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

question 9

Multiple Choice

Find $\mathbf { r } ( t )$ satisfying the conditions for $\mathbf { r } ^ { \prime } ( t ) = 5 \mathbf { i } + 8 t \mathbf { j } - 6 t ^ { 2 } \mathbf { k }$ $\mathbf { r } ( 0 ) = \mathbf { i } + \mathbf { j }$

• A) \(( 5 t + 1 ) \mathbf { i } + \left( 4 t ^ { 2 } + 1 \right) \mathbf { j } - 2 t ^ { 3 } \mathbf { k }\)
• B) \(( 5 t + 1 ) \mathbf { i } + \left( 8 t ^ { 2 } + 1 \right) \mathbf { j } - 6 t ^ { 3 } \mathbf { k }\)
• C) \(5 t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } - 2 t ^ { 3 } \mathbf { k }\)
• D) \(5 t \mathbf { i } + 8 t ^ { 2 } \mathbf { j } - 6 t ^ { 3 } \mathbf { k }\)

---

Definitions:

Net Income

The amount of earnings left after all expenses and taxes have been deducted from total revenue.

Variable Expenses

Costs that vary directly with the level of production or sales volume.

Capital Budgeting

The process a business undertakes to evaluate potential major projects or investments, assessing their viability and profitability.

Expenditure Decisions

Expenditure decisions involve choosing how to allocate resources among various options for spending, often evaluating costs and benefits to achieve financial objectives.