Solve the Initial Value Problem $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = - 9 \mathrm { ti } + 4 \mathrm { tj } + 7 \mathrm { tk }$

question 86

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = - 9 \mathrm { ti } + 4 \mathrm { tj } + 7 \mathrm { tk }$
Initial Condition: $\mathbf { r } ( 0 ) = - 7 \mathbf { i } + 4 \mathbf { k }$

• A) \(\mathbf { r } ( \mathrm { t } ) = \left( - 9 \mathrm { t } ^ { 2 } - 14 \right) \mathbf { i } + 4 \mathrm { t } ^ { 2 } \mathbf { j } + \left( 7 \mathrm { t } ^ { 2 } + 8 \right) \mathbf { k }\)
• B) \(r ( t ) = \frac { - 9 t ^ { 2 } - 7 } { 2 } i + 2 t ^ { 2 } j + \frac { 7 t ^ { 2 } + 4 } { 2 } k\)
• C) \(\mathbf { r } ( \mathrm { t } ) = \frac { - 9 \mathrm { t } ^ { 2 } - 7 } { 2 } \mathrm { i } + 2 \mathrm { t } ^ { 2 } \mathbf { j } - \frac { 7 \mathrm { t } ^ { 2 } + 4 } { 2 } \mathbf { k }\)
• D) \(\mathbf { r } ( \mathrm { t } ) = \frac { - 9 \mathrm { t } ^ { 2 } - 14 } { 2 } \mathbf { i } + 2 \mathrm { t } ^ { 2 } \mathbf { j } + \frac { 7 \mathrm { t } ^ { 2 } + 8 } { 2 } \mathbf { k }\)

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