Solve the Initial Value Problem Initial Condition $\mathbf { r } ( 0 ) = 5 \mathbf { i } - 6 \mathbf { j }$

question 69

Multiple Choice

Solve the initial value problem.
-Differential Equation: $\frac { \mathrm { d } \mathbf { r } } { \mathrm { dt } } = \left( \mathrm { t } ^ { 4 } + 5 \mathrm { t } ^ { 2 } \right) \mathbf { i } + 4 \mathrm { t } \mathbf { j }$
Initial Condition: $\mathbf { r } ( 0 ) = 5 \mathbf { i } - 6 \mathbf { j }$

• A) \(r ( t ) = \left( \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } - 6 \right) i + \left( 2 t ^ { 2 } + 5 \right) \mathbf { j }\)
• B) \(\mathbf { r } ( \mathrm { t } ) = \left( \frac { \mathrm { t } ^ { 5 } } { 5 } + \frac { 5 \mathrm { t } ^ { 3 } } { 3 } \right) \mathbf { i } + 2 \mathrm { t } ^ { 2 } \mathbf { j }\)
• C) \(r ( t ) = \left( \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } + 5 \right) i + \left( 2 t ^ { 2 } - 6 \right) \mathbf { j }\)
• D) \(r ( t ) = \left\{ \frac { t ^ { 5 } } { 5 } + \frac { 5 t ^ { 3 } } { 3 } + 5 \right) i + \left( t ^ { 2 } - 6 \right) j\)

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Definitions:

Effective Tax Rate

The average percentage of income that an individual or corporation pays in taxes, considering various deductions and credits.

Fair Value

The estimated market value of an asset, liability, or financial instrument at a given point in time.

Goodwill Impairment

A decrease in the value of a company's goodwill asset, indicating that the value of an acquired company's brand, customer base, or proprietary technology has declined.

Depreciation Expense

The allocation of the cost of a tangible asset over its estimated useful life to account for wear and tear, obsolescence, or decay.