Let $\mathbf { F } ( x , y , z ) = x \mathbf { j }$

question 154

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x \mathbf { j }$ . Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the rectangular path from $( 0,0,0 )$ to $( 1,0,1 )$ to $( 1,1,1 )$ to $( 0,1,0 )$ to $( 0,0,0 )$ .

• A) \(1\)
• B) \(\sqrt { 2 }\)
• C) \(\sqrt { 3 }\)
• D) \(2\)
• E)\(\frac { \sqrt { 2 } } { 2 }\)
• F) \(\frac { \sqrt { 3 } } { 2 }\)

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Definitions:

Mark-up

The upcharge on the cost of merchandise to accommodate overhead expenses and profitability.

Retail Price

The total cost at which a product is sold to the end consumer, inclusive of all taxes, shipping, and handling fees.

Operating Expenses

Costs associated with running a day-to-day business operation, such as salaries, rent, and utilities.

Mark-up

An extra charge on top of the cost price for items, aimed at covering both overhead expenses and profits, described in terms of a percentage of the initial cost.