Assignment: Pythagorean Quadratic Algebra has been around for many years. Some people feel there is no use for algebra in the... real world. There are those who feel it is a waste of time because only certain professions really use it. However, algebra is used in many ways which can relate to everyday situations. Algebra truly is a part of our everyday life and there really is no escaping it. This week, we are asked to solve a problem using the Pythagorean Theorem. The Pythagorean Theorem is...
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Pythagorean Quadratic Member MAT 222 Introduction to Algebra Instructor Yvette Gonzalez-Smith August 04, 2013... Pythagorean Quadratic The Pythagorean Theorem is an equation that allows a person to find the length of a side of a right triangle, as long as the length of the other two sides is known. The theorem basically relates the lengths of three sides of any right triangle. The theorem states that the square of the hypotenuse is the sum of the squares...
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Pythagorean Quadratic MAT 221: Introduction to Algebra Pythagorean Quadratic The... Pythagorean Theorem was termed after Pythagoras, who was a well-known Greek philosopher and mathematician, and the Pythagorean Theorem is one of the first theorems identified in ancient civilizations. “The Pythagorean theorem says that in any right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse” (Dugopolski, 2012, p. 366 para. 8). For this...
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Farhrenheit = 1.8 x (Celsius) + 32 8. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is... equal to the square of the hypotenuse. For example, if two sides of a right triangle have lengths 3 and 4, then the hypotenuse must have a length of 5. The integers 3, 4, and 5 together form a Pythagorean triple. There is an infinite number of such triples. Given two positive integers, m and n, where m > n, a Pythagorean triple can be generated by the following formulas: ...
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Pythagorean Triples Tammie Strohl MAT 126 David Gualco November 9, 2009 Pythagorean Triples Pythagorean... Theorem states that the sum of the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest. ￼ If a, b, and c are positive integers, they are together called Pythagorean Triples. The smallest such Pythagorean Triple is 3, 4 and 5. It can be seen that 32 + 42 = 52 (9+16=25). Here are some examples: ...
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The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek... mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students. The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend...
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Pythagorean Triples Ashley Walker MAT126 Bridget Simmons November 28, 2011 A Pythagorean triple is a triple of positive... integers a, b, and c such that a right triangle exists with legs a, b, and hypotenuse c (Bluman, 2005). A Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. A triple is simply a right triangle whose sides are positive integers. An easy way to generate Pythagorean triples is to multiply any known Pythagorean triple by an integer (any integer)...
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In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right... triangle (right-angled triangle). In terms of areas, it states: In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths...
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A quadratic equation is an equation that has a second-degree term and no higher terms. A second-degree term is a variable raised to the second... power, like x2. When you graph a quadratic equation, you get a parabola, and the solutions to the quadratic equation represent where the parabola crosses the x-axis. A quadratic equation can be written in the form: quadratic equation, where a, b, and c are numbers (a ≠0), and x is the variable. x is a solution (or a root) if it satisfies the equation...
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Quadratic Equation: Quadratic equations have many applications in the arts and sciences, business, economics, medicine and... engineering. Quadratic Equation is a second-order polynomial equation in a single variable x. A general quadratic equation is: ax2 + bx + c = 0, Where, x is an unknown variable a, b, and c are constants (Not equal to zero) Special Forms: * x² = n if n < 0, then x has no real value * x² = n if n > 0, then x = ± n * ax² + bx = 0 x = 0, x = -b/a ...
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Introduction The aim of this investigation is to identify the nature of the roots of quadratics and cubic functions. Part One Case One... For Case One, the discriminant of the quadratic will always be equal to zero. This will result in the parabola cutting the axis once, or twice in the same place, creating a distinct root or two of the same root. For PROOF 1, the equation y=a(x-b)2 is used. PROOF 1 y = 3 (x – 2)2 = y = 3 (x2 – 4x + 4) = y = 3x2 – 12x + 12 ^ = b2 – 4ac = (-12)2 – 4 x 3...
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Historical Account: Pythagoras, the namesake and supposed discoverer of the Pythagorean Theorem, was born on the Greek island of Samos in the... early in the late 6th century. Not much is known about his early years of life, however, we do know that Pythagoras traveled through Egypt in the attempt to learn more about mathematics. Besides his famous theorem, Pythagoras gained fame for founding a group, the Brotherhood of Pythagoreans, which was dedicated solely to study of mathematics and worship of numbers...
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Pythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to... learn from. I'll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion, a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears...
