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

question 244

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $$\mathbf { F } = \frac { \mathrm { y } } { \mathrm { z } } \mathbf { i } + \frac { \mathrm { x } } { \mathrm { z } } \mathbf { j } + \frac { \mathrm { x } } { \mathrm { y } } \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \mathrm { t } ^ { 7 } \mathbf { i } + \mathrm { t } ^ { 5 } \mathbf { j } + \mathrm { t } ^ { 2 } \mathbf { k } , 0 \leq \mathrm { t } \leq 1$$

• A) \(W = \frac { 17 } { 10 }\)
• B) \(W = 14\)
• C) \(W = 0\)
• D) \(W = 1\)

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Definitions:

Industrial Revolution

A period of major industrialization that took place during the late 1700s and early 1800s, leading to significant advancements in technology, manufacturing, and transportation.

Information Age

The current era characterized by the rapid creation, sharing, and manipulation of information, largely facilitated by digital technology.

Development of Computers

The historical and ongoing advancement of computer technology, from early mechanical calculators to modern digital computers.

Productivity Growth

Productivity growth refers to an increase in the efficiency of production or output per unit of input, typically measured over time and considered crucial for economic development.