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The position of a particle in the xy-plane at time t is r(t) = (t - 4) i+ (t~ +3) j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t = 4.7 The position of a particle in the xy-plane at time t is r(t) = (e ) i + 3t 27 j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors att = In 3.The path r(t) = (t) i+ (t" +7) j describes motion on the parabola y = x + 7. Find the particle's velocity and acceleration vectors at t= -4, and sketch them as vectors on the curve.The equation r{t] = (2H 3} i+ {t} j+ (Sf?) it is the position of a particle in space at time t. Find the angle between the 1velocity and acceleration 1.rectors at time t = l}. ' E 1u"'."hat is the angle'? |:| radians [Type an exact answer: using 11: as needed.) The equation r(t) = 2+ + 2312 j is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t = 0. The angle between the velocity and acceleration vectors at time t = 0 is radians. (Type an exact answer, using x as needed.)Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (6 cost) i+ (t* - 3 sint) j+ (4e* 3t] k . 1 = 0 What is the standard parameterization for the tangent line? Z (Type expressions using t as the variable.)Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (t? ) i+ (3t - 4) j + (3t' ) k, t = to = 1 What is the standard parameterization for the tangent line? X = V= Z = (Type expressions using t as the variable.)Find the value(s) of t so that the tangent line to the given curve contains the given point. r(t) = 3ti + 2t j - 2+~k; (0, - 50,50) t= (Use a comma to separate answers as needed.)