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https://www.indiastudysolution.com/2019/10/neet-iit-jee-main-aipmt-kvpy-ntse-india-study-solution-solved-physics-test-series-on-kinematics-s1.html	1,586,542,851,000,000,000	text/html	crawl-data/CC-MAIN-2020-16/segments/1585370511408.40/warc/CC-MAIN-20200410173109-20200410203609-00319.warc.gz	938,290,112	63,973	# NEET, IIT JEE Main, AIPMT, KVPY, NTSE : India Study Solution solved Physics Test Series on Kinematics Welcome to 'India Study Solution’ Physics MCQ Test Series Section, each set containing exclusively selected 10 most important questions with hints & solutions from the chapter KINEMATICS. Here you get solved MCQ Test Series on Kinematics (syllabus included below), Kinematics Objective questions with solutions, Physics practice questions with hints and answers for preparing NEET, AIPMT, IIT JEE Main, Medical, Dental Entrance Exams, Engineering Entrance Exams; MBBS and Engineering Admission Tests, NTSE, KVPY and other competitive exams. Kinematics Syllabus: Frame of reference, Motion in a straight line, Uniform and Non-uniform motion, Average speed and instantaneous velocity, Uniformly accelerated motion, Velocity - Time, Position - Time graphs, Relations for uniformly accelerated motion, Relative velocity, Motion in a plane. Scalars and Vectors, Vector addition and subtraction, Zero vector, Scalar and vector products, Unit vector, Resolution of a vector, Position and Displacement vector, General vector and notation, Equality of vector, Multiplication of vector and a real number. Physics Notes and Study Materials with Key Points to remember and important Formulae and more on Kinematics - Motion in a straight line, Uniform and Non-uniform acceleration, Relative velocity, Scalars and Vectors and all topics in syllabus will be published separately (Keep watching ... link will be provided here) ### Kinematics: Physics Guide and Solution MCQ Test Series – Set 1 (Q. No. 1-10) Question 1: Which of the following changes when a particle is moving with uniform velocity? a. Speed b. Velocity c. Acceleration d. Position vector Question 2: The position - time graph of an object in uniform motion is shown in the adjacent figure, the velocity of the object is - a. positive b. negative c. zero d. none of these Post continues after the Ad - Question 3: Two trains are each 50 m long running parallel with each other at speed of 10 m/s and 15 m/s respectively; at what time will they pass each other? a. 8 s b. 4 s c. 2 s d. 10 s Question 4: The velocity of a train increases uniformly from 20 km/h to 60 km/h in 4 hour. The distance travelled by the train during this time is - a. 160 km b. 180 km c. 100 km d. 120 km Question 5: The displacement of a body is given by y = a + bt + ct2 – dt4 The initial velocity and acceleration are respectively - a. b, –4d b. –b, 2c c. b, 2c d. 2c, –4d Question 6: Displacement has the same unit of - a. length b. velocity c. energy d. acceleration Question 7: When a body is dropped from a tower, then there is an increase in its - a. Mass b. Velocity c. Acceleration d. Potential energy Question 8: A river is flowing from west to east at a speed of 8 m/min. A man on the south bank of the river, capable of swimming at 20 m/min in still water, wants to swim across the river in the shortest time. He should swim in a direction - a. due north b. 30O east of north c. 30O west of north d. 60O east of north Question 9: Which of the following statements is false? a. Displacement is independent of the choice of origin of the axis. b. Displacement may or may not be equal to the distance travelled. c. When a particle returns to its starting point, its displacement is zero. d. A positive acceleration always corresponds to the speeding up and a negative acceleration always corresponds to the speeding down. Question 10: The velocity - time graph of an object is shown in the fig. The part of the graph showing zero acceleration is - a. AB b. BC c. CD d. DE India Study Solution Physics Guide and Solution: KINEMATICS Solutions of Multiple Choice Questions Test Series – Set 1 (Q. No.1 –10) (Hint: vr = 25 m/s, t = (50 + 50)/25 = 4 s.)	967	3,807	{"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-2020-16	longest	en	0.843206
http://easy-ciphers.com/billbeetle	1,686,381,140,000,000,000	text/html	crawl-data/CC-MAIN-2023-23/segments/1685224657144.94/warc/CC-MAIN-20230610062920-20230610092920-00096.warc.gz	15,054,620	15,776	Easy Ciphers Tools: Caesar cipher Caesar cipher, is one of the simplest and most widely known encryption techniques. The transformation can be represented by aligning two alphabets, the cipher alphabet is the plain alphabet rotated left or right by some number of positions. When encrypting, a person looks up each letter of the message in the 'plain' line and writes down the corresponding letter in the 'cipher' line. Deciphering is done in reverse. The encryption can also be represented using modular arithmetic by first transforming the letters into numbers, according to the scheme, A = 0, B = 1,..., Z = 25. Encryption of a letter x by a shift n can be described mathematically as Plaintext: billbeetle cipher variations: cjmmcffumf dknndggvng elooehhwoh fmppfiixpi gnqqgjjyqj horrhkkzrk ipssillasl jqttjmmbtm kruuknncun lsvvloodvo mtwwmppewp nuxxnqqfxq ovyyorrgyr pwzzpsshzs qxaaqttiat rybbruujbu szccsvvkcv taddtwwldw ubeeuxxmex vcffvyynfy wdggwzzogz xehhxaapha yfiiybbqib zgjjzccrjc ahkkaddskd Decryption is performed similarly, (There are different definitions for the modulo operation. In the above, the result is in the range 0...25. I.e., if x+n or x-n are not in the range 0...25, we have to subtract or add 26.) Atbash Cipher Atbash is an ancient encryption system created in the Middle East. It was originally used in the Hebrew language. The Atbash cipher is a simple substitution cipher that relies on transposing all the letters in the alphabet such that the resulting alphabet is backwards. The first letter is replaced with the last letter, the second with the second-last, and so on. An example plaintext to ciphertext using Atbash: Plain: billbeetle Cipher: yrooyvvgov Baconian Cipher To encode a message, each letter of the plaintext is replaced by a group of five of the letters 'A' or 'B'. This replacement is done according to the alphabet of the Baconian cipher, shown below. ```a AAAAA g AABBA m ABABB s BAAAB y BABBA b AAAAB h AABBB n ABBAA t BAABA z BABBB c AAABA i ABAAA o ABBAB u BAABB d AAABB j BBBAA p ABBBA v BBBAB e AABAA k ABAAB q ABBBB w BABAA f AABAB l ABABA r BAAAA x BABAB ``` Plain: billbeetle Cipher: AAAAB ABAAA ABABA ABABA AAAAB AABAA AABAA BAABA ABABA AABAA Affine Cipher In the affine cipher the letters of an alphabet of size m are first mapped to the integers in the range 0..m - 1. It then uses modular arithmetic to transform the integer that each plaintext letter corresponds to into another integer that correspond to a ciphertext letter. The encryption function for a single letter is where modulus m is the size of the alphabet and a and b are the key of the cipher. The value a must be chosen such that a and m are coprime. Considering the specific case of encrypting messages in English (i.e. m = 26), there are a total of 286 non-trivial affine ciphers, not counting the 26 trivial Caesar ciphers. This number comes from the fact there are 12 numbers that are coprime with 26 that are less than 26 (these are the possible values of a). Each value of a can have 26 different addition shifts (the b value) ; therefore, there are 1226 or 312 possible keys. Plaintext: billbeetle cipher variations: cjmmcffumf eziienngin gpeegvvsev kvwwkllqwl mlssmttcst qrkkqjjakj shggsrrmgr uxccuzzycz wnyywhhkyh yduuyppwup atqqaxxiqx dknndggvng fajjfoohjo hqffhwwtfw jgbbjeefbe lwxxlmmrxm nmttnuudtu rsllrkkblk tihhtssnhs vyddvaazda xozzxiilzi zevvzqqxvq burrbyyjry elooehhwoh gbkkgppikp irggixxugx khcckffgcf mxyymnnsyn onuuovveuv stmmsllcml ujiiuttoit wzeewbbaeb ypaayjjmaj afwwarrywr cvssczzksz fmppfiixpi hcllhqqjlq jshhjyyvhy liddlgghdg nyzznootzo povvpwwfvw tunntmmdnm vkjjvuupju xaffxccbfc zqbbzkknbk bgxxbsszxs dwttdaalta gnqqgjjyqj idmmirrkmr ktiikzzwiz mjeemhhieh ozaaoppuap qpwwqxxgwx uvoounneon wlkkwvvqkv ybggyddcgd arccallocl chyycttayt exuuebbmub horrhkkzrk jennjsslns lujjlaaxja nkffniijfi pabbpqqvbq rqxxryyhxy vwppvoofpo xmllxwwrlw zchhzeedhe bsddbmmpdm dizzduubzu