their intent. The unit “Do Bees Build It Best?” helped me realize and confirm the previous. I studied geometry for the past two months- believe me; I know what I’m doing. To be able to make that statement‚ I studied the area and perimeter of all polygons‚ trigonometry‚ inverse trigonometry‚ and volume of surface area of three dimensional shapes. I did all of that just to find an answer. And bees really do build it best. [pic] Tessellation Tessellation is everywhere in our
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SOUTH AFRICAN MATHEMATICS OLYMPIAD Organised by the SOUTH AFRICAN MATHEMATICS FOUNDATION 2012 FIRST ROUND SENIOR SECTION: GRADES 10‚ 11 AND 12 19 March 2012 Time: 60 minutes Number of questions: 20 Instructions 1. This is a multiple choice question paper. Each question is followed by answers marked A‚ B‚ C‚ D and E. Only one of these is correct. 2. Scoring rules: 2.1. Each correct answer is worth 5 marks. 2.2. There is no penalty for an incorrect answer or any unanswered question. 3. You
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Regular Expressions This ppt is the work by Dr. Costas Busch‚ used with permission‚ and available from http://csc.lsu.edu/~busch/courses/theorycomp/fall2008/ 1 Regular Expressions Regular expressions describe regular languages Example: (a b c) * describes the language a‚ bc * ‚ a‚ bc‚ aa‚ abc‚ bca‚... 2 Recursive Definition Primitive regular expressions: ‚ ‚ Given regular expressionsr1 r2 and r1 r2 r1 r2 r1 * Are regular expressions r1 3 Examples A regular expression:
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that is 4.0 meters wide makes a 90◦ turn as shown below. Is it possible to cross the river by bridging it with only two planks laid flat‚ each 3.9 meters long. If so‚ how? River Figure 4: River and Planks. Problem 8. In the distant future‚ regular travel between planets will become possible. Suppose spacecraft travel along the following routes: Earth–Mercury‚ Pluto–Venus‚ Earth–Pluto‚ Pluto– Mercury‚ Mercury–Venus‚
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CS 3133 Foundations of Computer Science C term 2014 Solutions of the Sample Problems for the Midterm Exam 1. Give a regular expression that represents the set of strings over Σ = {a‚ b} that contain the substring ab and the substring ba. Solution: a+ b+ a(a ∪ b)∗ ∪ b+ a+ b(a ∪ b)∗ (20 points) 2. Consider the following grammar G: S → SAB|λ A → aA|a B → bB|λ (a) Give a leftmost derivation of abbaab. (b) Build the derivation tree for the derivation in part (1). (c) What is L(G)? Solution:
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Classic Koch Snowflake and a Variation of the Koch Snowflake Jarred Sareault Introduction: In this project‚ we need to find the area and perimeter of both the Classic and Variation Koch Snowflake for the first five levels. Also we need to create and implement general forms for the area and perimeter of the Classic/Variation Snowflakes to find the total area and perimeter of the final snowflake for each. For both the Classic and Variation Koch Snowflake‚ an equilateral triangle is used to start.
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and 8cm. How many possibilities are there for the length of the third side of the triangle? A1 B2 C3 D4 21. The square ABCD has an area of 196. It contains two overlapping E more than 4 A B squares; the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1. What is the total area of the shaded regions? A 44 B 72 E more information is needed C 80 MT UK UK MT 20. Jack’s teacher asked him to draw a triangle of area
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Regular Verbs and Irregular Verbs English verbs are tricky. Even the regular verbs are not always so regular‚ but what makes a verb regular exactly? Regular verbs can be written in the past tense by adding either -d or -ed to the base verb form (jump‚ jumped). Irregular verbs‚ however‚ have different spellings to change a verb to the past tense. Sometimes the change is as simple as one letter (know‚ knew)‚ and other times the change is more complicated (go‚ went). Most irregular verb forms come
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International Kangaroo Mathematics Contest 2012 – Cadet Level Cadet (Class 7 & 8) Time Allowed : 3 hours SECTION ONE - (3 points problems) 1. Four chocolate bars cost 6 EUR more than one chocolate bar. What is the cost of one chocolate bar? (A) 1 EUR (B) 2 EUR (C) 3 EUR (D) 4 EUR (E) 5 EUR 2. 11.11 − 1.111 = (A) 9.009 (B) 9.0909 (C) 9.99 (D) 9.999 (E) 10 3. A watch is placed face up on a table so that its minute hand points north-east. How many minutes pass before the minute hand points
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Then graph the circle. center: (–1‚ –3) radius: 6.....B A The volumes of 2 similar solids are 27 and 125 The surface area of the larger solid is 250 What is the surface area of the smaller solid? Round your answer to the tenths place....C A regular nonagon has a side length of feet. A similar nonagon has a side length of 5 feet. What is the ratio of the first nonagon’s perimeter to the second nonagon’s perimeter? What is the ratio of the first nonagon’s area to the second nonagon’s area
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