Solve the Problem $\mathbf { F }$ Of a Fluid Has a Constant Magnitude

question 204

Essay

Solve the problem.
-The velocity field $\mathbf { F }$ of a fluid has a constant magnitude $\mathrm { k }$ and always points towards the origin. Following the smooth curve $y = f ( x )$ from $( a , f ( a ) )$ to $( b , f ( b ) )$ , show that the flow along the curve is
$$\int _ { C } \mathbf { F } \cdot \mathbf { T } d s = k \left[ \left( a ^ { 2 } + ( f ( a ) ) ^ { 2 } \right) ^ { 1 / 2 } - \left( b ^ { 2 } + ( f ( b ) ) ^ { 2 } \right) ^ { 1 / 2 } \right]$$

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Definitions:

Unemployment Rate

The fraction of job-seekers within the labor force who do not have a job.

Exogenous

Factors or influences arising outside of a system that affect a model or process, without being affected in turn by that system.

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A sudden event that increases or decreases demand for goods or services in an economy, often leading to changes in prices and output.

Expansion Phase

A period in the business cycle when the economy moves from a trough to a peak, characterized by an increase in economic activity, production, and employment.