Answered: at a unit-speed regular parametrised… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

See similar textbooks

Related questions

Question

Please solve correct as soon as possible

A1. (a) Give an example of parametrised curve y: (0, 1) → R' which is
i. not regular; ii. regular but not unit-speed; iii. regular and unit-speed.
(b) Assume that a unit-speed regular parametrised curve ß:(-7, 7) → R? with
Frenet frame (T, N) has constant curvature k > 0. Show that its tangent vector
T is of the form T(s) = cos(ks) a + sin(xs) b, for some a, b e R?.
Deduce that |a||? = 1, ||b||2 = 1, while a b = 0. Furthermore, prove that 3 is
(part of) a circle of radius K.
%3D
%3D

Expert Solution

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.90 s, it is at point (4.60 m, 5.00 m) with velocity (2.00 m/s)ĵ and acceleration in the positive x direction. At time t2 = 13.6 s, it has velocity (–2.00 m/s)î and acceleration in the positive y direction. What are the x and y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.
. Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)
Show that the ellipse x = a cos t, y = b sin t, a> b>0, has its largest curvature on its major axis and its smallest curvature on its minor axis.
Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?
Find the length of parametrized curve given by x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t goes from 0 to 1
What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?
If a parametrized curve is given by: r⃗ (t)=⟨2t^3,10ln(t),5t^2+9t⟩ At t==2, the position vector is ⟨16,10ln(2),38⟩ Find the curvature at t=2, K(2)
Find the curvature of a superellipse defined by the parametric equations x(t)=acosnt,y(t)=bsinnt,where a,b and n are positive real numbers.
Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line with parametric equations x = 2 − 4t, y = 1 + 8t, and z = 3 − 2t
The Cornu spiral is the plane curve r(t) = ⟨x(t), y(t)⟩, wherex(t) =Z t0sin(u2/2) du, y(t) =Z t0cos(u2/2) duVerify that κ(t) = |t|. Since the curvature increases linearly, the Cornuspiral is used in highway design to create transitions between straight andcurved road segments.
Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS