly and wasp, determine signs (+-, or 0) of the tangential and normal/centripetal components of acceleration for each insect. Explain your reasoning.
Transcribed Image Text:For problems #5 and #6, we consider the trajectories of a butterfly and a wasp (with time t in seconds and displacement in inches): Butterfly: ri(t) = (6 cos (t),6 sin (t),t+ 1) Wasp : r(t) = (t? – 9, –2t² + 12,3t? – 23) 5. Use the given formulas to determine the following : (a) Describe the paths of the butterfly and the wasp (you do not have to sketch). (b)Verify that the butterfly and wasp collide at t = 3, and determine the angle at (c) Find the speeds of both the butterfly and the wasp when they collide. 6. Using only the velocity and speed functions of the butterfly and wasp, determine signs (+-, or 0) of the tangential and normal/centripetal components of acceleration for each insect. Explain your reasoning.
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