A point P moves such that its position vector at timet is r(t) = 2a cost i + 2a sint j+ 2ct k circular helix 1. Find the arc length for 0 stS 2T 2. Calculate the acceleration a at t = 2TT

Q: Find the point on the curve r(t) (12 sin t)i – (12 cos t)j + 9tk at a distance a) 5n units and b)…

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Q: Find the arclength of the curve z 9 cos(9t), y = 9 sin(9t) with 0 <t< 36

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Q: Find an arc length parametrization of the line y = 2x – 6 %3D |

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Q: Calculate the arc length of the curve r (t) = 2cos (t)i + 2sin (t) j + tk from point (2,0,0) to…

A: Given curver (t) = 2cos (t)i + 2sin (t) j + tk

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

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Q: Find the length of one turn of the helix given by…

A: Given: The parametric equation of the curve: .

Q: a) Find the arc length parametrization of the line x = t, y = t that has the same orientation as the…

A: a)The given line is x = t, y = t.We can write it as a vector valued function as r(t)→ =x(t) i^ +…

Q: The position vector of a particle moving along a helix is c(t) = (cos(t), sin(t), t²). (a) Find the…

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Q: onent. Determine the moment exerted about the steering column at O.

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Q: Find the arc length of the ellipse x = 11 cos t, y = sin t, (0<t< 2 T) */2 V1+sin² t dt 7/2 V1+120…

A: Given problem:-

Q: estion 6 a) Find the arc length of the curve C parametrized by -t², 2t for 0 <t<1.

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Q: Find an arc length parametrization of r(t) = (et sin t,et cost,et)

A: Given that, rt=etsint, etcost, et       ...(1)

Q: te the line integral c 3 == 1 from A=(2, 0) to (0, -1) Jax + 2xyay where is the arc on the ellipse

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Q: Find the arc length traced out by the endpoint of the vector-valued function 7(t) = t cos t î + t…

A: Solved below.

Q: Find the arc length of the parametric curve: x (t) = 1+ 3t2, y (t) = 4+ 2t³ ,0 <t < 6. Give your…

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Q: Given a particle is moving ina curve r(t) = cos 6t i + sin 6t j+ 8t k. Find the normal component of…

A: Given the curve

Q: Keparametrize the curve rit) = with respect to its arclength measured from the point (e"20,e"2) in…

A: Given curver(t)=etsint,etcost,et Above curve is passes from the point eπ2,0,eπ2.we need to find the…

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 - 3t) %3D Find the…

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j – 12tk at a distance 65r units along the…

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Q: Calculate the arc length of the following vector function. E(1) = 4 In i+j+ 4t k; 1sts2.

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Q: consider a particle moving on a circular path of radius b described by r(t) = b cos(ωt)i + b…

A: Consider a particle moving on a circular path of radius b given as, rt=bcosωti+bsinωtj Where ω=dudt…

Q: Parameterize the curve r(t) = (2+ cos 3t, 3 – sin 3t, 4t) using arc length, s, as a parameter. Use t…

A: Given the curve rt=2+cos3t, 3-sin3t, 4t---1. Differentiating, we get vt=r't=-3sin3t,…

Q: da 2 dy 3. Use L = ) dt find the arc length of the curve dt dt e (sint + cost), y = e'(cost – sint),…

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Q: Starting from the point (0, 4, -2) reparametrize the curve r (t) = (0 – 2t) i + (4 – 2t) j + (-2 +…

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Q: Find the point on the curve r(t)=(5sint)i+(−5cost)j−12tk at a distance 13π units along the curve…

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Q: If the hydraulic cylinder AB is extending at a constant rate of 1 ft/s, determine the dumpster's…

A: image is attached

Q: Find the arc length of the vector curve 7(t) = (2t, t², (1/3)t³), 0<t< 2.

A: Find the arc length of the curve

Q: Find the arc length of the curve on the given interval. Parametric Equations     x = √t, y = 3t − 1…

A: Given: Parametric Equations x = √t, y = 3t − 1 Interval 0 ≤ t ≤ 1

Q: Find the arclength of the curve r(t) (6 sin t, 2t, 6 cost), -2 < t <2

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Q: Find the arclength L(C) of the helix C parametrized by C: r(t) = (2 cos t, -3t, 2 sin t) for 0 <t <…

A: The arc length of the parametric curve is given by: ∫ab(x'(t))2+(y'(t))2+(z'(t))2dt...(1); a≤t≤b…

Q: Find the momen

A: Given: r2=a2sin2θ

Q: Parametrize the following curve: y = tan−1(x2 + 1)

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Q: Find the arc length of the curve on the given interval. Parametric Equations    x = 6t2 , y = 2t3…

A: Given parametric equations are x(t)=6t2, y(t)=2t3

Q: Q1: Consider the curve in E' parameterized by C:(t) = 1- Find the arc-length of the curve r(t)? 2-…

A: Given equation of the curve is rt=cos5t, sin5t, 12t

Q: the of the curve d:laaR? Find detined by is čonstant. 870 Curiature a(t) =|1 Cost, 1 sint, o where…

A: A vector is a quantity that has both magnitude and direction. In general vectors are represented as…

Q: Find the motion of the mass-spring system in Fig. 72 with mass 0.125 kg, damping 0, spring constant…

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Q: Find the motion of the mass-spring system in Fig. 72 with mass 0.125 kg, damping 0, spring constant…

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Q: 3. Find the exact arc length of the curve y = 2Vx' on the interval [0,11]. ( -. TV +70 +60 +50 +40…

A: To find  The exact arc length of the given curve.

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

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Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j+ 12tk at a distance 26™ units along the…

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Q: find the arc length of the ellipse x 2 cos t, y = sin t, (0 <t < 2 T). Use 2 dx dy L dt dt dt 4…

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Q: Find the arc length over the domain 0<t<5 7t 1 10) x= V-7t – 2, y=- + | 4 2

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Q: Find an arc length parametrization of the curve r(t) = (1/1+t^2,-1,t/1+t^2)

A: Find an arc length parametrization of the curve r(t) = (1/1+t^2,-1,t/1+t^2)

Q: Given the following vector-valued function, draw its graph and then calculate its arc length. j =…

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Q: (D) The arc length of the curve x = 4(3 + y)² on [1, 4] is approximately (i) (ii) (iii) None of…

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Q: The position of a baseball (in ft) is represented by r(t) = 55/2ti + (4 + 55/2t- 16t2)j. Find the…

A: This is a problem related to vector. Based on the general formula we will answer the question.

Q: The position vector of the particle is 1 R = î cos(t) + ĝ sin(t) + k log (0 <t < T/2). sin t' (a)…

A: Differentiate the position vector R→=costi^+sintj^+log1sintk^ with respect to t, to obtain the…