...The Cartesian Plane Before the end of the European Renaissance, math was cleanly divided into the two separate subjects of geometry and algebra. You didn't use algebraic equations in geometry, and you didn't draw any pictures in algebra. Then, around 1637, a French guy named René Descartes (pronounced "ray-NAY day-CART") came up with a way to put these two subjects together. Rene Descartes was born on March 31, 1596, in Touraine, France. He was entered into Jesuit College at the age of eight, where he studied for about eight years. Although he studied the classics, logic and philosophy, Descartes only found mathematics to be satisfactory in reaching the truth of the science of nature. He then received a law degree in 1616. Thereafter, Descartes chose to join the army and served from 1617-1621. Descartes resigned from the army and traveled extensively for five years. During this period, he continued studying pure mathematics. Finally, in 1628, he devoted his life to seeking the truth about the science of nature. At that point, he moved to Holland and remained there for twenty years, dedicating his time to philosophy and mathematics. During this time, Descartes had his work "Meditations on First Philosophy" published. It was in this work that he introduced the famous phrase "I think, therefore I am." Descartes hoped to use this statement to find truth by the use of reason. He sought to take complex ideas and break them down into simpler ones that were clear...
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...Algebraic Identities Boolean Addition and Subtraction Complementary Gates (NOT) Boolean complementation finds equivalency in the form of the NOT gate, or a normallyclosed switch or relay contact: Topic Notes: • Boolean addition is equivalent to the OR logic function, as well as parallel switch contacts. • Boolean multiplication is equivalent to the AND logic function, as well as series switch contacts. • Boolean complementation is equivalent to the NOT logic function, as well as normallyclosed relay contacts. 1 Boolean algebraic identities The algebraic identity of x + 0 = x tells us that anything (x) added to zero equals the original ”anything,” no matter what value that ”anything” (x) may be. Like ordinary algebra, Boolean algebra has its own unique identities based on the bivalent states of Boolean variables. The first Boolean identity is that the sum of anything and zero is the same as the original ”anything.” This identity is no different from its real-number algebraic equivalent: No matter what the value of A, the output will always be the same: when A=1, the output will also be 1; when A=0, the output will also be 0. The next identity is most definitely different from any seen in normal algebra. Here we discover that the sum of anything and one is one: Next, we examine the effect of adding A and A together, which is the same as connecting both inputs of an OR gate to each other and activating them with the same signal: Introducing the uniquely Boolean...
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...History of algebra The history of algebra began in ancient Egypt and Babylon, where people learned to solve linear (ax = b) and quadratic (ax2 + bx = c) equations, as well as indeterminate equations such as x2 + y2 = z2, whereby several unknowns are involved. The ancient Babylonians solved arbitrary quadratic equations by essentially the same procedures taught today. They also could solve some indeterminate equations. The Alexandrian mathematicians Hero of Alexandria and Diophantus continued the traditions of Egypt and Babylon, but Diophantus's book Arithmetica is on a much higher level and gives many surprising solutions to difficult indeterminate equations. This ancient knowledge of solutions of equations in turn found a home early in the Islamic world, where it was known as the "science of restoration and balancing." (The Arabic word for restoration, al-jabru,is the root of the word algebra.) In the 9th century, the Arab mathematician al-Khwarizmi wrote one of the first Arabic algebras, a systematic exposé of the basic theory of equations, with both examples and proofs. By the end of the 9th century, the Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities of algebra and solved such complicated problems as finding x, y, and z such that x + y + z = 10, x2 + y2 = z2, and xz = y2. Ancient civilizations wrote out algebraic expressions using only occasional abbreviations, but by medieval times Islamic mathematicians were able to talk about arbitrarily...
