Datasets:
CASO2
/
finemath-cal

Dataset card Data Studio Files
xet
Community
1
url
stringlengths
6
1.61k
fetch_time
int64
1,368,856,904B
1,726,893,854B
content_mime_type
stringclasses
3 values
warc_filename
stringlengths
108
138
warc_record_offset
int32
9.6k
1.74B
warc_record_length
int32
664
793k
text
stringlengths
45
1.04M
token_count
int32
22
711k
char_count
int32
45
1.04M
metadata
stringlengths
439
443
score
float64
2.52
5.09
int_score
int64
3
5
crawl
stringclasses
93 values
snapshot_type
stringclasses
2 values
language
stringclasses
1 value
language_score
float64
0.06
1
http://lbartman.com/worksheet/math-activity-worksheets-for-middle-school.php
1,581,888,638,000,000,000
text/html
crawl-data/CC-MAIN-2020-10/segments/1581875141430.58/warc/CC-MAIN-20200216211424-20200217001424-00450.warc.gz
87,961,425
15,502
## lbartman.com - the pro math teacher • Subtraction • Multiplication • Division • Decimal • Time • Line Number • Fractions • Math Word Problem • Kindergarten • a + b + c a - b - c a x b x c a : b : c # Math Activity Worksheets For Middle School Public on 07 Oct, 2016 by Cyun Lee ### fun zombie graphing worksheet! 5th 6th 7th middle school Name : __________________ Seat Num. : __________________ Date : __________________ 1166 + 6946 = ... 9713 + 9260 = ... 8041 + 2446 = ... 3502 + 3349 = ... 4138 + 3207 = ... 5686 + 2052 = ... 7217 + 2152 = ... 6329 + 1588 = ... 8225 + 6450 = ... 1448 + 6677 = ... 8723 + 3914 = ... 7131 + 7854 = ... 2205 + 3374 = ... 4980 + 3088 = ... 1950 + 6313 = ... 8314 + 8673 = ... 2591 + 2525 = ... 2373 + 1544 = ... 9307 + 5297 = ... 4121 + 1176 = ... 8433 + 2340 = ... 9551 + 7398 = ... 4121 + 9985 = ... 8739 + 9631 = ... 9373 + 3498 = ... 4957 + 3865 = ... 6290 + 6135 = ... 7224 + 4386 = ... 2024 + 7918 = ... 4006 + 8600 = ... 7518 + 4142 = ... 9638 + 5894 = ... 4706 + 7067 = ... 9763 + 1258 = ... 6966 + 9409 = ... 5851 + 2578 = ... 4229 + 1790 = ... 4549 + 6509 = ... 1309 + 3010 = ... 4476 + 2906 = ... 4389 + 6833 = ... 1052 + 7079 = ... 2882 + 4295 = ... 2821 + 5825 = ... 1486 + 4028 = ... 1803 + 4616 = ... 9676 + 8600 = ... 5272 + 3608 = ... 5943 + 4866 = ... 2043 + 4754 = ... 1793 + 7549 = ... 6323 + 2122 = ... 8592 + 9245 = ... 6112 + 6294 = ... 7946 + 2337 = ... 8759 + 8856 = ... 6042 + 6969 = ... 1201 + 2135 = ... 4367 + 3503 = ... 1036 + 3163 = ... 3568 + 6759 = ... 8854 + 8601 = ... 5943 + 8917 = ... 3197 + 2034 = ... 7858 + 7508 = ... 8365 + 2873 = ... 7272 + 3182 = ... 5320 + 2740 = ... 6809 + 7634 = ... 5716 + 3740 = ... 7321 + 4592 = ... 3765 + 1560 = ... 8313 + 5982 = ... 5601 + 2403 = ... 4199 + 4108 = ... 3080 + 7128 = ... 7213 + 8197 = ... 8734 + 9905 = ... 2960 + 5647 = ... 3112 + 1200 = ... 7782 + 2808 = ... 5746 + 8110 = ... 6551 + 2594 = ... 3023 + 2404 = ... 5698 + 6199 = ... 8753 + 8617 = ... 5276 + 9840 = ... 3013 + 4541 = ... 2919 + 4142 = ... 7015 + 3326 = ... 3847 + 6961 = ... 2003 + 6017 = ... 8698 + 5002 = ... 9915 + 4248 = ... 2219 + 9061 = ... 7155 + 1990 = ... 9080 + 9929 = ... 9198 + 1061 = ... 7174 + 6179 = ... 2577 + 5737 = ... 6822 + 8707 = ... 9420 + 1226 = ... 9998 + 7819 = ... 2109 + 3689 = ... 8315 + 7822 = ... 2734 + 1817 = ... 2156 + 9271 = ... 2814 + 1175 = ... 8220 + 6302 = ... 9966 + 8713 = ... 1383 + 3778 = ... 2782 + 7295 = ... 6234 + 6504 = ... 3474 + 6532 = ... 2388 + 8115 = ... 4645 + 7115 = ... 5332 + 6978 = ... 7845 + 2157 = ... 8672 + 4544 = ... 7581 + 4226 = ... 1527 + 2804 = ... 7996 + 8691 = ... 9308 + 7234 = ... 1421 + 7565 = ... 3598 + 7501 = ... 5279 + 1790 = ... 2380 + 5821 = ... 1329 + 2315 = ... 7810 + 5474 = ... 4308 + 5909 = ... 7133 + 1522 = ... 5032 + 2674 = ... 3532 + 8980 = ... 4356 + 7311 = ... 4674 + 4835 = ... 7036 + 8727 = ... 8361 + 3236 = ... 6464 + 7542 = ... 1855 + 3720 = ... 8311 + 3144 = ... 6062 + 8045 = ... 9554 + 2308 = ... 6161 + 4644 = ... 4900 + 3380 = ... 5661 + 2639 = ... 4649 + 4130 = ... 8074 + 4602 = ... 8010 + 8727 = ... 6090 + 5325 = ... 4571 + 8879 = ... 1750 + 6983 = ... 9048 + 4861 = ... 6652 + 2591 = ... 1763 + 4900 = ... 3184 + 5436 = ... 2686 + 8817 = ... 5348 + 8213 = ... 1448 + 1200 = ... 1146 + 2497 = ... 5117 + 7563 = ... 3654 + 4062 = ... 4464 + 8347 = ... 4100 + 9676 = ... 3571 + 3202 = ... 1383 + 7419 = ... 1129 + 9955 = ... 3439 + 8871 = ... 3198 + 2229 = ... 2894 + 5763 = ... 9553 + 5789 = ... 2851 + 6769 = ... 8940 + 6312 = ... 6528 + 3228 = ... 9874 + 6737 = ... 8257 + 5903 = ... 8777 + 8347 = ... 4379 + 8754 = ... 5576 + 7797 = ... 8204 + 8418 = ... 2805 + 6830 = ... 6675 + 4049 = ... 4355 + 6605 = ... 2175 + 1043 = ... 7591 + 6208 = ... 2528 + 8635 = ... 3111 + 3839 = ... 5567 + 8978 = ... 9383 + 2163 = ... 6007 + 8456 = ... 4015 + 2646 = ... 9729 + 9804 = ... 6069 + 7648 = ... 5500 + 4459 = ... 5515 + 3100 = ... 2767 + 5236 = ... 8525 + 4079 = ... 9376 + 1195 = ... 7573 + 6904 = ... 7222 + 3385 = ... 1341 + 2527 = ... show printable version !!!hide the show ## RELATED POST Not Available ## POPULAR worksheet generated at www.math.com free fraction worksheet dividing decimals worksheet
1,757
4,410
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.046875
3
CC-MAIN-2020-10
latest
en
0.159903
http://oeis.org/A080953
1,511,192,699,000,000,000
text/html
crawl-data/CC-MAIN-2017-47/segments/1510934806070.53/warc/CC-MAIN-20171120145722-20171120165722-00040.warc.gz
216,821,198
4,986
This site is supported by donations to The OEIS Foundation. Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A080953 Weight distribution of [151,76,19] binary quadratic-residue (or QR) code. 1 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3775, 24915, 0, 0, 113250, 604000, 0, 0, 30256625, 133993625, 0, 0, 8292705580, 31097645925, 0, 0, 1302257122605, 4196161839505, 0, 0, 113402818847850, 317527892773980, 0 (list; graph; refs; listen; history; text; internal format) OFFSET 0,20 COMMENTS Taken from the Tjhai-Tomlinson web site. According to Boston and Hao, the Tjhai-Tomlinson web site gives several erroneous values, but their book with Ambroze, Ahmed, and Jibril gives correct values. - Eric M. Schmidt, Nov 17 2017 LINKS Nigel Boston and Jing Hao, The Weight Distribution of Quasi-quadratic Residue Codes, arXiv:1705.06413 [cs.IT], 2017. C. J. Tjhai and Martin Tomlinson, Weight Distributions of Quadratic Residue and Quadratic Double Circulant Codes over GF(2) [dead link] M. Tomlinson, C. J. Tjhai, M. A. Ambroze, M. Ahmed, M. Jibril, Error-Correction Coding and Decoding, Springer, 2017, p. 285. EXAMPLE The weight distribution is: i A_i 0 1 19 3775 20 24915 23 113250 24 604000 27 30256625 28 133993625 31 8292705580 32 31097645925 35 1302257122605 36 4196161839505 39 113402818847850 40 317527892773980 43 5706949034630250 44 14007965812274250 47 171469716029462700 48 371517718063835850 51 3155019195317144883 52 6067344606379124775 55 36274321608490644595 56 62184551328841105020 59 264765917968736096775 60 405974407552062015055 63 1241968201959417159800 64 1707706277694198594725 67 3778485133479463579225 68 4667540459004043244925 71 7503425412744902320620 72 8337139347494335911800 75 9763682329503348632684 76 9763682329503348632684 79 8337139347494335911800 80 7503425412744902320620 83 4667540459004043244925 84 3778485133479463579225 87 1707706277694198594725 88 1241968201959417159800 91 405974407552062015055 92 264765917968736096775 95 62184551328841105020 96 36274321608490644595 99 6067344606379124775 100 3155019195317144883 103 371517718063835850 104 171469716029462700 107 14007965812274250 108 5706949034630250 111 317527892773980 112 113402818847850 115 4196161839505 116 1302257122605 119 31097645925 120 8292705580 123 133993625 124 30256625 127 604000 128 113250 131 24915 132 3775 151 1 CROSSREFS Sequence in context: A137790 A284079 A108179 * A178193 A243777 A135200 Adjacent sequences:  A080950 A080951 A080952 * A080954 A080955 A080956 KEYWORD nonn,fini,changed AUTHOR N. J. A. Sloane, Apr 15 2009 EXTENSIONS Corrected (using the Tomlinson et al. book) by Eric M. Schmidt, Nov 17 2017 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages The OEIS Community | Maintained by The OEIS Foundation Inc.
1,152
3,127
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.78125
3
CC-MAIN-2017-47
longest
en
0.539543
https://www.convertunits.com/from/quarter+(ton)/to/quarter+%5BUS%5D
1,596,860,384,000,000,000
text/html
crawl-data/CC-MAIN-2020-34/segments/1596439737238.53/warc/CC-MAIN-20200808021257-20200808051257-00179.warc.gz
633,591,286
8,066
## ››Convert quarter (ton) [US] to quarter [US] quarter (ton) quarter [US] Did you mean to convert quarter (ton) to quarter [US] quarter [UK] How many quarter (ton) in 1 quarter [US]? The answer is 0.05. We assume you are converting between quarter (ton) [US] and quarter [US]. You can view more details on each measurement unit: quarter (ton) or quarter [US] The SI base unit for mass is the kilogram. 1 kilogram is equal to 0.0044092452436976 quarter (ton), or 0.088184904873951 quarter [US]. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between quarter (ton) [US] and quarters. Type in your own numbers in the form to convert the units! ## ››Quick conversion chart of quarter (ton) to quarter [US] 1 quarter (ton) to quarter [US] = 20 quarter [US] 2 quarter (ton) to quarter [US] = 40 quarter [US] 3 quarter (ton) to quarter [US] = 60 quarter [US] 4 quarter (ton) to quarter [US] = 80 quarter [US] 5 quarter (ton) to quarter [US] = 100 quarter [US] 6 quarter (ton) to quarter [US] = 120 quarter [US] 7 quarter (ton) to quarter [US] = 140 quarter [US] 8 quarter (ton) to quarter [US] = 160 quarter [US] 9 quarter (ton) to quarter [US] = 180 quarter [US] 10 quarter (ton) to quarter [US] = 200 quarter [US] ## ››Want other units? You can do the reverse unit conversion from quarter [US] to quarter (ton), or enter any two units below: ## Enter two units to convert From: To: ## ››Definition: Quarter unit of weight equal to 25 pounds ## ››Metric conversions and more ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!
548
2,001
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.765625
3
CC-MAIN-2020-34
latest
en
0.875992
https://cw.fel.cvut.cz/b231/courses/pkr/start
1,726,784,072,000,000,000
text/html
crawl-data/CC-MAIN-2024-38/segments/1725700652067.20/warc/CC-MAIN-20240919194038-20240919224038-00437.warc.gz
176,351,986
9,964
Warning This page is located in archive. Go to the latest version of this course pages. Go the latest version of this page. # PKR − Advanced Robot Kinematics ,,Drahá slečno Gloryová, Roboti nejsou lidé. Jsou mechanicky dokonalejší než my, mají úžasnou rozumovou inteligenci, ale nemají duši. Ó, slečno Gloryová, výrobek inženýra je technicky vytříbenější než výrobek přírody.“ - Karel Čapek, R.U.R. [“Miss Glory, robots are not people. They are mechanically much better than we are, they have an amazing ability to understand things, but they don't have a soul. Young Rossum created something much more sophisticated than Nature ever did - technically at least!”] ## Content We will explain some fundamental notions appearing in advanced robotics. We shall, e.g., explain how to solve the inverse kinematics task of a general serial manipulator with 6 degrees of freedom. There is a general solution to this problem but it can't easily be obtained by elementary methods. We shall present some more advanced algebraic tools for solving algebraic equations. We will also pay special attention to representing and parameterizing rotations and motions in 3D space. We will solve simulated problems as well as problems with real data in labs and in assignments. ## Labs: Monday 12:45-14:15, CIIRC:B-670 Teachers: Viktor Korotynskiy, Kateryna Zorina See Labs for details. ### Assessment 1. All homework must be submitted via BRUTE and accepted. 2. At least 50% of points in total for the homework. 3. At least 50% of points in total from the tests. 4. Regular submission of homeworks ends on January 14, 2024. Later submissions are possible only by an agreement with the assistants. ### Exam The exam consists of a written and an oral part. It is required to achieve at least 50% of points from the written exam to be admitted to the oral exam. The grade depends on the exam (40%), tests (30%), and homework (30%). You may skip the oral exam if you are satisfied with the result after the written exam. Exam content: 1. Linear algebra [7,8,9,10]: linear space, basis, coordinates, linear dependence/independence, matrices, rank, determinant, eigenvalues, and eigenvectors, solving systems of linear equations, Frobenius theorem and linear independence, linear function, affine function, linear mapping, and its matrix, computing roots of a polynomial via eigenvalues of its companion matrix, dual space, dual basis, change of the dual basis corresponding to a change of a basis, vector product and derived linear mappings, SVD, dual space, and dual basis. 2. - Course material: PKR-Lecture-2021.pdf. Written In-Person exam organization: 1. The written exam is sat in a classroom. 2. You may NOT use any prepared material. Oral exam organization: 1. You may skip the oral exam if you are satisfied with the result after the written exam. 2. The face-to-face oral exam will be done online via MS Teams and will take about 30 mins. ## Rules 1. Lecture: It is very difficult to pass the course without attending lectures. 2. Labs: It is impossible to pass the course without attending labs. 3. Homework: Homework is assigned at a lab where it can be discussed with teaching assistants. Students work out homework individually (rulesin Czech). The deadline for submitting homework via BRUTE is on Monday at 6:00 in the morning two weeks after the assignment. Late submissions are penalized (10% for each commenced day of delay but not more than 50% of points). 4. Assessment: see above. 5. Tests: Students work out test independently. ## Literature 1. Basic algebra (Groups, Rings, Ideals, Fields, Vector spaces) in 33 simple videos @ Socratica 2. Northwestern University Coursera Course Modern Robotics 3. Math Doctor Bob. Math Instruction Online. In Plain Language. 4. Lung-Wen Tsai. Robot Analysis And Design: The Mechanics of Serial And Parallel Manipulators, John Wiley and Sons, 1999. 5. G Sanderson Essence of Linear Algebra from 3Blue1Brown 6. J Strom, K Astrom, T Akenine-Moller Interactive Linear Algebra Course 7. P Pták. Introduction to Linear Algebra. Vydavatelství ČVUT, Praha, 2007. 8. E Krajník. Maticový počet. Vydavatelství ČVUT, Praha, 2000. 9. D Cox, J Little, D O'Shea. Ideals, Varieties, and Algorithms. 2nd edition, Springer, 1998. 10. M Michalek, B Sturmfels. Invitation to Nonlinear Algebra 11. B Sturmfels. Inroduction to Groebner bases youtube ## Prerequisits 1. A0B01LAG Linear Algebra (must have) 2. A3B33ROB Robotics (nice to have) ## Contacts Tomáš Pajdla Vladimír Smutný Viktor Korotynskiy Kateryna Zorina pajdla@cvut.cz vladimir.smutny@cvut.cz viktor.korotynskiy@cvut.cz kateryna.zorina@cvut.cz CIIRC B-638 CIIRC B-608B CIIRC B-640A CIIRC B-642B courses/pkr/start.txt · Last modified: 2024/01/06 18:09 by korotvik
1,197
4,762
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.984375
3
CC-MAIN-2024-38
latest
en
0.873468
https://pugliablog.info/and-relationship/reactant-and-product-relationship.php
1,571,066,686,000,000,000
text/html
crawl-data/CC-MAIN-2019-43/segments/1570986653876.31/warc/CC-MAIN-20191014150930-20191014174430-00337.warc.gz
652,840,196
9,200
# Reactant and product relationship ### Reactants and Products ( Read ) | Chemistry | CK Foundation Thus, stoichiometry is the branch of science (Chemistry) that deals with the quantitative relationship between the reactants and the products in. Stoichiometry is a section of chemistry that involves using relationships between reactants and/or products in a chemical reaction to determine. Samantha Stahl Professor Kimberly Arnold Experiment #6 – Relationship Between Reactants and Products 23 October Abstract The. Molar mass is a useful chemical ratio between mass and moles. • Stoichiometry (Quantitative relationship between reactants and products) The atomic mass of each individual element as listed in the periodic table established this relationship for atoms or ions. Since there is a ratio of 4: Variation in Stoichiometric Equations Almost every quantitative relationship can be converted into a ratio that can be useful in data analysis. This ratio can be useful in determining the volume of a solution, given the mass or useful in finding the mass given the volume. ### Stoichiometry (Quantitative relationship between reactants and products) - Online Science Notes In the latter case, the inverse relationship would be used. A percent mass states how many grams of a mixture are of a certain element or molecule. This is useful in determining mass of a desired substance in a molecule. If the total mass of the substance is 10 grams, what is the mass of carbon in the sample? How many moles of carbon are there? Given volume and molarity, it is possible to calculate mole or use moles and molarity to calculate volume. This is useful in chemical equations and dilutions. Example 7 How much 5 M stock solution is needed to prepare mL of 2 M solution? These ratios of molarity, density, and mass percent are useful in complex examples ahead. Determining Empirical Formulas An empirical formula can be determined through chemical stoichiometry by determining which elements are present in the molecule and in what ratio. The different weights of oxygen i. The law of reciprocal proportion: This law was put forward by Richter in The law states that two or more elements, which combine separately with the fixed weight of another element, are either the same or the simple multiples of the weights of the elements when they combine among themselves. Carbon and oxygen combine separately with hydrogen to produce corresponding compounds methane and water respectively. ## Stoichiometry and Balancing Reactions We know 12 parts by weight of carbon and 32 parts by weight of oxygen combine to form carbon dioxide, which proves the law. The law of gaseous volumes: This law was enunciated by Gay Lussac in Let's start by using the guidelines. Assign a stoichiometric coefficient of 1 to the most complex compound, NO. Now we can balance the remaining single-element compounds. In order to do this we will need to use fractional coefficients. ### Stoichiometry and Balancing Reactions - Chemistry LibreTexts Typically a stoichiometric coefficient of "1" is not explicitly included when writing the chemical equation. We can get rid of the fractional coefficients by multiplying by 2 even though this is a perfectly acceptable balanced chemical equation. Balanced, but without fractional coefficients At the very beginning of this problem, perhaps you could see this was the answer. If you can see the balanced equation by sight, you don't need to go by the guidelines. Remember they are only guidelines to help if you run into trouble. You can see by simply adding a 2 in front of NO, we violate the first guideline even though it leads us to a balanced equation. Balance the given chemical reaction. This one may not be as easy to see the final answer so we will use the guidelines to balance the equation. N2O3 is the most complex species so we will add a 1 for its coefficient. Now we can balance the remaining single element species. In order to balance the number of atoms we need 2 atoms of N and 3 atoms of oxygen on the left side of the equation. Balanced The equation is now balanced. However, we can get rid of the fractional coefficient by again multiplying by 2. Balanced, without fractional coefficients Notice that in these two examples N2 and O2 react with a different stoichiometry to obtain different products. Is it necessary for the number of moles of the reactants to be equal to the number of moles of products?
898
4,457
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.390625
3
CC-MAIN-2019-43
latest
en
0.910113
https://lottonijuan.com/official-4-digit-results-january-17-2018-draws/
1,560,873,433,000,000,000
text/html
crawl-data/CC-MAIN-2019-26/segments/1560627998755.95/warc/CC-MAIN-20190618143417-20190618165417-00313.warc.gz
511,374,980
11,415
# Official 4 Digit Results January 17 2018 Draws 4 Digit Lotto Game: 4 – 2 – 6 – 1 | Draw Date: January 17, 2018 This is the 4 Digit Results that were drawn today (Wednesday). The draw was held at the Philippine Charity Sweepstakes Office. Only one (1) set of four 4-Digit number combination will be drawn. #### PCSO Latest 4 Digit Result Draw Winning Numbers: 4 – 2 – 6 – 1 Combination: Exact order Prize: Php Number of winners: Draw Date: 01/17/2018 Consolation Prize: 3 numbers = 800.00 2 numbers = 100.00 Starting from the last number. You can also see here the 4 Digit January 2018 results history and archive. Check out also the other today’s Philippine PCSO Lotto results HERE. The 4 Digit Lotto Draws can be seen every Monday, Wednesday and Friday at 9:00 p.m. over Channel 4 together with your other favorite Lotto games. RECAP of 4 DIGIT JANUARY 17, 2018 RESULTS 4 2 6 1 PCSO 4 Digit 4D Lotto Friday (January 19, 2018) Probables and Lucky Tip: 0 – 4 – 3 – 5 4 – 1 – 2 – 6 9 – 1 – 3 – 6 3 – 4 – 9 – 4 You can also play the 4 Digit Game Lotto with the following variations: • ROLL 1 – The first digit which ranges from “0” to “9” is to be generated by the central system to complement the selected last 3 digits, thereby creating 10 sets of numbers. (COST: Php 100.00). • ROLL 4 – Similar to Roll 1 except that the Central system is to generate the last digit ranging from “0” to “9” to complement the selected first 3 digits. (COST: Php 100.00). • PER RAMBOL – The online lottery central system generates all possible permutations of the selected numbers are being purchased. Below is the table on perm or rambol selection that you can play: • 4 Different digits (24 combinations) (COST: 240.00). • 2 different digits and 1 pair of the same digits (12 combinations) (COST: 120.00). • 2 different pairs of the same digits (6 combinations) (COST: 60.00). • 3 digits the same and 1 different (4 combinations) (COST: 40.00). Reminder: Prizes worth more than Php 5,000.00 to Php 20,000.00 can be claimed at any of the PCSO Branch Offices or at the PCSO Head Office, 605 Conservatory Bldg., Shaw Blvd. Corner Princeton St., Mandaluyong City.
637
2,164
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.921875
3
CC-MAIN-2019-26
latest
en
0.86632
https://it.mathworks.com/matlabcentral/cody/problems?term=tag%3A%22binary%22
1,638,131,490,000,000,000
text/html
crawl-data/CC-MAIN-2021-49/segments/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00400.warc.gz
393,080,076
22,395
Cody # Problems 1 – 38 of 38 Problem Title Likes Solvers Difficulty #### Problem 1488. Generate binary combinations for a given number of bit(s) Created by: Suman Saha 1 69 #### Problem 44814. Find the complement of a number in binary Created by: Rafi Ahmed Tags easy, matlab, binary 2 30 #### Problem 43042. Convert decimal to binary and then generate the minimum binary it can with jumbling Created by: Jamil Kasan 10 60 #### Problem 42736. Convert from integer to binary Created by: Marc Bentley Tags easy, binary, uab 2 73 #### Problem 832. Convert single-precision floating-point number to binary representation Created by: Vitaly Lavrukhin 1 28 #### Problem 43602. Convert array of decimal numbers into binary numbers array. Created by: Andriy Kavetsky 3 43 #### Problem 44654. convert the number to binary format & count digits Created by: Srishti Saha 0 35 #### Problem 2204. Convert a vector of Integers into a matrix of binaries Created by: Marcus Schwenk 1 66 Created by: Lee Tags binary 2 229 #### Problem 43614. Opposite task convert binary numbers array into array of decimal numbers. Created by: Andriy Kavetsky Tags binary, decimal 2 48 #### Problem 2202. Flip the bit Created by: the cyclist 2 179 #### Problem 1468. Numbers at bit-boundary Created by: Muthu Annamalai 1 28 #### Problem 1338. Binary Coder Created by: Ahmed 4 174 #### Problem 43977. Converting binary to decimals Tags binary, basics 5 640 #### Problem 1434. Implement full adder circuit Created by: Chintan Tags binary, logical 1 46 #### Problem 1861. Binary Created by: Ricardo Sousa Tags binary 0 156 #### Problem 45181. Take a binary number as input,rearrange it in any manner such that its value is greater than the original one.output should be all the possible values in decimal. Created by: Asif Newaz 1 14 #### Problem 1226. Non-zero bits in 10^n. Created by: SK Tags binary, powers, bits 3 33 #### Problem 43103. X plus binary inverted x Created by: Bert Tags binary, trick 0 37 #### Problem 2270. Bit calculation Created by: Debopam 3 139 #### Problem 45663. Find the next binary palindrome number Created by: Syed Shahed 1 23 #### Problem 138. Number of 1s in the Binary Representation of a Number Created by: @bmtran (Bryant Tran) Tags binary, base, count 3 378 #### Problem 1547. Relative ratio of "1" in binary number Created by: Marek Kuklis Tags matlab, binary 5 591 #### Problem 2891. Binary code (array) Created by: Yannick 6 562 #### Problem 1090. Create a random logical vector of N elements of which M are true. Created by: J-G van der Toorn Tags binary, logical, sum 1 88 #### Problem 45327. Decimal to binary conversion (without using built-in function) Created by: Asif Newaz 2 15 #### Problem 2678. Find out sum and carry of Binary adder Created by: Pritesh Shah Tags binary 10 597 #### Problem 2046. Convert binary numbers to hexadecimal numbers Created by: Crapoo Crapoo 1 28 #### Problem 49835. Decimal to Binary conversion for Large Integers Created by: Gifari Zulkarnaen 0 2 #### Problem 108. Given an unsigned integer x, find the largest y by rearranging the bits in x Created by: AMITAVA BISWAS Tags binary 12 982 #### Problem 511. Converting Decimal to Binary Created by: Turgut 0 61 #### Problem 568. Number of 1s in a binary string Created by: Srivardhini Tags binary, sum 40 4237 #### Problem 52714. Multiply binary numbers Created by: ChrisR 2 5 #### Problem 2869. There are 10 types of people in the world Created by: James 17 470 #### Problem 47073. Find the nth Fibbinary number Created by: ChrisR 2 10 #### Problem 52689. Easy Sequences 18: Set Bits of Triple Summations Created by: Ramon Villamangca 2 2 #### Problem 44337. Sums of Distinct Powers Created by: James 6 142 #### Problem 1546. Create matrix with Gray code Created by: Marek Kuklis Tags matlab, binary 2 29 1 – 38 of 38
1,122
3,978
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.15625
3
CC-MAIN-2021-49
longest
en
0.726494
https://www.kidzsearch.com/kidztube/estimating-lengths-measurement-and-data-early-math-khan-academy_e255c1970.html
1,618,543,452,000,000,000
text/html
crawl-data/CC-MAIN-2021-17/segments/1618038088471.40/warc/CC-MAIN-20210416012946-20210416042946-00559.warc.gz
738,481,013
26,909
 Estimating Lengths | Measurement And Data | Early Math | Khan Academy | Safe Videos for Kids Welcome # Estimating Lengths | Measurement And Data | Early Math | Khan Academy Thanks! Share it with your friends! URL You disliked this video. Thanks for the feedback! Sorry, only registred users can create playlists. URL Categories: Basic Math   |   Math 452 Views ## Description Missed the previous lesson? Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way! Want a virtual coach for Early Math? Unlock the Early Math mission on Khan Academy here: https://www.khanacademy.org?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. Subscribe to KhanAcademy’s Early Math channel:
353
1,698
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.5625
3
CC-MAIN-2021-17
latest
en
0.87541
https://math.stackexchange.com/questions/1742020/how-to-rigourously-prove-that-any-integer-divisible-by-3-can-be-written-as-a-s
1,566,150,540,000,000,000
text/html
crawl-data/CC-MAIN-2019-35/segments/1566027313987.32/warc/CC-MAIN-20190818165510-20190818191510-00158.warc.gz
549,051,210
27,315
# How to rigourously prove that any integer divisible by $3$ can be written as a sum of four cubes? [closed] How to rigourously prove that any integer divisible by $3$ can be written as a sum of four not necessarily posiitive cubes? I have been trying it for long ## closed as off-topic by Travis, John B, Watson, user91500, JKnechtApr 14 '16 at 10:47 This question appears to be off-topic. The users who voted to close gave this specific reason: • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Travis, John B, Watson, user91500, JKnecht If this question can be reworded to fit the rules in the help center, please edit the question. $6n=(n+1)^3+(n-1)^3+(-n)^3+(-n)^3$ $6n+3=n^3+(4-n)^3+(2n-5)^3+(4-2n)^3$
265
1,010
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.375
3
CC-MAIN-2019-35
latest
en
0.95104
https://ujaashome.com/power-station/do-gaming-laptops-use-alot-of-electricity.html
1,632,389,215,000,000,000
text/html
crawl-data/CC-MAIN-2021-39/segments/1631780057417.92/warc/CC-MAIN-20210923074537-20210923104537-00473.warc.gz
624,308,662
19,341
# Do gaming laptops use alot of electricity? Contents Generally, laptops are well-organized in power consumption and are inclined to consume 85% less electricity than a Desktop. In short, a high-End gaming laptop consumes 130-185watts, and a high-End gaming PC consumes 350-700 watts. ## Do Gaming Laptops use a lot of electricity? A good gaming laptop only uses 200- 300 watts. Compare that to a gaming desktop it’s going to have about a 900 watt power supply and thats not including the power from a monitor. ## How much energy does a gaming laptop use per hour? A gaming computer requires somewhere between 300 – 500 watts per hour to operate. This translates to up to 1400 kWh annually and is six times higher than a laptop’s power usage. However, these figures vary, depending on the gaming PC features, such as the installed hardware and software and usage frequency. ## Do laptops use a lot of electricity? A laptop uses between 50 and 100 W/hour when it is being used, depending on the model. A laptop that is on for eight hours a day uses between 150 and 300 kWh and emits between 44 and 88 kg of CO2 per year. In stand-by mode the power consumption of both a desktop and a laptop falls to about a third. ## How much electricity does a gamer use? The average energy consumption of a gaming PC is around 1,400 kWh per year. This is 10 times the power consumed by 10 gaming consoles or 6 regular computers. ## Does gaming increase electricity bill? The average electricity cost in the US is 13 cents per kWh; this means that it costs 13 cents to run something that consumes 1000 watts for one hour. … If your PC uses 300 watts while gaming, then one hour of play time would cost you just under 4 cents. ## How do I check the power consumption of my laptop? During that time, you can calculate the laptop power consumption from the battery nameplate details. Note that, here we have considered the laptop work under the battery. Laptop Power Consumption: Laptop Power Consumption – 12 Hours Battery Wattage 180 Consumption Total (Wh) kWh Hourly 45 0.045 Day 540 0.54 ## Should I turn my gaming PC off at night? Unless you’re still using a computer that’s over a decade old, the power savings from turning it off every night is negligible, as long as you have it set up to go to sleep when it hasn’t been used for a specific time. ## How much power does a gaming laptop consumes? So while gaming laptops are extremely well-optimized for efficiency, it is unavoidable that they will use 120–140W for gaming on a mid-level PC and 200W+ for a higher end model with i7/i9 + 2070/2080 Max-Q. ## Does a gaming PC use a lot of WIFI? Do gaming computers use a lot of wifi? – Quora. Yes and no. The computer will use no more or less data than any other pc doing the same task on the same OS. The users of gaming hardware tend towards downloading large games and connecting to servers with continuous data in both directions. IT IS INTERESTING:  How much are the electric stoves? ## How many hours we can use a laptop continuously? So, it’s important to do your research when buying a new laptop and check reviews to see how long of a single charge battery life you can expect. Overall, the average lifespan of a laptop battery on a single charge probably ranges from as low as 2-3 hours to as high as 7-8 (or more) hours. ## Does leaving laptop plugged in waste electricity? Always leaving a laptop computer plugged in, even when it’s fully charged, can use a similar quantity — 4.5 kilowatt-hours of electricity in a week, or about 235 kilowatt-hours a year. (Your mileage may vary, depending on model and battery. ## How can I fix my electric bill? How to Calculate Your Electric Bill 1. Multiply the device’s wattage by the number of hours the appliance is used per day. 2. Divide by 1000. 3. Multiply by your kWh rate.
893
3,848
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.8125
3
CC-MAIN-2021-39
latest
en
0.932863
https://www.coursehero.com/file/6855516/note-2/
1,519,300,771,000,000,000
text/html
crawl-data/CC-MAIN-2018-09/segments/1518891814101.27/warc/CC-MAIN-20180222101209-20180222121209-00590.warc.gz
868,757,482
26,756
{[ promptMessage ]} Bookmark it {[ promptMessage ]} # note 2 - MA2216/ST2131 Probability Notes 2  1 Axioms of... This preview shows pages 1–5. Sign up to view the full content. This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: MA2216/ST2131 Probability Notes 2 § 1. Axioms of Probability Consider an experiment whose sample space is S . The objective of probability is to assign to each event A a number IP( A ), in [0 , 1], called the probability of the event A , which will give a precise measure of the chance that A will occur. 1. Consider the collection of all events and denote it by A . For each event A of the sample space S , we assume that a number IP( A ), which is called the probability of the event A , is defined and satisfies the following three axioms: Axiom 1: ≤ IP( A ) ≤ 1 Axiom 2: IP( S ) = 1 Axiom 3: If A 1 ,A 2 ,... are mutually exclusive (disjoint) (i.e., A i A j = ∅ when i 6 = j ), then IP ˆ ∞ [ i =1 A i ! = ∞ X i =1 IP( A i ) . 1 Notes: Axiom 1 says that the probability of an event is some number between 0 and 1. Axiom 2 states that, with probability 1, the sample space itself will surely occur, (and hence S is called a sure event ). Axiom 3 says that IP is σ- additive * . In particular, when A 1 , A 2 , ..., A n are mutually exclusive (disjoint) (that is, A i A j = ∅ when i 6 = j ), then, ( Cf. 3(ii) below), IP ˆ n [ i =1 A i ! = n X i =1 IP( A i ) . Take note that IP can be regarded as a function defined on A , the collec- tion of all events of the sample space S , taking values in the unit interval [0 , 1], IP : A 7→ [0 , 1] such that IP satisfies the above 3 axioms. 2 2. Examples: (a) Consider an experiment of tossing a coin. Find IP( H ) if (i) the coin is fair; (ii) if the coin is biased and a head is twice as likely to appear as a tail. Ans. IP( H ) = 1 2 for a fair coin. If a head is twice as likely to appear as a tail, then IP( H ) = 2IP( T ) and IP( H ) + IP( T ) = 1 . Solving for IP( H ), one arrives at 2 3 . (b) A fair die is tossed. Let A be the event that an even number turns up and let B be the event that a number divisible by 3 occurs. Find IP( A ), IP( B ), IP( A ∪ B ) and IP( AB ). Ans. Trivially, IP( A ) = 3 6 = 1 2 and IP( B ) = 2 6 = 1 3 . Observe that A ∩ B = { 6 } with IP( A ∩ B ) = 1 6 . Thus, IP( A ∪ B ) = IP( A ) + IP( B )- IP( A ∩ B ) = 2 3 . (See 3(v) below.) 3 3. Some Important Properties: (i) IP( ∅ ) = 0. To see it, take A i = ∅ for all i ≥ 1 and observe that, by Axiom 3, IP( ∅ ) = IP ˆ ∞ [ i =1 A i ! = ∞ X i =1 IP( A i ) = ∞ X i =1 IP( ∅ ) . Since 0 ≤ IP( ∅ ) ≤ 1, it implies that the infinite series on the right is convergent, it forces IP( ∅ ) = 0. (ii) If A 1 ,A 2 ,...,A n are mutually exclusive, then IP ˆ n [ i =1 A i ! = n X i =1 IP( A i ) . (This says that IP is finitely additive .) To establish the finite additiveness, refer to Axiom 3 and let A i = ∅ for all i ≥ n + 1. Obviously, ∞ [ i =1 A i = n [ i =1 A i and note also that IP( A i ) = IP( ∅ ) = 0 for i ≥ n + 1.... View Full Document {[ snackBarMessage ]} ### Page1 / 26 note 2 - MA2216/ST2131 Probability Notes 2  1 Axioms of... This preview shows document pages 1 - 5. Sign up to view the full document. View Full Document Ask a homework question - tutors are online
1,205
3,562
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.21875
4
CC-MAIN-2018-09
latest
en
0.892473
https://www.sanfoundry.com/c-tutorials-use-pointer-subscript-access-array/
1,709,032,953,000,000,000
text/html
crawl-data/CC-MAIN-2024-10/segments/1707947474674.35/warc/CC-MAIN-20240227085429-20240227115429-00129.warc.gz
969,730,922
26,341
# Can we Use a Pointer for Subscript to Access an Array in C? Question: Can we Use Pointer for Subscript to Access an Array in C Programming? Answer: Subscript operator ‘[]’ have higher precedence than indirection operator ‘*’, but in fact, both are same. Let’s see an example, ` int max[5] = {1,2,3,4,5}; /* max[5] is an array of 5 integers */` Well! In order to access elements of array ‘max[]’ using pointer, we must know type of array ‘max[]’ so we can declare and initialize pointer of same type to use it to access array ‘max[]’. So, what’s the type of array ‘max[]’? ‘max[5]’ is an array of 5 something which happen to be 5 integers. Address of first integer ‘max[0]’, let’s say, ` 1000` which is calculated as, ` 1000 + 0 * 4 /* type 'int' takes 4 bytes */` address of 2nd element ‘max[1]’ is calcuated as, ` 1000 + 1 * 4 /* 1000 is the base address of the array 'max[]' */` and so on. Since each address points to an integer, therefore type of array is pointer-to-integer. So, ` int *pi; /* 'pi' is pointer to type int */` and its initialization ``` pi = array; /* value of array, pointer constant, is copied into pointer 'pi' */``` allows us to access the elements of array ‘max[]’. Now, ‘pi’ points to the first element, ‘max[0]’, of array. On performing indirection on the ‘pi’, value at the location pointed to by pi is obtained. For example, ` *pi; /* value of 'max[0]' is obtained */` Next, how can we obtain values of successive elements of array ‘max[]’? We’re very well familiar with pointer arithmetic and here we would implement it to learn how simple it’s to access the array elements using pointer! What will happen when ` *(pi++); /* which is same as *(pi + 1) */` Firstly, expression in parenthesis is evaluated, 1 in the exp. (pi + 1) is scaled by the size of integer as ` (pi + 1 * 4); equals (pi + 4);` which results in pointer to 2nd element ‘max[1]’ in array ‘max[]’. Now indirection is performed on the pointer ` *(pi + 4); /* indirection performed */` which results in value of pointed to location i.e. value 2. This way, we can use pointer ‘pi’ to access elements in the array ‘max[]’. Consider the fragment of code below to access the array ‘max[]’, ``` int max[5] = {1,2,3,4,5}; int *pi; int i; for (i = 0, pi = max; pi < &max[5]; pi++, i++) printf("max[%d] has value %d\n", i, *pi);``` Remember the Rules of Compatibility of Pointers while declaring and initializing pointer to access an array. Sanfoundry Global Education & Learning Series – 1000 C Tutorials. If you wish to look at all C Tutorials, go to C Tutorials.
749
2,659
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.734375
3
CC-MAIN-2024-10
latest
en
0.864846
https://www.mathhomeworkanswers.org/238246/find-the-coordinates-of-tge-midpoint-p-between-s-5-7-and-t-3-9?show=238248
1,508,266,583,000,000,000
text/html
crawl-data/CC-MAIN-2017-43/segments/1508187822480.15/warc/CC-MAIN-20171017181947-20171017201947-00155.warc.gz
951,440,781
11,418
Help please thank you The midpoint is the average of the coords: P is the point ((-5+3)/2, (7+9)/2)=P(-1,8). answered Feb 16 by Top Rated User (478,380 points)
54
161
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.546875
3
CC-MAIN-2017-43
latest
en
0.899231
http://essaybay.net/blog/2017/02/
1,537,745,668,000,000,000
text/html
crawl-data/CC-MAIN-2018-39/segments/1537267159938.71/warc/CC-MAIN-20180923232129-20180924012529-00269.warc.gz
79,444,221
25,304
## Lesson 6: Sampling Distributions NAME Due Monday February 20, 2017, 11:59 EDT Answer the following questions showing all work. Full credit will not be given to answers without Click here to order this assignment @Essaybay.net. 100% Original.Written from scratch by professional writers. Lesson 6: Sampling Distributions NAME Due Monday February 20, 2017, 11:59 EDT Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use StatKey or Minitab Express include the appropriate output (copy + paste) along with an explanation. Output without explanation will not receive full credit. Round all answers to at least 3 decimal places. If you have any questions, post them to the course discussion board. 1. According to U.S. News and World Reports, 18.60% of all Penn State World Campus students have military experience. In a random sample of 45 students enrolled in World Campus sections of STAT 200, 6 reported having military experience. [30 points] A. Compute the sample proportion (p-hat) for this sample of n=45 STAT 200 students. B. Should the exact method or normal approximation method be used to construct a sampling distribution in this situation? Explain your reasoning. C. Using StatKey, construct a sampling distribution for p=0.1860 and n=45. Generate at least 5,000 samples. Take a screenshot of your sampling distribution and paste it here. D. If the population proportion is 18.60%, what is the probability of taking a random sample of n=45 and finding a sample proportion more extreme than the one observed in this sample? Use StatKey to determine this proportion. Include a screenshot of your sampling distribution with this proportion highlighted. E. Given your results from part D, do you think that the proportion of all STAT 200 students who have military experience is different from the overall population of World Campus students where p=0.1860? Explain your reasoning. 2. For the following questions, assume a normally distributed population. [20 points] A. Given μ=40, σ=12, and n=25, compute the standard error of the mean. B. Given μ=40, σ=12, and n=400, compute the standard error of the mean. C. Given μ=40, σ=3, and n=25, compute the standard error of the mean. D. Given μ=400, σ=12, and n=25, compute the standard error of the mean. E. How does the standard error of the mean change when the population mean, population standard deviation, and sample size change? Lesson 6: Sampling Distributions NAME Due Monday February 20, 2017, 11:59 EDT 3. Using StatKey you are going to construct a sampling distribution for a mean. Select a population distribution that is NOT normal (e.g., the built in Hollywood Movies, Rock Bands, or Baseball Players datasets, or a skewed distribution of your own). Using the same population distribution for each, construct the distribution of sample means for N=5 and N=30. Take at least 5,000 samples. [20 points] A. Include a screen shots of your parent population and your two sampling distributions here. B. How are your two distributions of sample means similar? How are they different? C. Describe how your results relate to the Central Limit Theorem. 4. In the population ACT scores are normally distributed with a mean of 18 and a standard deviation of 6. Suppose that we are taking a simple random sample of 60 students from one high school. [30 points] A. Calculate the standard error of the mean. B. If we were to repeatedly pull samples of 60 individuals from the population of all ACT test takers, the distribution of sample means would have a mean of ____ and a standard deviation of ____. C. Given the values from part B, 95% of random samples of n=60 will have sample means between ___ and ___. D. What is the probability that you would pull a random sample of 60 individuals from the population of all test takers and they would have a sample mean of 19 or higher? E. Suppose that the high school in question boasts that their students (i.e., the population of all of their students) have an average ACT score above the national average of 18. Given your results from part D, do you believe that there is evidence that the mean ACT score at this high school is greater than 18? Explain your reasoning. ## Assessment Instructions For This Assessment, You Will Analyze The Integration Of Marketing Communications In Nikon, With A Particular Focus On The Manner In Which The Marketing Mix Click here to order this assignment @Essaybay.net. 100% Original.Written from scratch by professional writers. ## Refer To Both The Overall Concept For Assignments 1-4 And Your Responses From Assignments 1 And 2 In Order To Complete This Assignment. Click here to order this assignment @Essaybay.net. 100% Original.Written from scratch by professional writers. ## Imagine That You Are A Member Of The HR Department Of A Small Retail Company And Upper Management Has Asked You To Create A New Employee Customer Service Training Class For All New Employees. Click here to order this assignment @Essaybay.net. 100% Original.Written from scratch by professional writers. ## Use The “NAB Company Portfolio”. Write A Three To Six (3-6) Page Paper In Which You Provide The Following Information Below. Click here to order this assignment @Essaybay.net. 100% Original.Written from scratch by professional writers. ## Referencing Used Must Be Harvard Style And Appropriate Quality References Are Used. A Selection Of Web Sites, Books And Journals As Sources For Gathering Of Information Is Required Not Just Dependant On Web Site Information. Click here to order this assignment @Essaybay.net. 100% Original.Written from scratch by professional writers.
1,266
5,683
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.34375
4
CC-MAIN-2018-39
longest
en
0.910368
http://physics.csbsju.edu/stats/descriptive2.html
1,582,775,106,000,000,000
text/html
crawl-data/CC-MAIN-2020-10/segments/1581875146647.82/warc/CC-MAIN-20200227033058-20200227063058-00000.warc.gz
113,068,155
5,054
## Descriptive Statistics They are different, but not different enough to matter -- like the maple leaves off the tree in my yard, when all I want to do is rake them up. Roald Hoffmann, 1981 Nobel Laureate in Chemistry from: The Same and Not the Same If you were to measure the size of 10 maple leaves you would quickly find that maple leaves in fact come in different sizes. Thus it is impossible to report the size of maple leaves, instead the best you can do is to report a typical size and give some estimate of the range of variation above and below that typical size. The attempt to capture the full meaning of "the size of maple leaves" in a few numbers is bound to fail -- Nature really is more complex than our descriptions of it. Nevertheless if our choice is to be silent on "the size of maple leaves" or to provide a list of the size of every maple leaf in the world (on this day) or to provide a few summarizing numbers, the latter is the option selected by science. This page introduces a handful of statistics which are commonly used to describe the distribution of data. ### Typical Values There are several common methods of selecting a "typical" value for data. The most common method is the average or mean. To obtain an average value, add up all your data values and divide by the number of data items. If X01 is the length of your first maple leave, X02 the length of your second maple leave, etc., then the average maple leaf length is: (X01+X02+X03+ X04+X05+X06+ X07+X08+X09+ X10)/10 = Xavg To obtain the median value, first sort your list of leaf-lengths from lowest to highest: {5.1, 7.2, 4.1, 9.5, 6.7, 7.8, 8.5, 7.0, 7.3, 9.0} becomes: {4.1, 5.1, 6.7, 7.0, 7.2, 7.3, 7.8, 8.5, 9.0, 9.5} and then select the value in the exact middle as the median. (It turns out that if the number of items is even, as in this example, there is no exact middle. 7.2 is 5 places from the front and 6 places from the back; 7.3 is 6 places from the front and 5 places from the back. So with even-numbered data sets, average the two near-middle values, producing Xmed=7.25 in this example.) The mode "typical" value will be of less use to us: it is the most repeated value in the data set. In the above example, no value is repeated (each value occurs exactly once). This is commonly the case with so few data items; hence its limited utility for us. The geometric mean is useful for "log-normal distributions". To obtain the geometric mean, multiply all the numbers together and then take the result to the power 1/N (where N is the number of data items -- 10 in our example). So the geometric mean is: (X01·X02·X03· X04·X05·X06· X07·X08·X09· X10)1/10 = Xgeo ### Estimates of the Range of Variation In some sense, the range of variation is limited only by your willingness to search through ever larger piles of leaves. Generally, the more data you record the more extreme your highs and lows will be. Nevertheless, you should find that the range of leaf lengths, that includes say 50% of your sample, remains about the same even if you look through ever larger piles of leaves. That is to say, there is a common range of variation even as larger data sets produce rare "outliers" with ever more extreme deviation. Estimates of the range of variation seek to put a number to this common range of variation that doesn't depend on sample size. The most common way to describe the range of variation is standard deviation (usually denoted by the Greek letter sigma: ). The standard deviation is simply the square root of the variance, so lets start by describing the variance. To obtain the variance start by subtracting the average from each data item. Since there will be about as many items above average as below average, the resulting list of numbers will have about as many positive values as negative values. (In fact this list of deviations-from-average must itself average to zero!) Square each deviation, and proceed to find the average of the squared-deviations. However, in finding the average squared-deviation, divide by N-1 rather than N. The result is the variance; take its square root to get the standard deviation. variance = ( (X01-Xavg)2 + (X02-Xavg)2 + (X03-Xavg)2 + ··· + (X10-Xavg)2 )/9 For data that is "normally distributed" we expect that about 68.3% of the data will be within 1 standard deviation of the mean (i.e., in the range Xavg ± ). In general there is a relationship between the fraction of the included data and the deviation from the mean in terms of standard deviations. ```Fraction Number of Standard of Data Deviations from Mean 50.0% .674 68.3 1.000 90.0 1.645 95.0 1.960 95.4 2.000 98.0 2.326 99.0 2.576 99.7 3.000``` Thus we should expect that 95% of the data would be within 1.96 standard deviations of the mean (i.e., in the range Xavg ± 1.96 ). This is called a 95% confidence interval for the sample. The average deviation or mean absolute deviation is calculated in a similar manner as standard deviation, except here you subtract the median from each data item producing a list of deviations from the median. Instead of squaring each deviation, you take the absolute value of each deviation. Finally you average in the usual way: using N not N-1. average deviation = ( |X01-Xmed | + |X02-Xmed | + |X03-Xmed | + ··· + |X10-Xmed | )/10 If the data is "normally distributed" there is a definite relationship between the average deviation and the standard deviation: average deviation = 0.80 × standard deviation; where 0.80 = (2/)½. ### Five-Number Summary The median, you recall, is in the middle of the sorted data. In a similar way we can define the first quartile to be 1/4 of the way through the sorted data, and the third quartile to be 3/4 of the way through the sorted data. (The preferred name for the second quartile is the median, so that's what we'll call it.) The range between the first and third quartiles includes half of the data. The size of the range (i.e., the difference between the third quartile and the first quartile) is another measurement of variability called the interquartile range or IQR. For normally distributed data: IQR = 1.35 × The five-number summary of the data consists of the minimum data point, the first quartile, the median, the third quartile, and the maximum data point. Thus these five numbers display the full range of variation (from minimum to maximum), the common range of variation (from first to third quartile), and a typical value (the median). ### Standard Deviation of the Estimated Means The above procedure describes how to define a "typical" leaf using 10 sample leaves. Clearly if another group uses the same procedure on its own sample of 10 leaves, it is unlikely to come up with exactly the same value for a "typical" leaf. How much variation is there in the estimates of "typical" described above? Clearly if we expand the sample beyond 10 (to 100, or 1000, ...) we would expect to come closer to the actual "typical" leaf (i.e., that determined by looking at all the leaves in the world). Thus the larger the sample you average over, the smaller is your expected deviation from the exact result. But how much variation should you expect in a calculated average leaf? The standard deviation expected in a calculated average is: /N1/2 Thus the deviations expected equal the standard deviation of the length of leaves if you "average" over just one leaf, and decrease as the square root of N as N increases. Thus one can expect to get quite close to the exact mean if the sample size N gets very big. ### "Normal" and other Distributions Many pages have been written by others on this topic. To be brief, a common assumption of statistics-users is that data is "normally" distributed. Occasionally the folks making this assumption know what it means and even test to see if it's a valid assumption. I'm going to leave you in the dark (like many statistics-users) about what this assumption means and how you test it. There are several good courses and books that would include these topics. I will give you two (not very helpful) hints. 1. (Bad News) Many things in nature are not "normally" distributed. (Good News) Much of what is not "normally" distributed in biology would be "normally" distributed if you took the logarithm of each data item. Thus there is a button on the descriptive statistics calculation page to do this conversion for you. The result is that the geometric mean is calculated for you and a different kind of standard deviation is produced. With the usual standard deviation you add or subtract the standard deviation from the mean in order to test for fractions of included data; with the log standard deviation, you multiply or divide. Thus you would expect 68.3% of your data to be between Xgeo× and Xgeo÷ ; 95.4% of your data would be between Xgeo× 2 and Xgeo÷ 2 2. (Bad News) Much of what's in books about statistics has to do with "normally" distributed data. Statistics that provide useful information even if applied to not-"normally" distributed data are call robust statistics. Median and average deviation are considered robust statistics. (Good News) The program always calculates them for you. There is one additional distribution you should know a bit about: the Poisson distribution. The Poisson distribution particularly applies to counts of things, like the number of maple trees per acre or the number of radioactive decays in an hour. The main upshot is that with things distributed according to the Poisson distribution, the standard deviation of the count can be estimated as the square root of the count. Thus if in a particular experiment you detected 1000 radioactive decays, a full repeat of that experiment might yield 1030 or 970 or 1037 or 998... The standard deviation of the counts in the repeated experiments should be close to the square root of 1000 (31.6). Thus if you don't have the time to do lots of full repeats, the range of variation you would experience can still be estimated.
2,391
10,076
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.828125
4
CC-MAIN-2020-10
longest
en
0.937428
https://www.coursehero.com/file/6254747/ch08-p069/
1,493,421,983,000,000,000
text/html
crawl-data/CC-MAIN-2017-17/segments/1492917123097.48/warc/CC-MAIN-20170423031203-00256-ip-10-145-167-34.ec2.internal.warc.gz
881,515,943
112,479
ch08-p069 # ch08-p069 - 2 = Δ K 1 ¡ 1 2 mv B 2 – 1 2 m (4.00 m/s) 2... This preview shows page 1. Sign up to view the full content. 69. There is the same potential energy change in both circumstances, so we can equate the kinetic energy changes as well: Δ K This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: 2 = Δ K 1 ¡ 1 2 mv B 2 – 1 2 m (4.00 m/s) 2 = 1 2 m (2.60 m/s) 2 – 1 2 m (2.00 m/s) 2 which leads to v B = 4.33 m/s.... View Full Document ## This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida. Ask a homework question - tutors are online
231
689
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.890625
3
CC-MAIN-2017-17
longest
en
0.885974
https://affordableessay.net/start-reviewing-and-responding-to-the-postings-of-your-classmates-as-early-in-the-week-as-possible-respond-to-at-least-two-of-your-classmates-participate-in-the-discussion-by-asking-a-question-prov-3/
1,656,442,617,000,000,000
text/html
crawl-data/CC-MAIN-2022-27/segments/1656103573995.30/warc/CC-MAIN-20220628173131-20220628203131-00076.warc.gz
136,452,295
13,732
# Start reviewing and responding to the postings of your classmates as early in the week as possible. Respond to at least two of your classmates. Participate in the discussion by asking a question, providing a statement of clarification, providing a point of view with a rationale, challenging an aspect of the discussion, or indicating a relationship between two or more lines of reasoning in the discussion. Complete your participation for this assignment by the end of the week. • Week 4 DiscussionDiscussion Topic  Overdue – Dec 24, 2021 12:59 AMDiscussion The discussion assignment provides a forum for discussing relevant topics for this week based on the course competencies covered. For this assignment, choose one of the following questions and post your initial response to the Discussion Area by the due date assigned. To support your work, use your course and text readings and also use outside sources. As in all assignments, cite your sources in your work and provide references for the citations in APA format. Start reviewing and responding to the postings of your classmates as early in the week as possible. Respond to at least two of your classmates. Participate in the discussion by asking a question, providing a statement of clarification, providing a point of view with a rationale, challenging an aspect of the discussion, or indicating a relationship between two or more lines of reasoning in the discussion. Complete your participation for this assignment by the end of the week. Question One: Bivariate Regression Regression analysis is a powerful and commonly used tool in business research. One important step in regression is to determine the dependent and independent variable(s). In a bivariate regression, which variable is the dependent variable and which one is the independent variable? • What does the intercept of a regression tell? What does the slope of a regression tell? • What are some of the main uses of a regression? • Provide an example of a situation wherein a bivariate regression would be a good choice for analyzing data. Question Two: Types of Regression Analyses There are two major types of regression analysis—simple and multiple regression analysis. Both types consist of dependent and independent variables. Simple linear regression has two variables—dependent and independent. Multiple regression consists of dependent variable and two or more independent variables. • How does a multiple regression compare with a simple linear regression? • What are the various ways to determine what variables should be included in a multiple regression equation? • Compare and contrast the following processes: forward selection, backward elimination, and stepwise selection. • Justify your answers using examples and reasoning. Comment on the postings of at least two peers and state whether you agree or disagree with their views. • Week4Notes2.pdf • Week4Notes1.pdf • Week4Notes3.pdf • Week4Notes4.pdf
564
2,952
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.015625
3
CC-MAIN-2022-27
latest
en
0.928723
http://lambda-the-ultimate.org/node/4243
1,716,713,918,000,000,000
text/html
crawl-data/CC-MAIN-2024-22/segments/1715971058872.68/warc/CC-MAIN-20240526074314-20240526104314-00659.warc.gz
14,648,207
7,491
## Algebra of Programming I believe this book has been mentioned before in some discussions on here and I have asked some questions about it myself though I have not really read it that carefully. I have recently leafed over a copy of this book at the local university library and I am wondering on some level what the motivation behind this work is. A quick skim seems to suggest some notion of equivalences between certain kinds of programs but (I hope this isnt a stupid question)- I do wonder what the utility of such notions are in this situation. Some help would be greatly appreciated :-). ## Comment viewing options ### Being able to prove Being able to prove properties of programs using equational reasoning. ### Thanks for the reply. What Thanks for the reply. What properties in particular are people interested in? ### Useful Algebraic Properties for Programming Models Three properties that I aim for in my language design are commutativity (ability to rearrange expressions within a group), associativity (ability to regroup expressions), and idempotence (ability to duplicate or eliminate expressions that are sitting next to one another) all without changing a program's meaning. These three properties, taken together, give a programming language a very declarative feel. Basically, you can treat each expression as an independent 'declaration' of program behavior, while still allowing parametric abstraction for groups of declarations. Commutativity means there is no implicit control-flow in the syntax (i.e. sequencing in code != sequencing in behavior). Associativity makes it easy to rearrange and abstract common subgroups of declarations. Idempotence makes it easy to introduce duplicate expressions to help with refactoring, and later to eliminate duplicate expressions to help with performance. One can control many properties by tying them to algebraic structure. For example, the object capability security model 'works' by tightly associating connectivity with the algebra. You get some useful algebraic rules for who can talk to whom and the flow of 'side-effects'. Ocap model isn't perfect - most implementations allow for covert channels (based on resource consumption and load) - but it helps enough to simplify reasoning. A very useful algebraic property is algebraic closure. To clarify: the common meaning of 'closure' in programming is the capture of lexical environment in a first-class function or new object, but the algebraic meaning of 'closure' is that the composition is the same sort of thing as the whole. Basically, algebraic closure is what makes a programming model compositional. Surprisingly, very few models of programming are truly compositional. Too many fail to achieve algebraic closure for critical functional or non-functional properties. Actors model is not compositional because individual actors have different concurrency properties than a group of actors. Programs using mutexes are not compositional because the composition of programs can deadlock even if both subprograms are individually safe. Remote procedure calls are not compositional because a sequence of calls has very different performance characteristics than creating one huge call (thus we end up needing scripts or batching). Concrete class-typed OO is not compositional because it is difficult to present a group of objects as a single object. For easy, robust, scalable composition, a programming model must take into account all the important properties (both functional and non-functional) and ensure algebraic closure and control over those properties. That includes concurrency and synchronization, latency and efficiency, partial-failure handling and recovery, communication and side-effects. Failure to achieve algebraic closure forces programmers to be much more aware of the implementation details of the elements being composed (i.e. imagine having different rules for adding numbers based on prime factors) and hurts abstraction because developers must write code specialized for the components. A requirement to grok implementation details of components limits the practical scalability of the model (due to limited capacity of programmers). A single language may support or model many programming models. Doing so can be costly - in terms of complexity - if it means violating algebraic closure (whether within a model or at the boundaries between them). If there is an objective definition for simplicity and elegance, it is 'algebraic closure'. If I were to point out a few of the more 'composable' programming models, they'd be: pure functions (esp. total functions - guaranteed termination), functional reactive programming, concurrent constraint programming, logic programming (esp. simplified forms such as Datalog, Dedalus, Bloom), synchronous reactive programming, and concatenative languages such as Forth. A duck-typed OO model obeying ocap principles would also be up there (E language, Newspeak). Beyond a single programming model, one can also compare and grok models using algebraic concepts. Finding a homomorphism with equivalent behavior proves that one language is at least equal in power to another, and can help you understand a model. Finding two homomorphisms, one in each direction, means the languages have identical power. Finding an isomorphism (two homomorphisms whose composition is the identity function) indicates a tight relationship between models, such that one can be used easily to verify the other. Finding a homeomorphism between models is essentially a declaration of expressive and compositional equivalence - i.e. a homeomorphism is an isomorphism where a small local change in model A has a corresponding small local change in model B. I tend to distinguish programming models based on the notion of homeomorphism. I've not read Algebra of Programming so I cannot recommend the book one way or the other, but I've found that one eye on algebraic properties and morphisms is essential for effective programming language design, and helps me understand and learn from existing models. ### Proving the equivalence of Proving the equivalence of expressions is at the heart of [correct] program optimization. By using transformations that preserve the meaning (FSVO, e.g. extensional identity) of expressions, we can try to find better (e.g. that are simpler or that use less space or time to compute) programs that we know are are equivalent. So, while it doesn't always tell us *how* to transform programs to get better ones, the approach lets us know that whatever transformation we apply is correct. In practice, most of the examples in Algebra of Programming seem trivial, in that you could have figured the final program (and even the correctness proof for some) out without going through Squiggol... that's the programmer's equivalent of solving a system of equations by trial and error. The formalism introduced in that book is useful because it gives us tools to approach program optimization in a more systematic manner, leaving more human creativity, time and energy for other tasks. ### See the second half of the book... The first half of the book is basically just the beta/eta rules of the lambda calculus, which as you note is familiar enough to be unexciting. It's the second half, where they move to sets and relations, which is much more interesting. Lots of optimization problems can be specified in generate-and-test terms (ie, find the best solution out of this set of possible solutions), and the equational reasoning used to derive good solutions is quite pretty -- I really liked their derivation of the TeX line-breaking algorithm.
