Question 4 Find r'(t) given the following vector function. r(t) = 2/³i+34j+37²k O r'(t) = 6t²i+12t³j+6tk O r'(t) = 6t²i+3t³j+3tk ○ r'(t) = 2t²i+3ť³j+ 3tk O r'(t) = 2t²i+3tj+3t³k r'(t) = 6t³i+12tªj+ 6t²k Question 5
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- A 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 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=2a) Find F‘(0) for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find 3a +2b Note: an arrow representing direction should be on the alphabets
- Vector v with initial point P = (x1, yı) and terminal point P, = (x2, y2) is equal to the vector v = ()i + (_j.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) xFind the vectors T, N, and B at the given point. r(t) = <t^2, 2/3 t^3, t> (4, 16/3, 2)
- For which real values of A do the following vectors form a linearly dependent set in R³? V₁ = 1₂ V2= V3 X₁ = 1 3' 3 1 (-₁^,-) = 1 3 2 3 - 1/3,^) A₂ =A particle travels along curve C be described by vector function →r (t) =< 2t, 2t, 4 − t >. Find the distancethe particle travels from (2, 2, 3) to (4, 4, 2).The position vector of a particle is r(t). Find the requested vector. The acceleration at t=2 for r(t)=(8t-3t^4)i + (2-t)j + (5t^2-4t)k
- The position vector of a moving particle in space at time t is given by the vector function r (t) = - (5 - t)2i + (2t - 1) j + (5 - t)3/2 K Find the largest possible time when the particle reaches the speed of 4 units. Enter an integer or a fully reduced fraction such as 0, 15, 3/4 , etc. No Spaces Please.Find the requested vector. The velocity at t=pi/4 for r(t)=4sec^2(t)i-5tan(t)j+10t^2kLet 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.