Methods of computing square roots

Intro: Newtons Method: Haley F. / Andrew H. Newton’s Method, also known as Newton-Raphson method, is a method used for finding the zeros, roots or in more simple terms where any given function exactly crosses the x access. In calculus we may be presented with problems given that we cannot find a definite answer to, but we can use Newton’s Method to calculate a group of answers that get closer and closer to the actual solution. Newton’s Method has given the world of calculus a method of finding extremely refined educated guesses to once before impossible questions to answer. The numerical definition of Newton’s Method is defined as follows: If X1 is an initial guess for a solution to the equation f(x) = 0 , then Xn + 1 = − . If we are asked to f(Xn) f′(Xn) + Xn compute the √5 algebraically, without using a calculator, we can use newton 's method to get an approximate solution. First we know that the √5 is…

moment education is a big part of my life. I am still finishing up my time at high school. I say that because I feel like my high school is more of a prison than a school. I am required to go there work eight hours a day five days a week with a little twenty minute break for lunch. Honestly, school is a part time jail cell. Even though I do not like being forced to learn I still go, because I know what I achieve now will help me later. I know I have been told over and over I will use Algebra in…

Before the man even looked at him, he climbed onto the stage and began writing on the stone. “Can I clear a few things up?” he said. “The book, the title is written in Akkadian. It says, On Triangles, written by Sudines. And the spell? It’s a theorem that can find the length of the hypotenuse of any right triangle. It’s amazing, but it’s not witchcraft.” Using the chalk he sketched out two square frames, each filled with different shapes. “The square frames are equal in size, but there are…

Aim The aim of this assignment is to investigate the method to correct the power factor within an AC power generation system. Once the power factor is found we shall improve the power factor in said theoretical circuit by modifying the existing one and calculating the differences this makes to the output across the circuit as a whole. Then we shall use a circuit design software package to confirm our theoretical results and identify whether our improved mathematical skills have solved the task…

A gap-filling method was developed based on the Principal Component Analysis (PCA) method. PCA is a widely used dimensionality reduction method to find a new set of variables as linear combinations of original variables, capturing most of the observed variance in the original data (Storch and Zwiers, 2002). It has been used in various climate studies for decomposing dominant mode (Storch and Zwiers, 2002) and time-series gap-filling (Beckers and Rixen, 2003; Kondrashov et al., 2014). The…

Impulses delivered by the electrodes are typically very small, such that orthodromic action potentials are generated to cause coordinated muscle contraction (Popovic, Masani, and Micera, 2015). The impulses are typically delivered in trains, usually as biphasic balanced pulses to reduce the discomfort associated with sensory nerve stimulation (ibid). In developing a protocol, trial and error is required to maximize benefit to the patient and reduce adverse effect. Devices are either current-…

the experimental responses. Multi-criterion decision making method, TOPSIS has been employed for…

important information about the components of electrical activity—namely motor unit (MU) activation—during a muscle contraction (Cashaback, Cluff & Potvin, 2013). Observing electrical activity of a muscle with EMG is a user friendly and non-invasive tool researchers use when investigating muscle physiology (Camata et al., 2009). EMG is commonly used to correlate EMG signal with fatigue by identifying the EMG-force relationship (Ertl, Kruse & Tilp, 2016). Additionally, EMG is used as a means of…

When the state equation of a model is an autoregressive process with unknown constant coefficients, EnKF can be easily modified to include Monte Carlo estimation of the constant coefficients. We recall that the standard particle filtering method suffers from weight degeneracy especially when the estimation includes static parameters. EnKF, however, does not suffer from degeneracy and provides a good estimate of the coefficients by integrating a sample minimum mean square estimate (MMSE) of the…

programs continue to evolve pi. William L. Schaaf said, "Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi" (Wilson). The first approximations of pi came in ancient Egypt and ancient Babylonia where they attempted to derive pi for practical reasons. The Egyptians, in the Rhind papyrus (1650), computed pi to be 3.1604 (Book). The writer of the Rhind papyrus Ahmes wrote "Cut off 1/9 of a diameter and construct a square…