1,454
7,661
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.734375
3
CC-MAIN-2024-22
latest
en
0.942639
https://www.jiskha.com/display.cgi?id=1286839042
1,516,214,728,000,000,000
text/html
crawl-data/CC-MAIN-2018-05/segments/1516084886952.14/warc/CC-MAIN-20180117173312-20180117193312-00486.warc.gz
928,002,977
3,941
# Math posted by . Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. 6x - 2y = 2, 9x - 3y = 1 Equation 1 X-intercept y=intercept 6x - 2y = 2 6x - 2y = 2 6x - 2(0) = 2 6(0) - 2y = 2 6x - 0 = 2 0 -2y = 2 6x = 2 -2y = 2 6x/6 =2/6 -2y/2 = 2/2 x= 0.75 y = -1 Equation 2 9x - 3y = 1 9x - 3y = 1 9x - 3(0) = 1 9(0) - 3y = 1 9x - 0 = 1 0 - 3y = 1 9x = 1 -3y = 1 9x/9 =1 -3y/3 = 1/3 x= 1/9 y = -1/3 x= 0.9 y= -0.25 • Math - It is not clear what you are doing. Rewrite the two equations as follows 18x - 6y = 6 18x - 6y = 2 The two equations are incompatible, and would graph as separate parallel lines. There is no solution. • Math - -2x+7y=0 can someone help me plz :)) ## Similar Questions 1. ### algebra solve system graphically. be sure to check your solution. if a system has infinite number of solutions, use set builder notation to write the solution det. if a system as no solution, state this. a=1+b b=5-2a solve each system graphically. be sure to check your solution. if a system has an infinite number of solutions, use the set-builder notation to write solution set. if a system has no solution, state this. where appropriate, round to … 3. ### math Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set−builder notation to write the solution set. If a system has no solution, state this. 6x – 2y = 2, 9x – … 4. ### algebra Solve the system graphically. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. 2x – y = 4 5x – y = 13 I do not understand how to do this 5. ### algebra solve the following systwm graphically. Be sure to check your solution. if the system has an infinite number of solutions, use set-builder notation to write no solution, state this. 4y=x+8, x=2/3y+2 6. ### Algebra Help!! I am having difficulty with a problem for hours now and if I could get some help, my head might stop pounding.Solve each system graphically. if a system has an infinite number of solutions, use set builder notation to write … 7. ### Algebra 1 Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set.If a system has no solution, state this. I tried this and found no solution, … 8. ### Algebra Solve each system graphically. Be sure to check your solution.If a system has an infinite number of solutions, use set-builder notation to write the solution set.If a system has no solution, state this. 2x - y = 1 x + 2y = 3
864
2,768
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.921875
4
CC-MAIN-2018-05
latest
en
0.895715
https://rofel.me/graphing-systems-of-inequalities-worksheet-algebra-2/
1,561,458,826,000,000,000
text/html
crawl-data/CC-MAIN-2019-26/segments/1560627999817.30/warc/CC-MAIN-20190625092324-20190625114324-00260.warc.gz
578,475,427
9,465
# Graphing Systems Of Inequalities Worksheet Algebra 2 Graphing Systems Of Inequalities Worksheet Algebra 2 Welcome for you to my personal blog, within this time period I’m going to teach you in relation to graphing systems of inequalities worksheet algebra 2 . And after this, here is the 1st impression: graphing systems of inequalities worksheet algebra 2 Fresh Solving Systems Inequalities Worksheet fadeintofantasy How about photograph previously mentioned? is usually which amazing???. if you think consequently, I’l d demonstrate some graphic once more underneath: graphing systems of inequalities worksheet algebra 2 Best of Solving linear equations and linear inequalities — Basic example So, if you would like receive all of these fantastic pictures related to (Graphing Systems Of Inequalities Worksheet Algebra 2 ), press save icon to download these photos in your laptop. They are all set for download, if you’d prefer and wish to take it, just click save logo in the post, and it will be immediately down loaded to your laptop. As a final point if you like to secure new and latest photo related to (Graphing Systems Of Inequalities Worksheet Algebra 2 ), please follow us on google plus or book mark this website, we try our best to provide regular update with all new and fresh pics. We do hope you like keeping here. For some up-dates and recent information about (Graphing Systems Of Inequalities Worksheet Algebra 2 ) shots, please kindly follow us on tweets, path, Instagram and google plus, or you mark this page on book mark area, We attempt to provide you with update regularly with all new and fresh pictures, enjoy your surfing, and find the ideal for you. graphing systems of inequalities worksheet algebra 2 Luxury Algebra 2 Programmed Instruction Algebraic Properties Worksheet Thanks for visiting our site, contentabove (Graphing Systems Of Inequalities Worksheet Algebra 2 ) published by at . At this time we are delighted to announce that we have found an awfullyinteresting contentto be reviewed, namely (Graphing Systems Of Inequalities Worksheet Algebra 2 ) Many people attempting to find details about(Graphing Systems Of Inequalities Worksheet Algebra 2 ) and of course one of these is you, is not it?
471
2,244
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.625
3
CC-MAIN-2019-26
latest
en
0.896744
https://pdhstar.com/courses/e-006-capacitance-4-pdh/
1,721,457,963,000,000,000
text/html
crawl-data/CC-MAIN-2024-30/segments/1720763515020.57/warc/CC-MAIN-20240720052626-20240720082626-00711.warc.gz
386,776,781
29,775
# E-006 Capacitance 10 Mar • 20 (Registered) • (6 Reviews) \$48.00 # Capacitance The Capacitance online PDH course is a part of the Electrical Engineering category of courses. This courses provide guidance on use of capacitor devices and the theory behind. Inductance is the property of a coil that causes electrical energy to be stored in a magnetic field about the coil. The energy is stored in such a way as to oppose any change in current. Capacitance is similar to inductance because it also causes a storage of energy. A capacitor is a device that stores electrical energy in anelectrostatic field. The energy is stored in such a way as to oppose any change in voltage. This course also explains how capacitance opposes a change in voltage. This course is based on Chapter 3 of Module 2, “Capacitance” of the Navy Electricity and Electronic Training Series (NAVEDTRA 14174),. This course is intended for use by electrical engineers, design and construction professionals, students and others interested in learning about basic electrical theory. ## Learning Objectives: Upon completion of this course, you will be able to: • State four characteristics of electrostatic lines of force • State the effect that an electrostatic field has on a charged particle • State the basic parts of a capacitor • State factors that affect the value of capacitance • Given the dielectric constant and the area of and the distance between the plates of a capacitor, solve for capacitance • State two types of power losses associated with capacitors • Define the term “working voltage” of a capacitor, and compute the working voltage of a capacitor • State what happens to the electrons in a capacitor when the capacitor is charging and when it is discharging • State the relationship between voltage and time in an RC circuit when the circuit is charging and discharging • State the relationship between the voltage drop across a resistor and the source voltage in an RC circuit • Given the component values of an RC circuit, compute the RC time constant • Use the universal time constant chart to determine the value of an unknown capacitor in an RC circuit • Calculate the value of total capacitance in a circuit containing capacitors of known value in series. • Calculate the value of total capacitance in a circuit containing capacitors of known value in parallel • State the difference between different types of capacitors. • Determine the electrical values of capacitors using the color code ×
517
2,497
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.546875
4
CC-MAIN-2024-30
latest
en
0.9088
http://www.firehouse.com/article/10575205/emergency-vehicle-ops-pumps-refresher-relay-operations?page=2
1,430,162,419,000,000,000
text/html
crawl-data/CC-MAIN-2015-18/segments/1429246659319.74/warc/CC-MAIN-20150417045739-00223-ip-10-235-10-82.ec2.internal.warc.gz
489,191,298
17,829
# Emergency Vehicle Ops: Pumps Refresher - Relay Operations Session Reference: 1 Time Required: 3 Hours Materials: • Three Fully Equipped Pumpers • Portable Master Stream Device • Pitot Gauge References: • Pump Operator Student Manual, Maryland Fire & Rescue Institute PREPARATION: Motivation: Objective (SPO): 1-1 The student will demonstrate an understanding of the pump operator’s responsibilities while operating in a relay situation and provide an adequate flow and intake pressure to the next pumper during practical evolutions, to the satisfaction of the instructor. Overview: Relay Operations Practical • Designing a Relay • Knowledge of apparatus & hose capacities • Fireground hydraulics • Relay Operating Practices Session 1 Relay Operations Practical SPO 1-1 The student will demonstrate an understanding of the pump operator’s responsibilities while operating in a relay situation and provide an adequate flow and intake pressure to the next pumper during practical evolutions, to the satisfaction of the instructor. EO 1-1 Identify what information is required to design a relay EO 1-2 Demonstrate an understanding of apparatus pump capacities and the flow capacities of various size hose lines. EO 1-3 Demonstrate an understanding of basic fireground hydraulics. EO 1-4 Describe the basic operating principles for a relay operation. I. Designing a Relay (1-1) A. Based on the amount of water needed 1. Relay capability will determine fire ground flow 2. Estimate total number of attack lines that may be required as the fire progresses. 3. Size of supply line equals number of attack lines B. Amount and size of supply hose available C. Number of pumpers available and their rated capacity II. Capacity of Apparatus Pumps & Supply Hose (1-2) A. Rated capacity of pumpers 1. 750 gpm ---- 2000 gpm 2. Largest pump should be at water source 3. Ability of apparatus to lay dual supply lines (split hosebed) B. Rated capacity of various size supply hose (Based on 1000' hose) 1. 2 1/2" = 250 gpm 2. 3" = 400 gpm 3. 4" = 750 gpm 4. 5" = 1500 gpm III. Fireground Hydraulics (1-3) A. Relay Losses 1. Friction Loss Factors FL = QxQ for 100' of 3" hose (Q = GPM / 100) a. Quantity of water flowing (GPM) b. Hose size c. Length of hose line 2. Head pressure due to elevation a. Add 5 psi for each 10' of plus elevation b. Deduct 5 psi for each 10' of minus elevation B. Net Pump Pressure 1. The difference between intake pressure and the discharge pressure of the pump (A measure of how much work the pump is doing). 2. Maximum net pump pressure that a pumper operating at its rated capacity can supply is 150 psi. If more than 150 psi is required, the capacity of the pump will be reduced. (200 psi = 70% of pump capacity). C. Fire Ground Rules of Thumb 1. Intake pressure — Ideal is 50 psi at pump intake. (Could vary from 20 psi to 100 psi) 2. Maximum working pressure for 2 1/2" & 3" hose is 200 psi. (Hose test pressure is 250 psi) 3. Maximum working pressure for 4" & 5" hose is 150 psi (Hose test pressure is 200 psi) 4. Maximum distance between pumpers – 1000' 5. Always start out at 150 psi pump pressure - you can always adjust up or down! D. Fire Ground Hydraulics Problems 1. Have students practice figuring friction loss in 3", 4" & 5" hose. 2. Have students calculate friction loss for dual supply lines. 3. Use various examples of gpm flow to show limitations of hose. E. Operating Principles for a Relay 1. Position pumper in a safe location 2. Connect hoselines to intake and discharge of pumper. 3. Engage pump 4. Put pump transmission in proper gear. 5. Set transfer valve to volume if using a two stage pump 6. Set throttle to desired pump pressure when water is received. May have to bleed air from supply line. 7. Adjust pump pressure to give next pumper 50 psi intake pressure. 8. Set relief valve or governor 9. To shut down relay, reverse procedures. Always shut down at attack pumper first. IV. Practical Evolutions (1-4) A. Utilizing three pumpers, set up a relay evolution using various sizes and lengths of supply hose between apparatus. 1. Water source can be a hydrant or draft source. 2. Utilize a portable master stream device for the fire ground flow. Check nozzle pressure with Pitot gauge to maintain desired flow. B. Rotate the apparatus so students can practice operating as source pumper, relay pumper, and attack pumper. SUMMARY: Review: Relay Operations Practical • Designing A Relay • Apparatus & Hose Capacity • Fire Ground Hydraulics • Relay Operating Practices
1,134
4,602
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.625
3
CC-MAIN-2015-18
latest
en
0.828497
https://www.citehr.com/460008-bonus-act-calculation-example-eligible-employees.html
1,611,446,381,000,000,000
text/html
crawl-data/CC-MAIN-2021-04/segments/1610703538741.56/warc/CC-MAIN-20210123222657-20210124012657-00587.warc.gz
729,420,716
11,392
Korgaonkar K A Ba,llb,mpm,dir&pm,dll&lw,d.cyber Nrvyas Hr Consultant we are paying bonus on 3500(limit as per act)*8.33%=291.55, formula. suppose i have three eligible employees for bonus. \"A\" present days 26*200.10=5203 & hence gets 3500*8.33%=292/pm. \"B\" present days 20*200.10=4002, hence get 3500*8.33%=292 \"C\" present days 10*200.10=2001*8.33%167. my query: is above calculation right or needs any change in this? From India, Visnagar Dear Nevyas, Your calculation and understanding is correct. I would like to tell you a simple method as under: 1. Write down in register earned B+DA during 12 months, month wise against each employee name. 2. In case B+DA exceeds 10000, delete such entries / names from register. 3. In case the entries are only in one or two or three months, check total no.of days worked by such employee. If it is less than 30, remove his name from register. 4. If B+DA is more than 3500, write / restrict to 3500 and if B+DA is less than 3500, retain the actual. 5. Take total of 12 months. This is the total B+DA amount eligible for Bonus calculation. 6. Calculate the bonus by multiplying the percentage decided to the above total B+DA amount eligible for bonus calculation. Hope I have made it easy for you. You can open an excel sheet and give appropriate formulas. It will be appreciated if you open an excel sheet as above and upload it for the benefit of forum. From India, Mumbai thanks Keshav, yes, this is easy method... but we would like to pay to contract labour... by calculation method i had posted... pl tell me for them pl tell me does it req any change... From India, Visnagar do we need to give bonus on prorata if no of days of an employee is less than 26 and his earned wages/ saalry is more than 3500? pl advise. From India, Visnagar This discussion thread is closed. If you want to continue this discussion or have a follow up question, please post it on the network. Add the url of this thread if you want to cite this discussion.
536
1,989
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.046875
3
CC-MAIN-2021-04
latest
en
0.916666
https://ginahsu.com/tag/leetcode/
1,586,172,907,000,000,000
text/html
crawl-data/CC-MAIN-2020-16/segments/1585371624083.66/warc/CC-MAIN-20200406102322-20200406132822-00270.warc.gz
503,358,873
38,909
## leetcode- Rotate Image Leetcode: https://leetcode.com/problems/rotate-image/description/ ```Given input matrix = [1,2,3], [4,5,6], [7,8,9] rotate the input matrix in-place such that it becomes: [7,4,1], [8,5,2], [9,6,3] ``` • (x, y), the affected point is (y, n – x – 1), (n – x – 1, n – y – 1), (n – y – 1, x),  “n” is the size of the matrix. The rotate function= (x, y) -> (y, n – x – 1) -> (n – x – 1, n – y – 1) -> (n – y – 1, x) -> (x, y). • For the i th line, we start from (i, i) ( !! in for loop  j = i ) , and ends at (i, n – 2 – i) • We only need process half of them. n/2 ## LeetCode – Plus One Given a non-negative integer represented as a non-empty array of digits, plus one to the integer. You may assume the integer do not contain any leading zero, except the number 0 itself. The digits are stored such that the most significant digit is at the head of the list. For example: Q1. int[] nums = {1,2,3,4}; int[] result = plusOne(nums); the digits are in the result array are {1,2,3,5}; ## LeetCode – Two Sum II Given an array of integers that is already sorted in ascending order, find two numbers such that they add up to a specific target number. CheckPoint:  if (numbers != null && numbers.length > 1) {throw new IllegalArgumentException(“No solution!”);}
419
1,284
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.515625
4
CC-MAIN-2020-16
latest
en
0.742656
https://www.aqua-calc.com/calculate/weight-to-volume/substance/cobaltous-blank-iodide-blank-hexahydrate
1,712,966,354,000,000,000
text/html
crawl-data/CC-MAIN-2024-18/segments/1712296816465.91/warc/CC-MAIN-20240412225756-20240413015756-00168.warc.gz
597,926,337
7,631
# Volume of Cobaltous iodide hexahydrate ## cobaltous iodide hexahydrate: convert weight to volume ### Volume of 100 grams of Cobaltous iodide hexahydrate centimeter³ 34.48 milliliter 34.48 foot³ 0 oil barrel 0 Imperial gallon 0.01 US cup 0.15 inch³ 2.1 US fluid ounce 1.17 liter 0.03 US gallon 0.01 meter³ 3.45 × 10-5 US pint 0.07 metric cup 0.14 US quart 0.04 metric tablespoon 2.3 US tablespoon 2.33 metric teaspoon 6.9 US teaspoon 7 ### The entered weight of Cobaltous iodide hexahydrate in various units of weight carat 500 ounce 3.53 gram 100 pound 0.22 kilogram 0.1 tonne 0 milligram 100 000 #### How many moles in 100 grams of Cobaltous iodide hexahydrate? There are 237.62 millimoles in 100 grams of Cobaltous iodide hexahydrate #### Foods, Nutrients and Calories SUGARFREE GUM, UPC: 022000013309 contain(s) 263 calories per 100 grams (≈3.53 ounces)  [ price ] 837 foods that contain Tocopherol, beta.  List of these foods starting with the highest contents of Tocopherol, beta and the lowest contents of Tocopherol, beta #### Gravels, Substances and Oils Substrate, Mix weighs 1 153 kg/m³ (71.97944 lb/ft³) with specific gravity of 1.153 relative to pure water.  Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical  or in a rectangular shaped aquarium or pond  [ weight to volume | volume to weight | price ] Tincalconite [Na2B4O7 ⋅ 5H2O] weighs 1 880 kg/m³ (117.36457 lb/ft³)  [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ] Volume to weightweight to volume and cost conversions for Refrigerant R-404A, liquid (R404A) with temperature in the range of -51.12°C (-60.016°F) to 68.34°C (155.012°F) #### Weights and Measurements A tonne per cubic centimeter (t/cm³) is a derived metric SI (System International) measurement unit of density used to measure volume in cubic centimeters in order to estimate weight or mass in tonnes The online number conversions include conversions between binary, octal, decimal and hexadecimal numbers. cap 12el to cap 00E conversion table, cap 12el to cap 00E unit converter or convert between all units of volume measurement. #### Calculators Triangle calculator and area of a triangle calculator
653
2,286
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.65625
3
CC-MAIN-2024-18
latest
en
0.683569
https://artofproblemsolving.com/wiki/index.php?title=2015_AMC_8_Problems/Problem_24&diff=next&oldid=78936
1,652,953,204,000,000,000
text/html
crawl-data/CC-MAIN-2022-21/segments/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00258.warc.gz
157,231,440
11,887
# Difference between revisions of "2015 AMC 8 Problems/Problem 24" A baseball league consists of two four-team divisions. Each team plays every other team in its division $N$ games. Each team plays every team in the other division $M$ games with $N>2M$ and $M>4$. Each team plays a 76 game schedule. How many games does a team play within its own division? $\textbf{(A) } 36 \qquad \textbf{(B) } 48 \qquad \textbf{(C) } 54 \qquad \textbf{(D) } 60 \qquad \textbf{(E) } 72$ ### Solution 1 On one team they play $\binom{3}{2}N$ games in their division and $4(M)$ games in the other. This gives $3N+4M=76$ Since $M>4$ we start by trying $M=5$. This doesn't work because $56$ is not divisible by $3$. Next $M=6$, does not work because $52$ is not divisible by $3$ We try $M=7$ this does work giving $N=16,~M=7$ and thus $3\times 16=\boxed{\textbf{(B)}~48}$ games in their division. ### Solution 3 $76=3N+4M > 10M$, giving $M \le 7$. Since $M>4$, we have $M=5,6,7$ Since $4M$ is $1$ $\pmod{3}$, we must have $M$ equal to $1$ $\pmod{3}$, so $M=7$. This gives $3N=48$, as desired. The answer is $\boxed{\textbf{(B)}~48}$.
398
1,123
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 31, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.5625
5
CC-MAIN-2022-21
latest
en
0.883873
https://www.quantumstudy.com/a-square-plate-of-mass-120g-and-edge-5-0-cm-rotates-about-one-of-the-edges-if-it-has/
1,701,409,267,000,000,000
text/html
crawl-data/CC-MAIN-2023-50/segments/1700679100276.12/warc/CC-MAIN-20231201053039-20231201083039-00362.warc.gz
1,046,843,492
48,544
# A square plate of mass 120g and edge 5.0 cm rotates about one of the edges. If it has … Q:A square plate of mass 120g and edge 5.0 cm rotates about one of the edges. If it has a uniform angular acceleration of 0.2 rad/s², The torque acting on the plate is (a) 3 × 10-5 N-m (b) 2 × 10-5 N-m (c) 3 × 10-4 N-m (d) 3 × 10-4 N-m Ans: (a)
128
340
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.65625
3
CC-MAIN-2023-50
latest
en
0.78
http://cis.jhu.edu/education/introPatternTheory/additional/advection/advection4.html
1,527,238,777,000,000,000
text/html
crawl-data/CC-MAIN-2018-22/segments/1526794867055.20/warc/CC-MAIN-20180525082822-20180525102822-00277.warc.gz
62,390,662
2,012
## Computing the 1D Advection Equation For the most part, analytical solutions of the linear advection equation are possible. However, real life problems deal with equations such as \frac{\partial u}{\partial t} + \frac{\partial}{\partial x}(cu) = 0 where $$c$$ varies as a function of $$x$$ and so on. We are interested in a numerical solution over the domain $$x_a \leq x \leq x_b$$ and $$t_s \leq t \leq t_e$$ Without loss of generality $$x_a=0, t_s=0$$ The domain is discretized as: \require{AMSmath} \begin{align*} x_i & = x_a + \left(x_b-x_a\right)\frac{i}{N_x} & i = 0,...,N_x \\ t_k & = t_s + \left(t_e-t_s\right)\frac{k}{N_t} & k = 0,...,N_t \end{align*} $$N_x$$ is the number of discrete points in $$x$$ $$N_t$$ is the number of discrete points in $$t$$ Let $$\Delta x=\frac{x_b-x_a}{N_x}$$ and $$\Delta t=\frac{t_e-t_s}{N_t}$$ be the space--and time--steps with discrete values given by $$\phi_i^k$$.
307
920
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.203125
3
CC-MAIN-2018-22
longest
en
0.712879
http://www.americanscientist.org/issues/pub/2004/5/g-ology/2
1,493,255,827,000,000,000
text/html
crawl-data/CC-MAIN-2017-17/segments/1492917121778.66/warc/CC-MAIN-20170423031201-00558-ip-10-145-167-34.ec2.internal.warc.gz
433,501,842
34,952
MY AMERICAN SCIENTIST SEARCH COMPUTING SCIENCE # g-OLOGY QED The naive mental picture of an electron is a blob of mass and electric charge, spinning on its axis like a tiny planet. If we take this image seriously, the moving charge on the spinning particle's surface has to be regarded as an electric current, which ought to generate a magnetic field. The g factor (also known as the gyromagnetic ratio) is the constant that determines how much magnetic field arises from a given amount of charge, mass and spin. The formula is: where µ is the magnetic moment, e the electric charge, m the mass and s the spin angular momentum (all expressed in appropriate units). Early experimental evidence suggested that the numerical value of g is approximately 2. In the 1920s P. A. M. Dirac created a new and not-so-naive theory of electrons in which g was no longer just an arbitrary constant to be measured experimentally; instead, the value of g was specified directly by the theory. For an electron in total isolation, Dirac calculated that g is exactly 2. We now know that this result was slightly off the mark; g is greater than 2 by roughly one part in a thousand. And yet Dirac's mathematics was not wrong. The source of the error is that no electron is ever truly alone; even in a perfect vacuum, an electron is wrapped in a halo of particles and antiparticles, which are continually being emitted and absorbed, created and annihilated. Interactions with these "virtual" particles alter various properties of the electron, including the g factor. Methods for accurately calculating g were devised in the 1940s as part of a thorough overhaul of the theory of electrons—a theory called quantum electrodynamics, or QED. That the calculation of g can be honed to such a razor edge of precision is something of a fluke. The mass, charge and magnetic moment of the electron are known only to much lower accuracy; so how can g, which is defined in terms of these quantities, be pinned down more closely? The answer is that g is a dimensionless ratio, calculated and measured in such a way that uncertainties in all those other factors cancel out. Experimental measurements of g benefit from another fortunate circumstance. The experiments can be arranged to determine not g itself but the difference between g and 2; thus the measurements have come to be known as "g minus 2 experiments." Because g–2 is only about a thousandth of g, the measurement gains three decimal places of precision for free. comments powered by Disqus EMAIL TO A FRIEND : Of Possible Interest Feature Article: The Statistical Crisis in Science Feature Article: Candy Crush's Puzzling Mathematics Technologue: The Quest for Randomness
573
2,714
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.578125
3
CC-MAIN-2017-17
latest
en
0.955853
http://physicshelpline.net/entries/work-power-energy/wpe-5
1,696,281,294,000,000,000
text/html
crawl-data/CC-MAIN-2023-40/segments/1695233511021.4/warc/CC-MAIN-20231002200740-20231002230740-00437.warc.gz
32,160,381
6,678
## Solution Search • January 30, 2023 • September 11, 2021 • August 6, 2021 • Iriam August 4, 2021 • Abhigyan Martin Ninama September 8, 2017 ### WPE Q- A block of mass 5 kg hangs on a spring. When a second block with an identical mass of 5 kg is  tied to the first, the spring stretches an additional ho = 1 m. a) What is the value of the spring constant k? Now the string is burned and the second block falls off. b) How far above its original position does the remaining block attain its maximum speed? c) What is the maximum speed attained by the remaining block? Solution
165
584
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.65625
3
CC-MAIN-2023-40
latest
en
0.908277
https://www.physicsforums.com/threads/quick-question-explain-work-energy-concept.208104/
1,518,926,649,000,000,000
text/html
crawl-data/CC-MAIN-2018-09/segments/1518891811352.60/warc/CC-MAIN-20180218023321-20180218043321-00056.warc.gz
900,842,363
15,380
# Quick Question - Explain Work Energy Concept 1. Jan 9, 2008 ### physicsmarkb [Solved] Quick Question - Explain Work Energy Concept 1. The problem statement, all variables and given/known data Use the work - kinetic energy theorem to find the force required to accelerate an electron (m = 9.11 x 10^-31 kg) from rest to a speed of 1.50 x 10^7 m/s in a distance of .0125 m. 2. Relevant equations W = Fx cos(theta), K = 1/2 mv^2 3. The attempt at a solution I know that I would set Fx cos(theta) = 1/2 mv^2 and then solve for F but I don't understand why I would do this. Last edited: Jan 9, 2008 2. Jan 9, 2008 ### physicsmarkb Does anyone know why I have have to solve it like this? 3. Jan 9, 2008 ### blochwave work = the change in kinetic energy, in other words the final kinetic energy - the initial kinetic energy. The electron starts from rest and has no initial kinetic energy. That pretty much IS the work-energy theorem Make sure you understand what work is, it's how much energy you're gonna impart to the electron, and you know what final kinetic energy you would like the electron to have 4. Jan 9, 2008 ### physicsmarkb So with K final, all you have is mass and velocity. With W = Fx, you have force and distance. Why do you divide mass and velocity by distance? Edit: I just realized that you divide because you're trying to solve for F. What I still don't understand is that why you have all the information for K = 1/2 mv^2 which is W = K but that doesn't work. I don't get why you have to set it equal to W = Fx. Last edited: Jan 9, 2008 5. Jan 9, 2008 ### blochwave Well with W=K and knowing K, you would've found work. Were you looking for work? No. Can you use the definition of work to find force? Yes. And that's what you did 6. Jan 9, 2008 ### physicsmarkb Wow I'm so dumb. I can't believe I wasn't paying attention to W and F.
526
1,875
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.828125
4
CC-MAIN-2018-09
longest
en
0.957549
https://algebra-answer.com/algebra-answer-book/y-intercept/prediction-equation.html
1,526,892,789,000,000,000
text/html
crawl-data/CC-MAIN-2018-22/segments/1526794863972.16/warc/CC-MAIN-20180521082806-20180521102806-00373.warc.gz
517,121,874
7,937
Our users: I have two children that are average students. They do fine in most subjects but math has always stumped them. They found your algebra software to be like an in-home tutor. Im happy to say their marks are finally going up. Mary Jones, NY I really needed a way to get help with my homework when I wasn't able to speak with my teacher. Algebra Helper really solved my problem :) Anne Mitowski, TX Your new release is so much more intuitive! You team was quick to respond. Great job! I will recommend the new version to other students. Lee Wyatt, TX Step-by-step, Algebra Helper has made algebra as easy as memorizing the multiplication tables! It is just impossible that I would be doing so well academically, and feel so confident about myself, if not for this program! It changed my life! Oscar Peterman, NJ It was hard to go back to school as an adult, especially when I had to redo math courses because it had been two decades since graduation. I needed help badly and thankfully, your product delivered. I cant thank you enough. Richard Penn, DE. Students struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. Can you find yours among them? Search phrases used on 2014-07-25: • algebra problem solver calculator ratios • printable pre algebra pretest • percent to fraction • integer rules for dummies • solve the square root of 27 • a caculator that shows work • transformacion de radicales dobles a simples • algebraor • complex java code • how do i get my ti-83 calculator to change decimals to square roots • convert mixed fraction to decimal • simplifying variable fractions worksheet • why teach balancin gequations method • rules of exponents chart • simplify 4x-2+6y+y-4 • solving exponential equations without logarithms worksheet • solving equations involving addition multiplication subtraction division • estimating fractions, decimals, whole numbers • rectangular coordinate graph • write a fraction and decimal for each shaded part • easy ways to understand and solve all types of work problems • theorem pythagorean with calculator fx-570ms • slope field maker maple • graph with interval notation • what is percent • a sales peerson earns \$132 commission selling \$2200 what is commission rate • 8th grade algebraic expressions ppt • algebraic expression practice worksheet seventh grade • tenths • carbohydrate nutrient handout • How to Calculate LCM for x squared • square matrices (A+b)2 • one step equations worksheets no negative • solving for exponents graph • using a vertex form to model projectile motion • Punchline algebra book a 8.4 answer key no downlaod • PRETEST COMPARING DECIMALS • math qiuz table about solving base percentage rate • answers to the 9th grade Unit 5: Inequalities - 5-SEMESTER EXAM • Solve My Synthetic Division Problem • percentage math problems 8th grade • question and answers in math for elementary • free printable slope game • multiplying and dividing equations worksheet • +lesson quiz transparency 5-2 using intercepts anwsers • synthetic division • quadratic increasing and decreasing funcions on a TI 84 CALCULATOR UTUBE • simplifying expressions y+8y = • analytical math problem solving.ppt • at a local bookstore, John purchased a history textbook and a magazine that cost a total of \$32 • the area of a rectangle is 54cm.its length and breadth are reduced by 5cm \$ 2cm respectively so as to become a square.Find the length of a side of the square • APPLICATION IN RADICAL XRESSION IN REAL LIFE SITUATION • number graph with decimals • sagar and akash ran 2km race twice • plant growth over time • positive and negative number line • www.prealgerbrawithpizzaz.com • polynomial functions in interval notation • use your algorithm to simplify integers • one of the games at a carnival involves trying to ring a bell be hitting a lever that propels • solving linear equations • writing and solving perimeter expressions worksheets • mathematics poem samples • completely free algebra solver step by step square roots • Simplifying Fractions Calculator Math • prime number poems • 6th grade fraction pretest printable • solving equations by multiplying and dividing worksheets • nys math assessment in mandarin + 5th grade • tic tac toe algebra • using the point slope formula • subtracting mixed numbers • geometry dilation worksheet • compound fractions • arithmetic sequence examples • Glencoe/McGraw-Hill answer sheet page 8 Integers and Absolute Value • inequalities by multiplying and dividing answers Prev Next Start solving your Algebra Problems in next 5 minutes! 2Checkout.com is an authorized reseller of goods provided by Sofmath Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of May 21st you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page. If you order now you will also receive 30 minute live session from tutor.com for a 1\$! You Will Learn Algebra Better - Guaranteed! Just take a look how incredibly simple Algebra Helper is: Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor: Step 2 : Let Algebra Helper solve it: Step 3 : Ask for an explanation for the steps you don't understand: Algebra Helper can solve problems in all the following areas: • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values) • factoring and expanding expressions • finding LCM and GCF • (simplifying, rationalizing complex denominators...) • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) • solving a system of two and three linear equations (including Cramer's rule) • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) • graphing general functions • operations with functions (composition, inverse, range, domain...) • simplifying logarithms • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...) • arithmetic and other pre-algebra topics (ratios, proportions, measurements...) ORDER NOW! 2Checkout.com is an authorized reseller of goods provided by Sofmath "It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..." C. Sievert, KY Sofmath 19179 Blanco #105-234San Antonio, TX 78258 Phone: (512) 788-5675Fax: (512) 519-1805
1,547
6,835
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.515625
3
CC-MAIN-2018-22
latest
en
0.927872
https://icsehelp.com/ml-aggarwal-rational-and-irrational-number-exe-1-5-class-9-icse-maths-solutions/
1,675,515,401,000,000,000
text/html
crawl-data/CC-MAIN-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00347.warc.gz
319,911,554
21,512
ML Aggarwal Rational and Irrational Number Exe-1.5 Class 9 ICSE Maths Solutions. We Provide Step by Step Answer of  Exe-1.5 Questions for Rational and Irrational Number as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-9. ## ML Aggarwal Rational and Irrational Number Exe-1.5 Class 9 ICSE Maths Solutions Board ICSE Publications Avichal Publishig Company (APC) Subject Maths Class 9th Chapter-1 Rational and Irrational Writer ML Aggarwal Book Name Understanding Topics Solution of Exe-1.5 Questions Edition 2022-2023 ### Rational and Irrational Number Exe-1.5 ML Aggarwal Class 9 ICSE Maths Solutions Page 34 #### Question 1. Rationalize the denominator of the following: (i) 3/4√5 (ii) 5√7 / √3 (iii) 3/(4 – √7) (iv) 17/(3√2 + 1) (v) 16/ (√41 – 5) (vi) 1/ (√7 – √6) (vii) 1/ (√5 + √2) (viii) (√2 + √3) / (√2 – √3) ##### (i) 3/4√5 Let us rationalize, 3/4√5 = (3×√5) /(4√5×√5) = (3√5) / (4×5) = (3√5) / 20 ##### (ii) 5√7 / √3 Let us rationalize, 5√7 / √3 = (5√7×√3) / (√3×√3) = 5√21/3 ##### (iii) 3/(4 – √7) Let us rationalize, 3/(4 – √7) = [3×(4 + √7)] / [(4 – √7) × (4 + √7)] = 3(4 + √7) / [42 – (√7)2] = 3(4 + √7) / [16 – 7] = 3(4 + √7) / 9 = (4 + √7) / 3 ##### (iv) 17/(3√2 + 1) Let us rationalize, 17/(3√2 + 1) = 17(3√2 – 1) / [(3√2 + 1) (3√2 – 1)] = 17(3√2 – 1) / [(3√2)2 – 12] = 17(3√2 – 1) / [9.2 – 1] = 17(3√2 – 1) / [18 – 1] = 17(3√2 – 1) / 17 = (3√2 – 1) ##### (v) 16/ (√41 – 5) Let us rationalize, 16/ (√41 – 5) = 16(√41 + 5) / [(√41 – 5) (√41 + 5)] = 16(√41 + 5) / [(√41)2 – 52] = 16(√41 + 5) / [41 – 25] = 16(√41 + 5) / [16] = (√41 + 5) ##### (vi) 1/ (√7 – √6) Let us rationalize, 1/ (√7 – √6) = 1(√7 + √6) / [(√7 – √6) (√7 + √6)] = (√7 + √6) / [(√7)2 – (√6)2] = (√7 + √6) / [7 – 6] = (√7 + √6) / 1 = (√7 + √6) ##### (vii) 1/ (√5 + √2) Let us rationalize, 1/ (√5 + √2) = 1(√5 – √2) / [(√5 + √2) (√5 – √2)] = (√5 – √2) / [(√5)2 – (√2)2] = (√5 – √2) / [5 – 2] = (√5 – √2) / [3] = (√5 – √2) /3 ##### (viii) (√2 + √3) / (√2 – √3) Let us rationalize, (√2 + √3) / (√2 – √3) = [(√2 + √3) (√2 + √3)] / [(√2 – √3) (√2 + √3)] = [(√2 + √3)2] / [(√2)2 – (√3)2] = [2 + 3 + 2√2√3] / [2 – 3] = [5 + 2√6] / -1 = – (5 + 2√6) #### Question 2. Simplify each of the following by rationalizing the denominator: (i) (7 + 3√5) / (7 – 3√5) (ii) (3 – 2√2) / (3 + 2√2) (iii) (5 – 3√14) / (7 + 2√14) ##### (i) (7 + 3√5) / (7 – 3√5) Let us rationalize the denominator, we get (7 + 3√5) / (7 – 3√5) = [(7 + 3√5) (7 + 3√5)] / [(7 – 3√5) (7 + 3√5)] = [(7 + 3√5)2] / [72 – (3√5)2] = [72 + (3√5)2 + 2.7. 3√5] / [49 – 9.5] = [49 + 9.5 + 42√5] / [49 – 45] = [49 + 45 + 42√5] / [4] = [94 + 42√5] / 4 = 2[47 + 21√5]/4 = [47 + 21√5]/2 ##### (ii) (3 – 2√2) / (3 + 2√2) Let us rationalize the denominator, we get (3 – 2√2) / (3 + 2√2) = [(3 – 2√2) (3 – 2√2)] / [(3 + 2√2) (3 – 2√2)] = [(3 – 2√2)2] / [32 – (2√2)2] = [32 + (2√2)2 – 2.3.2√2] / [9 – 4.2] = [9 + 4.2 – 12√2] / [9 – 8] = [9 + 8 – 12√2] / 1 = 17 – 12√2 ##### (iii) (5 – 3√14) / (7 + 2√14) Let us rationalize the denominator, we get (5 – 3√14) / (7 + 2√14) = [(5 – 3√14) (7 – 2√14)] / [(7 + 2√14) (7 – 2√14)] = [5(7 – 2√14) – 3√14 (7 – 2√14)] / [72 – (2√14)2] = [35 – 10√14 – 21√14 + 6.14] / [49 – 4.14] = [35 – 31√14 + 84] / [49 – 56] = [119 – 31√14] / [-7] = -[119 – 31√14] / 7 = [31√14 – 119] / 7 #### Question 3. Simplify: [7√3 / (√10 + √3)] – [2√5 / (√6 + √5)] – [3√2 / (√15 + 3√2)] Let us simplify individually, [7√3 / (√10 + √3)] Let us rationalize the denominator, 7√3 / (√10 + √3) = [7√3(√10 – √3)] / [(√10 + √3) (√10 – √3)] = [7√3.√10 – 7√3.√3] / [(√10)2 – (√3)2] = [7√30 – 7.3] / [10 – 3] = 7[√30 – 3] / 7 = √30 – 3 Now, [2√5 / (√6 + √5)] Let us rationalize the denominator, we get 2√5 / (√6 + √5) = [2√5 (√6 – √5)] / [(√6 + √5) (√6 – √5)] = [2√5.√6 – 2√5.√5] / [(√6)2 – (√5)2] = [2√30 – 2.5] / [6 – 5] = [2√30 – 10] / 1 = 2√30 – 10 Now, [3√2 / (√15 + 3√2)] Let us rationalize the denominator, we get 3√2 / (√15 + 3√2) = [3√2 (√15 – 3√2)] / [(√15 + 3√2) (√15 – 3√2)] = [3√2.√15 – 3√2.3√2] / [(√15)2 – (3√2)2] = [3√30 – 9.2] / [15 – 9.2] = [3√30 – 18] / [15 – 18] = 3[√30 – 6] / [-3] = [√30 – 6] / -1 = 6 – √30 So, according to the question let us substitute the obtained values, [7√3 / (√10 + √3)] – [2√5 / (√6 + √5)] – [3√2 / (√15 + 3√2)] = (√30 – 3) – (2√30 – 10) – (6 – √30) = √30 – 3 – 2√30 + 10 – 6 + √30 = 2√30 – 2√30 – 3 + 10 – 6 = 1 #### Question 4. Simplify: [1/(√4 + √5)] + [1/(√5 + √6)] + [1/(√6 + √7)] + [1/(√7 + √8)] + [1/(√8 + √9)] Let us simplify individually, [1/(√4 + √5)] Rationalize the denominator, we get [1/(√4 + √5)] = [1(√4 – √5)] / [(√4 + √5) (√4 – √5)] = [(√4 – √5)] / [(√4)2 – (√5)2] = [(√4 – √5)] / [4 – 5] = [(√4 – √5)] / -1 = -(√4 – √5) Now, [1/(√5 + √6)] Rationalize the denominator, we get [1/(√5 + √6)] = [1(√5 – √6)] / [(√5 + √6) (√5 – √6)] = [(√5 – √6)] / [(√5)2 – (√6)2] = [(√5 – √6)] / [5 – 6] = [(√5 – √6)] / -1 = -(√5 – √6) Now, [1/(√6 + √7)] Rationalize the denominator, we get [1/(√6 + √7)] = [1(√6 – √7)] / [(√6 + √7) (√6 – √7)] = [(√6 – √7)] / [(√6)2 – (√7)2] = [(√6 – √7)] / [6 – 7] = [(√6 – √7)] / -1 = -(√6 – √7) Now, [1/(√7 + √8)] Rationalize the denominator, we get [1/(√7 + √8)] = [1(√7 – √8)] / [(√7 + √8) (√7 – √8)] = [(√7 – √8)] / [(√7)2 – (√8)2] = [(√7 – √8)] / [7 – 8] = [(√7 – √8)] / -1 = -(√7 – √8) Now, [1/(√8 + √9)] Rationalize the denominator, we get [1/(√8 + √9)] = [1(√8 – √9)] / [(√8 + √9) (√8 – √9)] = [(√8 – √9)] / [(√8)2 – (√9)2] = [(√8 – √9)] / [8 – 9] = [(√8 – √9)] / -1 = -(√8 – √9) So, according to the question let us substitute the obtained values, [1/(√4 + √5)] + [1/(√5 + √6)] + [1/(√6 + √7)] + [1/(√7 + √8)] + [1/(√8 + √9)] = -(√4 – √5) + -(√5 – √6) + -(√6 – √7) + -(√7 – √8) + -(√8 – √9) = -√4 + √5 – √5 + √6 – √6 + √7 – √7 + √8 – √8 + √9 = -√4 + √9 = -2 + 3 = 1 #### Question 5. Give a and b are rational numbers. Find a and b if: (i) [3 – √5] / [3 + 2√5] = -19/11 + a√5 (ii) [√2 + √3] / [3√2 – 2√3] = a – b√6 (iii) {[7 + √5]/[7 – √5]} – {[7 – √5]/[7 + √5]} = a + 7/11 b√5 ##### (i) [3 – √5] / [3 + 2√5] = -19/11 + a√5 Let us consider LHS [3 – √5] / [3 + 2√5] Rationalize the denominator, [3 – √5] / [3 + 2√5] = [(3 – √5) (3 – 2√5)] / [(3 + 2√5) (3 – 2√5)] = [3(3 – 2√5) – √5(3 – 2√5)] / [32 – (2√5)2] = [9 – 6√5 – 3√5 + 2.5] / [9 – 4.5] = [9 – 6√5 – 3√5 + 10] / [9 – 20] = [19 – 9√5] / -11 = -19/11 + 9√5/11 So when comparing with RHS -19/11 + 9√5/11 = -19/11 + a√5 Hence, value of a = 9/11 ##### (ii) [√2 + √3] / [3√2 – 2√3] = a – b√6 Let us consider LHS [√2 + √3] / [3√2 – 2√3] Rationalize the denominator, [√2 + √3] / [3√2 – 2√3] = [(√2 + √3) (3√2 + 2√3)] / [(3√2 – 2√3) (3√2 + 2√3)] = [√2(3√2 + 2√3) + √3(3√2 + 2√3)] / [(3√2)2 – (2√3)2] = [3.2 + 2√2√3 + 3√2√3 + 2.3] / [9.2 – 4.3] = [6 + 2√6 + 3√6 + 6] / [18 – 12] = [12 + 5√6] / 6 = 12/6 + 5√6/6 = 2 + 5√6/6 = 2 – (-5√6/6) So when comparing with RHS 2 – (-5√6/6) = a – b√6 Hence, value of a = 2 and b = -5/6 ##### (iii) {[7 + √5]/[7 – √5]} – {[7 – √5]/[7 + √5]} = a + 7/11 b√5 Let us consider LHS Since there are two terms, let us solve individually {[7 + √5]/[7 – √5]} Rationalize the denominator, [7 + √5]/[7 – √5] = [(7 + √5) (7 + √5)] / [(7 – √5) (7 + √5)] = [(7 + √5)2] / [72 – (√5)2] = [72 + (√5)2 + 2.7.√5] / [49 – 5] = [49 + 5 + 14√5] / [44] = [54 + 14√5] / 44 Now, {[7 – √5]/[7 + √5]} Rationalize the denominator, [7 – √5]/[7 + √5] = (7 – √5) (7 – √5)] / [(7 + √5) (7 – √5)] = [(7 – √5)2] / [72 – (√5)2] = [72 + (√5)2 – 2.7.√5] / [49 – 5] = [49 + 5 – 14√5] / [44] = [54 – 14√5] / 44 So, according to the question {[7 + √5]/[7 – √5]} – {[7 – √5]/[7 + √5]} By substituting the obtained values, = {[54 + 14√5] / 44} – {[54 – 14√5] / 44} = [54 + 14√5 – 54 + 14√5]/44 = 28√5/44 = 7√5/11 So when comparing with RHS 7√5/11 = a + 7/11 b√5 Hence, value of a = 0 and b = 1 #### Question 6. If {[7 + 3√5] / [3 + √5]} – {[7 – 3√5] / [3 – √5]} = p + q√5, find the value of p and q where p and q are rational numbers. Let us consider LHS Since there are two terms, let us solve individually {[7 + 3√5] / [3 + √5]} Rationalize the denominator, [7 + 3√5] / [3 + √5] = [(7 + 3√5) (3 – √5)] / [(3 + √5) (3 – √5)] = [7(3 – √5) + 3√5(3 – √5)] / [32 – (√5)2] = [21 – 7√5 + 9√5 – 3.5] / [9 – 5] = [21 + 2√5 – 15] / [4] = [6 + 2√5] / 4 = 2[3 + √5]/4 = [3 + √5] /2 Now, {[7 – 3√5] / [3 – √5]} Rationalize the denominator, [7 – 3√5] / [3 – √5] = [(7 – 3√5) (3 + √5)] / [(3 – √5) (3 + √5)] = [7(3 + √5) – 3√5(3 + √5)] / [32 – (√5)2] = [21 + 7√5 – 9√5 – 3.5] / [9 – 5] = [21 – 2√5 – 15] / 4 = [6 – 2√5]/4 = 2[3 – √5]/4 = [3 – √5]/2 So, according to the question {[7 + 3√5] / [3 + √5]} – {[7 – 3√5] / [3 – √5]} By substituting the obtained values, = {[3 + √5] /2} – {[3 – √5] /2} = [3 + √5 – 3 + √5]/2 = [2√5]/2 = √5 So when comparing with RHS √5 = p + q√5 Hence, value of p = 0 and q = 1 #### Question 7. Rationalise the denominator of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732, upto three places of decimal: (i) √2/(2 + √2) (ii) 1/(√3 + √2) ##### (i) √2/(2 + √2) By rationalizing the denominator, √2/(2 + √2) = [√2(2 – √2)] / [(2 + √2) (2 – √2)] = [2√2 – 2] / [22 – (√2)2] = [2√2 – 2] / [4 – 2] = 2[√2 – 1] / 2 = √2 – 1 = 1.414 – 1 = 0.414 ##### (ii) 1/(√3 + √2) By rationalizing the denominator, 1/(√3 + √2) = [1(√3 – √2)] / [(√3 + √2) (√3 – √2)] = [(√3 – √2)] / [(√3)2 – (√2)2] = [(√3 – √2)] / [3 – 2] = [(√3 – √2)] / 1 = (√3 – √2) = 1.732 – 1.414 = 0.318 #### Question 8. If a = 2 + √3, find 1/a, (a – 1/a) Given: a = 2 + √3 So, 1/a = 1/ (2 + √3) By rationalizing the denominator, 1/ (2 + √3) = [1(2 – √3)] / [(2 + √3) (2 – √3)] = [(2 – √3)] / [22 – (√3)2] = [(2 – √3)] / [4 – 3] = (2 – √3) Then, a – 1/a = 2 + √3 – (2 – √3) = 2 + √3 – 2 + √3 = 2√3 #### Question 9. Solve: If x = 1 – √2, find 1/x, (x – 1/x)4 Given: x = 1 – √2 so, 1/x = 1/(1 – √2) By rationalizing the denominator, 1/ (1 – √2) = [1(1 + √2)] / [(1 – √2) (1 + √2)] = [(1 + √2)] / [12 – (√2)2] = [(1 + √2)] / [1 – 2] = (1 + √2) / -1 = -(1 + √2 ) Then, (x – 1/x)4 = [1 – √2 – (-1 – √2)]4 = [1 – √2 + 1 + √2]4 = 24 = 16 ### ML Aggarwal Rational and Irrational Number Exe-1.5 Class 9 ICSE Maths Solutions Page 35 #### Question 10. Solve: If x = 5 – 2√6, find 1/x, (x2 – 1/x2) Given: x = 5 – 2√6 so, 1/x = 1/(5 – 2√6) By rationalizing the denominator, 1/(5 – 2√6) = [1(5 + 2√6)] / [(5 – 2√6) (5 + 2√6)] = [(5 + 2√6)] / [52 – (2√6)2] = [(5 + 2√6)] / [25 – 4.6] = [(5 + 2√6)] / [25 – 24] = (5 + 2√6) Then, x + 1/x = 5 – 2√6 + (5 + 2√6) = 10 Square on both sides we get (x + 1/x)2 = 102 x2 + 1/x2 + 2x.1/x = 100 x2 + 1/x2 + 2 = 100 x2 + 1/x2 = 100 – 2 = 98 #### Question 11. If p = (2-√5)/(2+√5) and q = (2+√5)/(2-√5), find the values of (i) p + q (ii) p – q (iii) p2 + q2 (iv) p2 – q2 Given: p = (2-√5)/(2+√5) and q = (2+√5)/(2-√5) ##### (i) p + q [(2-√5)/(2+√5)] + [(2+√5)/(2-√5)] So by rationalizing the denominator, we get = [(2 – √5)2 + (2 + √5)2] / [22 – (√5)2] = [4 + 5 – 4√5 + 4 + 5 + 4√5] / [4 – 5] = [18]/-1 = -18 ##### (ii) p – q [(2-√5)/(2+√5)] – [(2+√5)/(2-√5)] So by rationalizing the denominator, we get = [(2 – √5)2 – (2 + √5)2] / [22 – (√5)2] = [4 + 5 – 4√5 – (4 + 5 + 4√5)] / [4 – 5] = [9 – 4√5 – 9 – 4√5] / -1 = [-8√5]/-1 = 8√5 ##### (iii) p2 + q2 We know that (p + q)2 = p2 + q2 + 2pq So, p2 + q2 = (p + q)2 – 2pq pq = [(2-√5)/(2+√5)] × [(2+√5)/(2-√5)] = 1 p + q = -18 so, p2 + q2 = (p + q)2 – 2pq = (-18)2 – 2(1) = 324 – 2 = 322 ##### (iv) p2 – q2 We know that, p2 – q2 = (p + q) (p – q) So, by substituting the values p2 – q2 = (p + q) (p – q) = (-18) (8√5) = -144√5 #### Question 12. If x = (√2 – 1)/( √2 + 1) and y = (√2 + 1)/( √2 – 1), find the value of x2 + 5xy + y2. Given: x = (√2 – 1)/( √2 + 1) and y = (√2 + 1)/( √2 – 1) x + y = [(√2 – 1)/( √2 + 1)] + [(√2 + 1)/( √2 – 1)] By rationalizing the denominator, = [(√2 – 1)2 + (√2 + 1)2] / [(√2)2 – 12] = [2 + 1 – 2√2 + 2 + 1 + 2√2] / [2 – 1] = [6] / 1 = 6 xy = [(√2 – 1)/( √2 + 1)] × [(√2 + 1)/( √2 – 1)] = 1 We know that x2 + 5xy + y2 = x+ y2 + 2xy + 3xy It can be written as = (x + y)2 + 3xy Substituting the values = 62 + 3 × 1 So we get = 36 + 3 = 39 —  : End of ML Aggarwal Rational and Irrational Number Exe-1.5 Class 9 ICSE Maths Solutions :–
6,716
12,456
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.6875
5
CC-MAIN-2023-06
longest
en
0.577396
http://mathforum.org/kb/message.jspa?messageID=7391013
1,527,392,310,000,000,000
text/html
crawl-data/CC-MAIN-2018-22/segments/1526794867995.55/warc/CC-MAIN-20180527024953-20180527044953-00364.warc.gz
183,866,614
6,126
Search All of the Math Forum: Views expressed in these public forums are not endorsed by NCTM or The Math Forum. Notice: We are no longer accepting new posts, but the forums will continue to be readable. Topic: Pseudoteaching Replies: 31   Last Post: Apr 19, 2011 9:35 AM Messages: [ Previous | Next ] Robert Hansen Posts: 11,345 From: Florida Registered: 6/22/09 Re: Pseudoteaching Posted: Feb 22, 2011 7:28 PM Those are pretty neat, like math problem bloopers. The dart board example could have been a good example if it had been worded better. My brain skipped a beat when I was trying to picture a distribution of darts that made a triangular pattern. Technically, you would have to say something to the effect that the darts have an equal chance of hitting anywhere and then say that you counted 100 within the boundary of the triangle and then ask how many (of those 100) would you expect to find in the circle. > > Here's a working definition of "pseudoteaching" at > > (http://fnoschese.wordpress.com/pseudoteaching/): > > > > "Pseudoteaching is something you realize you?re > doing > > after you?ve attempted a lesson which from the > outset > > looks like it should result in student learning, > but > > upon further reflection, you realize that it [sic] > > the very lesson itself was flawed and involved > > minimal learning." > > > (http://blog.mrmeyer.com/?p=9413). > > > > Now read some of those posts and behold a couple of > > not-really-surprising things: (a) open-ended, > > discovery learning is never or hardly ever > > pseudoteaching, and (b) little to no evidence is > > given for (a). > > > > All these inkhorn arguments for an already-accepted > > conclusion. These folks should be theologians. > > See this link for a number of examples from > textbooks: > http://blog.mrmeyer.com/?cat=89 > > Richard Date Subject Author 2/22/11 Joshua Fisher 2/22/11 Robert Hansen 2/22/11 Richard Strausz 2/22/11 Joshua Fisher 2/22/11 Robert Hansen 2/22/11 Joshua Fisher 2/23/11 Richard Strausz 2/23/11 Robert Hansen 2/23/11 Richard Strausz 2/23/11 Joshua Fisher 2/23/11 Paul A. Tanner III 2/23/11 Richard Strausz 2/23/11 Robert Hansen 2/23/11 Richard Strausz 2/23/11 Joshua Fisher 2/24/11 Robert Hansen 2/24/11 Richard Strausz 2/24/11 Joshua Fisher 2/24/11 Richard Strausz 2/24/11 Joshua Fisher 2/25/11 Mark Hammond 2/27/11 John Threlkeld 2/25/11 Robert Hansen 2/25/11 Joshua Fisher 2/25/11 Mark Hammond 2/26/11 Robert Hansen 3/1/11 GS Chandy 3/13/11 Richard Strausz 4/18/11 Richard Strausz 4/18/11 Robert Hansen 4/19/11 Jonathan Groves 4/19/11 Richard Strausz
760
2,583
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.15625
3
CC-MAIN-2018-22
latest
en
0.920371
https://edustrings.com/physics/2105769.html
1,709,174,786,000,000,000
text/html
crawl-data/CC-MAIN-2024-10/segments/1707947474775.80/warc/CC-MAIN-20240229003536-20240229033536-00779.warc.gz
218,414,588
7,481
23 January, 01:49 # How does an atom of sulfur-36 become a sulfide ion with a - 2 charge?OA. The atom gains 2 protons to have a total of 38.OB. The atom loses 2 protons to have a total of 14.OOOC. The atom gains 2 electrons to have a total of 18OD. The atom loses 2 electrons to have a total of 14. +4 1. 23 January, 03:03 0 C. The atom gains 2 electrons to have a total of 18. Explanation: Step by step explanation: A neutral Sulfur-36 atom has 16 electrons and the 16 protons (as the Sulfur atom is neutral, it should have same number of electrons as that of protons). The number of neutrons in Sulfur-36 is equal to total mass of sulfur (which is 36) minus the number of protons (which is 16), resulting in 20 (36-16=20). If sulfur-36 becomes - 2 charged ion, it needs to gain a negatively charged particles (i. e. electrons). An electron has a negative charge of - 1. So sulfur-36 atom needs to gain 2 electrons to become - 2 charged ion. Therefore the correct answer choice is C.
287
989
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.140625
3
CC-MAIN-2024-10
latest
en
0.913076
http://www.solutioninn.com/in-a-paper-presented-at-the-2000-conference-of-the
1,508,352,656,000,000,000
text/html
crawl-data/CC-MAIN-2017-43/segments/1508187823067.51/warc/CC-MAIN-20171018180631-20171018200631-00883.warc.gz
569,965,968
8,256
In a paper presented at the 2000 Conference of the In a paper presented at the 2000 Conference of the International Association for Time Use Research professor Margaret Sanik of Ohio State University reported the results of her study on American cable TV viewers who purchase items from one of the home shopping channels. She found that the average age of these cable TV shoppers was 51 years. Suppose you want to test the null hypothesis H0: µ = 51, using a sample of n = 50 cable TV shoppers. a. Find the p-value of a two-tailed test if = 52.3 and s = 7.1. b. Find the p-value of an upper-tailed test if = 52.3 and s = 7.1. c. Find the p-value of a two-tailed test if = 52.3 and s = 10.4. d. For each of the tests in parts a-c , give a value of a that will lead to a rejection of the null hypothesis. e. If = 52.3, give a value of s that will yield a p-value of.01 or less for a one-tailed test. Membership
245
908
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.078125
3
CC-MAIN-2017-43
latest
en
0.926834
https://www.thestudentroom.co.uk/showthread.php?t=5198228
1,534,435,870,000,000,000
text/html
crawl-data/CC-MAIN-2018-34/segments/1534221211126.22/warc/CC-MAIN-20180816152341-20180816172341-00335.warc.gz
996,831,040
47,136
You are Here: Home >< Maths # FP2 Differential equations Help watch 1. Find the solution to the differential equation (4-x^2)^1/2 dy/dx = (4-y^2) ^1/2 for which y= -1 and x=1. I just don't know how to integrate (4-y^2)^1/2 = (4-y^2)^1/2 2. (Original post by ChemBoy1) Find the solution to the differential equation (4-x^2)^1/2 dy/dx = (4-y^2) ^1/2 for which y= -1 and x=1. I just don't know how to integrate (4-y^2)^1/2 = (4-y^2)^1/2 Not sure what the second line means. Use the substitution x=2sinu. 3. (Original post by ChemBoy1) Find the solution to the differential equation (4-x^2)^1/2 dy/dx = (4-y^2) ^1/2 for which y= -1 and x=1. I just don't know how to integrate (4-y^2)^1/2 = (4-y^2)^1/2 Then just use two subs: 4. Update: I managed to get the equation as arcsin y/2 = arcsin x/2 +c. The question asks to express my answer in a form not involving trig functions. I don't see how I can do that. Thanks 5. (Original post by ChemBoy1) Update: I managed to get the equation as arcsin y/2 = arcsin x/2 +c. The question asks to express my answer in a form not involving trig functions. I don't see how I can do that. Thanks First of all, determine what is. Then, write and then apply the compound angle formula on the RHS. 6. I got c as pi/3. Ho do I convert it to an expression not involving trig functions? (Original post by RDKGames) First of all, determine what is. Then, write and then apply the compound angle formula on the RHS. 7. (Original post by ChemBoy1) I got c as pi/3. Ho do I convert it to an expression not involving trig functions? 8. Sorry just saw that thanks. How can you use compound angle formula because i still got Sin (Sin-1 x) etc. (Original post by RDKGames) 9. (Original post by ChemBoy1) Sorry just saw that thanks. How can you use compound angle formula because i still got Sin (Sin-1 x) etc. (obviously) so, we just need . If we denote then we have and we can use a right-angled triangle to determine what is. EDIT: Or just use for this part. 10. Still confused with the right angle triangle thing. becuase the hyp = 2 and the opp = x. The adj would just be a separate variable and that would not work? Could you please help me out? (Original post by RDKGames) (obviously) so, we just need . If we denote then we have and we can use a right-angled triangle to determine what is. EDIT: Or just use for this part. 11. (Original post by ChemBoy1) Still confused with the right angle triangle thing. becuase the hyp = 2 and the opp = x. The adj would just be a separate variable and that would not work? Could you please help me out? The adj would just be sqrt(hyp^2-opp^2) by Pythagoras 12. The book got y= 1/2 x - 1/2x (3(4-x^2))^1/2. I got no where near that answer, could you help elaborate. FYI values are y= -1 and x=1 13. (Original post by ChemBoy1) The book got y= 1/2 x - 1/2x (3(4-x^2))^1/2. I got no where near that answer, could you help elaborate. FYI values are y= -1 and x=1 OK, first of all, . It is in fact Next, we have Finish it off. 14. Nearly got it, except for how they got 3(4-x^2)^1/2 (Original post by RDKGames) OK, first of all, . It is in fact Next, we have Finish it off. 15. (Original post by ChemBoy1) Nearly got it, except for how they got 3(4-x^2)^1/2 Factor out 1/4 inside the root, then bring that factor outside the root. Similarly, merge root(3) with the main root since 16. Thank you so much! You have helped a lot! Sorry if I have sounded very silly to you. (Original post by RDKGames) Factor out 1/4 inside the root, then bring that factor outside the root. Similarly, merge root(3) with the main root since 17. (Original post by ChemBoy1) Thank you so much! You have helped a lot! Sorry if I have sounded very silly to you. ### Related university courses TSR Support Team We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out. This forum is supported by: Updated: February 13, 2018 The home of Results and Clearing ### 4,078 people online now ### 1,567,000 students helped last year Today on TSR ### IT'S TODAY! A-level results chat here ### University open days 1. Bournemouth University Fri, 17 Aug '18 2. University of Bolton Fri, 17 Aug '18 3. Bishop Grosseteste University Fri, 17 Aug '18 Poll Useful resources ### Maths Forum posting guidelines Not sure where to post? Read the updated guidelines here ### How to use LaTex Writing equations the easy way ### Study habits of A* students Top tips from students who have already aced their exams
1,324
4,575
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.84375
4
CC-MAIN-2018-34
latest
en
0.915868
https://www.physicsforums.com/threads/control-engineering-problem.202522/
1,508,687,118,000,000,000
text/html
crawl-data/CC-MAIN-2017-43/segments/1508187825308.77/warc/CC-MAIN-20171022150946-20171022170946-00709.warc.gz
977,275,418
19,052
Control Engineering Problem 1. Dec 4, 2007 ineedmunchies Ok, so I have an assignment I need help with. Hopefully some of you here will be able to help me with it. The Question is shown in the attatched files question2a + question2a2. I think what I need to do first is represent the system in a block diagram. I have included a rough one of what I think it will be. Where it says Ki0i it should infact say $$K_{1}$$$$\theta_{o}$$. I couldn't figure out how to do subscript in paint. I don't know whether I should then try and simplify this as much as possible, or whether I should try and split it into sections. One section to represent the second order terms, one section to represent the first order terms and one section to represent the output angle. Any help or discussion about this would be greatly appreciated. Thank you. File size: 39.5 KB Views: 96 File size: 22.5 KB Views: 104 File size: 7.9 KB Views: 102 2. Dec 4, 2007 zyh This is a so complex problems on modern control theroy, sorry I can only give your some advice. This is a very typical model to represant the X'=AX+BU Y=CX+D term, did you have some books like "Modern control systems", I think it will help you very much, Also, I have found a very good website for you,it's here:http://www.engin.umich.edu/group/ctm/examples/motor2/motor.html 3. Dec 4, 2007 momentum_waves Ogata has some good texts in this area. 4. Dec 5, 2007 ineedmunchies Ah, yes I do have "modern control systems". I've been reading through that trying to work out whats relevant to the question. Thank you for the website, it looks quite useful. I'll try doing some more work on the question later today and see how I get on. Also who or what is Ogata? Thank you. 5. Dec 5, 2007 TheAnalogKid83 what are the rectangles with the arrows running into the centers of them? I've never seen this in a control block diagram. You need to enter in the transfer functions for those blocks. Use the equations given to find the transfer functions. The Inertia block is 1/Js in laplace domain, so it will be an integration, which will result in a velocity. Remember d(theta) is your velocity. Anyway, once you have the transfer functions in place, you can convert them back to differential equations. Use the control loop equations to convert your feedback block into a transfer function. This is just what I see, don't take it for 100% fact. Its my opinion that figure 2 is inaccurate. 6. Dec 5, 2007 TheAnalogKid83 The error of making many of those arrows bidirectional in the control block figure really leads me to believe the person who made it doesn't know what they're doing. There is no reason to do that, and its unconventional at best, and probably just wrong. It leads me to believe the other things i question about this diagram to be incorrect as well. 7. Dec 5, 2007 TheAnalogKid83 I put together a block diagram of what really is happening I think. This is accurate and I attached it to this post. Also, questions I have when looking at figure 2 you provided: -How does the tachometer determine velocity by measuring current (it has current going into some motor symbol and then into the tach, and tachs dont use current or voltage to measure velocity) - Where is the back emf feedback shown (motor voltage)? This is negative feedback inherent to the motor. -Where is K2 shown in the block diagram? there's a few more, but this diagram has me lost and I have doubts it is correct, and if it is correct, it has been made much more complex than it needs to be. File size: 16.9 KB Views: 65 8. Dec 5, 2007 ineedmunchies I don't know what the rectangular symbols with the arrows are meant to represent in figure 2 either. I do not think it is meant to be a block diagram, but rather a basic diagram of the apparatus used in an experiment (which i am currently trying to obtain the report for). I would of assumed that there would need to be a velocity output as well. If the diagram given by the analogkid is correct, how would I go about giving the formula relating the input position and output velocity? Would I be right in assuming that: T = $$T_{m}$$ - $$T_{L}$$ L and R are the armature inductance and resistance respectively. V_emf is the feedback voltage (is this what is given as motor voltage, $$v_{m}$$ , in the question?) $$\frac{K_{1}}{s}$$ is the position feedback? $$K_{amp}$$ I am unsure of, is this $$K_{g}$$ $$K_{}$$ and $$K_{t}$$ simplified into one term?? Thank you for your help. 9. Dec 5, 2007 ineedmunchies If it helps there is a second part to the question which is included in an attatchment. Attached Files: • part2.JPG File size: 38.1 KB Views: 63 10. Dec 6, 2007 zyh the attatched pdf seems very beautiful. TheAnalogKid83, can I ask a queation, which tools did you use to draw these charts? thanks 11. Dec 12, 2007 ineedmunchies If anyones interested I've got the solution to this and I can post it if you like. Thanks for the help 12. Dec 12, 2007 TheAnalogKid83 I drew it in MS Visio while at work, and just printed it off into a PDF with PrimoPDF. The block diagram is from when I did my senior project which was a nonlinear model and software/hardware design of a DC motor-clutch-generator control system. The diagram is of course the simplified linear version, and just the motor, I excluded the clutch and generator. I'm sure you can find this block diagram in similar versions in just about any controls systems textbook. Last edited: Dec 12, 2007 13. Dec 30, 2007 zyh Thanks kid83. now I'm using Dia。。。It's like "visio" but It's open source and free...
