A) $\frac { d w } { d t } = 8 t ^ { 8 } - \sqrt { 1 - t ^ { 2 } }$

question 50

Multiple Choice

$\text { Let } w = x y \cos z \text {, where } x = t ^ { 3 } , y = t ^ { 5 } \text {, and } z = \arccos t \text {. Find } \frac { d w } { d t } \text {. }$

• A) \(\frac { d w } { d t } = 8 t ^ { 8 } - \sqrt { 1 - t ^ { 2 } }\)
• B) \(\frac { d w } { d t } = 8 t ^ { 8 } + \sqrt { 1 - t ^ { 2 } }\)
• C) \(\frac { d w } { d t } = t ^ { 8 } \left( 8 + \sqrt { 1 - t ^ { 2 } } \right)\)
• D) \(\frac { d w } { d t } = 9 t ^ { 8 }\)
• E) \(\frac { d w } { d t } = t ^ { 8 } \left( 8 - \sqrt { 1 - t ^ { 2 } } \right)\)

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Definitions:

Segment Margin

The amount of profit or loss generated by one part of a business, after accounting for the direct and indirect costs of that segment.

Financial Advantage

The benefit gained in financial terms, which could be through savings, profits, or reduced costs.

Outside Supplier

An outside supplier is an external entity that provides goods or services to a company, not tied by corporate affiliation.

Unit Product Cost

The total cost to produce one unit of a product, including direct materials, direct labor, and overhead.