Math 32B‚ Lecture 2 Fall 2010 Practice Problems for Final (sections 17.6-17.9 1. (0 points) (a) Let C be a simple closed piecewise-smooth space curve which lies entirely in a plane‚ and suppose that the plane has upward-pointing unit normal vector given by n = ai + bj + ck. Show that the area of the portion of the plane enclosed by C is 1 2 C (bz − cy) dx + (cx − az) dy + (ay − bx) dz. (b) Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2‚ oriented counter-clockwise
Premium Mathematics Elementary algebra Analytic geometry
Mediterranean basin. After 1200 they began to have an impact on southern Europe. These progressions included the discovery of bullion sources‚ the emergence of a new mathematics‚ the pioneering of trade routes‚ the trade in tropical spices‚ the cultivation of southern crops such as sugar and cotton‚ and the invention of various technologies. Indians also invented the concept of zero‚ which the Arabs eventually conveyed to the Europeans. What the West called Arabic numerals‚ the Arabs called Hindi numerals
Premium Indian Ocean India Southeast Asia
Pertinent Questions Part I 1 & 2. Education was “central to the Republican vision of America” because‚ Jefferson called benignly for a national “crusade against ignorance.” The Republicans believed in the creation of a nationwide system of public schools to create the educated electorate they believed a republic required. Some states endorsed public education for all in the early years of the republic‚ but none actually created a working system of free schools. The republicans argued that
Premium
expand where as Japan didnt. 2.What internal and external pressures did Japan face during its period of reunification? How did Japan deal with these challenges? Toyotomi Hideyoshi dreamed of ruling Korea‚ China‚ and even India with his power base in Japan. His attacks on Korea eventually stalled and he died before he could fulfill his dreams. but his actions sparked the unification of Japan‚ for the first time in history‚ a step that would be crucial in the country’s rise to world power 3 centuries
Premium Japan Tokugawa Ieyasu Samurai
important question. This question is: “why did God‚ and for what reason did God‚ become man?” Anselm addresses this question because the people want to find delight in the understanding and contemplation of what they already believe‚ and also to be “ready always to satisfy everyone that asks them a reason of what hope which is in us” (Book 1). Nonbelievers who deride Christian simplicity as absurd also throw out this question. Anselm also says that it is not only the learned who want the question about
Premium Human Religion Meaning of life
Some form of slavery existed in Africa before Europeans arrived; however it was a system of temporary consequences. People were enslaved as punishment for a crime‚ to pay a debt‚ or as captives of war. African slavery was very different from what was to come later with the Europeans because it was not for personal gain and inhumane suffering of others. Unlike European slavery‚ African slaves could work to buy their freedom and their children were not automatically slaves. Captive Africans and their
Premium Slavery Atlantic slave trade Slavery in the United States
The European colonized Africa for numerous reasons such as the medical advancement for malaria which was devastating the European population. During the industrial revolution‚ the Europeans perfected the gun which gave them an advantage over Africa. The European-built an empire in Africa by converting them to Christianity and introducing two types of government‚ direct rule‚ and indirect rule. They established missionaries that change the culture and religion which resulted in modern schools and
Premium Africa Colonialism Europe
grocery retail market between Western European and Hong Kong‚ focusing on the customer behaviour and influences in the grocery retail store formats. This is an attempt to see how logistics operations to fulfill in structure and control in the grocery market‚ thereby‚ to enhance the efficient and effective operations and inventory availability. Finally‚ the recommendation of entry into the Hong Kong grocery retail market. 2. The differences between Western European and Hong Kong consumer behaviour
Premium Supermarket Retailing Grocery store
Marxism By:Hasan Armour L.I.T.3 The play of Macbeth aspects plays a major influence on the topic of Marxism. Marxism acknowledges the numerous amount of power or authority oneself has. To point out the relation marxism has on the people within the play we all would first start by stating who had the most authority‚ and how it was use. Having the power to be in one’s hand changes the way one another act towards each other. To fully introduce marxism amongst the people in the story you would say the
Premium Macbeth Macbeth Duncan I of Scotland
AP World History Midterm Review History The study of past events and changes in the development‚ transmission‚ and transformation of cultural practices. Earliest Farming Location Fertile crescent Swidden Agriculture a place temporarily cleared for agriculture by cutting back and burning off previous growth Catal Huyuk early urban culture based on sedentary agriculture Mesopotamia "between the rivers"; civilizations that arose between the Tigris-Euphrates river valleys Hyksos a member of an ancient
Premium Ancient Greece Zhou Dynasty China