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Jaquavia Jacques Ms. Cordell 1st period December 9, 2014 Quadratics is used to help to determine what is on a graph. There are many formulas... that are used to put points on a graph to create parabolas. Parabolas are “U” shaped figures on a graph. Parabolas are examples of quadratics on a graph. Parabolas can be positioned up or down, which means if the arrows are going up it has a minimum point, and if the arrows are going down that means it has a maximum point. When graphing using the vertex formula:...
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among things in nature and of the best government in the universe. As a rule it assumes the guise of harmony in the universe, of lawful government in a... state, and of a sensible way of life in the home. It brings together and unites." - The Pythagoreans Every school student will recognize his name as the originator of that theorem which offers many cheerful facts about the square on the hypotenuse. Many European philosophers will call him the father of philosophy. Many scientists will call...
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Quadratic equation In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having... the form where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, the quadratic coefficient, the linear coefficient and the...
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Pythagorean Theorem Pythagoras was born in Samos, Greece around 570 BCE. From there he emigrated to Croton, Italy where most of his most... important ideas and theories would develop. Early on, Pythagoras founded a society of disciples where he introduced the idea eternal recurrence into Greek thought, and it was Pythagoras’ ambition to reveal the basis of divine order. This is how Pythagoras came to mathematics, and he saw math as a purifier of the soul, and saw numbers in everything. He was...
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LESSON 3 - 6 : The Zeros of a Quadratic Function MCR3U1 (Nature of the Roots) MINDS ON... The demand to create automotive parts is... increasing. BMW developed three different methods to develop these parts. The profit function for each method is given below, where y is the profit and x is the quantity of parts sold in thousands: PROCESS A: P(x) = -0.5x2 + 3.2x –5.12 PROCESS B: P(x) = -0.5x2 + 4x – 5.12 PROCESS C: P(x) = -0.5x2 + 2.5x – 3.8 The graphs of the corresponding...
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Real World Quadratic Functions Read the following instructions in order to complete this assignment: 1. Solve problem 56 on pages 666-667 of... Elementary and Intermediate Algebra. 2. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include: o An explanation of the basic shape and location of the graph and what...
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NAME: __________________________________________ DATE: __________________ REVIEW FOR QUADRATICS TEST 1 ALG II CP1 I. Graphing from Vertex... Form – Graph the following functions (a) (b) II. Graphing from Factored Form (a) (b) III. Graphing from Standard Form by Completing The Square – Graph the following functions by completing the square to get vertex form (a) (b) IV. Graphing from Standard Form using –b/2a – Graph the following...
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The assignment for the week is on page 371 number 98. We will be using Pythagorean Theorem, quadratic, zero factor, and... compound equation, to solve this equation. We will explain step by step to solve how many paces to reach Castle Rock for Ahmed and Vanessa had to accomplish to meet there goal. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure...
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Name: ________________________ Date:__________________ Year & Section: _________________ Teacher: _______________ Reviewer:... Quadratic Equations I. Multiple Choice: Choose the letter of the correct answer. Show your solution. 1. What are the values of x that satisfy the equation 3 – 27x2 = 0? A. x = [pic]3 B. x = [pic] C. x = [pic] D. x = [pic] 2. What are the solutions of the equation 6x2 + 9x – 15 = 0? A. 1, - 15 B. 1, [pic] C. – 1, - 5 D. 3, [pic] ...
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location. Using a piece of paper I drew the triangle and it is a right triangle. Now I can use the Pythagorean Theorem to help solve for x.... The Pythagorean Theorem is a^2+b^2=c^2. Letting a = x, b = 2x+4, and c = 2x+6 a^2+b^2=c^2 Pythagorean Theorem x^2+〖(2x+4)〗^2=〖(2x+6)〗^2 Putting the binomials into the Pythagorean Theorem. x^2+〖4x〗^2+16x+16=〖4x〗^2+24x+36 Binomials squared. x^2+16x+16=24x+36 ...
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------------------------------------------------- Pythagorean Theorem In mathematics, the Pythagorean theorem or Pythagoras'... theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). ...
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Pythagorean Theorem Diana Lorance MAT126 Dan Urbanski March 3, 2013 Pythagorean Theorem In this paper we are going to... look at a problem that can be seen in the “Projects” section on page 620 of the Math in our World text. The problem discusses Pythagorean triples and asks if you can find more Pythagorean triples than the two that are listed which are (3,4, and 5) and (5,12, and 13) (Bluman, 2012). The Pythagorean theorem states that for any right triangle, the sum of the squares of the length...
