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- The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(22t – sin(22t))i + 3(1 – cos(22t))} Find the velocity vector of the point. v(t) = (66 – 66 cos(22t) )i + 66 sin( 22t)jv Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = 66y cos( 22t) + sin( 22t) xThe motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) Find the speed of the point. s(t) =Define two vector functions (t) 9 sin(t)+7 cos(t)] + (t³ - 15) k = = (t) 7 sin(t)+9 cos(t)] + tk = . Compute (t) (t) =
- 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j + (3t)k If the particle begins its motion at t = 0 and ends at t = pi, find the difference between the length of the path traveled and the distance between start position and end positionFind the location at t = 3 of a particle whose path satisfies dr = (181-1712-21-4) dt + r(0) = (8,7) (Use symbolic notation and fractions where needed. Give your answer in vector form.) r(3) = (54,4) Incorrectlinearise R = AT + BT2
- What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?Find the velocity and acceleration vectors in terms of u, and ug- de r=a cos 20 and dt = 5t, where a is a constant (- 10at sin 20 ) u, + ( 5at cos 20 ) ue y = - a cos (20) • (4 + 5t)) u, + (5a( cos (20) – 4t sin (20)) ue a =A bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 seconds. Where is the bee located at time t = 6 if [°r' (Use symbolic notation and fractions where needed.) r' (u) du = 0 location:
- What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) do not hold?6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of the unit vector u = cos i+sinj. (b) What is the maximum value of the directional derivative of w = ²y at (1,-3) and it what direction is it attained? Q Search A2) r(1) = ti -t j-t'k, t20 Draw the graph of the vector-valued function, explaining it in detail.