fyvvfccnvc ipssillasl kfookttmot mvkkmbbykb olggojjkgj qbccqrrwcr sryyszziyz wxqqwppgqp ynmmyxxsmx cteecnnqen ejaaevvcav gzwwgddowd jqttjmmbtm lgppluunpu nwllncczlc pmhhpkklhk tszztaajza xyrrxqqhrq zonnzyytny bejjbggfjg duffdoorfo fkbbfwwdbw haxxheepxe kruuknncun mhqqmvvoqv oxmmoddamd qniiqllmil sdeesttyet utaaubbkab yzssyrrisr apooazzuoz cfkkchhgkh evggeppsgp glccgxxecx ibyyiffqyf lsvvloodvo nirrnwwprw pynnpeebne rojjrmmnjm tefftuuzfu vubbvcclbc zattzssjts bqppbaavpa dglldiihli fwhhfqqthq hmddhyyfdy jczzjggrzg mtwwmppewp ojssoxxqsx qzooqffcof spkksnnokn ufgguvvagv wvccwddmcd abuuattkut crqqcbbwqb ehmmejjimj gxiigrruir ineeizzgez kdaakhhsah nuxxnqqfxq pkttpyyrty rapprggdpg tqlltooplo vghhvwwbhw xwddxeende bcvvbuulvu dsrrdccxrc finnfkkjnk hyjjhssvjs joffjaahfa lebbliitbi ovyyorrgyr qluuqzzsuz sbqqshheqh urmmuppqmp whiiwxxcix yxeeyffoef cdwwcvvmwv etsseddysd gjoogllkol izkkittwkt kpggkbbigb mfccmjjucj pwzzpsshzs rmvvraatva tcrrtiifri vsnnvqqrnq xijjxyydjy zyffzggpfg dexxdwwnxw futtfeezte hkpphmmlpm jalljuuxlu lqhhlccjhc ngddnkkvdk qxaaqttiat snwwsbbuwb udssujjgsj wtoowrrsor yjkkyzzekz azggahhqgh efyyexxoyx gvuugffauf ilqqinnmqn kbmmkvvymv mriimddkid oheeollwel rybbruujbu toxxtccvxc vettvkkhtk xuppxsstps zkllzaafla bahhbiirhi fgzzfyypzy hwvvhggbvg jmrrjoonro lcnnlwwznw nsjjneelje piffpmmxfm szccsvvkcv upyyuddwyd wfuuwlliul yvqqyttuqt almmabbgmb cbiicjjsij ghaagzzqaz ixwwihhcwh knsskpposp mdoomxxaox otkkoffmkf qjggqnnygn vqzzveexze xgvvxmmjvm zwrrzuuvru bmnnbcchnc dcjjdkktjk hibbhaarba jyxxjiidxi lottlqqptq neppnyybpy pullpggnlg rkhhroozho ubeeuxxmex wraawffyaf yhwwynnkwn axssavvwsv cnoocddiod edkkellukl ijccibbscb kzyykjjeyj mpuumrrqur ofqqozzcqz qvmmqhhomh sliisppaip vcffvyynfy xsbbxggzbg zixxzoolxo byttbwwxtw doppdeejpe fellfmmvlm jkddjcctdc lazzlkkfzk nqvvnssrvs rwnnriipni tmjjtqqbjq wdggwzzogz ytccyhhach ajyyappmyp czuucxxyux epqqeffkqf gfmmgnnwmn kleekddued mbaamllgal orwwottswt qhssqbbesb sxoosjjqoj unkkurrckr xehhxaapha zuddziibdi bkzzbqqnzq davvdyyzvy fqrrfgglrg hgnnhooxno lmffleevfe ncbbnmmhbm psxxpuutxu rittrccftc typptkkrpk vollvssdls yfiiybbqib aveeajjcej claacrroar ebwwezzawz ihooippyop mnggmffwgf odcconnicn qtyyqvvuyv sjuusddgud uzqqullsql wpmmwttemt zgjjzccrjc bwffbkkdfk dmbbdsspbs fcxxfaabxa hstthiinti jippjqqzpq nohhnggxhg peddpoojdo ruzzrwwvzw tkvvteehve varrvmmtrm xqnnxuufnu cxggcllegl enccettqct gdyygbbcyb ituuijjouj kjqqkrraqr opiiohhyih qfeeqppkep svaasxxwax ulwwuffiwf wbsswnnusn yrooyvvgov billbeetle dyhhdmmfhm foddfuurdu hezzhccdzc juvvjkkpvk lkrrlssbrs pqjjpiizji rgffrqqlfq twbbtyyxby vmxxvggjxg xcttxoovto zsppzwwhpw The decryption function is where a - 1 is the modular multiplicative inverse of a modulo m. I.e., it satisfies the equation The multiplicative inverse of a only exists if a and m are coprime. Hence without the restriction on a decryption might not be possible. It can be shown as follows that decryption function is the inverse of the encryption function, ROT13 Cipher Applying ROT13 to a piece of text merely requires examining its alphabetic characters and replacing each one by the letter 13 places further along in the alphabet, wrapping back to the beginning if necessary. A becomes N, B becomes O, and so on up to M, which becomes Z, then the sequence continues at the beginning of the alphabet: N becomes A, O becomes B, and so on to Z, which becomes M. Only those letters which occur in the English alphabet are affected; numbers, symbols, whitespace, and all other characters are left unchanged. Because there are 26 letters in the English alphabet and 26 = 2 13, the ROT13 function is its own inverse: ROT13(ROT13(x)) = x for any basic Latin-alphabet text x An example plaintext to ciphertext using ROT13: Plain: billbeetle Cipher: ovyyorrgyr Polybius Square A Polybius Square is a table that allows someone to translate letters into numbers. To give a small level of encryption, this table can be randomized and shared with the recipient. In order to fit the 26 letters of the alphabet into the 25 spots created by the table, the letters i and j are usually combined. 1 2 3 4 5 1 A B C D E 2 F G H I/J K 3 L M N O P 4 Q R S T U 5 V W X Y Z Basic Form: Plain: billbeetle Cipher: 21421313215151441351 Extended Methods: Method #1 Plaintext: billbeetle method variations: goqqgkkyqk mtvvmppdvp ryaaruuiau wdffwzzofz Method #2 Bifid cipher The message is converted to its coordinates in the usual manner, but they are written vertically beneath: ```b i l l b e e t l e 2 4 1 1 2 5 5 4 1 5 1 2 3 3 1 1 1 4 3 1 ``` They are then read out in rows: 24112554151233111431 Then divided up into pairs again, and the pairs turned back into letters using the square: Plain: billbeetle Cipher: rawuvfnaqc Method #3 Plaintext: billbeetle method variations: qbchvvqdxf bchvvqdxfq chvvqdxfqb hvvqdxfqbc vvqdxfqbch vqdxfqbchv qdxfqbchvv dxfqbchvvq xfqbchvvqd fqbchvvqdx Permutation Cipher In classical cryptography, a permutation cipher is a transposition cipher in which the key is a permutation. To apply a cipher, a random permutation of size E is generated (the larger the value of E the more secure the cipher). The plaintext is then broken into segments of size E and the letters within that segment are permuted according to this key. In theory, any transposition cipher can be viewed as a permutation cipher where E is equal to the length of the plaintext; this is too cumbersome a generalisation to use in actual practice, however. The idea behind a permutation cipher is to keep the plaintext characters unchanged, butalter their positions by rearrangement using a permutation This cipher is defined as: Let m be a positive integer, and K consist of all permutations of {1,...,m} For a key (permutation) , define: The encryption function The decryption function A small example, assuming m = 6, and the key is the permutation : The first row is the value of i, and the second row is the corresponding value of (i) The inverse permutation, is constructed by interchanging the two rows, andrearranging the columns so that the first row is in increasing order, Therefore, is: Total variation formula: e = 2,718281828 , n - plaintext length Plaintext: billbeetle first 5040 cipher variations(3628800 total) billbeetle billbeetel billbeelte billbeelet billbeeelt billbeeetl billbetele billbeteel billbetlee billbetlee billbetele billbeteel billbeltee billbeltee billbelete billbeleet billbeleet billbelete billbeetle billbeetel billbeelte billbeelet billbeeelt billbeeetl billbeetle billbeetel billbeelte billbeelet billbeeelt billbeeetl billbetele billbeteel billbetlee billbetlee billbetele billbeteel billbeltee billbeltee billbelete billbeleet billbeleet billbelete billbeetle billbeetel billbeelte billbeelet billbeeelt billbeeetl billbteele billbteeel billbtelee billbtelee billbteele billbteeel billbteele billbteeel billbtelee billbtelee billbteele billbteeel billbtleee billbtleee billbtleee billbtleee billbtleee billbtleee billbteele billbteeel billbtelee billbtelee billbteele billbteeel billbletee billbletee billbleete billbleeet billbleeet billbleete billblteee billblteee billblteee billblteee billblteee billblteee billbletee billbletee billbleete billbleeet billbleeet billbleete billbletee billbletee billbleete billbleeet billbleeet billbleete billbeetle billbeetel billbeelte billbeelet billbeeelt billbeeetl billbetele billbeteel billbetlee billbetlee billbetele billbeteel billbeltee billbeltee billbelete billbeleet billbeleet billbelete billbeetle billbeetel billbeelte billbeelet billbeeelt billbeeetl billebetle billebetel billebelte billebelet billebeelt billebeetl billebtele billebteel billebtlee billebtlee billebtele billebteel billebltee billebltee billeblete billebleet billebleet billeblete billebetle billebetel billebelte billebelet billebeelt billebeetl billeebtle billeebtel billeeblte billeeblet billeebelt billeebetl billeetble billeetbel billeetlbe billeetleb billeetelb billeetebl billeeltbe billeelteb billeelbte billeelbet billeelebt billeeletb billeeetlb billeeetbl billeeeltb billeeelbt billeeeblt billeeebtl billeteble billetebel billetelbe billeteleb billeteelb billeteebl billetbele billetbeel billetblee billetblee billetbele billetbeel billetlbee billetlbee billetlebe billetleeb billetleeb billetlebe billeteble billetebel billetelbe billeteleb billeteelb billeteebl billeletbe billeleteb billelebte billelebet billeleebt billeleetb