A Child Is Sliding Down a Helical Slide $\vec { r } = \cos t \vec { i } + \sin t \vec { j } + ( 12 - t ) \vec { k }$

question 16

Short Answer

A child is sliding down a helical slide.Her position at time t after the start is given in feet by $\vec { r } = \cos t \vec { i } + \sin t \vec { j } + ( 12 - t ) \vec { k }$ .The ground is the xy-plane.
At time t = 2 $\pi$ , the child leaves the slide on the tangent to the slide at that point.What is the equation of the tangent line?

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Definitions:

Revised Secularization

A contemporary interpretation of secularization that accounts for the persistence of religion in modern societies, adjusting traditional views that predicted the decline of religion.

Émile Durkheim

A founding figure in sociology, known for his studies on social solidarity, religion, and the collective conscience.

Karl Marx

A 19th-century philosopher, economist, and revolutionary socialist whose ideas about society, economics, and politics collectively laid the foundation for modern socialism and communism.

Religious Practice

A set of rituals and beliefs followed by individuals in accordance with their faith.