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Let SS Be the Cube with Vertices (±1,±1,±1)( \pm 1 , \pm 1 , \pm 1 )

question 45

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Let SS be the cube with vertices (±1,±1,±1) ( \pm 1 , \pm 1 , \pm 1 ) . Approximate Sx2+2y2+7z2\iint _ { S } \sqrt { x ^ { 2 } + 2 y ^ { 2 } + 7 z ^ { 2 } } by using a Riemann sum as in Definition 1, taking the patches SijS _ { i j } to be the squares that are the faces of the cube and the points PijP _ { i j } to be the centers of the squares.

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Definitions:

Indirect Costs

Expenses not directly traceable to a specific cost object, such as a product or project, including utilities, rent, and managerial salaries.

Product Costs

Costs that are directly incurred in the production of goods, including direct materials, direct labor, and manufacturing overhead.

Direct Materials

Raw materials that are directly traceable to the production of a specific product and are a major component of its cost.

Direct Labor

Wages paid to workers directly involved in the production of goods or services, as opposed to administrative or managerial staff.

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