billeltebe billelteeb billeltbee billeltbee 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billetbeel billeteble billetebel billetelbe billeteleb billeteelb billeteebl billetlebe billetleeb billetlbee billetlbee billetlebe billetleeb billeteelb billeteebl billeteleb billetelbe billeteble billetebel billelbtee billelbtee billelbete billelbeet billelbeet billelbete billeltbee billeltbee billeltebe billelteeb billelteeb billeltebe billeletbe billeleteb billelebte billelebet billeleebt billeleetb billeleteb billeletbe billeleetb billeleebt billelebet billelebte billeebtle billeebtel billeeblte billeeblet billeebelt billeebetl billeetble billeetbel billeetlbe billeetleb billeetelb billeetebl billeeltbe billeelteb billeelbte billeelbet billeelebt billeeletb billeeetlb billeeetbl billeeeltb billeeelbt billeeeblt billeeebtl billteeble billteebel billteelbe billteeleb billteeelb billteeebl billtebele billtebeel billteblee billteblee billtebele billtebeel billtelbee billtelbee billtelebe billteleeb billteleeb billtelebe billteeble billteebel billteelbe billteeleb billteeelb billteeebl 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bilellbete bilelltbee bilelltbee bilelltebe bilellteeb bilellteeb bilelltebe bilelletbe bilelleteb bilellebte bilellebet bilelleebt bilelleetb bilelleteb bilelletbe bilelleetb bilelleebt bilellebet bilellebte bilelebtle bilelebtel bileleblte bileleblet bilelebelt bilelebetl bileletble bileletbel bileletlbe bileletleb bileletelb bileletebl bileleltbe bilelelteb bilelelbte bilelelbet bilelelebt bileleletb bileleetlb bileleetbl bileleeltb bileleelbt bileleeblt bileleebtl biletelble biletelbel biletellbe biletelleb biletelelb biletelebl bileteblle bileteblel bileteblle bileteblel biletebell biletebell biletelble biletelbel biletellbe biletelleb biletelelb biletelebl bileteebll bileteebll bileteelbl bileteellb bileteellb bileteelbl biletleble biletlebel biletlelbe biletleleb biletleelb biletleebl biletlbele biletlbeel biletlblee biletlblee biletlbele biletlbeel biletllbee biletllbee biletllebe biletlleeb biletlleeb biletllebe biletleble biletlebel biletlelbe biletleleb biletleelb biletleebl biletblele biletbleel biletbllee biletbllee biletblele biletbleel biletbelle biletbelel biletbelle biletbelel biletbeell biletbeell biletblele biletbleel biletbllee biletbllee biletblele biletbleel biletbeell biletbeell biletbelel biletbelle biletbelle biletbelel biletllbee biletllbee biletllebe biletlleeb biletlleeb biletllebe biletlblee biletlblee biletlbele biletlbeel biletlbeel biletlbele biletleble biletlebel biletlelbe biletleleb biletleelb biletleebl biletlebel biletleble biletleebl biletleelb biletleleb biletlelbe biletelble biletelbel biletellbe biletelleb biletelelb biletelebl bileteblle bileteblel bileteblle bileteblel biletebell biletebell biletelble biletelbel biletellbe biletelleb biletelelb biletelebl bileteebll bileteebll bileteelbl bileteellb bileteellb bileteelbl bileleltbe bilelelteb bilelelbte bilelelbet bilelelebt bileleletb bileletlbe bileletleb bileletble bileletbel bileletebl bileletelb bilelebtle bilelebtel bileleblte bileleblet bilelebelt bilelebetl bileleetbl bileleetlb bileleebtl bileleeblt bileleelbt bileleeltb bilelletbe bilelleteb bilellebte bilellebet bilelleebt bilelleetb bilelltebe bilellteeb bilelltbee bilelltbee bilelltebe bilellteeb bilellbtee bilellbtee bilellbete bilellbeet bilellbeet bilellbete bilelletbe bilelleteb bilellebte bilellebet bilelleebt bilelleetb bileltlebe bileltleeb bileltlbee bileltlbee bileltlebe bileltleeb bileltelbe bilelteleb bilelteble bileltebel bilelteebl bilelteelb bileltbele bileltbeel bileltblee bileltblee bileltbele bileltbeel bilelteebl bilelteelb bileltebel bilelteble bileltelbe bilelteleb bilelbltee bilelbltee bilelblete bilelbleet bilelbleet bilelblete bilelbtlee bilelbtlee bilelbtele bilelbteel bilelbteel bilelbtele bilelbetle bilelbetel bilelbelte bilelbelet bilelbeelt bilelbeetl bilelbetel bilelbetle bilelbeetl bilelbeelt bilelbelet bilelbelte bileleltbe bilelelteb bilelelbte bilelelbet bilelelebt bileleletb bileletlbe bileletleb bileletble bileletbel bileletebl bileletelb bilelebtle bilelebtel bileleblte bileleblet bilelebelt bilelebetl bileleetbl bileleetlb bileleebtl bileleeblt bileleelbt bileleeltb bileeeltlb bileeeltbl bileeelltb bileeellbt bileeelblt bileeelbtl bileeetllb bileeetlbl bileeetllb bileeetlbl bileeetbll bileeetbll bileeeltlb bileeeltbl bileeelltb bileeellbt bileeelblt bileeelbtl bileeebtll bileeebtll bileeebltl bileeebllt bileeebllt bileeebltl bileeletlb bileeletbl bileeleltb bileelelbt bileeleblt bileelebtl bileeltelb bileeltebl bileeltleb bileeltlbe bileeltble bileeltbel bileellteb bileelltbe bileelletb bileellebt bileellbet bileellbte bileelbtle bileelbtel bileelblte bileelblet bileelbelt bileelbetl bileetlelb bileetlebl bileetlleb bileetllbe bileetlble bileetlbel bileetellb bileetelbl bileetellb bileetelbl bileetebll bileetebll bileetlelb bileetlebl bileetlleb bileetllbe bileetlble bileetlbel bileetbell bileetbell bileetblel bileetblle bileetblle bileetblel bileellteb bileelltbe bileelletb bileellebt bileellbet bileellbte bileeltleb bileeltlbe bileeltelb 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bilelbtlee bilelbtele bilelbteel bilelbltee bilelbltee bilelblete bilelbleet bilelbleet bilelblete bilelbetle bilelbetel bilelbelte bilelbelet bilelbeelt bilelbeetl Read more ...[1] , [2] , [3]	30,264	65,756	{"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}	3.109375	3	CC-MAIN-2023-23	latest	en	0.831426
https://betterlesson.com/lesson/reflection/12671/thinking-about-how-we-get-kids-to-decide-if-their-answer-makes-sense-mp1	1,498,455,808,000,000,000	text/html	crawl-data/CC-MAIN-2017-26/segments/1498128320679.64/warc/CC-MAIN-20170626050425-20170626070425-00661.warc.gz	709,099,518	20,136	## Reflection: Adjustments to Practice Quiz: Word Problems and Multiplying Fractions by Whole Numbers - Section 3: The Quiz It is the end of the year. As I reflect on word problem instruction, the thing that screams at me that needs attention is the development of student's ability to decide if an answer makes sense. MP 1 needs to be more of a part of my math dialogue and design in every unit. I share my thoughts about how I am going to change my practice to address this issue. Adjustments to Practice: Thinking about how we get kids to decide if their answer makes sense! MP1 # Quiz: Word Problems and Multiplying Fractions by Whole Numbers Unit 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers Lesson 5 of 8 ## Big Idea: Students take a quiz that shows they understand the processes involving multiplying whole numbers and fractions. Print Lesson 1 teacher likes this lesson Standards: Subject(s): 60 minutes ### Mary Ellen Kanthack ##### Similar Lessons ###### Multiplying Whole Number with a Fraction 4th Grade Math » Operations with Fractions Big Idea: In this lesson, students will multiply a whole number with a unit fraction through modeling in order to build conceptual understanding. Favorites(14) Resources(9) Helena, MT Environment: Suburban ###### Fraction Multiplication with Clocks Big Idea: Students will model how to multiply a fraction and whole number using a clock model, equation, and repeated addition. Favorites(7) Resources(47) MT Environment: Urban ###### Multiplying Fractions by a whole number Using Models 4th Grade Math » Number & Operations-Fractions Big Idea: Using a mathematical model, students will be able to visually see the process of how to multiply a fraction by a whole number to find its product in order to gain a deeper understanding to ultimately be able to do it on their own. Favorites(30) Resources(17) Jackson, MS Environment: Urban	416	1,912	{"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}	3.796875	4	CC-MAIN-2017-26	longest	en	0.902902
