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Use a Computer Algebra System to Compute the Flux of F

question 44

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Use a computer algebra system to compute the flux of F across S. S is the surface of the cube cut from the first octant by the planes x=π2,y=π2,z=π2x = \frac { \pi } { 2 } , y = \frac { \pi } { 2 } , z = \frac { \pi } { 2 } F(x,y,z) =3sinxcos2yi+3sin3zcos4zj+3sin5zcos6xk\mathbf { F } ( x , y , z ) = 3 \sin x \cos ^ { 2 } y \mathbf { i } + 3 \sin ^ { 3 } z \cos ^ { 4 } z \mathbf { j } + 3 \sin ^ { 5 } z \cos ^ { 6 } x \mathbf { k }


Definitions:

Common Fixed Expenses

Expenses that do not change in total amount with changes in the volume of production or sales, such as rent, salaries, and insurance.

Net Operating Income

The total profit of a company after operating expenses are subtracted from total revenue, but before deducting interest and taxes.

Total Period Cost

The sum of all expenses associated with operating a business during a specific accounting period.

Absorption Costing

An accounting method that includes all manufacturing costs (direct and indirect) in the cost of a product.

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