Test the Vector Field F to Determine If It Is

question 188

Multiple Choice

Test the vector field F to determine if it is conservative.
- $$\mathbf { F } = \left( \frac { 9 x ^ { 8 } \left( y - x ^ { 2 } \right) ^ { 9 } } { z } \right) i + \left( \frac { 5 x ^ { 9 } \left( y - x ^ { 2 } \right) ^ { 8 } } { z } \right) j - \left( \frac { x ^ { 9 } \left( y - x ^ { 2 } \right) ^ { 5 } } { z ^ { 2 } } \right) \mathbf { k }$$

• A) Conservative
• B) Not conservative

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Definitions:

National Income

The total amount of money earned within a country, including wages, profits, rentals, and pension income.

Nominal GDP

The gross domestic product measured in current prices, without adjusting for inflation.

Intermediate Goods

Products used as inputs in the production of other goods or services, such as raw materials or components, which are not finished goods sold to end consumers.

Deflation

A drop in the overall pricing of goods and services, typically signaling a shrinkage in the money or credit available in the economy.