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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BINOMIAL THEOREM : AKSHAY MISHRA XI A ‚ K V 2 ‚ GWALIOR In elementary algebra‚ the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem‚ it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc‚ where the coefficient of each term is a positive integer‚ and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in the binomial expansion are known as binomial coefficients.
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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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Taylors Theorem: Taylor’s theorem gives an approximation of a n times differentiable function around a given point by a n-th order Taylor-polynomial. For analytic functions the Taylor polynomials at a given point are fixed order truncations of its Taylor’s series‚ which completely determines the function in some locality of the point. There are numerous forms of it applicable in different situations‚ and some of them contain explicit estimates on the approximation error of the function by its Taylor-polynomial
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Thomas Theorem A teacher believing a student is more intelligent than they really are could change the interaction between this student and the teacher in many ways. This student could see the teacher having faith in them and perhaps seeing something in them that they don’t see in themselves. It could cause the student to have higher self esteem by this teacher thinking positively about them. This could be detrimental to the student because other students could consider the extra attention
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FERMAT ’S LAST THEOREM I am going to do my project in the field of number theory. Number theory‚ a subject with a long and rich history‚ has become increasingly important because of its application to computer science and cryptography. The core topics of number theory are such as divisibility‚ highest common factor‚ primes‚ factorization‚ Diophantine equations and so on‚ among which I chose Diophantine equations as the specific topic I would like to go deep into. Fermat ’s Last Theorem
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The binomial theorem is a simplified way of finding the expansion of a binomial to a certain power. We can of course find the expanded form of any binomial to a certain power by writing it and doing each step‚ but this process can be very time consuming when you get into let’s say a binomial to the 10th power. Example: (x+y)^0=1 of course because anything to the power if 0 equal 1 (x+y)^1= x+y anything to a power of 1 is just itself. (x+y)^2= (x+y)(x+y) NOT x^2+y^2. So expand (x+y)(x+y)=x^2+xy+yx+y^2
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Experiment No. 1: Bernoulli’s Theorem Object: To verify Bernoulli’s theorem for a viscous and incompressible fluid. Theory: In our daily lives we consume a lot of fluid for various reasons. This fluid is delivered through a network of pipes and fittings of different sizes from an overhead tank. The estimation of losses in these networks can be done with the help of this equation which is essentially principle of conservation of mechanical energy. Formal Statement: Bernoulli’s Principle is
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Bernoulli’s Principle states that for an ideal fluid (low speed air is a good approximation)‚ with no work being performed on the fluid‚ an increase in velocity occurs simultaneously with decrease in pressure or a change in the fluid’s gravitational potential energy. This principle is a simplification of Bernoulli’s equation‚ which states that the sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is the same at any two points in that path. It is named after the
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Chinese remainder theorem The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by Chinese mathematician Sun Tzu. In its basic form‚ the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders. For example‚ what is the lowest number n that when divided by 3 leaves a remainder of 2‚ when divided by 5 leaves a remainder
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