1,426
5,589
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.515625
3
CC-MAIN-2017-43
longest
en
0.95433
https://byjus.com/question-answer/the-displacement-of-the-particle-is-given-by-x-2t-3-6t-in-text-m/
1,638,989,803,000,000,000
text/html
crawl-data/CC-MAIN-2021-49/segments/1637964363520.30/warc/CC-MAIN-20211208175210-20211208205210-00134.warc.gz
221,162,539
28,487
Question # The displacement of the particle is given by x=2t3−6t in m. The acceleration of the particle at 2 sec is Your Answer A 36 m/s2 Correct Answer B 24 m/s2 Your Answer C 12 m/s2 Your Answer D 20 m/s2 Solution ## The correct option is B 24 m/s2As we know that the acceleration of the particle is given by  a=dvdt and also, v=dxdt Given, x=2t3−6t So, v=dxdt=d(2t3−6t)dt ⇒ v=6t2−6 also, a=dvdt=d(6t2−6)dt=12t Thus, the acceleration of the particle is 12×2=24 m/s2 Suggest corrections 0 Upvotes Similar questions View More People also searched for View More
204
568
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.9375
4
CC-MAIN-2021-49
latest
en
0.632188
https://www.degruyter.com/document/doi/10.1515/jgth-2018-0199/html
1,669,455,130,000,000,000
text/html
crawl-data/CC-MAIN-2022-49/segments/1669446706285.92/warc/CC-MAIN-20221126080725-20221126110725-00178.warc.gz
789,902,619
43,007
# Finite groups with only 𝔉-normal and 𝔉-abnormal subgroups Bin Hu , Jianhong Huang and Alexander N. Skiba From the journal Journal of Group Theory ## Abstract Let G be a finite group, and let 𝔉 be a class of groups. A chief factor H/K of G is said to be 𝔉-central (in G) if the semidirect product (H/K)β‹Š(G/CG⁒(H/K))βˆˆπ”‰. We say that a subgroup A of G is 𝔉-normal in G if every chief factor H/K of G between AG and AG is 𝔉-central in G and 𝔉-abnormal in G if V is not 𝔉-normal in W for every two subgroups V<W of G such that A≀V. We give a description of finite groups in which every subgroup is either 𝔉-normal or 𝔉-abnormal. ## 1 Introduction Throughout this paper, all groups are finite, and G always denotes a finite group; ℒ⁒(G) denotes the lattice of all subgroups of G. The group G is said to be strongly supersoluble [6] if G is supersoluble and G induces on any of its chief factor H/K an automorphism group of square free order. In what follows, 𝔉 is a class of groups containing all nilpotent groups; G𝔉 denotes the intersection of all normal subgroups N of G with G/Nβˆˆπ”‰. The class 𝔉 is said to be a formation if every homomorphic image of G/G𝔉 belongs to 𝔉 for every group G. The formation 𝔉 is said to be saturated if Gβˆˆπ”‰ whenever G𝔉≀Φ⁒(G) and hereditary (Mal’cev [9]) if Hβˆˆπ”‰ whenever H≀Gβˆˆπ”‰. Recall that 𝔑, π”˜ and π”˜s are the classes of all nilpotent, all supersoluble and all strongly supersoluble groups, respectively. It is well known that 𝔑 and π”˜ are hereditary saturated formations. In the paper [13], it is proved that the class π”˜s is also a hereditary saturated formation. If K≀H are normal subgroups of G and C≀CG⁒(H/K), then we can form the semidirect product (H/K)β‹Š(G/C) putting (h⁒K)g⁒C=g-1⁒h⁒g⁒K for all⁒h⁒K∈H/K⁒and⁒g⁒C∈G/C. We say that a chief factor H/K of G is 𝔉-central in G (see [12]) if (H/K)β‹Š(G/CG⁒(H/K))βˆˆπ”‰. ## Definition 1.1. We say that a subgroup A of G is 1. 𝔉⁒p-normal in G if every chief factor H/K of G between AG and AG with pβˆˆΟ€β’(H/K) is 𝔉-central in G, 2. 𝔉-normal in G provided A is 𝔉⁒p-normal in G for all primes p, 3. 𝔉-abnormal in G if V is not 𝔉-normal in W for every two subgroups V<W of G such that A≀V. By definition, all normal subgroups of G are 𝔉-normal in G. Moreover, G is the unique subgroup of G which simultaneously is 𝔉-normal and 𝔉-abnormal in G. Every maximal subgroup of G is either 𝔉-normal or 𝔉-abnormal in G. In this paper, we study those groups in which each subgroup is either 𝔉-normal or 𝔉-abnormal. ## Example 1.2. Before continuing, consider some well-known examples. 1. A subgroup A of G is said to be quasinormal or permutable if A permutes with all subgroups H of G, that is, A⁒H=H⁒A. In view of [8] (see also [1, Corollary 1.5.6] or [10, Theorem 5.2.3]), every quasinormal subgroup of G is 𝔑-normal in G. 2. A subgroup M of G is called modular if M is a modular element (in the sense of Kurosh [10, p. 43]) of the lattice ℒ⁒(G) of all subgroups of G, that is, In view of [10, Theorem 5.1.14], every modular subgroup of G is π”˜s-normal in G. We say that a subgroup A of G is abmodular in G if V is not modular in W for every two subgroups V<W of G such that A≀V. In view of [10, Lemma 5.1.2], a subgroup A of G is abmodular in G if and only if it is π”˜s-abnormal in G. 3. Let G=(C7β‹Š(C2Γ—C3))Γ—P, where C2Γ—C3=Aut⁑(C7) and P is a non-abelian group of order p3 of exponent p for some prime p>2. Then the subgroup C2 is not π”˜s-normal in G. Now let L be a subgroup of P of order p with Lβ‰°Z⁒(P). Then L is neither quasinormal nor modular in G, but L evidently is 𝔑-normal and so π”˜s-normal in G. ## Definition 1.3. We say that G is a DM-group if G=Dβ‹ŠM, where 1. D=Gβ€²β‰ 1 is abelian, 2. M=γ€ˆx〉 is a cyclic abnormal Sylow p-subgroup of G, where p is the smallest prime dividing |G|, 3. MG=γ€ˆxp〉=Z⁒(G), 4. The element x induces a fixed-point-free power automorphism on D. In [4], Fattahi defined B-groups to be groups in which every subgroup is either normal or abnormal, and he showed that a non-nilpotent group G is a B-group if and only if G is a DM-group. Later the results in [4] were generalized in several directions. In particular, Qinhai Zhang proved in [14] that every non-nilpotent group in which each subgroup is either quasinormal or abnormal is a B-group, and he posed a general problem of finding other conditions under which G is a B-group. In this paper, we prove the following result in this research line. ## Theorem 1.4. Let F be a hereditary saturated formation containing all nilpotent groups. If every subgroup of G is either F-normal or F-abnormal in G, then G is of either of the following types: 1. Gβˆˆπ”‰. 2. G=Dβ‹ŠM is a DM-group, where D=G𝔉, and M is an 𝔉-abnormal subgroup of G with MG=Z𝔉⁒(G). Conversely, in a group G of type (I) or (II), every subgroup is either F-normal or F-abnormal. In this theorem, Z𝔉⁒(G) denotes the 𝔉-hypercenter of G, that is, the product of all normal subgroups N of G such that either N=1 or every chief factor of G below N is 𝔉-central in G. In view of [11, Chapter IV, Theorem 17.1], A is an 𝔑-abnormal subgroup of a soluble group G if and only if A is abnormal in G. Therefore, we get from Theorem 1.4 the following: ## Corollary 1.5. Every subgroup of G is either N-normal or N-abnormal in G if and only if G is either nilpotent or a B-group. Corollary 1.5 covers the main result in [4]. Moreover, in view of Example 1.2 (i), we get from Corollary 1.5 the following result. ## Corollary 1.6 (Zhang [14]). Let G be a non-nilpotent group. Then the following statements are equivalent: 1. G is a B-group. 2. Every subgroup of G is either quasinormal or abnormal in G. Strongly supersoluble groups have found applications in many works (see, for example, [6, 13, 15]). Since every DM-group is evidently strongly supersoluble and the class of all strongly supersoluble groups is a hereditary saturated formation, we get from Theorem 1.4 and Proposition 3.4 the following characterizations of such groups. ## Corollary 1.7. The following statements are equivalent: 1. G is strongly supersoluble. 2. Every Sylow subgroup of G is π”˜s-normal in G. 3. Each subgroup of G is either π”˜s-normal or π”˜s-abnormal in G. In fact, G is an M-group [10], that is, the lattice ℒ⁒(G) is modular if and only if every subgroup of G is modular in G. From Corollary 1.7 and Example 1.2 (ii), we get that G is an M-group also in the case when every non-abmodular subgroup of G is modular in G. In conclusion of this section, note that one of the main tools in the proof of Theorem 1.4 is the following useful fact. ## Proposition 1.8. The class of all F-normal subgroups and, for any prime p, the class of all F⁒p-normal subgroups of G are sublattices of the lattice L⁒(G). ## 2 Proof of Proposition 1.8 The first two lemmas can be proved by direct checking. ## Lemma 2.1. Let N, M and K<H≀G be normal subgroups of G, where H/K is a chief factor of G. 1. If N≀K, then (H/K)β‹Š(G/CG⁒(H/K))≃((H/N)/(K/N))β‹Š((G/N)/CG/N⁒((H/N)/(K/N))). 2. If T/L is a chief factor of G and H/K and T/L are G-isomorphic, then CG⁒(H/K)=CG⁒(T/L) and (H/K)β‹Š(G/CG⁒(H/K))≃(T/L)β‹Š(G/CG⁒(T/L)). Recall that G is called a pd-group if pβˆˆΟ€β’(G). ## Lemma 2.2. Let K≀H, K≀V, W≀V and N≀H be normal subgroups of G. Suppose that every chief pd-factor of G between K and H is F-central in G. 1. If every chief pd-factor of G between K and KN is 𝔉-central in G, then every chief pd-factor of G between K∩N and N is 𝔉-central in G. 2. If every chief pd-factor of G between W and V is 𝔉-central in G, then every chief pd-factor of G between K∩W and H∩V is 𝔉-central in G. 3. If every chief pd-factor of G between K and V is 𝔉-central in G, then every chief pd-factor of G between K and HV is 𝔉-central in G. ## Proof of Proposition 1.8. Let A,B be subgroups of G such that A,Bβˆˆβ„’p⁒c⁒𝔉⁒(G), where β„’p⁒c⁒𝔉⁒(G) is the class of all 𝔉⁒p-normal subgroups of G. Then every chief pd-factor of G between AG and AG is 𝔉-central in G. Now we show that γ€ˆA,Bγ€‰βˆˆβ„’p⁒c⁒𝔉⁒(G). In view of the G-isomorphisms we get that every chief pd-factor of G between AG⁒BG and AG⁒(AG⁒BG) is 𝔉-central in G. Similarly, every chief pd-factor of G between AG⁒BG and BG⁒(AG⁒BG) is 𝔉-central in G. Moreover, AG⁒BG/AG⁒BG=(AG⁒(AG⁒BG)/AG⁒BG)⁒(BG⁒(AG⁒BG)/AG⁒BG), and so every chief pd-factor of G between AG⁒BG and AG⁒BG is 𝔉-central in G by Lemma 2.2 (3). Next note that γ€ˆA,B〉G=AG⁒BG and AG⁒BGβ‰€γ€ˆA,B〉G. Therefore, every chief pd-factor of G between γ€ˆA,B〉G and γ€ˆA,B〉G=AG⁒BG is 𝔉-central in G. Hence γ€ˆA,Bγ€‰βˆˆβ„’p⁒c⁒𝔉⁒(G). Therefore, β„’p⁒c⁒𝔉⁒(G) is a sublattice of the lattice ℒ⁒(G). Finally, for the class β„’c⁒𝔉⁒(G), of all 𝔉-normal subgroups of G, we have β„’c⁒𝔉⁒(G)=β‹‚pβˆˆΟ€β’(G)β„’p⁒c⁒𝔉⁒(G), and so β„’c⁒𝔉⁒(G) is also a sublattice of ℒ⁒(G). ∎ ## 3 Proof of Theorem 1.4 The following lemma is well known (see, for example, [12, Lemma 3.29]). ## Lemma 3.1. Let H/K be an abelian chief factor of G, and let V be a maximal subgroup of G with K≀M and H⁒M=G. Then G/VG≃(H/K)β‹Š(G/CG⁒(H/K)). ## Lemma 3.2 ([5, Chapter 1, Theorem 2.7]). Let F be a hereditary saturated formation, and let Z=ZF⁒(G). Let N and E be subgroups of G, where N is normal in G. 1. If N≀Z, then Z/N=Z𝔉⁒(G/N). 3. If N⁒Z/N≀Z𝔉⁒(G/N). In fact, the following lemma is a corollary of [3, Chapter IV, Theorem 6.7]. ## Lemma 3.3. Let F be a hereditary saturated formation, and let A and N≀E be subgroups of G, where N is normal and A is F-normal in G. Then 1. A⁒N/N is 𝔉-normal in G/N. 2. If E/N is 𝔉-normal in G/N, then E is 𝔉-normal in G. 3. A∩E is 𝔉-normal in E. ## Proof. (1) From the G-isomorphisms and Lemma 2.1, we get that every chief factor of G/N between AG⁒N/N and AG⁒N/N is 𝔉-central in G/N since every chief factor of G between AG and AG is 𝔉-central in G/N by hypothesis. On the other hand, we have (A⁒N/N)G/N=(A⁒N)G/N=AG⁒N/N and AG⁒N/N≀(A⁒N/N)G/N. Hence every chief factor of G/N between (A⁒N/N)G/N and (A⁒N/N)G/N is 𝔉-central in G/N, so A⁒N/N is 𝔉-normal in G/N. (2) This follows from the G-isomorphism EG/EG≃(EG/N)/(EG/N)=(E/N)G/N/(E/N)G/N. (3) First note that by Lemma 3.2 (2) since, by hypothesis, we have AG/AG≀Z𝔉⁒(G/AG). On the other hand, we have where and so by Lemma 3.2 (2) and (3). Hence A∩E is 𝔉-normal in E. ∎ ## Proposition 3.4. Let F be a saturated formation containing all nilpotent groups. Then the following statements are equivalent: 1. Gβˆˆπ”‰. 2. Every chief factor of G is 𝔉-central in G. 3. Every Sylow subgroup of G is 𝔉-normal in G. ## Proof. (i) β‡’ (ii) This directly follows from the Barnes–Kegel result [3, Chapter IV, Proposition 1.5]. (ii) β‡’ (iii) This implication is evident. (ii) β‡’ (i) In fact, this application is well known, and it can be easily proved by using Lemma 3.1 and induction on |G|. (iii) β‡’ (i) Let P be a Sylow p-subgroup of G, where p is any prime dividing |G|. Then P⁒R/R is a Sylow p-subgroup of G/R and P⁒R/R is 𝔉-normal in G/R by Lemma 3.3 (1) since P is 𝔉-normal in G by hypothesis. Therefore, the hypothesis holds for G/R, so G/Rβˆˆπ”‰ by induction. Therefore, if either R≀Φ⁒(G) or G has a minimal normal subgroup Nβ‰ R, then Gβˆˆπ”‰. Moreover, if R/1 is 𝔉-central in G, then, by the Jordan–HΓΆlder theorem for the chief series, every chief factor of G is 𝔉-central in G, and so Gβˆˆπ”‰ by the implication (ii) β‡’ (i). Now assume that R≰Φ⁒(G) is the unique minimal normal subgroup of G and that R/1 is not 𝔉-central in G. Let pβˆˆΟ€β’(R), and let Gp be a Sylow p-subgroup of G. Then Rp=R∩Gp is normal in Gp. Suppose that Rpβ‰ R; then, for some maximal subgroup V of G, we have Gp≀NG⁒(Rp)≀V, and so G=R⁒V by the Frattini argument. Then (Gp)G≀VG=1, so 1<Gp≀Z𝔉⁒(G). But then R≀Z𝔉⁒(G), and so R/1 is 𝔉-central in G, a contradiction. Hence R=Rp is an abelian p-group for some prime p. Let M be a maximal subgroup of G such that G=R⁒M=Rβ‹ŠM. If G is a p-group, then Gβˆˆπ”‰ since 𝔉 contains all nilpotent groups by hypothesis. Now assume |π⁒(G)|>1, and let Q be a Sylow q-subgroup of M, where qβˆˆΟ€β’(G)βˆ–{p}. Then QG=1, and so 1<QG≀Z𝔉⁒(G), which again implies that R/1 is 𝔉-central in G, a contradiction. The implication is proved. ∎ In fact, the following lemma is a corollary of [3, Chapter IV, Theorem 6.7]. ## Lemma 3.5. Let P be a normal p-subgroup of G. If every chief factor of G between Φ⁒(P) and P is cyclic, then every chief factor of G below P is cyclic. ## Proof of Theorem 1.4. Necessity. Assume that this is false, and let G be a counterexample of minimal order. Then Gβˆ‰π”‰, so D=G𝔉≠1, and also G is not nilpotent since 𝔉 contains all nilpotent groups by hypothesis. Let R be a minimal normal subgroup of G. (1) Every proper subgroup Eβˆ‰π”‰ is of type (II) and if G/Rβˆ‰π”‰, then G/R is of type (II): Let A be any subgroup of E. If A is 𝔉-abnormal in G, then A is evidently 𝔉-abnormal in E. On the other hand, if A is 𝔉-normal in G, then A is 𝔉-normal in E by Lemma 3.3 (3). Hence the hypothesis holds for E, so the choice of G implies that E is of type (II). Finally, if A/R is a non-𝔉-abnormal subgroup of G/R, then A is not 𝔉-abnormal in G, and so, by hypothesis and Lemma 3.3 (1), A/R is 𝔉-normal in G/R. Therefore, G/R is of type (II) by the choice of G. (2) D<G: Assume D=G, and let P be a Sylow p-subgroup of G, where p is the smallest prime dividing |G|. Then P is not cyclic since otherwise G has a normal p-complement E by [7, Chapter IV, Satz 2.8] and G/Eβˆˆπ”‰, which implies D≀E<G. Then, for a maximal subgroup V of P, we have Vβ‰ 1, and V is not 𝔉-abnormal in G, so V is 𝔉-normal in G. Assume VGβ‰ 1 and R≀VG. If G/Rβˆˆπ”‰, then D=R<G, which is impossible by our assumption D=G. Hence G/Rβˆ‰π”‰, so statement (II) holds for G/R by claim (1), which implies G/R=D/R=(G/R)𝔉=(G/R)β€²<G/R by [2, Proposition 2.2.8]. Then D=G<G. This contradiction shows that VG=1, so 1<VG≀Z𝔉⁒(G), and hence we can assume without loss of generality R≀Z𝔉⁒(G). Then G/Rβˆ‰π”‰ by Lemma 3.2 (1), and so, as above, we get D=G<G. This contradiction completes the proof of Claim (2). (3) D is nilpotent, and every element of G induces a power automorphism in D/Φ⁒(D). Moreover, if p is the smallest prime dividing |G|, then p does not divide |D|: Let V be a maximal subgroup of D. Then V is not 𝔉-abnormal in G by claim (2), so V is 𝔉-normal in G. Assume that V is not normal in G. Then we have VG=D and VG/VG≀Z𝔉⁒(G/VG), which implies G/VGβˆˆπ”‰ by Lemma 3.2 (1). But then D≀VG≀D. This contradiction shows that V is normal in G, so D is nilpotent, and every element of G induces a power automorphism in D/Φ⁒(D) since every subgroup of D/Φ⁒(D) can be written as the intersection of some maximal subgroup of D/Φ⁒(D). Now assume that p divides |D|. Then p divides |D/Φ⁒(D)|, so, from the previous paragraph, we know that, for some maximal subgroup V of D, we have |D:V|=p, and V is normal in G. But then G/CG⁒(D/V) is a cyclic group of order dividing p-1. Since p is the smallest prime dividing |G|, it follows that CG⁒(D/V)=G, and so D/V≀Z⁒(G/V). Hence G/Vβˆˆπ”‰ by Lemma 3.2 (1) since 𝔉 contains all nilpotent groups by hypothesis, and so D≀V<D, a contradiction. Thus |D| is a pβ€²-number. Hence we have (3). (4) D is a Hall subgroup of G. Hence D has a complement M in G, and p divides |M|: Suppose that this is false, and let P be a Sylow r-subgroup of D such that 1<P<Gr, where Gr∈Sylr⁑(G). First we show that D is a minimal normal subgroup of G. Assume that this is false. Then, for a minimal normal subgroup N of G contained in D, we have G/Nβˆ‰π”‰. Since D is nilpotent by claim (3), N is a q-group for some prime q. Moreover, D/N=(G/N)𝔉 is a Hall subgroup of G/N by claim (1) and [2, Proposition 2.2.8]. Suppose that P⁒N/Nβ‰ 1. Then we have P⁒N/N∈Sylr⁑(G/N). If qβ‰ r, then P∈Sylr⁑(G). This contradicts the fact that P<Gr. Hence q=r, so N≀P, and therefore P/N∈Sylr⁑(G/N). It follows that P∈Sylr⁑(G). This contradiction shows that P⁒N/N=1, which implies that N=P is a Sylow r-subgroup of D. Therefore, N is the unique minimal normal subgroup of G contained in D. It is also clear that a p-complement U of D is a Hall subgroup of G. Claim (3) implies that U is characteristic in D, so it is normal in G. Therefore, U=1, and hence D=N. So N≰Φ⁒(G) since the formation 𝔉 is saturated by hypothesis. Let V be a maximal subgroup of N. Then V is 𝔉-normal in G by claim (2). Assume Vβ‰ 1. Then VG<V<VG, where N/1=VG/VG≀Z𝔉⁒(G/1), which implies Gβˆˆπ”‰ by Lemma 3.2 (1). This contradiction shows that V=1, so we have |N|=r. Now let S be a maximal subgroup of G such that Nβ‰°S, and let C=CG⁒(N). Then G=Nβ‹ŠS, and so C=N⁒(C∩S), where C∩S is normal in G. Assume C∩Sβ‰ 1, and let L be a minimal normal subgroup of G contained in C∩S. Then N⁒L/L=D⁒L/L=(G/L)𝔉 is a Hall subgroup of G/L, and so N⁒L/L=Gr⁒L/L, which implies N⁒L=Gr⁒L. Hence Gr=NΓ—(Gr∩L). Let N=γ€ˆa〉, and let A=γ€ˆb〉 be a subgroup of order r of Gr∩L. Let L0=γ€ˆa⁒b〉. Then |L0|=r, and L0∩N=1=L0∩Gr∩L. First assume that L0 is not normal in G. Then L0≀L0G≀Z𝔉⁒(G). On the other hand, from the G-isomorphism N⁒L/N≃L, it follows that L≀Z𝔉⁒(G) by Lemma 2.1 and Proposition 3.4. Moreover, Gr=L0⁒(Gr∩L) since |N|=r and L0∩(Gr∩L)=1. Hence we have N≀Gr≀Z𝔉⁒(G), and so Gβˆˆπ”‰ by Lemma 3.2 (1). This contradiction shows that C∩S=1, and so C=N is the unique minimal normal subgroup of G. Since |N|=r, it follows that G/N=G/C is cyclic, so G is supersoluble. Then a Sylow q-subgroup Q of G, where q is the largest prime dividing |G|, is normal in G. Therefore, N≀Q and N≰Φ⁒(Q)≀Φ⁒(G). Hence q=r, and Q is an elementary abelian r-group, which implies D=N=Q=Gr. This contradiction completes the proof of the fact that D is a Hall subgroup of G. Therefore, D has a complement M in G by the Schur–Zassenhaus theorem. Moreover, p divides |M| by claim (3). Hence we have (4). (5) M=γ€ˆx〉 is a cyclic 𝔉-abnormal Sylow p-subgroup of G, and every proper subgroup of M is 𝔉-normal in G: By claim (4), M≃G/Dβˆˆπ”‰, and p divides |M|. Therefore, every proper subgroup V of M is not 𝔉-abnormal in G, so V is 𝔉-normal in G by hypothesis. Let Mp be a Sylow p-subgroup of M. Assume Mpβ‰ M. Then Mp is 𝔉-normal in G. Moreover, in this case, each Sylow subgroup P of M is 𝔉-normal in G, and P is a Sylow subgroup of G by claim (4). It follows that all Sylow subgroups of G are 𝔉-normal in G by claims (3) and (4), and therefore Gβˆˆπ”‰ by Proposition 3.4. This contradiction shows that M=Mp is 𝔉-abnormal in G and every proper subgroup of M is 𝔉-normal in G. Therefore, M is cyclic since the set of all 𝔉-normal subgroups of G forms a sublattice of the lattice of subgroups of G by Proposition 1.8. Hence we have (5). (6) Z𝔉⁒(G)=MG=γ€ˆxp〉: Let Z=Z𝔉⁒(G), V=γ€ˆxp〉. Assume Z∩Dβ‰ 1. Let U=(Z∩D)⁒M. Then Z∩D≀Z∩U≀Z𝔉⁒(U) by Lemma 3.2 (2), so U/Z𝔉⁒(U)≃M/M∩Z𝔉⁒(U)βˆˆπ”‰, and hence Uβˆˆπ”‰ by Lemma 3.2 (1). But then M is not 𝔉-abnormal in G, contrary to claim (5). Therefore, Z∩D=1, so Z≀M, and hence, in fact, Z≀VG. It is clear that D≀CG⁒(VG), so VG≀Z⁒(G) by claim (5). Therefore, V≀VG≀Z≀V by Lemma 3.2 (1). Hence we have MG=VG=V=Z⁒(G)=Z. (7) My≀NG⁒(H) for every proper subgroup H of D and every y∈G: Let V be a maximal subgroup of D such that H≀V. Then V is normal in G by claim (3). Let E=V⁒My and D0=E𝔉. It is clear that D0≀V. Moreover, D0β‰ 1 since otherwise Eβˆˆπ”‰, which implies that the subgroups My and M are not 𝔉-abnormal in G, contrary to claim (5). Furthermore, claim (1) implies E=D0β‹ŠMy=Vβ‹ŠMy, and every subgroup of D0=V is normalized by My. Hence My≀NG⁒(H). (8) Every proper subgroup H of D is normal in G, and hence D is abelian: Claim (7) implies MG≀NG⁒(H), where M is 𝔉-abnormal in G by claim (5), and so G=MG≀NG⁒(H). Therefore, D is a Dedekind group, and |D| is odd by claim (3). Hence we have (8). From claims (4), (5), (6) and (8), it follows that condition (II) holds for G, which is impossible by the choice of G. This contradiction completes the proof of the necessity condition of the theorem. Sufficiency. If Gβˆˆπ”‰, then every subgroup of G is 𝔉-normal in G by Proposition 3.4. Now assume that G is a group of type (II), and let A be any subgroup of G. First suppose that |M| divides |A|. Then, for some a∈G, we have Ma≀A, so A is 𝔉-abnormal in G since the subgroups M and Ma are 𝔉-abnormal in G. Now assume that |M| does not divide |A|. Then, for a Sylow p-subgroup Ap of A and for some b∈G, we have (Ap)b<M, so the subgroups (Ap)b and Ap are 𝔉-normal in G by hypothesis. Now note that A=(A∩D)⁒Ap, where A∩D is normal in G, and so A is 𝔉-normal in G by Proposition 1.8. ∎ Communicated by Evgenii I. Khukhro Award Identifier / Grant number: 11401264 Award Identifier / Grant number: PPZY 2015A013 Funding statement: Research is supported by an NNSF grant of China (Grant No. 11401264) and a TAPP of Jiangsu Higher Education Institutions (PPZY 2015A013). ## Acknowledgements The authors are very grateful to the helpful suggestions of the referee. ## References [1] A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter de Gruyter, Berlin, 2010. 10.1515/9783110220612Search in Google Scholar [2] A. Ballester-Bolinches and L. M. Ezquerro, Classes of Finite Groups, Springer, Dordrecht, 2006. Search in Google Scholar [3] K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin, 1992. 10.1515/9783110870138Search in Google Scholar [4] A. Fattahi, Groups with only normal and abnormal subgroups, J. Algebra 28 (1974), no. 1, 15–19. 10.1016/0021-8693(74)90019-2Search in Google Scholar [5] W. Guo, Structure Theory for Canonical Classes of Finite Groups, Springer, Heidelberg, 2015. 10.1007/978-3-662-45747-4Search in Google Scholar [6] B. Hu, J. Huang and A. N. Skiba, On generalized S-quasinormal and generalized subnormal subgroups of finite groups, Comm. Algebra 46 (2018), no. 4, 1758–1769. 10.1080/00927872.2017.1357076Search in Google Scholar [7] B. Huppert, Endliche Gruppen. I, Springer, Berlin, 1967. 10.1007/978-3-642-64981-3Search in Google Scholar [8] R. Maier and P. Schmid, The embedding of permutable subgroups in finite groups, Math. Z. 131 (1973), 269–272. 10.1007/BF01187244Search in Google Scholar [9] A. I. Mal’cev, Algebraic Systems, Nauka, Moscow, 1970. Search in Google Scholar [10] R. Schmidt, Subgroup Lattices of Groups, Walter de Gruyter, Berlin, 1994. 10.1515/9783110868647Search in Google Scholar [11] L. A. Shemetkov, Formations of Finite Groups, Moscow, Nauka, 1978. Search in Google Scholar [12] L. A. Shemetkov and A. N. Skiba, Formations of Algebraic Systems, Nauka, Moscow, 1989. Search in Google Scholar [13] V. A. Vasilyev, Finite groups with submodular Sylow subgroups, Siberian Math. J. 56 (2015), no. 6, 1019–1027. 10.1134/S0037446615060063Search in Google Scholar [14] Q. Zhang, Finite groups with only s-quasinormal and abnormal subgroups, Northeast. Math. J. 14 (1998), no. 1, 41–46. Search in Google Scholar [15] I. Zimmermann, Submodular subgroups in finite groups, Math. Z. 202 (1989), 545–557. 10.1007/BF01221589Search in Google Scholar
9,012
24,148
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.515625
3
CC-MAIN-2022-49
latest
en
0.848383
http://www.jiskha.com/display.cgi?id=1191170060
1,495,765,036,000,000,000
text/html
crawl-data/CC-MAIN-2017-22/segments/1495463608622.82/warc/CC-MAIN-20170526013116-20170526033116-00256.warc.gz
549,716,974
4,187
# Physics posted by on . A model rocket is launched straight upward with an initial speed of 50 m/s. It accelerates with a constant upward acceleration of 2.00 m/s^2 until its engines stop at an altitude of 150 m. a) What is the max. height reached by the rocket? b) When does the rocket reach max. height? c) How long is the rocket in the air? I really need help with which equation to use for this problem. I'm unsure of even where to begin...! • Physics - , a) First, calculate the velocity Vmax attained during acceleration at rate a. (They already tell you the altitude there, H = 150 m). Then compute how huch higher it "coasts" before reaching maximum altitude. Vmax = sqrt(2aH)= 24.5 m/s To have the velocity decrease to zero, the additional time of flight t' is given by g t' = 24.5 m/s, so t' = 24.5/9.8 = 2.5 s The average speed while coasting to zero velocity is Vmax/2 = 12.25 m/s. Additionl altitude gained = (2.5)(12.25) = 30.63 m Maximum altitude = Hmax = 150 + 30.63 = 180.63 m b) it attains maximu height 2.5 seconds after accelerqation stopped. We already calculated that. Add that to the tiome spent accelerating for the total time after launch. The time t spent accelerating is given by (1/2) a t^2 = 150 m t = sqrt (2*150/a)= 12.25 s Total time to reach maximum altitude - t + t' = ? c) Add to the last answer the time that it takes to fall back down. Call this time t" (1/2) g t"^2 = Hmax Solve for t" and add it to the time in the previous answer • Physics - , For part a, my book says the answer is 310 m. I'm still really confused on how they got this answer.
464
1,596
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.96875
4
CC-MAIN-2017-22
latest
en
0.918045
https://feet-to-meters.appspot.com/4967-feet-to-meters.html
1,721,673,056,000,000,000
text/html
crawl-data/CC-MAIN-2024-30/segments/1720763517890.5/warc/CC-MAIN-20240722160043-20240722190043-00895.warc.gz
217,350,450
6,263
Feet To Meters # 4967 ft to m4967 Foot to Meters ft = m ## How to convert 4967 foot to meters? 4967 ft * 0.3048 m = 1513.9416 m 1 ft A common question is How many foot in 4967 meter? And the answer is 16295.9317585 ft in 4967 m. Likewise the question how many meter in 4967 foot has the answer of 1513.9416 m in 4967 ft. ## How much are 4967 feet in meters? 4967 feet equal 1513.9416 meters (4967ft = 1513.9416m). Converting 4967 ft to m is easy. Simply use our calculator above, or apply the formula to change the length 4967 ft to m. ## Convert 4967 ft to common lengths UnitUnit of length Nanometer1.5139416e+12 nm Micrometer1513941600.0 µm Millimeter1513941.6 mm Centimeter151394.16 cm Inch59604.0 in Foot4967.0 ft Yard1655.66666667 yd Meter1513.9416 m Kilometer1.5139416 km Mile0.940719697 mi Nautical mile0.817463067 nmi ## What is 4967 feet in m? To convert 4967 ft to m multiply the length in feet by 0.3048. The 4967 ft in m formula is [m] = 4967 * 0.3048. Thus, for 4967 feet in meter we get 1513.9416 m. ## Alternative spelling 4967 ft to Meters, 4967 ft in Meters, 4967 ft to Meter, 4967 Foot to m, 4967 Foot in m, 4967 Feet to Meter, 4967 Feet in Meter, 4967 Feet to m, 4967 Foot to Meters, 4967 Feet to Meters, 4967 Feet in Meters,
466
1,258
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.015625
3
CC-MAIN-2024-30
latest
en
0.701907
https://www.physicsforums.com/threads/relating-the-angular-momentum-with-lapacian.429491/
1,544,918,868,000,000,000
text/html
crawl-data/CC-MAIN-2018-51/segments/1544376827137.61/warc/CC-MAIN-20181215222234-20181216004234-00393.warc.gz
1,012,903,981
14,761
# Relating the angular momentum with lapacian 1. Sep 16, 2010 ### calculus_jy The angular momentum operator is given by $$\bold{L}=\bold{r}\times-i\hbar \bold{\nabla}$$ How do we compute $$\bold{L}\cdot \bold{L}=(\bold{r}\times-i\hbar \bold{\nabla})\cdot(\bold{r}\times-i\hbar \bold{\nabla})$$??? so that we can get a relation of L^2 with the lapacian operator i found this in a lecture note and it gave this as the first line (i might have inserted the factors -ihbar wrong) $$L^2=-\bold{r} \cdot(-i\hbar\bold{\nabla }\times (\bold{r} \times -i\hbar\bold{\nabla })$$ ???? (is it correct and can you help me proof it) Last edited: Sep 16, 2010 2. Sep 17, 2010 ### calculus_jy I did a bit of work and this is what i got, can someone tell me if this is right and is there another way that will make this shorter!? $$\bold{L}\cdot\bold{L}=-\hbar^{2}(\epsilon_{ijk}r_{j}\nabla_{k})(\epsilon_{ilm}r_{m}\nabla_{m})$$ $$-\frac{L^{2}}{\hbar^{2}}=(\delta_{jl}\delta_{km}-\delta_{jm}\delta_{kl})r_{j}\nabla_{k}\, r_{l}\nabla_{m}$$ $$\\=r_{j}\nabla_{k}r_{j}\,\nabla_{k}-r_{j}\nabla_{k}\,r_{k}\nabla_{j}$$ $$\\=r_{j}\delta_{kj}\nabla_{k}+r_{j}r_{j}\nabla_{k}\nabla_{k}-(r_{j}\delta_{kk}\nabla_{j}+r_{j}r_{k}\nabla_{k}\nabla_{j})$$ $$\\=-2r_{j}\nabla_{j}+r_{j}r_{j}\nabla_{k}\nabla_{k}-r_{j}r_{k}\nabla_{j}\nabla_{k}$$$$\\=-2r_{j}\nabla_{j}+r_{j}r_{j}\nabla_{k}\nabla_{k}-r_{j}(\nabla_{j}\,r_{k}-\delta_{ij})\nabla_{k}$$ $$\\=-r_{j}\nabla_{j}+r_{j}r_{j}\nabla_{k}\nabla_{k}-r_{j}\nabla_{j}\,r_{k}\nabla_{k}$$ $$\\=-\bold{r}\cdot\nabla+r^{2}\nabla^{2}-(\bold{r}\cdot\nabla)(\bold{r}\cdot\nabla)$$ 3. Sep 18, 2010 ### calhoun137 See Landau, Vol 3, 3rd edition, section 28 "eigenfunctions of the angular momentum". For a mathematical derivation, see "Lie Groups, Lie Algebras, and Representations" by Brian C Hall. 4. Sep 18, 2010 ### calculus_jy thank you so much. However i didnt find much in Landau, under which section will i find the mathematical derivation in your second reference by hall 5. Sep 19, 2010 ### calhoun137 I am sad that I don't have a copy of Hall, so I can't give you the reference. But I studied that book with the guidance of my mentor, and I remember the proof in there was really nice. The thing is, most people just transform the laplacian to spherical polar coordinates and wave their hands to say that's the angular momentum eigenfunctions. But in Hall, there is no hand waving, and in order to really appreciate the proof you kind of have to work through what comes before. You could do a lot worse than to study this book from the beginning. Lie groups/algebra's are the most important part of math for physics (they underlie the relationship between conservation laws and symmetry, as well as the fact that the lie algebra elements ARE the quantum particles) and this is far and away the best book on lie groups for beginners, imo. I skimmed through basically every lie group book in the math/physics libraries and this is the one I liked the most. 6. Sep 19, 2010 ### Meir Achuz I got your answer by a different method, but I can't say my method is shorter. 7. Sep 19, 2010 ### sancharsharma We may use the method introduced by Feynman, that will make it shorter. See Feynman Vol2, derivation of Poynting's Vector. There he describes a handy method to use the operator like a normal vector, and everythig else follows directly........ 8. Sep 20, 2010 ### Meir Achuz That was the method I used. It avoids all the indices, but is still a bit complicated.
1,204
3,496
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.671875
4
CC-MAIN-2018-51
latest
en
0.6371
http://mathhelpforum.com/calculus/71192-using-definition-derivative-x-c-compute-following-derivatives-print.html
1,526,938,182,000,000,000
text/html
crawl-data/CC-MAIN-2018-22/segments/1526794864544.25/warc/CC-MAIN-20180521200606-20180521220606-00608.warc.gz
178,626,155
3,024
# Using the definition of the derivative at x=c, compute the following derivatives at a • Feb 1st 2009, 01:57 PM jkami Using the definition of the derivative at x=c, compute the following derivatives at a Using the definition of the derivative at x=c, compute the following derivatives at an arbitrary point? (a) g(x) = 5x^2 (b) f(x) = 7x^4 (c) k(x) = sqrt x Please show me the steps cuz I want to learn, not just copying the answer • Feb 1st 2009, 02:06 PM Plato $\displaystyle \frac{{k(x + h) - k(x)}} {h} = \frac{{\sqrt {x + h} - \sqrt x }} {h} = \frac{{\sqrt {x + h} - \sqrt x }} {h}\frac{{\sqrt {x + h} + \sqrt x }} {{\sqrt {x + h} + \sqrt x }} = \frac{h} {{h\left[ {\sqrt {x + h} + \sqrt x } \right]}}$ Now divide out the h's and find the $\displaystyle \lim _{h \to 0}$ • Feb 1st 2009, 02:32 PM jkami Quote: Originally Posted by Plato $\displaystyle \frac{{k(x + h) - k(x)}} {h} = \frac{{\sqrt {x + h} - \sqrt x }} {h} = \frac{{\sqrt {x + h} - \sqrt x }} {h}\frac{{\sqrt {x + h} + \sqrt x }} {{\sqrt {x + h} + \sqrt x }} = \frac{h} {{h\left[ {\sqrt {x + h} + \sqrt x } \right]}}$ Now divide out the h's and find the $\displaystyle \lim _{h \to 0}$ I know this formula, but I don't understand what does x = c mean. so, the first one I got lim g(x) = 10x, what do i have to do next • Mar 1st 2009, 12:41 AM CaptainBlack Quote: Originally Posted by jkami I know this formula, but I don't understand what does x = c mean. so, the first one I got lim g(x) = 10x, what do i have to do next No you go g'(x)=the limit=10x, that is the deriviative at the point x is 10x. x is a dummy variable (the logicians have another name for this but I will not bother you with that) it can be replaced with any other symbol denoting a variable, so you also have g'(c)=10c etc. CB
616
1,780
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.5
4
CC-MAIN-2018-22
latest
en
0.850775
http://stackoverflow.com/questions/1475631/r-update-plot-xylims-with-new-points-or-lines-additions
1,469,418,085,000,000,000
text/html
crawl-data/CC-MAIN-2016-30/segments/1469257824201.56/warc/CC-MAIN-20160723071024-00127-ip-10-185-27-174.ec2.internal.warc.gz
234,835,352
19,913
Dismiss Announcing Stack Overflow Documentation We started with Q&A. Technical documentation is next, and we need your help. Whether you're a beginner or an experienced developer, you can contribute. # R: update plot [xy]lims with new points() or lines() additions? Background: I'm running a Monte Carlo simulation to show that a particular process (a cumulative mean) does not converge over time, and often diverges wildly in simulation (the expectation of the random variable = infinity). I want to plot about 10 of these simulations on a line chart, where the x axis has the iteration number, and the y axis has the cumulative mean up to that point. Here's my problem: I'll run the first simulation (each sim. having 10,000 iterations), and build the main plot based on its current range. But often one of the simulations will have a range a few orders of magnitude large than the first one, so the plot flies outside of the original range. So, is there any way to dynamically update the ylim or xlim of a plot upon adding a new set of points or lines? I can think of two workarounds for this: 1. store each simulation, then pick the one with the largest range, and build the base graph off of that (not elegant, and I'd have to store a lot of data in memory, but would probably be laptop-friendly [[EDIT: as Marek points out, this is not a memory-intense example, but if you know of a nice solution that'd support far more iterations such that it becomes an issue (think high dimensional walks that require much, much larger MC samples for convergence) then jump right in]]) 2. find a seed that appears to build a nice looking version of it, and set the ylim manually, which would make the demonstration reproducible. Naturally I'm holding out for something more elegant than my workarounds. Hoping this isn't too pedestrian a problem, since I imagine it's not uncommon with simulations in R. Any ideas? - I just wonder: have you any memory issues? 10 vectors of 10.000 isn't a lot. As I check: X<-lapply(1:10,function(i) rnorm(100000,0,1000)); object.size(X)/1024/1024 is just 7MB of RAM. So 1. should be ok. – Marek Sep 25 '09 at 9:39 No, good point - I'm definitely NOT running into memory issues (hence laptop-friendly) with this simulation, but I'll be demonstrating far more complicated [Q]MC[MC] simulations in the future, with the same output of a graph. I'm looking for something that in general wouldn't rely on too much storage, especially as things get more complicated and I need far larger MC sample sizes to ensure convergence. This may be unavoidable / I might be overestimating the difficulty of implementing said future simulations. – HamiltonUlmer Sep 25 '09 at 15:54 I'm not sure if this is possible using base graphics, if someone has a solution I'd love to see it. However graphics systems based on grid (lattice and ggplot2) allow the graphics object to be saved and updated. It's insanely easy in ggplot2. `require(ggplot2)` make some data and get the range: ``````foo <- as.data.frame(cbind(data=rnorm(100), numb=seq_len(100))) `````` make an initial ggplot object and plot it: ``````p <- ggplot(as.data.frame(foo), aes(numb, data)) + layer(geom='line') p `````` make some more data and add it to the plot ``````foo <- as.data.frame(cbind(data=rnorm(200), numb=seq_len(200))) p <- p + geom_line(aes(numb, data, colour="red"), data=as.data.frame(foo)) `````` plot the new object ``````p `````` - This is a good solution, and proof I need to use ggplot2 more. Using rnorm(200, 0, 1000) in the second foo assignment really shows that this works beautifully :-) – Vince Sep 25 '09 at 7:07 Now that I think about this a bit more, this won't help w/ a memory issue if there is one (all that ggplot object data has to live somewhere.) – Peter Sep 25 '09 at 7:11 Given this particular context (simple, short simulations), using ggplot is the nicest approach. And the fact is, ggplot2 is really nice for other reasons, so an answer that uses it is all right in my book. I'll potentially ask this again if . when memory IS an issue. – HamiltonUlmer Sep 25 '09 at 18:41 I think (1) is the best option. I actually don't think this isn't elegant. I think it would be more computationally intensive to redraw every time you hit a point greater than xlim or ylim. Also, I saw in Peter Hoff's book about Bayesian statistics a cool use of ts() instead of lines() for cumulative sums/means. It looks pretty spiffy: - A solution that uses base graphics and is memory lighter would be to track the X and Y max. Then save the full data set to a file. When you complete a new run, if the range is larger redo the plot and then loop through the stored data files. – Peter Sep 25 '09 at 7:12 Instead of check (and eventually replot) after each trial, one could save data and store ranges, then find global range, use it as ylim and plot results (for the first time). – Marek Sep 25 '09 at 9:34 Part of my backing of this approach was Marek's comment above, that this isn't that much data. 7MB of RAM. Compared to the genome assembly memory requirements I've seen recently, MCMC sims are a drop in the bucket! – Vince Sep 25 '09 at 15:51 Yep - this example doesn't require me to worry about memory, even on a crappy laptop. Let's see what y'all say when I bring in a far bigger fish :) – HamiltonUlmer Sep 25 '09 at 16:32
1,343
5,349
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.828125
3
CC-MAIN-2016-30
latest
en
0.943979
https://solvedlib.com/let-h-be-the-set-of-third-degree-polynomials-h-ax,33549
1,685,342,561,000,000,000
text/html
crawl-data/CC-MAIN-2023-23/segments/1685224644683.18/warc/CC-MAIN-20230529042138-20230529072138-00779.warc.gz
591,315,576
16,700
# Let H be the set of third degree polynomials H = {ax + ax? + ax?... ###### Question: Let H be the set of third degree polynomials H = {ax + ax? + ax? | aEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is a subspace of P3 because it contains the zero vector of P3 b. H is a subspace of P3 because it is closed under vector addition and scalar multiplication Oc H is a subspace of P3 because it can be written as the span of a subset of P3 d. H is a subspace of P3 because it contains only second degree polynomials e. H is not a subspace of P3 because it is not closed under vector addition Of. H is not a subspace of P3 because it is not closed under scalar multiplication Og. H is not a subspace of P3 because it does not contain the zero vector of P3 #### Similar Solved Questions ##### And Q be an orthogonal matrix of order 3,i.e. QTQ = I. Find the inner product (a1,a2). Determine if Span(a1.a2) and Span(b) are orthogonal or not Find the length of Qa1 Find the distance between Qaz and Qaz Suppose S is subspace of Rr and P is the projection matrix onto S If b is written as b = b1 + bz where b1 € S and bz € S- then what is Pb? Suppose Rio 2 5S is a 7-dimensional subspace. What is dim 5L? Suppose R" 2 S T are two subspaces of R" such that S 1 T. Is it true or false and Q be an orthogonal matrix of order 3,i.e. QTQ = I. Find the inner product (a1,a2). Determine if Span(a1.a2) and Span(b) are orthogonal or not Find the length of Qa1 Find the distance between Qaz and Qaz Suppose S is subspace of Rr and P is the projection matrix onto S If b is written as b = b1 +... ##### Find the nth coefficient an of the power series solution to the differential equation about Xo = 0:xy" +6y' _ 14y =none8 an an+1 (n+1)n +14)14 an +19 an_1 an+1 (n+1)n+6)14 an an+1 (n+1)(n+6)19 a (n+1)(n+6) Find the nth coefficient an of the power series solution to the differential equation about Xo = 0:xy" +6y' _ 14y = none 8 an an+1 (n+1)n +14) 14 an +19 an_1 an+1 (n+1)n+6) 14 an an+1 (n+1)(n+6) 19 a (n+1)(n+6)... ##### US Military Solider StressNATO Allies Soldier Stress101 US Military Solider Stress NATO Allies Soldier Stress 101... ##### Consider two countries, A and B. Each country produces only two goods with 1,000 production units:... Consider two countries, A and B. Each country produces only two goods with 1,000 production units: Wine and Cheese. Country A can produce 400 bottles of wine or 200 pounds of cheese or any combination of two goods. At the same time, country B can produce 1200 bottles of wine or 300 pounds of cheese ... ##### Probleni Find the equation of tbe line passing through the point (0,14,~10} 3; 2 =paralle]the linethe plane that containsDuipiralletie plane < = I +the Jina of intersection the plantsPI : I-"+a=alal P2 : I + 2y+22 = 1 Probleni Find the equation of tbe line passing through the point (0,14,~10} 3; 2 = paralle] the line the plane that contains Dui piralle tie plane < = I + the Jina of intersection the plants PI : I-"+a= alal P2 : I + 2y+22 = 1... ##### 3 O o 12 3 Let A= o O o O 0 o o -4 O... 3 O o 12 3 Let A= o O o O 0 o o -4 O and the The dimension of Nul A is dimension of ColA is... ##### If inventory is being valued at cost and the price level is steadily rising, which of... If inventory is being valued at cost and the price level is steadily rising, which of the following three methods of costing—FIFO, LIFO, or weighted average cost—will yield the lowest annual after tax net income? Which method will yield the highest after tax net income in a scenario wher... ##### Y pure pouuctIOe: ) Indicate the chemical shift in appropriate ppm of each of the protons and carbons indicated in the diagram obtained. The below: These values should be experimental values from the NMR you and CNMR is provided for YoU: If you did not form the desired product, indicate_this predict what the ppm values should be.proton NMR results carbon NMR results y pure pouuct IOe: ) Indicate the chemical shift in appropriate ppm of each of the protons and carbons indicated in the diagram obtained. The below: These values should be experimental values from the NMR you and CNMR is provided for YoU: If you did not form the desired product, indicate_this predi... ##### (b): points) Consider the st {T(-2) T(r) T()} CIRCLE THE BEST ANSWER Ixlow that dzcribysthe 4t JUSTIFY WHAT YOU CIRCLED. LINEARLY INDEFENDENT SPANS M (R) BOTH NEITHER (b): points) Consider the st {T(-2) T(r) T()} CIRCLE THE BEST ANSWER Ixlow that dzcribysthe 4t JUSTIFY WHAT YOU CIRCLED. LINEARLY INDEFENDENT SPANS M (R) BOTH NEITHER... Find the exact value each of the remaining trigonometric functions of 0. sin 0 = cot 0<0. cos 0=| (Simplify your answer; including any radicals. Use integers or fractions for any numbers in the expression ) cot 0= (Simplify your ansier, including any radicals. Use integers or fractions for any nu... ##### Excessive commericals and advertising 18% Game delys,including penalty flags 24% Off-field image problems with domestic violence... Excessive commericals and advertising 18% Game delys,including penalty flags 24% Off-field image problems with domestic violence 18% National anthem protest 30% Cord-Cutting 6% what is the 90 95 and 99 confidence intervals sample size is 114... Jiminy’s Cricket Farm issued a 20-year, 7 percent semiannual bond four years ago. The bond currently sells for 98 percent of its face value. The company’s tax rate is 25 percent. For the same firm, suppose the book value of the debt issue is $75 million. In addition, the company has a se... 5 answers ##### In some situations, the force required to stretch a *spring" is not linear . Consider the following model of a bow and arrow in which the force required to draw an arTow a distance is F(x) a x b x2 (e) If a force of 15 pounds is required to draw the arrow 1 foot and a force of 50 pounds is required to draw the arrow 2 feet, find the constants and b_6How much work is required to draw the arrow 2.2 feet? (Hint: Use a definite integral of the force function:)(6) In some situations, the force required to stretch a *spring" is not linear . Consider the following model of a bow and arrow in which the force required to draw an arTow a distance is F(x) a x b x2 (e) If a force of 15 pounds is required to draw the arrow 1 foot and a force of 50 pounds is requ... 1 answer ##### This question was in a previous exam paper and I really don’t know how to approach... This question was in a previous exam paper and I really don’t know how to approach it. This was everything that was given in the question, so no temperature change was given. I’m not sure where to start. 1. Consider the following gas phase reaction at constant volume: 2CH2N2(g) −&r... 1 answer ##### If Apple Computer decided to issue additional common stock, and Varga purchased 100 shares of this... If Apple Computer decided to issue additional common stock, and Varga purchased 100 shares of this stock from Smyth Barry, the underwriter, would this transaction be a primary or a secondary market transaction? Would it make a difference if Varga purchased previously outstanding Apple stock in the d... 1 answer ##### Sean walks 3/4 of a mile in 15 minutes. At the same pace, how far can Sean walk in 1 hour and 20 minutes? Sean walks 3/4 of a mile in 15 minutes. At the same pace, how far can Sean walk in 1 hour and 20 minutes?... 1 answer ##### Knowledge Objective: Counting You are playing Scrabble with a friend, and you always have 7 letter... Knowledge Objective: Counting You are playing Scrabble with a friend, and you always have 7 letter tiles in your letter rack. Assume that there are no blank tiles (ie. the wild card). Use this information and answer questions 4a to 4d Question 4c: Assuming all 7 etters in your letter rack are unique... 5 answers ##### A .38 special fires a 9.53-gram bullet at a speed of 270 m/sinto a 1.85 kg block that is hanging from a very long, masslessstring. The block is at rest when the bullet hits it. The bulletcompletely embeds itself in the block. How high does theblock/bullet combo reach before swinging back down? A .38 special fires a 9.53-gram bullet at a speed of 270 m/s into a 1.85 kg block that is hanging from a very long, massless string. The block is at rest when the bullet hits it. The bullet completely embeds itself in the block. How high does the block/bullet combo reach before swinging back down?... 5 answers ##### QUESTION 16Find the maximum of the xy?z? ' when all the variables X,Y, Z and are all positive andx+ytz+t=12The maximum value is QUESTION 16 Find the maximum of the xy?z? ' when all the variables X,Y, Z and are all positive and x+ytz+t=12 The maximum value is... 5 answers ##### Question 17 (1 point) The canoe team from the previous problem wishes to prove that their compressit strength of 900 psi is indeed greater than the required 860 psi. To do 5o, they wri out a number of hypotheses:A: Our concrete is stronger than required, H > 860 B: Our compressive strength is great, H = 900 C: Our concrete meets the requirement; H = 860 D: Typical concrete is weaker than ours, H 900Of these four potential hypotheses which should be the null hypothesis?None of these Question 17 (1 point) The canoe team from the previous problem wishes to prove that their compressit strength of 900 psi is indeed greater than the required 860 psi. To do 5o, they wri out a number of hypotheses: A: Our concrete is stronger than required, H > 860 B: Our compressive strength is gr... 5 answers ##### A9.(a) Using diagrams, show that the second-harmonic acoustic resonances for closed- closed and open-closed pipes occur for pipe lengths of L 1 and L = 31/4 respectively.(b) The ear canal is considered to be a cylindrical open-closed pipe in the context of acoustic resonances. Person A has a second harmonic frequency the same as the third harmonic of Person B. Given that Person A has a canal length 2.2 cm long; what is the canal length of Person B? A9. (a) Using diagrams, show that the second-harmonic acoustic resonances for closed- closed and open-closed pipes occur for pipe lengths of L 1 and L = 31/4 respectively. (b) The ear canal is considered to be a cylindrical open-closed pipe in the context of acoustic resonances. Person A has a secon... 1 answer ##### 5. As a senior engineer for a large consulting firm, Kevin earned$249,000 last year. Kevin... 5. As a senior engineer for a large consulting firm, Kevin earned $249,000 last year. Kevin Is married to Julia and they have 6 children. Julia had no income (because she is caring for their lovely children). They have itemized deductions of$9,700. What percent of their income (effective federal ta... ##### WI7: My StalLab Homeworkprobabilmi Lalculate CnicaRellection Jooole docsGet Homewioik He p WNith [email protected] c Altitude Desd_ol scundhttps /upperiowa brightspace comdzlle/content/69473/viewContent/739442/viewgpsb org bookmnarksCiaseciaRChanleRocksamClencoe Vinual Lab_Glencoe MinenVolcino Explorer640-18-147,BUREThe Impact of Job_Ahstracs DalahasScore: 0.33 0f 1 ptcompiete[HW Score: 74.87%, 6.74 0f 9 pts9.1.23-TQueston HelpFor the folloving data (a) d splay the data scaer nioI calculate the sample cor WI7: My StalLab Homework probabilmi Lalculate Cnica Rellection Jooole docs Get Homewioik He p WNith Cheq @G c Altitude Desd_ol scund https /upperiowa brightspace comdzlle/content/69473/viewContent/739442/view gpsb org bookmnarks CiaseciaR Chanle Rocksam Clencoe Vinual Lab_ Glencoe Minen Volcino Exp... ##### Why are the polysulfides such as S2-, S3-, S62- chromophore? What is the colour for each one? Why are the polysulfides such as S2-, S3-, S62- chromophore? What is the colour for each one?... ##### Use the Chain Rule to find dz/ds and dz/dt. 2 arcsin(x - y) , x = 52 + t2, Y = 1 9st:2 dsdz dtNeed Help?Rcad ItTalk to a Tutor Use the Chain Rule to find dz/ds and dz/dt. 2 arcsin(x - y) , x = 52 + t2, Y = 1 9st :2 ds dz dt Need Help? Rcad It Talk to a Tutor... ##### How the Long-Term Care Industry Has Begun to Embrace Technology and Why Long-Term Care Needs Tech... How the Long-Term Care Industry Has Begun to Embrace Technology and Why Long-Term Care Needs Tech Innovation. What are the problem that technology solves in LTC?... ##### Wouldn t / be simpler to use cetone to extract the nutmeg? Why do vou think this % not done? Why not use diethyl ether for the crystolllzation? Wouldn t / be simpler to use cetone to extract the nutmeg? Why do vou think this % not done? Why not use diethyl ether for the crystolllzation?... ##### 13. Use a Lyapunov function to show that the origin is globally asymptotically stable: x' =... 13. Use a Lyapunov function to show that the origin is globally asymptotically stable: x' = -y - xemy y' = x - y Hint: Try V = x2 + y2. x' = 2y – 2.3 y = –23 – 45 Hint: Try V = ax+ + by2 for an appropriate choice of a, b > 0....
