Suppose the Outer Edge of a Playground Slide Is in the Shape

question 56

Multiple Choice

Suppose the outer edge of a playground slide is in the shape of a helix of radius 10.5 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix.

• A) \(\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4 \pi\)
• B) \(\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 2 \pi\)
• C) \(\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 2 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 2 \pi\)
• D) \(\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 10.5 \sin t \mathbf { j } + \frac { 1 } { \pi } t \mathbf { k } , \quad 0 \leq t \leq 4 \pi\)
• E) \(\mathbf { r } ( t ) = 10.5 \cos t \mathbf { i } + 2 \sin t \mathbf { j } + t \mathbf { k } , \quad 0 \leq t \leq 4 \pi\)

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Definitions:

Integrity

The quality of being honest and having strong moral principles, or the state of being whole and undivided.

Collaboration

The action of working with someone to produce or create something.

Beneficial

Having a positive effect; helpful or advantageous to individuals or situations.

Compromise

A method of resolving disagreements where all parties make concessions to reach a mutually acceptable decision.