Find the Work Done by the Force Field $\mathbf { F } ( x , y ) = x \sin ( y ) \mathbf { i } + y \mathbf { j }$

question 54

Multiple Choice

Find the work done by the force field $\mathbf { F } ( x , y ) = x \sin ( y ) \mathbf { i } + y \mathbf { j }$ on a particle that moves along the parabola $y = x ^ { 2 }$ from $( 1,1 )$ to $( 2,4 )$ .

• A) \(\frac { ( 15 + \sin ( 1 ) - \cos ( 4 ) ) } { 2 }\)
• B) \(\frac { ( 17 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }\)
• C) \(\frac { ( 15 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }\)
• D) \(\frac { ( 15 + \sin ( 1 ) - \sin ( 4 ) ) } { 2 }\)
• E) \(\frac { ( 17 - \cos ( 1 ) + \cos ( 4 ) ) } { 2 }\)

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Definitions:

Daily Demand Rate

The average quantity of a product or service that is requested by customers over the course of a single day.

Production Rate

The speed at which goods are manufactured or produced within a given time period.

Average Inventory

The mean value of inventory held over a certain period of time, indicating the level of stock being maintained.

Single-Period Model

is a decision-making tool used in inventory management, assuming demand is uncertain and there is only one opportunity to order stock for a particular period.