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

question 21

Multiple Choice

$\text { Find } \mathbf { r } ^ { t } ( t ) \cdot \mathbf { r } ^ {tt } ( t ) \text { given the following vector function. }$
$\mathbf { r } ( t ) = \left( 2 t ^ { 2 } + 2 t \right) \mathbf { i } + \left( 3 t ^ { 2 } + 4 t \right) \mathbf { j }$

• A) \(32 + 52 t\)
• B) \(16 + 52 t\)
• C) \(32 + 26 t\)
• D) \(16 + 26 t\)
• E) \(32 + 52 t ^ { 2 }\)

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Definitions:

Welfare

Governmental support aimed at ensuring the basic physical and material well-being of individuals, often including provisions for health care, education, and housing.

Helping

The act of providing assistance or support to others in need, often motivated by empathy, moral obligations, or the anticipation of reciprocation.

Bystander Effect

A social psychological phenomenon in which individuals are less likely to offer help to a victim when other people are present.

Zero-sum Game

A situation or game in which one person's gain is equivalent to another's loss, so the net change in wealth or benefit is zero.