Given the curve a(t) = at e, + bt e, + t²e; where a, b € N. If the curvature at t = 0, k(0) = 1 Then: a = 1, b = 1 a = 1,b = 2 O The above answer The above answer a = 2,b = 1 a = 2, b = 2 O The above answer The above answer

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

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Q: Find the curvature of the plane curve Y = 4t* at the point t = 1. K(1) =

A: que: Curvature of a plane curve y = f(x) is given by K = y||(x)|(1+(y1(x))2)32 Here y = 4t4

Q: Q2/Find the curvature of the curve, r= (4 cos n i+4 sin n j)

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Q: a The curvature of the helix r(t) = (a cos t) i + (a sin t) j + bt k (a,bz 0) is K=- What is the…

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Q: If the curve I=3+ at? y= at + bt has a tangent line y=r-4 at t 1, what is a+b? %3D

A: We have to find a+b

Q: Find the curvature of the curve r(t) = e2ti + e2t cos tj + e2t sin tk.

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Find the curvature and the radius of curvature at the point t = 0. e' cos(t), y = e' sin(t), = 3e* x…

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Q: (a) Find the curvature and the radius of curvature of the curve r(t) = 3 cos ti +4 sin tj + tk at t…

A: Given r(t) = 3 cost i + 4 sint j + t k

Q: Find the curvature of the curve r(t) = 4ti + 3 cos tj + 3 sin tk .

A: curve r(t) = 4ti + 3 cos tj + 3 sin tk . We need to find the curvature of the given curve.

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = et sin(t), z =…

A: r(t)=etcost i + et sint j + 11et kr'(t)=(etcost-etsint) i+(etsint+etcost) j                + 11et…

Q: The curvature of the curve 7(t)=<6t, 6t+1, sin2t) at t= 4 is

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Q: For the curve given by r(t)=⟨−9sin(t),−1t,9cos(t)⟩, Find the curvature,

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Q: Let C be the curve represented by R(t) = (cos 2t, 2√3t, 5 — sin 2t). Determine the curvature of C at…

A: Let us consider the curve r(t)→ The curvature is obtained as κ=r'(t)→xr''(t)→|r'(t)|

Q: Find the curvature K of the plane curve at the given value of the parameter. = ti +tj, t = 3 36 r(t)…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), Y = e' sin(t), z =…

A: Given;  x=etcost, y=etsint, z=11et.

Q: a) Find a plane curve whose signed curvature is given by k,(s) where a is a positive constant and s>…

A: The given signed curvature is ks(s)=12as

Q: Find the curvature and the radius of curvature at the point t = 0. e* cos(t), y= e' sin(t), z=7e' K…

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Q: 1. Given the space curve r(t) = (2e¹,e²¹.e^¹), find the curvature at t = 0

A: I am attaching image so that you understand each and every step.

Q: 22. Find an equation for the circle of curvature of the curve r(r) = (2 In )i- [t + (1/]j, esIse, at…

A: The formula for the curvature is given by  κ(t)=r⇀'(t)×r⇀''(t)r⇀'(t)3 In order to use this formula,…

Q: Q2/Find the curvature of the curve, r= (4 cos n i+4 sin n j) .n=(In 2t)

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Q: Calculate the curvature of the curve defined by r(t)=9cos(4t)i+9sin(4t)j. Give the answer with 4…

A: Given that: r(t)=9cos(4t)i+9sin(4t)j

Q: Find an equation for the circle of curvature of the curve r(t) = (2 ln t)i - 3t + (1/t)4j, e-2…

A: Consider the given curve as,

Q: The curvature of a point moving along the curve given as R(t)=(In sec t) i+ tj is: O t O sec t O…

A: Here, Rt=lnsecti+tj

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A: We have to find the curvature and the radius of curvature at the point t = 0. x = et cos(t)  ,…

Q: Find the curvature of the plane curve at the given value of the parameter.           r(t) = ⟨5 cos…

A: Formula: curvature k =r't×r''tr't3.

Q: The curvature of the curve (t) = 6t, 6t+1, sin2t at t= TT 0 1 8. 01 01 18 O 2 1/2

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: H.W.// Find the curvature of the curve, r= (c cos ti + c sin t j)

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Q: Find the curvature of the curve r(t) = et cos ti + et sin tj + etk at the point P(1, 0, 1) .

A: Given curve is rt=etcosti+etsintj+etk.…

Q: Find the curvature K of the curve, where s is the arc length parameter. r(e) = (1 + 2) s li + K =

A: Given : r(s)=1+22si +1-22sj     To Find : Curvature K

Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cos t î + sint ĵ+ k.

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Q: Find the curvature K of the plane curve at the given value of the r(t) = 4ti – 4tj, t = 1 K =

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Q: Find the curvature of the plane curve at the pointindicated. y = t^4, t = 2

A: By Curvature we mean that to which extent any plane or graphical function is curved along onto a…

Q: Find the curvature K of the curve given below. r(t) = ti+8t²j+2tk

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Q: 1. Find the equation of the circle of curvature for the following curves: 1.1 x+y =x + y +x at…

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Q: 3. Consider the curve 7() = i+(Vī lm(1) +-R. b) Find the curvature at the point where t =1. Hint:…

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Q: Find the curvature K of the plane curve at the given value of the parameter. (Give your answer…

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Q: r(t) = 4i + tj + ²/²2 k 2

A: Given is the curve r(t)=4i+tj+t22k. The objective is to find the curvature. The formula for…

Q: The curvature of a point moving along the curve given as R(t)=(ln sec t) i+ tj is

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Q: Find the curvature K of the curve, where s is the arc length parameter. M03 - (1+²)+(1-2) r(s) K =

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Find the curvature K of the curve, where s is the arc length parameter. M(²) = (₁ + √2/2 =) ₁ - (₁ -…

A: we have to find curvature.

Q: (b) Find the curvature and the radius of curvature of the curve r (t) = e'i+e-tj+ tk at t = 0.

A: The given problem is to find the curvature and radius of curvature of the given vector curve.

Q: Find the curvature of the curve at the given position. r(1) = (r, t², 31), at t=1

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Q: LP |, calculate curvature for the curve 7(t) = 3t²i + 2tj + 5k at t = 1. sing the curvature formula…

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Q: Find the curvature of the curve 7(t) = (4cos(4t), 4 sin(4t), 5t) at the point t = 0 Give your answer…

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: Given a parametric curve r(t) (tcos t, tsin t, 5) find the curvature at t=n/2.

A: Given: rt=t cos(t), t sin(t), 5 at t=π2

Q: Consider the curve y(2) = sin z. Which one of the following statements is true? O The curvature at =…

A: Here to find curvature of curve, y(x)=sin(x) Curvature of curve is given as,…

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = et sin(t), z =…

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