1
answer
1
watching
262
views
8 Aug 2021
5. Do the following tasks using Mathematica.
![](data:image/png;base64,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)
- Parametric equations of the cycloid are:
![](data:image/png;base64,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)
Graph the cycloid for 0 ≤ θ ≤ 10
- Show that the curvature at top of any one on cycloid’s aches is
Hint: At top of any one of it’s arches y is maximum
- Parametric equations of a circle of radius r are:
![](data:image/png;base64,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)
Show that the curvature of each point of a circle of radius r is ![](data:image/png;base64,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)
5. Do the following tasks using Mathematica.
- Parametric equations of the cycloid are:
Graph the cycloid for 0 ≤ θ ≤ 10
- Show that the curvature at top of any one on cycloid’s aches is
Hint: At top of any one of it’s arches y is maximum
- Parametric equations of a circle of radius r are:
Show that the curvature of each point of a circle of radius r is
1
answer
1
watching
262
views
For unlimited access to Homework Help, a Homework+ subscription is required.
![Avatar image](https://s3.us-east-1.wasabisys.com/prealliance-avatars.oneclass.com/avatars/4083946/small/Untitled_design-2.png?1637925277)
Liked by orangerhinoceros356 and 2 others