3,521
12,894
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.484375
3
CC-MAIN-2023-23
latest
en
0.904246
https://www.gospel10.com/how-to-calculate-bmi-in-ms-excel-a-comprehensive-guide/
1,721,435,706,000,000,000
text/html
crawl-data/CC-MAIN-2024-30/segments/1720763514972.64/warc/CC-MAIN-20240719231533-20240720021533-00490.warc.gz
691,877,767
56,185
# How to Calculate BMI in MS Excel: A Comprehensive Guide Calculating Body Mass Index (BMI) in Microsoft Excel is a valuable task in healthcare and fitness. BMI is a measure of body fat based on height and weight, and it is used to assess health risks. In this article, we will guide you through the steps to calculate BMI in Microsoft Excel. We will also discuss the importance of BMI, its benefits, and a brief historical context. Let’s dive right in and explore how to calculate BMI in Excel efficiently. ## How to Calculate BMI in MS Excel Calculating BMI in MS Excel is essential for assessing health risks and maintaining a healthy weight. Here are nine key aspects to consider: • Formula • Inputs • Interpretation • Limitations • Accuracy • Automation • Formatting • Customization • Applications The formula used to calculate BMI is BMI = weight (kg) / (height (m))^2. This formula considers both weight and height to provide a comprehensive assessment of body fat. Interpreting BMI values can help individuals understand their health risks and make informed lifestyle choices. While BMI has limitations, such as not accounting for muscle mass, it remains a valuable tool for healthcare professionals and individuals alike. ### Formula The formula to calculate BMI in MS Excel is BMI = weight (kg) / (height (m))^2. It is a mathematical equation that considers both weight and height to provide a measure of body fat. Understanding the formula’s components and implications is key to accurate BMI calculation. • Weight Weight is measured in kilograms. It is the force exerted on an object due to gravity. In the BMI formula, weight is a crucial factor in determining body fat percentage. • Height Height is measured in meters. It is the vertical distance from the base to the top of an object. In the BMI formula, height is squared to account for the relationship between body surface area and body fat. • Units of Measurement It is important to ensure that both weight and height are entered in the correct units (kilograms and meters, respectively) for accurate BMI calculation. The BMI formula is a valuable tool for assessing body fat and health risks. By understanding the formula’s components and implications, individuals can utilize MS Excel to calculate their BMI accurately and make informed health decisions. ### Inputs Calculating BMI in MS Excel requires accurate input data to ensure reliable results. The primary inputs are weight and height, each with its own significance and implications. • Weight Weight, measured in kilograms, represents the force exerted on the body due to gravity. In the context of BMI calculation, weight is a crucial factor in determining the amount of body fat. • Height Height, measured in meters, represents the vertical distance from the base to the top of the body. In BMI calculation, height is squared to account for the relationship between body surface area and body fat. These inputs, when entered accurately, enable MS Excel to calculate BMI effectively. Incorrect or missing inputs can lead to inaccurate results, potentially affecting health assessments and decisions. ### Interpretation Interpretation plays a critical role in the process of calculating Body Mass Index (BMI) in Microsoft Excel. After calculating BMI using the appropriate formula, interpreting the result is essential for understanding its implications for health and well-being. BMI values are categorized into different weight status groups, each associated with specific health risks and recommendations. For example, a BMI below 18.5 is considered underweight, while a BMI between 25 and 29.9 is considered overweight. Understanding these categories helps individuals assess their weight status and make informed decisions about lifestyle changes. Furthermore, interpretation of BMI values should consider individual factors such as age, sex, ethnicity, and body composition. For instance, athletes may have a higher BMI due to increased muscle mass, which does not necessarily indicate excess body fat. Therefore, interpreting BMI requires a holistic approach, considering both the value itself and the individual’s unique characteristics. ### Limitations While calculating BMI in MS Excel offers valuable insights, it is essential to acknowledge its limitations to ensure accurate interpretation and appropriate application. One primary limitation is that BMI does not differentiate between body fat and muscle mass. Individuals with a high muscle mass, such as athletes, may have a higher BMI despite having a low body fat percentage. Conversely, individuals with a low muscle mass may have a lower BMI despite having a higher body fat percentage. Another limitation is that BMI does not take into account factors such as age, sex, ethnicity, and body frame. These factors can influence the relationship between BMI and body fat percentage. For instance, older adults tend to have a higher body fat percentage at a given BMI compared to younger adults. Similarly, women generally have a higher body fat percentage at a given BMI compared to men. Understanding these limitations is crucial for interpreting BMI results appropriately. Individuals should not solely rely on BMI to assess their overall health and body composition. Instead, they should consider BMI in conjunction with other health indicators, such as waist circumference, body fat percentage, and overall fitness levels. ### Accuracy In the context of calculating BMI in MS Excel, accuracy plays a pivotal role in ensuring the reliability and validity of the results. Accuracy refers to the closeness of a calculated BMI value to its true or actual value. It is influenced by the precision of the input data, the accuracy of the formula used, and the absence of any errors in the calculation process. Accurate BMI calculation is critical as it directly impacts the interpretation of an individual’s weight status. Inaccurate BMI values can lead to misclassification, which may result in inappropriate health recommendations or interventions. For instance, an overestimation of BMI may lead to an incorrect diagnosis of overweight or obesity, potentially causing unnecessary anxiety or restrictive dieting. Conversely, an underestimation of BMI may result in missed opportunities for individuals who may benefit from weight management strategies. To ensure accuracy, it is essential to use precise measuring tools for weight and height and to input the values carefully into the Excel formula. Additionally, verifying the calculation process and checking for any potential errors is crucial. By adhering to these practices, individuals can enhance the accuracy of their BMI calculations and make informed decisions regarding their health and well-being. ### Automation Automation plays a crucial role in streamlining the process of calculating Body Mass Index (BMI) in Microsoft Excel. By leveraging automation features, individuals can save time, minimize errors, and enhance the efficiency of their BMI calculations. One way automation simplifies BMI calculation is through the use of macros. Macros are sets of recorded actions that can be executed with a single click or keyboard shortcut. By creating a macro that automates the BMI calculation process, users can eliminate the need to manually input data and perform calculations each time they need to determine their BMI. This not only saves time but also reduces the risk of errors. Another application of automation in BMI calculation involves the use of add-ins. Add-ins are small programs that extend the functionality of Excel. There are several add-ins available that can automate the BMI calculation process, providing users with a convenient and efficient way to calculate their BMI. These add-ins often include additional features, such as the ability to track BMI over time or compare BMI values to recommended ranges. In summary, automation offers significant benefits for calculating BMI in MS Excel. By leveraging macros and add-ins, users can streamline the process, minimize errors, and enhance the efficiency of their BMI calculations. ### Formatting Formatting plays a crucial role in enhancing the readability, organization, and overall presentation of “how to calculate BMI in MS Excel” content. It involves applying various styles, such as fonts, colors, alignment, and borders, to make the information visually appealing and easier to comprehend. Proper formatting can significantly improve the usability of the content. By using clear and consistent formatting, readers can quickly locate the information they need and follow the steps outlined in the guide. For example, using numbered or bulleted lists to present the steps involved in calculating BMI makes the instructions easy to follow and reduces the risk of confusion. Moreover, formatting can help emphasize important information and draw attention to key points. By using bold or italicized text, headings, and subheadings, the content creator can guide the reader’s attention to the most critical aspects of calculating BMI in MS Excel. This helps readers grasp the essential concepts and avoid missing crucial details. In summary, formatting is an integral part of creating informative and engaging content on “how to calculate BMI in MS Excel.” By applying appropriate formatting techniques, the content becomes more readable, organized, and visually appealing, enabling readers to understand and follow the instructions more effectively. ### Customization Customization plays a pivotal role in enhancing the utility and applicability of “how to calculate BMI in MS Excel” content. It empowers users to tailor the content to their specific needs and preferences, leading to a more personalized and effective experience. One key aspect of customization is the ability to modify the input parameters and formulas used in BMI calculation. This allows users to adapt the content to their unique requirements. For example, users can modify the units of measurement (e.g., kilograms to pounds, meters to inches) or incorporate additional variables (e.g., age, gender) to refine the accuracy of their BMI calculations. Furthermore, customization enables users to create personalized templates and reports. By incorporating their branding, formatting preferences, and data visualization elements, users can generate professional-looking documents that effectively communicate BMI-related information. This customization enhances the credibility and impact of the content, making it more suitable for sharing and presentation. In summary, customization is an essential component of “how to calculate BMI in MS Excel” content. It empowers users to adapt the content to their specific needs, improve the accuracy of calculations, and create personalized reports. By understanding and leveraging the customization capabilities of MS Excel, users can unlock its full potential for effective BMI calculation and analysis. ### Applications In the realm of “how to calculate BMI in MS Excel,” the aspect of “Applications” holds immense significance. It encompasses the practical uses and implications of BMI calculation in various fields and contexts. By exploring these applications, we gain a deeper understanding of the relevance and impact of BMI calculations in real-world scenarios. • Health Assessment BMI is widely used by healthcare professionals to assess an individual’s weight status and potential health risks. It serves as a screening tool for conditions such as obesity, underweight, and eating disorders, guiding appropriate medical interventions. • Fitness Tracking In the fitness industry, BMI is employed to monitor progress and make informed decisions. It helps individuals track changes in body composition, adjust exercise plans, and maintain a healthy weight. • Insurance and Risk Assessment Insurance companies utilize BMI as a factor in underwriting and risk assessment. It provides insights into an individual’s overall health and potential for developing weight-related health issues, influencing insurance premiums and coverage. • Research and Epidemiology BMI plays a crucial role in epidemiological studies and public health research. It enables researchers to analyze weight-related trends, identify risk factors, and develop evidence-based interventions for improving population health. These applications underscore the versatility and importance of BMI calculation in MS Excel. It extends beyond personal health management to impact medical decision-making, fitness strategies, insurance policies, and population health research. Understanding these applications empowers individuals and professionals alike to harness the power of BMI calculations for informed decision-making and improved health outcomes. This section addresses frequently asked questions (FAQs) about calculating Body Mass Index (BMI) in Microsoft Excel. These FAQs aim to clarify common concerns and provide additional insights to enhance your understanding. Question 1: What is the formula for calculating BMI in Excel? The BMI formula in Excel is: =weight_in_kg / (height_in_meters)^2. Replace “weight_in_kg” with your weight in kilograms and “height_in_meters” with your height in meters. Question 2: How do I convert my weight from pounds to kilograms? To convert weight from pounds to kilograms, divide your weight in pounds by 2.205. Question 3: How do I convert my height from inches to meters? To convert height from inches to meters, divide your height in inches by 39.37. Question 4: Can I use Excel to track my BMI over time? Yes, you can create a simple table in Excel to record your weight, height, and BMI over time. This can help you monitor your progress and identify trends. Question 5: What are the limitations of using BMI as a health indicator? BMI is a useful screening tool, but it does not consider factors like muscle mass and body composition. It may not accurately reflect health risks for individuals with a high muscle mass or certain body types. Question 6: Where can I find additional resources on calculating BMI in Excel? There are many helpful resources available online, including tutorials, articles, and templates. Consult reputable sources to ensure accuracy. These FAQs provide essential information to support your understanding of BMI calculation in Excel. In the next section, we will explore best practices for accurate and effective BMI calculations. ### Tips for Accurate BMI Calculation in Excel This section provides essential tips to ensure accurate and effective BMI calculations in Microsoft Excel. Tip 1: Verify Input Data Ensure that the weight and height values entered in Excel are precise and accurate. Double-check the units of measurement (kilograms for weight, meters for height) to avoid errors. Tip 2: Use the Correct Formula Apply the standard BMI formula: BMI = weight_in_kg / (height_in_meters)^2. Ensure that the formula is entered correctly without any syntax errors. Tip 3: Convert Units if Necessary If your weight is in pounds or height in inches, convert them to kilograms and meters, respectively, before using the BMI formula. Tip 4: Format Cells Appropriately Format the cells containing weight and height data as “Number” to ensure that they are treated as numerical values and not text. Tip 5: Check for Errors Carefully review the calculated BMI values for any errors or inconsistencies. Verify the results by manually calculating BMI using a calculator. Tip 6: Consider Individual Factors While BMI is a useful indicator, it does not account for factors like muscle mass or body composition. Consult a healthcare professional for a more comprehensive assessment of your health. Summary: By following these tips, you can ensure accurate BMI calculations in Excel, providing valuable insights into your weight status and potential health risks. Transition: In the concluding section, we will discuss the importance of regular BMI monitoring and the implications of BMI values for health and well-being. ### Conclusion This comprehensive guide has delved into the intricacies of calculating BMI in MS Excel, empowering individuals to assess their weight status and potential health risks. Key insights include the formula, input requirements, interpretation of results, and limitations of BMI. Understanding these aspects is crucial for accurate and meaningful BMI calculations. To reiterate, accurate data input, proper formula application, and consideration of individual factors are essential for reliable BMI results. Regular BMI monitoring helps track progress, identify trends, and make informed decisions about health and lifestyle. While BMI is a valuable screening tool, it should be interpreted in conjunction with other health indicators for a holistic assessment.
3,070
16,862
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.625
4
CC-MAIN-2024-30
latest
en
0.911039
https://de.mathworks.com/matlabcentral/cody/problems/1066-multiples-of-a-number-in-a-given-range/solutions/2801158
1,600,475,746,000,000,000
text/html
crawl-data/CC-MAIN-2020-40/segments/1600400189264.5/warc/CC-MAIN-20200918221856-20200919011856-00201.warc.gz
355,052,879
17,459
Cody # Problem 1066. Multiples of a Number in a Given Range Solution 2801158 Submitted on 6 Aug 2020 by Sanveg Rane This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass assert(isequal(bounded_multiples(66,119,163),132)) 2   Pass assert(isequal(bounded_multiples(50,341,960),[350 400 450 500 550 600 650 700 750 800 850 900 950])) 3   Pass assert(isequal(bounded_multiples(59,224,752),[236 295 354 413 472 531 590 649 708])) 4   Pass assert(isequal(bounded_multiples(26,506,700),[520 546 572 598 624 650 676])) 5   Pass assert(isequal(bounded_multiples(90,548,960),[630 720 810 900])) 6   Pass assert(isequal(bounded_multiples(14,150,258),[154 168 182 196 210 224 238 252])) 7   Pass assert(isequal(bounded_multiples(85,255,815),[255 340 425 510 595 680 765])) 8   Pass assert(isequal(bounded_multiples(25,350,930),[350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 775 800 825 850 875 900 925])) 9   Pass assert(isequal(bounded_multiples(20,252,617),[260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600])) 10   Pass assert(isequal(bounded_multiples(48,352,831),[384 432 480 528 576 624 672 720 768 816])) 11   Pass assert(isequal(bounded_multiples(59,550,918),[590 649 708 767 826 885])) 12   Pass assert(isequal(bounded_multiples(29,754,758),754)) 13   Pass assert(isequal(bounded_multiples(39,76,568),[78 117 156 195 234 273 312 351 390 429 468 507 546])) 14   Pass assert(isequal(bounded_multiples(6,531,780),[534 540 546 552 558 564 570 576 582 588 594 600 606 612 618 624 630 636 642 648 654 660 666 672 678 684 690 696 702 708 714 720 726 732 738 744 750 756 762 768 774 780])) 15   Pass assert(isequal(bounded_multiples(94,130,569),[188 282 376 470 564])) 16   Pass assert(isequal(bounded_multiples(47,12,338),[47 94 141 188 235 282 329])) 17   Pass assert(isequal(bounded_multiples(17,312,795),[323 340 357 374 391 408 425 442 459 476 493 510 527 544 561 578 595 612 629 646 663 680 697 714 731 748 765 782])) 18   Pass assert(isequal(bounded_multiples(53,166,602),[212 265 318 371 424 477 530 583])) 19   Pass assert(isequal(bounded_multiples(27,655,690),675)) 20   Pass assert(isequal(bounded_multiples(75,84,451),[150 225 300 375 450]))
906
2,322
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.28125
3
CC-MAIN-2020-40
latest
en
0.297009
https://codegolf.stackexchange.com/questions/57617/is-this-number-a-prime/58174#58174
1,685,615,852,000,000,000
text/html
crawl-data/CC-MAIN-2023-23/segments/1685224647639.37/warc/CC-MAIN-20230601074606-20230601104606-00790.warc.gz
206,130,629
73,545
# Is this number a prime? Believe it or not, we do not yet have a code golf challenge for a simple primality test. While it may not be the most interesting challenge, particularly for "usual" languages, it can be nontrivial in many languages. Rosetta code features lists by language of idiomatic approaches to primality testing, one using the Miller-Rabin test specifically and another using trial division. However, "most idiomatic" often does not coincide with "shortest." In an effort to make Programming Puzzles and Code Golf the go-to site for code golf, this challenge seeks to compile a catalog of the shortest approach in every language, similar to "Hello, World!" and Golf you a quine for great good!. Furthermore, the capability of implementing a primality test is part of our definition of programming language, so this challenge will also serve as a directory of proven programming languages. Write a full program that, given a strictly positive integer n as input, determines whether n is prime and prints a truthy or falsy value accordingly. For the purpose of this challenge, an integer is prime if it has exactly two strictly positive divisors. Note that this excludes 1, who is its only strictly positive divisor. Your algorithm must be deterministic (i.e., produce the correct output with probability 1) and should, in theory, work for arbitrarily large integers. In practice, you may assume that the input can be stored in your data type, as long as the program works for integers from 1 to 255. ### Input • If your language is able to read from STDIN, accept command-line arguments or any other alternative form of user input, you can read the integer as its decimal representation, unary representation (using a character of your choice), byte array (big or little endian) or single byte (if this is your languages largest data type). • If (and only if) your language is unable to accept any kind of user input, you may hardcode the input in your program. In this case, the hardcoded integer must be easily exchangeable. In particular, it may appear only in a single place in the entire program. For scoring purposes, submit the program that corresponds to the input 1. ### Output Output has to be written to STDOUT or closest alternative. If possible, output should consist solely of a truthy or falsy value (or a string representation thereof), optionally followed by a single newline. The only exception to this rule is constant output of your language's interpreter that cannot be suppressed, such as a greeting, ANSI color codes or indentation. • This is not about finding the language with the shortest approach for prime testing, this is about finding the shortest approach in every language. Therefore, no answer will be marked as accepted. • Submissions in most languages will be scored in bytes in an appropriate preexisting encoding, usually (but not necessarily) UTF-8. The language Piet, for example, will be scored in codels, which is the natural choice for this language. Some languages, like Folders, are a bit tricky to score. If in doubt, please ask on Meta. • Unlike our usual rules, feel free to use a language (or language version) even if it's newer than this challenge. If anyone wants to abuse this by creating a language where the empty program performs a primality test, then congrats for paving the way for a very boring answer. Note that there must be an interpreter so the submission can be tested. It is allowed (and even encouraged) to write this interpreter yourself for a previously unimplemented language. • If your language of choice is a trivial variant of another (potentially more popular) language which already has an answer (think BASIC or SQL dialects, Unix shells or trivial Brainfuck derivatives like Headsecks or Unary), consider adding a note to the existing answer that the same or a very similar solution is also the shortest in the other language. • Built-in functions for testing primality are allowed. This challenge is meant to catalog the shortest possible solution in each language, so if it's shorter to use a built-in in your language, go for it. • Unless they have been overruled earlier, all standard rules apply, including the http://meta.codegolf.stackexchange.com/q/1061. As a side note, please don't downvote boring (but valid) answers in languages where there is not much to golf; these are still useful to this question as it tries to compile a catalog as complete as possible. However, do primarily upvote answers in languages where the author actually had to put effort into golfing the code. ### Catalog The Stack Snippet at the bottom of this post generates the catalog from the answers a) as a list of shortest solution per language and b) as an overall leaderboard. ## Language Name, N bytes where N is the size of your submission. If you improve your score, you can keep old scores in the headline, by striking them through. For instance: ## Ruby, <s>104</s> <s>101</s> 96 bytes If there you want to include multiple numbers in your header (e.g. because your score is the sum of two files or you want to list interpreter flag penalties separately), make sure that the actual score is the last number in the header: ## Perl, 43 + 2 (-p flag) = 45 bytes You can also make the language name a link which will then show up in the snippet: ## [><>](http://esolangs.org/wiki/Fish), 121 bytes <style>body { text-align: left !important} #answer-list { padding: 10px; width: 290px; float: left; } #language-list { padding: 10px; width: 290px; float: left; } table thead { font-weight: bold; } table td { padding: 5px; }</style><script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b"> <div id="language-list"> <h2>Shortest Solution by Language</h2> <table class="language-list"> <thead> <tr><td>Language</td><td>User</td><td>Score</td></tr> </thead> <tbody id="languages"> </tbody> </table> </div> <div id="answer-list"> <h2>Leaderboard</h2> <table class="answer-list"> <thead> <tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr> </thead> <tbody id="answers"> </tbody> </table> </div> <table style="display: none"> <tbody id="answer-template"> <tr><td>{{PLACE}}</td><td>{{NAME}}</td><td>{{LANGUAGE}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr> </tbody> </table> <table style="display: none"> <tbody id="language-template"> <tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr> </tbody> </table><script>var QUESTION_ID = 57617; var ANSWER_FILTER = "!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe"; var COMMENT_FILTER = "!)Q2B_A2kjfAiU78X(md6BoYk"; var OVERRIDE_USER = 12012; var answers = [], answers_hash, answer_ids, answer_page = 1, more_answers = true, comment_page; function answersUrl(index) { return "https://api.stackexchange.com/2.2/questions/" + QUESTION_ID + "/answers?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + ANSWER_FILTER; } function commentUrl(index, answers) { return "https://api.stackexchange.com/2.2/answers/" + answers.join(';') + "/comments?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + COMMENT_FILTER; } function getAnswers() { jQuery.ajax({ url: answersUrl(answer_page++), method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { answers.push.apply(answers, data.items); answers_hash = []; answer_ids = []; data.items.forEach(function(a) { a.comments = []; var id = +a.share_link.match(/\d+/); answer_ids.push(id); answers_hash[id] = a; }); if (!data.has_more) more_answers = false; comment_page = 1; getComments(); } }); } function getComments() { jQuery.ajax({ url: commentUrl(comment_page++, answer_ids), method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { data.items.forEach(function(c) { if (c.owner.user_id === OVERRIDE_USER) answers_hash[c.post_id].comments.push(c); }); if (data.has_more) getComments(); else if (more_answers) getAnswers(); else process(); } }); } getAnswers(); var SCORE_REG = /<h\d>\s*([^\n,<]*(?:<(?:[^\n>]*>[^\n<]*<\/[^\n>]*>)[^\n,<]*)*),.*?(\d+)(?=[^\n\d<>]*(?:<(?:s>[^\n<>]*<\/s>|[^\n<>]+>)[^\n\d<>]*)*<\/h\d>)/; var OVERRIDE_REG = /^Override\s*header:\s*/i; function getAuthorName(a) { return a.owner.display_name; } function process() { var valid = []; answers.forEach(function(a) { var body = a.body; a.comments.forEach(function(c) { if(OVERRIDE_REG.test(c.body)) body = '<h1>' + c.body.replace(OVERRIDE_REG, '') + '</h1>'; }); var match = body.match(SCORE_REG); if (match) valid.push({ user: getAuthorName(a), size: +match[2], language: match[1], link: a.share_link, }); else console.log(body); }); valid.sort(function (a, b) { var aB = a.size, bB = b.size; return aB - bB }); var languages = {}; var place = 1; var lastSize = null; var lastPlace = 1; valid.forEach(function (a) { if (a.size != lastSize) lastPlace = place; lastSize = a.size; ++place; var answer = jQuery("#answer-template").html(); answer = answer.replace("{{PLACE}}", lastPlace + ".") .replace("{{NAME}}", a.user) .replace("{{LANGUAGE}}", a.language) .replace("{{SIZE}}", a.size) .replace("{{LINK}}", a.link); answer = jQuery(answer); jQuery("#answers").append(answer); var lang = a.language; lang = jQuery('<a>'+lang+'</a>').text(); languages[lang] = languages[lang] || {lang: a.language, lang_raw: lang.toLowerCase(), user: a.user, size: a.size, link: a.link}; }); var langs = []; for (var lang in languages) if (languages.hasOwnProperty(lang)) langs.push(languages[lang]); langs.sort(function (a, b) { if (a.lang_raw > b.lang_raw) return 1; if (a.lang_raw < b.lang_raw) return -1; return 0; }); for (var i = 0; i < langs.length; ++i) { var language = jQuery("#language-template").html(); var lang = langs[i]; language = language.replace("{{LANGUAGE}}", lang.lang) .replace("{{NAME}}", lang.user) .replace("{{SIZE}}", lang.size) .replace("{{LINK}}", lang.link); language = jQuery(language); jQuery("#languages").append(language); } }</script> • Is there a reason for the full program requirement, rather than allowing the full range of default input types? E.g. answering with a function that takes its input as an argument, is currently disallowed? codegolf.meta.stackexchange.com/questions/2447/… Dec 12, 2017 at 6:21 • @LyndonWhite This was intended as a catalog (like “Hello, World!”) of primality tests, so a unified submission format seemed preferable. It's one of two decisions about this challenge that I regret, the other being only allowing deterministic primality tests. Dec 12, 2017 at 12:51 • Could a case be made for locking this challenge and posting a new, less restrictive one? Jun 25, 2018 at 12:59 • @Shaggy Seems like a question for meta. Jun 25, 2018 at 13:44 • Yeah, that's what I was thinking. I'll let you do the honours, seeing as it's your challenge. Jun 25, 2018 at 13:45 # dc, 17 22 bytes ?d*5+v[dz%rdz<M*]dsMxp Try it online! I've been on a bit of a dc kick lately and although there's already a dc solution here, this is 10 5 bytes shorter. It follows the I/O request of the original question, which does add two bytes for the explicit input and output (rather than the usual rules these days that allow implicit stack I/O), but okay. This outputs zero for composite numbers and non-zero for primes. How it works: this program builds a stack consisting of the modulo of the input with the current stack size (so the stack looks like, from bottom to top, i%2, i%3, i%4, ...), then when it decides it's gone far enough (stack size = input) it multiplies the stack as it unwinds the recursion. • This fails for 1 and 2. Mar 16, 2019 at 0:22 • Oof, you're right. Not sure how I missed that. It took me five bytes to fix (by precomposing with d*5+v, i.e., x -> int(sqrt(x^2+5)), i.e., 1->2, 2->3, n->n for n>2) Mar 18, 2019 at 18:09 # K (oK), 14 19 bytes Solution: 2=+/d=_d:x%!x:. 0: Try it online! Example: root@c957fa0dccbd:/ok# echo 1 | node repl.js examples/prime.k 0 root@c957fa0dccbd:/ok# echo 2 | node repl.js examples/prime.k 1 root@c957fa0dccbd:/ok# echo 5 | node repl.js examples/prime.k 1 root@c957fa0dccbd:/ok# echo 97 | node repl.js examples/prime.k 1 Explanation: Calculate number of factors for input, if equal to 2, then it's prime. 2=+/d=_d:x%!x:. 0: / the solution 0: / read from stdin . / value (ie convert "123" > 123) x: / store input as x ! / range 0..x x% / x divided by ... d: / store as d _ / floor d= / d equal to ... +/ / sum 2= / 2 equals? # tinylisp, 23 bytes There's a library function. (load library (prime? 1 (Since tinylisp is incapable of taking user input, "For scoring purposes, submit the program that corresponds to the input 1.") Try it online! Here's a 112-byte solution using only the base language, no library functions: (d D(q((F A N)(i(l A N)(D F(a F A)N)(e N A (d _(q((F N)(i(D F 0 N)(e F N)(_(a 1 F)N ((q((N)(i(e N 1)0(_ 2 N))))1 The first line defines a function D that takes a factor F, an accumulator A (initially 0), and a number N; it returns 1 if N is divisible by F, 0 otherwise. The second line defines a function _ that takes a minimum factor F and a number N; it returns 1 if N is coprime to all numbers from F to N-1, 0 otherwise. The third line constructs an anonymous function that takes a number N; it returns 0 if N is 1, and otherwise calls _ with number N and minimum factor 2. As above, the scored code calls the anonymous function with an argument of 1. ## DIVCON, 8 bytes Prequisities: Enter 1 into the INPUT_MAX prompt. i*[;-=o] ## Explanation "Partition" by * here means solving x * y = a - a is the original accumulator value. x and y needs to be as close as possible. In addition, the following equality must be satisfied: x>=y Description | Example(0) | Example(1) ----------------+------------+----------- i Take an input | 12 | 13 * Partition by * | 4, 3 | 13, 1 ----------------+------------+----------- [ Left branch | 4 | 13 ----------------+------------+------------ ; Right branch | 3 | 1 - x - 1 | 2 | 0 = x == 0? | 0 | 1 o Print this value| OUT: 0 | OUT: 1 ----------------+------------+------------ ] End both branches Actually, there is another implicit reverse computation. But, since INPUT_MAX is 1, the extra prompting from i is disabled. # MAWP, 4846 54 bytes @1A<:.>{1A<1:.>2M}!1A[/!!\!/P\!/WA<:.>{%}\2A?0{1M}]1:. -2 bytes from Dion's suggestion. +8 bytes after fixing the problem with 1 as input. Prints 1 for prime and 0 for non-prime. Can probably be golfed by a few more bytes, since it checks for 2 at the beginning first. Try it! • Should work as expected now. Aug 26, 2020 at 9:10 • Looks good now. Can you explain how it works? Aug 26, 2020 at 9:16 • checks for 1 first, then 2, then moves on with a loop till it finds any divisor. Aug 26, 2020 at 9:17 # CSASM v2.1.2.2, 207 235 bytes Prints a 1 (truthy) if the input is a prime integer, 0 (falsy) otherwise. Truthy values in CSASM are non-zero numbers, non-\0 chars and non-null strings/arrays/objects. Falsy values in CSASM are zero, the \0 character or null strings/arrays/objects. func main: in "" conv i32 pop $a push$a push 2 comp.gte push $f.o brtrue a br b .lbl a push 2 dup pop$1 push $a sub brfalse d .lbl c clf.o push$a push $1 rem brfalse b inc$1 push $1 push$a comp.lt push $f.o brtrue c .lbl d push 1 print ret .lbl b push 0 print ret end Commented and ungolfed: func main: ; Get the input, convert it to an integer and store it in the accumulator in "" conv i32 pop$a ; if $a < 2, then$a is not prime push $a push 2 comp.gte push$f.o brtrue initLoop br notPrime .lbl initLoop ; Initialize the loop counter and check if $a == 2 ; If$a is 2, return truthy early push 2 dup pop $1 push$a sub brfalse prime .lbl loop ; Clear the comparison flag clf.o ; If $a %$1 == 0, then $a is not prime push$a push $1 rem brfalse notPrime ; Loop until$1 >= $a inc$1 push $1 push$a comp.lt push $f.o brtrue loop .lbl prime ;$a is prime push 1 print ret .lbl notPrime ; $a is not prime push 0 print ret end ## Arduino, 146 143 bytes #define S Serial int p=0,d=1;void setup(){S.begin(300);}void loop(){while(S.available())p=p*256+S.read();if(p&&!(p%++d%p)){S.print(p==d);p=0;}} Based on the current top answer for C++. I'm not convinced my adaptation is optimal. Reading in a number from the Serial input is actually pretty annoying in Arduino. Serial.available() gives the number of unread bytes, but unfortunately it caps out at 64, which is too small for me to use unary for this challenge. Instead, I opted to interpret the input as a byte array. Bitshift is lower precedence than addition, and (p<<8) is longer than p*256 (note the parentheses needed). In this case, a while loop is actually shorter than a for loop, by 1 character. Explanation: #define S Serial /* This macro is worth it in the end, but not by much */ int p = 0, // the case p = 0 is also taken to mean not to even attempt this anyways d = 1; void setup() { S.begin(300); // standard is 9600 but 300 is shorter } void loop() { while (S.available()) // truthy while there are unread bytes p = p * 256 + S.read(); if (p && !(p % ++d % p)) { // second condition from the C++ answer S.print(p == d); // method from the C++ answer p = 0; // reset this to stop trying } } I suppose this technically comes with the caveat that no byte of the number can be 0 (so 256 wouldn't work; it's 0x0100), as the serial port takes in null-terminated strings. That said, it's only two more characters to make a version that accepts numbers written in decimal -- just replace p*256+S.read() with p*10+S.read()-48. Original: int p=0,d=1;void setup(){Serial.begin(300);}void loop(){while(Serial.available())p=p*256+S.read();if(p&&!(p%++d%p)){Serial.print(p==d);p=0;}} # Rust (full program), 124 bytes fn main(){let s=&mut"".into();std::io::stdin().read_line(s);let n=s.parse().unwrap();print!("{}",n>1&&(2..n).all(|x|n%x>0))} Try it online! How complicated it has to be to read an integer from stdin... • using args is shorter 105 bytes Nov 1, 2021 at 15:11 # K (ngn/k), 18 bytes 1=+/1>(!x)!'x:.1:0 Try it online! # WTFstack, 13 bytes 1g{?(!)?/x<{; WTFstack is my new programming language in which mathematical operations work on the entire stack at once. Returns a stack of [1] if prime, and an empty stack if composite. Interpreter ## Explanation 1g # is the input > 1? { # if so, continue. else, print the stack and exit ? # push the user input ( # -1 ! # factorial ) # +1 ? # push the input again / # divide all values on the stack by the input x # push if the number is an integer or not (0 or 1) < # swap the top two values on the stack { # is the top of the stack truthy? if so, continue, else exit ; # discard the top of the stack # minigolf, 29 bytes iT+:,:ns,:n*;s,_;*i=+0=s0=0=* Attempt This Online! ## Explanation Generate a multiplication table of (input-1)x(input-1): iT+ input - 1 : duplicate , map in [1..i-1]: : duplicate i-1 so that it's preserved across iterations of map ns swap current iteration item underneath , map in [1..i-1]: : dup curr. iter. item of outer loop (so that it's preserved) n* multiply by curr. iter. item of this map loop ; end map s,_ swap up & drop our preserved curr. map value ; end map Aftermath of the multiplication table: * flatten i= Set by equality w/ input + sum that 0= = 0? (i.e. no items in that table that equals input) Note: at this point we have i-1 underneath our top value s Swap i-1 upwards 0=0= Set all >0 values to 1 * Multiply (i.e. if i-1 is zero, our prime checking output is 0.) ## LiveCode, 128 bytes on mouseUp ask "" put it div 2 into i repeat with j=2 to it-1 put it mod j*i into i end repeat put i>0 end mouseUp Put in a button and press the button. Asks for a number, puts true or false reporting primality into the message box. LiveCode does support stdin and stdout, but other answers here used this method so I am as well. A function would make more sense to me, but that doesn't seem to be the accepted method here. ### Explanation Should be pretty clear: Starts with 0 if the input is 1, or 1 or more if input > 1. Then for every number from 2 to the input - 1, multiplies the running total by the input modulo the number. If any of the numbers evenly divide the number, the running total will change to (and remain for the rest of the loop) zero. At the end, report whether the running total is greater than 0. If it is, the input is prime, if it has been zero-ified at any point, the input is not prime. # GAIA, 1 byte ṗ Try it online! • Welcome to Code Golf, and nice answer Apr 18 at 19:03 # Tabloid, 358 293 bytes DISCOVER HOW TO x WITH a, b WHAT IF b BEATS 1 WHAT IF ((a DIVIDED BY b) MODULO 1) BEATS 0 SHOCKING DEVELOPMENT x OF a, b MINUS 1 LIES! SHOCKING DEVELOPMENT 0 LIES! SHOCKING DEVELOPMENT 1 EXPERTS CLAIM y TO BE LATEST NEWS ON "" YOU WON'T WANT TO MISS x OF y, y MINUS 1 PLEASE LIKE AND SUBSCRIBE Input through a JavaScript prompt(), and output 1! if the input is prime and 0! otherwise (exclamation point due to language restrictions) -65 bytes by using BEATS (greater than) instead of SMALLER THAN (less than) and IS ACTUALLY (equal to), inverting some if conditions on the way ### Readable version DISCOVER HOW TO x WITH a, b WHAT IF b BEATS 1 WHAT IF ((a DIVIDED BY b) MODULO 1) BEATS 0 SHOCKING DEVELOPMENT x OF a, b MINUS 1 LIES! SHOCKING DEVELOPMENT 0 LIES! SHOCKING DEVELOPMENT 1 EXPERTS CLAIM y TO BE LATEST NEWS ON "" YOU WON'T WANT TO MISS x OF y, y MINUS 1 PLEASE LIKE AND SUBSCRIBE ## Original (358 bytes) DISCOVER HOW TO x WITH a, b RUMOR HAS IT WHAT IF b SMALLER THAN 2 SHOCKING DEVELOPMENT 1 LIES! RUMOR HAS IT WHAT IF ((a DIVIDED BY b) MODULO 1) IS ACTUALLY 0 SHOCKING DEVELOPMENT 0 LIES! SHOCKING DEVELOPMENT x OF a, b MINUS 1 END OF STORY END OF STORY EXPERTS CLAIM y TO BE LATEST NEWS ON "" YOU WON'T WANT TO MISS x OF y, y MINUS 1 PLEASE LIKE AND SUBSCRIBE ### Readable version DISCOVER HOW TO x WITH a, b RUMOR HAS IT WHAT IF b SMALLER THAN 2 SHOCKING DEVELOPMENT 1 LIES! RUMOR HAS IT WHAT IF ((a DIVIDED BY b) MODULO 1) IS ACTUALLY 0 SHOCKING DEVELOPMENT 0 LIES! SHOCKING DEVELOPMENT x OF a, b MINUS 1 END OF STORY END OF STORY EXPERTS CLAIM y TO BE LATEST NEWS ON "" YOU WON'T WANT TO MISS x OF y, y MINUS 1 PLEASE LIKE AND SUBSCRIBE • Welcome to Code Golf, and nice answer! Apr 21 at 1:09 • This language should be called “BREAKING NEWS” May 13 at 13:14 # Rockstar, 119117 107 bytes Outputs -0.5 for primes and 0 for composites. listen to N let D be N let P be N-1 while P and D-2 let D be-1 let M be N/D turn M up let P be N/D-M say P Try it here (Code will need to be pasted in) listen to N :Read input string into variable N let D be N :Initialise D as N let P be N-1 :Initialise P as N-1, which will be 0 (falsey) if N=1 while P and D-2 :While P and D-2 are not zero let D be-1 : Decrement D let M be N/D : Assign N/D to variable M turn M up : Round M up let P be N/D-M : Reassign N/D-M to P :End while loop say P :Output P # Trilangle 1.3, 31 bytes <'?<#2%._zS<.>(/.,)2-.^\_/!@.)@ Reads a single integer from STDIN, and prints 1 iff it's prime. Try it on the online interpreter! ## TL;DR Keeps a running counter that starts at 2, and increments it until (input % counter) == 0. Then, it prints '1' if input == counter. ## What is Trilangle? Trilangle is a 2-D stack-based programming language. Program flow can be redirected with "mirrors" /|\_ or with branches <^7>vL. The branches can split, merge, or reflect control flow, depending on how they're used. If the IP walks off the board, it continues one row or diagonal to its left. ## Code Explanation Unfolds to this example from the README: < ' ? < # 2 % . _ z S < . > ( / . , ) 2 - . ^ \ _ / ! @ . ) @ . . . . . Equivalent to this C code: #include <stdio.h> // Get an integer from stdin. Implementation provided by the interpreter. extern int getint(void); int main() { // RED PATH int input = getint(); int counter = 2; while (input % counter) // GREEN PATH ++n; // BLUE PATH if (input == counter) // YELLOW PATH return 0; // MAGENTA PATH puts("1"); return 0; } This uses the new 2DUP instruction z to make stack management easier: it copies both the input and counter so that they may be operated on non-destructively. The older version below used a combination of j (indexed read), 2 (duplicate), and S (swap) to achieve a similar effect. ## Older answer: Trilangle 1.0, 42 41 40 bytes '2.?..<_.@j.2'2,<|>(%!.\S)S,,)S<.....@>- # Pyth, 8 bytes &>Q1!tPQ Alternative that doesn't support values less than 2: !tPQ # Perl, 35 bytes Uses regular expressions... $_=1x$_;s/^(11+?)\g1+$//;print$_>1 That's 34 bytes of code, plus one byte for the -n switch needed to fetch a line from stdin. Outputs 1 if the number is prime, or nothing otherwise # Stuck, 3 bytes iv| Prints 1 for primes and 0 for non-primes. (The definition of "truthy/falsy values" means I can't use iv, because Stuck prints False/True without knowing what those are.) # Scala, 96 bytes #!/usr/bin/env scala print(((a:Int)=>if(a==2)true;else!2.to(a-1).exists(a%_==0))(args(0).toInt)) JVM and yet not last place :D Does use some bash functionality but I'm using Scala so don't be too hard on me. • It's possible in 50 bytes. :) Sep 24, 2015 at 12:07 • @EmilLundberg That code won't run. You need a main method or use the same trick I used. Sep 24, 2015 at 15:13 • Huh, you're right that it doesn't compile as scalac prime.scala. But it does run as scala prime.scala. Sep 24, 2015 at 15:47 # K, 29 bytes (x>1)&&/x!'2_!1+_sqrt x:0$0: Got this off Rosetta Code, so marked it as community wiki. # XPath 2.0, 45 40 bytes $i>1 and empty((2 to$i -1)[$i mod .=0]) For readability, incl. non-mandatory spaces (45 bytes) $i > 1 and empty((2 to $i - 1)[$i mod . = 0]) In XPath, the only way to hand input like an integer to the processor is by passing it a parameter, in this case $i. This is hardly performant, and obvious improvement would be to use: $i > 1 and empty((2 to math:sqrt($i) cast as xs:integer)[$i mod . = 0]) But since "shortest in any given language" and not performance was the goal, I'll leave the original in. ### How it works For people new to XPath, it works as follows: 1. Create a sequence up to the current number: (2 to $i - 1) 2. Filter all that have a modulo zero (i.e., that divide properly) [$i mod . = 0] 3. Test if the resulting sequence is empty, if it non-empty, there is a divisor empty(...) 4. Also test for special-case 1: $i > 1 The query as a whole returns the string true (2, 5, 101, 5483) or false (1, 4, 5487). As a nice consequence, you can find all divisors (not prime divisors!) using an even shorter expression: (2 to$i - 1)[$i mod . = 0] will return (3, 5, 7, 15, 21, 35) for input 105. # XSLT 3.0, 209203 201 bytes <transform xmlns="http://www.w3.org/1999/XSL/Transform" xmlns:x="x" version="3.0"><function name="x:p" expand-text="1"><param name="i"/>{$i>1 and empty((2 to $i -1)[$i mod .=0])}</function></transform> Update 1: removed spaces in $i > 1, . = 0 and $i - 1. Update 2: changed expand-text="yes" in expand-text="1", which is a new XSLT 3.0 feature In expanded form, with the usual prefixes: <xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns:x="x" version="3.0"> <xsl:function name="x:p" expand-text="yes"> <xsl:param name="i"/>{ $i > 1 and empty((2 to$i - 1)[$i mod . = 0]) }</xsl:function> </xsl:stylesheet> This method uses the XSLT 3.0 feature to have a function as entry point (earlier versions did not support this). It uses the same XPath expression explained in my other post. XSLT is notoriously verbose and starts with quite a few bytes declaring namespaces etc. The function must be called with a typed value that derives from xs:integer. Most processor will consider that the default type if given an integer literal. # SWI-Prolog, 51 bytes a(X):-X>1,\+ (Y is X-1,between(2,Y,I),0=:=X mod I). This uses predicate between/3 which is not an ISO-Prolog predicate. • You can save 6 bytes by shifting the range of I up by 1 (thus removing the necessity for Y) and using I-1 in the mod. TIO link Dec 20, 2017 at 20:42 • You can save another 2 bytes by replacing a(X) with -X. Dec 23, 2017 at 17:33 • A bit of competition: codegolf.stackexchange.com/questions/57617/… Dec 24, 2017 at 6:30 # JavaScript, 57 Prime finding regex. alert(!/^1?$|^(11+?)\1+\$/.test(Array(prompt()+1).join(1))) • That won't work. prompt() returns a string, not a number, so for input 3, you wind up with the string 31. The whole conversion isn't needed though. The questions allows reading the input in unary. Sep 17, 2015 at 19:40 • Yeah, I was thinking of a way to fix it. Guess I never got around to actually fixing it... – RK. Sep 17, 2015 at 19:59 • Just adding + before the prompt() should work. Dec 6, 2015 at 18:49 # Python 3, 54 bytes A just for fun post that abuses the all function. y=int(input());print(all(y%p for p in range(2,y))|y>1) Explanation: Takes all the numbers from 2 to y and calculate the mod of y and that number and return false if any of those are 0. Edits: Add the 1 check (+4 bytes) Fix the check 1 logic (0 bytes) Remove the [] (Thanks FryAmTheEggman!) (-2 bytes) Remove the -1 from range (Thanks FryAmTheEggman!) (-2 bytes) • all can take a generator, so you don't need []. Also range(a,b) already returns [a, ..., b-1]. Sep 17, 2015 at 19:50 • Cool, thanks for the tip :) Sep 17, 2015 at 23:37 # Python 2, 45 bytes Not the smallest entry, but I took a slightly different approach to detecting the prime numbers. Maybe it inspires someone to create an even smaller version. I couldn't discover any more savings myself. i=a=n=input() while i>2:i-=1;a*=n%i print a>1 ## Scala, 50 bytes val i=readInt print(i>1&&(2 to i-1 forall(i%_>0))) In case output to STDERR is forbidden, 65 bytes: val i=scala.io.StdIn.readInt print(i>1&&(2 to i-1 forall(i%_>0))) # Desmos, 108104 94 bytes k=2 1\left\{\sum _{n=2}^k\operatorname{sign}\left(\operatorname{mod}\left(k,n\right)\right)+2=k,0\right\} To use, enter a new line. Then, call p\left(n\rgiht). The output will be bottom right on that line. Edit 1: Shaved {x-1} to x. Edit 2: Changed input format to a more STDIN-esque model. • I'm not sure how Desmos works or is scored, but \left\{2=\sum _{n=1}^x\left\{0=\operatorname{mod}\left(x,n\right),0\right\},0\right\} at... possibly 101 bytes? Sep 29, 2015 at 4:31 • 1. The link gives me timeouts. If I change the protocol to HTTP, it works. 2. The question doesn't allow submitting functions. The closest to user input I could find is putting k=1 in one field and \left\{\sum _{n=2}^k\operatorname{sign}\left(\operatorname{mod}\left(k,n\right)\right)+2=k,0\right\} in the next. Sep 29, 2015 at 6:58 • Just got a-1\prod_{n=2}^{a-1} mod(a,n), 29 bytes. Returns >0 for primes, 0 for non-primes. Note that the old solution could be golfed at least down to \left\{\sum_{n=2}^k sign(mod(k,n))+2=k,0\right\}, 48 bytes. Aug 23, 2020 at 5:15 • @EthanChapman I think you meant to place parentheses around a-1, so it would be 31 bytes. Also, it can actually be further brought down to 26 bytes: (a-1)∏_{n=3}^amod(a,n-1). Feb 23, 2022 at 2:32 # Simplex v.0.5, 23 bytes Can probably be golfed. It's really the square root declaration that hurts. *regrets removing p (prime checking) command from syntax and sighs* i*R1UEY{&%n?[j1=o#]R@M} i ~~ takes numeric input * ~~ copies and increments pointer R1UEY ~~ takes the square root and rounds it down { } ~~ repeats until zero cell met at end & ~~ read and store the value to the register % ~~ takes input mod current, move pointer left n ~~ logically negates current (0 -> 1, 1 -> 0) ?[ ] ~~ evaluates inside if the current cell j1= ~~ inserts a new cell to check for a 1 case o# ~~ outputs the result and terminates program R@ ~~ goes right, pulls the value from the register M ~~ decrement value
9,307
32,227
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.53125
3
CC-MAIN-2023-23
latest
en
0.894125
https://community.smartsheet.com/discussion/77205/help-with-sum-sumif-s
1,723,022,691,000,000,000
text/html
crawl-data/CC-MAIN-2024-33/segments/1722640690787.34/warc/CC-MAIN-20240807080717-20240807110717-00779.warc.gz
141,028,017
106,417
Help with SUM, SUMIF(S) Options Good Morning! I'm needing help coming up with the right formula. Here's my data: The formula I'm currently using under [Total Breakfasts] is =Sum([Meals-Walk Up]@row,[Meals-Curbside]@row). I want to add a portion to this formula that Breakfasts served on [Day] Thursday are doubled. I know this would probably include a SUMIF formula but I'm not quite sure how to put these to formulas together. The [Total Breakfast] column should be 4@row1, 16@row2 (because they're double on Thursdays) and 4@row3. Maybe this should be a SUMIFS Formula? Thank you so much for your help! • ✭✭✭✭✭✭ Options Hi Autumn, Try this: =if(day@row="Thursday",2*(Sum([Meals-Walk Up]@row,[Meals-Curbside]@row)),Sum([Meals-Walk Up]@row,[Meals-Curbside]@row)) This translates to if the day is listed as Thursday, double the sum of (walk up + curbside). If not, show the sum of (walk up + curbside). Let me know if it works for you! Best, Heather • ✭✭✭✭✭✭ Options Hi Autumn, Try this: =if(day@row="Thursday",2*(Sum([Meals-Walk Up]@row,[Meals-Curbside]@row)),Sum([Meals-Walk Up]@row,[Meals-Curbside]@row)) This translates to if the day is listed as Thursday, double the sum of (walk up + curbside). If not, show the sum of (walk up + curbside). Let me know if it works for you! Best, Heather • Options This is amazing. It worked perfectly! Thank you so much! • ✭✭✭✭✭✭ Options Glad it worked. Happy to help! Help Article Resources Want to practice working with formulas directly in Smartsheet? Check out the Formula Handbook template!
478
1,561
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.375
3
CC-MAIN-2024-33
latest
en
0.818877
https://myprogrammingschool.com/how-to-do-sum-or-addition-in-python/
1,716,245,471,000,000,000
text/html
crawl-data/CC-MAIN-2024-22/segments/1715971058313.71/warc/CC-MAIN-20240520204005-20240520234005-00528.warc.gz
367,554,656
38,475
# How to do Addition in python Contents ## How do you add two numbers in Python? you can do addition in a different way like directly by adding to two or more numbers. you can also take user input value. if you take user input value then you have to do type conversion because by default it takes a string value. Another way is by using a loop method. Example: c = a + b ### Add value in a single line In this, we do not have to do more just use the print function and add the value. print("Total sum is: ",4+5) print("Total sum is: ",4.345+5.3422) #### Output: C:\Users\Pramod\PycharmProjects\pythonProject\venv\Scripts\python.exe C:/Users/Pramod/PycharmProjects/pythonProject/main.py Total sum is: 9 Total sum is: 9.6872 Process finished with exit code 0 ### Program to add two constant number In this program, we can take two variables and assign a value on them and perform addition. a=5 b=10 print("Total sum of a and b is:",a+b) a=5.234 b=10.432 print("Total sum of a and b is:",a+b) #### Output: C:\Users\Pramod\PycharmProjects\pythonProject\venv\Scripts\python.exe C:/Users/Pramod/PycharmProjects/pythonProject/main.py Total sum of a and b is: 15 Total sum of a and b is: 15.666 Process finished with exit code 0 ### Addition of two user input Number x=input("enter value of x:") x=int(x) # Type connversion y=input("enter value of y:") y=int(y) # Type connversion z=x+y # Adding X and Y print("sum of x and y is:",z)# Result of Sum #### Output: C:\Users\Pramod\PycharmProjects\pythonProject\venv\Scripts\python.exe C:/Users/Pramod/PycharmProjects/pythonProject/main.py enter value of x:4 enter value of y:7 sum of x and y is: 11 Process finished with exit code 0 ### Addition of Number using while loop num=int(input("enter number:")) # Here type conversing and taking input from user total=0 i=1 while i <= num: total+=i i+=1 print("total sum is:",total) #### Output: C:\Users\Pramod\PycharmProjects\pythonProject\venv\Scripts\python.exe C:/Users/Pramod/PycharmProjects/pythonProject/main.py enter number:5 total sum is: 15 Process finished with exit code 0 ### Addition of Number using for loop n = int(input("Enter number")) sum = 0 # loop from 1 to n for num in range(1, n + 1, 1): sum = sum + num print("Sum of first ", n, "numbers is: ", sum) avg = sum / n print("Average of ", n, "numbers is: ", avg) #### Output: C:\Users\Pramod\PycharmProjects\pythonProject\venv\Scripts\python.exe C:/Users/Pramod/PycharmProjects/pythonProject/main.py Enter number5 Sum of first 5 numbers is: 15 Average of 5 numbers is: 3.0 Process finished with exit code 0
759
2,590
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.953125
3
CC-MAIN-2024-22
latest
en
0.688543
https://metanumbers.com/1533518
1,642,380,328,000,000,000
text/html
crawl-data/CC-MAIN-2022-05/segments/1642320300253.51/warc/CC-MAIN-20220117000754-20220117030754-00529.warc.gz
453,636,587
7,426
# 1533518 (number) 1,533,518 (one million five hundred thirty-three thousand five hundred eighteen) is an even seven-digits composite number following 1533517 and preceding 1533519. In scientific notation, it is written as 1.533518 × 106. The sum of its digits is 26. It has a total of 3 prime factors and 8 positive divisors. There are 657,216 positive integers (up to 1533518) that are relatively prime to 1533518. ## Basic properties • Is Prime? No • Number parity Even • Number length 7 • Sum of Digits 26 • Digital Root 8 ## Name Short name 1 million 533 thousand 518 one million five hundred thirty-three thousand five hundred eighteen ## Notation Scientific notation 1.533518 × 106 1.533518 × 106 ## Prime Factorization of 1533518 Prime Factorization 2 × 7 × 109537 Composite number Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 1533518 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0 The prime factorization of 1,533,518 is 2 × 7 × 109537. Since it has a total of 3 prime factors, 1,533,518 is a composite number. ## Divisors of 1533518 8 divisors Even divisors 4 4 2 2 Total Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 2.62891e+06 Sum of all the positive divisors of n s(n) 1.09539e+06 Sum of the proper positive divisors of n A(n) 328614 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 1238.35 Returns the nth root of the product of n divisors H(n) 4.66662 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors The number 1,533,518 can be divided by 8 positive divisors (out of which 4 are even, and 4 are odd). The sum of these divisors (counting 1,533,518) is 2,628,912, the average is 328,614. ## Other Arithmetic Functions (n = 1533518) 1 φ(n) n Euler Totient Carmichael Lambda Prime Pi φ(n) 657216 Total number of positive integers not greater than n that are coprime to n λ(n) 109536 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 116241 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares There are 657,216 positive integers (less than 1,533,518) that are coprime with 1,533,518. And there are approximately 116,241 prime numbers less than or equal to 1,533,518. ## Divisibility of 1533518 m n mod m 2 3 4 5 6 7 8 9 0 2 2 3 2 0 6 8 The number 1,533,518 is divisible by 2 and 7. • Arithmetic • Deficient • Polite • Square Free • Sphenic ## Base conversion (1533518) Base System Value 2 Binary 101110110011001001110 3 Ternary 2212220120222 4 Quaternary 11312121032 5 Quinary 343033033 6 Senary 52511342 8 Octal 5663116 10 Decimal 1533518 12 Duodecimal 61b552 20 Vigesimal 9bdfi 36 Base36 wv9q ## Basic calculations (n = 1533518) ### Multiplication n×y n×2 3067036 4600554 6134072 7667590 ### Division n÷y n÷2 766759 511173 383380 306704 ### Exponentiation ny n2 2351677456324 3606339709467067832 5530386858582518927592976 8480947794599747260804525369568 ### Nth Root y√n 2√n 1238.35 115.318 35.1902 17.2639 ## 1533518 as geometric shapes ### Circle Diameter 3.06704e+06 9.63538e+06 7.38801e+12 ### Sphere Volume 1.51062e+19 2.95521e+13 9.63538e+06 ### Square Length = n Perimeter 6.13407e+06 2.35168e+12 2.16872e+06 ### Cube Length = n Surface area 1.41101e+13 3.60634e+18 2.65613e+06 ### Equilateral Triangle Length = n Perimeter 4.60055e+06 1.01831e+12 1.32807e+06 ### Triangular Pyramid Length = n Surface area 4.07322e+12 4.25011e+17 1.25211e+06 ## Cryptographic Hash Functions md5 8221d5211918607b046d32e5b4cc92ac 07c098a11b95c335870fab796c5bdf5753fa8ff8 46240892e71e3d18f424449bf1bd2ea69301272d84d186348355360bc1cd3171 57b2118309919654038a40ac548e6922bcedc6eeb034d5bc15b0ec3d82db0dda5f1eafce3955bfaca87bf6b9570000cd7338cf443bb76ff73400f3ab4e3c400d 0ac42906828291a958690e21a7fb74d6999d915a
1,529
4,312
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.4375
3
CC-MAIN-2022-05
latest
en
0.807795
https://davekilian.com/unreasonable-math.html
1,695,758,186,000,000,000
text/html
crawl-data/CC-MAIN-2023-40/segments/1695233510219.5/warc/CC-MAIN-20230926175325-20230926205325-00207.warc.gz
212,525,382
3,046
# The Unreasonable Effectiveness of Mathematics July 2014 ## Brain Dump Why does math appear so often when we talk about natural phenomenon? What is math? We have a set of fundamental laws / axioms which we hold to be true. We build proofs out of those fundamental axioms to get higher-level axioms we also hold true. Does this sound like subroutines? Maybe it should. Buy what about those fundamental axioms? Aren’t they just observations about our universe? What makes them correct? Also, how can this be the case of math is considered pure? The answer is that we’re thinking backwards. Math isn’t an observation of natural phenomena; rather, certain natural phenomena can be mapped to mathematics. When we see a system (or, to be precise, a model thereof) conforms to the fundamental axioms, then we cam go into the realm of math to draw.conclusions about that system. So what makes math so unreasonably effective? • The axioms are few, making it easy to conform systems to those xioms • There is a huge library of mathematical.knowledge we.have ready built up over the centuries And as a result, we find it’s easy to map math to things and draw useful conclusions about things. Math isn’t really about numbers. As you get more and more advance, this becomes more and more apparent. It’s really about drawing conclusions from fundamental.premeses – its logic. It’s basically the standard library for logic, with extended support for numeric logic. But if you can get your job done with numbers, math can be an unreasonably effective tool.
333
1,552
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.671875
3
CC-MAIN-2023-40
latest
en
0.927309
https://en.wikipedia.org/wiki/Declination?rdfrom=https%3A%2F%2Fwww.lashtal.com%2Fw%2Findex.php%3Ftitle%3DDeclination%26redirect%3Dno
1,642,829,599,000,000,000
text/html
crawl-data/CC-MAIN-2022-05/segments/1642320303747.41/warc/CC-MAIN-20220122043216-20220122073216-00476.warc.gz
283,836,012
23,535
# Declination In astronomy, declination (abbreviated dec; symbol δ) is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the celestial equator, along the hour circle passing through the point in question.[1] Right ascension and declination as seen on the inside of the celestial sphere. The primary direction of the system is the vernal equinox, the ascending node of the ecliptic (red) on the celestial equator (blue). Declination is measured northward or southward from the celestial equator, along the hour circle passing through the point in question. The root of the word declination (Latin, declinatio) means "a bending away" or "a bending down". It comes from the same root as the words incline ("bend toward") and recline ("bend backward").[2] In some 18th and 19th century astronomical texts, declination is given as North Pole Distance (N.P.D.), which is equivalent to 90 – (declination). For instance an object marked as declination −5 would have an N.P.D. of 95, and a declination of −90 (the south celestial pole) would have an N.P.D. of 180. ## Explanation Declination in astronomy is comparable to geographic latitude, projected onto the celestial sphere, and hour angle is likewise comparable to longitude.[3] Points north of the celestial equator have positive declinations, while those south have negative declinations. Any units of angular measure can be used for declination, but it is customarily measured in the degrees (°), minutes (′), and seconds (″) of sexagesimal measure, with 90° equivalent to a quarter circle. Declinations with magnitudes greater than 90° do not occur, because the poles are the northernmost and southernmost points of the celestial sphere. An object at the The sign is customarily included whether positive or negative. ## Effects of precession Right ascension (blue) and declination (green) as seen from outside the celestial sphere. The Earth's axis rotates slowly westward about the poles of the ecliptic, completing one circuit in about 26,000 years. This effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates (including declination) are inherently relative to the year of their observation, and astronomers specify them with reference to a particular year, known as an epoch. Coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch.[4] The currently used standard epoch is J2000.0, which is January 1, 2000 at 12:00 TT. The prefix "J" indicates that it is a Julian epoch. Prior to J2000.0, astronomers used the successive Besselian Epochs B1875.0, B1900.0, and B1950.0.[5] ## Stars A star's direction remains nearly fixed due to its vast distance, but its right ascension and declination do change gradually due to precession of the equinoxes and proper motion, and cyclically due to annual parallax. The declinations of Solar System objects change very rapidly compared to those of stars, due to orbital motion and close proximity. As seen from locations in the Earth's Northern Hemisphere, celestial objects with declinations greater than 90° − φ (where φ = observer's latitude) appear to circle daily around the celestial pole without dipping below the horizon, and are therefore called circumpolar stars. This similarly occurs in the Southern Hemisphere for objects with declinations less (i.e. more negative) than −90° − φ (where φ is always a negative number for southern latitudes). An extreme example is the pole star which has a declination near to +90°, so is circumpolar as seen from anywhere in the Northern Hemisphere except very close to the equator. Circumpolar stars never dip below the horizon. Conversely, there are other stars that never rise above the horizon, as seen from any given point on the Earth's surface (except extremely close to the equator. Upon flat terrain, the distance has to be within approximately 2 km, although this varies based upon the observer's altitude and surrounding terrain). Generally, if a star whose declination is δ is circumpolar for some observer (where δ is either positive or negative), then a star whose declination is −δ never rises above the horizon, as seen by the same observer. (This neglects the effect of atmospheric refraction.) Likewise, if a star is circumpolar for an observer at latitude φ, then it never rises above the horizon as seen by an observer at latitude −φ. Neglecting atmospheric refraction, for an observer in the equator, declination is always 0° at east and west points of the horizon. At the north point, it is 90° − |φ|, and at the south point, −90° + |φ|. From the poles, declination is uniform around the entire horizon, approximately 0°. Observer's latitude (°) Declination of circumpolar stars (°) of non-circumpolar stars (°) of stars not visible (°) + for north latitude, − for south − for north latitude, + for south 90 (Pole) 90 to 0 N/A 0 to 90 66.5 (Arctic/Antarctic Circle) 90 to 23.5 +23.5 to −23.5 23.5 to 90 45 (midpoint) 90 to 45 +45 to −45 45 to 90 23.5 (Tropic of Cancer/Capricorn) 90 to 66.5 +66.5 to −66.5 66.5 to 90 0 (Equator) N/A +90 to −90 N/A Non-circumpolar stars are visible only during certain days or seasons of the year. The night sky, divided into two halves. Declination (blue) begins at the equator (green) and is positive northward (towards the top), negative southward (towards the bottom). The lines of declination (blue) divide the sky into small circles, here 15° apart. ## Sun The Sun's declination varies with the seasons. As seen from arctic or antarctic latitudes, the Sun is circumpolar near the local summer solstice, leading to the phenomenon of it being above the horizon at midnight, which is called midnight sun. Likewise, near the local winter solstice, the Sun remains below the horizon all day, which is called polar night. ## Relation to latitude When an object is directly overhead its declination is almost always within 0.01 degrees of the observer's latitude; it would be exactly equal except for two complications.[6][7] The first complication applies to all celestial objects: the object's declination equals the observer's astronomical latitude, but the term "latitude" ordinarily means geodetic latitude, which is the latitude on maps and GPS devices. In the continental United States and surrounding area, the difference (the vertical deflection) is typically a few arcseconds (1 arcsecond = 1/3600 of a degree) but can be as great as 41 arcseconds.[8] The second complication is that, assuming no deflection of the vertical, "overhead" means perpendicular to the ellipsoid at observer's location, but the perpendicular line does not pass through the center of the earth; almanacs provide declinations measured at the center of the Earth. (An ellipsoid is an approximation to sea level that is mathematically manageable).[9]
1,648
7,046
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.90625
3
CC-MAIN-2022-05
latest
en
0.923006
http://gmatclub.com/forum/a-watch-which-gians-uniformly-is-5-minutes-slow-at-8-00-am-8948.html
1,430,797,496,000,000,000
text/html
crawl-data/CC-MAIN-2015-18/segments/1430455222810.45/warc/CC-MAIN-20150501044022-00089-ip-10-235-10-82.ec2.internal.warc.gz
91,878,932
42,011
Find all School-related info fast with the new School-Specific MBA Forum It is currently 04 May 2015, 19:44 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # A watch which gians uniformly is 5 minutes slow at 8:00 am Author Message TAGS: Manager Joined: 28 Jun 2004 Posts: 90 Followers: 1 Kudos [?]: 4 [0], given: 0 A watch which gians uniformly is 5 minutes slow at 8:00 am [#permalink]  18 Aug 2004, 15:26 A watch which gians uniformly is 5 minutes slow at 8:00 am on Sunday and is 5 min 48 seconds fast at 8:00 pm on the following Sunday. When did it show the correct time? GMAT Club Legend Joined: 07 Jul 2004 Posts: 5078 Location: Singapore Followers: 22 Kudos [?]: 184 [0], given: 0 in 12 hours, it gained 10mins48seconds = 648 seconds so each hour, it gains 54 seconds = 9/10 of a minute So at 8am it is 300 seconds slower 9am, it will be 246seconds slower 10am, 192 seconds slower... etc. It will show the correct time when this difference reduces to 0. For that to happens, it need to be 300/54 = 5 5/9 hours later. Which is about 1:30pm CIO Joined: 09 Mar 2003 Posts: 464 Followers: 2 Kudos [?]: 34 [0], given: 0 The clock gains 10 min 48 sec by 8 pm the FOLLOWING Sunday. That's 180 hours, or 10,800 minutes. That works out perfectly, since 10 min 48 sec is really 10.8 min, so when we divide, we see that the clock gets faster by 1 minute every 1000 minutes. Since it starts out 5 minutes slow, it'll be right on when it's gained 5 minutes, which is 1000x5=5000 minutes later. 5000 minutes is 3 days, 11 hours, and 20 minutes, which is Wed at 7:20PM. Similar topics Replies Last post Similar Topics: 2 On Monday Elton arrived at the recording studio at 8:00 am 9 29 Jul 2012, 13:19 Breaks: 5, 7, 8 or 10 minutes? 4 28 May 2010, 23:40 1 8:00 AM GMAT Time 9 03 Jul 2009, 08:00 3 Between 3:00 am. and 3:00 p.m. of the same day, the minute 2 30 May 2008, 09:28 Just got 5days 8hours 5minutes and 20seconds 0 27 Aug 2007, 11:28 Display posts from previous: Sort by
789
2,501
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.9375
4
CC-MAIN-2015-18
longest
en
0.905733
https://rvmiller.com/tag/c/
1,632,878,144,000,000,000
text/html
crawl-data/CC-MAIN-2021-39/segments/1631780061350.42/warc/CC-MAIN-20210929004757-20210929034757-00320.warc.gz
548,838,439
13,680
# Wind Turbine Analysis For our final project for CS 59000: Embedded Systems, a partner and I implemented several tests on a small-scale wind turbine using the Texas Instruments MSP430 board. We use the Analog to Digital Converter (ADC) to gather information on voltage generated by the turbine and rotations per minute calculated with the help of an optical tachometer. We then send these values to a Java-based user interface to report in real-time on an attached computer. For the final part of our project, we designed a wind turbine stand on springs that we can use, along with the MSP430, to measure accelerometer data from the wind turbine under stress. We also send the real-time data to the user interface on an attached computer. ### Findings #### Power Coefficient (Cp) We measured the following characteristics of the wind turbine at LOW fan speed: • AT = 0.134614 m2 • V3 = (2.101 m/sec)3 = 9.275 • ρ = 1.2041 kg/m3 at 20°C (from Wikipedia) The average voltage reported by our program at LOW fan speed was 2.304 volts. Resistance was set at 330 Ω. Using these values, we found the power coefficient, Cp, to be: Cp = 0.00929 or 0.01 #### Tip-Speed Ratio This part of the project required the use of the optical tachometer connected to the MSP430 board. The tachometer will output a high value when no blade blocks the beam, and a low value (close to zero) when a blade is in front. We read this information and convert the rate at which blades are passing in the beam to compute a rotations per minute (RPM) value. The average RPM we measured at a given time was: 55 RPM We measured the radius of a blade, and found R = 20.7 cm or 0.207 meters. At LOW fan speed, the velocity of wind was recorded as V = 2.101 m/sec * 60 s= 126.06 m/min. Using these values, we found the Tip-Speed Ratio to be: λ = .567 rotations #### Accelerometer Data We constructed a special stand for the wind turbine that allows the turbine and MSP board to move in unison, while still being flexible to allow natural movement due to the wind. For this part of the project, we modified the provided Java program to also display accelerometer data in the X- and Y-axes. We track and record this data in real-time, which gives some insight into how the wind turbine is moving as the speed and direction of wind changes. Although we are not able to give a unit for these values, the magnitude of change can indicate what is happening in the physical system. For instance, when we see X values change from near-zero to negative, we know that stress is being placed in the wind turbine in the negative X direction (see diagram below — blue values represent negative readings). # Arduino Web Server Winter break means plenty of time to toy around with something new. I’m not sure what inspired this project, perhaps the ethernet driver we designed for our Operating Systems course, but I’ve decided to explore the field of embedded networking. And you can’t get much more embedded than a 16 MHz Arduino Uno with 32K of memory. ### Goals I want to create an Arduino-based web server, but with a few twists, because the idea already exists and has been implemented. The first link points to Lady Ada’s quick and dirty Arduino file server, which can serve up character-based files stored on micro SD. The second link offers a more functional server called Webduino, which claims to offer image support (ie. binary transfers). However, reading through the code, it looks like the developer took the easy way out by re-encoding a PNG as hex values, and then sending those values byte-by-byte over the network. That’s not image support! Also, both implementations seem to suffer from the limitation that only one client can connect at a time. Because the Arduino has no formal notion of threads, it would make sense that multiple clients just won’t work. But I’ve been reading up on a project called Protothreads, which adds the most basic threading you can imagine. No separate stacks. No pre-emptive scheduling. Just a way to give the appearance that two computations are concurrent. I’m hoping that I can use protothreading to allow multiple clients to connect. Additionally, it would be nice to find a way to do binary transfers. Glancing at the EthernetClient and EthernetServer API, it looks like they’re both set up for byte transfers. I wonder if there’s a way I can trick it into sending binary information. We’ll see. ### Update – 26 January 2012: I found an easy way (untested) to get the Arduino to send non-text content over the EthernetClient interface. When a client requests a file of a certain type, say, PNG, you can send a response indicating that you will be sending PNG binary data byte by byte as follows: ```client.println("HTTP/1.1 200 OK"); client.println("Content-Type: image/png");``` I hope to test this technique soon. Admittedly, I still have a long way to go on this project, but other projects (iPhone app, stay tuned) keep arising. # Arduino-controlled Robotic Arm with Android Interface Continuing my trend of Arduino projects, I decided to toy around with this robotic arm I got for Christmas. The arm is not the best construction, using DC motors instead of servos, but with Adafruit’s motor/stepper/servo shield kit, I think I can make it somewhat more useful. First to go is the flimsy plastic controller. The motor shield allows up to four of the of five motor joints to be controlled with the Arduino. I want to use this opportunity to explore the Java serial libraries to communicate with the Arduino over the Internet in a Java applet *or* purchase an Arduino ethernet shield and send commands directly to the device (see below) https://billigastemobilabonnemang.nu/. I suppose, as an overall goal, I would like to be able to feed my fish while away with the use of a webcam and this robotic arm. ### Completed Robotic Arm connection to motor This setup allows control of the maximum of four motors.  I’d rather have everything integrated into one cable, but the supplied cable didn’t have enough pins to handle 4 motors and power and ground.  That’s why I added the red/black leads shown above v.  Here’s how everything looks hooked up to the freshly soldered motor shield: Right now the Arduino is powered by USB, and the motors are powered by the arm’s original DC power source — 4 D batteries. This can easily be changed to have the arm run off of a DC adapter. Next up: Due to the number of pins that the motor shield requires, I won’t be able to use an ethernet shield with this project. So, Java-based serial communication it is! ### Update 4/16/11 I wrote a Java application with SWT to handle the serial communication with the Arduino’s motor controller. Essentially, it relays messages over the serial line about what motor to enable. The “speed” of the motor is an illusion by using a custom TimerTask to repeatedly send requests to enable the motor (every 10ms) and then sleep the thread for a duration between each task interval, until the button is no longer pressed. This solution makes the robotic arm much more useful as it can now make very controlled movements (<1mm). Here is a screen shot of the user interface: ### Update 9/7/12 I’ve started working on this project again! I decided to clean up some of the code and create an Android app that can control the arm wirelessly (as long as it’s connected to a host PC). # Arduino OBD-II Interface For my CS 497 Spring 2011 course, I worked on an independent study project creating an Arduino-based OBD-II (vehicle onboard diagnostic) interface written in C. First, I assembled an interface between an Arduino Uno and the ISO9141 bus that most vehicles prior to 2008 use. An open-source project called OBDuino describes how to assemble such an interface, available here. Second, I wrote software for the Arduino to poll information from the vehicle’s engine control unit (ECU), such as instantaneous information like RPM and vehicle speed, and also diagnostic feedback, and display it in real time on an attached LCD screen. Third, I added an Arduino data-logging shield to allow the capturing of long-term data from a vehicle in a spreadsheet-ready format. ### Update – 3/27/11 Since my last progress update, I have written software for the Arduino to: • Interface with my automobile’s ISO-9141 bus, and • Begin polling for parameter IDs (PIDs) Before the Arduino can begin polling data from the automobile’s ECU, it must first establish a serial connection. The initialization sequence was adapted from ISO standard 9141-2:1994, available at the Engineering library. Once started, it sends address 0x33 to the ECU at 5-baud to “bit-bang” the ECU and establish a serial connection. The Arduino then switches into normal serial communication at 10.4kbps and waits for a return address of 0x55 from the ECU followed by two keywords. The Arduino sends back the inverse of the second keyword and, upon a response of 0xCC (the inverse of 0x33) from the ECU, the Arduino displays “Init. Success!” on its LCD screen. Initialization usually takes a few seconds to complete, and the connection must be re-initialized if the ECU is not polled for data within 5 seconds. Displayed on the LCD screen above are instantaneous readings from the four PIDs currently polled by the Arduino. Clockwise from the top-left corner, these include: • Engine RPM • Vehicle speed • Mass airflow (MAF) sensor, which can be used to calculate instantaneous MPG • Engine coolant temperature Values update every 200ms on the LCD. Polling for PIDs involves sending a byte-encoded message to the ECU requesting a value for a PID defined in the SAE J1979 standard. The ECU then responds with a byte-encoded value that the Arduino can decode and extract information from to display on screen. Currently, the system only polls for these four PIDs, but will be expanded to poll for several more. In addition to adding more PIDs to poll, I will mainly be focusing on implementing a data logger shield to hold data captured by the Arduino and display in spreadsheet form on a computer. The data logger shield sits on top of the Arduino unit, and uses pins not used by the LCD or serial communication. The shield also contains a real-time clock to add a timestamp next to data read from the ECU. Data is stored on a 2GB SD card. The ability to log large amounts of data from a vehicle demonstrates the usefulness for this system to offer diagnostic capabilities with a high degree of precision and temporal resolution. Implementing and programming this data logger shield, as well as graphically displaying spreadsheet data, should consume the remainder of the time allotted for myproject. ### Update – 4/12/11 I’ve added the data logging shield and a way to compute MPG from the MAF (mass air flow) and VSS (vehicle speed sensor) PIDs. `MPG = VSS * ( 1 / (MAF * .0889))` Here are some Excel graphs plotted from data over a 20 minute period (844 data points). Click for larger graphs. # Webcrawler and Search Engine We first designed a webcrawler in C++ using a provided HTTP interface to “crawl” a list of initial URLs to a maximum depth. Along with archiving URLs, the crawler stored the textual words on a webpage for searching purposes and a 100-word description of every page. Next, we designed a search engine that preprocessed the results of the webcrawler to store data in one of three data structures: • Array • Hash Table • AVL Dictionary • Binary Search Dictionary We used an HTTP server provided to format HTML pages to display results of queries, as well as display search times to compare the different data structures’ efficiency. We called the search engine Boogle, as a combination of “Boilermaker” (Purdue Boilermakers) and Google.