https://petewarden.com/2015/10/25/an-engineers-guide-to-gemm/comment-page-1/	1,501,246,409,000,000,000	text/html	crawl-data/CC-MAIN-2017-30/segments/1500550967030.98/warc/CC-MAIN-20170728123647-20170728143647-00029.warc.gz	682,048,166	40,561	# An Engineer’s Guide to GEMM I’ve spent most of the last couple of years worrying about the GEMM function because it’s the heart of deep learning calculations. The trouble is, I’m not very good at matrix math! I struggled through the courses I took in high school and college, barely getting a passing grade, confident that I’d never need anything so esoteric ever again. Right out of college I started working on 3D graphics engines where matrices were everywhere, and they’ve been an essential tool in my work ever since. I managed to develop decent intuitions for 3D transformations and their 4×4 matrix representations, but not having a solid grounding in the theory left me very prone to mistakes when I moved on to more general calculations. I screwed up the first version of all my diagrams in a previous blog post, and most recently had to make a breaking API change to the open-source gemmlowp library, all because I’d messed up the ordering of the matrix multiplies. The best way I know to fix something in my own mind is to try to explain it to somebody else, so here are my notes on the areas I found most confusing about matrix math as an engineer. I hope they’ll be helpful, and I look forward to getting corrections on anything I screwed up! Row versus Column Major The root of a lot of my difficulties are the two competing ways you can store matrix values in RAM. Coming from an image-processing world, when I see a 2D array of values my in-grained assumption is that it’s stored like letters on a page, starting in the top-left corner, and moving from left to right and jumping down at the end of the row. For example, if you have a matrix that you’d draw like this:``` \| 0 \| 1 \| 2 \| \| 3 \| 4 \| 5 \| \| 6 \| 7 \| 8 \|``` You would store it in memory in this order:``` \| 0 \| 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7 \| 8 \|``` This is known as ‘row major’, because each row is stored in adjacent locations in memory. The alternative storage scheme is ‘column major’, and the same matrix would be laid out like this in memory:``` \| 0 \| 3 \| 6 \| 1 \| 4 \| 7 \| 2 \| 5 \| 8 \|``` What this means is that we’re walking down the columns to get adjacent memory locations instead. It’s important to know that both of these are just ways of storing the same matrix in memory, they’re an implementation detail that should not affect the underlying math, or the way you diagram your equations. There’s also no widespread agreement on what the ‘correct’ or canonical storage order to use is, so you’ll need to pay attention to what convention the code you’re interacting with expects. Transpose One thing you may notice about row versus column ordering is that if you screw it up and pass a square row-major matrix into a library that expects column major, or vice-versa, it will be read as the transpose of the actual matrix. Visually, you transpose a matrix by flipping all the columns into rows, like this: ``` \| 0 \| 1 \| 2 \| 3 \| \| 4 \| 5 \| 6 \| 7 \| \| 8 \| 9 \|10 \|11 \|``` Original ``` \| 0 \| 4 \| 8 \| \| 1 \| 5 \| 9 \| \| 2 \| 6 \|10 \| \| 3 \| 7 \|11 \|``` Transpose Another way of visualizing this is drawing a line through the top-left to bottom-right corners, and flipping everything around on that diagonal. You’ll often see the transpose of a matrix indicated by adding an apostrophe to the name, so that the transpose of a matrix A is A’. Argument Ordering If you multiply two numbers, A * B is always the same as B * A. This is not true for matrix multiplications! Indeed, you can only multiply two matrices together at all if the number of columns on the left-hand-side is equal to the number of rows in the right-hand argument. Even if they’re both the same square size, and so can potentially be swapped, the result will still depend on the order. There is one mathematical identity that crops up a lot in practice with transposes. If you have the standard GEMM equation of C = A * B, then C’ = B’ * A’. In words, if you swap the order of the two input matrices and transpose both of them, then multiplying them will give the transpose of the result you’d get in the original untransposed order. #Errors % 2 == 0 What really led me into danger is that all three of storage order, transposing, and input order have effects that can mimic and cancel each other out. It’s like Jim Blinn’s old quote about all correct graphics programs having an even number of sign errors, except that there are three different ways to screw things up instead of one! For example, what I realized last week was that I was working in a new code base that assumes row-major order, but gemmlowp assumes column major. Because I had been in a hurry and couldn’t figure out why my unit tests weren’t working, so I ended up swapping the input argument order. Since C’ = B’ * A’, the storage order error was canceled out by the argument order error! It made for very confusing code, so thankfully a co-worker slapped me round the back of the head (very politely) when he ran across it and I revisited it and figured out my errors. Because I know I’m so prone to these kind of errors, I’ve forced myself to slow down when I’m tackling this kind of problem, and start off by working through a couple of examples on pen and paper. I find working visually with the diagram at the top of this post in mind has helped me immensely. Once I’ve got those examples straight, I’ll turn them into unit tests, with the hand calculations in the comments. You can see an example in gemmlowp/test/test.cc:698: My other key tool is keeping around a simple reference GEMM function that’s unoptimized, but that I can easily step through and add logging statements to. Since a lot of my work involves cutting corners with precision to increase speed, it’s important that I have an understandable implementation that I can play with, and compare against more complex versions. You can see my version for gemmlowp at test.cc:36: This includes some eight-bit specific code, but the structure is common across all my reference versions, with three nested loops across the m, n, and k dimensions of the matrices. It also doesn’t include some of the standard arguments like alpha or beta. This particular code assumes column major by default, but if any of the transpose flags are set to true, then the matrix is treated as row major. Leading Dimensions The final pieces of the puzzle for me were the lda, ldb, and ldc arguments. These left me confused initially because I struggled to find a clear representation of that they meant. I finally realized that they were the number of values you moved forward in memory when you reached the end of a row (in row-major order) or column (in column major). They’re strides that give a lot of flexibility when you only want to work with smaller tiles inside a larger matrix, since they let you skip over values you want to ignore. If you’re not dealing with sub-tiles, then they’ll be the number of columns for a row-major matrix, and the number of rows for a column-major one. Anyway, I hope these notes help any other lost souls who are struggling with matrices. I’m now feeling a lot more confident, and I wish I’d taken the time to study them more carefully before. They’re very powerful tools, and actually a lot of fun once I moved past some of my confusion! ### 9 responses 1. Ankur says: Hi, Can you please throw some light on why multiplication operation on the 8 bit inputs is done by blasting the inputs to int32 first? I am assuming variables like “a_offset” are used to align quantized 8 bit values to actual zero value in floating point domain, is conversion to int32 before multiplication done to avoid overflow caused by adding this offset value? Thanks • The reference implementation expands to 32-bit to keep the code simple, but the various assembler versions in gemmlowp itself operate on 8×8 multiplies, producing 16-bit results, that are summed into a 32-bit accumulator. The offset parts are handled in the O(n^2) outer loops, leaving the O(n^3) inner loop as pure eight-bit multiplies. Different SIMD instruction sets between x86 and various ARM NEON flavors make the exact bit depth choices at each stage flexible (e.g. sometimes it makes sense to promote the 8-bit values to 16-bit to do a faster 16×16 multiply and accumulate directly into 32-bit) but this is the general idea. • Ankur says: Thanks for the clarification. I have one more doubt which may be a bit naive! I am going through the 8 bit quantization discussed by you in various posts and the code on github, and I understand that we add offset values to make the quantized values align to actual 0 value to hold special properties of zero true. However I am not able to find out where and how are we handling overflows when we add the offset value(location of zero on the quantized scale) as the variable already holds values in range [0,255] and might overflow.. 2. Brilliant article, your gemm link points to dgemm – majority of the DNN calls are sgemm? 3. A very nice way to learn GEMM is to follow the tutorial by Ulrich Drepper in “What every programmer should know about memory” (https://people.freebsd.org/~lstewart/articles/cpumemory.pdf). The article shows how to start with some “naive code” (page 49) and optimisations are added until you get to the final code in Appendix A.1. OpenBLAS has some dgemm and sgemm assembly kernels here: https://github.com/xianyi/OpenBLAS/tree/develop/kernel/x86_64 (different versions optimised for Sandy Bridge, Haswell, Bulldozer, Piledriver, etc). On the other hand, not all optimisations for floating point matrix multiplication will necessarily translate to integer matrix multiplications (but apparently, the matrix transpose does, and possibly the optimisations for cache as well).	2,236	9,713	{"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-2017-30	longest	en	0.947759
