Solve the Initial Value Problem Initial Condition $\mathbf { r } ( 0 ) = - 9 \mathbf { i } + 5 \mathbf { j } + 11 \mathbf { k }$

question 85

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = \left( 9 \mathrm { t } ^ { 2 } - 5 \right) \mathbf { i } - \mathbf { j } + \frac { 1 } { \sqrt { 1 + \mathrm { t } } } \mathbf { k }$
Initial Condition: $\mathbf { r } ( 0 ) = - 9 \mathbf { i } + 5 \mathbf { j } + 11 \mathbf { k }$

• A) \(r ( t ) = \left( 3 t ^ { 3 } - 5 t - 9 \right) i + ( 5 - t ) j + ( \sqrt { 1 + t } - 9 ) \mathbf { k }\)
• B) \(r ( t ) = \left( 3 t ^ { 3 } + 5 t + 9 \right) i + ( 5 + t ) j + ( \sqrt { 1 + t } + 9 ) k\)
• C) \(r ( t ) = \left( 3 t ^ { 3 } - 5 t - 9 \right) \mathbf { i } + ( 5 - t ) j + ( 2 \sqrt { 1 + t } + 9 ) \mathbf { k }\)
• D) \(\mathbf { r } ( \mathrm { t } ) = \left( 9 \mathrm { t } ^ { 3 } - 5 \mathrm { t } - 9 \right) \mathbf { i } + ( 5 - \mathrm { t } ) \mathbf { j } + ( \sqrt { 1 + \mathrm { t } } + 9 ) \mathbf { k }\)