Prove that at the point of intersection of the surfaces x² + y² = 2², z = a tan` X where y = x tan 0, the radius of curvature and torsion are given by a(2+0²) ³/2 (8+50+0¹) ¹² P = and o = a (8+50² +0¹) 6+0²

Q: Indicate the truth value of these propositions: 1. It is not true that, either February is 30 days…

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Q: Exercise 8. Show that the sum of the angles of a geodesic triangle on a surface of positive…

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Q: r(t) = (² + 2)i + (² – 4t)j + 2tk

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Q: ind the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

A: To find the parametrization of the curve defined by the intersection of the two surfaces  and ,…

Q: Calculate the curvature of r (t) = 〈t,t^2,t^3 〉 at the point (1,1,1)

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Q: 2) The (Beltrami) pseudo sphere is given by the chart xlu,v) = (cosculsinlv), sincu) sincv) , cos(vl…

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Q: PCt) =<5-t, 4t -3,3t7 uking are length Reparami tize parameter from the point (4,113).

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Q: Find the curvature of ƒ(x) = ln cos x, < x < 2 -- 2°

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Q: 2. Calculate the curvature, unit binormal vector and torsion for r(t) (e'cost)i+(e'sint)j +5k

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Q: A: Find the distance from the point (2,2,3) to the line x=1+t,□( ) y=3-t,□( ) z=2t.

A: As per bartleby guidelines only 1 question is answered please upload the rest separately. The line…

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Q: a(0)=(r(0)cos0,r(0)sin@) Find the curvature of the curve. What are the coefficients a and b if its…

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Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: Consider a plane curve defined by the parametric equations :  x(t)=acos^3 (t) and  y(t)=asin^3 (t)…

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Q: Find the radius of curvature for the curve y = 3 sin(2x) at the point a) Op= b) Op= d) Op= 31 31 2…

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A: α(t)=(1rcost ,1rsint ,0)r is constantTo find the curvature of the given curve