Find the Work Done by F Over the Curve in the Direction

question 77

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $$\mathbf { F } = x y \mathbf { i } + 3 \mathbf { j } + 8 x \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \cos 7 \mathrm { ti } + \sin 7 \mathrm { tj } + \mathrm { t } \mathbf { k } , 0 \leq \mathrm { t } \leq \frac { \pi } { 14 }$$

• A) \(W = \frac { 86 } { 21 }\)
• B) \(W = \frac { 94 } { 21 }\)
• C) \(W = 0\)
• D) \(W = \frac { 80 } { 21 }\)

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Definitions:

Customer Profitability Analysis

The process of determining the profit or loss attributed to a particular customer, identifying which relationships are most beneficial.

Product Contribution Analysis

A financial evaluation technique that assesses how individual products contribute to the overall profit of a company based on their contribution margins.

Break-Even Time

The period it takes for a business or project to generate enough revenue to cover all its costs and start producing a profit.

Product Development Cycle

The series of stages a product goes through from conception and development to market launch and beyond.