(A)Is $\vec { F } = F _ { 1 } ( y , z ) \vec { i } + F _ { 2 } ( x , z ) \vec { j } + F _ { 3 } ( x , y ) \vec { k }$

question 72

Short Answer

(a)Is $\vec { F } = F _ { 1 } ( y , z ) \vec { i } + F _ { 2 } ( x , z ) \vec { j } + F _ { 3 } ( x , y ) \vec { k }$ a divergence free vector field?
(b)Do all divergence free vector fields have the form of the vector field in (a)?
(c)If $\vec { F }$ has the form given in (a)can we conclude that $\int _ { S } \vec { F } \cdot \vec { d A } = 0$ for any closed surface S?

Describe the physiological adaptations to environmental temperature changes.

Explain the biological significance of brown fat in thermogenesis.

Understand the concept of basal metabolic rate and its importance in endothermy and ectothermy.

Identify the adaptive strategies animals use to cope with temperature extremes, including hibernation and hypothermia.

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Definitions:

Demand

The measure of a commodity or service consumers intend and are able to acquire at multiple price levels during a set time span.

Economic Profits

Profits exceeding the opportunity costs of all resources employed, including both explicit and implicit costs, signifying above-normal returns.

Long Run

An economic term referring to a period in which all factors of production and costs are variable, allowing for full adjustment to changes in the market.

Price-taking

A market condition in which individual buyers or sellers have no influence over the market price of a product, commonly seen in perfectly competitive markets.