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(a) True or false? The same curve can be described by parametric equations in many different ways. O True O False (b) The parametric equations x = 2t, y = (2t)2 model the position of a moving object at time t. When t = 0, the object is at and when t = 1, the object is at (c) If we eliminate the parameter, we get the equation , which is the same as the equation for the path of an object with parametric equations x = t, y = 2, tz 0. So the two objects move along the same path but traverse the path differently. Indicate the position of each object when t = and when t = 1 on a graph. (Let A be the object whose motion is given by the parametric equations x = t, y = t2, and let B be the object with equations x = 2t, y = (2t)2.)

(a) True or false? The same curve can be described by parametric equations in many different ways. O True O False (b) The parametric equations x = 2t, y = (2t)2 model the position of a moving object at time t. When t = 0, the object is at and when t = 1, the object is at (c) If we eliminate the parameter, we get the equation , which is the same as the equation for the path of an object with parametric equations x = t, y = 2, tz 0. So the two objects move along the same path but traverse the path differently. Indicate the position of each object when t = and when t = 1 on a graph. (Let A be the object whose motion is given by the parametric equations x = t, y = t2, and let B be the object with equations x = 2t, y = (2t)2.)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.4: Plane Curves And Parametric Equations
Problem 2E
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(a) True or false? The same curve can be described by parametric equations in many different ways. O True False (b) The parametric equations x = 2t, y = (2t)² model the position of a moving object at time t. When t = 0, the object is at and when t = 1, the object is at (c) If we eliminate the parameter, we get the equation which is the same as the equation for the path of object with parametric equations x = t, y = t², t> 0. So the two objects move along the same path but traverse the path differently. Indicate the position of each object when t = 0 and whent = 1 on a graph. (Let A be the object whose motion is given by the parametric equations x = t, y = t2, and let B be the object with equations x = 2t, y = (2t)².) V
Transcribed Image Text:(a) True or false? The same curve can be described by parametric equations in many different ways. O True False (b) The parametric equations x = 2t, y = (2t)² model the position of a moving object at time t. When t = 0, the object is at and when t = 1, the object is at (c) If we eliminate the parameter, we get the equation which is the same as the equation for the path of object with parametric equations x = t, y = t², t> 0. So the two objects move along the same path but traverse the path differently. Indicate the position of each object when t = 0 and whent = 1 on a graph. (Let A be the object whose motion is given by the parametric equations x = t, y = t2, and let B be the object with equations x = 2t, y = (2t)².) V
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