A Activity diagram used in UML 6/9 and SysML B Bachman diagram Booch used in software engineering Block diagram Block Definition Diagram BDD used in SysML C Carroll diagram Cartogram Catalytic cycle Chemical equation Curly arrow diagram Category theory diagrams Cause-and-effect diagram Chord diagram Circuit diagram Class diagram from UML 1/9 Collaboration diagram from UML 2.0 Communication diagram from UML 2.0 Commutative diagram Comparison diagram Component diagram from UML 3/9 Composite structure diagram from UML 2.0 Concept map Constellation diagram Context diagram Control flow diagram Contour diagram Cordier diagram Cross functional flowchart D Data model diagram Data flow diagram Data structure diagram Dendrogram Dependency diagram Deployment diagram from UML 9/9 Dot and cross diagram Double bubble map used in education Drakon-chart E Entity-Relationship diagram ERD Event-driven process chain Euler diagram Eye diagram a diagram of a received telecommunications signal Express-G Extended Functional Flow Block Diagram EFFBD F Family tree Feynman diagram Flow chart Flow process chart Flow diagram Fusion diagram Free body diagram G Gantt chart shows the timing of tasks or activities used in project management Grotrian diagram Goodman diagram shows the fatigue data example: for a wind turbine blades H Hasse diagram HIPO diagram I Internal Block Diagram IBD used in SysML IDEF0 IDEF1 entity relations Interaction overview diagram from UML Ishikawa diagram J Jackson diagram K Karnaugh map Kinematic diagram L Ladder diagram Line of balance Link grammar diagram M Martin ERD Message Sequence Chart Mind map used for learning, brainstorming, memory, visual thinking and problem solving Minkowski spacetime diagram Molecular orbital diagram N N2 Nassi Shneiderman diagram or structogram a representation for structured programming Nomogram Network diagram O Object diagram from UML 2/9 Organigram Onion diagram also known as "stacked Venn diagram" P Package diagram from UML 4/9 and SysML Parametric diagram from SysML PERT Petri net shows the structure of a distributed system as a directed bipartite graph with annotations Phylogenetic tree - represents a phylogeny evolutionary relationships among groups of organisms Piping and instrumentation diagram P&ID Phase diagram used to present solid/liquid/gas information Plant Diagram Pressure volume diagram used to analyse engines Pourbaix diagram Process flow diagram or PFD used in chemical engineering Program structure diagram R Radar chart Radial Diagram Requirement Diagram Used in SysML Rich Picture R-diagram Routing diagram S Sankey diagram represents material, energy or cost flows with quantity proportional arrows in a process network. Sentence diagram represents the grammatical structure of a natural language sentence. Sequence diagram from UML 8/9 and SysML SDL/GR diagram Specification and Description Language. SDL is a formal language used in computer science. Smith chart Spider chart Spray diagram SSADM Structured Systems Analysis and Design Methodology used in software engineering Star chart/Celestial sphere State diagram are used for state machines in software engineering from UML 7/9 Swim lane Syntax diagram used in software engineering to represent a context-free grammar Systems Biology Graphical Notation a graphical notation used in diagrams of biochemical and cellular processes studied in Systems biology System context diagram System structure Systematic layout planning T Timing Diagram: Digital Timing Diagram Timing Diagram: UML 2.0 TQM Diagram Treemap U UML diagram Unified Modeling Language used in software engineering Use case diagram from UML 5/9 and SysML V Value Stream Mapping Venn diagram Voronoi diagram W Warnier-Orr Williot diagram Y Yourdon-Coad see Edward Yourdon, used in software engineering
e for some x, namely, for x = g2i 1; 0 i 2011. Since f(x) x is positive for x of large absolute value, the graph of f(x) x crosses the x axis wice and f(x) x has two real roots, say a < b. Factoring gives f(x) x = (x a)(x b), or f(x) = (x a)(x b) x. Now, for x < , f(x) > x > a, while for x > b, f(x) > x > b. Let
4th Annual Harvard MIT November Tournament Saturday 12 November 2011
4th Annual Harvard MIT November Tournament Saturday 12 November 2011 General Test 1. [3] Find all ordered pairs of real numbers (x, y) such that x2y = 3 and x xy = 4. 2. [3] Let ABC be a triangle, and let D, E, and F be the midpoints of sides BC, CA, and AB, respectively. Let the angle bisectors of ∠FDE and ∠FBD meet at P.
ee Z 1 ln 2011 x 10. Evaluate dx. 1 x 1. Mike and Harry play a game on an 8 8 board. For some positive integer k, Mike cho ses k squares and writes an M in each of them. Harry then chooses k 1 squares and writes an H in each of them. After Harry is done, Mike wins if there is a sequence of letters forming \HMM" or \MMH;" when read either horizo
4th Annual Harvard MIT November Tournament Saturday 12 November 2011 Guts Round [5] Determine the remainder when 1 2 2014 is divided by 2012.
8. [6] Find the smallest k such that for any arrangement of 3000 checkers in a 2011 2011 checkerboard, with at most one checker in each square, there exist k rows and k columns for which every checker is contained in at least one of these rows or columns.
4THANNUAL HARVARD MIT NOVEMBER TOURNAMENT, 12 NOVEMBER 2011 | GUTS ROU ND Round 9 The answers to the following three problems are mutually dep endent, although your answer to each will be graded independently. Let A be the answer to problem 25, B the answer to problem 26, and C be the answer to problem 27. 25.
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