$\text { Find } \mathbf { r } ^ { t } ( t ) \text { given the following vector function. }$

question 44

Multiple Choice

$\text { Find } \mathbf { r } ^ { t } ( t ) \text { given the following vector function. }$ $\mathbf { r } ( t ) = \frac { 4 } { t ^ { 2 } } \mathbf { i } - 6 t ^ { 4 } \mathbf { j } + \frac { t ^ { 5 } } { 6 } \mathbf { k }$

• A)\(\mathbf { r } ^ { t } ( t ) = - \frac { 8 } { t ^ { 3 } } \mathbf { i } - 24 t ^ { 3 } \mathbf { j } + \frac { 5 } { 6 } t ^ { 4 } \mathbf { k }\)
• B) \(\mathbf { r } ^ { t } ( t ) = \frac { 8 } { t ^ { 3 } } \mathbf { i } - 24 t ^ { 3 } \mathbf { j } - \frac { 5 } { 6 } t ^ { 5 } \mathbf { k }\)
• C) \(\mathbf { r } ^ { t } ( t ) = \frac { 8 } { t ^ { 3 } } \mathbf { i } - 24 t ^ { 3 } \mathbf { j } + \frac { 5 } { 6 } t ^ { 4 } \mathbf { k }\)
• D) \(\mathbf { r } ^ { t } ( t ) = - \frac { 8 } { t ^ { 3 } } \mathbf { i } - 24 t ^ { 4 } \mathbf { j } + \frac { 5 } { 6 } t ^ { 4 } \mathbf { k }\)
• E) \(\mathbf { r } ^ { t } ( t ) = - \frac { 8 } { t ^ { 3 } } \mathbf { i } - 24 t ^ { 3 } \mathbf { j } + 30 t ^ { 4 } \mathbf { k }\)

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Definitions:

Habitat Isolation

A prezygotic reproductive isolating mechanism in which reproduction between similar species is prevented because they live and breed in different habitats.

Interbreed

To produce offspring by mating individuals of different species, breeds, varieties, etc.

Black Bears

A species of bear native to North America, known for its varied diet and adaptability to different habitats.

Brown Bears

Large omnivorous mammals found in various regions across the globe, characterized by their brown fur and significant size.