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...Algebra 1: Simplifying Algebraic Expressions Lesson Plan for week 2 Age/Grade level: 9th grade Algebra 1 # of students: 26 Subject: Algebra Major content: Algebraic Expressions Lesson Length: 2 periods of 45 min. each Unit Title: Simplifying Algebraic Expressions using addition, subtraction, multiplication, and division of terms. Lesson #: Algebra1, Week 2 Context This lesson is an introduction to Algebra and its basic concepts. It introduces the familiar arithmetic operators of addition, subtraction, multiplication, and division in the formal context of Algebra. This lesson includes the simplification of monomial and polynomial expressions using the arithmetic operators. Because the computational methods of variable quantities follows from the computational methods of numeric quantities, then it should follow from an understanding of basic mathematical terminology including the arithmetic operators, fractions, radicals, exponents, absolute value, etc., which will be practiced extensively prior to this lesson. Objectives • Students will be able to identify basic algebraic concepts including: terms, expressions, monomial, polynomial, variable, evaluate, factor, product, quotient, etc. • Students will be able to simplify algebraic expressions using the four arithmetic operators. • Students will be able to construct and simplify algebraic expressions from given parameters. • Students will be able to evaluate algebraic expressions. • Students...
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...1. Specify the scope of the planning and its time frame. 2. For the present situation, develop a clear understanding that will serve as the common departure point for each of the scenarios. 3. Identify predetermined elements that are virtually certain to occur and that will be driving forces. 4. Identify the critical uncertainties in the environmental variables. If the scope of the analysis is wide, these may be in the macro-environment, for example, political, economic, social, and technological factors (as in PEST). 5. Identify the more important drivers. One technique for doing so is as follows. Assign each environmental variable two numerical ratings: one rating for its range of variation and another for the strength of its impact on the firm. Multiply these ratings together to arrive at a number that specifies the significance of each environmental factor. For example, consider the extreme case in which a variable had a very large range such that it might be rated a 10 on a scale of 1 to 10 for variation, but in which the variable had very little impact on the firm so that the strength of impact rating would be a 1. Multiplying the two together would yield 10 out of a possible 100, revealing that the variable is not highly critical. After performing this calculation for all of the variables, identify the two having the highest significance. 6. Consider a few possible values for each variable, ranging between extremes while avoiding highly improbable values...
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...Monomials and Polynomials A monomial is a number, a variable, or a product of numbers and variables raised to natural number powers. Examples of monomials: [pic] The degree of monomial is the sum of the exponents of the variables. If the monomial has only one variable, its degree is the exponent of that variable. The number in a monomial is called the coefficient of the monomial. Determine whether the expression is a polynomial. If it is, state how many terms and variables the polynomial contains and its degree. a. 9y2 + 7y + 4 b. 7x4 – 2x3y2 + xy – 4y3 c. [pic] Solution a. The expression is a polynomial with three terms and one variable. The term with the highest degree is 9y2, so the polynomial has degree 2. b. The expression is a polynomial with four terms and two variables. The term with the highest degree is 2x3y2, so the polynomial has degree 5. c. The expression is not a polynomial because it contains division by the polynomial x + 4. multiply monomials [pic][pic][pic][pic] [pic][pic] [pic][pic][pic] multiply polynomials [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] Product of a Sum and Difference [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] Division by a Monomial [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] Factoring [pic] [pic] [pic] [pic] [pic] [pic] Factoring Trinomial [pic] [pic] [pic] [pic] [pic] ...
