A Particle Starts at the Point $( - 3,0 )$ , Moves Along the X-Axis to (3, 0) and Then

question 33

Multiple Choice

A particle starts at the point $( - 3,0 )$ , moves along the x-axis to (3, 0) and then along the semicircle $y = \sqrt { 9 - x ^ { 2 } }$ to the starting point. Use Green's Theorem to find the work done on this particle by the force field $\mathbf { F } ( x , y ) = \left\langle 24 x , 8 x ^ { 3 } + 24 x y ^ { 2 } \right\rangle$

• A) \(486\)
• B) \(48 \pi\)
• C) 0
• D) \(486 \pi\)
• E) \(972 \pi\)

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Definitions:

Direct Labor Efficiency Variance

The difference between the budgeted amount of direct labor required to produce an output and the actual direct labor used.

Favorable

A term used in budgeting and finance to indicate results that are better than expected, such as lower costs or higher revenues.

Unfavorable

A term used to describe outcomes or variances that negatively impact financial performance or expectations.

Unfavorable Variances

Occurrences when actual costs exceed budgeted or expected costs, indicating a potential need for management action to address inefficiencies.