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Chapter Test Chapter 10: Solving Quadratic Equations Lesson 1. The Zero Product Property Lesson 2. Solving Quadratic Equations... by Factoring Lesson 3. Solving Quadratic Equations By Taking The Square Root of Both Sides Lesson 4. Solving Quadratic Equations By Completing The Square Lesson 5. Solving Quadratic Equations By Using The Quadratic Formula Lesson 6. The Discriminant Lesson 7. Quadratic Equation Word Problems Chapter Review Chapter Test Chapter 11: Quadratic Functions Lesson 1. Graphing...
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Pythagorean Triples To begin you must understand the Pythagoras theorem is an equation of a2 + b2 = c2. This simply means that the sum of... the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest. Let a, b, and c be the three sides of a right angled triangle. To define, a right angled triangle is a triangle in which any one of the angles is equal to 90 degrees. The longest side of the right angled triangle...
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some big discoveries. In order to go back to the first signs of Algebra, we have to go back over 3700 years, to the Babylonian civilization. Babylonians... were particularly proficient algebraists and in the ancient civilizations they could solve quadratic problems (Kleiner, 2007). Records show that in 1600 B.C equations and symbols were not used in these problems, rather they were written out and solved verbally (Corry, 2005). Corry’s (2005) study found that a typical example of a problem made by...
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QUADRATIC EQUATIONS Quadratic equations Any equation of the form ax2 + bx + c=0, where a,b,c are real numbers, a 0 is a... quadratic equation. For example, 2x2 -3x+1=0 is quadratic equation in variable x. SOLVING A QUADRATIC EQUATION 1.Factorisation A real number a is said to be a root of the quadratic equation ax2 + bx + c=0, if aa2+ba+c=0. If we can factorise ax2 + bx + c=0, a 0, into a product of linear factors, then the roots of the quadratic equation ax2 + bx + c=0 can be found...
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exponents ��n ��m = ��m+n , (��m )n = ��mn Square roots √��2 =|��| (����)n = ��n �� n , �� �� �� �� = ����−�� = �� ��−�� ���� �� ≠ 0 ,... ( )�� = �� �� �� �� ���� , ���� �� ≠ 0 Geometry Review �� 2 = ��2 + �� 2 Pythagorean Theorem Geometry Formulas 1 Area = LW Perimeter = 2L + 2W Area = 2bh Circumference = 2πr = πd Area = π�� 2 Volume = LWH Surface area= 2LW+ 2LH+2WH Volume= π�� 2 ℎ =π�� 2 ℎ + 2πrℎ Surface area= Volume= 3 ���� 3 4 Surface...
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This article is about quadratic equations and solutions. For more general information about quadratic functions,... see Quadratic function. For more information about quadratic polynomials, see Quadratic polynomial. A quartic equation is a fourth-order polynomial equation of the form. A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Monomial – is a polynomial with only one term. Binomial...
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Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share... their information, then they can find x and save a lot of digging. What is x? The Pythagorean Theorem states to find the missing side of a right triangle you can square to know lengths and add the two together. The result will be the distance of the missing length squared. A^2+b^2=C^2 We know that Ahmed has a map with a distance to...
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f(x)= 2x^2 + 8x + 5 Vertex: In order to find the vertex of the quadratic equation, begin by using the proper formula - b / 2(a) to find... it. In the equation there is an (a) (b) (c) which is needed for the vertex equation. First look at the equation and determine what are the values of the three variable. In this case (a)= 2, (b)= 8, (c)= 5. Now plug them in properly into the vertex equation. * Notice in the vertex equation there is a negative sign!!! DO NOT FORGET! When plugged into the equation...
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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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Quadratic functions are used all the time, every day, all over the world. Even though right now, it doesn’t seem like this kind of math is ever... going to creep back into our life. That is actually far from true. These math skill are crucial to have if one ever decides to do anything in engineering, or something like that. Those types of jobs are now becoming more and more popular, because the world is always going to need educated people who know how to construct or refurbish buildings and homes. ...
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time period in which Pythagoras graced his presence on Earth happened so long ago that research on Pythagoras and his mathematical concept were not... documented. This is important because many researchers argue if Pythagoras really came up with the Pythagorean Theorem or if it was just a legend or Greek story. After researching this topic, I have found that Pythagoras was more than just a “Greek story”. Pythagoras was born in the Samos Islands of Samos. Samos is a Greek island that is found beside...
