On the binormal to a given curve, a point Q is taken at a constant distance c from the curve. Prove that curvature k, of the locus of Q is given by k² (1 + c²²²)³² = c²+² (1 + c² ₁³² ) + (k − c T ¹ + c²k ²² ) ² tª -

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A: Compute unit binormal and curvature at t=pi/6

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A: Curvature: The curvature of the curve given by the vector function r is:…

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A: Given that C(t)=12cost,12sint be the circle of radius 1/2 where t is from 0 to 2π. Here C(t) is a…

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A: Since you have asked multiple questions, we will answer the first question for you. If you want any…

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

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A: This is a problem of differential geometry.

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Q: 5. Given r = F(0), prove that the curvature is given by dr p2 + 2 do () dr - r de? K = 3 2 dr () p2…

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Q: s question is differential geometry. Prove that the coordinate lines of a su

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Q: Find the length of the curve. The curve r= 8,/1+ sin(20), 0 <0< 4 A) 27 C) 8(7+ In(m

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A: We need to find the which of the given statements are true. For (a), Statement: An arc-length…

Q: Let P, Q be two points on the sphere of radius 1. Assume that P ≠ -Q. Show that there exists a curve…

A: Given P and Q be two points on the sphere of radius 1 P ≠ -Q. We need to show that there exists a…

Q: 17. Find the curvature of an elliptical helix that is described by r(t) = a cos ti + b sin tj + ctk,…

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Q: Find the curvature of r(t) = (2 sin 1, cos 31, t) at t = 4 and t = 5 (Figure ). 3. FIGURE The curve…

A: We will use concept of vector functions to solve it. A vector-valued function, also referred to as a…

Q: The path equation of a particle is given by r = -t²î + cos(2t)ŷ. Find, for t = T/4 s, (а) г, v, а;…

A: Due to guidelines, I'll be solving first three subparts and giving hints to fourth subpart.

Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

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Q: Write a formula for the curvature K(t) in terms of ( r' (t) and r" 0) )? And prove it?

A: The curvature Kt is given by Kt=r't×r''tr't3 Now prove this formula in the following.

Q: the derivative of

A: We find derivative of given function Use formula sin2x = 2sinx cosx

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Q: Suppose we have the parametric curve associated with 1 2t, 1 r (t) = t > 0. -- t2' 3t3 Evaluate k,…

A: Find r'(t) and r"(t) then find cross product and put in the formula of curvatur

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Q: 4) Use technology (like Desmos?) to graph each of the following functions along with its tangent…

A: Hey, since there are multiple subparts posted, we will answer first question. If you want any…