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:

Amortized Amount

The portion of a loan or intangible asset's cost that has been allocated as an expense over a specific period.

Fair Value

The estimated market value of an asset or liability, based upon current conditions and mutually informed and willing parties.

Long-Term Investments

Assets that a company intends to hold for more than one year, such as stocks, bonds, or real estate.

Unrealized Gain

An unrealized gain is an increase in the value of an investment or asset that has not been sold, and consequently, the profit has not yet been taken or considered as income.