Find the Flux of the Curl of Field F Through

question 112

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $$\mathbf { F } = ( 4 \mathrm { y } + 2 ) \mathbf { i } - 5 \mathrm { xj } + \left( \mathrm { e } ^ { \mathrm { z } } - 1 \right) \mathbf { k } ; \mathrm { S } : \mathbf { r } ( \mathrm { r } , \theta ) = 2 \sin \varphi \cos \theta \mathbf { i } + 2 \sin \varphi \sin \theta \mathbf { j } + 2 \cos \varphi \mathbf { k } , 0 \leq \theta \leq 2 \pi \text { and } 0 \leq \varphi \leq \frac { \pi } { 2 }$$

• A) 72
• B) \(- 72 \pi\)
• C) \(- 36 \pi\)
• D) \(36 \pi\)

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Definitions:

Direct Labor-hours

The total hours of labor directly involved in the manufacturing process of a product.

Labor Rate Variance

It is the difference between the actual cost of labor and the budgeted or expected cost of labor.

Standard Cost System

A standard cost system is a method of cost accounting that uses estimated costs for materials, labor, and overheads to compare against actual costs incurred, facilitating variance analysis and budgeting.

Actual Results

The real outcomes or data achieved at the end of a specified period, measured against planned or forecasted figures.