QI/ Find the curve unit tangent vector and length of the indicated portion of the curve r(t) = (9 sin 2t)i + (6cos 2t)j + 5t k OstSt

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Q: Arc length: Find the length of the space curve with vector equation r(t) =(4, 3cost, 3 sint ) over […

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Q: A particle is moving in the velocity of v(t) = . %3D Find the unit tangent of the particle's…

A: Given- vt=<9sint, 9cost,4> To Find- The unit tangent of the particle's movement.

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Q: 4.a. Find the unit tangent and normal vectors to r(t) = 4 cost i + sin t j at t = /2. Sketch a…

A: Given that rt=4cost i +sin t j Then r't=-4sin t i  +cos t. The formula for tangent vector is…

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Q: Find the for the radii vector maxima and minima the Curve 2. a 2. sin'o Costo

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Q: (b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D %3D…

A: As you mentioned part b is solved

Q: A parametric curve C is given by the position vector F(1)=sin(21). sin" (+),e' osis Osis". a) Find…

A: a)The given position vector is, r→(t)=12sin(2t),sin2t,et

Q: (a) Find parametric equations for the tangent line to the curve -tcost, y-t, -tsint at the point…

A: We have to find parametric equations for given point-

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Q: a) Find the equation of tangent line of curve that is given by parametric equations X = 3cost + sint…

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Q: 3. Find the unit tangent vector and principal unit normal vector for curve with parametric equation…

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Q: g(x,y,z)=x^2+y^2+(z-3)^2

A: For (a), We need to find the equation of the tangent plane to the level set g(x, y, z) = c at the…

Q: Find the unit tangent vector T(t). r(t) = (5 cos t, 5 sin t, 8), PG 8) Find a set of parametric…

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Q: QI/ Find the curve unit tangent vector and length of the indicated portion of the curve rt) = (9 sin…

A: Given curve, rt=9 sin2ti+6 cos2tj+5tk Firstly, find the curve unit tangent vector.

Q: 3. 3. 3, r(t) = 6t°i + 2t°j + 3t°k 1sts2

A: Given that r(t)=6t3i+2t3j+3t3k  1≤t≤2. The objective is to find the unit tangent vector and also…

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Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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Q: Find parametric equations for the tangent line at the point (cos(), sin(5 ), ) on the curve a = cos…

A: Here, the given parametric equation of the curver(t)=(x,y,z) where x=cos t, y=sin t, z=t. To find…

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Q: Please show your answer to 4 decimal places. Find the direction in which the maximum rate of change…

A: Note:-   Maximum rate of change of f(x,y) at (a,b) occurs in the direction   ∇f(a,b).

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Q: The path r(t) = (t– sin t) i + (1- cos t) j describes motion on the cycloid x=t- sin t, y = 1- cos…

A: Given:           r(t)=(1−sint)i+(1−cost)j

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Q: For the curve attached, how do I get the  1) unit tangent vector 2) the unit normal vector  3)…

A: Solution :-

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Q: Find the parametric equations for the tangent line to the curve x=t^2−1,y=t^4+1,z=t^4 at the point…

A: Given: x=t2-1, y=t4+1, z=t4 Point 8, 82, 81, is for t=3 as you can see substituting it in the three…

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: Given Data: Equation of Curve: r(t)=(cos3t)j(sin3t)k Interval: 0≤t≤π3 The derivative of the curve…

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve.…

A: Vector: r=(6 sin 2t)i + (6 cos 2t)j + 5tk =>v=drdt=12cos (2t)i-12sin(2t) j+5k…

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