https://forum.gdevelop.io/t/creating-sprite-bitmasking/43461	1,701,580,807,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679100484.76/warc/CC-MAIN-20231203030948-20231203060948-00659.warc.gz	302,787,332	6,211	# Creating Sprite BitMasking Hello, i made procedural world generation for my game and I need help with creating bitmasking I am trying to make a 8 bitmasking following this tutorial also i created every needed aniamation for my “color” object: link Here is my code: Result: I actually have no idea how to make it and hope you will help me ## Project files (optional) Edit: IDKW, but in the formula I typed below the site removed my asterisks. It should be a * 1 + b * 2 etc but when I omit the space, it removes the . I can’t say i understand the code but the formula where it seems to be converting from binary to decimal doesn’t look right. I apologize if I’m making the wrong assumption. Is it missing variables e and g? If this is meant to be a binary conversion then the sequence would be a1 +b2 +c4 + d8 + e16 + f32 + g64 +h128 (this is just the formula, you would need to add the Variable() ) I looked at the link some more and I understand a little. I still think e and g are needed. For 8-bit masking it seems like you need to convert the number before assigning the animation. Under “Tile Order” is says "Another problem you may notice is that the values calculated by the 8-bit bit masking procedure no longer correlate to the sequential order of the tiles in the sprite sheet. There are only 48 tiles, but our possible calculated values range from 0 to 255, so we can no longer use the calculated value as a direct reference when grabbing the appropriate sprite. What we need, therefore, is a data structure to contain the list of calculated values and their corresponding tile values. How you want to implement this is up to you, but remember that the order in which you check for surrounding tiles dictates the order in which your tiles should be placed in the sprite sheet. " This is wrong: You have 32 0, 16 * D and 16 * H What I’ve always used is the following patter - if the letters go: `A B C` `H _ D` `G F E` then I use `A + B2 + C4 + D8 + E16 + F32 + G64 + H*128`	498	2,015	{"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-2023-50	latest	en	0.921942
https://gmatclub.com/forum/when-a-positive-integer-n-is-divided-by-3-what-is-the-remainder-272380.html#p2106533	1,726,184,580,000,000,000	text/html	crawl-data/CC-MAIN-2024-38/segments/1725700651498.46/warc/CC-MAIN-20240912210501-20240913000501-00783.warc.gz	251,332,730	128,854	Last visit was: 12 Sep 2024, 16:42 It is currently 12 Sep 2024, 16:43 Toolkit 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 Your Progress 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 Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. Request Expert Reply # When a positive integer n is divided by 3, what is the remainder? SORT BY: Tags: Show Tags Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 10131 Own Kudos [?]: 17271 [8] Given Kudos: 4 GMAT 1: 760 Q51 V42 GPA: 3.82 GMAT Club Legend Joined: 12 Sep 2015 Posts: 6803 Own Kudos [?]: 31291 [2] Given Kudos: 799 Location: Canada Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 10131 Own Kudos [?]: 17271 [0] Given Kudos: 4 GMAT 1: 760 Q51 V42 GPA: 3.82 Non-Human User Joined: 09 Sep 2013 Posts: 34824 Own Kudos [?]: 878 [0] Given Kudos: 0 Re: When a positive integer n is divided by 3, what is the remainder? [#permalink] Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. Re: When a positive integer n is divided by 3, what is the remainder? [#permalink] Moderator: Math Expert 95478 posts	539	1,914	{"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}	3.890625	4	CC-MAIN-2024-38	latest	en	0.879635
https://alzarschool.org/solving-math-problems-with-several-unknowns/	1,695,468,575,000,000,000	text/html	crawl-data/CC-MAIN-2023-40/segments/1695233506480.7/warc/CC-MAIN-20230923094750-20230923124750-00352.warc.gz	111,451,133	17,084	# Solving math problems with several unknowns The Algebra II class at the Alzar School has been working through some interesting problems with systems of equations. A basic system of equations involves two equations that each relate two unknown quantities. The system can be solved through techniques of substituting one equation into the other, combining equations to eliminate a variable, or graphing both equations and identifying where two lines intersect. The unit on systems of equations lends itself to word problems. For example: “A golf club offers two choices for a membership. You can pay \$18/month and pay an additional \$7 each round, or buy a premium membership for \$54/month and pay \$3 per round.” If we assign variables d=number of days you go golfing and C=the total monthly membership cost, the basic membership cost is modeled by C = 7d + 18. Likewise, the second equation is modeled by C = 3d + 54. Solving the system gives a result of C = \$81 and d = 9 days, meaning that if you play 9 rounds of golf each month, both membership options cost the same. More regular golfers will benefit from the premium membership and hobbyists such as myself should choose the basic option. In Algebra II, we focus very heavily on translating written situations into mathematical equations that can be solved to determine unknown quantities. These word problems often frustrate students at first, but demonstrate the important practical applications of the material we are learning. For more advanced problems, we have gotten into systems with three variables and three equations. The following word problem was a project the students toiled over during our Chilean paddling expedition: “A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C is required to kill a destructive crop insect. Commercial spray X contains 1, 2, and 2 parts, respectively, of each chemical. Commercial spray Y contains only chemical C. Commercial spray Z contains only chemicals A and B in equal amounts. How much of each type of commercial spray is needed to get the desired mixture?” This problems tests students’ ability to explicitly define variables, understand unknown quantities, and write algebraic expressions to represent the system. The hardest part of this problem is writing out three different equations with three variables to create a system that can be solved. The math is easy. Take a shot at it; see if you can translate the situation into usable equations. (Hint: x, y, and z are you unknowns, not A, B, and C. A, B, and C are the equations you must write.) This problem can also be solve by graphing. The solution is the point where all three planes intersect in space! -Dan Thurber, Math Teacher	586	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}	4.34375	4	CC-MAIN-2023-40	latest	en	0.921785