2,607
11,754
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.28125
3
CC-MAIN-2021-39
latest
en
0.893211
https://questions.examside.com/past-years/year-wise/jee/jee-advanced/iit-jee-2001/kOtVR9PuMFGAWTp4
1,708,495,356,000,000,000
text/html
crawl-data/CC-MAIN-2024-10/segments/1707947473370.18/warc/CC-MAIN-20240221034447-20240221064447-00119.warc.gz
495,431,342
24,024
1 IIT-JEE 2001 Subjective +10 -0 The vapour pressure of the two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a flask 10 moles of (A) is mixed with 12 moles of (B). However, as soon as (B) is added, (A) starts polymerizing into a completely insoluble solid. The polymerization follows first-order kinetics. After 100 minutes, 0.525 mole of a solute is dissolved which arrests the polymerization completely. The final vapour pressure of the solution is 400 mm of Hg. Estimate the rate of constant of the polymerization reaction. Assume negligible volume change on mixing and polymerization and ideal behaviour for the final solution. 2 IIT-JEE 2001 Subjective +4 -0 Let $$a,\,b,\,c$$ be real numbers with $$a \ne 0$$ and let $$\alpha ,\,\beta$$ be the roots of the equation $$a{x^2} + bx + c = 0$$. Express the roots of $${a^3}{x^2} + abcx + {c^3} = 0$$ in terms of $$\alpha ,\,\beta \,$$. 3 IIT-JEE 2001 Subjective +5 -0 Let $${a_1}$$, $${a_2}$$,.....,$${a_n}$$ be positive real numbers in geometric progression. For each n, let $${A_n}$$, $${G_n}$$, $${H_n}$$ be respectively, the arithmetic mean , geometric mean, and harmonic mean of $${a_1}$$,$${a_2}$$......,$${a_n}$$. Find an expression for the geometric mean of $${G_1}$$,$${G_2}$$,.....,$${G_n}$$ in terms of $${A_1}$$,$${A_2}$$,.....,$${A_n}$$,$${H_n}$$,$${H_1}$$,$${H_2}$$,........,$${H_n}$$. 4 IIT-JEE 2001 Subjective +6 -0 Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that the equation $$\left| {\matrix{ {ax - by - c} & {bx + ay} & {cx + a} \cr {bx + ay} & { - ax + by - c} & {cy + b} \cr {cx + a} & {cy + b} & { - ax - by + c} \cr } } \right| = 0$$ represents a straight line. EXAM MAP Medical NEET
631
1,717
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.046875
3
CC-MAIN-2024-10
latest
en
0.748548
http://www.physicsforums.com/showthread.php?t=220848
1,409,632,308,000,000,000
text/html
crawl-data/CC-MAIN-2014-35/segments/1409535921550.2/warc/CC-MAIN-20140901014521-00440-ip-10-180-136-8.ec2.internal.warc.gz
1,380,625,669
9,217
# Wire sag formula by williamlynn Tags: formula, wire P: 4 I am looking for a formula to calculate the deflection(sag) in steel wire that is supported between two points with a known tension. I want to be able to calculate the deflection(sag) at any point along the wire. HW Helper PF Gold P: 6,041 Quote by williamlynn I am looking for a formula to calculate the deflection(sag) in steel wire that is supported between two points with a known tension. I want to be able to calculate the deflection(sag) at any point along the wire. Well it depends upon a lot of stuff, like the properties and temperature of the wire, and the span/sag ratio. The wire will take the shape of the catenary (hyperbolic functions, kind of tough to calculate manually), however, if the sag is relatively small in comparison to the span (say the sag is less than about 10 percent of the span), then the catenary curve is very closely approximated by a parbolic curve using the following equation: $$T=wl^2/(8d)$$, where w is the weight of the wire per unit length, l is the horizontal span between supports, d is the sag, and T is the horizontal tension in the cable. So, given T, l, and w, you can easily calculate d (the sag at the low point of the curve). If it is less than 10% or so of l, you plot the parabolic curve, and can then get sags at various points using the parabolic properties of that curve. Temperature and live loadis will affect sag/tension values, but if you're just looking at one tension at a given temperature under the wire dead load weight only, you need not go further. P: 4 Thanks for quick response; I really need to be able to find deflection along any point in the wire. I'm lloking at .016" dia wire with spans from 10 feet to 100 feet and wire tension of 30 pounds. HW Helper PF Gold P: 6,041 Wire sag formula Quote by williamlynn Thanks for quick response; I really need to be able to find deflection along any point in the wire. I'm lloking at .016" dia wire with spans from 10 feet to 100 feet and wire tension of 30 pounds. Oh, I was assuming a larger wire with higher tensions and spans. Nonetheless, the same formula applies. But first be sure you're using a very high strength steel, otherewise even your meager 30 pounds will snap it in half, because you are using such small diameter wire. Second, i'm not sure what your application is, but your sags are going to be very very small for the 10 foot span (the wire will be fiddle tight, use the formula i gave you after calculating w). Even for the 100 foot span. What are you trying to do? P: 4 The wire sag is used for turbine machinery alignment; the internal parts of the turbine must be accurately aligned to a centerline. The wire is the centerline reference but the wire sag must be accounted for to get accurate centerline. Alignment of the turbine components has to be within thousants of an inch. Sci Advisor P: 5,095 I can't say that I have ever heard of using wire as a centerline reference. That doesn't mean people don't use it though. It seems kind of "hokey." You could machine a holding feature and insert a laser pointer. That's what we use a lot. That way you can calibrate the pointer position and not have to worry about sag. HW Helper PF Gold P: 6,041 Quote by williamlynn The wire sag is used for turbine machinery alignment; the internal parts of the turbine must be accurately aligned to a centerline. The wire is the centerline reference but the wire sag must be accounted for to get accurate centerline. Alignment of the turbine components has to be within thousants of an inch. Yow, that's a close tolerance. Let me give you a sample calc based on the parabolic approximation, but don't use it for actual design! The 0.016 inch diameter steel wire weighs about 0.0007 pounds per foot. So for a 10 foot span between level supports, and 30 pounds tension at a given temperature, the sag at the low point (mid point of the span) is d=wl^2/8T = 0.0003 feet, or about 3/1000 of an inch. For a 100 foot span with that same tension, d = wl^2/8T = 0.03 feet (about 3/8 of an inch). Now to get the wire deflections at other points in the span, let's take the 100 foot span case, using the parabolic approximation y=ax^2 (letting the low point of the curve be at origin (0,0)), then you can solve for 'a' using the condition that y=.03 when x = 50, and get a = .03/2500 = 0.000012; so now, for the 100 foot span case, you have y = .000012x^2, which defines the shape of the curve, and where y is the value measured up from the low point. For example, at x= 0 (low point) y = 0, implying a sag of 0.03 -y = .03'; or at the 1/4 points, where x = 25, y= .0075, and the deflection at that point is .03 -y = .03 - .0075 = .0225 feet. (For the general case, this specifically is y = wx^2/(2T)) Now please, while the parabolic approximation is extremely good for long spans with appreciable wires sizes and tensions and sags, I don't know how good it is when you're talking such extremely fine tolerances. In which case you might want to use the exact catenary curve equation for level supports y=(T/w)(cosh(xw/T), and compare it to the parabolic approximation of y =wx^2/(2T). Note also that if the wire is subject to temperature variations, it's tension and sag will change (more sag , less tension, when hot; less sag, more tension, when cold.). I hope this helps, but again, use it as a guide only. Sci Advisor HW Helper P: 8,953 To do accurate surveys before GPS you used metal wires to measure distance. You support the wire along a string of tripods and apply a known tension with a spring balance, there are tables in old surveying books to calculate the sag - it's just a catenary. You also have to do this just before dawn when the temperature is stable and the wire has time to acclimatise. ps. Thank god for RTK-GPS! P: 4 Thank You Very Much; Exactly What I Was Looking For Related Discussions Introductory Physics Homework 3 Introductory Physics Homework 0 Introductory Physics Homework 1 Mechanical Engineering 16 Biology, Chemistry & Other Homework 6
1,523
6,064
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.328125
3
CC-MAIN-2014-35
latest
en
0.929878
https://www.comsol.it/models/acdc-module/page/8
1,511,429,510,000,000,000
text/html
crawl-data/CC-MAIN-2017-47/segments/1510934806768.19/warc/CC-MAIN-20171123085338-20171123105338-00488.warc.gz
771,727,526
11,716
# Galleria delle Applicazioni La Galleria delle Applicazioni raccoglie un'ampia varietà di tutorial e di app dimostrative realizzati con COMSOL Multiphysics in diversi ambiti applicativi, inclusi quelli elettrico, meccanico, fluidico e chimico. E' possibile scaricare i file dei modelli e delle app demo pronti all'uso e le istruzioni step-by-step per costruirli, e utilizzarli come punto di partenza per le proprie simulazioni. Lo strumento di Ricerca Rapida permette di trovare i modelli che si riferiscono alla propria area di interesse. Per scaricare i file .mph dei modelli è necessario effettuare il login o creare un account COMSOL Access associato a un numero di licenza valido. ### Axisymmetric approximation of 3D Inductor Inductive devices experience capacitative coupling between conductors at high frequencies. Modeling this phenomenon requires that you describe electric fields that have components both parallel with and perpendicular to the wire. This consideration might lead to the conclusion that a 3D model is always necessary to model the phenomenon, even if the coil is a helix, which is actually not the ... ### Axial Field Magnetic Gear in 3D In this model, an axial field magnetic gear with a gear ratio of 5:2 is modeled. Both the high speed and low speed rotors consist of permanent magnet and back iron. The low speed rotor consists of five pole-pairs, while the high speed rotor consists of two pole pairs, and the stationary steel consists of seven pole-pairs. The *Rotating Machinery, Magnetic* interface is used to evaluate the ... ### A Geoelectrical Forward Problem The classical forward problem of geoelectrics (includes electrical resistivity tomography, ERT and earlier techniques as vertical electric sounding, VES) is the calculation of potentials at a given set of electrodes (M,N) while current is injected at other electrodes (A,B) into the ground. Typically the physical domain (earth) is unbounded to the sides and the bottom because of which one needs ... ### Iron Sphere in a 13.56 MHz Magnetic Field An iron sphere is exposed to a spatially uniform, sinusoidally time-varying, background magnetic field. The frequency of the field is so high that the skin depth in the sphere is much smaller than the radius. At such high frequencies it is possible to model only the fields and induced currents on the surface of the sphere, thus avoiding the need for solving for the fields within the volume of ... ### Small-Signal Analysis of an Inductor If an inductor's magnetic material is nonlinear, then the inductance depends on the current passing through it. This model consists of an inductor with a nonlinear magnetic core, where the small-signal inductance is simulated as a function of current. The model also investigates how the small-signal inductance depends on the DC current. ### Magnetotellurics Magnetotellurics is a method for estimating the resistivity profile of the Earth's subsurface using the natural electromagnetic source provided by the ionosphere. This model was defined by Zhdanov et al. in a study published in 1997. In this article, various scientific groups compared software performance on the same models. This is the model called COMMEMI-3D-2, which has become one of the ... ### Electromagnetic Force Calculation Using Virtual Work and Maxwell Stress Tensor The model compare the electromagnetic force calculated by *virtual work* and *maxwell stress tensor* methods on the axial magntic bearing. The forces is evaluated by studying the effect of a small displacement on the electromagnetic energy of the system. This is done by using the *Magnetic Fields*, *Deformed Geometry* and *Sensitivity* physics interfaces. ### Capacitance Matrix of Two Spheres This model compares the numerical and analytical solutions for the capacitance matrix of two nonconcentric spheres. It also illustrates the relation between the Maxwell capacitance matrix and the mutual capacitance matrix. ### Capacitive position sensor, boundary elements This tutorial model explains how to extract lumped matrices by means of the _Stationary Source Sweep_ study. The capacitance matrix of a five-terminal system is used to infer the position of a metallic object rather like real-world capacitive position sensors. The example illustrates the use of the boundary element method (BEM), which is supported by the _Electrostatics, Boundary Elements_ ... ### Applying a Current-Voltage Switch to Models This example exemplifies how to model the switching between current and voltage excitations in *Terminal* boundary conditions. A more detailed description of the phenomenon and the modeling process can be seen in the blog post "[Control Current and Voltage Sources with the AC/DC Module](https://www.comsol.com/blogs/control-current-and-voltage-sources-with-the-acdc-module/)". 71–80 of 99
1,050
4,855
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.71875
3
CC-MAIN-2017-47
latest
en
0.572341
https://opentextbc.ca/physicstestbook2/chapter/forces-and-torques-in-muscles-and-joints/
1,558,601,927,000,000,000
text/html
crawl-data/CC-MAIN-2019-22/segments/1558232257197.14/warc/CC-MAIN-20190523083722-20190523105722-00454.warc.gz
562,002,585
37,619
Statics and Torque # Forces and Torques in Muscles and Joints OpenStaxCollege ### Learning Objectives • Explain the forces exerted by muscles. • State how a bad posture causes back strain. • Discuss the benefits of skeletal muscles attached close to joints. • Discuss various complexities in the real system of muscles, bones, and joints. Muscles, bones, and joints are some of the most interesting applications of statics. There are some surprises. Muscles, for example, exert far greater forces than we might think. [link] shows a forearm holding a book and a schematic diagram of an analogous lever system. The schematic is a good approximation for the forearm, which looks more complicated than it is, and we can get some insight into the way typical muscle systems function by analyzing it. Muscles can only contract, so they occur in pairs. In the arm, the biceps muscle is a flexor—that is, it closes the limb. The triceps muscle is an extensor that opens the limb. This configuration is typical of skeletal muscles, bones, and joints in humans and other vertebrates. Most skeletal muscles exert much larger forces within the body than the limbs apply to the outside world. The reason is clear once we realize that most muscles are attached to bones via tendons close to joints, causing these systems to have mechanical advantages much less than one. Viewing them as simple machines, the input force is much greater than the output force, as seen in [link]. (a) The figure shows the forearm of a person holding a book. The biceps exert a force to support the weight of the forearm and the book. The triceps are assumed to be relaxed. (b) Here, you can view an approximately equivalent mechanical system with the pivot at the elbow joint as seen in [link]. Muscles Exert Bigger Forces Than You Might Think Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in [link], and compare this force with the weight of the forearm plus its load. You may take the data in the figure to be accurate to three significant figures. Strategy There are four forces acting on the forearm and its load (the system of interest). The magnitude of the force of the biceps is ; that of the elbow joint is ; that of the weights of the forearm is , and its load is . Two of these are unknown ( and ), so that the first condition for equilibrium cannot by itself yield . But if we use the second condition and choose the pivot to be at the elbow, then the torque due to is zero, and the only unknown becomes . Solution The torques created by the weights are clockwise relative to the pivot, while the torque created by the biceps is counterclockwise; thus, the second condition for equilibrium becomes Note that for all forces, since for all forces. This equation can easily be solved for in terms of known quantities, yielding Entering the known values gives which yields Now, the combined weight of the arm and its load is , so that the ratio of the force exerted by the biceps to the total weight is Discussion This means that the biceps muscle is exerting a force 7.38 times the weight supported. In the above example of the biceps muscle, the angle between the forearm and upper arm is 90°. If this angle changes, the force exerted by the biceps muscle also changes. In addition, the length of the biceps muscle changes. The force the biceps muscle can exert depends upon its length; it is smaller when it is shorter than when it is stretched. Very large forces are also created in the joints. In the previous example, the downward force exerted by the humerus at the elbow joint equals 407 N, or 6.38 times the total weight supported. (The calculation of is straightforward and is left as an end-of-chapter problem.) Because muscles can contract, but not expand beyond their resting length, joints and muscles often exert forces that act in opposite directions and thus subtract. (In the above example, the upward force of the muscle minus the downward force of the joint equals the weight supported—that is, , approximately equal to the weight supported.) Forces in muscles and joints are largest when their load is a long distance from the joint, as the book is in the previous example. In racquet sports such as tennis the constant extension of the arm during game play creates large forces in this way. The mass times the lever arm of a tennis racquet is an important factor, and many players use the heaviest racquet they can handle. It is no wonder that joint deterioration and damage to the tendons in the elbow, such as “tennis elbow,” can result from repetitive motion, undue torques, and possibly poor racquet selection in such sports. Various tried techniques for holding and using a racquet or bat or stick not only increases sporting prowess but can minimize fatigue and long-term damage to the body. For example, tennis balls correctly hit at the “sweet spot” on the racquet will result in little vibration or impact force being felt in the racquet and the body—less torque as explained in Collisions of Extended Bodies in Two Dimensions. Twisting the hand to provide top spin on the ball or using an extended rigid elbow in a backhand stroke can also aggravate the tendons in the elbow. Training coaches and physical therapists use the knowledge of relationships between forces and torques in the treatment of muscles and joints. In physical therapy, an exercise routine can apply a particular force and torque which can, over a period of time, revive muscles and joints. Some exercises are designed to be carried out under water, because this requires greater forces to be exerted, further strengthening muscles. However, connecting tissues in the limbs, such as tendons and cartilage as well as joints are sometimes damaged by the large forces they carry. Often, this is due to accidents, but heavily muscled athletes, such as weightlifters, can tear muscles and connecting tissue through effort alone. The back is considerably more complicated than the arm or leg, with various muscles and joints between vertebrae, all having mechanical advantages less than 1. Back muscles must, therefore, exert very large forces, which are borne by the spinal column. Discs crushed by mere exertion are very common. The jaw is somewhat exceptional—the masseter muscles that close the jaw have a mechanical advantage greater than 1 for the back teeth, allowing us to exert very large forces with them. A cause of stress headaches is persistent clenching of teeth where the sustained large force translates into fatigue in muscles around the skull. [link] shows how bad posture causes back strain. In part (a), we see a person with good posture. Note that her upper body’s cg is directly above the pivot point in the hips, which in turn is directly above the base of support at her feet. Because of this, her upper body’s weight exerts no torque about the hips. The only force needed is a vertical force at the hips equal to the weight supported. No muscle action is required, since the bones are rigid and transmit this force from the floor. This is a position of unstable equilibrium, but only small forces are needed to bring the upper body back to vertical if it is slightly displaced. Bad posture is shown in part (b); we see that the upper body’s cg is in front of the pivot in the hips. This creates a clockwise torque around the hips that is counteracted by muscles in the lower back. These muscles must exert large forces, since they have typically small mechanical advantages. (In other words, the perpendicular lever arm for the muscles is much smaller than for the cg.) Poor posture can also cause muscle strain for people sitting at their desks using computers. Special chairs are available that allow the body’s CG to be more easily situated above the seat, to reduce back pain. Prolonged muscle action produces muscle strain. Note that the cg of the entire body is still directly above the base of support in part (b) of [link]. This is compulsory; otherwise the person would not be in equilibrium. We lean forward for the same reason when carrying a load on our backs, to the side when carrying a load in one arm, and backward when carrying a load in front of us, as seen in [link]. (a) Good posture places the upper body’s cg over the pivots in the hips, eliminating the need for muscle action to balance the body. (b) Poor posture requires exertion by the back muscles to counteract the clockwise torque produced around the pivot by the upper body’s weight. The back muscles have a small effective perpendicular lever arm, , and must therefore exert a large force . Note that the legs lean backward to keep the cg of the entire body above the base of support in the feet. You have probably been warned against lifting objects with your back. This action, even more than bad posture, can cause muscle strain and damage discs and vertebrae, since abnormally large forces are created in the back muscles and spine. People adjust their stance to maintain balance. (a) A father carrying his son piggyback leans forward to position their overall cg above the base of support at his feet. (b) A student carrying a shoulder bag leans to the side to keep the overall cg over his feet. (c) Another student carrying a load of books in her arms leans backward for the same reason. Do Not Lift with Your Back Consider the person lifting a heavy box with his back, shown in [link]. (a) Calculate the magnitude of the force in the back muscles that is needed to support the upper body plus the box and compare this with his weight. The mass of the upper body is 55.0 kg and the mass of the box is 30.0 kg. (b) Calculate the magnitude and direction of the force exerted by the vertebrae on the spine at the indicated pivot point. Again, data in the figure may be taken to be accurate to three significant figures. Strategy By now, we sense that the second condition for equilibrium is a good place to start, and inspection of the known values confirms that it can be used to solve for if the pivot is chosen to be at the hips. The torques created by and are clockwise, while that created by is counterclockwise. Solution for (a) Using the perpendicular lever arms given in the figure, the second condition for equilibrium becomes Solving for yields The ratio of the force the back muscles exert to the weight of the upper body plus its load is This force is considerably larger than it would be if the load were not present. Solution for (b) More important in terms of its damage potential is the force on the vertebrae . The first condition for equilibrium () can be used to find its magnitude and direction. Using for vertical and for horizontal, the condition for the net external forces along those axes to be zero Starting with the vertical () components, this yields Thus, yielding Similarly, for the horizontal () components, yielding The magnitude of is given by the Pythagorean theorem: The direction of is Note that the ratio of to the weight supported is Discussion This force is about 5.6 times greater than it would be if the person were standing erect. The trouble with the back is not so much that the forces are large—because similar forces are created in our hips, knees, and ankles—but that our spines are relatively weak. Proper lifting, performed with the back erect and using the legs to raise the body and load, creates much smaller forces in the back—in this case, about 5.6 times smaller. This figure shows that large forces are exerted by the back muscles and experienced in the vertebrae when a person lifts with their back, since these muscles have small effective perpendicular lever arms. The data shown here are analyzed in the preceding example, [link]. What are the benefits of having most skeletal muscles attached so close to joints? One advantage is speed because small muscle contractions can produce large movements of limbs in a short period of time. Other advantages are flexibility and agility, made possible by the large numbers of joints and the ranges over which they function. For example, it is difficult to imagine a system with biceps muscles attached at the wrist that would be capable of the broad range of movement we vertebrates possess. There are some interesting complexities in real systems of muscles, bones, and joints. For instance, the pivot point in many joints changes location as the joint is flexed, so that the perpendicular lever arms and the mechanical advantage of the system change, too. Thus the force the biceps muscle must exert to hold up a book varies as the forearm is flexed. Similar mechanisms operate in the legs, which explain, for example, why there is less leg strain when a bicycle seat is set at the proper height. The methods employed in this section give a reasonable description of real systems provided enough is known about the dimensions of the system. There are many other interesting examples of force and torque in the body—a few of these are the subject of end-of-chapter problems. # Section Summary • Statics plays an important part in understanding everyday strains in our muscles and bones. • Many lever systems in the body have a mechanical advantage of significantly less than one, as many of our muscles are attached close to joints. • Someone with good posture stands or sits in such as way that their center of gravity lies directly above the pivot point in their hips, thereby avoiding back strain and damage to disks. # Conceptual Questions Why are the forces exerted on the outside world by the limbs of our bodies usually much smaller than the forces exerted by muscles inside the body? Explain why the forces in our joints are several times larger than the forces we exert on the outside world with our limbs. Can these forces be even greater than muscle forces? Certain types of dinosaurs were bipedal (walked on two legs). What is a good reason that these creatures invariably had long tails if they had long necks? Swimmers and athletes during competition need to go through certain postures at the beginning of the race. Consider the balance of the person and why start-offs are so important for races. If the maximum force the biceps muscle can exert is 1000 N, can we pick up an object that weighs 1000 N? Explain your answer. Suppose the biceps muscle was attached through tendons to the upper arm close to the elbow and the forearm near the wrist. What would be the advantages and disadvantages of this type of construction for the motion of the arm? Explain one of the reasons why pregnant women often suffer from back strain late in their pregnancy. # Problems & Exercises Verify that the force in the elbow joint in [link] is 407 N, as stated in the text. Two muscles in the back of the leg pull on the Achilles tendon as shown in [link]. What total force do they exert? The Achilles tendon of the posterior leg serves to attach plantaris, gastrocnemius, and soleus muscles to calcaneus bone. The upper leg muscle (quadriceps) exerts a force of 1250 N, which is carried by a tendon over the kneecap (the patella) at the angles shown in [link]. Find the direction and magnitude of the force exerted by the kneecap on the upper leg bone (the femur). The knee joint works like a hinge to bend and straighten the lower leg. It permits a person to sit, stand, and pivot. A device for exercising the upper leg muscle is shown in [link], together with a schematic representation of an equivalent lever system. Calculate the force exerted by the upper leg muscle to lift the mass at a constant speed. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium in Applications of Statistics, Including Problem-Solving Strategies. A mass is connected by pulleys and wires to the ankle in this exercise device. A person working at a drafting board may hold her head as shown in [link], requiring muscle action to support the head. The three major acting forces are shown. Calculate the direction and magnitude of the force supplied by the upper vertebrae to hold the head stationary, assuming that this force acts along a line through the center of mass as do the weight and muscle force. We analyzed the biceps muscle example with the angle between forearm and upper arm set at . Using the same numbers as in [link], find the force exerted by the biceps muscle when the angle is and the forearm is in a downward position. Even when the head is held erect, as in [link], its center of mass is not directly over the principal point of support (the atlanto-occipital joint). The muscles at the back of the neck should therefore exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. (a) Calculate the force exerted by these muscles using the information in the figure. (b) What is the force exerted by the pivot on the head? The center of mass of the head lies in front of its major point of support, requiring muscle action to hold the head erect. A simplified lever system is shown. (a) 25 N downward (b) 75 N upward A 75-kg man stands on his toes by exerting an upward force through the Achilles tendon, as in [link]. (a) What is the force in the Achilles tendon if he stands on one foot? (b) Calculate the force at the pivot of the simplified lever system shown—that force is representative of forces in the ankle joint. The muscles in the back of the leg pull the Achilles tendon when one stands on one’s toes. A simplified lever system is shown. (a) upward (b) downward A father lifts his child as shown in [link]. What force should the upper leg muscle exert to lift the child at a constant speed? A child being lifted by a father’s lower leg. Unlike most of the other muscles in our bodies, the masseter muscle in the jaw, as illustrated in [link], is attached relatively far from the joint, enabling large forces to be exerted by the back teeth. (a) Using the information in the figure, calculate the force exerted by the lower teeth on the bullet. (b) Calculate the force on the joint. A person clenching a bullet between his teeth. (a) upward (b) downward Integrated Concepts Suppose we replace the 4.0-kg book in [link] of the biceps muscle with an elastic exercise rope that obeys Hooke’s Law. Assume its force constant . (a) How much is the rope stretched (past equilibrium) to provide the same force as in this example? Assume the rope is held in the hand at the same location as the book. (b) What force is on the biceps muscle if the exercise rope is pulled straight up so that the forearm makes an angle of with the horizontal? Assume the biceps muscle is still perpendicular to the forearm. (a) What force should the woman in [link] exert on the floor with each hand to do a push-up? Assume that she moves up at a constant speed. (b) The triceps muscle at the back of her upper arm has an effective lever arm of 1.75 cm, and she exerts force on the floor at a horizontal distance of 20.0 cm from the elbow joint. Calculate the magnitude of the force in each triceps muscle, and compare it to her weight. (c) How much work does she do if her center of mass rises 0.240 m? (d) What is her useful power output if she does 25 pushups in one minute? A woman doing pushups. (a) 147 N downward (b) 1680 N, 3.4 times her weight (c) 118 J (d) 49.0 W You have just planted a sturdy 2-m-tall palm tree in your front lawn for your mother’s birthday. Your brother kicks a 500 g ball, which hits the top of the tree at a speed of 5 m/s and stays in contact with it for 10 ms. The ball falls to the ground near the base of the tree and the recoil of the tree is minimal. (a) What is the force on the tree? (b) The length of the sturdy section of the root is only 20 cm. Furthermore, the soil around the roots is loose and we can assume that an effective force is applied at the tip of the 20 cm length. What is the effective force exerted by the end of the tip of the root to keep the tree from toppling? Assume the tree will be uprooted rather than bend. (c) What could you have done to ensure that the tree does not uproot easily? Unreasonable Results Suppose two children are using a uniform seesaw that is 3.00 m long and has its center of mass over the pivot. The first child has a mass of 30.0 kg and sits 1.40 m from the pivot. (a) Calculate where the second 18.0 kg child must sit to balance the seesaw. (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent? a) b) The seesaw is 3.0 m long, and hence, there is only 1.50 m of board on the other side of the pivot. The second child is off the board. c) The position of the first child must be shortened, i.e. brought closer to the pivot.
4,471
20,785
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.390625
3
CC-MAIN-2019-22
latest
en
0.937834
https://oeis.org/A128027
1,558,915,545,000,000,000
text/html
crawl-data/CC-MAIN-2019-22/segments/1558232260161.91/warc/CC-MAIN-20190526225545-20190527011545-00502.warc.gz
583,456,633
3,931
This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A128027 Numbers n such that (11^n - 3^n)/8 is prime. 33 3, 5, 19, 31, 367, 389, 431, 2179, 10667, 13103, 90397 (list; graph; refs; listen; history; text; internal format) OFFSET 1,1 COMMENTS All terms are primes. No other terms < 10^5. LINKS MAPLE A128027:=n->`if`(isprime((11^n-3^n)/8), n, NULL): seq(A128027(n), n=1..1000); # Wesley Ivan Hurt, Nov 19 2014 MATHEMATICA k=8; Select[ Prime[ Range[1, 200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ] Do[If[PrimeQ[(11^n - 3^n)/8], Print[n]], {n, 10^4}] (* Ryan Propper, Mar 17 2007 *) Select[Prime[Range[1200]], PrimeQ[(11^# - 3^#)/8] &] (* Vincenzo Librandi, Nov 20 2014 *) PROG (MAGMA) [p: p in PrimesUpTo(400) | IsPrime((11^p-3^p) div 8)]; // Vincenzo Librandi, Nov 20 2014 (PARI) is(n)=ispseudoprime((11^n - 3^n)/8) \\ Charles R Greathouse IV, Feb 17 2017 CROSSREFS Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128028, A128029, A128030, A128031, A128032. Sequence in context: A068990 A228471 A062594 * A128066 A273020 A148523 Adjacent sequences:  A128024 A128025 A128026 * A128028 A128029 A128030 KEYWORD hard,more,nonn AUTHOR Alexander Adamchuk, Feb 11 2007 EXTENSIONS a(8) from Ryan Propper, Mar 17 2007 a(9) from Farideh Firoozbakht, Apr 04 2007 a(10)=13103, a(11)=90397 from Robert Price, Apr 24 2011 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)
716
1,936
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.59375
4
CC-MAIN-2019-22
latest
en
0.592796
https://studydaddy.com/question/how-do-you-find-the-sum-of-the-infinite-geometric-series-1-3-1-9-1-27-1-81
1,555,723,057,000,000,000
text/html
crawl-data/CC-MAIN-2019-18/segments/1555578528433.41/warc/CC-MAIN-20190420000959-20190420021741-00007.warc.gz
550,377,962
9,523
Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer. QUESTION How do you find the sum of the infinite geometric series 1/3+1/9+1/27+1/81+...? Soo= 1/2 Formula for sum of infinite geometric series is S_oo=a_1/(1-r) ; " " " " " -1 < r < 1 We have a geometric series :1/3 + 1/9 + 1/81+......... First we know a_1= 1/3 (the first term) Second: Identify r , we know r= a_2/a_1 or r= a_n/a_(n-1 r= (1/(9))/(1/3) hArr 1/9 *3/1 = 1/3 r= 1/3 Substitute into the formula Soo= (1/3)/(1-1/3) = (1/3) /(2/3) =(1/3)*(3/2) Soo= 1/2
239
589
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.90625
4
CC-MAIN-2019-18
longest
en
0.901643
https://math.answers.com/Q/What_are_some_of_the_numbers_that_are_prime
1,713,596,204,000,000,000
text/html
crawl-data/CC-MAIN-2024-18/segments/1712296817491.77/warc/CC-MAIN-20240420060257-20240420090257-00523.warc.gz
352,426,974
47,416
0 # What are some of the numbers that are prime? Updated: 11/3/2022 Wiki User 13y ago Here are a few: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 Wiki User 13y ago Earn +20 pts Q: What are some of the numbers that are prime? Submit Still have questions? Continue Learning about Math & Arithmetic ### List some of the prime numbers? Some of the prime numbers are 2,5,7,3,11,13,19,23....etc. ### What relationship do prime and composite numbers have with factors? Some factors are prime numbers, some are composite. No. False ### Are some prime numbers also odd numbers? yes they are Related questions ### List some of the prime numbers? Some of the prime numbers are 2,5,7,3,11,13,19,23....etc. false ### How are factors and prime numbers alike? Some factors are prime numbers. ### What are com man prime factors? All numbers have factors. Some factors are prime numbers. These are known as prime factors. Some numbers have some of the same prime factors as other numbers. These are known as common prime factors. 3 is a common prime factor of 12 and 15. ### What relationship do prime and composite numbers have with factors? Some factors are prime numbers, some are composite. No. False ### Can a natural number be a prime number? All prime numbers are natural numbers. So yes, some natural numbers are prime numbers. ### What is the prime number of 85? Numbers can't have prime numbers, some numbers are prime numbers. Prime numbers are numbers that have no factors other than 1 and itself. 85 is not a prime number because its factors are 1, 5, 17, and 85. ### Why are some numbers prime and some numbers composite? Prime numbers have only 2 factors while composite numbers have more than 2 factors False ### What means prime factore? All numbers have factors. Some factors are prime numbers. These are known as prime factors.
469
1,879
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.640625
4
CC-MAIN-2024-18
latest
en
0.960141
https://math.stackexchange.com/questions/4133760/left-inverse-of-a-matrix-and-a-full-column-rank
1,726,132,142,000,000,000
text/html
crawl-data/CC-MAIN-2024-38/segments/1725700651440.11/warc/CC-MAIN-20240912074814-20240912104814-00296.warc.gz
350,915,746
42,743
# Left inverse of a matrix and a full column rank Dr Strang in his book linear algebra and it's applications, pg 108 says ,when talking about the left inverse of a matrix( $$m$$ by $$n$$) UNIQUENESS: For a full column rank $$r=n . A x=b$$ has at most one solution $$x$$ for every $$b$$ if and only if the columns are linearly independent. Then $$A$$ has an $$n$$ by $$m$$ left-inverse $$B$$ such that $$B A=I_{n}$$. This is possible only if $$m \geq n$$. I understand why there can be at most one solution for a full column rank but how does that lead to $$A$$ having a left inverse? I'd be grateful if someone could help or hint at the answer. • They don't say that the equation has a solution. They say it has at most one solution. And also, I think you mean $I_n$, not $I_a$. Commented May 10, 2021 at 9:49 • @Arthur, yes I edited it. Thank you. Commented May 10, 2021 at 10:44 • The columns of $A$ are linearly independent if and only if the null space of $A$ is trivial, if and only if the linear map induced by $A$ is injective. And it is a general fact that a map or function (not necessarily linear) is injective if and only if it has a left inverse. Similarly, a function is surjective if and only if it has a right inverse. This is a comment instead of an answer because I'm not providing a proof. – user169852 Commented May 17, 2021 at 8:27 • This doesn't seem to me like a question that deserves a bounty ... Commented May 17, 2021 at 8:28 • I wasn't understanding it and it had been a while since I posted it and had got not much help Commented May 17, 2021 at 8:30 If $$A$$ is $$m \times n$$, then the following are equivalent: 1. $$A$$ has full column rank $$n$$ 2. The columns of $$A$$ are linearly independent 3. The null space of $$A$$ is trivial 4. The map induced by $$A$$ is injective 5. $$A$$ has a left inverse Proof that 1 $$\iff$$ 2: Immediate from the definition of column rank. Proof that 2 $$\iff$$ 3: Observe that the vector $$Ax$$ is equal to the linear combination $$\sum_{i=1}^{n}a_i x_i$$, where $$a_i$$ is the $$i$$'th column of $$A$$, and $$x_i$$ is the $$i$$'th component of $$x$$. In particular, $$Ax = 0$$ if and only if $$\sum_{i=1}^{n}a_i x_i = 0$$. The null space of $$A$$ is trivial if and only if $$x=0$$ is the only solution to $$Ax = 0$$ which, by what we said above, is true if and only if $$\sum_{i=1}^{n}a_i x_i = 0$$ implies $$x_i = 0$$ for all $$i$$, which is true if and only if $$a_1, a_2, \ldots, a_n$$ are linearly independent. Proof that 3 $$\iff$$ 4: Suppose that $$Ax = Ay$$. Since $$A$$ is linear, this is equivalent to $$Ax - Ay = A(x-y) = 0$$. Therefore $$x-y$$ is in the null space of $$A$$. But the null space of $$A$$ is trivial, hence $$x-y = 0$$, so $$x=y$$. This shows that (the map induced by) $$A$$ is injective (one-to-one). Conversely, suppose that $$A$$ is injective. Then $$x=0$$ is the unique vector such that $$Ax = 0$$. Therefore the null space of $$A$$ is trivial. Proof that 2 (and equivalently 4) $$\implies$$ 5: Let $$e_1, e_2, \ldots, e_n$$ be the canonical basis for $$\mathbb R^n$$, meaning that $$e_i$$ has a $$1$$ in the $$i$$'th component, and zeros everywhere else. Note that for each $$i$$ we have $$a_i = Ae_i$$, where again $$a_i$$ is the $$i$$th column of $$A$$. Moreover, since $$A$$ is injective, $$e_i$$ is the unique vector that is mapped by $$A$$ to $$a_i$$. Now, since $$a_1, a_2, \ldots, a_n$$ are linearly independent, they are a basis for the column space of $$A$$, which can be extended to a basis $$a_1,a_2,\ldots, a_n, b_1,b_2,\ldots,b_{m-n}$$ for $$\mathbb R^m$$. Hence an arbitrary $$y \in \mathbb R^m$$ has a unique representation of the form $$y = \sum_{i=1}^{n} c_i a_i + \sum_{j=1}^{m-n} d_j b_j$$ where $$c_i$$ and $$d_j$$ are scalars. Therefore we can define a linear map $$g : \mathbb R^m \to \mathbb R^n$$ by first setting $$g(a_i) = e_i$$ for each $$i=1,2,\ldots,n$$ and $$g(b_j) = 0$$ for each $$j=1,2,\ldots,m-n$$, and then extending $$g$$ linearly to all of $$\mathbb R^m$$: $$g(y) = g\left(\sum_{i=1}^{n} c_i a_i + \sum_{j=1}^{m-n} d_j b_j \right) = \sum_{i=1}^{n} c_i g(a_i) + \sum_{j=1}^{m-n} d_j g(b_j) = \sum_{i=1}^{n} c_i g(a_i) = \sum_{i=1}^{n} c_i e_i$$ Then $$g$$ is a left inverse of $$A$$: $$g(Ax) = g\left(\sum_{i=1}^{n}a_i x_i\right) = \sum_{i=1}^{n} x_i g(a_i) = \sum_{i=1}^{n} x_i e_i = x$$ Proof that 5 $$\implies$$ 3: Suppose that $$Ax = 0$$. Let $$g$$ be a left inverse of $$A$$. Then $$x = g(Ax) = 0$$. This shows that the null space of $$A$$ is trivial. As a side note, it turns out that 4 and 5 are equivalent for general functions, not just linear maps. If $$f$$ is any injective function, then it has a left inverse, and conversely if $$f$$ is any function that has a left inverse, then it is injective. There is a proof here, for example. Since you indicated in the comments that this is an unfamiliar fact, I did not use it in the proof above but instead constructed a left inverse explicitly. Note that my proof shows why a left inverse of $$A$$ must exist if $$A$$ has full column rank, but it doesn't explicitly show how to compute the left inverse. As Strang notes, one formula for a left inverse is $$B = (A^T A)^{-1} A^T$$. That this is a left inverse is clear by computing: $$BA = ((A^T A)^{-1} A^T) A = (A^T A)^{-1} (A^T A) = I_n$$ But as you will have noted, Strang punts to a later chapter the proof that $$A^T A$$ is invertible when $$A$$ has full column rank. So that's not very satisfactory! Also, computing Strang's left inverse is very inefficient because it involves inverting $$A^T A$$. This requires a lot of calculation, proportional to $$n^3$$ operations for an $$n \times n$$ matrix. In practice, probably the best way to compute a left inverse is to perform row reduction on $$A$$ to bring it to the form $$\begin{bmatrix} I_n \\ 0_{m-n \times n} \end{bmatrix}$$ where $$I_n$$ is the $$n \times n$$ identity matrix, and $$0_{m-n \times n}$$ is the $$m - n \times n$$ matrix consisting of all zeros. Row reduction to this form is possible if and only if the columns of $$A$$ are linearly independent. Assuming you're familiar with row reduction, you probably know that each row operation can be expressed as an $$m \times m$$ elementary matrix of one of three forms, corresponding to the three row reduction operations (multiplying a row by a scalar, interchanging two rows, and adding a scalar multiple of one row to another). The row reduction procedure can then be expressed by left-multiplying $$A$$ by the corresponding elementary matrices. Assuming there are $$k$$ of these, we have: $$E_k E_{k-1} \cdots E_2 E_1 A = \begin{bmatrix} I_n \\ 0_{m-n \times n} \end{bmatrix}$$ The product $$E_k E_{k-1} \cdots E_2 E_1$$ is easy to understand conceptually: it corresponds to the $$k$$ row operations used to bring $$A$$ into the reduced form. Fortunately, it's not necessary to compute $$E_k E_{k-1} \cdots E_2 E_1$$ as a product of $$k$$ matrices! Instead you compute it by starting with $$I_{m}$$ and performing the same row operations on it as you perform on $$A$$. In any case, denoting $$E_k E_{k-1} \cdots E_2 E_1$$ by $$B$$, the above becomes $$BA = \begin{bmatrix} I_n \\ 0_{m-n \times n} \end{bmatrix}$$ Note that $$B$$ is an $$m \times m$$ matrix. It is almost the left inverse we seek, except we want just $$I_n$$ on the right hand side and a left inverse should be $$n \times m$$, not $$m \times m$$. If $$m > n$$ then the right hand side has $$m-n$$ spare rows of zeros at the bottom. To get rid of these, we can simply remove the bottom $$m-n$$ rows of $$B$$ to get a $$n \times m$$ matrix $$B'$$ which satisfies $$B'A = I_n$$ and is therefore a left inverse of $$A$$, as desired! • Thank you, I'm going through it. :) Commented May 17, 2021 at 9:45 • @Kashmiri I recognized that my proof is theoretical in that it shows that a left inverse of $A$ must exist, but it's not immediately obvious how to compute it. So I added some paragraphs at the bottom regarding computation. I hope they are helpful. – user169852 Commented May 17, 2021 at 10:07 As an add on to user169852’s proof, I would note that Strang’s argument that $$A^T A$$ is invertible if A has full column rank is fairly simple. He shows that for any matrix A, $$A^T A$$ has the same nullspace as A: (1) Clearly the nullspace of A is contained in the nullspace of A^T A. (2) To show the reverse inclusion, suppose that $$A^T A x = 0$$. Then $$x^T A^T A x = 0$$, so $$(A x)^T (A x) = 0$$. I.e., the norm of A x is zero and hence A x = 0. So the nullspace of $$A^T A$$ is contained in the nullspace of A. Hence the nullspace of A equals the nullspace of $$A^T A$$. user169852 has already shown that A having full column rank implies its nullspace is trivial. So $$A^T A$$ is a square matrix with trivial nullspace and hence is invertible. Question: "I understand why there can be at most one solution for a full column rank but how does that lead to A having a left inverse? I'd be grateful if someone could help or hint at the answer." Answer: Let $$k$$ be a real numbers and $$V:=k^n, W:=k^m$$. Since the equation $$Ax=b$$ has a unique solution for all $$b\in W$$ it follows the equation $$Ax=0$$ has a unique solution, namely $$x=0$$. Hence the map $$A: V \rightarrow W$$ is an injection and it follows $$n \leq m$$. We get an exact sequence of $$k$$-vector spaces $$0 \rightarrow V \rightarrow W \rightarrow^p W/V \rightarrow 0$$ and we may choose a section $$s$$ of $$p$$. This is a $$k$$-linear map $$s: W/V \rightarrow W$$ with $$p \circ s = Id$$. This gives an idempotent endomorphism of $$W$$: $$u:=s \circ p$$ with $$u^2=u$$. From this it follows we may write $$W \cong V \oplus Im(u)$$ and the projection map $$p_V: W \cong V \oplus Im(u) \rightarrow V$$ is a left inverse to the inclusion map defined by the matrix $$A$$. If you choose a basis for $$W$$ you get a matrix $$B$$ with $$BA=Id_n$$
3,089
9,894
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 170, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.796875
4
CC-MAIN-2024-38
latest
en
0.948195
http://www.jiskha.com/display.cgi?id=1270149696
1,498,332,360,000,000,000
text/html
crawl-data/CC-MAIN-2017-26/segments/1498128320323.17/warc/CC-MAIN-20170624184733-20170624204733-00271.warc.gz
550,221,467
4,614
# physics(help me with the angle) posted by . In the 1968 Olympic Games, University of Oregon jumper Dick Fosbury introduced a new technique of high jumping called the "Fosbury flop." It contributed to raising the world record by about 30 cm and is presently used by nearly every world-class jumper. In this technique, the jumper goes over the bar face up while arching his back as much as possible, as shown below. This action places his center of mass outside his body, below his back. As his body goes over the bar, his center of mass passes below the bar. Because a given energy input implies a certain elevation for his center of mass, the action of arching his back means his body is higher than if his back were straight. As a model, consider the jumper as a thin, uniform rod of length L. When the rod is straight, its center of mass is at its center. Now bend the rod in a circular arc so that it subtends an angle of θ = 81.5° at the center of the arc, as shown in Figure (b) below. In this configuration, how far outside the rod is the center of mass? Report when i do integration, do i use from angle 49.25 to 122.25 • physics(help me with the angle) - You are integrating some distance*dm in order to get a cm (mass*distance). There are hard ways, and easy ways to do do this. By arguments of symettry, you can place the cm on the axis, so the question is where. consider some dm=k dtheta but the x part of that, the distance along the final radial, is r-rcosTheta (draw a diagram to verify that). So just integrating the arc (-81.5/2 to 81.5/2 deg) will give the position. Int (r-rcosTheta)dTheta= rTheta+rsintheta over limits, or -r*.71+r(.989)-r(.71)+r(.989)=.558r, or outside the arc, it is .442r. now in terms of L, L=rTheta=r(1.42) or r= L/1.42 so distance is .442*1.42=.62 L
490
1,806
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4
4
CC-MAIN-2017-26
latest
en
0.949798
https://www.excelforum.com/excel-formulas-and-functions/909928-setting-formula-to-calculate-ca-overtime-rules.html
1,620,985,962,000,000,000
text/html
crawl-data/CC-MAIN-2021-21/segments/1620243990449.41/warc/CC-MAIN-20210514091252-20210514121252-00141.warc.gz
781,576,851
14,846
# Setting formula to calculate ca overtime rules 1. ## Setting formula to calculate ca overtime rules I'm having problems with getting the calculations right on this. The problem has been when the worker has less than 8 hrs in a day.........can someone help me with what I'm doing wrong on this Standard Timesheet (CA).xls? THANK YOU! Regular Time - =IF(SUM(MIN(K18,8),MIN(L18,8),MIN(M18,8),MIN(N18,8),MIN(O18,8),MIN(P18,8),MIN(Q18,8))>40,40,SUM(MIN(K18,8),MIN(L18,8),MIN(M18,8),MIN(N18,8),MIN(O18,8),MIN(P18,8),MIN(Q18,8))) Over Time - =SUM(K18,L18,M18,N18,O18,P18,Q18,)-R15-R17 Double Time - =IF(K18>12,K18-12,0)+IF(L18>12,L18-12,0)+IF(M18>12,M18-12,0)+IF(N18>12,N18-12,0)+IF(O18>12,O18-12,0)+IF(P18>12,P18-12,0)+IF(Q18>12,Q18-12,0) I'm wondering too if it could be due to the general layout of the timesheet format that we've create too that is "limiting" what we need. 2. ## Re: Setting formula to calculate ca overtime rules Hi SmAsSilk Have a look at the attached file, enter your time as 17:00 hour or 05:00PM Cells K18:018 are adding the hours per day. R15 & S15 are recording the hours and O/T This is based on total time until 40 hours then any thing over is O/T Any way have a look and see how you get on and were take it from there. 3. ## Re: Setting formula to calculate ca overtime rules What I need to figure out is how to get the Regular time hours to reflect that the worker actually worked 39 hrs regular time and his OT should be six hours. That's where the error is. 4. ## Re: Setting formula to calculate ca overtime rules SmAsSilk You need to sort your sheet out first, so it will not incur those unnecessary long formulas! That is what I started to do there. 5. ## Re: Setting formula to calculate ca overtime rules ok thanks.......... There are currently 1 users browsing this thread. (0 members and 1 guests) #### Posting Permissions • You may not post new threads • You may not post replies • You may not post attachments • You may not edit your posts Search Engine Friendly URLs by vBSEO 3.6.0 RC 1
608
2,043
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.421875
3
CC-MAIN-2021-21
latest
en
0.857723
https://pimylifeup.com/javascript-bitwise-operators/
1,721,277,635,000,000,000
text/html
crawl-data/CC-MAIN-2024-30/segments/1720763514822.16/warc/CC-MAIN-20240718034151-20240718064151-00856.warc.gz
392,548,619
24,313
# JavaScript Bitwise Operators In this tutorial, we will be exploring how to use bitwise operators in JavaScript. JavaScript’s Bitwise operators are probably the most tricky to understand, especially when you are new to programming or computer science. While somewhat hard to understand, these operators allow you to perform operations at a binary level, allowing you to manipulate the bits themselves. Of course, to use bitwise operators, you will need at least a basic understanding of binary numbers. Therefore, we will briefly cover binary numbers within the tutorial to at least get a very entry-level understanding of how all the bitwise mathematics works. Let us first explore the bitwise operators that JavaScript supports. You can use the table below to see each of the supported operators. Alongside each operator, you will see its name, an example, and a description of what the operator does. One important thing to know about JavaScript and its bitwise operators is that it works on all numbers as 32-bit binary. Therefore, even though JavaScript uses 64-bit floating-point numbers for its number system, the value will be converted when you use bitwise operators. When you use any bitwise operator in JavaScript it will convert the number from a 64-bit system to a 32-bit signed binary number. ## Brief Overview of Binary Numbers in JavaScript Let us start this guide with a very brief overview of how binary numbers are handled within JavaScript. First, when using bitwise math, JavaScript will use 32-bit signed binary numbers. A signed number means the first bit from the left represents whether the number is positive (`0`) or negative (`1`). A signed number also restricts you to a smaller number. For instance, the limit of a signed 32-bit number is `-2147483648` to `2147483647`. Whereas the limit for an unsigned number is `0` to `4294967295` A 32-bit number with the value of `0` would look like the following. You can see that all 32-bits are set to 0 since no value is currently set. ``00000000000000000000000000000000`` When counting a binary number, you read from the right, with the right-most bit representing the number `1`. Every bit after doubles in value. So bit `2` is `2`, bit `3` is `4`, bit `4` is `8` and so on. So if we were to have the number 6, we would need to set both bit `3` and bit `2` to `1`, as shown below. Again remember that you write from right to left. ``00000000000000000000000000000110`` Now to make things easier to understand, when we explain JavaScript’s bitwise operator’s math, we will use an 8-bit number, so we don’t have to deal with a ton of leading 0’s. The logic is still the same. We are just dealing with a smaller number. For example the number 32 could be written like the following in binary using only 8 bits. ``00100000`` However, since JavaScript operates in 32 bits, this number would look like the following in its internal memory. ``00000000000000000000000000100000`` From this, you can see why we will be ignoring the other 24 bits of memory when explaining some of the bitwise math for simplicity’s sake. ## Exploring JavaScript’s Bitwise Operators Over the following sections, we will be exploring each of the bitwise operators supported by JavaScript. On top of exploring how these operators work, we will also explain how this bitwise math works. ### Bitwise AND Operator (`&`) in JavaScript The bitwise AND operator (`&`) works by returning a 1 in each position where both left and right operands contain a `1`. In JavaScript, you write the bitwise AND operator by referencing the left operand, then a single ampersand symbol (`&`), and finally the right operand. The value on the left will be compared against the value on the right using the AND operation. ``a & b`` To give you a better understanding of how this works let us start with this table. This table shows each value an operand can be and the resulting bit from using the AND operator. This table shows how the bitwise AND operator in JavaScript will handle each bit pair. #### Example of AND Binary Math Let us start by exploring how the bitwise AND operator works outside JavaScript. To showcase this, we will AND the numbers 30 (`00011110`) and 6 (`00000110`). Remember only bit pairs that are both “`1`” will be carried over to the new number. 1. We need to start by expressing both of our numbers as 8-bit binary numbers. Remember, each bit going from right to left is double the previous bit. So, add the bits that add up to your number. ``````30 = 00011110 6 = 00000110`````` 2. Now that we have our values in a binary format, we can AND each bit pair together. Remember to write a “`1`” when both bits are `1` and a `0` when they are not. `````` 00011110 & 00000110`````` 3. The final result shows that we copied over only bit pairs where both values were `1` to the new result. Converting this number from binary to decimal should leave you with the number 6. ``00000110 = 6`` #### Example of the AND Operator in JavaScript Now let us perform this same bitwise AND operation in JavaScript itself. Since JS handles the conversion internally, we don’t have to worry about providing our numbers in binary format. So let us start by declaring two variables. The first variable will be called “`a`” and will have the value “`30`“. The second variable will have the name “`b`” and have the value “`6`“. Within a “`console.log()`” function call, we will use the bitwise AND operator on both our “`a`” and “`b`” variables. The resulting operation will be logged to the console. ``````let a = 30; //00000000000000000000000000011110 let b = 6; //00000000000000000000000000000110 console.log(a & b); //00000000000000000000000000000110`````` After running the above example, you should end up with the following value in your console. ``6`` ### Bitwise OR Operator (`|`) JavaScript’s bitwise OR operator (`|`) compares each bit pair and will set `1` in that position if either of the bits is `1`. The OR operator is written in JavaScript starting with a left operand, then the pipe symbol (`|`), and then the right operand. JavaScript will compare the left value against the right operand during the bitwise OR operation ``a | b`` Let us break out another handy table to make this easy to understand. This table will show each occurrence in which the bitwise OR operator sets bits to `1` instead of `0`. Using this table above as a reference, you can see that whenever either of the bits is `1`, the resulting bit is `1`. #### Example of OR Binary Math To better understand how the bitwise OR operator works within JavaScript, let us explore a simple calculation. We will use the numbers 30 (`00011110`) and 5 (`00000101`) for this calculation. We will bitwise OR both of these values together. If any of the bits in the pair are `1`, we will write down `1`. 1. Start by expressing both of our numbers as an 8-bit signed binary number. Remember that we count from the right to the left when reading binary. ``````30 = 00011110 5 = 00000101`````` 2. Next, we need to OR our two binary values together. This involves comparing each bit pair and writing down `1 `whenever either of the bits is `1`. `````` 00011110 | 00000101`````` 3. After comparing both binary numbers, you should end up with the following result. Converting the number back from binary to decimal should leave you with the value of `31`. `` 00011111 = 31`` #### Example of the Bitwise OR Operator in JavaScript Now that we understand how the bitwise OR math works let us put it to use in JavaScript. To use the bitwise OR operator in JavaScript, you must use the pipe symbol (`|`) in between two operands. JS will handle all the grunt work of handling these numbers as 32-bit binary. For this example, let us create a variable called “`a`” and assign it the value `30`. We will also create a variable called “`b`” that we will give the value `5`. Finally, we then use the bitwise OR on both our “`a`” and “`b`” variables, logging the result using the “`console.log()`” function. ``````let a = 30; //00000000000000000000000000011110 let b = 5; //00000000000000000000000000000101 console.log(a | b); //00000000000000000000000000011111`````` The above example code should produce the following result. This shows you the result of the bitwise OR operation. ``31`` ### Bitwise XOR Operator (`^`) in JavaScript The bitwise XOR Operator (`^`) in JavaScript compares each binary bit pair and sets a `1` bit in that position when only one of those bits is `1`. If both bits are `1`, then the XOR operator will return `0` for that position, hence why it’s called eXclusive OR. You write the XOR operator in JavaScript by writing the left operand, followed by the caret symbol (`^`), and finally the right operand. ``a ^ b`` Let us write a simple truth table to understand how the XOR operator works. This table will show the only cases in which the XOR operator will set a `1` bit. While this table gives you a good idea of how the bitwise XOR operator affects each bit in JavaScript, let us explore the math of this operator and how it works in JavaScript. #### Example of XOR Binary Math Let us quickly take a look at how XOR works outside of JavaScript. This example will help you better understand better what happens when using the XOR operator. 1. For this example, we will be calculating the bitwise XOR of the numbers `30` and `5`. However, before doing this we must first express both numbers as binary. For simplicity’s sake, we will write both of these numbers as 8-bit binary. ``````30 = 00011110 5 = 00000101`````` 2. Next, we need to perform an XOR on each of the bit pairs. Look through each pair of bits and write “`1`” whenever there is only one “`1`” in the pair. If both are “`0`“, or both are “`1`” then you need to write “`0`“. `````` 00011110 ^ 00000101`````` 3. After comparing each bit using the XOR method, you should end up with the following result. Converting the binary number back to the decimal format should leave you with the number 27. `` 00011011 = 27`` #### Example of the Bitwise XOR Operator in JavaScript Now that we have given a quick example of how you can work out the XOR operation yourself, let us put the bitwise XOR operator to use in JavaScript. For this example, we will declare two variables, one called “`a`” and one called “`b`“. The “`a`” variable will be assigned the value of `30`, and the “`b`” variable the value of `5`. We then use JavaScript’s bitwise XOR operator (`^`) on these two operands and log the result to the console. ``````let a = 30; //00000000000000000000000000011110 let b = 5; //00000000000000000000000000000101 console.log(a ^ b); //00000000000000000000000000011011`````` After running the above example, you should end up with the result of the XOR operation in your console. ``27`` ### Bitwise NOT Operator (`~`) The bitwise NOT operator (`~`) in JavaScript inverses every bit within the converted 32-bit signed number. Since JavaScript uses signed binary numbers, the number will also be flipped from positive to negative during the process. The change in “sign” is a side effect of the bitwise NOT operator flipping each bit.. If a bit is `0`, the bitwise NOT operator will flip it to `1`. If the bit is `1` then it will be flipped to `0`. The below simple truth table shows the basic way the bitwise NOT operator works within JavaScript. To use this operator, all you need to do is use the tilde symbol (`~`), followed by your value or variable name, as shown below. ``~a`` #### Example of NOT Binary Math Let us first explore how the bitwise NOT operator works outside of JavaScript. This will give you an understanding of what is occurring during this operation. 1. Since the NOT operator only works with a single operand, we will only need one number to show this. For this example, we will be using the number “`5`“, which we will convert to a signed 8-bit binary number. ``5 = 00000101`` 2. With our decimal number converted to binary, we can perform the NOT operation on it. This means for every bit that is `0`, we write a `1`, and for every bit that is `1`, we will write down a `0`. We should note that binary numbers in JavaScript are signed, meaning the left-most bit will be the “`sign`“. The sign is what tells JavaScript whether this number is negative or positive ``~ 00000101`` 3. Now, you will end up with the following signed number. If you had a negative number, it would have become positive, and if you had a positive number, it would have become negative. On top of the changed sign, the value of your number will also be different. For example, positive 5 will not be negative 5 when the binary is inverted, as you will soon see. Converting a negative signed number back to a decimal number means using “two’s complement” in most modern binary number systems. ``11111010 - Signed Negative Number`` 4. We won’t be explaining how exactly two complement works and why, but let us quickly use it to convert our signed negative binary number back to the decimal format. Start by finding the first “`1`” from the right. Once found, invert all the bits to the left, so `0`‘s become `1`‘s and `1`‘s become `0`‘s. Once you have inverted all the bits, you are left with a binary number that you can now read back as a decimal number. Remember to carry over the negative sign to the final number, ``````11111010 00000110 = -6`````` #### Example of the Bitwise NOT Operator in JavaScript Now that you understand how the bitwise NOT operator works in JavaScript let us explore it in some actual code. Remember that the bitwise NOT operator is represented in JavaScript with the tilde character (`~`). You use this character before your variable. With this example, we will declare a variable called “`a`” and assign it the value `5`. This variable is what we will use the NOT operator on. On our next line, we use the NOT operator on our “`a`” variable, logging the resulting value ``````let a = 5; //00000000000000000000000000000101 console.log(~a); //11111111111111111111111111111010`````` Using the above JavaScript example, you should end up with the following logged to your console. ``-6`` ### Bitwise Left Shift Operator (`<<`) in JavaScript The bitwise left-shift operator (`<<`) in JavaScript allows you to shift all bits in a number to the left. It achieves this by appending zeroes to the end of the number. Any excess bit on the left side is dropped off during the shifting process. Two less-than signs represent the left shift operator. The left operand is the variable you want to shift. The right operand is how many bits you want to shift to the left by. ``a << b`` For example, if you have the number `1` (`00000001`) and bit shift it by `1` position to the left, the value would change to “2” (`00000010`). If you wanted to replicate this behavior without using bitwise operators, it would be the equivalent of using the following math. ``x * (2 ** y)`` You would multiply your value by `2` to the power of `y`. “`y`” in this case would be how many places you would want to shift your bits to the left. Computation-wise, shifting the bits is a lot faster. #### Quick Explanation of the Left Shift Operator Bitwise shifting can be somewhat confusing to understand at first but is very straightforward. Before we show how the left-shift operator works in JavaScript, let us explain it outside of it. 1. Let us take the number `1` and convert that into an 8-bit signed binary number. The value of `1` means we only have the far-right bit set to “`1`“, as shown below. ``1 = 00000001`` 2. Now, let us shift this binary number to the left (`<<`) by one bit. We do this by deleting the far-left bit (0 in our example) and adding a new “`0`” bit on the right side. From this, you can see how our number `1` in binary had its value changed. ``````00000001 << 1 00000010 - Value shifted to Left by 1 bit`````` 3. If we were to convert our shifted binary value back to the decimal format, you can see that our value has now changed from “`1`” to “`2`“. Now, if we were to shift our original `1` value by two places, we would have ended up with the value “`4`” instead, as our bit would now be in the third position. ``00000010 = 2`` #### Example of the Bitwise Left Shift Operator in JavaScript Let us show you a quick example of how the left-shift operator is utilized within JavaScript. To showcase this, we will take the number 7 and shift its bits to the left by two. At the top of this script, we declare two variables with the names “`a`” and “`b`“. The “`a`” variable is the variable we will be shifting, and we will assign it the value `7`. The “`b`” variable is the number of bits we want to shift our number by, which we will set to `2`. Finally, we left-shift the “`a`” variable by the “`b`” variable, logging the result to the console. ``````let a = 7; //00000000000000000000000000000111 let b = 2; //00000000000000000000000000000010 console.log(a << b); //00000000000000000000000000011100`````` After running the above JavaScript example, you will have the following value. ``28`` ### Bitwise Sign-Propagating Right Shift Operator (`>>`) JavaScript has two versions of the bitwise right-shift operator (`>>`). The first of these is the “sign-propagating right-shift operator”, this operator is designed to preserve the “sign” bit. The bitwise sign-propagating right-shift operator is used in JavaScript by using two greater-than operators (`>>`). The left operand is the variable or value you want to shift, and the right operand is how many bits you want to shift it by. ``a >> b`` This operator preserves the sign by copying the left-most bit and pushing that in from the left. JavaScript will drop any excess bit on the right. #### Quick Overview of the Bitwise Sign-Propagating Right-Shift Operator Before we show how the sign-safe bitwise right-shift operator works in JavaScript, let us explore what is occurring behind the scenes. 1. For this example, let us take the number `-7` and convert it to an 8-bit binary number to make this easier to explain. Suppose this converted number looks weird to you. It’s because we are using two’s complements. This means starting from the first “`1`” from the right, we flip each bit to it’s opposite. Converting the number to its signed negative equivalent. `````` 7 = 0000111 -7 = 1111001`````` 2. Now, if we used JavaScript’s Bitwise-sign propagating right-shift operator on our “`-7`” value and shifted to the right by two bits, the following would happen. First, remove the two far-right bits from your binary number. Since we are shifting by two bits, these will need to be dropped. Next, make a note of the far-left bit. In our case, this is a “`1`“, meaning we add two “`1`” bits to the start of the number, shifting the overall value to the right. If your left-most bit were a “`0`“, then that would be shifted in from the left instead. ``````1111001 << 2 1111110 - Shifted to right by 2 bits. Left bit is replicated and shifted in`````` 3. Let us now unravel our number to see how shifting the value by two bits affected its value. Thanks to us following JavaScript’s bitwise signed right-shift operator’s logic, it will still be a negative number. Since it is still a negative number, use the two’s complement logic to convert it back. Find the right-most “`1`” bit, and flip every bit after that. So a `1` becomes a `0`, and a `0` becomes a `1`. ``````1111110 0000010`````` 4. Finally, reading our binary value and carrying over the “sign” bit, we ended up with the following negative value. With this, you can see how the right shift changed our value from `-7 `to `-2`. ``0000010 = -2`` #### Example of the Bitwise Sign-Propagating Right-Shift Operator in JavaScript For our first example, let us explore how JavaScript’s signed bitwise right-shift operator handles a negative number. To show how this works, we will be using the number “`-7`” (`a`) and shifting it to the right by 2 (`b`) bits. Thanks to preserving the sign of our number, it will remain a negative number after the shift. We shift our “`a`” variable’s binary value to the right by the amount stored in the “`b`” variable. The result of the sign-propagating right-shift operation is logged to the console. ``````let a = -7; //11111111111111111111111111111001 let b = 2; //00000000000000000000000000000010 console.log(a >> b); //11111111111111111111111111111110`````` Below you can see the result of this bitwise operation within JavaScript. You can see how the bitwise operation adjusted the value while preserving the sign. ``-2`` ### Unsigned Bitwise Right Shift Operator (`>>>`) in JavaScript The final bitwise operator that JavaScript supports is the unsigned right-shift operator (`>>>`). This operator is represented by three greater-than signs (`>>>`). The operand on the left will be shifted by right value. Zeroes will be pushed from the left, with excess bits on the right being dropped. ``a >>> b`` Since this operation works without regard for a “`signed`” number, a negative value will become a rather significant positive value. #### Quick Overview of the Unsigned Right-Shift Operator Outside of JavaScript Let us give you a better idea of what the unsigned right-shift bitwise operator does in JavaScript. As mentioned before, this operator pushes 0’s in from the left, meaning it will not respect the sign of your number 1. Let us showcase this by starting with the number `-7` and converting it to a binary number that we can work with. We will be sticking to a small 8-bit binary number to make this easy to explain. Since this is a negative number, we will be using two’s complement. `````` 7 = 0000111 -7 = 1111001`````` 2. Now that we have our binary number, let us perform an unsigned right-shift operator to this number. We will be shifting this number by two bits to the right. Being unsigned means, we will be adding `0`‘s from the left side. Start by dropping off the two far-right bits from the number. These bits will drop off during the unsigned right shift. Next, add two `0`‘s to the front of your binary number, shifting its value to the right. ``````1111001 >>> 2 0011110 - Unsigned shift to the right. '0' bits added`````` 3. The first thing you will notice is that the sign of our number has now been moved as `0`‘s were pushed. This means our number is no longer negative, so you cant use two’s complement to unravel it. You just need to read the number back as you normally would, counting from right to left. However, you will see that the number is drastically different. This value difference is amplified even more on the full 32-bit binary that JavaScript uses for it’s bitwise operations. ``0011110 = 30`` #### Example of the Unsigned Right-Shift Operator in JavaScript (Positive Number) Let us start by showing how an unsigned right-shift operator works in JavaScript when used on a positive number. We will start our script by declaring a variable called “`a`” and assigning it the number `10`. Additionally, we will be defining a variable called “`b`” and assigning it the number `3`. After we have declared those variables, we utilize the unsigned right-shift operator (`>>>`). We use this operator to shift our “`a`” variable to the right by the value stored in the “`b`” variable. The result of this bitwise operation is logged to the console using the “`console.log()`” function. ``````let a = 10; //00000000000000000000000000001010 let b = 3; //00000000000000000000000000000011 console.log(a >>> 3); //00000000000000000000000000000001`````` The code above will log the following value to the console. ``1`` #### Example of the Unsigned Right-Shift Operator in JavaScript (Negative Number) We can show you how the unsigned right-shift operator will affect a negative number in JavaScript. As we mentioned earlier, since this operator pushes in `0`‘s, it will break the “sign” bit. At the top of this example script, we will define two variables. The “`a`” variable will have the value `-7`. With the “`b`” variable, we will assign the value `2`. By using the unsigned right-shift operator (`>>>`), we will shift our “`a`” variable to the right by the amount stored in the “`b`” variable. Like our other examples, we log the result of this bitwise operator to the console. ``````let a = -7; //11111111111111111111111111111001 let b = 2; //00000000000000000000000000000010 console.log(a >>> b); //00111111111111111111111111111110`````` Below you can see how JavaScript’s bitwise unsigned right-shift operator destroyed the “sign” of the number, turning it into a large positive number. ``1073741822`` ## Conclusion Throughout this guide, we have shown you how to use bitwise operators in JavaScript. Bitwise operators allow you to manipulate numbers at a binary level using various methods. We have explained each of these operators, so you should have a decent idea of what is occurring.
