Use the Given Transformation to Evaluate the Integral $$\begin{aligned}u = & 2 x + y - z , v = - x + y + z , w = - x + y + 2 z \\& \iiint ( 2 x + y - z ) ( z - x + y ) d x d y d z\end{aligned}$$

question 48

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{aligned}u = & 2 x + y - z , v = - x + y + z , w = - x + y + 2 z \\& \iiint ( 2 x + y - z ) ( z - x + y ) d x d y d z\end{aligned}$$
where $R$ is the parallelepiped bounded by the planes $2 x + y - z = 2,2 x + y - z = 6 , - x + y + z = 3 , - x + y + z = 4$ , $- x + y + 2 z = 6 , - x + y + 2 z = 8$

• A) \(\frac { 224 } { 3 }\)
• B) \(\frac { 112 } { 3 }\)
• C) 336
• D) 672

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Definitions:

Ability to Meet Obligations

A financial assessment of whether a company or individual has the resources necessary to pay off their debts as they come due.

Return on Assets

A profitability ratio that measures how efficiently a company is using its assets to generate earnings.

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In cash flow reporting, a method that shows the specific sources and uses of cash, categorizing cash flows into operating, investing, and financing activities.

Net Cash Provided

The amount of cash generated by a company’s operations after accounting for all cash inflows and outflows.