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...[pic] Aguirre, Jedidiah Joel C. 55 Doña Feliza Subd. Brgy Paciano, Calamba City Mobile Number: 0926-7368277 Email Ad: jed_aguirre@yahoo.com Objectives To acquire an exciting and challenging job as Mathematics High School Tutor. Experiences 3rd Year High School : Quarterly Remedial Class Instructor in Mathematics 3 (Geometry) : Personal Tutorial Sessions for Mathematics 2 (Intermediate Algebra) 4th Year High School : Quarterly Remedial Class Instructor in Mathematics 4 (Advanced Algebra and Trigonometry) Summer, 2009 :Personal Tutorial Sessions for Math-UPCAT. 2nd Semester, 2010 :Literacy Training Service 2: Kalayaan Elementary School Grade 6 Mathematics Teacher 1st Semester, 2011 :Tutor in Princeton Academy, BelAir, Sta. Rosa, Laguna 2nd Semester, 2011 : Student-instructor in UPLB Math Division’s Think Tank Toe Achievements Elementary School : 3rd Place: Metrobank-MTAP-DepEd NCR Math Challenge Sectoral Level 10th Place: Metrobank-MTAP-DepEd NCR Math Challenge Regional Level Best in Math, Valedictorian High School : Best in Math (3rd Year and 4th Year), Best in Physics (4th year), 1st place, 2008 Math Masters, Meycauayan College. College 1st Semester, AY 08-09 : 4th Placer, UPLB Math Wizard College Scholar 2nd Semester, AY 08-09 : Participant, 36th Annual Nationwide Search For...
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...Mathematisch-statistische Ansätze zur Aktienkursprognose Seite 1 1 1.1 Einführung Ziel der Arbeit Ziel dieser Arbeit ist die Einordnung, Darstellung, Erläuterung und Bewertung mathematisch-statistischer Verfahren zur Aktienkursprognose. In diesem Zusammenhang werden hierzu neben dem Fokus auf die Prognose von Aktienkursen bzw. -renditen auch die methodologischen Rahmenbedingungen der zugehörigen Finanzmarkttheorie sowie die grundsätzlichen Probleme bei der Anwendung von Prognoseverfahren auf Aktienkurszeitreihen angesprochen. 1.2 Einordnung der Thematik in den aktuellen Forschungsstand Verfahren zur Prognose von Aktienkursen werden schon seit Bestehen von Börsen und anderen Handelsplätzen diskutiert. Somit hat das Thema dieser Arbeit seine ideellen Wurzeln in der von Charles H. Dow begründeten Lable Dow Theorie, die die Technische Aktienanalyse um 1900 begründete. Durch die ab 1965 von Eugene F. Fama proklamierten Thesen informationseffizienter Kapitalmärkte, nach der technische Aktienanalysen wirkungslos sind, erlebte die Kursprognose einen ersten Rückschlag. Die Thematik dieser Arbeit ist der Technischen Aktienanalyse zuzuordnen – nicht zuletzt wurde aber genauso Kritik an den Thesen informationseffizienter Kapitalmärkte geübt, sodass sich diese Antithese in neuerer Zeit verweichlicht hat. Die empirische Kapitalmarktforschung bemüht in letzter Zeit Ansätze des Forschungsgebietes der Behavioral Finance, die versuchen, diese Thesen und real beobachtbare...
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...y=2x, Graph 1.2. Also, label the x-values of the intersections with the line y=x as they appear from left to right on the x-axis as a1 and a2; label the x-values of the intersections with the line y=2x as b1 and b2. Now, I will using the graph and graph calculator, find the values of a1-b1 and b2-a2 and name them respectively SL and SR. SL=a1-b1=2.381966-1.763932=0.618034 SR=b2-a2=6.236068-4.618034=1.618034 Now, calculate the quantity D= │SL-SR│ D= │SL-SR│=│0.618034-1.618034│=1 By algebra calculation, D=│SL-SR│ =│ a1-b1-(b2-a2) │ =│ a1-b1-b2+a2 │ =│ (a1+ a2 )-(b1+b2) │ Now, I will try other parabolas of the form y=ax2+bx+c, a＞0, with vertices in quadrant 1, intersected by the lines y=x and y=2x. y=x2+2x+1 [pic] From the graph we can see there is no intersection of the parabola and y=x, y=2x. Using the algebra way: Solve: (a) x2+2x+1=x (b) x2+2x+1=2x (a) x2+2x+1=x x2+x+1=0 [pic] X=[pic] a1+a2= 1 (b) x2+2x+1=2x x2+1=0 x2=-1 x=±i b1+b2=0 so D =│ (a1+ a2 )-(b1+b2) │ =│ 1-0 │ =1 y=2x2+3x-1 D=│(a1+a2)-(b1+b2)│ =│(-1.366025+0.366025)+(-1+0.5)│ =│-1+0.5│ =0.5 Base on the example above, I think D is relate with the coefficient of the formula, and I guess it’s D=[pic]...
