A Particle Moves with Position Vector $\vec { r } ( t ) = \ln t \vec { i } + t ^ { - 1 } \vec { j } + e ^ { - t } \vec { k }$

question 47

Multiple Choice

A particle moves with position vector $\vec { r } ( t ) = \ln t \vec { i } + t ^ { - 1 } \vec { j } + e ^ { - t } \vec { k }$ . Describe the movement of the particle as t $\rightarrow$ $\infty$ .

• A)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\) \(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive y-axis with slower and slower speed.
• B)The particle will approach the positive y-axis asymptotically as t \(\rightarrow\)\(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive x-axis with slower and slower speed.
• C)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\) \(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive x-axis with increasing speed.
• D)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\)\(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive x-axis with slower and slower speed.
• E)The particle will approach the positive x-axis asymptotically as t \(\rightarrow\) \(\infty\).Also, since each component of \(\vec { v } ( t )\) approaches 0 as t \(\rightarrow\) \(\infty\), we expect the particle to approach the positive z-axis with slower and slower speed.

Understand the construction and interpretation of histograms.

Determine the appropriate measure of central tendency and variability for a given dataset.

Ability to interpret stem-and-leaf displays to analyze data distribution.

Recognize the skewness and modality of data distributions through graphical representations.

---

Definitions:

Dividend Income

Income received from owning shares in a company, paid out from the company's earnings to its shareholders.

Dividend Payable

The amount of money a company is committed to paying its shareholders in dividends for owning the company's stock.

Stock Split

A corporate action in which a company divides its existing shares into multiple shares to boost the liquidity of the shares, though the overall value remains the same.