Find the length of the following two-dimensional curve. r(t) = (16 cost, 16 sin t) , for 0 Stsx Set-up the integral that gives the arc length. L= dt O (Type exact answers.)Find the length of the following three-dimensional curve. r(t)=(5+2t,4-5t,-9+2t},for15t53 Set-up the integral that gives the arc length. D L: {at (Type exact answers.) Find the length of the following three-dimensional curve. r(t)= (sin t, cos t, t}, for 0 5t54 L=D (Type an exact answer, using radicals as needed.) An object moves on a trajectory given by r(t) = (20 cos 3t,20 sin 3t) for 0 Stat. How far does it travel? . . . The object travels units. (Type an exact answer, using it as needed.)For the following trajectory, nd the speed associated with the trajectory and then find the length of the trajectory on the given interval. r(t)=(4t3, -t3,3t3>,for05ts4 E> The speed associated with the trajectory is D. (Type an exact answer. using radicals as needed.) Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (3t + 1, 4t - 7,5t + 11) . . . T = (Type exact answers, using radicals as needed.)Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (9 cost,9 sin t, (3 t) Choose the correct answer for the unit tangent vector of r(t). 31/21 31/21 O A. T(t) = sin t, 14 14 cost, 14 31/21 31/21 B. T(1) = 7 14 sin t, 14 cost, 14 31/21 31/21 7 O C. T(t) = 14 sin t, 14 cost, 14 31/21 31/21 17 O D. T(t) = sin t, - 14 cost, 14 14 K =