Solve the Initial Value Problem Initial Condition $\mathbf { r } ( 0 ) = 0$

question 96

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = \frac { 3 } { 2 } ( \mathrm { t } + 3 ) ^ { 1 / 2 } \mathbf { i } + \mathrm { e } ^ { \mathrm { t } } \mathbf { j }$
Initial Condition: $\mathbf { r } ( 0 ) = 0$

• A) \(r ( t ) = \left[ ( t + 3 ) ^ { 3 / 2 } - 3 ^ { 3 / 2 } \right] \mathbf { i } + \left( e ^ { t } - 1 \right) \mathbf { j }\)
• B) \(r ( t ) = \left[ ( t + 3 ) ^ { 5 / 2 } - 3 ^ { 5 / 2 } \right] \mathbf { i } + \left( e ^ { t } - 1 \right) \mathbf { j }\)
• C) \(\mathbf { r } ( \mathrm { t } ) = \left[ ( \mathrm { t } + 3 ) ^ { 3 / 2 } + 3 ^ { 3 / 2 } \right] \mathbf { i } + \left( \mathrm { e } ^ { \mathrm { t } } + 1 \right) \mathbf { j }\)
• D) \(\mathbf { r } ( \mathrm { t } ) = ( \mathrm { t } + 3 ) ^ { 3 / 2 } \mathbf { i } + \mathrm { e } _ { \mathbf { j } } \mathbf { j }\)

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Definitions:

Intuition

An unconscious process of making decisions based on imagination and possibilities.

Intuition

A process of understanding or knowing something immediately, based on a person's feelings rather than facts or evidence.

Anchoring

A cognitive bias where an individual relies too heavily on an initial piece of information (the "anchor") when making decisions.

Satisficing

A decision-making strategy that entails choosing an option that meets a minimum standard of satisfaction or acceptability, rather than pursuing the best possible outcome.