https://bendertechconsultants.com/obhgcs/fe8278-co2-hybridization-orbital-diagram	1,620,302,664,000,000,000	text/html	crawl-data/CC-MAIN-2021-21/segments/1620243988753.97/warc/CC-MAIN-20210506114045-20210506144045-00025.warc.gz	161,596,175	25,490	Categories # co2 hybridization orbital diagram Step 6. sp 3 hybrid orbitals are oriented at bond angle of 109.5 o from each other. According to VSEPR theory, we can use the steric number ("SN") to determine the hybridization of an atom. The angle between them is 180o making CO 2 a linear molecule as predicted by VESPR. Each sp 3 hybrid orbital has 25% s character and 75% p character. We will use the $$D_{2h}$$ point group as a substitute since the orbital symmetries are retained in the $$D_{2h}$$ point group. With knowledge of both orbital symmetries and energies, we can construct the molecular orbital diagram. CO2 MOs MO Diagram for CO2 C 2p C 2s bonding MOs antibonding MOs C AOs O LCAOs 1 3 u 3 g 2 u 1 g 1 u 2 u 2 g 1 u 1 g 15. Click within an orbital to add electrons. orbitales d ne sont donc plus équivalentes vis-à-vis des six ligands : il y a levée de dégénérescence . So, it will not be wrong if you say that there is a sigma bond on each side and a PI bond above it. What is hybridisation. orbital ionization energies are listed in Section 5.3, information contact us at info@libretexts.org, status page at https://status.libretexts.org. The symmetries of C valence orbitals are listed below. & B_{1u} & 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\ How to draw molecular orbital diagram for co2 by signing up youll get thousands of step by step solutions to your homework questions. Although molecular orbital theory could be used to describe the bonding in the whole molecule, and without invoking hybridization in a separate step, here it is only used for the hydrogen bridges. The bonds in a methane (CH4) molecule are formed by four separate but equivalent orbitals; a single 2s and three 2p orbitals of the carbon hybridize into four. However, in order for Be to form two covalent bonds (see Lewis Structure, below), it clearly must have two single electrons in â¦ Post by g orloff 1J » Fri Nov 30, 2018 8:38 am . Use the buttons at the top of the tool to add orbitals. sp 3 d Hybridization. I hope you are clear with the Lewis structure. The approximate bond angle is 109. & A_{g} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ In order to explain this observation, valence bond theory relies on a concept called orbital hybridization. Use T, bond - How can the dipole moment of carbon monoxide be, Solved: Construct The Orbital Diagram Of Each Atom Or Ion, How to Represent Electrons in an Energy Level Diagram, covalent compounds - Why is the bond length of CO+ less, File:MO Diagram CO2.jpg - Wikimedia Commons, Solved: Part B. The two unhybridized p orbitals on carbon form p bonds to the oxygen atoms. Create the atomic orbital diagram for nitrogen. sp 3 d Hybridization. $\text{# of } i = \frac{1}{h}\sum(\text{# of operations in class)}\times(\chi_{\Gamma}) \times (\chi_i) \label{irs}$ "SN" = number of lone pairs + number of atoms directly attached to the atom. Orbital hybridization is essentially a process of mixing orbitals together and spitting out new ones that are all identical in symmetry and. It took me a full day to fix the mount figure out the wiring install magnets inside the old speedometer hub and tap the hub for the magn... 2009 2017 fuses and relays. The orbital ionization energies are listed in Section 5.3. 8 - For each of the following molecules, indicate the... Ch. Two $$B_{1u}$$ SALCs (one from $$s$$ and one from $$p_z$$): The Mulliken Label tells us that the $$B_{1u}$$ SALCs are each antisymmetric with respect to both the principle axis and the inversion center. This video shows how to replace the deck belt on an lt2000 tractor but this also applies to the lt1000 and many other models. The $$2s$$ orbitals of the oxygen are far lower in energy ($$-32.36 eV$$) than all other valence orbitals, and so we should expect that molecular orbitals that are constructed from these oxygen $$2s$$ will be mostly non-bonding. The carbon atom goes on one side of the diagram while the oxygen SALCs are drawn on the opposite side. Hybridization of atomic orbitals sigma and pi bonds sp sp2 sp3 organic chemistry bonding duration. Let's think about the shape of our new SP hybrid orbitals. Our tutors rated the difficulty ofDraw the orbital diagram for ion Co 2+....as medium difficulty. As the one pair remained alone, two double pairs are bonded and form a bent shape. To know about it, we have to look at each atom of CO2. Hybridization of an s orbital (blue) and a p orbital (red) of the same atom produces two sp hybrid orbitals (purple). sp hybridization (2 hybrid orbitals) Looking at the orbital diagram for the valence shell of Beryllium in BeCl 2, it shows a pair of electrons in the 2s subshell. However, the diagram will still yield correct bond order and magnetic behavior for these molecules. & A_{g} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ so2 hybridization diagram, Sulfur dioxide or sulphur dioxide (British English) is the chemical compound with the formula SO 2. to minimize formal charges. Click â¦ The other is by using the systematic approach for breaking a $$\Gamma$$ into reducible representations described previously in section 4.4.2 using the following formula: 8 - Sulfuric acid is manufactured by a series of... Ch. Salient features of hybridsation 3. 2. From the systematic process above, you have found the symmetries (the irreducible representations) of all eight SALCs under the $$D_{2h}$$ point group. 8 - Describe the molecular geometry and hybridization... Ch. [ "article:topic", "SALC", "showtoc:no", "license:ccbyncsa", "authorname:khaas" ]. The function, $$z$$, appearing with $$B_{1u}$$ in the character table tells us that these SALCs have the same symmetry as the $$z$$ axis, or a $$p_z$$ orbital on the central atom. Use the $$D_{2h}$$ character table to generate four reducible representations ($$\Gamma's$$); one for each of the four types of pendant atom orbitals ($$s, \;p_x, \;p_y, \;p_z$$). What charge would be needed on F2 to generate an ion with, Hund’s Rule for Atomic Energy Levels \| Aufbau Principle, tikz pgf - Molecular orbital diagrams in LaTeX? Thus, the SF6 molecule has an octahedral structure. The symmetry of a central $$s$$ orbital corresponds to the combination of functions $$x^2$$, $$y^2$$, and $$z^2$$ in the character table; this is $$A_g$$. Draw the orbital diagram for ion ca 2. hypochlorous thioanhydride. The CO$$_2$$ molecule is linear and its point group is $$D_{\infty h}$$. Its large and easy to read even on a phones browser. A radio button is provided to 'Switch contours on'. & B_{3u} & 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1 \\ But while you fill 3d orbital with electrons it becomes lower and lower in energy and eventually ends up lower in energy than. So no the atom doesnt have to get excited to 1s2 2s1 2p3 before in the case of sp3 hybridization say in methane the carbon s orbital. Nevertheless, it is very easy to determine the state of hybridization and geometry if we know the number of sigma bonds and lone pairs on the given atom. Construct SALCs and the molecular orbital diagram for CO$$_2$$. Nucleic Acids Research 2007, 35 (9) , 2875-2884. The energy diagram for this process is shown below. From this information, we know that these SALCs must have symmetry compatable with an $$s$$ orbital on the central atom, and we can draw the two $$A_g$$ SALCs shown in Figure $$\PageIndex{2}$$. The hybridized orbitals are higher in energy than the s orbital, but lower in energy than the p orbitals. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Why does co2 have 7 electrons in the 3d orbital and not 5 like mn. The $$p_z$$ orbital corresponds to the symmetry of the linear function, $$z$$ in the character table; this is $$B_{1u}$$. Figure 3. The location of the fuse blocks. the simplified diagram. Combine SALCs with AO’s of like symmetry. Click within an orbital to add electrons. If the applets on this page do not run correctly, consult the Virtual Chemistry Experiments FAQ or the Physlet Physics web site for establishing the correct security settings. 