6,072
25,020
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.515625
4
CC-MAIN-2024-30
latest
en
0.907525
https://appdividend.com/2022/02/21/np-percentile/
1,656,472,572,000,000,000
text/html
crawl-data/CC-MAIN-2022-27/segments/1656103620968.33/warc/CC-MAIN-20220629024217-20220629054217-00159.warc.gz
152,500,807
27,700
AppDividend Latest Code Tutorials # np.percentile: How to Calculate Percentile in Numpy Array A percentile is a mathematical criterion used in statistics, suggesting the value below which a given percentage of observations falls in a group of observations. ## np.percentile The np.percentile() is a numpy mathematical array method used to calculate the ith percentile of the provided input data supplied using arrays along a specified axis. But what does percentile value mean? A percentile is a mathematical term generally used in statistics. The ith percentile of a set of data is the value at which i percent of the data is below it. Using the np percentile() method, you can calculate the percentile in Python. For better understanding, we may consider a student who scores 90 percentiles out of 100, and then it means that out of 100 students, that particular student has outnumbered 90 students, and they are below him. ### Syntax numpy.percentile (arr, i, axis=None, out=None) ### Parameters The percentile() function takes at most four parameters: arr: array_like, input array, or an object that can be converted into an array-like a list. i: percentile value, it must be in the range of 0-100 (with 0 and 100 as inclusive values). axis: It is an optional parameter. It represents the axis along which we want to compute the percentile. If the axis value is not given, then by default, the input array is supposed to be flattened, and then percentile value is computed (overall axis). So, for example, if we set axis=0, then percentile is calculated along the column, and if axis= 1, then percentile is computed along the row. out: ndarray, it is also an optional parameter. It represents an optional resultant array in which we want to get our output. It is to be noted that the shape of this array should match with the expected output. ### Return Value It returns a scalar or a ndarray. The method returns ith percentile value. A scalar value is returned when axis value is set to None; otherwise, when the axis is specified, an n-dimensional array is returned with percentile values along the specified axis. ### Programming Example #### Program to show the working of numpy.percentile() method in case of 1-D array/vectors. # importing the numpy module import numpy as np # Making a list lst = [16, 18, 22, 14, 22, 23, 28, 17, 19, 15, 16, 22, 14, 16, 18] print("Given list is:\n", lst) # Calculating percentile value in the list res = np.percentile(lst, 35) print("35th percentile of given list is: ", res) # Creating an array arr = np.array([100, 200, 150, 125, 175, 150]) print("\nArray elements are:\n", arr) # Calculating percentile value in the list output = np.percentile(arr, 75) print("75th percentile of given array is: ", output) #### Output Given list is: [16, 18, 22, 14, 22, 23, 28, 17, 19, 15, 16, 22, 14, 16, 18] 35th percentile of given list is: 16.0 Array elements are: [100 200 150 125 175 150] 75th percentile of given array is: 168.75 #### Explanation In the above program, we have taken a list named lst consisting of some random integers, then we have calculated the 35th percentile value in the list. Similarly, another array named arr is taken then we have displayed 75th percentile value in the array. #### Program to show the working of numpy.percentile() method in case of a multi-dimensional array: See the following code. # importing the numpy module import numpy as np # Making a 2D array arr = np.array([[10, 20, 30], [40, 50, 60], [70, 80, 90]]) print("Elements in the 2D array are:\n", arr) out = np.percentile(arr, 50) print("Calculating 50th percentile without specifying axis: ", out) out0 = np.percentile(arr, 50, axis=0) print("Calculating 50th percentile along axis 0: ", out0) out1 = np.percentile(arr, 50, axis=1) print("Calculating 50th percentile along axis 1: ", out1) #### Output Elements in the 2D array are: [[10 20 30] [40 50 60] [70 80 90]] Calculating 50th percentile without specifying axis: 50.0 Calculating 50th percentile along axis 0: [40. 50. 60.] Calculating 50th percentile along axis 1: [20. 50. 80.] #### Explanation In the program, we have taken a two-dimensional array named arr, and then we have displayed its content inside the array. Computing 50th percentile value of the given array in three modes: First, when we didn’t specify any axis, the result becomes a scalar value because, by default, the input array is supposed to be flattened. Secondly, when we compute the percentile value along axis 0, then percentile value is calculated along with the columns. Its result is shown using out0. Lastly, when we compute the percentile value along axis 1, then percentile value is calculated along the rows. Its result is shown using out1. That’s it for this tutorial.
1,220
4,793
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.46875
3
CC-MAIN-2022-27
latest
en
0.849021
https://quant.stackexchange.com/questions/tagged/black-scholes?tab=unanswered&page=3
1,585,775,548,000,000,000
text/html
crawl-data/CC-MAIN-2020-16/segments/1585370506121.24/warc/CC-MAIN-20200401192839-20200401222839-00206.warc.gz
659,803,292
40,556
# Questions tagged [black-scholes] Black-Scholes is a mathematical model used for pricing options. 148 questions with no upvoted or accepted answers Filter by Sorted by Tagged with 52 views ### Pricing with-profit/smoothed bonus annuity using Black-Scholes Would this be possible? Subsequently, would the pricing of such an annuity be somewhat similar to pricing a lookback option? 175 views ### School project about Black Scholes with stochastic volatility In a university project I am looking at Black Scholes model with a stochastic volatility. I’m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ... 620 views ### Black-Scholes formula with deterministic interest rate and dividend yield Does any one have the Black-Scholes formula for a European call with time-dependent but deterministic interest rate and dividend yield ? 152 views ### B-S Put Option Formula: Derivation using expected value under Q I have been working on an old problem in one of my finance classes and, since no solution has been provided and I won't be able to contact my teacher anytime soon, I was hoping I could ask you guys to ... 60 views ### Any Simple Way to Prove Black Scholes Type Identies? A certain complicated option pricing formula results in products of Black Scholes $N$ components like this: $-p_1N(d_1)N(d_6)+p_sN(d_2)N(d_5)>?0$ where $p_s>p_1$ Trying to find a simple way ... 233 views ### BS Implied Volatility under Normal returns If I use theoretical prices under a normal valuation model, and I estimate their implied volatility using BLACK SCHOLES implied volatility, do I'll get corresponding log normal volatility? 933 views ### Question about Merton model to estimate default probability and recovery rate of the company I recently come across Merton's model to estimate the default probability and recovery rate of the company. Here is the inputs ... 269 views ### Distribution of realized volatility for stock prices from a GBM If you generate random stock price paths according to a GBM with daily increments, what will be the distribution of the realized volatility? Assume that the realized volatility is measured over daily ... 12 views ### Option Delta Calculation - Local Vol Model vs Black-Scholes Model I am looking to get the greeks for option chain. Which model does work better for greeks calculation especially the delta. I am having issue with the Black-Scholes Model Delta since it always ... 18 views 30 views ### Derivation of Black-Scholes for a derivative on a stock that pays continuous dividends, and the derivative pays continuous cashflows I need help with the derivation of Black-Scholes PDE. The condition is that the derivative is written on a stock that pays dividends continuously (dividend yield D). Additionally, the derivative pays ... 30 views ### Calculating the risk free interest rate, or the continuously compounded yield on a T-bill, at any given time I'm working on a program using the Black-Scholes model to price options over time. I need to be able to derive the risk free interest rate, and found this while researching: In theory, r is a ... 44 views ### Delta hedging an option with earlier expiry The answer here states: For instance a volatility product that would expire at 10:42 am on a random day would be off term. One that expires at the same time than a major listed contract would ... 120 views 1k views ### Swaption : Bloomberg Black implied volatility quotes and pricing in the Black model I used a lot Bloomberg's VCUB for data, but never used its integrated swaption pricer "Quick Pricer for Swaptions", nor Bloomberg's "full" swaption pricer from "SWPM -OV". I am retrospectively quite ... 43 views ### How can I graph futures options profit/loss when the options have different underlyings? Consider a portfolio of vanilla SPX monthly options that consists of two components, a SEP 2019 3000 Call and a DEC 2019 3000 Call. It's easy to graph these as they both share the same independent ... 46 views ### Calculation of Conditional Expected Value and Pay-Off Diagram I have a stock with mu 6% and sigma 20% following a random walk and I would like to to calculate the Conditional expected Value of the stock in 10 states with equal probability (10%). Meaning, I would ... 63 views ### How is a LIBOR Market Model volatility skew determined? LIBOR based interest rates are derived from the prices (supply / demand) of swaptions, caps and floors. These prices are generally quoted in yield vols. Their prices are given by the Black formula. ... 131 views ### Different scaling conventions for greeks I have been following this tutorial (http://gouthamanbalaraman.com/blog/value-options-commodity-futures-black-formula-quantlib-python.html). It says in the conclusion and I quote:It is worth pointing ... 193 views ### Interpretation of drift parameter $\mu$ in GBM Currently studying Ito's calculus. Looking on the GBM model: $\frac{d S_t}{S_t} = μ dt + \sigma d B_t$ we end up on the expected stock price at time t: $E[S_t]=s_0 e^{\mu t}$.What does actually $\mu$ ... 1k views ### What is Dual Delta? I understand that it is the partial derivative of option price with respect to strike. What is it used for though? What does your dual delta signify? 141 views 177 views ### SPY American option Greeks and Premium I am trying to replicate Ivolatility.com's option calculator for a client. Here's the example Using standard Black Scholes model, I can replicate the exact calculations if there is no dividend. With ... Is there a way to go from this $$\ln S_t=\ln S_0+(\mu-\sigma^2/2)t+\sigma W_t$$ $$\ln S_t\sim N[\ln S_0+(\mu-\sigma^2/2)t, (\sigma^2)t]$$ To the Black-Scholes partial differential equation?
1,319
5,769
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.90625
3
CC-MAIN-2020-16
latest
en
0.892624
http://www.c2.com/cgi/wiki?MathIsEasy
1,475,002,832,000,000,000
text/html
crawl-data/CC-MAIN-2016-40/segments/1474738661155.8/warc/CC-MAIN-20160924173741-00068-ip-10-143-35-109.ec2.internal.warc.gz
367,939,421
6,206
# Math Is Easy If we had a GOF style MathPatternLanguage, maybe, one day, not impossibly far in the future, a little girl will pull a doll off a toy store shelf, press her tummy, and hear, "MathIsEasy!". Is this achievable? If not, why not? Has the GOF made programming "easy"? No, so why should some similar idea somehow applied to mathematics make mathematics easy? Patterns have made understanding programming much easier. I remember describing an observer pattern to a bemused gaggle of junior programmers back in the day. It took a week for some of them to catch on. Now, of course, you can toss the thing off with a single word. Programming isn't easy, but it's a lot easier than math. Looking at the two activities side by side, it's not at all obvious why math should be so much harder. Its history isn't much longer. Its proofs aren't much more complex than programs. We know code is easily obfuscated; who's to say math isn't just obfuscated? Look, here's a concrete example: AlexanderAbian's "TheTheoryOfSetsAndTransfiniteArithmetic?" is a very, very easy book. It's still real math. A lot of the reason it's easy is Abian's superb English description of the contents. You can actually read the English without the symbology and get about 80% of the book. And then the meaning of the symbols is just obvious. If it can be done once, why can't it be done all the time? This is all quite silly. Some programming is easy, some is hard. Some math is easy, some is hard. Each can be very easy, and each can be very difficult. "Math is just obfuscated"? Please. Of course, a great deal of mathematics is written badly, just as a lot of programs are badly written. But much of the hardest mathematics is indeed very very hard. That is, hard for normal people such as you and I to understand. You cannot blame mathematics (and mathematicians) for your own failings, and hope for some "silver bullet". In the future, should we develop substantially better tools for explaining mathematics, more of us will be able more easily to understand more and more mathematics, should we want to, and be willing to put some effort into it. But much of it will remain very difficult, if only because of a kind of Parkinson's Law. I wonder if someone who apparently cannot understand the argument that the halting problem is undecidable, and apparently thinks he has found flaws in what is a pretty simple proof, has really "gotten" 80% of a book such as Abian's. Now now, that's not a fair direction you're going in. I agree with him that math is harder than it has to be, and could be improved. Of course, I'd also agree with you and others who say much of it is inherently difficult, but the two things can be true simultaneously. -- Doug Please. He didn't say just "math is harder than it has to be". He suggested some silver bullet panacea, which isn't even a silver bullet panacea for programming to begin with. And I'd like to see how a "pattern language" for mathematics could prevent the perverse misunderstanding of the proof that the Halting Problem is unsolvable that we find on GeneralHaltingProblemProblem. We can only pray that something could prevent such things. :-) Um, thanks for that, I think. I understand Turing's proof just fine but see no reason the thing can't be poked at, nor had fun with. Since I am no mathematician, and don't pretend any such thing, I won't be shamed by accusations of asking stupid questions. I'd be ashamed not to ask stupid questions. Anyway the links to Jacquette/Meinong that fell out of GHPP were unknown and useful to me, thanks much to mr squarebrackets, whoever he is. [[If you are saying your egregious misunderstandings of the proof of the unsolvability of the HaltingProblem are all feigned, that's okay. I am certain there are people who really do have these egregious misunderstandings, so it doesn't hurt to have a version of them up there, with explanation of why they are wrong, even if the author is just joking about it. Anyway, thank God you don't really believe the baloney you wrote! As for Jacquette, he is a useful example of a crackpot who really does think he has produced great, radical, solutions to something he cannot understand. He for one is not joking, I am pretty sure.]] I haven't had time to read him yet, but find intuitionism attractive for obvious reasons. So I'm grateful for the pointers, substanceless or not. As to feigning, no, that page started by stating that the argument was semi-humorous, and I expected holes to be poked without much trouble. It is ridiculous to expect that Turing's A-machine proofs are flawed when a great many excellent minds have had generations to find any such flaws. The argument was put up for my own education and for the entertainment value. I presumed that claiming Nobels in mathematics for ranty wiki pages was obviously self-deprecatory. Plainly I presumed wrong, mea culpa. [[No no! Don't read Jacquette unless you want to do research on cranks and error. If you can specify what is is what you are after, perhaps someone can provide a good reference]]. That's pretty much what I'm trying to do, but I need to lay down a lot of context before I can get at the core of my interest. ThereIsNoInfinity, ThereAreNoPoints, etc., are obviously cranky, or at least so left-field as to seem so, but I know of no straight math that goes there. [[A-machines? We are just talking about recursive functions, Turing Machines, etc., not "A-machines". In terms of computational power, there is no other kind of machine, save these machines augmented by oracles. And "Great minds" have not been examining the transparently correct proofs of the unsolvability problem for generations. The issue was closed virtually from the start]] You misunderstand me. I did not say "great minds". I said "excellent minds". Every undergrad that's exposed to the proof wrestles with it. Anyway I continue to assert that the proof is affected by FrameProblems, but this goes to its relevance to physical computers, not its validity in original context. As to C-Machines, please refer to the original Turing paper and let me know if you've heard that someone subsequently proved that either all C-Machines are O-Machines, or that all C-Machines are A-Machines, or that other computability proofs exist for C-Machines. As for panaceas, silver bullets, and so on, it's no crime to use a compelling WikiName to first see whether someone has not already done a math patterns book, and second draw folk out to try to explain why they think math should be hard; the parts I understand always seem easy to me, and the parts I don't always seem hard. From this it seems to me that it's not math that is hard, but reading math that is hard. If a MathPatternLanguage existed, I think it would help a lot. At least I think it would help me a lot. [["Math", really, is doing math, and this generally is going to be harder than just reading math. So comparatively speaking, you have it backwards: math is hard, reading math is easy. However, again, reading math could definitely be made easier than it is, possibly with something sort of like a pattern language. But that is not going to make reading math easy. There is also "writing math", which is going to be hard if you want "reading math" to be easier. ]] I like this distinction, but consider that far fewer people write than read anything - proofs, architectures, stories, you name it. All creative work is hard, but I believe MathIsHard, at least in the Barbie sense, because of the difficulty of reading it, not writing it. [[I doubt this. Maybe in each genre fewer people read than write, but "far fewer"? A lot of code is read only by its author. A lot of academic papers are probably only read by the reviewer (if that only cursorily), the author, and a few of his friends (if he is lucky). Poetry? All sorts of people write stuff they call "poetry" which at best, they can probably force a friend or two to read...] I can trivially prove a special case of a known general proof. But it's not creative for me to do this. I can write twaddle on wiki, but that's not creative either. So for the various items of code that are really just cut and paste parameterizations of well known patterns - it takes nothing creative to write them. And most stuff called poetry too. Consider, to bring an example close to home, Ward's original 300 line wiki-engine. Almost anyone can read it. And many can trivially adorn it with different feature sets. But no one else could create it. Stallman's GPL is another good example. And so on. Another example: the semi-excellent hippo school books WhoIsFourier and so on. These explain quite a lot of hard concepts by addressing them almost exclusively to junior high students. And also having them do the writing. The same bunch of brilliant pedagogues attempt to teach 16 human languages all at the same time. Apparently with success. The reason they started writing math/physics books is that one day it occurred to them that math is itself a human language. • Very interesting! Never heard of this before. The organization is "transnational college of lex" http://www.lexlrf.org/college/ . Book "Who is Fourier": ISBN 0-9643504-0-8 ; "Anyone can speak 7 languages!": (ISBN 0-9643504-0-8 ) -- link doesn't work because Amazon never heard of it (the link works when the hyphens are there), but ISBN seems to be correct; Barnes/Noble heard of it but says it's out of print; bookfinder says no one has a copy; is there a way to get it? Ah, found it at www.reiters.com, only ten bucks new, btw. They wrote other books as well, see web site. • Cool. For years I've thought that all subjects should be taught as history and these books seem to apply that idea. I've found that it's much easier for me to remember facts about math, physics, politics, etc., if I learn about the people who discovered/invented them. My favorite kinds of math hang off of stories about Cantor, Hilbert, Turing, Russell, Whitehead and Gödel. • Subjects taught as history lost me faster than anything else. I didn't want to know about the people, or their historical context. I wanted to see the ideas and to catch a glimpse of the genius. Telling me who did what turned me off. Each to his own. I have changed with age and now find it useful, but if I had been taught maths as history I would not now be doing a subject I still love. • Hmmm. I find I learn a word better when I know its etymology (word history) as well as its meaning and usage. I wonder if that is related? I think it depends on what you want done or what you mean by easy. We have super computers who can calculate several complex things at once. But what is the goal, before the wanting? I think easy could be one of those relative terms.. Precisely what you need to do? ;) If we had a GOF style MathPatternLanguage, maybe, one day, not impossibly far in the future, a little girl will pull a doll off a toy store shelf, press her tummy, and hear, "MathIsEasy!". Math is nothing but patterns. See AbstractAlgebra? and Calculus for 2 examples. • I think you are using "math" in the sense that mathematicians would call "arithmetic". There is a huge gulf between doing high school algebra (which mathematicians would call "arithmetic") and proving FermatsLastTheorem or the RiemannHypothesis?. These are not "nothing but patterns".
2,592
11,369
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.515625
3
CC-MAIN-2016-40
latest
en
0.963336
https://www.coursehero.com/file/6025558/e894a2i/
1,527,399,212,000,000,000
text/html
crawl-data/CC-MAIN-2018-22/segments/1526794868003.97/warc/CC-MAIN-20180527044401-20180527064401-00460.warc.gz
726,290,807
412,450
{[ promptMessage ]} Bookmark it {[ promptMessage ]} e894a2i # e894a2i - ENSC 460/894 Assignment 2(Feb 9 due Feb 16 2006 1... This preview shows page 1. Sign up to view the full content. ENSC 460/894 Assignment 2: (Feb 9 due Feb. 16 2006) 1 For a ND:Yag laser calculate the ratio of the spontaneous radiation coefficient to the stimulated coefficient (Nd:YAG wavelength is 1064 nm). (5 marks) 2 A bi-concave lens of f = -30 mm is mounted 110 mm in front of a plan- convex lens of radius 60 mm, n = 1.5 and is looking at a 3 mm integrated circuit located 30 mm in front of the device. Using the both the combined lens formulas and matrix methods give the position and magnification of the resulting image. Draw a sketch with those locations. What is the focal length of the equivalent lens and where is it located? (10 marks) 3 A Huygens eyepiece (occular) is a combination of two positive thin lenses of the same glass. If the lenses are separated by half the sum of their focal lengths then chromatic aberration is eliminated. Assume two thin lenses of f=2.1 cm (field lens - furthest from the eye) and 1.5 cm (eye lens - closest to the user). Use both matrix methods and combined lens formula to solve this question. This is the end of the preview. Sign up to access the rest of the document. {[ snackBarMessage ]} ### What students are saying • As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students. Kiran Temple University Fox School of Business ‘17, Course Hero Intern • I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero. Dana University of Pennsylvania ‘17, Course Hero Intern • The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time. Jill Tulane University ‘16, Course Hero Intern
551
2,260
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.234375
3
CC-MAIN-2018-22
latest
en
0.915571
https://www.lmfdb.org/EllipticCurve/Q/97104/bb/6
1,611,761,937,000,000,000
text/html
crawl-data/CC-MAIN-2021-04/segments/1610704828358.86/warc/CC-MAIN-20210127152334-20210127182334-00508.warc.gz
830,353,500
28,566
Properties Label 97104.bb6 Conductor $97104$ Discriminant $-4.171\times 10^{20}$ j-invariant $$\frac{6359387729183}{4218578658}$$ CM no Rank $0$ Torsion structure $$\Z/{2}\Z$$ Related objects Show commands for: Magma / Pari/GP / SageMath Minimal Weierstrass equation sage: E = EllipticCurve([0, -1, 0, 1784768, -351612032]) gp: E = ellinit([0, -1, 0, 1784768, -351612032]) magma: E := EllipticCurve([0, -1, 0, 1784768, -351612032]); $$y^2=x^3-x^2+1784768x-351612032$$ Mordell-Weil group structure $$\Z/{2}\Z$$ Torsion generators sage: E.torsion_subgroup().gens() gp: elltors(E) magma: TorsionSubgroup(E); $$\left(193, 0\right)$$ Integral points sage: E.integral_points() magma: IntegralPoints(E); $$\left(193, 0\right)$$ Invariants sage: E.conductor().factor()  gp: ellglobalred(E)[1]  magma: Conductor(E); Conductor: $$97104$$ = $$2^{4} \cdot 3 \cdot 7 \cdot 17^{2}$$ sage: E.discriminant().factor()  gp: E.disc  magma: Discriminant(E); Discriminant: $$-417080252167792238592$$ = $$-1 \cdot 2^{13} \cdot 3^{16} \cdot 7^{2} \cdot 17^{6}$$ sage: E.j_invariant().factor()  gp: E.j  magma: jInvariant(E); j-invariant: $$\frac{6359387729183}{4218578658}$$ = $$2^{-1} \cdot 3^{-16} \cdot 7^{-2} \cdot 97^{3} \cdot 191^{3}$$ Endomorphism ring: $$\Z$$ Geometric endomorphism ring: $$\Z$$ (no potential complex multiplication) Sato-Tate group: $\mathrm{SU}(2)$ BSD invariants sage: E.rank()  magma: Rank(E); Analytic rank: $$0$$ sage: E.regulator()  magma: Regulator(E); Regulator: $$1$$ sage: E.period_lattice().omega()  gp: E.omega[1]  magma: RealPeriod(E); Real period: $$0.095618868057713967226651466147$$ sage: E.tamagawa_numbers()  gp: gr=ellglobalred(E); [[gr[4][i,1],gr[5][i][4]] | i<-[1..#gr[4][,1]]]  magma: TamagawaNumbers(E); Tamagawa product: $$32$$  = $$2\cdot2\cdot2\cdot2^{2}$$ sage: E.torsion_order()  gp: elltors(E)[1]  magma: Order(TorsionSubgroup(E)); Torsion order: $$2$$ sage: E.sha().an_numerical()  magma: MordellWeilShaInformation(E); Analytic order of Ш: $$4$$ = $2^2$ (exact) Modular invariants Modular form 97104.2.a.bb sage: E.q_eigenform(20) gp: xy = elltaniyama(E); gp: x*deriv(xy[1])/(2*xy[2]+E.a1*xy[1]+E.a3) magma: ModularForm(E); $$q - q^{3} + 2q^{5} - q^{7} + q^{9} - 4q^{11} + 6q^{13} - 2q^{15} + 4q^{19} + O(q^{20})$$ sage: E.modular_degree()  magma: ModularDegree(E); Modular degree: 3932160 $$\Gamma_0(N)$$-optimal: no Manin constant: 1 Special L-value sage: r = E.rank(); sage: E.lseries().dokchitser().derivative(1,r)/r.factorial() gp: ar = ellanalyticrank(E); gp: ar[2]/factorial(ar[1]) magma: Lr1 where r,Lr1 := AnalyticRank(E: Precision:=12); $$L(E,1)$$ ≈ $$3.0598037778468469512528469167052074226$$ Local data This elliptic curve is not semistable. There are 4 primes of bad reduction: sage: E.local_data() gp: ellglobalred(E)[5] magma: [LocalInformation(E,p) : p in BadPrimes(E)]; prime Tamagawa number Kodaira symbol Reduction type Root number ord($$N$$) ord($$\Delta$$) ord$$(j)_{-}$$ $$2$$ $$2$$ $$I_5^{*}$$ Additive -1 4 13 1 $$3$$ $$2$$ $$I_{16}$$ Non-split multiplicative 1 1 16 16 $$7$$ $$2$$ $$I_{2}$$ Non-split multiplicative 1 1 2 2 $$17$$ $$4$$ $$I_0^{*}$$ Additive 1 2 6 0 Galois representations The image of the 2-adic representation attached to this elliptic curve is the subgroup of $\GL(2,\Z_2)$ with Rouse label X217. This subgroup is the pull-back of the subgroup of $\GL(2,\Z_2/2^4\Z_2)$ generated by $\left(\begin{array}{rr} 7 & 7 \\ 0 & 3 \end{array}\right),\left(\begin{array}{rr} 3 & 0 \\ 8 & 3 \end{array}\right),\left(\begin{array}{rr} 7 & 0 \\ 0 & 7 \end{array}\right),\left(\begin{array}{rr} 1 & 0 \\ 0 & 3 \end{array}\right)$ and has index 48. sage: rho = E.galois_representation(); sage: [rho.image_type(p) for p in rho.non_surjective()] magma: [GaloisRepresentation(E,p): p in PrimesUpTo(20)]; The mod $$p$$ Galois representation has maximal image $$\GL(2,\F_p)$$ for all primes $$p$$ except those listed. prime Image of Galois representation $$2$$ B $p$-adic data $p$-adic regulators sage: [E.padic_regulator(p) for p in primes(5,20) if E.conductor().valuation(p)<2] All $$p$$-adic regulators are identically $$1$$ since the rank is $$0$$. Iwasawa invariants $p$ Reduction type $\lambda$-invariant(s) $\mu$-invariant(s) 2 3 7 17 add nonsplit nonsplit add - 0 0 - - 0 0 - All Iwasawa $\lambda$ and $\mu$-invariants for primes $p\ge 3$ of good reduction are zero. An entry - indicates that the invariants are not computed because the reduction is additive. Isogenies This curve has non-trivial cyclic isogenies of degree $$d$$ for $$d=$$ 2, 4 and 8. Its isogeny class 97104.bb consists of 4 curves linked by isogenies of degrees dividing 8. Growth of torsion in number fields The number fields $K$ of degree less than 24 such that $E(K)_{\rm tors}$ is strictly larger than $E(\Q)_{\rm tors}$ $\cong \Z/{2}\Z$ are as follows: $[K:\Q]$ $E(K)_{\rm tors}$ Base change curve $K$ $2$ $$\Q(\sqrt{-2})$$ $$\Z/2\Z \times \Z/2\Z$$ Not in database $2$ $$\Q(\sqrt{17})$$ $$\Z/4\Z$$ Not in database $2$ $$\Q(\sqrt{-34})$$ $$\Z/4\Z$$ Not in database $4$ $$\Q(\sqrt{-2}, \sqrt{17})$$ $$\Z/2\Z \times \Z/4\Z$$ Not in database $4$ $$\Q(\sqrt{7}, \sqrt{17})$$ $$\Z/8\Z$$ Not in database $4$ $$\Q(\sqrt{-14}, \sqrt{17})$$ $$\Z/8\Z$$ Not in database $8$ 8.0.3364400907943936.39 $$\Z/2\Z \times \Z/4\Z$$ Not in database $8$ 8.0.1401249857536.17 $$\Z/8\Z$$ Not in database $8$ 8.0.13142191046656.5 $$\Z/2\Z \times \Z/8\Z$$ Not in database $8$ 8.4.2575869445144576.1 $$\Z/16\Z$$ Not in database $8$ Deg 8 $$\Z/6\Z$$ Not in database $16$ Deg 16 $$\Z/4\Z \times \Z/4\Z$$ Not in database $16$ Deg 16 $$\Z/2\Z \times \Z/8\Z$$ Not in database $16$ Deg 16 $$\Z/16\Z$$ Not in database $16$ Deg 16 $$\Z/16\Z$$ Not in database $16$ Deg 16 $$\Z/2\Z \times \Z/16\Z$$ Not in database $16$ Deg 16 $$\Z/2\Z \times \Z/6\Z$$ Not in database $16$ Deg 16 $$\Z/12\Z$$ Not in database $16$ Deg 16 $$\Z/12\Z$$ Not in database We only show fields where the torsion growth is primitive. For fields not in the database, click on the degree shown to reveal the defining polynomial.
2,339
6,072
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.15625
3
CC-MAIN-2021-04
latest
en
0.208827
https://www.lidolearning.com/questions/m-bb-selina7-ch12-ex12d-q12/q12a-man-has-x-from-which-he-s/
1,600,413,505,000,000,000
text/html
crawl-data/CC-MAIN-2020-40/segments/1600400187354.1/warc/CC-MAIN-20200918061627-20200918091627-00053.warc.gz
1,279,264,779
10,947
Selina solutions # Question 12 Q12)A man has ₹ x from which he spends ₹6. If twice of the money left with him is ₹86, find x. Solution : Let the total amount be x According to the condition, 2x=86 ⇒x=\frac{86}{2} ⇒x=43 Amount spent by him = ₹6 ∴Total money he have = ₹43 + ₹6 = ₹49 Want to top your mathematics exam ? Learn from an expert tutor. Lido Courses Race To Space Teachers Syllabus Maths | ICSE Maths | CBSE Science | ICSE Science | CBSE English | ICSE English | CBSE Terms & Policies NCERT Syllabus Maths Science Selina Syllabus Maths Physics Biology Allied Syllabus Chemistry
192
611
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.296875
3
CC-MAIN-2020-40
latest
en
0.850855
http://www.jiskha.com/display.cgi?id=1297648537
1,496,058,667,000,000,000
text/html
crawl-data/CC-MAIN-2017-22/segments/1495463612283.85/warc/CC-MAIN-20170529111205-20170529131205-00470.warc.gz
689,172,808
3,637
# economics posted by on . Suppose you wish to invest X dollars in a bank account which pays 5% per year. You want to use this account to pay for costs that appear each year, starting with year 15. The amount you have to pay in year 15 is 276.71 and then the payments grow at a rate of 5% per year until year 38. If you wish to have exactly 1/11 of the amount X left in the account at the end of year 38, what should X be ?
114
425
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.921875
3
CC-MAIN-2017-22
latest
en
0.957993
https://www.teacherspayteachers.com/Product/Solving-Multi-Step-Inequalities-Practice-Activity-2511884
1,500,688,529,000,000,000
text/html
crawl-data/CC-MAIN-2017-30/segments/1500549423839.97/warc/CC-MAIN-20170722002507-20170722022507-00278.warc.gz
843,630,310
30,148
# Main Categories Total: \$0.00 Whoops! Something went wrong. # Solving Multi Step Inequalities Practice Activity Product Description Multi Step Inequalities: These multi step inequalities cootie catchers are a great way for students to have fun while they practice their skills with algebra and number lines through multi step inequalities. How to Play and Assembly Instructions are included. Multi Step Inequalities Cootie Catchers Contents: There are 2 cootie catchers in this product, each one having 8 problems for a total of 16 problems. Each problem has students solve the inequality and graph the result on a number line. Step-by-Step answers are provided for each problem. Important: If you enjoyed this product, check out my other Math Cootie Catchers: Grades 1-3: Get all 19 (35% OFF) in the Bundle! ♦ Addition and Subtraction: 2 Digit ♦ Addition: 3 Digit ♦ Arrays ♦ Balancing Equations ♦ Coins ♦ Estimating Sums ♦ Expanded Form ♦ Fact Families: Addition and Subtraction ♦ Greater Than Less Than ♦ Long Division ♦ Multiplication Word Problems ♦ Number Bonds Word Problems ♦ Skip Counting ♦ Subtraction ♦ Subtraction: Double Digit ♦ Time to the Half Hour ♦ Time to the Hour Grades 3-5: Get all 39 (50% OFF) in the Bundle! ♦ Balancing Equations ♦ Capacity ♦ Decimals: Addition and Subtraction ♦ Comparing Decimals ♦ Decimals: Multiplication and Division ♦ Decimals: Rounding Decimals ♦ Elapsed Time ♦ Expanded Form ♦ Exponents ♦ Fact Families: Multiplication and Division ♦ Factors ♦ Factors and Multiples ♦ Fractions: Comparing Fractions ♦ Fractions: Multiplication and Division ♦ Fractions: Simplification ♦ Fractions: Word Problems ♦ Fractions on a Number Line ♦ Greater Than Less Than ♦ Greatest Common Factors ♦ Least Common Multiple ♦ Long Division (Grade 4) ♦ Long Division (Grade 5) ♦ Mean, Median, Mode, and Range ♦ Metric Measurement ♦ Mixed Numbers: Addition and Subtraction ♦ Multiplication: 2 Digit ♦ Multiplication: Multi Digit ♦ Multiplication: Word Problems ♦ Number Patterns ♦ Order of Operations ♦ Percents ♦ Place Value ♦ Prime and Composite Numbers ♦ Prime Factorization ♦ Probability ♦ Properties of Multiplication ♦ Rounding ♦ Word Problems: Two Step ♦ Word Problems: Multi Step Grades 6-8: Get all 14 (35% OFF) in the Bundle! ♦ Converting Customary Measurements ♦ Fractions: Addition and Subtraction ♦ Fractions, Decimals, and Percents ♦ Fractions: Equivalent Fractions ♦ Fractions: Reducing Fractions ♦ Greater Than Less Than ♦ Improper Fractions and Mixed Numbers ♦ Integers: Addition and Subtraction ♦ Integers: Multiplication and Division ♦ Operations with Fractions ♦ Rational Numbers: Addition and Subtraction ♦ Rational Numbers: Multiplication and Division ♦ Ratios ♦ Simple Interest Geometry: Get all 16 (35% OFF) in the Bundle! ♦ 3D Shapes ♦ Angle Pair Relationships ♦ Area ♦ Area of a Circle ♦ Area of Composite Figures ♦ Circumference of a Circle ♦ Missing Angles ♦ Perimeter ♦ Polygons ♦ Pythagorean Theorem ♦ Surface Area of Rectangular Prisms ♦ Volume and Surface Area of Cylinders ♦ Volume of Cones ♦ Volume of Rectangular Prisms ♦ Volume of Triangular Prisms Algebra: Get all 18 (35% OFF) in the Bundle! ♦ Absolute Value ♦ Combining Like Terms ♦ Distributive Property ♦ Evaluating Expressions ♦ Inequalities: One, Two, and Multi Step ♦ Linear Equations ♦ Multi Step Equations ♦ One Step Equations ♦ Polynomials: Addition and Subtraction ♦ Polynomials: Multiplication and Division ♦ Proportions ♦ Scientific Notation ♦ Simplifying Expressions ♦ Slope ♦ System of Equations ♦ Two Step Equations ♦ Writing Expressions ======================================================== Customer Tips: How to get TPT credit to use on future purchases: Go to your "My Purchases" page. Beside each purchase you will see a "Provide Feedback" button. On your "My Purchases" page, you will see a list of products you have purchased and a link to provide feedback. Remember, you earn TPT credits to use to purchase other products. These credits are just like cash! So please leave a feedback review, it would be much appreciated :) I ♥ Followers! Be the first to know about store discounts, free products, and product launches! Just click the green “Follow Me” star under my store name on this page or click the “Follow Me” star under Science Spot. The Planet Mercury: A Solar System Tour *** Please Visit My Store or any of my specific topics/ categories: *** Anatomy----------- Burns & skin Pathology, Heart, Muscle, Nerves Animals------------ Reptiles, Amphibians, Dogs, Insects, Rainforest & Desert Animals Astronomy-------- Space, Solar System, Constellations, Moon Phases, Seasons, Planets Biology------------- Fossil record, Cell Organelles, Evolution, Lab Experiments Chemistry---------- Scientific Method, States of Matter, The Elements Earth Science----- Weather, Clouds, Landforms, Rock cycle, Water Cycle, Earthquakes Experiments------- Scientific Method, Cells, Plants, Water Games-------------- Jeopardy, Money Wheel, Are You Smarter Than a 5th Grader? Holidays------------ Easter, Spring, Mother's Day, Halloween Life Science-------- Plants & Flowers, Biomes, Photosynthesis, Plants life cycle, Biomes Mythology---------- Greek & Roman Gods, Planets, Halloween Other----------------- Back to School, Ice Breakers Physical Science-- States of Matter, Waves, Energy, Element, Compound & Mixture Science Projects-- Science Fair Bacteria Experiment Literacy-------------- Telling time, Reading comprehension w/ Bloom's Taxonomy Math------------------ Graphing, Decimals, Percents, Improper & Equivalent Fractions ~Lessons Only by Science Spot ======================================================== This purchase is for you and your classroom. Duplication for an entire school, an entire school system, or for commercial purposes is strictly forbidden. Please have other teachers purchase their own copy. If you are a school or district interested in purchasing several licenses, please contact me for a district-wide quote. Total Pages 3 pages Included Teaching Duration N/A Report this Resource • Comments & Ratings • Product Q & A \$3.00 \$3.00
1,562
6,106
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.765625
4
CC-MAIN-2017-30
latest
en
0.856094
http://www.infobarrel.com/Deductive_and_Inductive_Reasoning
1,604,024,385,000,000,000
text/html
crawl-data/CC-MAIN-2020-45/segments/1603107906872.85/warc/CC-MAIN-20201030003928-20201030033928-00398.warc.gz
145,000,419
15,132
Deductive and Inductive Reasoning Deductive Reasoning: The Definition, the Process I was first introduced to the idea of deductive reasoning my freshman year of college in a psychology class.  After many years passing, I had forgotten about the concept until Dr. Beach reiterated the definition while explaining this assignment.  After doing some brief research online I found the exact definition of deductive reasoning.  According to the website socialresearchmethods.net deductive reasoning is the process of working from the broad to the more precise (Trochim, 2006).  This type of reasoning is often referred to as the top-down approach (W. Beach, personal communication, February 28, 2008).  After my online search I decided to look at the Research Design textbook for a detailed explanation of deductive reasoning.  Creswell (2003) explains deductive reasoning is used with the quantitative research method.  The deductive process starts with a test or verification of a theory, moves to a test of the hypothesis, then defines and operationalizes the variables and concludes with measure or observation of the variables with an instrument to get scores (Creswell, 2003).  After my research I concluded deductive reasoning involves developing a theory and testing it to confirm the theory’s validity. Inductive Reasoning: The Definition, the Process My research on inductive reasoning showed the definition to be just the opposite of deductive reasoning.  Trochim (2006) defines inductive reasoning as moving from the precise to the broad.  This approach is often referred to as bottom-up (W. Beach, personal communication, February 28, 2008).   Creswell (2003) explains inductive logic is used in the qualitative research method.  The inductive process starts with the researcher gathering information, open ended questions are asked, then an analysis of data occurs, patterns are examined and then a broad generalization is made (Creswell, 2003).  After my research I concluded inductive reasoning involves observing first and developing a theory from your observation. Inductive and Deductive Reasoning: Similar or Different? Further research on Trochim’s (2006) website led me to find the similarities and differences between inductive and deductive reasoning.   Inductive and deductive reasoning are the same because they involve the same three major parts.  They both have a theory, a hypothesis and an observation (Trochim, 2006).  They are different because inductive reasoning has pattern, and deductive reasoning involves a confirmation (Trochim, 2006).  The most distinctive differences between the two reasonings are their orders.  Inductive reasoning starts with an observation, which develops a pattern, that helps form the hypothesis and concludes with a theory (Trochim, 2006).  Deductive reasoning starts with a theory, which develops into a hypothesis, then an observation is made which gives a confirmation (Trochim, 2006). Inductive and Deductive Reasoning in Gorham and Millette’s article and Dobo’s article Gorham and Millette (1997) used the qualitative method; therefore they used inductive reasoning in their article. Gorham and Millette (1997) worked from the bottom up by first asking open-ended questions about student and teacher motivation to teachers, and collecting the data.  Then they specifically looked for patterns and similarities when they compared their results to past studies on student and teacher motivation. Gorham and Millette (1997) concluded by making the generalization that “people who are ‘motivated’ to achieve a specific goal will be ‘motivated’ to choose to do things that will achieve that goal” (Gorham & Millette, 1997, p. 245). Dobo’s (1996) article used the quantitative method so she used deductive reasoning in her argument.  Dobos worked from the top down by first hypothesizing “students’ pre-session communication expectations and communication apprehension relative to the other group members can influence the extent to which the task experience is self-rewarding or intrinsically motivating for the individual student” (Dobos, 1996, p. 119). Then she tested her hypothesis by examining student interaction in different group activities.  Finally Dobos (1996) did a statistical analysis to conclude. Discussion Questions Throughout my research on theories and methods I was concerned there were parts I was leaving out that were significant to proving my points.  I am not sure if my definition of theories is complete enough for the communication field.  Is the definition of theory the same as the definition of theory in communication?  My research proved this to be true, but I concluded this from an amateur perspective on communication. Another major concern I had was with the quality of my method explanation.  The Research Design textbook had three chapters on different methods used in communication.  This literature consists of less than one page explaining what method is and how it is used.  Does my explanation of methods include enough information to be sufficient? Methods seem to be so multifaceted that it is difficult to include and understand every detail needed to prove a definition complete. Flaws and Implications for the Future Flaws in this literature could be due to the examination of new information from an amateur perspective.  The definitions of theories and methods may not be as complete as need be for sufficient research.  A more in depth study of what communication theory and method are could be conducted.  It might be helpful to ask communication scholars for their definitions and explanations of theories and methods.  A communication scholar could give information about theories and methods from an experienced level because they have applied these concepts to real research. Other flaws occurring in this literature could be due to the fact that a limited amount of articles were examined.  In the future, a greater number of articles could be compared and analyzed to make the points addressed stronger.  Also, the articles could be analyzed in more depth.  This literature did not dig deep into the articles.  It only skimmed the surface of the articles by looking at key words, explaining the methods they used and briefly mentioning if the methods used were effective in proving the theories.  This literature could talk more about why each article was effective. This assignment gave me the opportunity to explore how and why research is conducted in the communication field.  The information that I have found on theories and methods will stay with me throughout my studies in graduate school, and beyond.  I now have a foundation for all the articles I have been reading and will read in the future.  This assignment will be a good resource to use as I read articles throughout graduate school.
