Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (V51 cos t,7 cost,10 sin t) ..... The unit tangent vector is T= (Type exact answers, using radicals as needed.)

Q: The parametric equations x= 3 - 8 sin 3t and y = 9 + 8 cos 3 t for 0 sts x/4 represent a curve C.…

A: Given data: x(t)=3-8sin(3t) y(t)=9+8cos(3t) for 0≤t≤π4 Solution: Length of parametric curve is given…

Q: For the curve given by r(t) = (9 sin(t), -2t, -9 cos(t)), Find the unit tangent T(t) = (000) Find…

A: For the curve given by , to find the unit tangent vector, unit normal vector, and the curvature.

Q: 7x Find an equation for the circle of curvature of the curve r(t) = 7t i + sin(t) j at the point 2…

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Q: What curves are represented by the following? Sketch them. [cos t, sin 2t, 0]

A: To Sketch: The curves represented by the parametric form [cos t, sin2t, 0].

Q: 1. Let C be a curve with a vector equation r(t) = (4 cos(t), -4 sin(t),-3t) where 0<t<÷. What is the…

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Consider the unit circle given by x² + y² = 1. Which of the following parametric equations describes…

A: Introduction: In trigonometry, the unit circle has a radius of 1 and is centered at the origin.…

Q: Find an equation for the circle of curvature of the curve r(t) = 8t i + sin(5t) ja

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Q: Find the curvature and the radius of curvature at any point on the curve given by y = ln x. Simplify…

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Q: Please sovle the following calc 3 problem and show all work by hand (explain answer)

A: Step 1: Given is the vector function below: r(t)=(8−2t)i+(2t−8)j+(7+t)k Step 2: The unit tangent…

Q: r(t) = (t cos(t), t sin(t), t)

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Q: 21. For the curve 7(t) = sin ti + cos tj, find 7 '(t) and sketch the position vector 7(÷) and the…

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Q: 2. Given that r(t) = 2 sin ti + 2 cos tj+ tan tk. Find the unit tangent vector T(t) at the point…

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Q: r(t) = cos(t)i + V2 sin(t)j+ cos(t)k. Find the unit tangent vector T(t), the curvature K(t), the…

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Q: 24. Find the curvature of r(t) = (r°, In 1, t In t) at the point (1, 0, 0). %3D

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Q: 2. Find the radius of curvature for the curve r*cos20 %3D 1.

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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 curvature correctly

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Q: Find the unit tangent vector of the given curve. r(t) = (6 sin 39t) i + (6 cos ³9t)j O A. T(t) = (6…

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Q: Find the curvature K of the curve. r(t) = 4 cos 2nti + 4 sin 2ntj K.

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Q: Find the radius of curvature of the following functions

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Q: For the following parameterized curve, find the unit tangent vector. r(t)= (3 sin (t),3 cos (1), cos…

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Q: Problem 1. Given the curve Find the following at point P(1,0,0). 1. the unit tangent. 2. the unit…

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Q: Given the parametric curve. x = cos t y = sin t 0 <t< 2T Please find the length of curve.

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Q: Which is the correct order in finding the radius of curvature of a circle? i. find the radius ii.…

A: We are asked to find the order of finding radius of curvature

Q: Find the radius of curvature of the curve generated by the position vector r (t) = (-40 sin(t),–9t,…

A: Given, r(t)=-40sint,-9t,40cost r'(t)=-40cost,-9,-40sint r'(t)=-40cost2+(-9)2+-40sint2=41…

Q: Give the equation of the tangent plane to each of these surfaces at the point indicated.

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