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

question 34

Multiple Choice

$\text { Find the vectors } \mathbf { r } ( t ) \text { and } \mathbf { r } ^ { t } ( t ) \text { for the following vector function. }$ $\mathbf { r } ( t ) = ( 1 + 2 t ) \mathbf { i } + \left( 2 + 5 t ^ { 2 } \right) \mathbf { j } + 2 \mathbf { k }$

• A) \(\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 2 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 18 \mathbf { i } + 30 \mathbf { j }\)
• B) \(\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 2 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 30 \mathbf { j }\)
• C) \(\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 4 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 30 \mathbf { j }\)
• D) \(\mathbf { r } ( 3 ) = 7 \mathbf { i } + 2 \mathbf { j } + 47 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 30 \mathbf { j }\)
• E) \(\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 2 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 90 \mathbf { j }\)

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Definitions:

Educated Mind

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An ancient Greek philosopher and polymath, whose writings covered a wide range of subjects and significantly influenced Western philosophy and science.

Premises Imply

The logical process where a set of stated propositions (premises) are shown to necessarily lead to a specific conclusion.

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A deduction or inference that does not logically follow from the premises or evidence provided.