For Exercises 5-6, find the velocity v(t) and acceleration a(t) of an object with the given position vector r(t). 6. r(t) = (3 cost, 2 sint, 1)
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- Using the vector addition simulation, what is the actual velocity of the boat? What is the actual direction the boat is traveling?VECTOR FUNCTIONSBased on the image attached, solve the question with a detailed solution. Thank you in advance.人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT 2. Determine the position function of the motion of a particle, if the velocity vector is r'(t)= (t+1)+/zi + e-tj+. -k, 1 t+1 3 With initial condition r(0) = k
- A particle moves at constant speed 1445 units along the curve of intersection of the two the two surfaces y = x and z = 2 in the direction of increasing x. Find its velocity when it is at the point (- 12, 144, - 1152). A the point (-12, 144, - 1152), the velocity vector is V = i + + k.Find the maximum rate of change of f(x, y) Maximum rate of change: 2/5 In(x? + y?) at the point (-4, -3) and the direction in which it occurs. Direction (unit vector) in which it occurs: -8/25 -6/25 出)(vector)
- 人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT 1. If r(t) is the position of a particle in space at time t. Find the velocity and acceleration vectors of the particle for the value of t= 1, and also determine the speed of the particle for said value oft. t2 r(t) = [2ln(t + 1)]i + t2j + =k人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT 3. The vector function A(t)=(t2,cost) describes the acceleration of an object. What is the vector function that describes the speed of the object?Find a unit vector u in the direction opposite of (-2,-8,-1). u ||