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Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as 5 (an integer), 3/4 (a rational number that is not an integer), 8.6 (a rational number expressed in decimal representation), and π (3.1415926535..., an irrational number). As a subset of the real numbers, the integers, such as 5, express discrete rather than continuous quantities. Complex numbers include real numbers as a special case. Real numbers can be divided into rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two. A real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue indefinitely. The real numbers are sometimes thought of as points on an infinitely long line called the number line or real line. History

Vulgar fractions had been used by the Egyptians around 1000 BC; the Vedic "Sulba Sutras" ("The rules of chords") in, ca. 600 BC, include what may be the first 'use' of irrational numbers. The concept of irrationality was implicitly accepted by early Indian mathematicians since Manava (c. 750–690 BC), who were aware that the square roots of certain numbers such as 2 and 61 could not be exactly determined. Around 500 BC, the Greek mathematicians led by Pythagoras realized the need for irrational numbers, in particular the irrationality of the square root of 2. The Middle Ages saw the acceptance of zero, negative, integral and fractional numbers, first by Indian and Chinese mathematicians, and then by Arabic mathematicians, who were also the first to treat irrational numbers as algebraic objects, which was made possible by the development of algebra. Arabic mathematicians merged the concepts of "number" and "magnitude" into a more general idea of real numbers. The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c. 850–930) was the first to accept irrational numbers as solutions...

...of RealNumbers
The numbers used to measure real-world quantities such as length, area, volume, speed, electrical charges, probability of rain, room temperature, gross national products, growth rates, and so forth, are called realnumbers. They include such number as , , , , , , , and .
The basic algebraic properties of the realnumbers can be expressed in terms of the two fundamental operations of addition and multiplication.
Basic Algebraic Properties:
Let and denotes realnumbers.
(1) The Commutative Properties
(a) (b)
The commutative properties says that the order in which we either add or multiplication realnumber doesn’t matter.
(2) The Associative Properties
(a) (b)
The associative properties tells us that the way realnumbers are grouped when they are either added or multiplied doesn’t matter. Because of the associative properties, expressions such as and makes sense without parentheses.
(3) The Distributive Properties
(a) (b)
The distributive properties can be used to expand a product into a sum, such as or the other way around, to...

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Real World Radical Formulas
Janeth Mendiola
MAT222: Intermediate Algebra
Instructor Lalla Thompson
March 21, 2014
Real World Radical Formulas
Radical formulas are used in the real world in the fields such as finance, medicine, engineering, and physics to name a few. In the finance department they use it to find the interest, depreciation and compound interest. In medicine it can be used to calculate the Body Surface of an adult (BSA), in engineering it can be used to measure voltage. These formulas are vital and important not only in algebra but also as we can see in our day-to-day lives. This assignment requires that we find the capsizing screening value for the Tartan 4100, solve the formula for variable of d, and find the displacement in which the Tartan 4100 is safe for ocean sailing. The problem is broken down into three parts. The utilization of formulas will be used.
The problem and work will be on the left hand side and a description will be to the right of the work describing the steps taken to solve this assignment. The following words will be bold throughout the assignment to indicate that there is a clear understanding of their definition and use: radical, root, and variable. The assignment requires solving problem 103 on page 605 of our reading material. With the given information we will solve three different parts using the information given and using radical...

...result just obtained (the first term of the eventual quotient). Write the result under the first two terms of the dividend (x2 · (x − 3) = x3 − 3x2).
3. Subtract the product just obtained from the appropriate terms of the original dividend (being careful that subtracting something having a minus sign is equivalent to adding something having a plus sign), and write the result underneath ((x3 − 12x2) − (x3 − 3x2) = −12x2 + 3x2 = −9x2) Then, "bring down" the next term from the dividend.
4. Repeat the previous three steps, except this time use the two terms that have just been written as the dividend.
5. Repeat step 4. This time, there is nothing to "pull down".
The polynomial above the bar is the quotient q(x), and the number left over (−123) is the remainder r(x).
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Applications
Factoring polynomials
Sometimes one or more roots of a polynomial are known, perhaps having been found using the rational root theorem. If one root r of a polynomial P(x) of degree n is known then polynomial long division can be used to factor P(x) into the form (x - r)(Q(x)) where Q(x) is a polynomial of degree n–1. Q(x) is simply the quotient obtained from the division process; since r is known to be a root of P(x), it is known that the remainder must be zero.
Likewise, if more than one root is known, a linear factor (x – r) in one of them (r) can be divided out to obtain Q(x), and then a linear term in...