6 180/90 sp 3 d 2 hybrid orbitals (6 total orbitals). Hybridisation of carbon. Draw the orbital diagram for the ion co2. Create the atomic orbital diagram for nitrogen. The molecular orbital diagram below may be used for the following problem(s). Draw the orbital diagram for ion co 2 clutch prep. Find the point group of the molecule and assign Cartesian coordinates so that z is the principle axis. Each hybrid orbital is oriented primarily in just one direction. Hence hybridization state of central carbon atom in CCl4 is. Let's get a little bit of room down here. * Write the orbital diagram of carbon before sp 3 hybridization. Draw the orbital diagram for the ion n3. The hybridization of carbon monoxide is sp as its geometrical structure is linear. If the bel... My manual for the 2014 jetta doesnt have a fuse box diagram. sp â¦ Each of the hydrogens has one valence electron in its 1s orbital ( ). For each $$s$$ orbital, assign a value of 1 if it remains in place during the operation or zero if it moves out of its original place. Problem draw the orbital diagram for carbon in co 2 showing how many carbon atom electrons are in each orbital. Solved enter the condensed electron configuration for. These valence electrons that form the double bond with the Carbon atom are in â¦ This 109.5 o arrangement gives tetrahedral geometry (Figure 4). Un électron occupant une de ces orbitales subit une répulsion moindre par les ligands donc lâénergie de ces orbitales est abaissée . Ch. We can look at the functions in the $$D_{2h}$$ character table that correspond to $$A_g$$ and see that it completely symmetric under the group (because the combination of $$x^2,y^2,z^2$$ shows that it is totally symmetric). Draw the orbital diagram for the ion co2. Draw the orbital diagram for the ion n3. - TeX, How to draw molecular orbital diagram of CO2? Click within the orbital to add electrons. The resulting hybrid orbitals are called sp hybrids. The unhybridized 2p1 orbital lies perpendicular to the three hybridised orbitals. Looking forward to it, if we start with the Carbon atom, there are two double bonds. Representation of sp 2 hybridization sp 2 hybridization is also known as trigonal hybridisation. Figure 3. â Talking about the Oxygen atoms, as they are symmetrical, we just need to examine only one atom. In sp³ hybridization, one s orbital and three p orbitals hybridize to form four sp³ orbitals, each consisting of 25% s character and 75% p character. Ð) âCCl3 + Clâ â CCl4. general chemistry textbooks, and actually most of them give you this as the answer, so some of them give you this as the answer. Molecular orbitals are drawn in the center column of the diagram: The set of two sp orbitals are oriented at 180°, which is consistent with the geometry for two domains. Use the buttons at the top of the tool to add orbitals in order of increasing energy starting at the bottom with the lowest energy orbitals. 8 - Methionine, CH3SCH2CH2CH(NH2)CO2H, is an amino... Ch. Have questions or comments? Orbital hybridization sp sp 2 and sp 3 carbon. These mostly non-bonding orbitals are the $$a_{1g}$$ and $$b_{1g}$$ orbitals shown at the bottom of Figure $$\PageIndex{3}$$. The large lobes of the orbitals lie in the plane at angles of 120 degrees and point toward the corners of a triangle. How to draw molecular orbital diagram for co2 by signing up youll get thousands of step by step solutions to your homework questions. Data Flow Diagram. Using either approach results in the following eight irreducible representations ($$2A_{g} + 2B_{1u} + B_{2g} + B_{3u} + B_{3g} + B_{2u}$$): \[\begin{array}{\|c\|c\|cccccccc\|} \hline \bf{D_{2h}} & E & C_2(z) & C_2(y) &C_2(x) & i &\sigma(xy) & \sigma(xz) & \sigma(yz)\\ \hline There is one p orbital on boron but there is no adjacent atom with another p orbital. The orbital ionization energies are listed in Section 5.3. atomic orbitals hybridized orbitals Carbon has 4 valence electrons. Draw "orbital box" diagrams showing how combinations of an atomic s orbital and various numbers of p orbitals create sp, sp 2, and sp 3 hybrid orbitals. Molecular Orbital Diagram. Now that we have identified symmetries of eight oxygen SALCs and the four valence orbitals on carbon, we know which atomic orbitals and SALCs may combine based on compatible symmetries. melting point of the isolated crude cholesterol. This is SP hybridization because our new hybrid orbitals came from one S orbital and one P orbital like that. \bf{\Gamma_{2s} = A_g + B_{1u}} &\bf{\Gamma_{2s}} & \bf{2} & \bf{2} & \bf{0} & \bf{0} & \bf{0} & \bf{0} & \bf{2} & \bf{2}\\ Hybridization of an s orbital with all three p orbitals (p x, p y, and p z) results in four sp 3 hybrid orbitals. Fuse box passat 2010 – Begagnad bil 2015 volkswa... 34 2012 Ford Fusion Serpentine Belt Diagram, 30 Universal Motorcycle Speedometer Wiring Diagram. Yes. The bond order between any two adjacent carbon atoms is therefore between 1 and 2. Note that one p orbital remains unchanged. Ask question asked 5 years. & B_{2u} & 1 & -1 & 1 & -1 & -1 & 1 & -1 & 1 \\ These will pair up with the carbon electrons to form four s (sigma) bonds. Important Points To Remember. Co2 Hybridization Orbital Diagram. Problem 7.45 Write The Electron Co, Solved: Draw the molecular orbital diagram for the cyanide, OCR Chemistry Unit 2: Module 3 - Transition Elements, 6.4 Electronic Structure of Atoms (Electron Configurations, CO2 Molecular Geometry - Hybridization, Chart \| Chemistry, Orbital Diagram Example and Practice Cobalt problem. How hybrid orbitals electrons in the right plugs relies on a concept called orbital hybridization essentially. – Begagnad bil 2015 volkswa... 34 2012 ford Fusion Serpentine belt diagram, from. Jetta fuse box passat 2010 – Begagnad bil 2015 volkswa... 34 2012 ford Fusion belt! Relies on a concept called orbital hybridization an \ ( C_\infty\ ) axis nucleic Acids co2 hybridization orbital diagram 2007, (! Look at each atom of CO2 down here bifluoride anion be added to the energy diagram CO\! Drawn in the molecules methane, water, and ammonia the p on... { \infty H } \ ) all other SALCs shown below simple cases deck on! 2H } \ ) character table of atomic s- and p- orbital wave functions give rise to pair... ( AX3 ) making it sp2 hybridization in C2H6, 1 s orbital one. Toward the corners of a triangle atoms is therefore between 1 and 2 atom has hybridization. And form a bent shape for these molecules valence level orbital diagram for this is. You fill 3d orbital with electrons it becomes lower and lower in energy than s! For more information contact us at info @ libretexts.org, status page at https: //status.libretexts.org process! Electrons are in each orbital must contain one electron each with the same energy, lower than p orbitals but... Before sp 3 hybridization: ethane ( C 2 H 6 ), methane drawn in the molecules methane water... G mol-1 Intermolecular Forces the observed trend is very differentâAr has the orbitales dxy,,., CH3SCH2CH2CH ( NH2 ) CO2H, is an amino... Ch atom in... Ch ''.. 2015 volkswa... 34 2012 ford Fusion Serpentine belt diagram, 30 motorcycle! Could have one of... Ch fuse box diagram the s orbital shaped like a sphere of 109.5 from., each orbital must contain one electron each with the geometry for two domains - the... The angle between them is 180o making CO 2 showing how many electrons does a fe atom have in 3... Libretexts.Org, status page at https: //status.libretexts.org, 3 from boron and 1 from each hydrogen.... Are unoccupied one atom ces orbitales est abaissée the 3d orbital with electrons it becomes lower and lower in than... Belt diagram, 30 Universal motorcycle Speedometer Wiring diagram ) bonds show how hybrid orbitals ’... Needs two sigma bonds to the oxygen SALCs are drawn on the opposite.! Putty cave will be permanently sealed with body inside for oxygen and fluorine, the orbital. - for each of the tool to add orbitals orbitals and 1d orbital to form four s ( sigma bonds... Works well for simple cases the difficulty ofDraw the orbital ionization energies are listed in Section 5.3, information us! Same energy, lower than p orbitals on carbon can be used do... Between two C-atoms derived using a similar strategy as in the center column of the regions around particles. Y a levée de dégénérescence perpendicular to the shortcut, we have to understand about the orbital diagram the! If the bel... My manual for the 2014 jetta doesnt have a fuse box 2010! Sigma bonds to find that number co2 hybridization orbital diagram the relative strength of orbital interactions the ofDraw! The lt1000 and many other models diagram while the oxygen SALCs are drawn on opposite... Trigonal planar shape has 3 orbitals ( 6 total orbitals ) these to. Identify the symmetry of each using the \ ( D_ { 2h } )... % s character and 75 % p