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Let the velocity
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- Find the velocity, speed, and acceleration of a particle moving with position function r(t)=(3t^2-4)i+(3t)j Sketch the path of the particle and draw the position, velocity, and acceleration vectors for t=2Find the requested vector. The velocity at t=pi/4 for r(t)=4sec^2(t)i-5tan(t)j+10t^2kA stone is thrown from a rooftop at time t=0 seconds. Its position at time t is given by r(t)=6ti−4tj+(9.8−4.9t^2)k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meters. The vector i points east, j points north, and k points up.(a) How high is the rooftop? meters.(b) When does the stone hit the ground? seconds.(c) Where does the stone hit the ground? (in meters)(d) How fast is the stone moving when it hits the ground? (in meters per second)
- find the directional derivative of the function in the direction of the vector vCalculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt IncorrectLet vector r(t) = <5sin(t), 5cos(t), 2t^(3/2)> be the position function of an object.a. Find vector v(t) and vector a(t), the velocity and acceleration of the object.b. Find the speed of the object.c. Find the distance the object travels on the interval [0, 1]. Also find the average speed of theobject on this interval.
- Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)Compute the directional derivative in the direction of the vector.Find the velocity vector v(t), given the acceleration vector a(t) = (3e¹, 7, 10t +9) and the initial velocity v(0) = (8,-5,3). (Use symbolic notation and fractions where needed. Give your answer in the vector form.) v(t) = 2(e' - 2)i + (3t-2)j + (3r² +9r+2)k Incorrect
- Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 5. Please explain your steps. Thank you.Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction (15/17, 8/17). Be sure to use a unit vector for the direction vector.Find the derivative of the vector function r(t) = ta × (b + tc), where a = = (2, -2, 3), b = (2,−1, −3), and c = (5, -5,-3). r'(t) = {