Methods of computing square roots

original work from Al-Karaji had lost, the later Persian mathematician Khayyam (1048-1122) referred Al-Karaji’s work about Pascal’s Triangle and uses it to find the nth roots according to the binomial expansion. Also around 11th century, Chinese mathematician Jia Xian (1010-1070) used Pascal’s Triangle to extract square roots and cube roots – more details will be mentioned later in this paper. He wrote down his discovery in the book Shi Shuo Suan Shu [The key to Mathematics]. Although the…

Acoustic Transponders Three main acoustic positioning systems (Fig. 3) used for localization of AUVs are introduced and discussed. They are short baseline (SBL) systems, ultra-short baseline (USBL) systems and long baseline (LBL) systems. The transponders of SBL and USBL systems are deployed on a anchored ship or pier before the start of mission. LBL systems require transponders to be mounted on the seafloor before localizing AUVs. These three acoustic positioning systems are stated as below. 1)…

and apply what has been learned, identify connections to other areas of work and be able to draw on their ideas to interpret/ explain their results and methods. Explore and Question – Pupils should be shown how to explore maths and look for patterns and question underlying concepts by being able to discuss and think through their ideas and methods putting them into real-life context. Differentiation – In order for all pupils to access the learning, feel challenged and supported, the work…

Testing the Validity of the Approach of Using Hydrogen and Helium Emission Spectra with the Rydberg Equation to Determine the Ionization Energy of Helium Michelle Plavnik Department of Chemistry, Emory University, Atlanta, GA, 30322, United States PAGE 2 ABSTRACT: The purpose of this lab is to determine how accurate the Rydberg equation is at modeling helium transitions and finding the ionization energy from those transitions. To accomplish this aim, the spectra of hydrogen and helium were…

15-9 The stand-alone cost-allocation method uses information pertaining to each user of a cost object as a separate entity to determine the cost-allocation weights. The incremental cost-allocation method ranks the individual users of a cost object in the order of users most responsible for the common costs and then uses this ranking to allocate costs among those users…

At the beginning of the period, the price of Computers, Inc. divided by the industry index was 0.39; by the end of the period, the ratio had increased to 0.50. As the ratio increased over the period, it appears that Computers, Inc. outperformed other firms in its industry. The overall trend, therefore, indicates relative strength, although some fluctuation existed during the period, with the ratio falling to a low point of 0.33 on day 19. 18. Five day moving averages: Days 1 – 5: (19.63 + 20 +…

Unfortunately, some companies have mismanaged their greatest asset—their brands. This is what befell the popular Snapple brand almost as soon as Quaker Oats bought the beverage marketer for $1.7 billion in 1994. Snapple had become a hit through powerful grassroots marketing and distribution through small outlets and convenience stores. Analysts said that because Quaker did not understand the brand’s appeal, it made the mistake of changing the ads and the distribution. Snapple lost so much…

or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Solutions Manual Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRRNX-20 = 20.34% The IRR criteria implies accepting the NX-20. c. The profitability index is the present value of all subsequent cash flows, divided by the initial investment, so the profitability index of…