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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1 Quadratic Equations in One Unknown (I) Review Exercise 1 (p. 1.4) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Let’s Discuss Let’s Discuss (p. 1.23) Angel’s method: Using the quadratic formula‚ Ken’s method: Using the quadratic formula‚ Let’s Discuss (p. 1.30) The solution obtained by using the factor method is the exact value of the root. However‚ the solution obtained
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a Function? 148 Graphs of Functions 158 ● DISCOVERY PROJECT Relations and Functions 171 vii viii Contents 2.3 2.4 2.5 2.6 2.7 2.8 Increasing and Decreasing Functions; Average Rate of Change 173 Transformations of Functions 182 Quadratic Functions; Maxima and Minima 193 Modeling with Functions 203 Combining Functions 214 ● DISCOVERY PROJECT Iteration and Chaos 223 One-to-One Functions and Their Inverses 225 Chapter 2 Review 233 Chapter 2 Test 237 ■ FOCUS ON MODELING Fitting Lines
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MATH133 UNIT 2: Quadratic Equations Individual Project Assignment: Version 2A Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. Problem 1: Modeling Profit for a Business IMPORTANT: See Question 3 below for special IP instructions. This is mandatory. Remember that the standard form for the quadratic function equation is y = f (x) = ax2 + bx + c and the vertex form is y = f (x) = a(x – h)2 + k‚ where (h‚ k) are
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Pythagoras: A Universe made of Numbers PART 1 Pythagoras & His Philosophy Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet there is relatively little known about his mathematical achievements. Unlike many later Greek mathematicians‚ where at least we have some of the books which they wrote‚ there is nothing of Pythagoras’s writings. The society which he led‚ half religious and half scientific
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03.01LessonSummary To achieve mastery of this lesson‚ make sure that you develop responses to the essential question listed below. How can a Greatest Common Factor be separated from an expression? By simplifying the equation . By breaking them up by dividing them up What methods can be used to rewrite square trinomials and difference of squares binomials as separate factors? distribution in what conditions can a factored expression be factored further? Greatest Common Factor A greatest common factor
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sin 2 θ Reduce the most complicated side first and collect like terms. Cross Multiplication Transposition cos θ (sec θ − cos θ ) = sin 2 θ cos θ sec θ − cos 2 θ = Expand the left side. By Reciprocal Identities. 1 − cos θ = 2 By Pythagorean Identities. sin2 θ = sin2 θ 1 Example 2 2. csc 3 x − csc x + cot x = cot 2 x + cos x csc x If you have only one term in the denominator and many in the numerator.....divide the denominator into each term in the
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Completing the Square: Quadratic Examples & Deriving the Quadratic Formula (page 2 of 2) Solve x2 + 6x + 10 = 0. Apply the same procedure as on the previous page: This is the original equation. x2 + 6x + 10 = 0 Move the loose number over to the other side. x2 + 6x = – 10 Take half of the coefficient on the x-term (that is‚ divide it by two‚ and keeping the sign)‚ and square it. Add this squares value to both sides of the equation. x^2 + 6x + 9 = –10 + 9 Convert the left-hand side to
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Cindy Hwang IB Math 11 SL 1-3 IB Math Portfolio Gold medal heights Aim: The aim of this task is to consider the winning height for the men’s high jump in the Olympic Games. Introduction: The Olympic Games which are held in every four years have an event called Men’s High Jump and usually an athlete tries to jump over a bar which is set up in a certain range from1 meter to 3 meters. The table 1 shows the record of the gold medalists during the Olympic Games held during 1932 to 1980. Note:
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sphere.[2] Based on one interpretation of the Plimpton 322 cuneiform tablet (c. 1900 BC)‚ some have even asserted that the ancient Babylonians had a table of secants.[7] There is‚ however‚ much debate as to whether it is a table of Pythagorean triples‚ a solution of quadratic equations‚ or a trigonometric table.The Egyptians‚ on the other hand‚ used a primitive form of trigonometry for building pyramids in the 2nd millennium BC.[2] The Rhind Mathematical Papyrus‚ written by the Egyptian scribe Ahmes
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