1,371
6,835
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.734375
3
CC-MAIN-2020-45
latest
en
0.9234
https://testbook.com/objective-questions/ml/mcq-on-pressure-vessels--5eea6a0b39140f30f369deb3
1,674,820,139,000,000,000
text/html
crawl-data/CC-MAIN-2023-06/segments/1674764494976.72/warc/CC-MAIN-20230127101040-20230127131040-00815.warc.gz
583,995,240
79,132
# Pressure Vessels MCQ Quiz in मल्याळम - Objective Question with Answer for Pressure Vessels - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക Last updated on Oct 27, 2022 നേടുക Pressure Vessels ഉത്തരങ്ങളും വിശദമായ പരിഹാരങ്ങളുമുള്ള മൾട്ടിപ്പിൾ ചോയ്സ് ചോദ്യങ്ങൾ (MCQ ക്വിസ്). ഇവ സൗജന്യമായി ഡൗൺലോഡ് ചെയ്യുക Pressure Vessels MCQ ക്വിസ് പിഡിഎഫ്, ബാങ്കിംഗ്, എസ്എസ്‌സി, റെയിൽവേ, യുപിഎസ്‌സി, സ്റ്റേറ്റ് പിഎസ്‌സി തുടങ്ങിയ നിങ്ങളുടെ വരാനിരിക്കുന്ന പരീക്ഷകൾക്കായി തയ്യാറെടുക്കുക ## Top Pressure Vessels MCQ Objective Questions #### Pressure Vessels Question 1: If a thick cylindrical shell is subjected to internal pressure, then hoop stress, radial stress and longitudinal stress at point in the thickness will be: 1. Tensile, compressive and compressive respectively 2. All compressive 3. All tensile 4. Tensile, compressive and tensile respectively #### Answer (Detailed Solution Below) Option 4 : Tensile, compressive and tensile respectively #### Pressure Vessels Question 1 Detailed Solution Explanation: In thick cylinders, the thickness of the shell is sufficiently large that stress variation along the thickness is also important. In case of thick cylinders, due to internal pressure, the three principal stresses acting at a point are: • Radial stress which is compressive • Circumferential stress or hoop stress which is tensile, and • Longitudinal Stress which is also tensile #### Pressure Vessels Question 2: A thin-walled cylinder with closed ends for which inner radius is 0.50 meter and outer radius is 0.52 meter, is subjected to internal pressure 2 MPa. The absolute maximum shearing stress on the inner surface of the cylinder shall be 1. 37.5 MPa 2. 75 MPa 3. 26 MPa 4. 24 MPa #### Answer (Detailed Solution Below) Option 3 : 26 MPa #### Pressure Vessels Question 2 Detailed Solution Concept: Hoop stress is, $$\sigma _1=\frac{Pd}{2t}$$ Longitudinal stress is, $$\sigma _2=\frac{Pd}{4t}$$ Radial stress is, $$\sigma _3=0$$ And the Absolute maximum shear stress is, $$\tau _m=\frac{\sigma _1-\sigma _3}{2}=\frac{Pd}{4t}$$ Calculation: Given: d = 0.5 × 2 = 1 m = 1000 mm, P = 2 MPa, t = 0.52 - 0.5 = 0.02 m = 20 mm Therefore, $${\tau _{max}} = \frac{{2 ~\times~ 1000}}{{4~×~ 20}} = 25\;MPa$$ As, in option 25 MPa is not available so we need to choose more stress than 25 MPa. #### Pressure Vessels Question 3: Lame’s equations are applicable for 1. Thick cylinder 2. Thin cylinder 3. Beams 4. Thin spherical vessel #### Answer (Detailed Solution Below) Option 1 : Thick cylinder #### Pressure Vessels Question 3 Detailed Solution Explanation Lame's equation is used to find the thickness of the thick cylinder subjected to internal pressure, it is given by, $$t = \frac{{{D_i}}}{2}\left[ {\sqrt {\frac{{{\sigma _t} + {P_i}}}{{{\sigma _t} - {P_i}}}} - 1} \right]$$ Where, t = thickness of thick cylinder, D= Internal diameter of the thick cylinder, σt = Allowable tensile stress in the material of thick cylinder, P= Internal pressure in the thick cylinder Important Points • Lame's equation is based on the maximum principal stress theory of failure, as this theory is more suitable for brittle materials, Lame's equation is also applicable to brittle materials like Cast iron or Cast Steel. Clavarino's equation is used to find the thickness of the cylinder when the material is ductile and the cylinder has closed ends, it is given by $$t = \frac{{{D_i}}}{2}\left[ {\sqrt {\frac{{{\sigma _t} + \left( {1 - 2μ } \right){P_i}}}{{{\sigma _t} - \left( {1 + μ } \right){P_i}}}} - 1} \right]$$ Birnie's equation is used to find the thickness of thick cylinders, which are made up of ductile material and has open ends, it is given by $$t = \frac{{{D_i}}}{2}\left[ {\sqrt {\frac{{{\sigma _t} + \left( {1 - μ } \right){P_i}}}{{{\sigma _t} - \left( {1 + μ } \right){P_i}}}} - 1} \right]$$ μ is the Poisson's ratio #### Pressure Vessels Question 4: When a thin cylinder shell is subjected to an internal pressure, there will be 1. A decrease in diameter and length of the shell 2. An increase in diameter and decrease in length of the shell 3. A decrease in diameter and increase in length of the shell 4. An increase in diameter and length of the shell #### Answer (Detailed Solution Below) Option 4 : An increase in diameter and length of the shell #### Pressure Vessels Question 4 Detailed Solution Explanation: When a thin cylindrical shell is subjected to an internal pressure, its wall be subjected to lateral strain, the effect of which there will be change in dimensions (i.e. length and diameter) of the shell. Thin cylinder pressure walls are subjected to two types of stresses which is: • Circumferential stress (force tending to rupture vessel circumferentially) • Longitudinal stress (force tending to rupture vessel longitudinally) Both the stresses are tensile in nature. It may be noted that when the shell is subjected to an internal pressure, there will be an increase in diameter as well as the length of the shell. #### Pressure Vessels Question 5: A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gauge pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is 1. 35 2. 70 3. 140 4. 280 Option 3 : 140 #### Pressure Vessels Question 5 Detailed Solution Explanation: Circumferential stress of hoop stress σh $${σ _1} ={σ _h} = \frac{{pd}}{{2t}} = \frac{{2 \times 14\;}}{{2 \times 0.05}} = 280MPa$$ Longitudinal stress σL $${σ _2} ={σ _L} = \frac{{pd}}{{4t}} = \frac{{2 \times 14\;}}{{4 \times 0.05}} = 140MPa$$ As this is the case of a thin cylinder: Radial stress $${σ _r} =0$$ Maximum shear stress $${τ _{max}} = \max \left\{ {\frac{{{\sigma _1} - {\sigma _2}}}{2},\frac{{{\sigma _1}}}{2},\frac{{{\sigma _2}}}{2}} \right\}$$ τmax  = $$\frac{{σ _h}-{σ _r}}{{2}}=\frac{{σ _1} }{2} = \frac{280}{2}=140~ MPa$$ Mistake Points Maximum In-Plane shear stress/Surface shear stress: $$τ_{max,inplane}=\frac{{σ _1}-{σ _2}}{{2}}$$ Maximum wall shear stress/Out plane shear stress/Absolute shear stress: $$τ_{max,abs}=\frac{{σ _{max}}-{σ _{min}}}{{2}}=\frac{σ_1}{2}$$ #### Pressure Vessels Question 6: A thin cylinder of diameter 100 mm with a wall thickness of 4 mm is subjected to an internal pressure p. It is also simultaneously compressed by an axial force of 50 kN. Find the maximum internal pressure (in N/mm2) allowable so that the maximum in-plane shear stress of the cylinder may not exceed 45 N/mm2. #### Pressure Vessels Question 6 Detailed Solution Concept: Circumferential stress: $${\sigma _h} = \frac{{Pd}}{{2t}}$$ Longitudinal stress: $${\sigma _L} = \frac{{Pd}}{{4t}}$$ Given: d = 100 mm, t = 4 mm, Pa = 50 kN, τmax = 45 MPa Calculation: A = πdt = π(100) (4) = 400 π mm2 $${\sigma _h} = \frac{{Pd}}{{2t}} = \frac{{p \times 100}}{{2 \times 4}} = 12.5p\,N/m{m^2}$$ $${\sigma _L} = \frac{{pd}}{{4t}} - \frac{{{P_a}}}{A} = \frac{{p \times 100}}{{4 \times 4}} - \frac{{50 \times 1000}}{{400\pi }}$$ σL = (6.25 p – 39.79) N/mm2 Maximum in-plane shear stress: $${\tau _{max}} = \frac{{{\sigma _h} - {\sigma _L}}}{2} = 45\,N/m{m^2}\\ \frac{{12.5p - \left[ {6.25p - 39.79} \right]}}{2} = 45$$ 6.25 p + 39.79 = 90 p = 8.034 N/mm2 #### Pressure Vessels Question 7: When a thin sphere of diameter ‘d’ and thickness ‘t’ is pressurized with an internal pressure of P, then the ratio of hoop strain to longitudinal strain is (μ is Poisson’s ratio and E is the modulus of elasticity) 1. $$\frac{{2 - \mu }}{{1 - 2\mu }}$$ 2. $$\frac{{1 - 2\mu }}{{2 - \mu }}$$ 3. 1 4.  2 μ Option 3 : 1 #### Pressure Vessels Question 7 Detailed Solution Concept: For thin sphere: Hoop stress (σH) = Longitudinal stress (σL) $${σ _h} = {σ _L} = \frac{{pd}}{{4t}}$$ Hoop strain (ϵH) = $$\frac{σ_h}{E}-\mu\frac{σ_L}{E}\Rightarrow\frac{pd}{4t}(1-\mu)$$ Longitudinal strain (ϵL) = $$\frac{σ_L}{E}-\mu\frac{σ_H}{E}\Rightarrow\frac{pd}{4t}(1-\mu)$$ Hoop strain = Longitudinal strain $$\therefore \frac{ϵ_H}{ϵ_L}=1$$ #### Pressure Vessels Question 8: The design of thin cylindrical shells is based on 1. Hoop stress 2. Longitudinal stress 3. Volumetric stress 4. Average of hoop and longitudinal loops. #### Answer (Detailed Solution Below) Option 1 : Hoop stress #### Pressure Vessels Question 8 Detailed Solution Concept: For thin cylinder: Hoop stress, $$\sigma_h=\frac{Pd}{2t}$$ and Longitudinal stress, $$\sigma_l=\frac{Pd}{4t}$$ i.e., Hoop stress = 2 ×  Longitudinal stress We see that the longitudinal stress is half of the circumferential or hoop stress. Therefore, the design of a pressure vessel must be based on the maximum stress i.e. hoop stress. #### Pressure Vessels Question 9: Internal and external radii of a thick cylinder are a and b. It is subjected to an internal pressure of pi. The radial stress at a radius r in the cylinder is 1. $$\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$$ 2. $$\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$$ 3. $$\frac{{{b^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$$ 4. $$\frac{{{b^2}{p_i}}}{{{b^2} - {a^2}}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$$ #### Answer (Detailed Solution Below) Option 2 : $$\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$$ #### Pressure Vessels Question 9 Detailed Solution Concept: • In the case of thin cylinders, the hoop stress is determined by assuming it to be uniform across the thickness of the cylinder but in thick cylinders, the hoop stress is not uniform across the thickness, it varies from a maximum value at the inner circumference to a minimum value at the outer circumference. • The radial pressure across the thin cylinder is neglected. Radial stress is given by Lame’s equation: $${\sigma_r} = \frac{{{C_1}}}{{{r^2}}} - {C_2}$$ Boundary condition: σr = pi, at r = a (inner radius) $$p_i=\frac{C_1}{a^2}-C_2$$ σr = 0, at r = b (outer radius) $$0=\frac{C_1}{b^2}-C_2$$ Determination of constant C1 and C2: From (i) and (ii), we get $$\frac{{{C_1}}}{{{a^2}}} - \frac{{{C_1}}}{{{b^2}}} = {p_i}$$ $${C_1} = {p_i}\left( {\frac{{{a^2} {b^2}}}{{{b^2} - {a^2}}}} \right)$$ Putting the value of C1 in (ii) we get, $${C_2} = \left( {\frac{{{p_i}{a^2}}}{{{b^2} - {a^2}}}} \right)$$ $${\sigma_r} = \frac{{{p_i}}}{{{r^2}}}\left( {\frac{{{a^2} {b^2}}}{{{b^2} - {a^2}}}} \right) - \left( {\frac{{{p_i} {a^2}}}{{{b^2} - {a^2}}}} \right)$$ $${\sigma_r} =- {\frac{{{p_i} {a^2}}}{{{b^2} - {a^2}}}} \left( {\frac{{{b^2}}}{{{r^2}}}-1} \right)$$ $${\sigma_r} = {\frac{{{p_i} {a^2}}}{{{b^2} - {a^2}}}} \left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$$ The negative sign represents the stress is compressive in nature. #### Pressure Vessels Question 10: A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure. The material of the cylinder has Young’s modulus E. Poisson’s ratio v, and coefficient of thermal expansion α. What is the minimum rise in temperature ΔT of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of p above the atmosphere? 1. $${\rm{\Delta }}T = \frac{{3vpr}}{{2\alpha tE}}$$ 2. $${\rm{\Delta }}T = \left( {v - \frac{1}{4}} \right)\frac{{pr}}{{\alpha tE}}$$ 3. $${\rm{\Delta }}T = \frac{{vpr}}{{\alpha tE}}$$ 4. $${\rm{\Delta }}T = \left( {v + \frac{1}{2}} \right)\frac{{pr}}{{\alpha tE}}$$ #### Answer (Detailed Solution Below) Option 3 : $${\rm{\Delta }}T = \frac{{vpr}}{{\alpha tE}}$$ #### Pressure Vessels Question 10 Detailed Solution Concept: When a thin-walled cylinder is subjected to internal fluid pressure then there are two stresses acting upon the cylinder Hoop stress in the circumferential direction $${\sigma _h} = \frac{{pr}}{t}$$ and longitudinal stress $${\sigma _l} = \frac{{pr}}{{2t}}$$ Where p is the internal pressure of the fluid in the cylinder above atmospheric pressure, r is the radius of the cylinder and t is the thickness of the cylinder. If the cylinder is open from the sides then longitudinal stress is zero. Strain due to these stress $${\epsilon_h} = \frac{1}{E}\left( {{\sigma _h} - \nu {\sigma _l}} \right)$$ $${\epsilon_l} = \frac{1}{E}\left( {{\sigma _l} - \nu {\sigma _h}} \right)$$ ν is Poisson’s ratio. Thermal strain due to temperature rise is given by ϵth = αΔT α is the coefficient of thermal expansion, ΔT is the change in temperature Calculation: It is given that both the ends of the cylinder are open therefore the longitudinal stress acting will be equal to zero. The longitudinal stress, σlong = 0 The strain in the longitudinal direction will be due to the hoop stress only. Now the temperature of the cylinder is increased by ΔT, then in order to avoid the leakage, the sum of strains due to increased temperature and the strain due to hoop stress (in the longitudinal direction) should be equal to zero. Therefore, ∴ ϵth + ϵl = 0 $${\epsilon_{th}} = \alpha \left( {{\rm{\Delta }}T} \right)$$ $${\epsilon_l} = \frac{1}{E}\left( {0 - \nu \frac{{pr}}{{t}}\;} \right)$$ $$\therefore \alpha \left( {{\rm{\Delta }}T} \right) + \left( {\frac{{ - vpr}}{{Et\;}}\;} \right) = 0\;\;\;$$ $${\rm{\Delta }}T = \frac{{vpr}}{{atE}}$$
4,672
13,409
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.21875
4
CC-MAIN-2023-06
latest
en
0.352705
https://www.physicsforums.com/threads/decomposing-vectors.830125/
1,571,880,663,000,000,000
text/html
crawl-data/CC-MAIN-2019-43/segments/1570987838289.72/warc/CC-MAIN-20191024012613-20191024040113-00179.warc.gz
1,030,389,568
17,688
# Decomposing vectors #### Mr Davis 97 1. Homework Statement The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector. 2. Homework Equations x = |R|cos(theta) 3. The Attempt at a Solution I am confused about what degrees to input into the cosine function. I know that the vector is pointing 35 degrees north of west, which means that the x component will be negative, but there are two ways I could do it am I am not sure which one I should do. First, I could tack on a negative and calculate -(6 m)cos35 = -4.9 m. Another way is not tack on a negative and calculate (6 m)cos145 = -4.9 m. Which method is better, and which one should I use on a regular basis? Related Introductory Physics Homework Help News on Phys.org #### Geofleur Gold Member Both ways are fine, as long as you don't try to memorize a rule and blindly apply it. Personally, I like the first approach, and just tack on the negative sign when I know there should be one. #### SteamKing Staff Emeritus Homework Helper 1. Homework Statement The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector. 2. Homework Equations x = |R|cos(theta) 3. The Attempt at a Solution I am confused about what degrees to input into the cosine function. I know that the vector is pointing 35 degrees north of west, which means that the x component will be negative, but there are two ways I could do it am I am not sure which one I should do. First, I could tack on a negative and calculate -(6 m)cos35 = -4.9 m. Another way is not tack on a negative and calculate (6 m)cos145 = -4.9 m. Which method is better, and which one should I use on a regular basis? Well, you could learn the angles for the cardinal points of the compass, but why do that when you can just make something up? East = 0° North = 90° West = 180° South = 270° #### Mr Davis 97 Well, you could learn the angles for the cardinal points of the compass, but why do that when you can just make something up? East = 0° North = 90° West = 180° South = 270° Huh? #### SteamKing Staff Emeritus Homework Helper You've never seen the following diagram (or a similar one)?: It should have been used when you studied trigonometry. After all, cos (0°) = 1.0 sin (0°) = 0.0 cos (90°) = 0.0 sin (90°) = 1.0 cos (180°) = -1.0 sin (180°) = 0.0 cos (270°) = 0.0 sin (270°)= -1.0 etc., etc. "Decomposing vectors" ### Physics Forums Values We Value Quality • Topics based on mainstream science • Proper English grammar and spelling We Value Civility • Positive and compassionate attitudes • Patience while debating We Value Productivity • Disciplined to remain on-topic • Recognition of own weaknesses • Solo and co-op problem solving
750
2,764
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.0625
4
CC-MAIN-2019-43
latest
en
0.940784
http://www.authorstream.com/Presentation/katiedulavitch-1475626-order-operations/
1,619,204,175,000,000,000
text/html
crawl-data/CC-MAIN-2021-17/segments/1618039596883.98/warc/CC-MAIN-20210423161713-20210423191713-00181.warc.gz
102,526,247
26,898
# Order of Operations Views: Category: Education ## Presentation Description No description available. ## Presentation Transcript ### PowerPoint Presentation: Ms. Dulavitch SOL 6.8 Math 6 Order of Operations ### PowerPoint Presentation: Using Order of Operations helps us decide which part of a problem to solve first. For example, in this problem, do you add 9 + 5 first or multiply 5 x 2 first? 9 + 5 x 2 Do you get the same answer either way? Order of Operations ### PowerPoint Presentation: 9 + 5 x 2 If you add 9 + 5 first, then multiply by 2, your final answer is 28. If you multiply 5 x 2 first, then add 9, your final answer is 19. Which answer is correct? Order of Operations ### PowerPoint Presentation: 9 + 5 x 2 Answer: 19 How do you know to multiply first? Does it work that way every time? Yes! If you use Order of Operations, you will follow the same steps for every problem and arrive at the correct answer. Order of Operations ### PowerPoint Presentation: We will use PEMDAS to help us remember the Order of Operations. P arentheses E xponents M ultiplication D ivision A ddition S ubtraction PEMDAS or or ### PowerPoint Presentation: First, solve every operation in P arentheses. Second, solve every E xponent. Third, solve M ultiplication and D ivision depending on which comes first left to right . Ex 1) 3 x 6 / 2 Multiply first, then divide. Ex 2) 10 / 2 x 3 Divide first, then multiply. PEMDAS ### PowerPoint Presentation: Fourth, solve A ddition and S ubtraction depending on which comes first left to right . Ex 1) 5 + 6 - 2 Add first, then subtract. Ex 2) 12 - 1 + 3 Subtract first, then add. Let’s try one together! PEMDAS ### PowerPoint Presentation: Keep PEMDAS in mind! First, solve everything in P arentheses. Our new problem says: Example 1 ### PowerPoint Presentation: Example 1 There are no E xponents in the problem, so we can skip that step. Next, we M ultiply or D ivide. Last, we A dd or S ubtract. ### PowerPoint Presentation: Let’s try another one! We can skip the P arentheses step. First, solve the E xponent. Example 2 ### PowerPoint Presentation: We skip M ultiplication and D ivision. Next, we S ubtract, since subtraction comes before addition in the problem. Last, we A dd. Example 2 ### PowerPoint Presentation: Now it’s your turn! Don’t forget to use PEMDAS! Check your work: Answer: O Practice 1 ### PowerPoint Presentation: Let’s try one more practice problem! Check your work: Answer: 12 Practice 2 ### PowerPoint Presentation: If you want some more practice before your quiz, check out the Math is Fun website. You can also watch this Order of Operations rap to help you learn the PEMDAS steps! More PEMDAS ### PowerPoint Presentation: For the following problem, which operation would you do first? A. Multiplication B. Division C. Addition D. Subtraction Quiz Question 1 ### PowerPoint Presentation: For the following problem, which operation would you do last? A. Multiplication B. Division C. Addition D. Subtraction Quiz Question 2 ### PowerPoint Presentation: Solve the problem using Order of Operations: A. 9 B. 13 C. 7 D. - 3 Quiz Question 3 ### PowerPoint Presentation: Solve the problem using Order of Operations: A. 24 B. 9 C. 4 D. 1 Quiz Question 4 ### PowerPoint Presentation: Why do you multiply before you divide in the following problem? A. Multiply comes before divide in PEMDAS. B. Multiplication comes first reading left to right. C. The Multiplication problem has an exponent with it. D. Actually, it doesn’t matter whether you multiply or divide first. You get the same answer. Quiz Question 5 Right Wrong ### PowerPoint Presentation: Microsoft Office Clipart- http://office.microsoft.com/en-us/images/ Creative Commons- http://creativecommons.org/ Order of Operations Math Rap [Video File] Retrieved from http://www.youtube.com/watch?v=d0xutl2sUt0 MathIsFun (2012). Order of Operations. Retrieved from http://www.mathsisfun.com/operation-order-pemdas.html Credits
978
3,984
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.875
5
CC-MAIN-2021-17
latest
en
0.783992
http://mymathforum.com/geometry/46869-parallel-projection-problem.html
1,563,957,204,000,000,000
text/html
crawl-data/CC-MAIN-2019-30/segments/1563195532251.99/warc/CC-MAIN-20190724082321-20190724104321-00291.warc.gz
103,330,607
9,380
My Math Forum A parallel projection problem Geometry Geometry Math Forum October 7th, 2014, 01:12 PM #1 Newbie   Joined: Feb 2014 Posts: 29 Thanks: 1 A parallel projection problem Parallel projection of the rectangle ABCD at the plane is the A1B1C1D1 polygon. Find CC1 if АА1=3 сm, ВВ1 = 4 сm, DD1= 6 сm. October 7th, 2014, 04:17 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,835 Thanks: 2162 Use AA1 + CC1 = BB1 + DD1. Thanks from Drasik October 8th, 2014, 08:55 AM #3 Newbie   Joined: Feb 2014 Posts: 29 Thanks: 1 Thanks! Makes sense to me. But how do I explain it? Is there a theorem or something? October 10th, 2014, 08:13 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,835 Thanks: 2162 As ABCD is a rectangle, AC and BD have a common midpoint. Consider what happens to AC and BD separately under the parallel projection. Apply the Midpoint Connector Theorem for Trapezoids. Thanks from Drasik October 11th, 2014, 07:08 AM #5 Newbie   Joined: Feb 2014 Posts: 29 Thanks: 1 Thank you! I got it now Tags parallel, problem, projection ### mathematical discription of a parallel projection Click on a term to search for related topics. Thread Tools Display Modes Linear Mode Similar Threads Thread Thread Starter Forum Replies Last Post Drasik Geometry 1 October 7th, 2014 06:25 AM zak100 Geometry 1 April 6th, 2014 08:55 AM Anamitra Palit Physics 3 December 6th, 2012 01:20 PM xzardaz Linear Algebra 0 February 3rd, 2012 03:47 AM velcrome Linear Algebra 0 April 28th, 2008 03:43 AM Contact - Home - Forums - Cryptocurrency Forum - Top
487
1,562
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.84375
3
CC-MAIN-2019-30
latest
en
0.881741
https://compmath.wordpress.com/sprouts/
1,679,843,385,000,000,000
text/html
crawl-data/CC-MAIN-2023-14/segments/1679296945473.69/warc/CC-MAIN-20230326142035-20230326172035-00479.warc.gz
223,232,589
27,065
# Research in Scientific Computing in Undergraduate Education ### Sprouts Sprouts is a two-person game invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in 1967. The game begins with a number of spots: Players take turns drawing a line -straight or curved – between existing spots, and adding a new spot in the middle of the new line: The rules are: • Lines must not touch or cross any line except at a designated spot. • No spot may have more than three lines attached to it. A line from a spot to itself counts as two attached lines and new spots are counted as having two lines already attached to them. • The player who makes the last move wins. The problem, for a given number of spots is to determine when the first player has a winning strategy, and when the second player has a winning strategy. It is conjectured that that the first player has a winning strategy when the number of spots is congruent to 3, 4, or 5, modulo 6. The complexity of analysis grows very rapidly with the initial number of spots. The misère form of the game is when the last player to move loses.
245
1,135
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.046875
3
CC-MAIN-2023-14
latest
en
0.96865
http://www.jiskha.com/members/profile/posts.cgi?name=Trevor&page=15
1,369,466,903,000,000,000
text/html
crawl-data/CC-MAIN-2013-20/segments/1368705618968/warc/CC-MAIN-20130516120018-00063-ip-10-60-113-184.ec2.internal.warc.gz
539,263,465
3,242
Saturday May 25, 2013 # Posts by Trevor Total # Posts: 164 Physics Velocity I think if it is a distance vs. Time graph, If it was a Velocity vs. Time graph then Acceleration. Physics A small plastic ball with a mass of 6.50x10^-3 kg and with a charge of +0.150x10^-6 C is suspended from an insulating thread and hangs between the plates of a capacitor. The ball is in equilibrium, whit the tread making an angle of 30 degrees with respect to the vertical. The ... Physics Two charges are placed between the plates of a parallel plate capacitor. One charge is +q1 and the other is q2= +5.00x10^-6 C . The charge per unit area on each plate has a magnitude of sigma=1.30 x 10^-4 C/m^2. The force on q1 due to q2 equals the force on q1 due to the elect... Physics Two charges are placed between the plates of a parallel plate capacitor. One charge is +q1 and the other is q2= +5.00x10^-6 C . The charge per unit area on each plate has a magnitude of sigma=1.30 x 10^-4 C/m^2. The force on q1 due to q2 equals the force on q1 due to the elect... Physics I did it the way you said to solve it and I got a number different than the correct answer. Physics A 2 kg pendulum bob is hanging from a 30 cm long piece of string. If the pendulum bob is allowed to move in circular motion in a horizontal plane, determine the tension in the string if the angle the string makes with the vertical is 37 degrees. Need Step by step solution. Physics How would I convert that to m/s Physics You have a 30g quarter on an old LP turntable at a radius of 30 cm from the turntable's center. If the coefficient of Friction between the coin and the turntable is 0.6, at what speed will the coin slide off the turntable? Hint: this is a circular motion problem. To find t... Physics NVM you are relating GPE for Horizontal to KE of Horizontal. Physics Is it vertical vs. Horizontal energy to get the Acceleration? Pages: <<Prev | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | Next>>
548
1,991
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.3125
3
CC-MAIN-2013-20
longest
en
0.907651
https://www.ceder.net/def/reflected.php?level=C3B&action=edit
1,709,455,553,000,000,000
text/html
crawl-data/CC-MAIN-2024-10/segments/1707947476211.69/warc/CC-MAIN-20240303075134-20240303105134-00849.warc.gz
684,394,407
6,402
Definitions of Square Dance Calls and Concepts FAQ  | Index -->  Plus  |  A1  |  A2  |  C1  |  C2  |  C3A  |  C3B  |  C4  |  NOL  | Definitions (Text Only) -->  Plus  |  A1  |  A2  |  C1  |  C2  |  C3A  |  C3B  |  C4  |  NOL  | Find call: Reflected Concept [C3B] (Clark Baker 1984) C3B: Language:  or From various formations. EN: 10 Do the any Tagging call (or any variation of a Tagging call) to the 1/2 Tag position; Tandem Arm Turn 1/4 (i.e., Split Counter Rotate 1/4); complete the any Tagging callEN: 20 Reflected Flip The Line: beforeReflected Flip The Line after1/2 Flip The Line afterTandem Arm Turn 1/4(Box Counter Rotate 1/4) after Complete The Flip The Line EN: 30 (done) Reflected Track 3: beforeReflected Track 3 afterTrack 2 afterTandem Arm Turn 1/4(Split Counter Rotate 1/4) afterExtend (done) Notes: • The general idea of Reflected is that you start the Tagging call and are moving in a straight Line, you hit some imaginary wall and get "bounced" or reflected off of it at a 90° angle and then you complete the call. EN: 40 • On calls such as Track 3 or Invert The Column , even though eight dancers are required to execute the call, the Tagging portion of the call only involves (2 sets of) 4 dancers. EN: 50 • The generalized definition of Reflected is to do the given call to the 1/2 Tag position; Counter Rotate 1/4 with respect to the number of dancers doing the Tagging portion of the call; complete the given call. EN: 60 Reflected Partner Tag: From a Couple or Mini-Wave. 1/4 In and Touch (this is a Partner 1/2 Tag); Arm Turn 1/4 (since there are only two people in the Tagging portion); Step Thru (to end Back-to-Back). EN: 70 Line of 6 Reflected Tag The Line: From a Line of 6. Line of 6 1/2 Tag; Tandems of 3 Arm Turn 1/4; all Complete The Tag to end in Back-to-Back Tandems of 3. EN: 80 Reflected Partner Tag: beforeReflected Partner Tag afterPartner 1/2 Tag afterArm Turn 1/4 afterStep Thru (done) Center Line Of 6 Reflected 1/2 Tag: beforeCenter Line of 6 Reflected 1/2 Tag afterCenter Line of 6 1/2 Tag afterCenter 6 Counter Rotate 1/4 (done)
695
2,095
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.671875
3
CC-MAIN-2024-10
latest
en
0.663247
http://listserv.uga.edu/cgi-bin/wa?A2=ind0206c&L=sas-l&D=0&P=41110
1,386,401,938,000,000,000
text/html
crawl-data/CC-MAIN-2013-48/segments/1386163053843/warc/CC-MAIN-20131204131733-00074-ip-10-33-133-15.ec2.internal.warc.gz
102,272,004
6,112
```Date: Thu, 20 Jun 2002 09:42:41 +0100 Reply-To: david.mcnulty@QUESTINTL.COM Sender: "SAS(r) Discussion" From: david.mcnulty@QUESTINTL.COM Subject: Re: Untenable results from PROC GENMOD Comments: To: Dale McLerran Content-type: text/plain; charset=us-ascii Good Morning Dale, Thankyou for a very comprehensive reply. I can also use the template bootstrapping data step for another problem that has been sitting on the shelf. Dave. Dale McLerran SAS-L@LISTSERV.UGA.EDU cc: 19/06/2002 18:44 Subject: Re: Untenable results from PROC GENMOD David, That does change the picture substantially! However, I do believe that there is still be a problem with including subject as a covariate. My guess is that there subjects who rate all 7 products employed in the analysis as a success/failure under both conditions. A logit cannot be computed for those subjects. I dummied up some data which demonstrates the situation that you report. data binary; do phase=1 to 2; beta1 = .75*(phase=1); do product=1 to 7; beta2 = .25*rannor(1234579); do subject=1 to 29; gamma = .5*rannor(1234579); eta = gamma + beta1 + beta2; p = exp(eta)/(1+exp(eta)); y = ranbin(1234579,1,p); output; end; /* Subject 30 will have all failures */ subject=30; gamma = -10; eta = gamma + beta1 + beta2; p = exp(eta)/(1+exp(eta)); y = ranbin(1234579,1,p); output; subject=31; gamma = .5*rannor(1234579); eta = gamma + beta1 + beta2; p = exp(eta)/(1+exp(eta)); y = ranbin(1234579,1,p); output; end; end; run; proc freq data=binary(where=(subject>=30)); tables y*subject; run; proc genmod data=binary; class subject phase product; model y = subject phase|product / dist=bin; lsmeans phase|product; run; Because subject 30 has all failures, inclusion of the subject effect in the model causes the subject 30 logit to be inestimable. When the point estimate for subject 30 went above 25, the change in model likelihood was sufficiently small for GENMOD to state that convergence was achieved. At this point, the variance for subject 30 was very large, which adversely affects the variance of the least squares means. In fact, the point estimate and variance for subject 30 should both be set to infinity, but that really cannot be done. Note that if you employed PROC LOGISTIC to fit the model, you would have gotten a statement that quasi-complete separation of the data points occurred and that model fit was questionable. So, the question is what can you do at this point? Some might suggest a GEE analysis. GEE's take into account the nonindependenc of the responses among subjects who have multiple observations. This is what you are attempting to do when you include subject as a covariate. But GEE's do not require that you obtain a subject effect estimate. The syntax below fits a GEE to the data generated above. proc genmod data=binary; class subject phase product; model y = phase|product / dist=bin; repeated subject=subject; lsmeans phase|product; run; GEE requires large samples for inference to be valid. Sample size refers to the number of independent observations which is the number of subjects employed in the analysis. For a very simple model, N=31 would be sufficient to support a GEE. For a model in which you estimate 14 parameters, N=31 is not sufficient. Another approach which one might consider is a random effects logit model. Random effects logits can be fit employing the procedure NLMIXED or employing the GLIMMIX macro which ships with SAS. However, the random effects logit conditions on subject, just as you did in the analysis which you presented. Conditioning on subject is what got you into trouble in the first place. So we will have to forget the random effects (any conditional) model and confine our attention to what are referred to as marginal models. There is one marginal model which I could heartily recommend for your present situation. The model does not rely on large sample theory for its validity. Rather, it relies on randomization theory. What I would urge you to consider is the use of a bootstrap regression approach. In the bootstrap analysis, we randomly pick with replacement Ni=31 subjects from the set of N=31 subjects. Some subjects are selected several times and some subjects are not selected for the bootstrap sample. Fit the logistic regression to the bootstrap sample and output the statistics of interest. In your case, you would output the LSMEANS and convert them to probability estimates. Draw a new sample of 31 subjects and fit the model again. Do this K=1000 times. Now, you can compute mean and variance for each probability value arising from your model. You can also compute a 95% confidence interval directly from the 1000*alpha/2 and 1001-1000*alpha/2 (25th and 976th) ordered statistics. The bootstrap does require approximately equal sample sizes for each subject. In your case, this holds perfectly. The bootstrap does not require large sample theory for its validity, so it is preferable over the GEE. You might want to look at our paper "A Comparison of Statistical Methods for Clustered Data Analysis with Gaussian Error". Feng, Z., McLerran, D, and Grizzle, J. Statistics in Medicine, 15, 1793-1806 (1996). While that paper discusses statistical models for gaussian data, the results hold for binary response as well. We performed the simulation to examine the various statistical models in the binary case, but we were letting a visiting faculty member take the lead on writing up results for the binary case. The paper never got written. You could fit a bootstrap model employing code something like the following (note that I have not tested the datastep below): data bootstrap; set mydata end=lastrec; by subject; array response {31,16} _temporary_; position = 8*(phase-1) + product; /* For phase coded 1,2 */ /* Use 8*phase for phase=0,1 */ response{subject,position} = correct; if lastrec then do; do bootstrap=1 to 1000; do i=1 to 31; subject = ceil(31*ranuni(seed)); /* Specify SEED */ do j=1 to 16; correct = response{subject,j}; phase = 1 + (j>8); product = j - 8*(phase-1); output; end; end; end; end; run; ods listing close; ods output lsmeans=lsmeans; proc genmod data=bootstrap; by bootstrap; model correct = phase|product / dist=bin; lsmeans phase|product; run; At this point, I am too lazy to figure out just what the LSMEANS dataset will look like. But you will want to convert the LSMEANS to probability estimates in a datastep and then run PROC UNIVARIATE against the probability estimates, requesting the 2.5th and 97.5th percentiles of the distributions along with mean and variance. Dale --- david.mcnulty@QUESTINTL.COM wrote: > Hi Dale, > > My apologies I have inadvertently mislead you. > > Further Info > > All 31 subjects test 8 products under condition 1 (scoring 1=success > 0=fail), has a break and re-tests all 8 products under condition 2. > Conditions 1 and 2 cannot be randomised. Total observations = 31*8*2 > = 496 > (434 ignoring Prod_8). > > Dave. > ===== --------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@fhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 --------------------------------------- __________________________________________________ Do You Yahoo!? Yahoo! - Official partner of 2002 FIFA World Cup http://fifaworldcup.yahoo.com IMPORTANT NOTICE: This email is confidential, may be legally privileged, and is for the intended recipient only. Access, disclosure, copying, distribution, or reliance on any of it by anyone else is prohibited and may be a criminal offence. Please delete if obtained in error and email confirmation to the sender. ``` Back to: Top of message | Previous page | Main SAS-L page
1,861
7,657
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.59375
3
CC-MAIN-2013-48
longest
en
0.818757
http://www.r-bloggers.com/scatterplot-matrices-in-r/
1,467,139,961,000,000,000
text/html
crawl-data/CC-MAIN-2016-26/segments/1466783396959.83/warc/CC-MAIN-20160624154956-00160-ip-10-164-35-72.ec2.internal.warc.gz
810,370,902
17,152
# Scatterplot matrices in R July 25, 2011 By (This article was first published on Getting Genetics Done, and kindly contributed to R-bloggers) I just discovered a handy function in R to produce a scatterplot matrix of selected variables in a dataset. The base graphics function is pairs(). Producing these plots can be helpful in exploring your data, especially using the second method below. Try it out on the built in iris dataset. (data set gives the measurements in cm of the variables sepal length and width and petal length and width, respectively, for 50 flowers from each of 3 species of iris. The species are Iris setosa, versicolor, and virginica). `# Load the iris dataset.data(iris) # Plot #1: Basic scatterplot matrix of the four measurementspairs(~Sepal.Length+Sepal.Width+Petal.Length+Petal.Width, data=iris)` Looking at the pairs help page I found that there’s another built-in function, panel.smooth(), that can be used to plot a loess curve for each plot in a scatterplot matrix. Pass this function to the lower.panel argument of the pairs function. The panel.cor() function below can compute the absolute correlation between pairs of variables, and display these in the upper panels, with the font size proportional to the absolute value of the correlation. `# panel.smooth function is built in.# panel.cor puts correlation in upper panels, size proportional to correlationpanel.cor <- function(x, y, digits=2, prefix="", cex.cor, ...){    usr <- par("usr"); on.exit(par(usr))    par(usr = c(0, 1, 0, 1))    r <- abs(cor(x, y))    txt <- format(c(r, 0.123456789), digits=digits)[1]    txt <- paste(prefix, txt, sep="")    if(missing(cex.cor)) cex.cor <- 0.8/strwidth(txt)    text(0.5, 0.5, txt, cex = cex.cor * r)} # Plot #2: same as above, but add loess smoother in lower and correlation in upperpairs(~Sepal.Length+Sepal.Width+Petal.Length+Petal.Width, data=iris,      lower.panel=panel.smooth, upper.panel=panel.cor,       pch=20, main="Iris Scatterplot Matrix")` Finally, you can produce a similar plot using ggplot2, with the diagonal showing the kernel density. `# Plot #3: similar plot using ggplot2# install.packages("ggplot2") ## uncomment to install ggplot2library(ggplot2)plotmatrix(with(iris, data.frame(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width)))` Update:  A tip of the hat to Hadley Wickham (@hadleywickham) for pointing out two packages useful for scatterplot matrices. The gpairs package has some useful functionality for showing the relationship between both continuous and categorical variables in a dataset, and the GGally package extends ggplot2 for plot matrices. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Tags: , ,
740
2,951
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.84375
3
CC-MAIN-2016-26
longest
en
0.602653
https://www.vedantu.com/question-answer/let-a-3-6-12-15-18-21-b-4-8-12-16-20-c-2-4-6-8-class-11-maths-cbse-5eeb0d81309073303c5f920b
1,618,470,204,000,000,000
text/html
crawl-data/CC-MAIN-2021-17/segments/1618038084601.32/warc/CC-MAIN-20210415065312-20210415095312-00379.warc.gz
1,142,019,859
85,899
Question # Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}. Find B – A. Hint: In set theory, the subtraction of a set A from a set B is given by the set obtained by removing all the elements of the set A from the set B. Using this concept, we can solve this question. $\Rightarrow$ B – A = {4, 8, 16, 20}
155
376
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.671875
4
CC-MAIN-2021-17
longest
en
0.915253
https://forums.ni.com/t5/LabVIEW/Space-Vector-PWM-Labview-3-ph/td-p/1655854/highlight/true/page/2
1,718,945,933,000,000,000
text/html
crawl-data/CC-MAIN-2024-26/segments/1718198862036.35/warc/CC-MAIN-20240621031127-20240621061127-00605.warc.gz
241,160,565
70,940
# LabVIEW cancel Showing results for Did you mean: Solved! Go to solution ## Re: Space Vector PWM Labview (3-ph) Julianne I am actually trying the matrix methods since its easy to follow. however, i would like to know if its possible to put changing values in the matrices. I want to put (sin and cosine values in the matrices, the angle is the control knob with 360dg limit. how to wire the matrices so that you can connect variable values to each row or column. I wonder if its possible using labview. thanks Message 11 of 18 (1,914 Views) Solution Accepted by topic author jackferz ## Re: Space Vector PWM Labview (3-ph) Hi jackferz, Yes you can continuously change your matrix using a "Set Matrix Elements" block, which is located on the Matrix Palette. You can input your angle control into the "new element" terminal and your angle matrix into the "matrix" input. If you want to output to the same matrix, you can just create a local variable of the angle matrix and connect that to the "output matrix" output terminal. You can also need to specify which matrix element (the row and column) that you want to modify. Hope this helps! Julianne K Systems Engineer, Embedded Systems Certified LabVIEW Architect, Certified LabVIEW Embedded Systems Developer National Instruments Message 12 of 18 (1,888 Views) ## Re: Space Vector PWM Labview (3-ph) Thanks for that. It was quite helpful. Is there a possibilty if one can convert the decimal to Fractional form e.g. if i want to convert 0.33 to 1/3. Secondly, i am no clear how to plot x axis waveform chart in terms of 360 degrees. e.g. 60, 120, .... 360. thanks Message 13 of 18 (1,871 Views) ## Re: Space Vector PWM Labview (3-ph) Hello jackferz, There is a Number to Fractional String vi, and then a Fract/Exp String to Number vi so playing around with those should get the result you seek. So you're working with just a regular waveform chart, correct? I see on previous posts Julianne showed how to set the x axis to be a function of frequency. As of right now, I don't think it's possible to set the x-axis to be anything other than a manipulation of time, but I'll look into it more closely. Would it be feasible for you to just use the conversion 180/pi? Regards, Deborah Y. Deborah Burke NI Hardware and Drivers Product Manager Certified LabVIEW Architect Message 14 of 18 (1,834 Views) ## Re: Space Vector PWM Labview (3-ph) I am workign with wavefomr chart. But i assume there must be some kind of plot where x axis can be define in such a manner, 60, 120, 180, ....300, 360. basically i am working with Compass Plot VI which has 360degress values. I want my waveform graph or chart, basically to have same 360 values limit in X axis of the plot so that i can plot sinusoidal signals. But the plot must be in above mentioned sequence. Secondly, ur suggestion to use number to fraction and then Fraction to number, is that going to convert the decimal to fraction form. I basically want to feed the fractional format in the matrix array. For example instead of manually putting 0.33 in the matrix array, is it possible to put 1/3 which means i need the expression to be in fractional form and all the results should be in fractional form. If this is not achievable i will stick to the decimal number. Just curious to know if there was an easy way to do this. Do you have any example to show me. Thanks Message 15 of 18 (1,830 Views) ## Re: Space Vector PWM Labview (3-ph) Hello Jackferz, If you go into the properties of an XY graph, you can change the name from time to angle and then instead of autoscale, set the minimum and maximum values (here 0-360). Using the chart property nodes you can then select the specific tick marks to be constant (60, 120, etc.). Have you tried just making those scale changes yet? If that doesn't work wit the inputted data, it may mean only functions of time are an option. If you choose the graph functionality and not the chart, the values will write over each other cycling through the angles each time. Also, just for future reference have you seen the functionality of the polar plot and/or this example? This might just be something to consider along with this community example that shows how to center the Compass plot. Yes, you should stick with the decimal format and then if you do any post-processing on the data outside of LabVIEW you could convert to fraction there. To do it in the code you'd first have to determine if it's repeating or not, multiply by 1000, find the lowest possible denominator, etc. which may take more than it's worth. Regards, Deborah Y. Deborah Burke NI Hardware and Drivers Product Manager Certified LabVIEW Architect Message 16 of 18 (1,807 Views) ## Re: Space Vector PWM Labview (3-ph) Hi all, I think the similar project that I am doing now, except I need to apply FPGA, and acquired the vector data from FIFO of FPGA. Therefore, I need to compile VI under the target rather than MY COMPUTER. In this case, it seems that the compass plot could not be used anymore, so is there anyother alternative way for displaying the space vector which received from FIFO? I am totally a beginner on labVIEW and FPGA. Thanks a lot! Sam Message 17 of 18 (1,554 Views) ## Re: Space Vector PWM Labview (3-ph) Hi Sam, Most of what has been explained on this forum is not applicable until you are able to get the data from your FPGA. Depending on your FPGA target you will either be passing from the FPGA to the Real Time OS or the Windows PC. If you comment with which FPGA product you are working with I will be able to explain in a bit more detail. Either way you will be using a DMA FIFO to transfer the data and once the data is to your Windows Operating system the rest of what is listed here should be enough to get everything working. You did mention that you are receiving data from a FIFO; does that mean that you already have the DMA FIFO setup?
1,399
5,929
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.6875
3
CC-MAIN-2024-26
latest
en
0.880911
https://stats.stackexchange.com/questions/367887/difference-between-using-a-confidence-interval-and-using-the-z-score-for-a-two-s
1,653,006,102,000,000,000
text/html
crawl-data/CC-MAIN-2022-21/segments/1652662530553.34/warc/CC-MAIN-20220519235259-20220520025259-00004.warc.gz
600,105,353
65,950
# Difference between using a confidence interval and using the z-score for a two-sided test? From what I have read so far, it seems that in a two-sided hypothesis test of the form: $H_0: \mu = 10$ $H_A: \mu \ne 10$ where you choose a significance level of let's say $\alpha = 0.05$, there are two methods of conducting the hypothesis test. 1. Creating a 95% confidence interval around the sample mean, $\bar{x}$ 2. Getting the z-score for $\bar{x}$ and doubling the corresponding p-value Are these methods inherently the same thing? Or are there cases where depending on $\bar{x}$, we could reject $H_0$ in favor of $H_A$ for method #1 but not for method #2, etc? • I will answer for z test as in your Question. If you are interested in t tests (now or later), please see @whuber's Answer to a related question. Sep 20, 2018 at 20:38 Assume you have normal data with $$\mu$$ unknown and $$\sigma$$ known, so that a z test and z confidence interval are both appropriate. In the z test, you reject $$H_0: \mu = \mu_0$$ vs $$H_a: \mu \ne \mu_0$$ at level $$\alpha = 5\%$$ precisely when $$Z = \frac{\bar X - \mu_0}{\sigma/\sqrt{n}}$$ has $$|T| \ge 1.96.$$ That is, $$P(|Z| < 1.96) = P\left(-1.96 < \frac{\bar X - \mu_0}{\sigma/\sqrt{n}} < 1.96\right)\\ = P\left(\bar X-1.96\frac{\sigma}{\sqrt{n}} <\mu_0 < \bar X+1.96\frac{\sigma}{\sqrt{n}}\right) = 0.95$$ and a 95% (two-sided) confidence interval is $$\bar X \pm 1.95\frac{\sigma}{\sqrt{n}}.$$ Thus, the 95% CI that is based on putting half of the error probability in each tail can be comsidered an interval of 'non-rejectable' null values $$\mu_0$$ for the specified two-sided test. Notes: (a) In the case discussed above, one says that the CI "inverts the test." Some confidence intervals are formed by inverting a test and some are not. So don't get the idea that this "duality" always holds true. (b) Bear in mind that we say $$\bar X \pm 1.95\frac{\sigma}{\sqrt{n}}$$ is a 95% confidence interval for $$\mu.$$ Another possible (but seldom used) kind of 95% CI would put 2% error probability in one tail and 3% in the other tail, instead of 2.5% in each tail: $$P(\bar X-2.054\sigma/\sqrt{n} \le\mu_0\le \bar X+1.881\sigma/\sqrt{n}) = 0.95.$$ [CIs that put equal probability in each tail are sometimes called 'probability-symmetric'. Confidence intervals that are not probability-symmetric are mainly used for asymmetrical distributions.] qnorm(c(.02, .97)) ## -2.053749 1.880794 qnorm(c(.025, .975)) ## -1.959964 1.959964
775
2,493
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.71875
4
CC-MAIN-2022-21
longest
en
0.878798
https://spiral.ac/sharing/66a2sub/analyzing-graphs-of-exponential-functions-high-school-math-khan-academy
1,547,846,549,000,000,000
text/html
crawl-data/CC-MAIN-2019-04/segments/1547583660529.12/warc/CC-MAIN-20190118193139-20190118215139-00193.warc.gz
668,112,644
9,072
# Interactive video lesson plan for: Analyzing graphs of exponential functions | High School Math | Khan Academy #### Activity overview: Given the graph of an exponential function, Sal finds the formula of the function and a value that is outside the graph. Watch the next lesson: https://www.khanacademy.org/math/high-school-math/math1/math1-exponential-func/math1-interpreting-graphs-and-tables-of-basic-exponential-functions/v/analyzing-exponential-graph-with-negative-initial-value?utm_source=YT&utm_medium=Desc&utm_campaign=highschoolmath Missed the previous lesson? https://www.khanacademy.org/math/high-school-math/math1/math1-exponential-func/math1-interpreting-graphs-and-tables-of-basic-exponential-functions/v/analyzing-tables-of-exponential-functions?utm_source=YT&utm_medium=Desc&utm_campaign=highschoolmath High School Math on Khan Academy: Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway? This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it. About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s High School Math channel: https://www.youtube.com/channel/UCAj83VTec-NC-g0BK8zpxzw?guided_help_flow=3?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy Tagged under: education,online learning,learning,lessons Clip makes it super easy to turn any public video into a formative assessment activity in your classroom. Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans Play this activity 1. Students enter a simple code 2. You play the video 3. The students comment 4. You review and reflect * Whiteboard required for teacher-paced activities ## Ready to see what elsecan do? With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach. Quickfire Carry out a quickfire formative assessment to see what the whole class is thinking Discuss Create interactive presentations to spark creativity in class Team Up Student teams can create and share collaborative presentations from linked devices Clip Turn any public video into a live chat with questions and quizzes ### 1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons. Now it's your turn Sign up ### Spiral Reviews by Teachers and Digital Learning Coaches @kklaster Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech @3rdgradeBCE Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks. @ordmiss Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral @strykerstennis Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks! @iladylayla A good tool for supporting active #learning. @BrettErenberg The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed! ## Get the Clip Chrome Extension & Create Video Lessons in Seconds Add Clip to Chrome
935
4,340
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.125
3
CC-MAIN-2019-04
latest
en
0.882412
https://www.ramlux.nl/cone/1231.html
1,632,240,895,000,000,000
text/html
crawl-data/CC-MAIN-2021-39/segments/1631780057225.57/warc/CC-MAIN-20210921161350-20210921191350-00185.warc.gz
976,816,023
7,845
>HOME>Critical Speed Of Ball Mill Calculation # Critical Speed Of Ball Mill Calculation • ### Ball Mill Critical Speed Mineral Processing & Metallurgy A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shell’s inside surface and no balls will fall from its position onto the shell. The imagery below helps explain what goes on inside a mill as speed varies. Use our online formula The mill speed is typically defined as the percent of the Theoretical ### SAGMILLING.COM .:. Mill Critical Speed Determination Mill Critical Speed Determination. The "Critical Speed" for a grinding mill is defined as the rotational speed where centrifugal forces equal gravitational forces at the mill shell's inside surface. This is the rotational speed where balls will not fall away from the mill's shell. ### Mill Speed Critical Speed Paul O. Abbe Mill Speed Critical Speed. Mill Speed . No matter how large or small a mill, ball mill, ceramic lined mill, pebble mill, jar mill or laboratory jar rolling mill, its rotational speed is important to proper and efficient mill operation. Too low a speed and little energy is imparted on the product. Too fast and inefficient media movement (known ### TECHNICAL NOTES 8 GRINDING R. P. King Figures 8.5 for the popular mill types. 3 c is the mill speed measured as a fraction of the critical speed. More reliable models for the prediction of the power drawn by ball, semi-autogenous and fully autogenous mills have been developed by Morrell and by Austin. (Morrell, S. Power draw of wet tumbling mills ### kolkata calculate critical speed of ball mill critical speed of ball mill calculation india. Ball Mill Critical Speed 911 Metallurgist. Mar 17, 2017 A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which The critical speed of a rotating mill is the RPM at which a grinding . The Formula derivation ends up as follow: Critical Speed ### Mill Critical Speed Calculation Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied. The mill was rotated at 50, 62, 75 and 90% of the critical speed. Six lifter bars of rectangular cross-section were used at equal spacing. The overall motion of the balls at the end of five revolutions is shown in Figure 4. ### How To Calculate Critical Speed Of Ball Mill How To Calculate Critical Speed Of Ball Mill. Raw mills usually operate at 72-74 critical speed and cement mills at 74-76calculation of the critical mill speed g weight of a grinding ball in kg angular velocity of the mill tube in radialsecond 23n60 di inside mill diameter in meter effective mill. ### how to calculate critical speed of a ball mill Exodus how to calculate critical speed of a ball mill,Ball mills have been successfully run at speeds between 60 and 90 percent of critical speed but most mills operate at speeds between 65 and 79 percent of critical speed Rod mills speed should be limited to a maximum of 70 of critical speed and preferably should be in the 60 to 68 percent critical speed range ### critical speed of ball mill calculation A General Model for Semi-autogenous and Autogenous Milling. ball mills. Several recent papers by. It is assumed that this type of mill . (5-9) . is fraction of critical speed and c. ### how to calculate critical speed of a ball mill Exodus how to calculate critical speed of a ball mill,Ball mills have been successfully run at speeds between 60 and 90 percent of critical speed but most mills operate at speeds between 65 and 79 percent of critical speed Rod mills speed should be limited to a maximum of 70 of critical speed and preferably should be in the 60 to 68 percent critical speed range ### critical speed of ball mill calculation A General Model for Semi-autogenous and Autogenous Milling. ball mills. Several recent papers by. It is assumed that this type of mill . (5-9) . is fraction of critical speed and c. ### how do i calculate the critical speed of a mill OVERVIEW ON THE GRINDING MILLS AND THEIR DUAL ABB. SAG mill, ball mill, ring gear, dual pinion, drive systems, variable speed .. Figure 7 shows one of the synchronous motors installed on Ball Mill 1. mill controller measures cascading of the material, by a decreasing torque, before the critical. ### How To Calculate Critical Speed Of A Ball Mill How To Calculate Critical Speed Of A Ball Mill. 2013-9-5ball acme lead screw technical information critical shaft speed operating speed of spinning shaft that produces severe vibrations during operationhis is a function of length, diameter, and end supportsaximum compressive load maximum load that can be axially applied to the screw before. ### How To Calculate Critical Speed Of A Ball Mill Critical Speed Ball Mill. How i calculate the optimam speed of a ball millall mill critical speed mineral processing metallurgyar 17, 2017 he critical speed of a rotating mill is the rpm at which a grinding medium oull find a good on-line tool for ball mill critical speed calculation morerinding an overview of operation and design minerals ### Ball Mill Parameter Selection & Calculation Power 30/08/2019· 2.2 Rotation Speed Calculation of Ball Mill \ Critical Speed_ When the ball mill cylinder is rotated, there is no relative slip between the grinding medium and the cylinder wall, and it just starts to run in a state of rotation with the cylinder of the mill. This instantaneous speed of the mill is as follows: ### Formula To Calculate Critical Speed In Ball Mill Formula To Calculate Critical Speed In Ball Mill. Determine Critical Speed Grinding Mill. What is the ball mill critical speed and how to improve ball mill formula on critical speed in Ball Mill to control the critical rotating formula of calculating the efficiency of a ball rolling grinding efficiency of ball mill calculating equation. grinding efficiency of ball mill calculating equation p12 ### Ball Mill Design Critical Speed Formula Ball Mill Design Critical Speed Formula The critical speed of the mill, &c, is defined as the speed at which a single ball will just remain against the wall for a full cycle. . steel balls in a ball mill, or large lumps of ore in an autogenous mills calculated using the formulas of Austin. ### How To Calculate Critical Speed In Ball Mill Process How To Calculate Critical Speed In Ball Mill Process，We is a large-sized joint-stock enterprise integrated with the scientific research, production and sales of heavy mining machinery. It is located in high and new technology industrial development zone, Zhengzhou with an area of 200,000 m². ### Ball Mills Mine Engineer.Com The point where the mill becomes a centrifuge is called the "Critical Speed", and ball mills usually operate at 65% to 75% of the critical speed. Ball Mills are generally used to grind material 1/4 inch and finer, down to the particle size of 20 to 75 microns. To achieve a reasonable efficiency with ball mills, they must be operated in a closed ### Ball Mill Parameter Selection & Calculation Power 30/08/2019· 2.2 Rotation Speed Calculation of Ball Mill \ Critical Speed_ When the ball mill cylinder is rotated, there is no relative slip between the grinding medium and the cylinder wall, and it just starts to run in a state of rotation with the cylinder of the mill. This instantaneous speed of the mill is as follows: ### Ball Mill Design Critical Speed Formula Ball Mill Design Critical Speed Formula The critical speed of the mill, &c, is defined as the speed at which a single ball will just remain against the wall for a full cycle. . steel balls in a ball mill, or large lumps of ore in an autogenous mills calculated using the formulas of Austin. ### How To Calculate Critical Speed In Ball Mill Process How To Calculate Critical Speed In Ball Mill Process，We is a large-sized joint-stock enterprise integrated with the scientific research, production and sales of heavy mining machinery. It is located in high and new technology industrial development zone, Zhengzhou with an area of 200,000 m². ### formula to calculate critical speed in ball mill Formula To Calculate Critical Speed In Ball Mill. formula critical speed ball mill . calculate critical speed of ball mill ugcnetnic.in. Ball Mill Critical Speed Mineral Processing . 10 A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shells inside ### Ball Mill Critical Speed Formula reisebuero.be Ball Mill. Ball mill is the key equipment for grinding after the crushing process, which is widely used in the manufacture industries, such as cement, silicate, new building material, refractory material, fertilizer, ferrous metal, nonferrous metal and glass ceramics and can be used for the dry and wet grinding for all kinds of ores and other grind-able materials. ### What it is the optimun speed for a ball mill 19/10/2006· What it is the optimun speed for a ball mill ? posted in Pyrotechnics: I have done a ball mill,recenly finished,but the motor has too rpms,is too fast for use in a ball mill (the pvc cylinder that i use,left of the shafts). With the motor i will use a 40 mm pulley,because i have a 50 mm driven pulley, in one of my two shafts. In the other side of my shafts there are two 40 mm ### critical speed ball mill calculation keithkirsten.co.za critical speed ball mill calculation; critical speed ball mill calculation. Ball Milling ResearchGate. Is there any equation or method to calculate the energy of milling and adjust the parameter between Milling speed was 350 rpm and it was a plantery ball mill. Chat Now. Critical speed of the ball mill . Aug 4, 2016 Rod and ball mills in Mular AL and Bhappu R B Editors Mineral ### Ball Mill Calculations Critical Speed Mining Heavy We have ball mill calculations critical speed,Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied The mill was rotated at 50 62 75 and 90 of the critical speed Six lifter bars of rectangular crosssection were used at equal spacing The overall motion of the balls at the end of five revolutions is shown in ### Ball Mills Mine Engineer.Com The point where the mill becomes a centrifuge is called the "Critical Speed", and ball mills usually operate at 65% to 75% of the critical speed. Ball Mills are generally used to grind material 1/4 inch and finer, down to the particle size of 20 to 75 microns. To achieve a reasonable efficiency with ball mills, they must be operated in a closed ### SAGMILLING.COM .:. tools tools Home Calculations Articles . Calculations. Millspeed Sliderule Pipe Launder Liner Height Mill filling. Calculations . Mill Critical Speed Calculation: Estimates the critical speed of a grinding mill of a given diameter given the mill inside diameter and liner thickness. If given a measured mill rotation (RPM), then the mill`s fraction of the critical speed is given. Internet Slide ### What it is the optimun speed for a ball mill 19/10/2006· What it is the optimun speed for a ball mill ? posted in Pyrotechnics: I have done a ball mill,recenly finished,but the motor has too rpms,is too fast for use in a ball mill (the pvc cylinder that i use,left of the shafts). With the motor i will use a 40 mm pulley,because i have a 50 mm driven pulley, in one of my two shafts. In the other side of my shafts there are two 40 mm ### Ball Mill Calculations Critical Speed Mining Heavy We have ball mill calculations critical speed,Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied The mill was rotated at 50 62 75 and 90 of the critical speed Six lifter bars of rectangular crosssection were used at equal spacing The overall motion of the balls at the end of five revolutions is shown in ### Ball Mill Critical Speed Calculator krauss-blumen.de Ball mill critical speed calculator ball mill critical speed calculator modeling the specific grinding energy and ballmill scaleup ballmill scale up bonds law data bond work index mill power draw calculation equations arbiter and the fraction of the m,Ball mill critical speed calculator. ### Ball Mill Critical Speed Calculator Ball Mill Critical Speed Calculator. 2018-5-25n rotational speed, min-1 dpgear pitch circle diameter, mm gear pressure angle, deg gear helix angle, deg because the actual gear load also contains vibrations and shock loads as well, the theoretical load obtained by the above formula should also be adjusted by the gear factor f z as shown in table 4 4earing load calculation. ### Critical Speed Of Ball Mill Calculation Pdf Critical Speed Of Ball Mill Calculation Pdf. 2018-10-9a ball mill is one kind of grinding machine, and it is a balls, and the rotational speed n of the mill was varied in a range from 40100 using the critical rotational speed nc defined by eq 11 as a referencehe criti-cal rotational speed nc is the limiting speed ### Critical Speed Calculations Of Ball Mill FTMLIE Heavy Critical Speed Calculations Of Ball Mill. The speed of the mill was kept at 63 of the critical speed The face angle was varied from 90 to 111 degrees for the three types of configuration 1 2 and 4 as shown in the figure Also the height of the lifter bar in configuration 3 was changed to observe the trajectory ### SAGMILLING.COM .:. tools tools Home Calculations Articles . Calculations. Millspeed Sliderule Pipe Launder Liner Height Mill filling. Calculations . Mill Critical Speed Calculation: Estimates the critical speed of a grinding mill of a given diameter given the mill inside diameter and liner thickness. If given a measured mill rotation (RPM), then the mill`s fraction of the critical speed is given. Internet Slide ### calculating critical speed in a ball mill Torque speed calculation for ball mill, designing calculation of critical speed of ball. Which calculations similar to those used in calculating change gear ratio for. rolling mill speed calculation formula pdf Empirical Sealed clean bearings for rolling mill roll neck Todays demands on productivity and quality in hot rolling mills for rod and ### critical speed of ball mill formula offthevine.co.za critical speed of ball mill formula pol recreatie.nl. A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which The mill speed is typically defined as the percent of the Theoretical The Formula derivation ends up as follow Critical Speed is Nc =76.6(D0.5). ### Bond formula for the grinding balls size calculation 19/10/2017· C the mill drum rotational speed,% of the critical speed; D the mill internal diameter, m. At result B = 25mm or less necessary to use the correction factor 1.3, i.e. the grinding balls average diameter should be 32.5 mm in the feed mixture. We draw your attention, a larger grinding balls need to use for future loads. As practice shows << Prev: Bearing Of A Jaw Crusher >> Next: Sesame Grinding Makine
3,270
15,136
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.28125
3
CC-MAIN-2021-39
latest
en
0.848735
https://fr.slideserve.com/kyria/with-mr-tyler
1,653,601,893,000,000,000
text/html
crawl-data/CC-MAIN-2022-21/segments/1652662625600.87/warc/CC-MAIN-20220526193923-20220526223923-00468.warc.gz
319,436,828
19,734
Download Download Presentation With Mr. Tyler # With Mr. Tyler Télécharger la présentation ## With Mr. Tyler - - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - - ##### Presentation Transcript 1. With Mr. Tyler 2. Algebraic Expressions 3. Verbal Expressions 4. Order of Operations 5. Properties of Identity & Equality 6. Commutative, Associative & Distributive 7. Simplifying Expressions 8. Order of Operations Properties of Identity & Equality Commutative, Associative & Distributive Simplifying Expressions Algebraic Expressions Verbal Expressions \$100 \$100 \$100 \$100 \$100 \$100 \$200 \$200 \$200 \$200 \$200 \$200 \$300 \$300 \$300 \$300 \$300 \$300 \$400 \$400 \$400 \$400 \$400 \$400 \$500 \$500 \$500 \$500 \$500 \$500 9. 1-100 1 - 100 Write a verbal expression: x + 3. \$100 10. 1-100A 1 - 100 What is "the sum of x and 3"? Answers may vary. \$100 11. 1-200 Write a verbal expression: 2y. \$200 12. 1-200A 1 - 100 What is "twice y"? Answers may vary. \$200 13. 1-300 Write a verbal expression: 3m - 2. \$300 14. 1 - 100 What is "three times m minus 2"? \$300 15. 1-400 Write a verbal expression: 3 ÷ a. \$400 16. 1-400A 1 - 100 What is "the quotient of 3 and a"? Answers may vary. \$400 17. 1-500 Write a verbal expression: 3(x - y). \$500 18. 1-500A 1 - 100 What is "three times the difference of x and y"? Answers may vary. \$500 19. 2-100 1 - 100 Write an algebraic expression: the product of 4 and t. \$100 20. 2-100A 1 - 100 What is "4t"? Answers may vary. \$100 21. 2-200 Write an algebraic expression: the difference of 4 and t. \$200 22. 2-200A 1 - 100 What is "4 - t"? \$200 23. 2-300 Write an algebraic expression: y squared. \$300 24. 2-300A What is " "? 1 - 100 \$300 25. 2-400 Write an algebraic expression: five less than b. \$400 26. 2-400A 1 - 100 What is "b - 5"? \$400 27. 2-500 Write an algebraic expression: half the sum of a and b. \$500 28. 2-500A What is " "? 1 - 100 \$500 29. 3-100 1 - 100 Evaluate. 12 - 3 • 2 \$100 30. 3-100A 1 - 100 What is 6? \$100 31. 3-200 Evaluate. 8 - 4 • 2 + 3 \$200 32. 3-200A 1 - 100 What is 3? \$200 33. 3-300 Evaluate a - bc if a=8, b=3, and c=2. \$300 34. 3-300A 1 - 100 What is 2? \$300 35. 3-400 Evaluate. \$400 36. 3-400A 1 - 100 What is 6? \$400 37. 3-500 Evaluate. 2 ÷ 2 + 8 ÷ (2 - 1) + 1 \$500 38. 3-500A 1 - 100 What is 10? \$500 39. 4-100 1 - 100 Name the property. 3 + 0 = 3 \$100 40. 4-100A 1 - 100 What is "Additive Identity"? \$100 41. 4-200 Name the property. x = x \$200 42. 4-200A 1 - 100 What is "Reflexive Property"? \$200 43. 4-300 Name the property (3 + 4)x = 7x. \$300 44. 4-300A 1 - 100 What is "Substitution Property"? \$300 45. 4-400 Name the property 0 = 7 + (-7). \$400 46. 4-400A 1 - 100 What is "Additive Inverse"? \$400 47. 4-500 Name the property If 3 + 4 = 7 then 7 = 3 + 4. \$500 48. 4-500A 1 - 100 What is "Symmetric Property"? \$500 49. 5-100 1 - 100 Name the property (3 + x)4 = 12 + 4x. \$100 50. 5-100A 1 - 100 What is "Distributive Property"? \$100
1,194
3,067
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.390625
3
CC-MAIN-2022-21
latest
en
0.611576
https://github.com/andhess/ChargeAlgorithms
1,544,927,790,000,000,000
text/html
crawl-data/CC-MAIN-2018-51/segments/1544376827175.38/warc/CC-MAIN-20181216003916-20181216025916-00316.warc.gz
619,924,180
20,938
# andhess/ChargeAlgorithms EE UGR Switch branches/tags Nothing to show Fetching latest commit… Cannot retrieve the latest commit at this time. Type Name Latest commit message Commit time Failed to load latest commit information. matlab chargeEvent.py chargePorts.py common.py csvGen.py dsac.py edf.py edf_AC_Basic.py edf_AC_Pro.py fcfs.py fcfs_AC.py llfSimple.py llfSimple_AC_Basic.py llfSimple_AC_Pro.py llfSmart.py llfSmart_AC_Basic.py main.py poissonGen.py subScheduleTest.py test.py testAlgs.py vehicle.py # Charging Algorithms This repository is part of a research project that I worked on for a semester with @samwdon through the School of Engineering and Applied Sciences at Washington University in St. Louis. The goal of the project was to test different scheduling and queueing algorithms to determine which is most effective in charging electric vehicles. To test the algorithms, we built out this entire simulation and then compared their performance on a few different metrics. # Simulation The simulation operates in discrete time at intervals of 1 minute. Before running an algorithm, we simulate a window in which vehicles will arrive, and then iterate through the simulation minute by minute. The arrival of vehicles is based on a poisson distribution, which is easily changeable. In our model, we commonly change the value of the arrival rate, which is the frequency of occurrences of our distribution. As each algorithm progresses through time, it attempts to make decisions based on its current state. No algorithm can know the future, and at each interval it only has information about its current state and any vehicle that just arrived. # Vehicles To know the best method for charging a vehicle, an algorithm is going to need some information about its needs. Vehicle objects thus have the following basic properties: • Arrival time • Departure time • Initial charge (amount of KWh upon arrival) • Charge needed (amount of KWh needed at departure) • Battery capacity • Charging rate Aside from arrival time and charging rate, these values are calculated from a normal distribution. Arrival time is fixed into the poisson distribtuion, while charging rate is fixed and part of the charge ports. # The Algorithms We implemented 11 different algorithms. These algorithms are built on 5 fundamentally different scheduling approaches. They are defined as follows: • FCFS - First Come First Serve - This is just a typical queue, as vehicles are kept in the order in which they arrive. • EDF - Earliest Deadline First - This is a type of priorty queue. It prioritizes vehicles based on their deadline. A vehicle with a deadline approaching will skip up in priority. • LLF-Simple - Least Laxity First - Laxity is defined as 1 - (time needed to charge / total time available for charging ). In this version, laxity is calculated when a vehicle enters the simulation and the priority queues use only that initial value for all sorting. • LLF-Smart - Here laxity is taken slightly differently. Instead, it is defined as 1 - ( time left to charge / time until deadline ). The difference between LLF-Smart is that the value of laxity is updated for all vehicles at the end of every discrete interval of simulation. • DSAC - Decision Scheduling Admission Control - This algorithm was suggested in a paper by researchers at Cornell University. It adds the ability to admit or decline a vehicle when it arrives. It will admit a vehicle if it finds that it can increase its projected profit. This was the most difficult algorithm to write mostly because vehicle objects needed to be cloned, acted upon independently, but updated in unison. Initially, we built FCFS, EDF, and both of the LLF algorithms where they were required to admit all vehicles. Since DSAC had the power of admission control, we also created a version of each that took advantage of admission control. Furthermore, our initial 4 algorithms used 1 queue for all charging ports, whereas DSAC had a separate queue for each port. To fairly compare DSAC, we implemented an additional admission control algorithm for FCFS, EDF, and LLF-Simple. It didn't make much sense for LLF-Smart in both implementation or practicality. These additions brought the total algorithm count to 11; they are as follows: • FCFS (single queue) • FCFS-AC (single queue) • EDF-AC-Basic (single queue) • EDF-AC-Pro (multiple queues) • LLF-Simple (single queue) • LLF-Simple-AC-Basic (single queue) • LLF-Simple-AC-Pro (multiple queues) • LLF-Smart (single queue) • LLF-Smart-AC (single queue) • DSAC (multiple queues) The reason the multiple queue algorithms are referred to as pro is that they absolutely guarantee that no failure will ever occur when they admit a vehicle. The basic ones will make a very accurate guess (about 99%, but not definite). # Charge Ports There is no charge port object, we just used an array. The algorithms perform all swaps between schedules and ports. For each time a vehicle enters a charge port, a charging activity object is created. This is stored in an array of the sime size, and just documents how long the vehicle was charging there and what it did. # Trying It Out main.py will run all algorithms and return a csv file with some of their performances. To get started, just pull in this entire repository into an empty directory. I have been running everything on Python 2.7.2 (standard on Macs); not sure how well previous versions are supported. When you simulate, you can also get a CSV output on every vehicle and chargePort activity. I suggest keeping that off for big simulations as it slows everything down a lot. In main.py, you will have to define some components of your simulation: how many simulations to run, across what intervals, and how many to run for an average. main.py will take in an integer, which is the interval of time that vehicles can arrive.
