Find the Work Done by the Force Field $\mathbf { F }$

question 50

Short Answer

Find the work done by the force field $\mathbf { F }$ on a particle that moves along the curve $C$ .
$$\mathbf { F } ( x , y ) = ( 5 x + 5 y ) \mathbf { i } + 5 x y \mathbf { j } ; \quad C : \mathbf { r } ( t ) = 2 t ^ { 2 } \mathbf { i } + t ^ { 2 } \mathbf { j } , 0 \leq t \leq 1$$

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Definitions:

Age Structure

The distribution of individuals among various age groups in a population, affecting the population's growth and sustainability.

Reproductive Class

A category or grouping within a species based on reproductive roles or capabilities, such as gender or capability to reproduce.

Pre-Reproductive

Individuals in a population who have not yet reached the age where they are capable of producing offspring, contributing to the population's growth potential.

Demographic Transition

Due to industrialization, a decline in the birthrate following a reduction in the death rate so that the population growth rate is lowered.