Use the Given Transformation to Evaluate the Integral $$\begin{array} { l } x = 5 u , y = 8 v , z = 9 w \\\quad \int _ { R } \iint x ^ { 2 } y ^ { 2 } z ^ { 2 } d x d y d z\end{array}$$

question 200

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } x = 5 u , y = 8 v , z = 9 w \\\quad \int _ { R } \iint x ^ { 2 } y ^ { 2 } z ^ { 2 } d x d y d z\end{array}$$
where $R$ is the interior of the ellipsoid $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } + \frac { z ^ { 2 } } { 81 } = 1$

• A) \(\frac { 48 } { 7 } \pi\)
• B) \(\frac { 96 } { 7 } \pi\)
• C) \(\frac { 32 } { 21 } \pi\)
• D) \(\frac { 16 } { 21 } \pi\)

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Definitions:

Cost of Goods Manufactured

The total cost incurred by a company to produce goods in a specific period, including materials, labor, and overhead.

Direct Materials Costs

The cost of raw materials that can be directly traced to the production of a specific product.

Direct Labor Costs

Expenses associated with the wages of employees who are directly involved in the production of goods or services.

Manufacturing Overhead

All indirect costs associated with the manufacturing process, including but not limited to utilities, depreciation, and salaries of supervisory staff.