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...LAB 3.1 Variable Name | Problem (Y or N) | If Yes, what’s wrong? | Declare Real creditsTaken | No | | Declare Int creditsLeft | Yes | The variable should be declared as Real so it can indicate decimal values | Declare Real studentName | Yes | The variable should be a String to store text | Constant Real creditsNeeded = 90 | No | | Step 2: The calculation should be “creditsLeft = creditsNeeded – creditsTaken” Step 3: “The student’s name is Nolan Owens” Step 4: “The Network Systems Administration degree is awarded after 90 credits and Nolan Owens has 70 left to take before graduation.” Step 5: 1. //Provide documentation on line 2 of what this program does 2. //This program calculates how many credits a student still needs to graduate the NSA program 3. //Declare variables on lines 4, 5, 6, and 7 4. Declare Real creditsTaken = 0 5. Declare Real creditsLeft = 0 6. Declare String studentName = “NO VALUE” 7. Declare Constant Real creditsNeeded = 90 8. //Ask for user input of studentName and creditsTaken on line 9 - 12. 9. Display “What is the student’s name?” 10. User input = studentName 11. Display “How many credits does the student have?” 12. User input = creditsTaken 13. //Calculate remaining credits on line 14 14. creditsLeft = creditsNeeded – creditsTaken 15. //Display student name and credits left on line 16 and 17 16. Display “The student’s name is “, studentName 17. Display “They require “, creditsLeft...
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...SEEMA KHEKARE1 and SUJATHA JANARDHAN2 1Department of Applied Mathematics, G.H.Raisoni. Inst. of Engg. & Tech. for Women, Nagpur. E-mail: seema.ssk83@yahoo.in 2Department of Mathematics, St. Francis De Sales College, Nagpur. E-mail: sujata_jana@yahoo.com Abstract: In this paper, we formulate and analyze a vector host epidemic model with non-monotonic incidence rates for vector and host both. We investigate the existence and stabilities of disease free equilibrium and endemic equilibrium. We prove that the disease reach to endemic state for the basic reproduction number greater than one the only possible equilibrium for basic reproduction number less than one is disease free equilibrium. We present numerical simulation to justify the theoretical results. Key words: vector borne disease, basic reproduction number, disease free equilibrium, endemic equilibrium, stability. 1 Introduction Parasites, viruses, or bacteria are transmitted by flies, mosquitoes, water snails, ticks and some other vectors amongst animals or people and cause the vector borne diseases such as dengue, malaria, yellow fever, West Nile fever, etc. Statement of WHO on World Health Day: Preventing vector born diseases shows that more than one billion people are infected and more than one million die from vector-borne diseases every year. WHO also highlights that vector born diseases are totally avoidable. Vector-borne diseases mostly invade the poorest population having lack of sanitation, safe drinking water...
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...MYKA E. AUTRIZ BSBM 101 B CHAPTER II SET OF NUMBERS Although the concepts of set is very general, important sets, which we meet in elementary mathematics, are set of numbers. Of particular importance is the set of real numbers, its operations and properties. NATURAL NUMBERS are represented by the set of counting numbers or real numbers. EXAMPLES: 6, 7.8.9.10.11.12.13.14.15.16.17, 18, 19, 20…………………. WHOLE NUMBERS are represented by natural numbers including zero. EXAMPLES: 1, 2, 3, 50, 178, 2, 856, and 1,000,000 INTEGERS are negative and positive numbers including zero. EXAMPLES: -4, -3, -2, -1, 0, 1, 2, 3, 4…………………….. RATIONAL NUMBERS are exact quotient of two numbers, which are set of integers, terminating decimals, non-terminating but repeating decimals, and mixed numbers. EXAMPLES: 4/5, -5/2, 8, 0.75, 0.3 IRRATIONAL NUMBERS EXAMPLES: 3, 11/4, -7, 5/8, 2.8 ABSOLUTE VALUE of number is positive (or zero). The absolute value of a real numbers x is the undirected distance between the graph of x and the origin. EXAMPLES: /7/-/3/ solution /7/-/3/=7-3=4 and /-8/-/-6/=8-6=2 OPERATIONS ON INTEGERS ADDITION SUBTRACTION MULTIPLICATION DIVISON 9+5=14 9 - -5=14 -45x8=-360 -108÷9=-12 -15+5=10 23 - -4=27 -8+-5=-13 -89 -136=-225 -13+20=7 ...
