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Matching surfaces Match functions ad with surfaces AD. a.

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 27 Chapter 12

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 27

Matching surfaces Match functions ad with surfaces AD. a. z = 22x2 + 3y2 + 1 - 1 b. z = -3y2 c. z = 2x2 - 3y2 + 1 d. z = 22x2 + 3y2 1

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ANTH 1003 Dr. Susan Johnston Class Notes for April 13-15 Why complex societies (April 13)  Childe’s managerial model: people in large groups need someone to manage them and effectively run society  Resource concentration: control of particular resources allows some people to exert control over others (irrigation) (Karl Wittfogel)  Ideology: a few people manipulated ideology to convince those at the bottom that elites should run things (Tim Pauketat)  Warfare: people in circumscribed environments competed for resources and formed ever-larger polities (Robert Carniero) o People have control of resources but have nowhere else to go) Egypt and Mesopotamia  Sumerian culture in southern Mesopotamia (4000 – 2350 BCE, ended when Sargon united Mesopotamia)  Egyptian culture (3100 – 1070 BCE); from when they were united into one society to when Egypt stops existing as an independent entity Mesopotamia Egypt Concentration of population Uruk, Iraq Most Egyptian cities may be (cities)  Maybe 40,000 people at its hidden under modern cities height  Within floodplain region, no Amarna real necessity for irrigation  Maybe 20,000 people at its height  Akhenaten’s city when he began to worship the new god Aten  Inhabited only during Akhenaten’s reign; Tut moved back to Thebes  Other cities were probably larger Full-time specialists Pottery, metalworking, writing, Pottery, metalworking, writing, rulers rulers King List: list of titles and Lots of gold/metal grave goods professions from 3000 BCE in tombs  Writing indicates a specialist activity, most people couldn’t do it Elites  Monumental art and  Monumental art and architecture architecture  Different residential house  Different residential house sizes and presence of sizes and presence of palaces palaces  Expensive or rare and large  Expensive or rare and large quantities of grave goods, quantities of grave goods, especially burials of children especially burials of children  Weld-Blundel Prism (1763 –  Abydos king list (1309 – 1753 BCE) 1291 BCE), Karnak king list  Grave goods at Ur and (1490 – 1436 BCE); king’s sacrificial victims names always written in o Elite burials are either cartouches not found or relatively  King Tut’s tomb and all the uncommon in stuff in it: staggering Mesopotamia amounts of wealth o Plan of “great death especially since he was a pit”; sacrificial victims in relatively meaningless kid some but not all burials suggests importance of individuals that were buried with them State organization  Best evidence in writing  Best evidence in writing  Secular leader, but clear  Secular leader, but clear overlaps of religion overlaps of religion  Entities are organized  United under a single ruler around a city (city-state) after 3100 BCE but mostly controlled by kings priesthood was similarly but also by a priesthood; influential (kinds had divine not unified nature or connections)  Temples were owed labor, taxes, etc. Monumentality, especially  Structures mostly if not only  Structures mostly if not only representative of or for benefitted rulers and priests benefitted rulers and priests political/religions persons  Ziggurat  Pyramids for a simple  Temples elevated above the important individual landscape (usually kings) Trade that is centrally  Resources that are not  Resources that are not controlled where they are found, where they are found, agreed-upon values for agreed-upon values for objects, written records or objects, written records or artistic representations artistic representations  3 major trade partners  Traded with Minoan and named in written records, Aegean cultures one many have been Indus  Artistic depictions of people Valley bringing in imported items from faraway places (pottery that looks like it’s from the Aegean and Crete) Writing  Cuneiform from c. 3100 BCE  Hieroglyphs from c. 3100 BCE  Used to represent a number of different languages such  Original pictorial as Sumerian and Akkadian hieroglyphs used for  Context for emergence of monuments and writing varied from place to ceremonies while day-to- place: solved difference day use adopted hieratic problems hieroglyphs (kind of like o Primary context in cursive, easier to use) Mesopotamia was  Earliest writing from Abydos economic, keeping track c. 3300 BCE, resemble tags of economic and may have been used as interactions between labels that indicate places people of many (identification) or some languages (especially on pottery) may represent personal names o May have emerged from need for rulers to identify themselves in ceremonial displays or things in tombs; identification Conflict  Weapons, defensive  Weapons, defensive structures, violent deaths in structures, violent deaths in large numbers, large numbers, documentary sources and documentary sources and depictions depictions  Documentary sources of  Histories told by Egyptians battles and conquest show their culture as having  Naram-Sin Stela shows been born out of conflict or conquest, depictions of chaos; “mn” took