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329 Quadratic Equations Chapter-15 Quadratic Equations Important Definitions and Related Concepts 1. Quadratic... Equation If p(x) is a quadratic polynomial, then p(x) = 0 is called a quadratic equation. The general formula of a quadratic equation is ax 2 + bx + c = 0; where a, b, c are real numbers and a 0. For example, x2 – 6x + 4 = 0 is a quadratic equation. 2. Roots of a Quadratic Equation Let p(x) = 0 be a quadratic equation, then the values of x satisfying p(x) = 0 are called its roots or...
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Rock. When she get there to walk x paces to the north, and then walk 2x + 4 paces to the east. I wonder what X could equal to, if Ahmed and Vanessa come... together in finding the treasure they would save a lot of time of digging. In this Pythagorean equation we will see how far Ahmed would walk 2x+6 paces and Vanessa would have to walk 2x+4, x in desert to find the Castle Rock. Ahmed and Vanessa would need equipment for their journey they will use rope, compasses and sticks with colored flags...
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When you are graphing quadratics, it is the same as graphing linear equations but, quadratics have the curvy line, called a... parabola. When you are graphing your points, it is best to graph three or more points. You are really going to need to point three or more points, because if there are less than three you will not have a correct graph, graphing more than three will insure that your graph will be correct. The biggest number that they say you have to graph will most likely not be able to be graphed...
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to math. There was no such thing as a calculator in our house, we had to be able to figure things out on our own and not by calculator or memorization of... the times tables. We had to know why it was so. For example, when I first learnt of the Pythagorean Theorem (), I wanted to know the basis behind it and how Pythagoras reached such a crucial conclusion. The reason I found was astonishing (in my opinion – remember I’m a math fanatic). It’s simple really, yet brilliant. This is an image of a square...
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sub-sections such as calculus, geometry, trigonometry and algebra. Who was Pythagoras? Pythagoras was born in 570 BCE in Samon, Ionia, and died 500-490 BCE.... He was a Greek mathematician and philosopher who is greatly known for his creation of the Pythagorean theorem. His principles influenced the work of Aristotle and Plato. Pythagoras migrated to Southern Italy in 532 BCE to supposedly leave the tyrannical rule in Samon. None of his writings have been recovered or found. He is said to have also been...
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theVatican Museum. Pythagoras of Samos was a famous Greek mathematician and philosopher, born between 580 and 572 BC, and died between 500 and 490 BC. He is... known best for the proof of the important Pythagorean theorem, which is about right triangles. He started a group of mathematicians, called the Pythagoreans, who worshiped numbers and lived like monks. He was an influence for Plato. He had a great impact on mathematics, theory of music and astronomy. His theories are still used in mathematics today...
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exercise 4 in the “Projects” section on page 620 of Mathematics in Our World. In the two step process is to sure you build or generate at least five more... Pythagorean Triples using one of the many formulas available online for doing this. Then after building the triples, verify each of them in the Pythagorean Theorem equation. The Pythagorean Theorem is based on Euclidian Geometry among the relation between the three sides of a right triangle which basically states a2+b2=c2. Or the fact that a2...
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innumerable theorems and research subjects. His two other major contributions are the, introduction of zero to the world and calculating the approximate... value of pie. His works are also spread in fields like include algebra, arithmetic, trigonometry, quadratic equations and the sine table. Ramanujam Srinivasa Ramanujan Iyengar, the greatest Indian mathematician of 20th century, contributed immensely in fields like number theory, mathematical analysis, string theory and crystallography. His genius has...
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PYTHAGOREAN THEOREM More than 4000 years ago, the Babyloneans and the Chinese already knew that a triangle with the sides of 3, 4 and 5 must... be a right triangle. They used this knowledge to construct right angles. By dividing a string into twelve equal pieces and then laying it into a triangle so that one side is three, the second side four and the last side five sections long, they could easily construct a right angle. A Greek scholar named Pythagoras, who lived around 500 BC, was also fascinated...
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Area can be understood as the amount of material with a given thickness. Circular Region The set of all points of the plane which lie either on the... circle or inside the circle form the circular region. Converse of the Pythagorean Theorem The converse of the Pythagorean Theorem helps you to find out if a triangle is right. Basically, the converse states that whenever the sum of the squares of two sides equal to the square of the third side of the triangle, the triangle is a right triangle...
