21. r(t) = t³ j + t² k %3D

Q: Find the curvature for the helix r(t) = (4cost)i +(4sin t) j +(3t)k

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Q: Use this theorem to find the curvature. r(t) = 7ti + 5sin(t)j + 5 cos(t) k

A: Consider the provided vector valued function, rt=7ti+5sintj+5costk Using the above theorem find the…

Q: Find the curvature of r(t) = (In t, 2t, t²) at (0, 2, 1).

A: Given r(t) = <ln t, 2t, t2> To find the curvature (k) at (0, 2,1)

Q: Find a formula for the curvature of the function P= nrt/v-nb - (an^2)/(v^2) ,where n, R, a, b,and T…

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Q: find the curvature of r(t)=⟨3t2, ln(t), t ln(t)⟩ at the point (3, 0, 0).

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Q: Find the curvature and radius of curvature of the parabola y=x² at the origin. O K= 2, p=1/2 O k=2x,…

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Q: Find the curvature when r(t)=  6t i + 1/2t2 j +t2 k

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Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = ti + j, t = 2 K…

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Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = 8 +²³₁ t=2 11…

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Q: Calculate the curvature function κ(t). r(t) =〈4t + 1, 4t − 3, 2t〉

A: Given: r(t)=4t+1,4t-3,2t Differentiate the function. r'(t)=ddt4t+1,4t-3,2t=4,4,2 Again…

Q: Find the curvature of r(t)=[e*,e2",e 3t] at t=0.

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Q: Given the vector function *(t) = (t, cos (2t)) Calculate the curvature when t=5.4

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Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay…

A: Given function is rt=3cost ax+4sint ay+ t az To find curvature and radius of curvature

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 K of the plane curve at the given value of the parameter. r(t) = 8ti – 4tj, t = 1…

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Q: Find the curvature of the plane curve at the given value of the parameter.          r(t) = ti + 1…

A: Given data: *The plane curve is  r(t)=ti+19t3j *The value of the Parameter is t=2. The derivative of…

Q: Show that along the plane curve x = #1(t)e, +2(t)e2 the curvature is 4.30. [(a)2(5)213/2 a0 + 3

A: The curvature K at a point of a curve defines the speed of rotation of the tangent of the curve at…

Q: The curve in the figure below is parametrized by F(t) = (t³ – 3t) · i + (3t² – 2) · j, for -00 <…

A: Here, the given parametric curve is: r→(t)=(t3-3t) i +(3t2-2) j

Q: The curvature of y=x? is: None .a 1 (1+4x)/2 .b O (1-4x2)2 .cO -1 (1+4x)2 .d o «17 jo 4 Jiull uo…

A: In this question we have to find the curvature of the given function which we can find out by using…

Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay +…

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Q: Use this theorem to find the curvature. r(t) = 2ti + 5 sin(t)j + 5 cos(t) k K(t)

A: →dcos(t)dt = -sin(t)→dsin(t)dt = cos(t)→ If, r→=a i + b j + c k    Then,  r→ = a2 + b2 + c2

Q: Find the currvature and radius of curvature of the plane curve at the given value of x. y%3D 5x+ 7.…

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Q: Find the curvature k(t) of the vector function r(t) at the indicated time. r(t)= (acos(t), bsen(t),…

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Q: Find the curvature of the given curve r(t) = 5ti +3sin(t)j + 3cos(t)k a. 2//34 b. 4//34 C. 3/34 d.…

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Q: Find the curvature of r(t) = √√7ti + etj + e-k at point P(0, 1, 1).

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Q: Find the curvature and the radius of curvature at the stated point for r(t) 3cos t ax + 4sint ay + t…

A: r(t)=3cost, 4sin t,t, t=π2 find r'(t) and r''(t) r'(t)=-3sin t,4cos t,1r''(t)=-3cos t,-4sin t,0 To…

Q: Find the curvature K(t). r(t) = (4t, 3t, 2) %3D

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Q: Which one is a formula for the curvature ? | ||r"(u)|| du a r' (u) du dT ds T'(t) T' O B(t) = T(t) ×…

A: let there be a smooth and continuous curve then the curvature on a smooth curve is defined to be the…

Q: Q11

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Q: 3. Find the moving trihedral and the curvature at any point of R(t) = (In(sect), t/V2,t/V2). %3D

A: Introduction: In differential geometry, the Frenet–Serret formulas define the kinematic properties…

Q: Determine the curvature of r(t) = t^2 i+ t k

A: In this question we have to find the curvature of the vector which we can find out by using the…

Q: Use this theorem to find the curvature. r(t) = 9t i + 2 sin(t) j + 2 cos(t) k

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Q: Find the curvature of r(t) = (t, 5, t²): at a general point, and at (1,5,1).

A: Given r→t=t,5,t2 and point is 1,5,1. We have to find the curvature of r→t=t,5,t2 at point 1,5,1 The…

Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Determine the curvature at any point on the curve given by R(t) = i +t?j+t³k. %3D

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Q: Suppose r(t) = i+t²j+2tk. Find the length of the portion of this curve that goes from the point G,…

A: We will find out the required value of length and expression for curvature.

Q: Find the curvature K and the radius of curvature R at (1,2). (A K= √/2. R=₁ R = √2 (В) K= R= 2√2 2√2…

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Q: Find the curvature K for the space curve r(t) = (/3sint)i + (sint)j+ (2cost)k.

A: Let, γ(t) be a space curve. The curvature of the space curve is given by, κ=γ'(t)×γ"(t)γ'(t)3.

Q: Find the curvature of the vector-valued function. r(t) = (e3t,e)

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Q: Hiwi fined the curvature for each the Fllbwing vector function Pt) =(44,-t, 2f>

A: Curvature of the 3d-vector

Q: 1) Calculate the curvature of the position vector F(t) = sin t ax+ 2cos tay + V3 sin tāz is a…

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Q: Find the curvature of r(t) = 5(cos t) i + 12(sin t) j + tk at t = m/2. Ok = 8/13 Ok = 5/13 O k =…

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Q: 4. Find the curvature of r(t) = (tv2, e', e-t) at the point (0,1,1).

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Q: find the curvature of the plane curve at the given value of the parameter. r(t)=4ti-2tj,    t=1

A: To find- curvature of the plane.

Q: Find the curvature of r(t) at the point (1, 1, 1). r(t) = (t, t², t³) k=

A: Given: vector valued function r(t)=&lt;t, t2, t3&gt;To Find: curvature at t=1

Q: Given x = t, y = 1/t, find the curvature at t = 2. 16 17√/17 O 16 17 O 16/17 17 16 √17

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Q: Find the curvature of r(t) = (2t, t²,-t³) as a function of the parameter t. Simplify your answer to…

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Q: Find the curvature of the plane curve. 13. r(t) =t² i+ j t = 2 14. r(t)=(t, sint) at t =- 2

A: 1)