have been the first person to produce a table for solving a triangle’s lengths and angles.[2] ------------------------------------------------- [edit]The Pythagorean Theorem Pythagoras‚ depicted on a 3rd-century coin In a right triangle: The square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagorean theorem is named after the Greek mathematician Pythagoras‚ who by tradition is credited with its discovery and proof‚[1][2] although it is often argued that
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includes an equation to determine whether a triangle is or isn’t right-angled. Haylock (2010) also identifies a concept‚ as the Pythagorean triple as three natural numbers that could be the lengths of the three sides of a right-angled triangle. For example‚ 5‚ 12 and 13 form a Pythagorean triple because 52 + 122 = 132. Other well known examples of Pythagorean tripes are 3‚ 4‚ 5 (because 9 + 16 = 25) and 5‚ 12‚ 13 (because 25 + 144 = 169). Discussion: As mentioned
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Running head: QUADRATIC FUNCTIONS 1 Real World Quadratic Functions Gail Frazier MAT 222 Week 4 Assignment Instructor: Simone Danielson March 6‚ 2014 Real World Quadratic Functions [no notes on this page] -1- QUADRATIC FUNCTIONS 2 Quadratic functions are perhaps the best example of how math concepts can be combined into a single problem. To solve these‚ rules for order of operations‚ solving equations‚ exponents‚ and radicals must be used. Because multiple variables
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C. D. y(y+4) Which is not a quadratic equation? A. C. B. D. (x+3) (x+5) How many terms are there in 7? A. 1 B. 2 C. 3 D. 4 What is the value of x will make the sentence A. 0 B. -10 C. 10 D. 20 What is the degree of the polynomial ? A. first B. second C. third D. fourth Which of the following conditions would disqualify from being a quadratic equation ? A. B. C. D. What quadratic equations has roots -5 and 6. Find
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from Tip (cm) 1 10 2 23 3 38 4 55 5 74 6 96 7 120 8 149 Define suitable variables and discuss parameters/constraints. Using Technology‚ pot the data points on a graph. Using matrix methods or otherwise‚ find a quadratic function and a cubic function which model this situation. Explain the process you used. On a new set of axes‚ draw these model functions and the original data points. Comment on any differences. Find a polynomial function which passes through
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example of a ball being thrown up into the sky and then landing on the ground‚ we can model a quadratic equation to show the path of the projectile at various points in time (projectile motion). That is to say‚ each point plotted on the graph (parabola) will be a measurement to this effect: Suppose a ball is thrown into the sky at a velocity of 64ft/sec from an initial height of 100ft. We would set the quadratic equation as (s)0=-gt^2+v0t+h0 and substitue values for gravity‚ velocity‚ and initial height
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Section 5.2 Trigonometric Functions of Real Numbers The Trigonometric Functions EXAMPLE: Use the Table below to find the six trigonometric functions of each given real number t. π π (a) t = (b) t = 3 2 1 EXAMPLE: Use the Table below to find the six trigonometric functions of each given real number t. π π (a) t = (b) t = 3 2 Solution: (a) From the Table‚ we see that the terminal point determined by √ t = √ is P (1/2‚ 3/2). Since the coordinates are x = 1/2 and π/3 y = 3/2‚ we have √ √ π 3
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the works of Diophantus who was a mathematician who worked methods on solving these equations. Fermat’s Last Theorem was based on Diophantus’s work. A more common Diophantine equation would be Pythagorean Theorem‚ where the solution would be the the Pythagorean triples(Weisstein). However‚ unlike Pythagorean Theorem‚ Fermat’s Last Theorem has no practical real world applications. Fermat had scribbled on the margin of Arithmetica‚ the book that inspired his theorem‚ that he had a proof that would
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believed that Pythagoras himself who revealed this mathematically changing idea because it went against his philosophy that all things are numbers. It was in reality a Pythagorean philosopher Hippasus who was able to demonstrate the irrationality of the square root of 2. The legend is that after doing so he was killed by other Pythagoreans who were scared and frantic by the thought of an irrational number. Pythagoras’ follower most likely used a geometrical proof when he was first discovering the irrationality
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Quadratic Equations ax2 + bx + c = 0 Examples of Quadratic equations 1. x2 +2x – 8 = 0 2. x2 – 10x + 25 = 0 3. 3x2 + x - 2 = 0 Quadratic Formula If [pic] a x2 + b x + c = 0‚ then [pic] Finding the zeros of the quadratic functions - The zeros of a function are the input values which result in an output value of zero. One way of solving quadratic equations is using factoring Examples are the following: 1) x2 + 5x + 6 = 0 Set this equal to zero:
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