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

question 261

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $\mathbf { F } = 6 x \mathbf { i } - 6 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 4 } \mathbf { j } + \left( - 3 \mathrm { z } - 7 \mathrm { y } ^ { 2 } \right) \mathbf { k }$ ; the path is $\mathrm { C } _ { 1 } \cup \mathrm { C } _ { 2 } \cup \mathrm { C } _ { 3 }$ where $\mathrm { C } _ { 1 }$ is the straight line from $( 0,0,0 )$ to $( 1,0,0 ) , \mathrm { C } _ { 2 }$ is the straight line from $( 1,0,0 )$ to $( 1,1,0 )$ , and $C _ { 3 }$ is the straight line from $( 1,1,0 )$ to $( 1,1,1 )$

• A) \(W = - \frac { 67 } { 10 }\)
• B) \(W = \frac { 9 } { 5 }\)
• C) \(W = - \frac { 57 } { 10 }\)
• D) \(W = 3\)

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Mass Marketing

A marketing strategy that targets a large audience with a general message, aiming to reach as many people as possible through broad communication channels.

Commodity Goods

Basic goods used in commerce that are interchangeable with other goods of the same type, often used in economic analysis and trading.

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The process of identifying and communicating with specific segments of the market that are considered more likely to buy a particular product or service.

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A manufacturing method that produces large quantities of standardized products, often on assembly lines, enabling economies of scale and cost reduction.