bernoulli’s theorem ABSTRACT / SUMMARY The main purpose of this experiment is to investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tape red duct and to measure the flow rate and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The apparatus used is Bernoulli’s Theorem Demonstration Apparatus‚ F1-15. In this experiment‚ the pressure difference taken is from h1- h5. The
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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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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 states
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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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A Friend in Need is a Friend indeed Essay There is nothing better than surrounded by good friends. You may look at some people and their friends with envy as they chat away happily and participate in activities together. It may be hard to figure out which friends are better when considering the friends who can have fun with and the friends that can get help from. From my perspective‚ the people who are willing to help me in the crisis time are much more cherished than who just want to stay with
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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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art of paper folding. It’s connected to the mathematics called geometry. When we fold origami we also create lots of surfaces. For instance‚ by folding a square piece of paper in half diagonally or from one tip to the opposite tip‚ we create two surfaces in the shape of triangles. Mathematicians’ related origami to a theorem called the Kawasaki theorem. The Kawasaki theorem states that if we add up the angle measurements of every angle around a point‚ the sum will be 180. It is a theorem giving
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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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