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influenced a group of early Greek scientific and religious thinkers, the Pythagoreans. They believed that the soul was immortal and separable... from the body. Because they believed that the soul was reincarnated in different animal bodies, they practiced vegetarianism. The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe," and the Pythagoreans gave numerical values to many objects and ideas. These numerical values...
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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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numbers. He also believed that mathematics was and is the core of everything mathematical. He also believed that geometry is the highest form of mathematics... and that the physical world could always be understood through the science of mathematics. Pythagoreans have and will continue to give recognition to Pythagoras for 1) the angles of a triangle equaling to two right angles. 2) The Pythagoras theorem, which is a right-angled triangle, and the square on the hypotenuse equaling to the sum of the squares...
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Marks (a) Find the value of given that: and , , 3 (b) The length of a block of land is 5... metres less than 4 times its width. The area of the block is 1071 m. (i) Write a quadratic equation to show this information 1 (ii) Solve the equation to find the dimensions of the block of land 2 (c) Simplify . Write your answer with a rational denominator 3 (d) Solve 3 ...
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trigonometry. | Pythagorean identities Identity 1: Proof 1: Refer to the triangle diagram above. Note that by Pythagorean... theorem. The following two results follow from this and the ratio identities. To obtain the first, divide both sides of by ; for the second, divide by . Similarly Proof of the Pythagorean identities To prove: | a) | sin²θ + cos²θ | = | 1 | | b) | 1 + tan²θ | = | sec²θ | | c) | 1 + cot²θ | = | csc ²θ | Proof 1. According to the Pythagorean theorem, x²...
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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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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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degree equation a. Linear b. Quadratic c. Cubic d. Power of Two _______. It is a number that if... substituted to a variable in a quadratic equation, it becomes a true statement. a. Quadrant b. Roots c. Radicals d. Discriminant _______. Which of the following is not a Quadratic Equation? a. (x-2)2 – 5 = 0 b. x(x+3) + 8 = 0 c. x2 = 0 d. x( 1x ) + 3x – 9 = 0 _______. In the quadratic equation, 30x2 = 15 + 5x, if both sides...
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is continuous because it is associated with a measurement and its possible to have the same y value for different x values. And since the data is measuring... height a decimal answer is possible. A function that would fit most of the data would be a quadratic function. The constraint that there is a12 year gap between 1936 and 1948 could skew the data. The data that we are missing could show us a much clearer model. e) The constraints of this task are that, when performing a regression analysis on...
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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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2 d) Real Numbers ---- 1 or 2 e) Ratio ---- 1 or 2 f) Percent ---- 1 or 2 2) ALGEBRA (8-10 Q’s opx.) a) Operations with Algebraic Expressions ---- 1 or... 2 b) Rules of Exponents ---- 1 or 2 c) Solving Linear Equations ---- 1 or 2 d) Solving Quadratic Equations ---- 1 or 2 e) Solving Linear Inequalities ---- 1 or 2 f) Functions ---- 1 or 2 g) Applications ---- 1 or 2 h) Coordinate Geometry ---- 1 or 2 i) Graphs of Functions ---- 1 or 2 3) GEOMETRY (7-9 Q’s opx.) a) Lines and Angles ----...
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cut by a transversal, the lengths of the six resulting segments satisfy Menelaus' theorem. The Triangle Inequality Theorem states that the sum of any 2... sides of a triangle must be greater than the measure of the third side. In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is a relation inEuclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states: In any right-angled triangle, the area of the square whose side is the hypotenuse (the...
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What is the quadratic formula? 2. What is it used for? 3. Provide an example, not found in the text. RESPONSE Many people may... have heard of the quadratic formula, but are probably unfamiliar what it is or what it is used for. The actual quadratic formula is , and its purpose is to solve quadratic equations and can only be applied to a quadratic equation that is in the standard form of (ax2+ bx +c = 0).It is important to differentiate between a quadratic formula and a quadratic equation...
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angle of elevation of the sun when the shadow of a pole ‘h’ meters high is 3 h m. long is… A) 30° B) 45° C) 60° D) 90° 2. The perimeter of a triangle... with vertices (0,4), (0,0) and (3,0) is … A) 5 B) 7 C) 11 D) 12 2 3. The roots of a quadratic equation 2 x -kx+k=0 are equal. The value of ‘k’ is … A) 0 only B) 4 C) 8 only D) 0 and 8 4. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is … A) 3:4 B) 4:3 C) 9:16 D) 16:9 5. If the common difference...
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