Find the function r(t) that satisfies the following conditions t5 3t2 r' (t) = t6 + 1 it (the-ts ) j + k Vt3 + 9 14 r(0) = -5i + - j + 2k OA) r(t) = (6In(t6 + 1) - 5)i + ze + 3) j +(5 (+3 + 9)2 - 4 k B ) r(t) = (6 In(t6 + 1) - 5)i+ Gets + 14 5 i + ($ (+3 + 9) 2 + 2) k O c) r (t ) = (= In ( to + 1) - 5) it ( - ge - t s + 5 ) i + ( 2 ( + 3 + 9 ) 2 + 2 ) k O D) I (t ) = ( 1 In ( + 6 + 1 ) - 5 ) i + ( - 5e-15 + 3) j + (2(13 + 9) 2 - 4) kCompute r"(t). r(t) = (8 cos t)i + (7 sin t)j A) r"(t) = (8 sin t)i + (7 cos t)j O B) r"(t) = (8 cos t)i + (7 sin t)j C) r" (t) = (-8 sin t)i + (-7 cos t)) O D) r"(t) = (-8 cos t)i + (-7 sin t)jSolve the problem. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the _ 2 objects. Use 9 ' 9'8 "1/3 f A projectile is launched from level ground with an initial speed of 569 m/sec and at an angle of 45. What is the greatest height reached by the projectile? Round your answer to the nearest tenth. A) 80,9403 m L) B) 82.1 m U C) 33,0368 m 0 D) 8,259.2 m If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. Find the acceleration vector. r(t) = (3 cos t)i + (7 sin t)j O A) a = (3 cos t)i + (7 sin t)j O B) a = (-3 sin t)i + (-7 cos t)j O C) a = (-3 cos t)i + (-7 sin t)j O D) a = (3 sin t)i + (7 cos t)jThe planes below intersect at a line. Find the equation of the line. 3x+y+2z=0 3x+3y+4z=12 ' A) =_t,y=129t,z=6+6t B)x=t,y=129t,z=6+6t q C) X=-t,y= 12 9t,z= -6-*6t r\": UDix=t,y=12-9t,Z=6'6t