Use the Given Acceleration Function and Initial Conditions to Find

question 77

Multiple Choice

Use the given acceleration function and initial conditions to find the position at time t = 3. $\mathbf { a } ( t ) = 5 \cos t \mathbf { i } - 3 \sin t \mathbf { j } , \quad \mathbf { v } ( 0 ) = 8 \mathbf { j } + 5 \mathbf { k } , \quad \mathbf { r } ( 0 ) = - 5 \mathbf { i }$

• A) \(\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } - ( 3 \sin 3 + 15 ) \mathbf { j } + 15 \mathbf { k }\)
• B) \(\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } + ( 3 \sin 3 - 15 ) \mathbf { j } + 15 \mathbf { k }\)
• C) \(\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } + ( 3 \sin 3 + 15 ) \mathbf { j } + 15 \mathbf { k }\)
• D) \(\mathbf { r } ( 3 ) = 5 \cos 3 \mathbf { i } + ( 3 \sin 3 + 15 ) \mathbf { j } + 15 \mathbf { k }\)
• E) \(\mathbf { r } ( 3 ) = - 5 \cos 3 \mathbf { i } + 15 \mathbf { j } + ( 3 \sin 3 + 15 ) \mathbf { k }\)

---

Definitions:

Selling Expenses

Costs associated with the selling of a company's goods or services, not including the cost of producing the goods.

Nonoperating Items

Revenue and expenses arising from activities outside of a company's normal business operations, such as investing or financing activities.

Gross Margin

The difference between sales revenue and the cost of goods sold, expressed as a percentage of sales revenue.

Operating Expenses

Costs related to the day-to-day functions of a business, excluding the cost of goods sold.