Find T, N, and B for the Given Space Curve $$r ( t ) = \left( 8 + 6 \sin \frac { 2 } { 3 } t \right) i + \left( 4 + 6 \cos \frac { 2 } { 3 } t \right) j + 3 t k$$

question 55

Multiple Choice

Find T, N, and B for the given space curve.
- $$r ( t ) = \left( 8 + 6 \sin \frac { 2 } { 3 } t \right) i + \left( 4 + 6 \cos \frac { 2 } { 3 } t \right) j + 3 t k$$

• A) \(\mathrm { T } = \frac { 4 } { 5 } ( \cos 0.667 \mathrm { t } ) \mathbf { i } - \frac { 4 } { 5 } ( \sin 0.667 \mathrm { t } ) \mathbf { j } ; \mathbf { N } = ( - \sin 0.667 \mathrm { t } ) \mathbf { i } - ( \cos 0.667 \mathrm { t } ) \mathbf { j } ; \mathbf { B } = \frac { 3 } { 5 } ( \cos 0.667 \mathrm { t } ) \mathbf { i } - \frac { 3 } { 5 } ( \sin 0.667 \mathrm { t } ) \mathbf { j } -\) \(\frac { 4 } { 5 } \mathbf { k }\)
• B) \(\mathrm { T } = \frac { 4 } { 5 } ( \sin 0.667 \mathrm { t } ) \mathbf { i } - \frac { 4 } { 5 } ( \cos 0.667 \mathrm { t } ) \mathbf { j } ; \mathbf { N } = ( - \sin 0.667 \mathrm { t } ) \mathbf { i } - ( \cos 0.667 \mathrm { t } ) \mathbf { j } ; \mathbf { B } = \frac { 3 } { 5 } ( \cos 0.667 \mathrm { t } ) \mathbf { i } - \frac { 3 } { 5 } ( \sin 0.667 \mathrm { t } ) \mathbf { j } -\) \(\frac { 4 } { 5 } \mathbf { k }\)
• C) \(\mathrm { T } = \frac { 4 } { 5 } ( \cos 0.667 \mathrm { t } ) \mathbf { i } - \frac { 4 } { 5 } ( \sin 0.667 \mathrm { t } ) \mathbf { j } + \frac { 3 } { 5 } \mathbf { k } ; \mathbf { N } = ( - \sin 0.667 \mathrm { t } ) \mathbf { i } - ( \cos 0.667 \mathrm { t } ) \mathbf { j } ; \mathbf { B } = - \frac { 4 } { 5 } \mathbf { k }\)
• D) \(\mathrm { T } = \frac { 4 } { 5 } ( \cos 0.667 \mathrm { t } ) \mathbf { i } - \frac { 4 } { 5 } ( \sin 0.667 \mathrm { t } ) \mathbf { j } + \frac { 3 } { 5 } \mathbf { k } ; \mathbf { N } = ( - \sin 0.667 \mathrm { t } ) \mathbf { i } - ( \cos 0.667 \mathrm { t } ) \mathbf { j } ; \mathbf { B } = \frac { 3 } { 5 } ( \cos 0.667 \mathrm { t } ) \mathbf { i } - \frac { 3 } { 5 } ( \sin\) \(0.667 t ) \mathbf { j } - \frac { 4 } { 5 } \mathbf { k }\)

Understand the defining characteristics and main drivers of globalization.

Identify the role of transnational corporations and their impact on global markets.

Recognize the relationship between globalization and cultural changes, including homogenization and cultural imperialism.

Comprehend the contributions and effects of international organizations in promoting human rights and globalization.

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Definitions:

Oppressive Acts

Behaviors or actions by directors or majority shareholders in a corporation that are burdensome, harsh, or wrongful against minority shareholders.

Directors

Members of a company's board of directors, who are elected to oversee and guide the management and policies of the corporation, representing the interests of the shareholders.

Consolidation

The process of combining multiple businesses, assets, or financial statements into one unified entity.

Debts

Debts are amounts of money that are owed or due to individuals, corporations, or governments.