Let S Be a Circular Cylinder of Radius 0 $( x ( \theta ) , y ( \theta ) , z ( \theta ) )$

question 23

Essay

Let S be a circular cylinder of radius 0.2, such that the center of one end is at the origin and the center of the other end is at the point (5, 0, 4).
Let P be the plane containing the base of the cylinder (i.e., the plane through the origin perpendicular to the axis of the cylinder).
In each case, give a parameterization $( x ( \theta ) , y ( \theta ) , z ( \theta ) )$ and specify the range of values your parameters must take on.
(i)the circle in which the cylinder, S, cuts the plane, P.
(ii)the surface of the cylinder S.

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Definitions:

Cardiovascular

Pertains to the system comprising the heart and blood vessels, responsible for circulating blood throughout the body.

Muscular

Relating to or involving the muscles, which are tissues in the body responsible for movement.

Skeletal

Relating to the skeleton, the internal framework of bones that supports the body and facilitates movement.