Following completion of your readings‚ complete exercise 4 in the “Projects” section on page 620 of Mathematics in Our World. Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this. After building your triples‚ verify each of them in the Pythagorean Theorem equation. The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs. Your introduction should
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/MAT117 Week 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
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Thales of Miletus (ca 624 - 546 BC) Greek domain Thales was the Chief of the Seven Sages of ancient Greece‚ and has been called the "Father of Science‚" the "Founder of Abstract Geometry‚" and the "First Philosopher." Thales is believed to have studied mathematics under Egyptians‚ who in turn were aware of much older mathematics from Mesopotamia. Thales may have invented the notion of compass-and-straightedge construction. Several fundamental theorems about triangles are attributed to Thales‚ including
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TOK Reflection: Mathematics To what extent is math relevant to your life and the lives of others you know and how can it become an even more viable area of knowledge. “In mathematics I can report no deficience‚ except it be that men do not sufficiently understand the excellent use of the Pure Mathematics.” Roger Bacon (1214-1294) Mathematics: the abstract science of number‚ quantity‚ and space; a subject considered by many to be useless‚ a waste of time‚ and too difficult. “When am
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Directions: Answer each of the following questions algebraically. You may sketch the graph of the parabola to help you visualize the flight of the ball. 1. A water balloon is tossed into the air with an upward velocity of 25ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = -16t2 + 25t + 3. a) After how many seconds will the balloon hit the ground? b) What will the height be at t = 1 second? 2. A football is passed through the air and caught at ground level for
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Exercise: Week Six Concept Check The theorem works In any right triangle. A key observation is that a and b are at right angles. Movement in one direction has no impact on the other. The Pythagorean Theorem can be used with any shape and for any formula that squares a number. The Pythagorean Theorem lets you use find the shortest path distance between orthogonal directions. So it’s not really about right triangles — it’s about comparing “things” moving at right angles. The area
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Where will I ever need algebra? Where do you need square roots? When will I ever use the Pythagorean Theorem? Will algebra even be ’relevant ’ in the future? These are a few of the many questions that one asks when they have to take an algebra course. This is a required subject in most colleges to further ones education. The first year of algebra is a prerequisite for all higher-level math: geometry‚ algebra II‚ trigonometry‚ and calculus. It is quite true‚ while many people get by without an education
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longer or shorter it is makes a difference in the tune of the note. In astronomy‚ he taught that the earth was a sphere‚ and in math he compared the difference between composite and prime numbers‚ discovered irrational numbers‚ and proved the Pythagorean Theorem. This stated that when the two shorter sides in a right triangle were squared and then added‚ it would equal the square of the longest side or hypotenuse. This was known earlier‚ but he was the first one to really prove it was true. He
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Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians‚ where at least we have some of the books which they wrote‚ we have nothing of Pythagoras’s writings. The society which he led‚ half religious and half scientific‚ followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure
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• A quadratic function (f) is a function that has the form as f(x) = ax2 + bx + c where a‚ b and c are real numbers and a not equal to zero (or a ≠ 0). • The graph of the quadratic function is called a parabola. It is a "U" or “n” shaped curve that may open up or down depending on the sign of coefficient a. Any equation that has 2 as the largest exponent of x is a quadratic function. ☺Forms of Quadratic functions: * Quadratic functions can be expressed in 3 forms: 1. General form: f (x) = ax2
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