Let S Be the Closed Surface Which Is the Portion $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$

question 62

Multiple Choice

Let S be the closed surface which is the portion of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ with $- 2 \leq \boldsymbol { z } \leq 1$ topped by the disk in the plane $\bar { z } = 1$ , oriented outward.Then the flux of $\vec { r } = x \vec { i } + y \vec { j } + z \vec { k }$ through S is:

• A) \(9 \pi\)
• B) \(24 \pi\)
• C) \(27 \pi\)
• D) \(18 \pi\)
• E) \(36 \pi\)

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Definitions:

Inferior Goods

For inferior goods, demand decreases as income increases.

Demand for Potatoes

The consumers' desire and willingness to purchase potatoes at a given price.

Decrease in Income

A reduction in the amount of money received, typically referring to wages, salaries, or investment returns.

MR

Marginal Revenue, which is the additional income derived from selling one more unit of a good or service.