1,288
5,877
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.859375
3
CC-MAIN-2018-51
latest
en
0.89866
http://at.metamath.org/ileuni/onsucelsucr.html
1,718,382,492,000,000,000
text/html
crawl-data/CC-MAIN-2024-26/segments/1718198861567.95/warc/CC-MAIN-20240614141929-20240614171929-00878.warc.gz
2,576,849
4,887
Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  onsucelsucr GIF version Theorem onsucelsucr 4234 Description: Membership is inherited by predecessors. The converse, for all ordinals, implies excluded middle, as shown at onsucelsucexmid 4255. However, the converse does hold where 𝐵 is a natural number, as seen at nnsucelsuc 6070. (Contributed by Jim Kingdon, 17-Jul-2019.) Assertion Ref Expression onsucelsucr (𝐵 ∈ On → (suc 𝐴 ∈ suc 𝐵𝐴𝐵)) Proof of Theorem onsucelsucr StepHypRef Expression 1 elex 2566 . . . 4 (suc 𝐴 ∈ suc 𝐵 → suc 𝐴 ∈ V) 2 sucexb 4223 . . . 4 (𝐴 ∈ V ↔ suc 𝐴 ∈ V) 31, 2sylibr 137 . . 3 (suc 𝐴 ∈ suc 𝐵𝐴 ∈ V) 4 onelss 4124 . . . . . . 7 (𝐵 ∈ On → (suc 𝐴𝐵 → suc 𝐴𝐵)) 5 eqimss 2997 . . . . . . . 8 (suc 𝐴 = 𝐵 → suc 𝐴𝐵) 65a1i 9 . . . . . . 7 (𝐵 ∈ On → (suc 𝐴 = 𝐵 → suc 𝐴𝐵)) 74, 6jaod 637 . . . . . 6 (𝐵 ∈ On → ((suc 𝐴𝐵 ∨ suc 𝐴 = 𝐵) → suc 𝐴𝐵)) 87adantl 262 . . . . 5 ((𝐴 ∈ V ∧ 𝐵 ∈ On) → ((suc 𝐴𝐵 ∨ suc 𝐴 = 𝐵) → suc 𝐴𝐵)) 9 elsucg 4141 . . . . . . 7 (suc 𝐴 ∈ V → (suc 𝐴 ∈ suc 𝐵 ↔ (suc 𝐴𝐵 ∨ suc 𝐴 = 𝐵))) 102, 9sylbi 114 . . . . . 6 (𝐴 ∈ V → (suc 𝐴 ∈ suc 𝐵 ↔ (suc 𝐴𝐵 ∨ suc 𝐴 = 𝐵))) 1110adantr 261 . . . . 5 ((𝐴 ∈ V ∧ 𝐵 ∈ On) → (suc 𝐴 ∈ suc 𝐵 ↔ (suc 𝐴𝐵 ∨ suc 𝐴 = 𝐵))) 12 eloni 4112 . . . . . 6 (𝐵 ∈ On → Ord 𝐵) 13 ordelsuc 4231 . . . . . 6 ((𝐴 ∈ V ∧ Ord 𝐵) → (𝐴𝐵 ↔ suc 𝐴𝐵)) 1412, 13sylan2 270 . . . . 5 ((𝐴 ∈ V ∧ 𝐵 ∈ On) → (𝐴𝐵 ↔ suc 𝐴𝐵)) 158, 11, 143imtr4d 192 . . . 4 ((𝐴 ∈ V ∧ 𝐵 ∈ On) → (suc 𝐴 ∈ suc 𝐵𝐴𝐵)) 1615impancom 247 . . 3 ((𝐴 ∈ V ∧ suc 𝐴 ∈ suc 𝐵) → (𝐵 ∈ On → 𝐴𝐵)) 173, 16mpancom 399 . 2 (suc 𝐴 ∈ suc 𝐵 → (𝐵 ∈ On → 𝐴𝐵)) 1817com12 27 1 (𝐵 ∈ On → (suc 𝐴 ∈ suc 𝐵𝐴𝐵)) Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98   ∨ wo 629   = wceq 1243   ∈ wcel 1393  Vcvv 2557   ⊆ wss 2917  Ord word 4099  Oncon0 4100  suc csuc 4102 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944  ax-un 4170 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-uni 3581  df-tr 3855  df-iord 4103  df-on 4105  df-suc 4108 This theorem is referenced by:  nnsucelsuc  6070 Copyright terms: Public domain W3C validator
1,457
2,617
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.328125
3
CC-MAIN-2024-26
latest
en
0.203432
https://domymatlab.com/what-is-the-significance-of-music-generation-and-transcription-with-deep-learning-and-matlab-4
1,726,312,044,000,000,000
text/html
crawl-data/CC-MAIN-2024-38/segments/1725700651579.22/warc/CC-MAIN-20240914093425-20240914123425-00331.warc.gz
194,981,664
22,511
WhatsApp Number Work Inquiries Back # What is the significance of music generation and transcription with deep learning and MATLAB? What is the significance of music generation and transcription with deep learning and MATLAB? 1. In this paper, to study how music can influence neural activity in humans we need to study the way music generation works. 2. To compute neural activity, we need to search for neural activation while in Fourier domain, the center frequency, or high-frequency band of the spectrum. At the same time, we work on applying gradient information in how its low frequency features (low-frequency band) are extracted. Our approach is inspired by the famous one generated by @skelly98a’s approach: The idea is to build high-frequency backpropagation circuits with signal sequence with predetermined properties. Without the sequence, any features are removed and only the features that have been already replaced in one of the channels are used to produce these circuits. In this way, our task is to find all neural activations that have similar characteristics. If we don’t have a way to address our problem, and only a few features are used, this paper will be easy on the way: \begin{figure}[b] {zeta} \includegraphics[width=12cm]{image/omega200} \end{figure} For computational experiments, we use a typical two-channel neural network(NB) architecture: Denoted as $N(c,\textbf{a}) = c$ for channel $c$ and denoted as $N(c,0)$, denoted as $N(c,\textbf{b}) = \text{max } (0, \textbf{a} – 0/\tau )$, denoted as $N(c,\textbf{b})$, where $\tau = \inf_{0 \le i \le b \le j} \textbf{R}(i,j)$. Figure 1 and Figure 2 below show how our architecture will work whenWhat is the significance of music generation and transcription with deep learning and MATLAB? I have a couple of questions for you, may this be for you or just want to submit a quote for me. How can a database by a MATLAB file can be used for creating files as a database in Python? I have to run a benchmark challenge for computing raw scores for 20 groups with matrix size 4100. Currently it comes up with a distribution (the original row, first and second value) that consists of 25.6%, 40.6% and 48.6% of the original rows, the second and third values are from random.dat with minimum minimum (3-10) and maximum (10-20) of the rows. I need to find a database that lets me use the first,and it shows 10/10 times the raw score. Can I draw a database on a 10/10 rows by batch or using the first row? On a 4100 file with Matlab built in a batch process on my computer. I need to find anchor table that shows the scores of the rows, the other six visit here that are in separate files. How can I visualize the results from a comparison with MATLAB? When I zoom into out through a window it gives me a box which the user can double click to give me list of rows with that data. ## Help With College Classes In the box the first and third values show that the one a matlab method (the one Click Here I read review managed to get from my server) has produced. The third element appears to be of different data format (filex format works with 10/10 matrix data and not with other types of matlab Go Here But, if I then zoom out the box and click on all the elements and add them to my model, the matlab can easily generate the first three rows. These are the results – in home row, the first three values shows that 0.2% and 1% (others got to 0.9What is the significance of music generation and transcription with deep learning and MATLAB? There is no database for music generation with deep neural or neural network forMATLAB. But we have deep neural and deep neural and deep neural and deep neural and neural networks networks. Different researchers used different approaches for this one! Let are we say as a beginning of music generation in MATLAB? We can divide it into two sets, named as a base and a middle, representing music generation. Let us look when we can define with high accuracy we can understand what’s going on in the database are we not at high code points…! In base, we can say that our hard data are raw videos on mp3. And again are we not at high code points? Here are we have chosen, database, and method to create with high accuracy and high precision. So, we can see now where is used for computing basic song-getting skills(and I hope in this post what’s new). Method {#method in video-encoded data} Base ‘P = small_path{1,2,3,4}’ is the hard_data that’s hard to load. In (a2) we can use base sequence or it can be the transform-image of input dataset. In (c) and B, we can use the multi-edge idea to create and decode a label and text by using innerProduct function: the innerProduct may also be used to encode a channel and then divide by the data type of this feed. 2D [**Single Dirichlet**]{} Since we were working with images in MATLAB, we can take the data above from base in MATLAB. 2D [**Giant Discrete**]{} So, it doesn’t mean that we have to write a function to display the content in two dimensions. ###### carrie http://domymatlab.com
1,191
5,049
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.765625
3
CC-MAIN-2024-38
latest
en
0.923382
https://www.ctspedia.org/do/view/CTSpedia/BiasDefinition
1,581,912,933,000,000,000
text/html
crawl-data/CC-MAIN-2020-10/segments/1581875141653.66/warc/CC-MAIN-20200217030027-20200217060027-00195.warc.gz
717,933,792
9,108
Tags: create new tag , view all tags, tagging instructions # Bias or Systematic Error (Validity) ## Origin of the Term Bias Bias refers to a systematic error. The origin of the word appears to come from the scholar, Bias, of Priene (which today is in Turkey), who was one of the seven sages of classical antiquity. Legend has it that Bias was once consulted by King Croesus about the best way to deploy warships against the Ionians. Because Bias wanted to avoid a war, he falsely advised the king that the Ionians were planning to use horses. Bias later confessed to the King that he had lied but the King was so pleased about his motives that he made peace with the Ionians. Subsequently, a deviation from truth became known as bias. ## Definition of Bias Systematic error is also known as bias. It is any systematic process in the conduct of a study that results in the incorrect estimate of a measure of disease occurrence or measure of association. • Because it is a systematic process, it will cause a distortion from the truth in a predictable (not random) direction. • We say that the amount of systematic error is captured in the validity of the inference. ## Diagram of Systematic Error As you can see below the difference between the average of different attempts and the truth (at the center of the target) is known as the systematic error or bias. ## Selection Bias Technical definition: Bias that is caused when individuals have different probabilities of being included in the study according to relevant study characteristics: namely, the exposure and the outcome of interest. Plain definition: Bias that is caused by some kind of problem in the process of selecting subjects initially or - in a longitudinal study - in the process that determines which subjects drop out of the study. For further descriptions of selection bias in different types of studies see Selection Bias. ## Confounding Bias A confounding bias is caused when there is another pathway to the disease, that is getting in the way of our ability to investigate our main question - a pathway different from the one you are interested in studying. ## Information/Measurement Bias A measurement bias is defined as Technical Definition: It is the bias, in other words deviation from the truth, that it is caused when any measurement collected about or from subjects is not completely valid (i.e., not completely accurate). Inaccuracy in the measurement of any kind of variable, be it an exposure variable, an outcome variable, or a confounder variable can lead to measurement bias. AKA: What are the other terms you might find for measurement bias? Measurement bias is also known as misclassification bias, information bias (the text uses that term) or identification bias. Misclassification bias is a good term and I will often use measurement bias and misclassification synonymously. Indeed, misclassification is a good term because misclassification of a variable is the immediate result of an error in measurement. ## Systematic Error in a Continuous Variable - Measurement Bias in Analytic Studies With a continuous variable there aren't broad categories, but rather a continuum of responses. Hence, systematic error in a continuous variable just results in everyone being systematically shifted up or down the scale. 1) In the above data the truth is that the mean is 100 in the exposed group and 50 in the unexposed group. Therefore the ratio of the means is 2 and the difference in means is 50. 2) If the measurement is off by a factor of 2, you can see that the exposed group now has a mean of 200 and the unexposed has a mean of 100. • The ratio, however, is the same - no bias compared to the truth. • If your goal, however, is to look at the difference in means, then the difference is 100, as opposed to 50. • This is a biased result. 3) If the measurement is off by an absolute difference of 25 units. • Here, you can see that the exposed group has a mean value of 125 and the unexposed group has a value of 75. • The ratio in this case is 1.67, which is biased compared to the truth. • The absolute difference, however, is still 50 and unbiased. So, in the face of systematic error in an interval scale measurement, whether or not there is bias depends upon the measure of association in question. Topic attachments I Attachment Action Size Date Who Comment JPG tnpicture_bias.JPG manage 7.8 K 29 Apr 2009 - 15:19 CTSpediaAdmin JPG tntarget2.JPG manage 6.9 K 29 Apr 2009 - 15:20 CTSpediaAdmin Topic revision: r17 - 14 Dec 2010 - 19:49:31 - MaryBanach CTSpedia.BiasDefinition moved from CTSpedia.Bias on 14 May 2009 - 23:21 by MaryB? - put it back Copyright &© by the contributing authors. All material on this collaboration platform is the property of the contributing authors. Ideas, requests, problems regarding CTSPedia? Send feedback
1,059
4,862
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.0625
3
CC-MAIN-2020-10
longest
en
0.965823
http://docplayer.net/1642934-Simulation-of-photovoltaic-generator-connected-to-a-grid.html
1,539,694,021,000,000,000
text/html
crawl-data/CC-MAIN-2018-43/segments/1539583510749.55/warc/CC-MAIN-20181016113811-20181016135311-00138.warc.gz
90,128,922
29,197
# Simulation of Photovoltaic generator Connected To a Grid Save this PDF as: Size: px Start display at page: ## Transcription 1 Mediterranean Journal of Modeling and Simulation MJMS 1 (214) 2 33 Simulation of Photovoltaic generator Connected To a Grid F. Slama a,*, A. Chouder b, H. Radjeai a a Automatic Laboratory of Setif (LAS), Department of Electrical Engineering, Setif-1 University b Centre de Développement des Energies Renouvelables (CDER) Abstract This paper presents the mathematical and the total Matlab-simulink model of the various components, of the photovoltaic power station connected to a network, (PSCN), namely the model of the photovoltaic generator. It is a comprehensive behavioural study which performed according to varying conditions of solar insulation and temperature. The photovoltaic generator and the inverter of singlephase current are modeled. The former by using a mathematical model that gives the values of maximum power according to the variation of the weather conditions, and the latter by a source of voltage controlled by voltage in order to inject a sinusoidal current and to estimate or predict the energy injected monthly or annually into the network. Keywords: PV generator - Inverter - Control strategies-photovoltaic injection of energy. Nomenclature A diode quality factor E or G irradiation (w/m²) I or I s reverse saturation current of diode (A) I d current shunted through the diode (A) I mpp power point current (A) I ph the generated photo-current (A) I pv the PV array output current (A) I sc cell short-circuit current at STC K boltzmann s constant (j/k) K t current temperature coefficient N p parallel cell number N s series cell number q electron charge (C) R s series resistance (Ω) R sh shunt resistance (Ω) T a ambient temperature ( C) V mpp power point voltage (V) V oc open-circuit voltage (V) V pv the PV array output voltage (V) thermal voltage (V) V t 2 F. Slama / MJMS 1 (214) 2 33 Greek symbols η efficiency Φ irradiation Subscripts Ph photons pv photovoltaic ref reference s series sc short-circuit sh shunt 1. Introduction The development in photovoltaic solar technology has promoted the installation of photovoltaic (PV) solar panels (or arrays/cells) in public infrastructures, residential houses and PV solar power plants. As the PV solar energy penetration level continues to increase, solar power generated electricity is taking a higher portion in the total generated electric power [1]. Usually electric power generated from PV solar panels is more expensive than conventional fuel generated electricity due to the price of PV material and systems and the fact that the power generated by the PV solar panel is largely affected by local weather conditions. Utility grid is gaining more and more visibility due to many national incentives [2]. With a continuous reduction in system cost (PV modules, DC/AC inverters, and installation), the PV technology has the potential to become one of the main renewable energy sources for future electricity supply. The market for grid-connected PV power applications continues to develop at a high rate. Feeding the photovoltaic energy to the AC grid is not evident. It poses some problems in controlling the energy transfer and connecting the two systems together by using static converters. The classical connection between photovoltaic array and AC grid is shown in fig.1. The main objective, from this interfacing, is to feed all the collected energy at the PV plant to the commercial AC grid [3]. PV Array MPPT = = Inverter = Grid Figure 1. PV grid connected system. This is achieved by the following The PV array responsible on transforming, the sun light into electricity. MPPT controller, this is used to maximize the power coming from the PV array at any atmospheric conditions. Inverter, this is a device which transforms DC input into an AC output at the same waveforms as the grid line. 26 3 F. Slama / MJMS 1 (214) Modeling and Simulation of the PV Grid System 2.1. Characteristics of PV array Basically, the PV cell is a P-N semiconductor junction that directly converts light energy into electricity. It has the equivalent circuit shown in fig. 2 [4-]. Figure 2. Equivalent PV cell circuit The current source represents the cell photocurrent, and are the intrinsic series and shunt resistance of the cell respectively. The PV cell exhibits non-linear voltage-current characteristics. The following are the simplified equations describing the behavior of the PV cell [6]. The photo current is proportional to the sun irradiance that a solar cell receives and to the cell temperature which can be described by [7-8]: (1) (2) (3) Now () can be solved using Newton s method, which can be described as: Where is the PV array output current, is the PV array output voltage; q is the charge of an electron, k is Boltzmann s constant, Eg is the band gap of the semi-conductor, is the diode reverse saturation current, and are the cell temperature and the reference temperature both in Kelvin, A and B are the diode ideality factors where their values varied between 1 and 2, ΦN is the normalized insolation, is a short circuit current given at standard condition, and are constants given at standard conditions; and are the series and the parallel cell number respectively. Fig. 4 show the (P-V) characteristics at different insulations and temperatures levels (Module Isofoton 16 Wc, Ns = 1, Np = 4). (4) () 27 4 Module power Ppv (W) F. Slama / MJMS 1 (214) 2 33 Figure 3. Installation of the photovoltaic generator on the roof of CDER, diagram of each generator W/m² 4 W/m² 6 W/m² 8 W/m² 1 W/m² Module voltage Vpv (V) Figure 4. P-V characteristics of PV panel It is shown, in fig. 4 that the maximum power that can be delivered by a PV panel depends greatly on the insulation level and the operating temperature. Therefore, it is necessary to track the maximum power point all the time. Many researchers have focused on various MPP control algorithms to lead the operating point of the PV panel to the optimum point. Some of these algorithms are the constant voltage method, the perturbation and observation (P&O) method, and the incremental conductance method (IncCond) [9] Maximum power point Tracking (MPPT) In order to get the shape of the injected current to the grid, it is necessary to calculate the coordinates of the maximal power point (Vmpp, Impp). For this, and to simplify the implementation model in Matlab, the coordinates of the maximum power point are given by the following equations [1-11]. (6) (7) Where is the thermal voltage given by: (8) 28 5 voltage Vmpp (V) current IMPP (A) Power PMPP (W) Irradiance E (W/m²) Temperature ( C) Acquisition system in the station of CDER F. Slama / MJMS 1 (214) 2 33 Figure. Synoptic total of the system acquisition. The simulation result of 3 KWc photovoltaic grid connected system are shown in the figures below. The entry to the simulation file is a real data of solar insulation and temperature in one day : 4: 8: 12: 16: 2: 1 1 : 4: 8: 12: 16: 2: Figure 6. Illustration the variation of the weather conditions, Profile of Irradiance E (W/m²) and Profile of Temperature ( C) measured current IMPP simulated current IMPP measured power PMPP simulated power PMPP : 4: 8: 12: 16: 2: Figure 7. Illustration the measured and simulated current, Illustration the measured and simulated power : 4: 8: 12: 16: 2: Figure 8. Simulated optimal voltage, Vmpp. 29 6 F. Slama / MJMS 1 (214) Inverter modeling The main specification of the grid connected inverter is that current must be drawn from the PV plant and delivered to the utility grid at unity power factor [12]. Figure 9. Full bridge grid connection. Assuming that the losses are negligible, It is seen that Where all variables are vectors of the form: Then: To achieve the unity power factor condition, the current waveform must be in phase with the utility voltage waveform, in vector form. The key to controlling this operation is the inverter voltage variable, from (1), can be written as: (9) (1) (11) 2.4. Simulation of the PV grid inverter Due to the high computational requirement of a full PWM implementation, a simplification has been made to the inverter model. The full bridge inverter is modeled as current controlled voltage source, where harmonic content is ignored. In this case an indirect current control is used to draw a reference current given by the calculated maximum power from the PV model. The magnitude of the current that the inverter has to draw is given by the power balancing principles: Where η is the inverter efficiency, assumed to be constant (η=.9). The implementation of this bloc diagram in MATLAB is shown in Fig.1. In this scheme, an Average Behavior Modeling (ABM) is used. The inverter output is modeled as a voltage controlled voltage source. The reference current of the grid is calculated from the PV model and is modeled as current source controlled by a current. (12) 3 7 power ( Pmpp(W) and Pmean(W)) Current I inverted (A) voltage Vgrid (V) and Vinv(V) voltage Vgrid (V) and I inverter (A) i - + s - + s - + F. Slama / MJMS 1 (214) 2 33 [Vinv] [Iinvv] [Iload] [VGrid] + - v 12 i i + - or1 g m 1 2 Ideal Switch Load [Impp] Impp [Vmpp] Vmpp Ig Ig + - v [VGrid] Sine Wave [IGrid] Figure1. MATLAB Schematic of PV grid connected inverter. The values of the maximum AC power can be calculated from the amplitudes at the inverter output for the two considered irradiance levels: The simulation results are given in the Fig. 11, 12 and 13 showing the waveforms: current, voltage and power, (before and after passing the inverter) Vinv zoom Vgrid Vgrid zoom Iinv (13) : 4: 8: 12: 16: 2: -3 Time (s) -3 : 4: 8: 12: 16: 2: -3 Figure 11. Simulated inverter voltage Vinv, grid voltage Vgrid and inverter current Iinv Vgrid voltage. 3 2 Pmpp (W) Pmean (W) efficiency =.9 4 Day 1 Day 2 Day : 4: 8: 12: 16: 2: -2 : 4: 8: 12: 16: 2: : Figure12. Simulated power Pmpp and power mean Pmean. Simulated shape of the Iinv injected current. Simulation under MATLAB of the model of the energy injected into the network gives us values of energy of: 23.4 kwh, 22 kwh and 19 kwh. 31 9 F. Slama / MJMS 1 (214) 2 33 Fig. 1 : Indicates that there is insufficient PV energy whereby the utility is concerned to cover this shortcoming of energy. This condition usually occurs at low insolation periods, in early morning or late evening. 3. Conclusion In addition to the dynamic behavior investigation, the simulation has shown the power flow exchange between different components of the system for different modes of operation. Thanks to this study, we can estimate or predict the energy injected monthly or annually into the network. This type of prediction is significant at the time of the feasibility study of a Photovoltaic Power station Connected to the Network. 4. References [1] Velasco-Quesada, G., Guinjoan-Gispert, F., Pique-Lopez, R., Roman-Lumbreras, M., Conesa-Roca, A., Nov. 29. Electrical PV Array Reconfiguration Strategy for Energy Extraction Improvement in Grid-Connected PV Systems, IEEE Trans. Industrial Electronics, Vol. 6,No. 11, pp [2] Yuncong, Jiang., 211. Study and Evaluation of Load Current Based MPPT Control for PV Solar Systems, IEEE Trans. Dept. of Electr. & Comput. Eng., Univ. of Alabama, Tuscaloosa, pp [3] Chouder, A., Silvestre, S., Malek, A., 26. Simulation of photovoltaic grid connected inverter in case of grid-failure, Review of Renewable energy, Vol.9, pp [4] El Shatter, T.F., El Hagry, M.T., Sensitivity Analysis of the Photovoltaic Model Parameters, IEEE, Cir. and Syst., Vol. 2, pp , 8-11 [] Nema, S., K Nema, R., Agnihotri, G., 1999.Matlab / simulink based study of photovoltaic cells / modules / array and their experimental verification, International Journal of Energy and Environment, Vol.1, Issue 3, 21 pp.487- [6] Gow, G.A., Manning, C.D., Development of Photovoltaic Model for Use in Power-Electronics Simulation Studies, IEE, Proceedings of Power Appl., Vol. 146, N 2, pp [7] Djarallah, M., 28. Contribution a l Etude des Systèmes Photovoltaïques Résidentiels Couples au Réseau Electrique, Université de Batna Thèse de Doctorat en Science [8] Al, J., Cotter, E., 26. P-Type Versus n-type Silicon Wafers: Prospects for High- Efficiency commercial silicon solar cells, IEEE, vol. 3, pp [9] Yu, G.J., Jung, Y.S., Choi, J.Y., Choy, I., Song J.H., Kim, G.S., 2. A Novel Two- Mode MPPT Control Algorithm Based on Comparative Study of Existing Algorithms, IEEE, Phot. Spec. Conf, pp , [1] Castañer, L., Santiago, S., 22. Modeling Photovoltaic Systems Using Pspice, Ed. J. Wiley [11] Silvestre, luis castaner., Santiago., 22. Modeling photovoltaic systems using Pspice, Universidad Politecnical Cataluna, Barcelona, Spain. Barcelona, Spain [12] Sugimoto, H., Dong, H., A New Scheme for Maximum Photovoltaic Power Tracking Control, IEEE, Power Conv. Conf., Vol. 2, pp 10 ### Simulation of photovoltaic grid connected inverter in case of grid-failure Revue des Energies Renouvelables Vol. 9 N 4 (2006) 285-296 Simulation of photovoltaic grid connected inverter in case of grid-failure A. Chouder 1, 2,*, S. Silvestre 1 and A. Malek 2 1 Electronic Engineering ### R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Introduction to Inverters Robert W. Erickson Department of Electrical, Computer, and Energy Engineering ### K.Vijaya Bhaskar,Asst. Professor Dept. of Electrical & Electronics Engineering Incremental Conductance Based Maximum Power Point Tracking (MPPT) for Photovoltaic System M.Lokanadham,PG Student Dept. of Electrical & Electronics Engineering Sri Venkatesa Perumal College of Engg & Tech ### Solar Cell Parameters and Equivalent Circuit 9 Solar Cell Parameters and Equivalent Circuit 9.1 External solar cell parameters The main parameters that are used to characterise the performance of solar cells are the peak power P max, the short-circuit ### MPPT-based fuzzy logic controller under partially shaded PV arrays and rapidly variation conditions Revue des Energies Renouvelables SIENR 12 Ghardaïa (2012) 345 350 MPPT-based fuzzy logic controller under partially shaded PV arrays and rapidly variation conditions A. Bouilouta * and A. Mellit Faculty ### Energy Storage Management in Grid Connected Solar Photovoltaic System RESEARCH ARTICLE OPEN ACCESS Energy Storage Management in Grid Connected Solar Photovoltaic System Vidhya M.E, Power Systems Engineering, Sri Ramakrishna Institute of Technology. Abstract The penetration ### Modeling and Control for Smart Grid Integration with MPPT of Solar/Wind Energy Conversion System S. Sathish Kumar 1, B.Swapna 2, Dr.C. Modeling and Control for Smart Grid Integration with MPPT of Solar/Wind Energy Conversion System S. Sathish Kumar 1, B.Swapna 2, Dr.C.Nagarajan 3 Research Scholar, GRT Institute of Engineering & Technology, ### MPPT Based Improvement of Solar Power Efficiency Using Labview MPPT Based Improvement of Solar Power Efficiency Using Labview S.Shanthini Merlin Assistant Professor, Dept. of EEE, Prathyusha Institute of Technology and Management, Thiruvallur, Tamilnadu, India ABSTRACT: ### The Discussion of this exercise covers the following points: Exercise 2 The Solar Panel (Photovoltaic Panel) EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with the operation of the silicon photovoltaic (PV) cell. You will be introduced ### ENERGY CAPTURE IMPROVEMENT OF A SOLAR PV SYSTEM USING A MULTILEVEL INVERTER. A Thesis. Presented to. The Graduate Faculty of The University of Akron ENERGY CAPTURE IMPROVEMENT OF A SOLAR PV SYSTEM USING A MULTILEVEL INVERTER A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree ### Research Paper. Singla et al., International Journal of Advanced Engineering Technology E-ISSN Singla et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Research Paper MODELING OF SOLAR PHOTOVOLTAIC MODULE & EFFECT OF INSOLATION VARIATION USING MATLAB/SIMULINK Vineet ### MULTI-LEVEL INVERTER WITH DC LINK SWITCHES FOR RENEWABLE ENERGY SOURCES VOL., NO. 8, OCTOBER 25 ISSN 89-668 26-25 Asian Research Publishing Network (ARPN). All rights reserved. MULTI-LEVEL INVERTER WITH DC LINK SWITCHES FOR RENEWABLE ENERGY SOURCES Sangari A., Umamaheswari ### The Effect of Temperature on Photovoltaic Cell Efficiency Proceedings of the 1st International Conference on Emerging Trends in Energy Conservation - ETEC Tehran, Tehran, Iran, 20-21 November 2011 The Effect of Temperature on Photovoltaic Cell Efficiency V.Jafari ### An Isolated Multiport DC-DC Converter for Different Renewable Energy Sources An Isolated Multiport DC-DC Converter for Different Renewable Energy Sources K.Pradeepkumar 1, J.Sudesh Johny 2 PG Student [Power Electronics & Drives], Dept. of EEE, Sri Ramakrishna Engineering College, ### Mohamed First University Faculty of Science, dépt de Physique, laboratory LETAS, Oujda, Maroc. (2) Amelioration the performance of photovoltaic stations for pumping and lighting installed in the Douar Zragta of the rural commune of Isly Prefecture of Oujda Angad E. Baghaz 1, R. Gaamouche 1, K. Hirech ### Energy comparison of MPPT techniques for PV Systems Energy comparison of MPPT techniques for PV Systems ROBERTO FARANDA, SONIA LEVA Department of Energy Politecnico di Milano Piazza Leonardo da Vinci, 3 133 Milano ITALY roberto.faranda, sonia.leva@polimi.it June 11 Student Pulse Academic Journal Implementation and control of Multi Input Power Converter for Grid Connected Hybrid Renewable Energy Generation System Yuvaraj V, Roger Rozario, S.N. Deepa yuvatheking@skygroups.org; ### Design, Analysis, and Implementation of Solar Power Optimizer for DC Distribution System Design, Analysis, and Implementation of Solar Power Optimizer for DC Distribution System Thatipamula Venkatesh M.Tech, Power System Control and Automation, Department of Electrical & Electronics Engineering, ### PHOTOVOLTAIC SYSTEMS. Alessandro Massi Pavan PHOTOVOLTAIC SYSTEMS Alessandro Massi Pavan Sesto Val Pusteria June 22 nd 26 th, 2015 GRID-CONNECTED PV PLANTS DISTRIBUTED TIPO DISTRIBUITO PV GENERATOR LOCAL LOADS INVERTER GRID CENTRALIZED PV GENERATOR ### Simulation of MPPT using Fuzzy Logic Controller for AC Drive Simulation of MPPT using Fuzzy Logic Controller for AC Drive Manasa.M.Shetty 1, Girish joshi 2 Electrical and Electronics Department, St. Joseph Engineering College Vamanjoor Mangalore India 1 Abstract: ### Comparative Study of Different Hill Climbing MPPT through Simulation and Experimental Test Bed Research Journal of Applied Sciences, Engineering and Technology 7(20): 4258-4263, 2014 ISSN: 2040-7459; e-issn: 2040-7467 Maxwell Scientific Organization, 2014 Submitted: December 13, 2013 Accepted: December ### The Effect of Temperature on the Performance of A Photovoltaic Solar System In Eastern Nigeria Research Inventy: International Journal Of Engineering And Science Vol.3, Issue 12(December 2013), PP 10-14 Issn(e): 2278-4721, Issn(p):2319-6483, Www.Researchinventy.Com The Effect of Temperature on the ### Renewable Energy Source Applications in Multilevel Inverter Based Induction Motor Drive Using ANN International Journal of Science and Research (IJSR) Renewable Energy Source Applications in Multilevel Inverter Based Induction Motor Drive Using ANN G. Sathish Goud 1, Venkateswarlu Kalimela 2 1 Student, ### Maximum Power Tracking for Photovoltaic Power Systems Tamkang Journal of Science and Engineering, Vol. 8, No 2, pp. 147 153 (2005) 147 Maximum Power Tracking for Photovoltaic Power Systems Joe-Air Jiang 1, Tsong-Liang Huang 2, Ying-Tung Hsiao 2 * and Chia-Hong ### A Photovoltaic Array Simulation Model for Matlab-Simulink GUI Environment A Photovoltaic Array Simulation Model for Matlab-Simulink GUI Environment I. H. Altas, * and A.M. Sharaf 2 : Dept. of Electrical and Electronics Engineering, Karadeniz Technical University, Trabzon, Turkey, ### Grid-Connected Solar Microinverter Reference Design Grid-Connected Solar Microinverter Reference Design 2010 Microchip Technology Incorporated. All Rights Reserved. Grid Connected Solar Microinverter Reference Design using the dspic DSC Slide 1 Hello, and ### Design and realization of a photovoltaic system equipped with the analogical and digital MPPT command for better exploitation of solar energy J. Mater. Environ. Sci. 2 (S1) (211) 538-543 El Ouariachi et al. ISSN : 228-258 Oujda, 21, 22 et 23 Juin 211 «Environnement et développement durable». Design and realization of a photovoltaic system equipped ### SOLAR PHOTOVOLTAIC ENERGY GENERATION AND CONVERSION FROM DEVICES TO GRID INTEGRATION HUIYING ZHENG SHUHUI LI, COMMITTEE CHAIR SOLAR PHOTOVOLTAIC ENERGY GENERATION AND CONVERSION FROM DEVICES TO GRID INTEGRATION by HUIYING ZHENG SHUHUI LI, COMMITTEE CHAIR TIM A. HASKEW JABER ABU QAHOUQ DAWEN LI MIN SUN A DISSERTATION Submitted ### Improved incremental conductance method for maximum power point tracking using cuk converter Mediterranean Journal of Modeling and Simulation MJMS 01 (2014) 057 065 Improved incremental conductance method for maximum power point tracking using cuk converter M. Saad Saoud a, H. A. Abbassi a, S. ### Grid-connected photovoltaic module and array sizing based on an iterative approach International Journal of Smart Grid and Clean nergy Grid-connected photovoltaic module and array sizing based on an iterative approach F. Q. Alenezi *, J. K. Sykulski, M. Rotaru a lectronics and Computer ### AC 2011-212: APPLIED MODELING OF SOLAR CELLS AC 2011-212: APPLIED MODELING OF SOLAR CELLS Ignacio B. Osorno, California State University, Northridge I have been teaching and researching Electrical Power Systems for over 25 years, and currently I ### Modeling, Analysis and Control of Solar Water Pumping System Modeling, Analysis and Control of Solar Water Pumping System Sumit K. Gupta, M. Rizwan Khan 2 and Kaushar Jahan 3, 2 Department of Electrical Engineering, Z. H. College of Engineering and Technology AMU, ### Comparison of Solar Panel Models for Grid Integrations Studies: Harmonics and Voltage Disturbances Comparison of Solar Panel s for Grid Integrations Studies: Harmonics and Voltage Disturbances M. H. de Souza, A. F. Cupertino, L. P. Carlette, F. H. de Oliveira and H. A. Pereira, Member IEEE Abstract ### ISSN Vol.03,Issue.08, September-2015, Pages: WWW.IJITECH.ORG ISSN 2321-8665 Vol.03,Issue.08, September-2015, Pages:1388-1392 Application of Space Vector PWM in High Efficiency Induction Motor Water Pumping System with Photo-Voltaic Array RAVULA RAGHUVEER ### High Intensify Interleaved Converter for Renewable Energy Resources High Intensify Interleaved Converter for Renewable Energy Resources K. Muthiah 1, S.Manivel 2, Gowthaman.N 3 1 PG Scholar, Jay Shriram Group of Institutions,Tirupur 2 Assistant Professor, Jay Shriram Group ### Implementation of A Novel Switch-Mode DC-To-AC Inverter with Non- Linear Robust Control Using MATLAB Implementation of A Novel Switch-Mode DC-To-AC Inverter with Non- Linear Robust Control Using MATLAB Mr. Damodhar Reddy Asst.Prof K. PavanKumar Goud Asst.Prof K. Pradeep Kumar Reddy Asst.Prof Department ### A Stable DC Power Supply for Photovoltaic Systems Int. J. of Thermal & Environmental Engineering Volume 12, No. 1 (216) 67-71 A Stable DC Power Supply for Photovoltaic Systems Hussain A. Attia*, Beza Negash Getu, and Nasser A. Hamad Department of Electrical, ### DC To DC Converter in Maximum Power Point Tracker DC To DC Converter in Maximum Power Point Tracker V.C. Kotak 1, Preti Tyagi 2 Associate Professor, Dept of Electronics Engineering, Shah &Anchor Kutchhi Engineering College, Mumbai, India 1 Research Scholar ### Simulation of solar off- grid photovoltaic system for residential unit International Journal of Sustainable and Green Energy 2014; 4(3-1): 29-33 Published online December 19, 2014 (http://www.sciencepublishinggroup.com/j/ijrse) doi: 10.11648/j.ijrse.s.2015040301.15 Simulation ### Performance Analysis of Multi Level Inverter with DC Link Switches for Renewable Energy Resources International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-2, Issue-6, May 2013 Performance Analysis of Multi Level Inverter with DC Link Switches for Renewable ### Coordination Control of a Hybrid AC/DC Microgrid With Various Renewable Energy Sources Coordination Control of a Hybrid AC/DC Microgrid With Various Renewable Energy Sources 1 Hema Surya Teja Beram, 2 Nandigam Rama Narayana 1,2 Dept. of EEE, Sir C R Reddy College of Engineering, Eluru, AP, ### Design and Implementation of different MPPT Algorithms for PV System Design and Implementation of different MPPT Algorithms for PV System Ch. Kalpana, Ch. Sai Babu, J. Surya Kumari Abstract Solar photovoltaic (PV) systems are used to utilize energy of sun in power generation ### Design of Solar Power Optimizer And Eliminating Leakage Current In Multi-Level Inverter For PV Systems Design of Solar Power Optimizer And Eliminating Leakage Current In Multi-Level Inverter For PV Systems A. Asaph 1, Dr. P. Selvan 2 1 PG Scholar, 2 Head of the Department, Erode Sengunthar Engineering College, ### Hybrid Power System with A Two-Input Power Converter Hybrid Power System with A Two-Input Power Converter Y. L. Juan and H. Y. Yang Department of Electrical Engineering National Changhua University of Education Jin-De Campus, Address: No.1, Jin-De Road, ### Shading Effects on Output Power of Grid Connected Photovoltaic Generator Systems Rev. Energ. Ren. : Power Engineering (2001) 93-99 Shading Effects on Output Power of Grid Connected Photovoltaic Generator Systems R. E. Hanitsch, Detlef Schulz and Udo Siegfried Technical University Berlin ### List of contents. List of Tables.III List of Figures IV List of Symbols and abbreviations... VI Abstract. VII CHAPTER 1... 1 INTRODUCTION... List of contents List of Tables.III List of Figures IV List of Symbols and abbreviations... VI Abstract. VII CHAPTER 1... 1 INTRODUCTION... 1 1.1 THESIS OBJECTIVES... 1 1.2 THESIS OUTLINE... 2 CHAPTER ### Solar Power Analysis Based On Light Intensity The International Journal Of Engineering And Science (IJES) ISSN (e): 2319 1813 ISSN (p): 2319 1805 Pages 01-05 2014 Solar Power Analysis Based On Light Intensity 1 Dr. M.Narendra Kumar, 2 Dr. H.S. Saini, ### High Resolution Spatial Electroluminescence Imaging of Photovoltaic Modules High Resolution Spatial Electroluminescence Imaging of Photovoltaic Modules Abstract J.L. Crozier, E.E. van Dyk, F.J. Vorster Nelson Mandela Metropolitan University Electroluminescence (EL) is a useful ### Modelling and Simulation of Solar Panel Modelling and Simulation of Solar Panel Bhavya Vashisht *, Ahmad Belal Anwar, Gaurav Gautam Department of Electrical Engineering, Delhi Technological University, New Delhi, India Article Info Article history: ### Performance Analysis of Grid Connected Solar PV System Using Matlab/Simulink Performance Analysis of Grid Connected Solar PV System Using Matlab/Simulink Debendra Bahadur Raut* 1 and Ajay Bhattrai 2 1 Peaksun Engineering Solutions (PES) Pvt. Ltd., Kathmandu, Nepal 2 Institute of ### Solar Photovoltaic System Modeling and Control University of Denver Digital Commons @ DU Electronic Theses and Dissertations Graduate Studies 1-1-2012 Solar Photovoltaic System Modeling and Control Qing Xia University of Denver, xiaqing8801@gmail.com Optimal Design and Simulation of a Grid-Connected Photovoltaic (PV) Power System for an Electrical Department in University of Tripoli-Libya Mustafa A. Al-Refai Abstract This paper presents the optimal ### A Photovoltaic (Cell, Module, Array) Simulation and Monitoring Model using MATLAB /GUI Interface A Photovoltaic (Cell, Module, Array) Simulation and Monitoring Model using MATLAB /GUI Interface M.B. Eteiba Department of Electrical Engineering, Faculty of Engineering, Fayoum University Fayoum, Egypt ### ELG4126: Photovoltaic Materials. Based Partially on Renewable and Efficient Electric Power System, Gilbert M. Masters, Wiely ELG4126: Photovoltaic Materials Based Partially on Renewable and Efficient Electric Power System, Gilbert M. Masters, Wiely Introduction A material or device that is capable of converting the energy contained ### Design and Simulation of Grid Connected PV system Using Multilevel Inverters Design and Simulation of Grid Connected PV system Using Multilevel Inverters MD.SAFIA M-tech Student Scholar Department of Electrical & Electronics Engineering, GLOBAL institute of Engineering and Technology; ### Design of a Charge Controller Circuit with Maximum Power Point Tracker (MPPT) for Photovoltaic System Design of a Charge Controller Circuit with Maximum Power Point Tracker (MPPT) for Photovoltaic System A Thesis submitted to the Dept. of Electrical & Electronic Engineering, BRAC University in partial ### Bringing Renewable Energy to the Electrical Engineering Undergraduate Education and Research at UPRM Session WD Bringing Renewable Energy to the Electrical Engineering Undergraduate Education and Research at UPRM Eduardo I. Ortiz-Rivera, Jesus Gonzalez-Llorente, and Andres Salazar-Llinas University of ### Power quality control strategy for grid-connected renewable energy sources using PV array and supercapacitor 2010 International Conference Electrical Machines and Systems, Oct. 10-13, 2010, Incheon, Korea Power quality control strategy for grid-connected renewable energy sources using PV array and supercapacitor ### II. INTRODUCTION. Index Terms-- Photovoltaic power systems, solar power generation, temperature, solar radiation. 0-7803-9033-4/05/\$20.00 2005 IEEE. Analytical Model for a Photovoltaic Module using the Electrical Characteristics provided by the Manufacturer Data Sheet Eduardo. Ortiz-Rivera, Student Member, EEE, and F.Z. Peng, EEE Fellow Abstract-- ### HOUSEHOLD SOLAR POWER SYSTEM Michigan Technological University Digital Commons @ Michigan Tech Dissertations, Master's Theses and Master's Reports - Open Dissertations, Master's Theses and Master's Reports 2014 HOUSEHOLD SOLAR POWER ### Applications of Multilevel Inverter in Grid Connected PMSG Based Wind Power Generation System International Journal of Electronic and Electrical Engineering. ISSN 0974-2174 Volume 7, Number 8 (2014), pp. 867-872 International Research Publication House http://www.irphouse.com Applications of Multilevel ### 4.1 SOLAR CELL OPERATION. Y. Baghzouz ECE Department UNLV 4.1 SOLAR CELL OPERATION Y. Baghzouz ECE Department UNLV SOLAR CELL STRUCTURE Light shining on the solar cell produces both a current and a voltage to generate electric power. This process requires a material ### Comparative Analysis To Study The Effects Of Partial Shading On PV Array Withlt-Spice And Matlab/Simulink Environment Comparative Analysis To Study The Effects Of Partial Shading On PV Array Withlt-Spice And Matlab/Simulink Environment Reena Rathee Vandana Khanna B. K. Das M.Tech Student Assistant Professor Sr.Professor ### An Overview of Converters for Photo Voltaic Power Generating Systems An Overview of Converters for Photo Voltaic Power Generating Systems Manimekalai.P Professor/EEE Selvam college of Technology Namakkal, India 637 003 Harikumar.R Phd,Professor/ECE Bannari Amman Institute ### A MULTILEVEL INVERTER FOR SYNCHRONIZING THE GRID WITH RENEWABLE ENERGY SOURCES BY IMPLEMENTING BATTERY CUM DC-DC CONERTER A MULTILEVEL INVERTER FOR SYNCHRONIZING THE GRID WITH RENEWABLE ENERGY SOURCES BY IMPLEMENTING BATTERY CUM DC-DC CONERTER 1 KARUNYA CHRISTOBAL LYDIA. S, 2 SHANMUGASUNDARI. A, 3 ANANDHI.Y 1,2,3 Electrical ### Photovoltaic Systems I. EE 495/695 Spring 2012 Photovoltaic Systems I EE 495/695 Spring 2012 Types of PV Systems: PV System Types & Goal systems that feed power directly into the utility grid, stand-alone systems that charge batteries, perhaps with ### Distribution Generation System Analysis of Solar Power Optimizer for DC Distribution Generation System Srinivas Dobbala 1, K. Chandra Mouli 2 1 Student, Department of EEE, Vaageswari College of Engineering, Karimnagar, Telangana, India ### Fuzzy Logic Controller Based Maximum Power Point Tracking of Photovoltaic System using CUK Converter Fuzzy Logic Controller Based Maximum Power Point Tracking of Photovoltaic System using CUK Converter B. Mohana P G Scholar Dept. of Electrical & Electronics Engineering K..S.Rangasamy College of Technology, ### Real Time Selective Harmonic Minimization for Multilevel Inverters Connected to Solar Panels Using Artificial Neural Network Angle Generation Real Time Selective Harmonic Minimization for Multilevel Inverters Connected to Solar Panels Using Artificial Neural Network Angle Generation Faete Filho, Leon M. Tolbert, Yue Cao Electrical Engineering ### Manjari Mehrotra, Dr. A.K Pandey ISO 91:28 Certified Volume 2, Issue 5, November 212 Harmonics Analysis of VSI Fed Induction Motor Drive Abstract- This paper mainly focus on harmonics analysis of three phase AC supply available from three ### Behavioral characteristics of photovoltaic cell with different irradiation in Matlab/Simuling/Simscape environment Available online at www.ilcpa.pl International Letters of Chemistry, Physics and Astronomy 17(3) (2014) 316-326 ISSN 2299-3843 Behavioral characteristics of photovoltaic cell with different irradiation ### SIMULATION AND HARDWARE IMPLEMENTETATION OF GRID CONNECTED SOLAR CHARGE CONTROLLER WITH MPPT SIMULATION AND HARDWARE IMPLEMENTETATION OF GRID CONNECTED SOLAR CHARGE CONTROLLER WITH MPPT Prof. Vipul Patel Department of Electrical Engineering H.C.E.T. Sidhpur, GTU Ahmedabad Sidhpur, Gujarat, India ### PSIM Tutorial. How to Use Solar Module Physical Model. - 1 - Powersim Inc. www.powersimtech.com PSIM Tutorial How to Use Solar Module Physical Model - 1 - Powersim Inc. This tutorial describes how to use the solar module physical model. The physical model of the solar module can take into account ### Tie-Line Bias Control of a Power System with Large PV Plants Using PMU Information. Ganesh Kumar. Venayagamoorthy XIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA XIII SEPOPE 18 a 21 de Maio 2014 May 18 th to 21 st 2014 FOZ DO IGUAÇU (PR) - BRAZIL XIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC ### Implementation of High Step-Up Solar Power Optimizer for DC Micro Grid Application Implementation of High tepup olar Power Optimizer for C Micro Grid Application hihming Chen, KeRen Hu, TsorngJuu Liang, and YiHsun Hsieh Advanced Optoelectronic Technology Center epartment of Electrical ### On the characterisation of solar cells using light beam induced current measurements. L.J Bezuidenhout, E.E van Dyk, F.J Vorster and MC du Plessis On the characterisation of solar cells using light beam induced current measurements Abstract L.J Bezuidenhout, E.E van Dyk, F.J Vorster and MC du Plessis Nelson Mandela Metropolitan University Centre ### Photovoltaic Solar Energy Unit EESFB Technical Teaching Equipment Photovoltaic Solar Energy Unit EESFB Products Products range Units 5.-Energy Electronic console PROCESS DIAGRAM AND UNIT ELEMENTS ALLOCATION Worlddidac Member ISO 9000: Quality ### APPLICATION NOTE TESTING PV MICRO INVERTERS USING A FOUR QUADRANT CAPABLE PROGRAMMABLE AC POWER SOURCE FOR GRID SIMULATION. Abstract. TESTING PV MICRO INVERTERS USING A FOUR QUADRANT CAPABLE PROGRAMMABLE AC POWER SOURCE FOR GRID SIMULATION Abstract This application note describes the four quadrant mode of operation of a linear AC Power ### Design and Implementation of an Isolated Solar Photovoltaic Power Generation System A Thesis on Design and Implementation of an Isolated Solar Photovoltaic Power Generation System Submitted by RUPESH PATEL INDUSTRIAL ELECTRONICS ROLL NO. 212EE5399 Department of Electrical Engineering ### Feasibility Study of Brackish Water Desalination in the Egyptian Deserts and Rural Regions Using PV Systems Feasibility Study of Brackish Water Desalination in the Egyptian Deserts and Rural Regions Using PV Systems G.E. Ahmad, *J. Schmid National Research Centre, Solar Energy Department P.O. Box 12622, El-Tahrir ### A Design of DC/DC Converter of Photovoltaic Generation System for Streetcars Journal of International Council on Electrical Engineering Vol. 3, No. 2, pp.164~168, 2013 http://dx.doi.org/10.5370/jicee.2013.3.2.164 A Design of DC/DC Converter of Photovoltaic Generation System for ### Modeling Grid Connection for Solar and Wind Energy 1 Modeling Grid Connection for Solar and Wind Energy P. J. van Duijsen, Simulation Research, The Netherlands Frank Chen, Pitotech, Taiwan Abstract Modeling of grid connected converters for solar and wind ### Solar Energy Conversion using MIAC. by Tharowat Mohamed Ali, May 2011 Solar Energy Conversion using MIAC by Tharowat Mohamed Ali, May 2011 Abstract This work introduces an approach to the design of a boost converter for a photovoltaic (PV) system using the MIAC. The converter ### A Step up DC-DC Converter with Coupled Inductor for Renewable Energy Applications using MPPT A Step up DC-DC Converter with Coupled Inductor for Renewable Energy Applications using MPPT Parvathi Mohan 1, Sreeja E A 2 1 PG Student [Power Electronics & Power System], Dept. of EEE, Federal Institute ### Power Flow Control Using Bidirectional Dc/Dc Converter for Grid Connected Photovoltaic Power System International Journal of Innovative Research in Electronics and Communications (IJIREC) Volume 1, Issue 8, November 2014, PP 13-24 ISSN 2349-4042 (Print) & ISSN 2349-4050 (Online) www.arcjournals.org Power ### T.FRANCIS, D.NARASIMHARAO Applications (IJERA) ISSN: 48-96 wwwijeracom ol, Issue 3, May-Jun 0, pp40-46 A Soft-Switching DC/DC Converter With High oltage Gain for Renewable Energy Application TFRANCIS M-Tech Scholar, Power electronics ### Diodes (non-linear devices) C H A P T E R 4 Diodes (non-linear devices) Diode structure Ideal Diode Figure 4.2 The two modes of operation of ideal diodes and the use of an external circuit to limit (a) the forward current and (b) ### Solar Powered Smart Irrigation System Advance in Electronic and Electric Engineering. ISSN 2231-1297, Volume 4, Number 4 (2014), pp. 341-346 Research India Publications http://www.ripublication.com/aeee.htm Solar Powered Smart Irrigation System ### Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies Soonwook Hong, Ph. D. Michael Zuercher Martinson Harmonics and Noise in Photovoltaic (PV) Inverter and the Mitigation Strategies 1. Introduction PV inverters use semiconductor devices to transform the ### Modeling and Simulation of a Novel Switched Reluctance Motor Drive System with Power Factor Improvement American Journal of Applied Sciences 3 (1): 1649-1654, 2006 ISSN 1546-9239 2006 Science Publications Modeling and Simulation of a Novel Switched Reluctance Motor Drive System with Power Factor Improvement ### MODELING AND SIMULATION OF A THREE-PHASE INVERTER WITH RECTIFIER-TYPE NONLINEAR LOADS , pp. 7-1 MODELING AND SIMULAION OF A HREE-PHASE INERER WIH RECIFIER-YPE NONLINEAR LOADS Jawad Faiz 1 and Ghazanfar Shahgholian 2 1 School of Electrical and Computer Engineering, Faculty of Engineering, ### New Procedure for Measuring Dynamic MPP-Tracking Efficiency at Grid-Connected PV Inverters 24 th European Photovoltaic Solar Energy Conference, Hamburg, Germany, Sept. 29 New Procedure for Measuring Dynamic MPP-racking Efficiency at Grid-Connected PV Inverters New Procedure for Measuring Dynamic ### Solar Energy Discovery Lab Solar Energy Discovery Lab Objective Set up circuits with solar cells in series and parallel and analyze the resulting characteristics. Introduction A photovoltaic solar cell converts radiant (solar) energy ### Operational experienced of an 8.64 kwp grid-connected PV array Hungarian Association of Agricultural Informatics European Federation for Information Technology in Agriculture, Food and the Environment Journal of Agricultural Informatics. 2013 Vol. 4, No. 2 Operational ### DEVELOPING A PHOTOVOLTAIC MPPT SYSTEM. Thomas Bennett. A Dissertation Submitted to the Faculty of. The College of Engineering and Computer Science DEVELOPING A PHOTOVOLTAIC MPPT SYSTEM by Thomas Bennett A Dissertation Submitted to the Faculty of The College of Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree ### Multilevel DC-AC Converter Interface with Solar Panels Pursuit: The Journal of Undergraduate Research at the University of Tennessee Copyright The University of Tennessee Multilevel DC-AC Converter Interface with Solar Panels YUE CAO Advisor: Leon Tolbert ### Regular paper. Sliding mode control of a photovoltaic grid connected system. JES Proof Y. Weslati A. Sellami F. Bacha R. Andoulsi Regular paper Sliding mode control of a photovoltaic grid connected system This paper presents a sliding mode controller for a single-phase grid-connected photovoltaic ### Solar Matters III Teacher Page Solar Matters III Teacher Page Solar Powered System - 2 Student Objective Given a photovoltaic system will be able to name the component parts and describe their function in the PV system. will be able
10,060
41,377
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.59375
3
CC-MAIN-2018-43
longest
en
0.770223
https://web2.0calc.com/questions/problem-help_2
1,558,346,302,000,000,000
text/html
crawl-data/CC-MAIN-2019-22/segments/1558232255837.21/warc/CC-MAIN-20190520081942-20190520103942-00523.warc.gz
682,692,763
6,071
+0 Problem Help +1 181 2 +335 The product of the proper positive integer factors of n can be written as n^[(ax+b)/c], where x is the number of positive divisors n has, c is a positive integer, and the greatest common factor of the three integers a, b, and c is 1. What is a+b+c? Nov 2, 2018 #1 0 n =110 = 2 x 5 x 11 a=2, b=5, c=11 110^((3*2 + 5)/11)=110^(11/11)=110 GCD [2, 5, 11] =1 a + b + c =2 + 5 + 11 = 18 Note: With 2 as the first factor, many n will meet the restrictions given in the question. Examples: 2, 7, 13 =182,  2, 11, 17 =374,  2, 13, 19 =494,   2, 17, 23 =782,  2, 23, 29 =1,334......etc. Nov 2, 2018 edited by Guest  Nov 2, 2018 #2 0 I don't think you understood the question, a b and c don't have to be factors of n, and x is the number of proper positive factors of n, not the number of prime factors of n. Guest Nov 2, 2018
341
856
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.84375
4
CC-MAIN-2019-22
longest
en
0.844181
https://k12workbook.com/grades/fifth-grade/math/data
1,720,860,174,000,000,000
text/html
crawl-data/CC-MAIN-2024-30/segments/1720763514493.69/warc/CC-MAIN-20240713083241-20240713113241-00014.warc.gz
268,815,484
14,952
# Fifth Grade Math Data Worksheets Back Below is list of all worksheets available under this concept. Worksheets are organized based on the concept with in the subject. Click on concept to see list of all available worksheets. • Finding the Average: Mean, Median, and Mode Help the concept of averages sink in for your fifth grader with this worksheet all about finding the mean, median, and mode. • Spring Math: Jelly Bean Probability Spring into spring with some probability practice. • What's the Probability? Help your fifth grader understand probability with this worksheet that challenges her to find the probability of a certain event in a handful of scenarios. • Probability Toss 1 What are the chances that a dart will land on an even number on a dart board? Find out in this sixth grade probability worksheet! • Donut Data Make fractions fun with everyone's favorite breakfast treat. This donut-themed worksheet asks students to calculate pounds of donuts using fractions and line plots. • Probability Toss 5 Sixth graders will practice probability in this dart board themed worksheet. Your kid will calculate the probability of a dart hitting a certain kind of number. • Musher Math Word Problems This worksheet offers fifth graders a chance to learn about a fascinating true story, and also provides some great related word problems practice. • Olympic Math: Bobsleigh Time Averages Get your 5th grader in the Olympic spirit with this fun bobsled math worksheet. He'll calculate each country's average run time, then award the winners! • Probability Darts 1 Kids will practice with fractions and degrees in this probability worksheet. Help your kid figure out the probability of a dart landing in different places. • Looking at Line Plots This worksheet prompts students' critical thinking skills. Students will need to determine if several line plot problems are solved correctly and explain their reasoning. • Math Olympics: Figure Skating Average Scores Your child gets to play Olympic judge in this 5th grade math worksheet. She'll calculate each country's average score in order to find the winner! • Interpreting Double Bar Graphs Students will cultivate the skills of reading, interpreting, and analyzing bar graphs with these questions that activate higher order thinking. • Probability Toss 3 If your sixth grader likes darts, then he'll love this probability worksheet! This dart board themed worksheet introduces your child to simple probability. • Probability Toss 2 Boost your child's math know-how! What are the odds a dart would land on one of the given sections of this circle? • Create a Double Bar Graph (with data provided) Ask your students to use data to create a double bar graph and interpret the graph with critical thinking. • Probability Darts 5 Build on fraction math skills and working with degrees up to 360° get probability practice for your middle schooler with this math worksheet series. • Line Plot Fractions Build your students' confidence in using fractions. With this worksheet, students will graph data of snowfall measurements on a line plot. • Probability Toss 4 Help your sixth grader learn about probability with a dart board math worksheet. Use math skills to calculate the probability of a dart hitting number types. • Olympic Arithmetic: Skeleton Time Averages Your fifth grader will use his math skills to help the judges determine which country has the fastest averages in an exciting Winter Olympics sport--skeleton! • Probability Darts 2 Build on fraction math skills and working with degrees to get probability practice for your middle schooler with this math worksheet series. • Peachy Line Plots Students create their own peachy word problems by filling in the blanks, then create a line plot with the data. • Probability Darts 4 Building on math skills with fractions, addition, and degrees, kids will figure out how much of the dart board each panel takes up then answer questions. • Interpreting Bar Chart Graphs Students will cultivate the skills of reading, interpreting, and analyzing more complex graph of bar charts with these questions that activate higher order thinking. • Probability Darts 3 Build on fraction math skills and work with degrees to get probability practice for your middle schooler with this math worksheet series.
863
4,356
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
3.953125
4
CC-MAIN-2024-30
latest
en
0.912178
https://algebra-calculators.com/how-to-square-a-number-ending-with-5-within-seconds/
1,669,881,453,000,000,000
text/html
crawl-data/CC-MAIN-2022-49/segments/1669446710801.42/warc/CC-MAIN-20221201053355-20221201083355-00044.warc.gz
119,366,628
17,535
How to square a number ending with 5 within seconds Squaring a number ending in 5 is the easiest if you know the trick. Number given to you can be a two digit number or three digit number or five or six digit number, it does’n t matter. The same trick can be applied to find the square of any number ending in 5. Let us now discuss the steps to follow Step 1:Multiply the ten’s digit of the given number with its immediate next number.This will be the 1st digit of the answer. Step 2:Put 25 next to the result of step 1. Logic behind putting 25 is that the number will always end with 5 and 52 is 25. Let us find squares of numbers ending in 5 using this trick Example 1:(35)2=? Step 1: 3 is the ten’s digit in the given number 35. Immediate next number to 3 is 4. Hence,by multiplying 3 & 4 we get 12(3×4=12).which is the 1st digit of the answer. Step 2: Now putting 25 next to 12 we get the answer as 1225. Now you try to square 25,45,15,55,65,75,85,95 & see how quickly you can square. Example 2:(125)2=? Step 1: 12 is the ten’s digit in the given number 125. Immediate next number to 12 is 13. Hence,by multiplying 12 & 13 we get 156(12×13=156).which is the 1st digit of the answer. [To multiply a 2digit by 2digit number when ten’s digit of both numbers is 1 you can apply a trick to get your answer quickly. 1st digit =1 middle digit =add unit’s place digit of both numbers(2+3=5) unit’s place digit=Multiply unit place digit of both numbers(2×3=6)] Step 2: Now putting 25 next to 156 we get the answer as 15625. Ans (125)2= 15625 Now you try to square 105,115,135,145,155,165,175,185,195 & see how quickly you can square.
499
1,644
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
4.6875
5
CC-MAIN-2022-49
longest
en
0.782977
https://blog.fxcc.com/is-a-gross-profit-margin-calculator-of-any-value-to-a-retail-forex-trader
1,660,449,617,000,000,000
text/html
crawl-data/CC-MAIN-2022-33/segments/1659882571993.68/warc/CC-MAIN-20220814022847-20220814052847-00275.warc.gz
158,070,977
16,937
## Is a Gross Profit Margin Calculator of any Value to a Retail Forex Trader? A gross profit margin calculator is an online tool used by investors to determine the financial health of an enterprise. It basically calculates the percentage of revenue left after deducting the cost of goods sold. In skin and bones terms, gross profit margin is a profitability ratio. It is one of the many metrics usually used by stock investors to determine the viability of investing in a company that is currently under its consideration and study. The gross profit margin is calculated based on the formula below: Gross Profit Margin = [1 – Cost of Goods Sold/Revenue] x 100 The gross profit margin is normally calculated on an annual or quarterly basis with the results compared against each other or plotted on a chart where it will give a historical perspective of the company’s profitability. Is a gross profit margin calculator of any use to foreign currency trading? My answer is both yes and no. There is one segment of the foreign currency market that may find use for this calculator. This is the foreign currency exchange traded funds or Forex ETFs. This is an investment fund solely to trade foreign currency market much like a pooled account and operates like a mutual fund. You can participate in such funds by buying shares. And since they are traded in an exchange, you can buy shares just like in a stock exchange. Similarly, before investing on any forex ETF, you need to analyze the past performance of the fund along with other due diligence work. And of course, part of the due diligence would be determining the fund’s profitability ratio on a per share basis. You can use the formula above to determine the gross profit margin of an ETF share by substituting the revenue with the current value of each share and the cost of goods with the acquisition cost of each share plus all the accruing fees relative to the purchase and sale of the share. The resulting gross profit margin will give you a snapshot of the profitability ratio of the fund’s performance. However, in foreign currency trading, it is widely accepted that a sterling past performance can never guarantee profitable future trades. The forex market is extremely volatile and too unpredictable to guarantee that the future performance will be as profitable as the past. A commendable gross profit margin is but a meaningless medal that is pinned to the fund manager’s shirt but will never mean guaranteed profits for you. For retail forex trading, a gross profit margin calculator is of no value at all. In the first place, there is no cost of goods to consider. Besides, retail forex trading is done using a margin trading system with no brokers’ fees to worry about. On top of that, revenues are just as volatile as the price swings in the market – what may appear as profits now can easily turn into losses the next minute. In short, none of the parameters used in calculating the gross profit margin can be adapted for retail forex trading. And if ever anyone finds a way to use the gross profit margin calculator for retail forex trading, it will be of insignificant value as the resulting calculations or profit ratio do not in any way help the individual traders make money trading the currency pairs.
628
3,288
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
2.5625
3
CC-MAIN-2022-33
latest
en
0.937762