For a Parametric curve r = r(t) , y = y(t) the curvature at a point p is:|dr dy dx dy|dt dt2dt? dt213/2drdtdt(a) Parametric equations of the cycloid are:I = 0 - sin 0y =1- cos eGraph the cycloid for 0 < 0 < 10x(b) Show that the curvature at top of any one of cycloid's arches isHint: At top of any one of it's arches y is maximum(c) Parametric equations of a circle of radius r are:1 = r cos 0y = r sin eShow that the curvature of each point of a circle of radius r is K =1/r

Use the following formulae, to find the required result.…

Answered: For a Parametric curve z = r(t) , y =…

For a Parametric curve z = r(t) , y = y(t) the curvature at a point p is: |dr d²y &xdy| dt dt dt? dt (a) Parametric equations of the cycloid are: I=0 - sin ở y =1- cos e Graph the cycloid for 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 31E

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Question

For a Parametric curve r = r(t) , y = y(t) the curvature at a point p is:
|dr dy dx dy|
dt dt2
dt? dt
213/2
dr
dt
dt
(a) Parametric equations of the cycloid are:
I = 0 - sin 0
y =1- cos e
Graph the cycloid for 0 < 0 < 10x
(b) Show that the curvature at top of any one of cycloid's arches is
Hint: At top of any one of it's arches y is maximum
(c) Parametric equations of a circle of radius r are:
1 = r cos 0
y = r sin e
Show that the curvature of each point of a circle of radius r is K =1/r

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