The Graph Below Is Most Likely the Graph of Which $\mathbf { r } ( t ) = 2 t \cos ( t ) \mathbf { i } + 2 t \sin t \mathbf { j } + 2 \mathbf { k } , \quad 0 \leq t \leq 2 \pi$

question 40

Multiple Choice

The graph below is most likely the graph of which of the following equations?

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

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Definitions:

Fixed Costs

Expenses that do not change in proportion to the activity of a business, such as rent, salaries, or insurance premiums.

Negative Returns

A situation in which an increase in the amount of inputs used leads to a decrease in the level of output, often seen in cases of over-investment or inefficient production processes.

Worker

An individual who performs tasks or services for compensation; an employee.

Variable Cost

Costs that change in proportion to the activity or volume of output in production, such as raw materials and direct labor costs.