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Solved: In Exercises 8994, evaluate the determinant in which the entries are functions

College Algebra | 9th Edition | ISBN: 9781133963028 | Authors: Ron Larson ISBN: 9781133963028 204

Solution for problem 7.4.91 Chapter 7

College Algebra | 9th Edition

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College Algebra | 9th Edition | ISBN: 9781133963028 | Authors: Ron Larson

College Algebra | 9th Edition

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Problem 7.4.91

In Exercises 8994, evaluate the determinant in which the entries are functions. Determinants of this type occur when changes of variables are made in calculus. e2x2e2xe3x3e3

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Physical Geography Lecture 9 Overview of Weather and Climate Weather: short­term condition of the atmosphere Meteorology: study of short term atmospheric phenomena that constitude day to day weather Climate: weather over time  The day to day changes in the weather are not isolated events but are controlle by larger scale systems ­air mass interactions ­rossby waves ­tropical cyclones  Generalized statement of the prevailing weather conditions at a given place based upon statistics of a long period of records  Climate is described in terms of energy and moisture inputs ­Geographical view is that climate is a source of heat energy and water needs for plants  Climatology: studies the graphic distribution and character of Earth’s climates  Climatic regions are areas with similar weather statistics Factors Affecting Climate  Latitude (sun angle) ­Intensity of radiation and length of day have direct impact on air temperature  Seasonality ­annual variation of sun angle influences seasonal temperature changes  Land and Water Distribution ­Impacts temperature and precipitation. Land and water respond differently in temp to insolation  Ocean Currents ­Warm currents off east coasts of continents in the sub­tropical and mid latitudes ­Moderate air temperatures, adds water vapor to air and promotes precipitation ­Cool and cold currents are located off the west coasts of continents ­produce arid climates along coasts. Chills overlying air, stabilizing it, and inhibiting precipitation  Elevation and Topography ­Influence atmospheric processes and precipitation ­Temperatures decrease with elevation ­Mountains block movement of air masses ­Orographic precipitation (windward) and Rainshadow (leeward)  Pressure and Winds ­Pressure influences atmospheric stability or instability ­winds transfer sensible and latent heat from tropics to poles  Air masses and air mass movements ­different temperature and humidity characteristics ­lead to predictable weather Earth’s Temperature Patterns  Thermal Equator: Imaginary line connecting points of highest temperatures for lines of longitude  January Temperature Map: Movement of Thermal equator southward ­more pronounced over large continents Air Masses  Large bodies of air that have uniform temperature and humidity characteristics at any given elevation. ­cover 100,000s of square miles ­the boundary between two air masses is called a front. Usually the site of pronounced weather changes  Temperate and humidity characteristics are derived from source regions  Source regions are areas of the earth over which air accumulates ­large, relatively flat surfaces such as oceans and plains ­mountainous areas are not good source areas ­turbulence caused by mountains breakup air masses Classes of Air Masses  A, AA­ Arctic and Antarctic ­bitterly cold and dry  P­ Polar ­seasonal changes in temperatures ­cool to warm in summer ­cool to bitterly cold in winter  T­ Tropical ­warm to hot  C­ Continental ­Dry  M­ Maritime ­moist Teleconnections: “Links between environmental events, particularly between climatic variations, separated () North Atlantic Oscillation  Oscillation of air and ocean masses that affect a large part of Europe and wetern Asia, as well as eastern North America  Function of the relative strengths of the Icelandic Low and the Azores High  Stronger pressure gradient (high index) leads to more northerly track of intense winter storms ­most of Europe is spared sever winter storms  Weaker pressure gradient (low index) leads to fewer and weaker winter storms ­higher temperatures in summer ­colder temperatures in winter El Nino­Southern Oscillation of La Nina El Nino­ Southern Oscillation  Reversal of the “normal” pressure and wind pattern in the southern pacific ocean ­Occur on average every 5 years (range is 2 to 8 years) ­Caused drought in Indonesia and Australia ­Heavy rains and flooding to coastal South American La Nina  Event that follows El Nino event  Reasserts the “normal” pressure and wind pattern  Causes flooding in Australia Lecture 10 Polar Weather Characteristics  Weather is dominated by Arctic and Antarctic air masses ­air masses are cold and dry year round  Polar Highs generate the Polar easterlies winds during the winter ­directs cold air towards the equator to warm up ­polar easterlies generally cases blowing during the summer ­least consistent of the planetary winds  Katabatic winds ­example of a small­scale circulation caused by localized pressure and temperature differences ­occur in Polar Regions and mountains ­very cold dense air drains off the sides of glaciers, mountains and plateaus ­can be strong Polar Climates  Cold to extremely cold year around and relatively dry  Often referred to as polar deserts  Tundra climate ­at least one month where temp average above freezing but under 10º C (50ºF) ­permafrost underlies many areas ­short “summers” lead to surface thawing ­ponded and standing water on the surface  Ice cap Climate ­every month averages below freezing  Polar Marine ­more moderate in winter ­colder than tundra in summer ­low annual range of temperature ­no month below ­7ºC (20º F) Mid Latitude Weather  Most precipitation in the mid­latitudes starts as snow because many clouds form at altitudes were temperatures are below freezing ­if temperatures near the surface are below freezing it remains as snow ­If temperatures near the surface are above freezing it melsa and falls as rain  Mid­latitude weather is dominated by the interactions of large air masses of unlike characteristics  Temperature Inversion ­layer of warm air overlying cooler air at the surface ­temporary phenomena common in the mid­latitudes ­air at surface cannot rise and mix ­leads to a build­up of air pollutants at and near the surface ­serious air pollution episodes Fronts Fronts are best described as transition zones from the surface and extending up into the atmosphere. Surface of Discontinuity.  Cold Fronts: cold air masses advance against warm air masses ­cold air forces warm air aloft ­400 km wind (250 miles)  Warm Fronts: warm air masses advance against cold air masses ­warm air moves up and over cold air ­1000 km wide (600 miles)  Stationary Fronts: air masses are stalled  Occluded Fronts: cold front overtakes a warm front. ­one fronts get lifted Violent Weather of the Mid­Latitudes and Beyond  Thunderstorms: most common storm type in the world ­caused by convergent, frontal and convectional lifting ­approximately 1800 in progress at any given time  Tornadoes: smallest but most violent storms known to humanity Characteristics of Continental Climate  Located from 35 degrees to 60 degrees norther. Large areas of this climate found only in Northern Hemisphere ­except in highland areas in southern hemisphere ­no large land masses in southern hemisphere  Large annual ranges of temperature  Annual moisture surpluses ­most precipitation is due to cyclonic activity Mid­Latitude Western Continental Edge Climates  Two major climate types ­Marine (often called marine west coast) climates ­Mediterranean or dry summer subtropical climates Mediterranean Climates

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Chapter 7, Problem 7.4.91 is Solved
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Textbook: College Algebra
Edition: 9
Author: Ron Larson
ISBN: 9781133963028

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Solved: In Exercises 8994, evaluate the determinant in which the entries are functions