Week Five Assignment-Pythagorean Quadratic MATT 221-Intro to Algebra Instructor Sharon Giles Saturday‚ March 15‚ 2014 This fifth and final week deals with the Pythagorean Quadratic. It comes from page 371 of the text as a matter of fact. It is number 98. The name of this particular problem is Buried treasure. The two key figures of the problem are Ahmed and Vanessa. The backdrop of this story is that they are searching for buried treasure and they each have half 0f he
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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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The Pythagorean Scale a mathematical method that is used to create all the notes of the musical scale from the harmonic series; this scale is called the Pythagorean Scale. The naturally happening harmonics are whole number multiples. To get the other notes of the scale‚ we must use fractions. The harmonic series gives us the ability to create periods of time of perfect 5ths‚ the ratio of 3/2f‚ "f" being the starting frequency. By using these 5ths‚ we can create the pythagorean scale. We can
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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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The four color theorem is a mathematical theorem that states that‚ given a map‚ no more than four colors are required to color the regions of the map‚ so that no 2 regions that are touching (share a common boundary) have the same color. This theorem was proven by Kenneth Appel and Wolfgang Haken in 1976‚ and is unique because it was the first major theorem to be proven using a computer. This proof was first proposed in 1852 by Francis Guthrie when he was coloring the counties of England and realized
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1 10/10/01 Fermat’s Little Theorem From the Multinomial Theorem Thomas J. Osler (osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2
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Kirchhoff’s Law Kirchhoff’s current law (KCL) imposes constraints on the currents in the branches that are attached to each node of a circuit. In simplest terms‚ KCL states that the sum of the currents that are entering a given node must equal the sum of the currents that are leaving the node. Thus‚ the set of currents in branches attached to a given node can be partitioned into two groups whose orientation is away from (into) the node. The two groups must contain the same net current. In general
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“The Arrow impossibility theorem and its implications for voting and elections” Arrow’s impossibility theorem represents a fascinating problem in the philosophy of economics‚ widely discussed for insinuating doubt on commonly accepted beliefs towards collective decision making procedures. This essay will introduce its fundamental assumptions‚ explain its meaning‚ explore some of the solutions available to escape its predictions and finally discuss its implications for political
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Geometry Definitions‚ Postulates and Theorems Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Same-side interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement
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a NOR gate. DeMorgan’s theorems state the same equivalence in "backward" form: that inverting the output of any gate results in the same function as the opposite type of gate (AND vs. OR) with inverted inputs De Morgan’s theorem is used to simplify a lot expression of complicated logic gates. For example‚ (A + (BC)’)’. The parentheses symbol is used in the example. _ The answer is A BC. Let’s apply the principles of DeMorgan’s theorems to the simplification of
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