Find $\mathbf { r } ( t )$ Satisfying the Conditions For

question 54

Multiple Choice

Find $\mathbf { r } ( t )$ satisfying the conditions for $\mathbf { r } ^ { t } ( t ) = 9 e ^ { 9 t } \mathbf { i } + 9 e ^ { - t } \mathbf { j } + e ^ { t } \mathbf { k }$ $\mathbf { r } ( 0 ) = \mathbf { i } - \mathbf { j } + 9 \mathbf { k }$

• A) \(\left( e ^ { 9 t } + 1 \right) \mathbf { i } - \left( 9 e ^ { - t } + 1 \right) \mathbf { j } + \left( e ^ { t } + 9 \right) \mathbf { k }\)
• B) \(9 e ^ { 9 t } \mathbf { i } - \left( 9 e ^ { - t } + 8 \right) \mathbf { j } + \left( e ^ { t } + 8 \right) \mathbf { k }\)
• C) \(e ^ { 9 t } \mathbf { i } - \left( 9 e ^ { - t } - 8 \right) \mathbf { j } + \left( e ^ { t } + 8 \right) \mathbf { k }\)
• D) \(\left( 9 e ^ { 9 t } + 1 \right) \mathbf { i } - \left( 9 e ^ { - t } - 1 \right) \mathbf { j } + \left( e ^ { t } + 9 \right) \mathbf { k }\)

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Definitions:

Deep Palpation

A technique in physical examination to press deeply into the body to feel the organs or tissues.

Fingertips

The extreme ends or tips of the fingers, sensitive to touch and important for fine motor skills.

Laceration

A deep cut or tear in the skin or flesh, often requiring medical treatment to prevent infection or further injury.