topics of Napoleon’s Theorem‚ the first thing that struck my mind was that it was somehow related to the French leader‚ Napoleon Bonaparte. But then a thought struck me: Napoleon was supposed to good at only politics and the art of warfare. Mathematics was never related to him. On surfing the internet to learn about the theorem‚ I came to know that this theorem was in fact named after the same Napoleon as he was good at Maths too (other than waging wars and killing people). The theorem was discovered in
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The Mean Value Theorem Russell Buehler b.r@berkeley.edu 1. Verify that f (x) = x3 − x2 − 6x + 2 satisfies the hypotheses of Rolle’s theorem for the interval [0‚ 3]‚ then find all c that satisfy the conclusion. www.xkcd.com 2. Let f (x) = tan(x). Show that f (0) = f (π)‚ but there is no number c in (0‚ π) such that f (c) = 0. Is this a counterexample to Rolle’s theorem? Why or why not? 3. Verify that f (x) = x3 − 3x + 2 satisfies the hypotheses of the mean value theorem on [−2‚ 2]‚ then
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When it comes to Euclidean Geometry‚ Spherical Geometry and Hyperbolic Geometry there are many similarities and differences among them. For example‚ what may be true for Euclidean Geometry may not be true for Spherical or Hyperbolic Geometry. Many instances exist where something is true for one or two geometries but not the other geometry. However‚ sometimes a property is true for all three geometries. These points bring us to the purpose of this paper. This paper is an opportunity for me to
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chloride 10. Sodium hydroxide reacts with carbondioxide forming sodium carbonate and water Maths : If you want you can do this or search in google for different methods OBJECTIVE:- To verify the Pythagoras theorem by method of Paper Folding‚ Cutting and Pasting THEORY:- Pythagoras theorem:- It states that in a right angled triangle‚ the square of the largest side (Hypotenuse) is equal to the sum of the squares of the other two sides(Perpendicular and the base). PRE-REQUISITE KNOWLEDGE:- •
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6 Discussion Question Version 8 Week 6 DQ 2 1. Other than those listed in the text‚ how might the Pythagorean theorem be used in everyday life? 2. Provide examples of each. RESPONSE 1. Other than those listed in the text‚ how might the Pythagorean theorem be used in everyday life? Well other than the way its listed in the text the way that the pythagorean theorem can be used any time is when we have a right triangle‚ we know the length of two sides‚ and we want to find the
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The Distance Formula In week one‚ we learned a simple yet extremely useful math concept‚ the Distance Formula. This formula uses the Pythagorean Theorem to determine the distance between two points on the rectangular coordinate system. Variations of the Pythagorean Theorem such as the Distance Formula can be used in building things or making plans to build something. Scenario Suppose you are volunteering at the local community center. The community center committee is planning to install
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BINOMIAL THEOREM OBJECTIVES Recognize patterns in binomial expansions. Evaluate a binomial coefficient. Expand a binomial raised to a power. Find a particular term in a binomial expansion Understand the principle of mathematical induction. Prove statements using mathematical induction. Definition: BINOMIAL THEOREM Patterns in Binomial Expansions A number of patterns‚ as follows‚ begin to appear when we write the binomial expansion of a b n‚ where n is a positive integer
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with the Pythagorean Theorem within trigonometry. However‚ some sources doubt that is was him who constructed the proof (Some attribute it to his students‚ or Baudhayana‚ who lived some 300 years earlier in India). Nonetheless‚ the effect of such‚ as with large portions of fundamental mathematics‚ is commonly felt today‚ with the theorem playing a large part in modern measurements and technological equipment‚ as well as being the base of a large portion of other areas and theorems in mathematics. But
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ECON 100A Public Goods and Coase theorem April 29-May 2 Part I Public Goods A good is a (pure) public good if once produced it meets two criteria: 1. Non-rival - A good is non-rival if consumption of additional units of the good involves zero social marginal costs of production. 2. Non-excludable - A good is non-excludable if it impossible‚ or very costly‚ to exclude individuals from benefiting from the good. Taking these two criteria we can categorize goods into four groups. Rival
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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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