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...THE ACCOUNTING REVIEW Vol. 88, No. 2 2013 pp. 463–498 American Accounting Association DOI: 10.2308/accr-50318 Managerial Ability and Earnings Quality Peter R. Demerjian Emory University Baruch Lev New York University Melissa F. Lewis University of Utah Sarah E. McVay University of Washington ABSTRACT: We examine the relation between managerial ability and earnings quality. We find that earnings quality is positively associated with managerial ability. Specifically, more able managers are associated with fewer subsequent restatements, higher earnings and accruals persistence, lower errors in the bad debt provision, and higher quality accrual estimations. The results are consistent with the premise that managers can and do impact the quality of the judgments and estimates used to form earnings. Keywords: managerial ability; managerial efficiency; earnings quality; accruals quality. Data Availability: Data are publicly available from the sources identified in the text. I. INTRODUCTION W e examine the relation between managerial ability and earnings quality. We anticipate that superior managers are more knowledgeable of their business, leading to better judgments and estimates and, thus, higher quality earnings.1 Alternatively, the benefit We thank two anonymous reviewers, Asher Curtis, Patty Dechow, Ilia Dichev, Weili Ge, Marlene Plumlee, Phil Shane, Terry Shevlin, Wayne Thomas (editor), Ben Whipple, and workshop participants at the 2010 Kapnick Accounting Conference...
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...MM150 Prof. Mowen May 21, 2011 INTRODUCTION This paper is on what kind of math I will be using in my chosen profession. My chosen profession is the paralegal profession. I know that I will not need to know a lot of math for this profession. As a paralegal professional I will be using math every day. I will be using math for everything from keeping track of billable hours to estimating damages in a lawsuit. I will need to know basic math, basic algebra, and first year algebra. Basic math and basic algebra consists of addition, subtraction, multiplication, fractions, decimals, percentages, and negative numbers (www.xpmath.com). First year algebra consists of using formulas (www.xpmath.com). In this paper I will explain in detail the math that I would use in the four different types of law offices for a paralegal professional that I am interested in. These types of law offices are family law, civil litigation, probate and estate law, and criminal law. Family Law In a family law office I would use basic math and first year algebra. I would be using addition, subtraction, multiplication, division, and a formula set by the courts to calculate child support and spousal support payments. I also would be using addition, subtraction, multiplication, and division to figure out how much the marital property is worth and how much each party would get if the clients decide to sell the property and split the value of the property. I would also use addition and multiplication to calculate...
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...| | | Domains of Rational Expressions The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. It is the set of all real numbers for which a function is mathematically defined. The denominator can not be zero because, nothing can be divided by zero and remain a real number. The first letter of my names starts with a "T" so these are the rational expressions that I'll be solving: 1 - x^2 and 2b - 2 x 2b^2- 8 1 - x^2 This is the first given expression. Since we know that denominator is the valuable, x can not equal zero be because it will make the expression undefined, but any x other real number will solve the expression. x = 0 The zero is the excluded value. We can see that the domain for this expression is a set of all real numbers where zero is excluded from the value. The expression is written like this:D = {x| x € R b ≠ 0}. For the second...
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