A particle moving along a curve in the xy-plane has position (x(1),y(t)) at time dy dx t with dt = sin(r' - t) and Y = ços(r -t). At time t = 3, the particle is at the dt %3D %3D point (1, 4). (a) Find the acceleration vector for the particle at t = 3. b) Find the equation of the tangent line to the curve at the point where t = 3. %3D c) Find the magnitude of the velocity vector at t = 3.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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6. A particle moving along a curve in the xy-plane has position (x(1),y(1)) at time
dy
= ços( - t). At time t = 3, the particle is at the
dt
dx
t with
sin(r` – t) and
dt
point (1, 4).
(a) Find the acceleration vector for the particle at t = 3.
eenee
(b) Find the equation of the tangent line to the curvė at the point where t = 3.
(c) Find the magnitude of the velocity vector at t= 3.
(d) Find the position of the particle at time t= 2.
Transcribed Image Text:6. A particle moving along a curve in the xy-plane has position (x(1),y(1)) at time dy = ços( - t). At time t = 3, the particle is at the dt dx t with sin(r` – t) and dt point (1, 4). (a) Find the acceleration vector for the particle at t = 3. eenee (b) Find the equation of the tangent line to the curvė at the point where t = 3. (c) Find the magnitude of the velocity vector at t= 3. (d) Find the position of the particle at time t= 2.
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