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This file MAT 222 Week 3 Assignment Real World Radical Formulas contains solutions to the following tasks: 1.103. Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 (www.sailing.com). For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function. a).Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet. b). Solve the equation for d. 2.104. Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the function a)Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. b) Write d in terms of A and S.
Mathematics - Algebra
Real World Radical Formulas . Read the following instructions in order to complete this assignment:
a. Solve parts a and b of problem 103 on page 605 and problem 104 on page 606 of Elementary and Intermediate Algebra .
b. 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:
§ An explanation of what the parts of the formula mean before...

...The smallest integer that can be expressed as the sum of the cubes of two other integers in two different ways. 1729 = 93 + 103 = 13 + 123. (This was the subject of a very famous mathematical anecdote involving Srinivasa Ramanujan and G.H. Hardy, circa 1917. See A Mathematician's Apology by Hardy.
Rank, Prime number, Found by, Found date, Number of digits
1st, 257,885,161 − 1, GIMPS, 2013 January 25, 17,425,170 2nd, 243,112,609 − 1, GIMPS, 2008 August 23, 12,978,189
3rd, 242,643,801 − 1, GIMPS, 2009 April 12, 12,837,064 4th, 237,156,667 − 1, GIMPS, 2008 September 6, 11,185,272
5th, 232,582,657 − 1, GIMPS, 2006 September 4, 9,808,358 6th, 230,402,457 − 1, GIMPS, 2005 December 15, 9,152,052
7th, 225,964,951 − 1, GIMPS, 2005 February 18, 7,816,230 8th, 224,036,583 − 1, GIMPS, 2004 May 15, 7,235,733
9th, 220,996,011 − 1, GIMPS, 2003 November 17, 6,320,430 10th, 213,466,917 − 1, GIMPS, 2001 November 14, 4,053,946
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History
The following table lists the progression of the largest known prime number in ascending order. Here Mn= 2n − 1 is the Mersenne number with exponent n.[4]
Number, Digits, Year found
M127, 39, 1876 180×(M127)2 + 1, 79, 1951 M521, 157, 1952 M607, 183, 1952 M1279, 386, 1952 M2203, 664, 1952 M2281, 687, 1952 M3217, 969, 1957 M4423, 1332, 1961 M9689,...

...Polynomial
The graph of a polynomial function of degree 3
In mathematics, polynomials are the simplest class of mathematical expressions (apart from the numbers and expressions representing numbers). A polynomial is an expression constructed from variables (also called indeterminates) and constants (usually numbers, but not always), using only the operations of addition, subtraction, multiplication, and non-negative integer exponents (which are abbreviations for several multiplications by the same value). However, the division by a constant is allowed, because the multiplicative inverse of a non-zero constant is also a constant. For example, x2 − x/4 + 7 is a polynomial, but x2 − 4/x + 7x3/2 is an algebraic expression that is not a polynomial, because its second term involves a division by the variable x (the term 4/x), and also because its third term contains an exponent that is not a non-negative integer (3/2).
A polynomial function is a function which is defined by a polynomial. Sometimes, the term polynomial is reserved for the polynomials that are explicitly written as a sum (or difference) of terms involving only multiplications and exponentiation by non negative integer exponents. In this context, the other polynomials are called polynomial expressions. For example, is a polynomial expression that represents the same thing as the polynomial The term "polynomial", as an adjective, can also be used for quantities that can...

...In mathematics, a realnumber is a value that represents a quantity along a continuous line. The realnumbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Realnumbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any realnumber can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include realnumbers as a special case.
These descriptions of the realnumbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the realnumbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently...

...Zach Snider
Investigative Task:
SPREAD OF DISEASE – The Task
Disease can spread quickly without use of universal precautions. Suppose the spread of a direct contact disease in a stadium is modeled by the exponential equation P(t) = 10,000/(1 + e3-t) where P(t) is the total number of people infected after t hours. (Use the estimate for e (2.718) or the graphing calculator for e in your calculations.)
1. Estimate the initial number of people infected with the disease. Show how you found your answer.
Answer: A total of 474 people would be initially infected.
Equation: p(0)=10,000/(1+3^3) ~ 474.26
2. Assuming the disease does not present symptoms for 24 hours, how many people will have been infected after 3 hours? Show how you found your answer.
Equation: Substitute 3 hours for the time.
Answer: About 5,000 people would be infected in a mere 3 hours.
3. What is the maximum number of people who can become infected? (Note: e(3-t) will approach 0 for very large values of t).
The maximum number of people who could become infected is 10,000.
4. Explain why your answer for Question #3 is the maximum.
Because when you graph the equation you can see it only reaches 10,000.
5. The stadium needs to warn its guests about a rapid disease spread if it affects over 800 people. After how many minutes should the stadium inform its guests of the disease? Show how you found...