charge soldiers, weaponry and instilled order  Narmer palette: clear record of conquest (Narmer shown smiting people, standing beside a bunch of headless bodies, also depicted wearing both crowns of Upper and Lower Egypt)  Depictions of soldiers and weapons Indus Valley (April 15)  Indus cities: Harappa (20,000 – 25,000 people) and Mohenjo-Daro (30,000 – 40,000 people) o Both include a “citadel” at one end with residence area down below and a substantial wall surrounds them  Specialists: o Pottery is made in certain areas and distributed from that area o Evidence for maritime travel o Metal (raw materials are not widely available and skill to make metal objects requires more input/knowledge)  Monumentality o Structures exist that may require similar amounts of work to build, but they are different from monuments in the sense of Egypt or Mesopotamia o “Granary” from Harappa; very big building o Great Bath at Mohenjo-Daro (fed by a well, drains down the middle, and lined with bitumen) o Function of these structures is questionable; involved in ritual or symbol of power Ritual purification o City walls (45 feet high at Harappa) o Large structures require large numbers of people to construct them o No obvious connection of these structures to a specific individual or small group of people  Trade o With Mesopotamia: copper and grain o Possible standardized set of weights and measures o Lothal: metal manufacturing, feature lined with bitumen that may have been a dry dock, objects manufactured here appear elsewhere  Conflict o Evidence of weapons o Harappan cemeteries: study of 160 individuals  3 with postcranial trauma  9 out of 58 had blunt force trauma wounds of cranium o No real evidence for armies except for the existence of weapons  Writing o Begins c. 2600 o Might be writing; most of it is on seals (but not much evidence that those seals were actually used) o Images of animals or people accompanied by what might be symbols o Problems:  3000 symbols  87% from Harappa and Mohenjo-Daro (may be because they’ve been excavated the most, or a cultural reason)  113 symbols used only once, 47 used twice, and 59 less than 5 times o Clearly a symbolic system but may have a different form of interpretation or meaning o Not ever translated; we don’t know what it says --> no documentary evidence from this culture  Elites o No monuments with specific dedication or obscenely wealthy burials o Arguably elite goods; bangles found everywhere vs. gold and agate ornaments that are rare o Subtle but not major differences in residences (no palaces) o Cemetery is extremely tiny for such a large city and individuals buried tend to be healthy/well-nourished --> being buried by itself may have been a status thing even without elaborate grave goods o Elite status expression was very different; may not have been preserved archaeologically  High status positions o Figurine from Mohenjo-Daro: having one shoulder bare is in more modern times associated with status, does it translate to back then too o Copper and silver “crown” from burials o Again, differences in how status is expressed and experienced materially from other known complex societies (Egypt and Mesopotamia)  Harappan standardization o Weights, writing… Indicates some kind of centralization o Does this indicate a state 2 states City-states No one knows…  Rose and fell relatively quickly; 1000 – 1500 years total o May have become more complex because of contact with Mesopotamia and then declined when trade routes changed and Mesopotamia began trading more with other areas; change of trade routes may also have been the result of decline of Indus Valley o Possibly also has to do with drought in the region Iron Age Temperate Europe (700 – 150 BCE)  Associated with the Celts o Term comes from documentary sources that were written by Greeks and Romans o Used inconsistently (in different ways) o As a name for a group of people, it was most consistently used for central France, parts of Spain, some others  Never used for Britain or Ireland  Most aspects of material culture vary a lot; similarities most likely have to do with trade more than cultural identification  Cities Depends on how you define city: size versus function o There are large sites with concentrations of people in them, but not nearly as big as other ancient cities o Called hillforts or oppida (Latin for “big-ass sites that aren’t cities and aren’t towns”) o Range from 500 to maybe 20,000 people but usually 5,000 to 10,000 o Smaller population than Egyptian or Mesopotamian cities o BUT they are functionally cities; largest population concentration in the area, surrounded by smaller villages o Manching, Germany (3 to 1 century BCE)  Up to 10,000 people  Dense habitation and specialized areas within the site for iron, pottery, and glass manufacturing  Some evidence for coinage (blanks and molds) o Bibracte, France  Trade evidence, metal objects, and specialized areas for craftswork  5,000 – 20,000 people (high-end size)  Specialization: lots o Metal, glass objects, pottery, “artisan quarters” o Coinage was probably not used for transactions; more of a status thing (like a $10,000 bill)

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Chapter 12, Problem 27 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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Matching surfaces Match functions ad with surfaces AD. a.