There are many Greek influences that still affect us today such as Democracy. The Greeks created the world’s first democracy. Athens started out as a monarchy and then advanced to and oligarchy until it finally reached a democracy. The government consisted of over 6‚000 assembly members all of whom were adult male citizens. The assembly voted on issues throughout Athens‚ and passed laws. The required number of votes to pass a law was simply the majority but in order to banish or exile someone 6‚000
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Period 7 Jack Whyte Reflection This year‚ both as a student and as a person‚ I learned a tremendous amount. For instance‚ I learned that in England‚ its spelled “grey”‚ but in America its spelled “gray”. That pretty much was the coolest and most useful thing I have heard in a long time‚ let alone in the past 10 months. But I am not in a position today to discuss this‚ and thus I will be detailing everything else I have learned that has fallen short. Scholastically‚ I’ve grown to appreciate
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MODULE 1: Quadratic Equation Lesson No. of Hours Learning Competency Activity Lesson 1: Illustrations of Quadratic Equations 1 Illustrate quadratic equations Activity 1 Lesson 2.1: Solving Quadratic Equations by Extracting Square Roots 1 Solve quadratic equations by extracting square roots Activity 2 Lesson 2.2: Solving Quadratic Equations by Factoring 1 Solve quadratic equations by factoring Lesson 2.3: Solving Quadratic Equations by Completing the Square 1 Solve quadratic equations
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Equations Reducible to Quadratic Equations Exercise 4.2 Solve the following equations: 1. x 4 − 6 x 2 + 8 = 0 Solution: x4 − 6 x2 + 8 = 0 Let y = x 2 and y 2 = x 4 The above equation becomes: y 2 − 6 y + 8 = 0 y2 − 6 y + 8 = 0 y2 − 4 y − 2 y + 8 = 0 y ( y − 4) − 2( y − 4) = 0 ( y − 2)( y − 4) = 0 y − 2 = 0 and y − 4 = 0 y=2 y=4 2 As‚ y = x x2 = 2 x2 = 4 x = ±2 x=± 2 solution set = { 2‚ − 2‚ 2‚ −2} 2. x −2 − 10 = 3 x−1 Solution: x −2 − 10 = 3 x −1 x −2 − 3 x −1 − 10 = 0 Let
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investigation is surrounding Lascap’s Fractions. They are a group of numbers set up in a certain pattern. A similar mathematical example to Lacsap’s Fractions is Pascal’s Triangle. Pascal’s Triangle represents the coefficients of the binomial expansion of quadratic equations. It is arranged in such a way that the number underneath the two numbers above it‚ is the sum. Ex. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
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and row 3 is 3. The second difference for each row is 1 and it shows that this is a geometric sequence. So‚ I will start by finding the equation using the quadratic formula‚ [pic]‚ in which x is the row number and y is the numerator. First‚ I will plug in the numbers in the second row‚ which is 2 for x and 3 for y to try finding the quadratic equation of the Lacsap’s sequence. Then‚ I will plug in the numbers in the third row and it forms a simultaneous equation. I will use substitution method to
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Section 1.2: Quadratic Equations Learning Objectives: 1. Solve a quadratic equation by (a) factoring‚ (b) completing the square‚ (c) the quadratic formula 2. Solve applied problems involving quadratic equations Examples: 1. Find the real solutions by factoring: [pic] 2. Find the real solutions by using the square root method: [pic] 3. Find the real solutions by completing the square: [pic] 4. Find the real solutions by using the quadratic formula: [pic]
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Week 1 – Discussion 1. Counting Number : Is number we can use for counting things: 1‚ 2‚ 3‚ 4‚ 5‚ ... (and so on). Does not include zero; does not include negative numbers; does not include fraction (such as 6/7 or 9/7); does not include decimals (such as 0.87 or 1.9) Whole numbers : The numbers {0‚ 1‚ 2‚ 3‚ ...} There is no fractional or decimal part; and no negatives: 5‚ 49 and 980. Integers : Include the negative numbers AND the whole numbers. Example: {...‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3‚
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Japan Temple Geometry Abstract In this science project the problems‚ which were written at Japanese temple boards are considered. These problems are differing from the European geometry by their solutions. Translated chapters from the book of Fukagawa and Pedoe were devoted to ellipses and n-gons‚ different combinations of the ellipses‚ circumferences and quadrilaterals‚ spheres‚ spheres and ellipsoids‚ different combination
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Albert Einstein (1879-1955) Born: March 14‚ 1879‚ in Ulm‚ Kingdom of Württemberg‚ German Empire Died: April 18‚ 1955 (at age 76) in Princeton‚ New Jersey Nationality: German Famous For: Father of the Atomic Age. Many contributions to science that transformed the modern world Awards: Nobel Prize in Physics (1921)‚ Time Magazine’s Person of the Century (1999) Einstein’s Contribution to Mathematics While Einstein was remembered for his contributions to physics‚ he also made contributions in mathematics
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