Find T, N, and B for the Given Space Curve

question 79

Multiple Choice

Find T, N, and B for the given space curve.
-r(t) = (cosh t) i + (sinh t) j + tk

• A) \(\mathbf { T } = - \frac { \sqrt { 2 } } { 2 } ( \tanh \mathrm { t } \operatorname { sech } \mathrm { t } ) \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j } + \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } \mathrm { t } ) \mathbf { k } ; \mathbf { N } = ( - \operatorname { sech } \mathrm { t } ) \mathbf { i } - ( \tanh \mathrm { t } ) \mathbf { k }\); \(\mathbf { B } = \frac { \sqrt { 2 } } { 2 } ( \sinh \mathrm { t } ) \mathbf { i } - \frac { \sqrt { 2 } } { 2 } \mathrm { j } - \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } t ) \mathbf { k }\)
• B) \(\mathbf { T } = \frac { \sqrt { 2 } } { 2 } ( \tanh t \operatorname { sech } t ) \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j } + \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } t ) \mathbf { k } ; \mathbf { N } = \left( \operatorname { sech } ^ { 2 } t \right) \mathbf { i } - ( \sinh t ) \mathbf { k } ;\) \(\mathbf { B } = \frac { \sqrt { 2 } } { 2 } ( \sinh t ) \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j } + \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } t ) \mathbf { k }\)
• C) \(\mathbf { T } = - \frac { \sqrt { 2 } } { 2 } ( \tanh t ) i + \frac { \sqrt { 2 } } { 2 } j + \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } t ) \mathbf { k } ; \mathbf { N } = ( - \operatorname { sech } t ) i - ( \sinh t ) \mathbf { k }\); \(\mathbf { B } = - \frac { \sqrt { 2 } } { 2 } ( \sinh t ) \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j } - \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } t ) \mathbf { k }\)
• D) \(\mathbf { T } = \frac { \sqrt { 2 } } { 2 } ( \tanh \mathrm { t } ) \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j } + \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } t ) \mathbf { k } ; \mathbf { N } = ( \operatorname { sech } t ) \mathbf { i } - ( \tanh t ) \mathbf { k } ; \mathbf { B } = - \frac { \sqrt { 2 } } { 2 } ( \tanh \mathrm { t } ) \mathbf { i } + \frac { \sqrt { 2 } } { 2 } \mathbf { j } - \frac { \sqrt { 2 } } { 2 } ( \operatorname { sech } \mathrm { t } ) \mathbf { k }\)

Understand the importance of using natural language for date entries and the role of proper capitalization.

Identify the use and purpose of the appointment area, including the creation of appointments and meetings.

Understand the concept of calendar management including adding personal and business items.

Comprehend the role of Outlook's automatic features such as date recognition and recurrence settings.

---

Definitions:

Comparing

The act of evaluating two or more items to determine similarities, differences, or the relative merit of each.

Rankings

Lists or grading systems that arrange items or entities in order based on certain criteria, often used for comparison or evaluation purposes.

Feedback

Involves providing information or opinions about someone's performance or work, aiming to reinforce strengths or identify areas for improvement.

Managers

Individuals responsible for directing and overseeing the work of a group of people in an organization.