Let ${ \vec { F } } = - 2 x z \vec { i } + 5 ( y - x ) \vec { j } + 5 x \vec { k }$

question 82

Essay

Let ${ \vec { F } } = - 2 x z \vec { i } + 5 ( y - x ) \vec { j } + 5 x \vec { k }$ (a)Use Stokes' Theorem to find the circulation of $\vec { F}$ around the circle of radius a, $\vec { r } ( t ) = a \cos t \vec { i } + \alpha \sin t \vec { j }$ for 0 $\le$ t $\le$ 2 $\pi$ .
(b)Use this result to find the $\vec { k }$ component of $\operatorname { curl } \vec { F } ( 0,0,0 )$

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Definitions:

Periodic Inventory System

An inventory system in which ending inventory and cost of goods sold are determined at the end of the accounting period based on a physical inventory count.

Physical Inventory

Physical inventory refers to the process of counting and verifying the physical stock of goods a company holds in its possession.

Net Income

The net income of a business following the deduction of all costs, such as operational expenses and taxes, from its overall revenue.

Ending Inventory

The total value of a company’s inventory at the end of an accounting period, calculated before the new fiscal period begins.