character right here is also sp hybridized since it bonded two... Energy than the other molecule and assign co2 hybridization orbital diagram coordinates so that no one could! The top of the orbitals lie in the molecules methane, water, and.! Subit une répulsion moindre par les ligands a radio button is provided to 'Switch contours on ' partial valence orbital. Top of the carbons and the molecular orbital diagram of carbon monoxide is sp hybridized since it to! I hope co2 hybridization orbital diagram are clear with the same energy, lower than p orbitals the Lewis structure ! Drovers side low beam headlight how many carbon atom electrons are in orbital! ) bonds Intermolecular Forces the observed trend is very differentâAr has the 's a..., if we start with the carbon atom electrons are in â¦ hybridization of atomic s- and orbital. Also known as trigonal hybridisation does CO2 have 7 electrons in the molecules methane, water, and.! For CO '' _2 % p character last orbital will overlap with one 3. Co 2+.... as medium difficulty - Methionine, CH3SCH2CH2CH ( NH2 ) CO2H, is amino... Systematically derive the SALCs for CO\ ( _2\ ) are identical in symmetry and of hybrid orbitals becomes and. Overlap with one sp 3 hybridized orbitals carbon has 4 valence electrons on form! ' valence orbitals are oriented at 180°, which is consistent with the symmetry... Our new sp hybrid orbitals came from one s orbital shaped like a sphere kb jpeg ford heater... Security Settings for correct operation low beam headlight out a diagram illustrating how the plots of s-... Are a total of 6 electrons to the molecular orbital diagram for ion 2... Involves the mixing of 3p orbitals and 1d orbital to form 5 sp3d hybridized orbitals are co2 hybridization orbital diagram, we to... ( AX3 ) making it sp2 hybridization will systematically derive the SALCs for (... Them is 180o making CO 2 a linear molecule as predicted co2 hybridization orbital diagram VESPR pairs are bonded and form bent. ( \Gamma\ ) into its component irreducible representations which is consistent with the same,. That z is the principle axis as trigonal hybridisation Joined: Fri Sep 28, 2018 8:38 am and. All identical in symmetry and 0 g mol-1 Intermolecular Forces the observed trend is very differentâAr the! A correct Lewis structure electrons does a fe atom have in its 3 atom CO2... And therefore only needs two sigma bonds and therefore only needs to hybridize two atomic orbitals sigma pi! P orbital on boron but there is no adjacent atom with another p orbital should lower., 1 s orbital, but this only works well for simple cases mention is... Body inside in Section 5.3, information contact us at info @ libretexts.org or check our... The Ï2 p orbitals on carbon co2 hybridization orbital diagram be added to the atomic and molecular orbitals example for the problem! Video takes you through all the basic parts of the molecule and assign Cartesian coordinates so that z is hybridization! Bonding molecular orbitals possesses a higher-energy antibonding partner like a sphere Settings: this web page employs,. Making CO 2 clutch prep strategies that can be used to do this content is by! Orbitals on carbon form p bonds to the atom a bent shape and assign Cartesian so! Is required whenever an atom is surrounded by four groups of electrons C valence orbitals could suffer the same,! For simple cases a formation of four sp 3 hybrid orbital is oriented primarily in just one.! Is lower in energy than 3d orbital with electrons it becomes lower and in... Of hybrid orbitals are involved in the 3d orbital with electrons it becomes lower and lower in energy than previous... Construct co2 hybridization orbital diagram molecular orbital it to the shortcut, we can construct the orbital diagram for the 2014 doesnt... Down here its molecular geometry and hybridization... Ch up with the claustrophobic... The orbitals are listed in Section 5.3, information contact us at info @ libretexts.org or check out status! Yield correct bond order and magnetic behavior for these molecules large and easy way to... Four sp 3 d hybridization involves the mixing of 3p orbitals and 1d orbital to 5. Of two sp orbitals are oriented at 180°, which requires specific Security Settings for correct operation for CO2 signing. The partial valence level orbital diagram for ion CO 2+.... as medium difficulty six... Of electrons energy, lower than p orbitals on carbon form p bonds to the orbital. In CO2 along with its molecular geometry and hybridization... Ch than p orbitals hybridization can also explain..., 2875-2884 can also practice orbital Diagrams concept each with the geometry for two domains are identical symmetry! Java, which is consistent with the carbon only needs to hybridize two atomic sigma. Of both orbital symmetries and energies, we can use the steric number ( ''. The hybridization of CO2 - carbon Dioxide mention diagram is the principle axis each sp orbital contains one that! If i have the hoses in the right plugs are derived using a similar strategy as the! We will systematically derive the SALCs for CO\ ( _2\ ) molecule linear! Atomic and molecular orbitals are unoccupied and the oxygens National Science Foundation support under grant 1246120... You will need to know about it, we have to understand about the orbital diagram, 30 motorcycle... Jpeg ford taurus heater core - Sulfuric acid is manufactured by a series...! Cartesian coordinates so that we can predict the relative orbital energy levels so that we can construct the molecular and... As predicted by VESPR add it to the atomic and molecular orbitals possesses a higher-energy antibonding partner can also orbital! One p orbital, lower than p orbitals, but lower in energy than the example! To those described in the previous example of sp 3 d hybridization the. ( ) behavior for these molecules relative orbital energy levels so that z the. Electrons it becomes lower and lower in energy than 1246120, 1525057, 1413739. Is manufactured co2 hybridization orbital diagram a series of... Ch energy-level diagram for ion CO 2+ as... 2 showing how many carbon atom are in each orbital must contain electron!	5,800	23,225	{"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": 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}	2.578125	3	CC-MAIN-2021-21	latest	en	0.82744
http://mathoverflow.net/questions/94632/higher-order-fractional-laplacian/94654	1,469,822,711,000,000,000	text/html	crawl-data/CC-MAIN-2016-30/segments/1469257831771.10/warc/CC-MAIN-20160723071031-00275-ip-10-185-27-174.ec2.internal.warc.gz	154,265,629	16,384	# Higher order fractional laplacian when consider the fractional laplacian $(-\triangle)^\alpha$,is there an essential difference between $0<\alpha<1$ and $\alpha>1$ ? As far as I'm concern,the higer order laplacian ($\alpha>1$ ) ,unlike the lower case, has little connection with stochastic process.(lack of positivy.) Since most paper i have met is the case of $0<\alpha<1$.And i wonder how things change when considering the higer order laplacian? - The fractional Laplacian can be represented as a hypersingular integral operator, an integral operator with a singularity higher than the space dimension. Its convergence is provided by a regularization whose form depends on the order. From its form the difference in positivity properties is immediately clear. See S. G. Samko, Hypersingular Integrals and their applications, Taylor and Francis, London, 2002. On the other hand, there exists a theory of parabolic equations with fractional Laplacians (and more general pseudodifferential operators) of any order. See S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic methods in the theory of differential and pseudo-differential equations of parabolic type, Birkhauser, Basel, 2004. - thanks for the useful reference.i'm considering the fractional shrodinger equation and it's $L^p$ estimate ,so i first want to know more about it'e kernel – user23078 Apr 20 '12 at 16:45 i try to look for that book,but it's not available.. I'm really appreciated that if you can send me a copy of the pdf file of your book mentioned above .here is my adress: hsl_lovemath@163.com. thank you very much! – user23078 Apr 24 '12 at 15:14 Well, the answer is in your question. When $0<\alpha<1$, and only then, $(-\Delta)^\alpha$ has a positive inverse. In particular, equations like $$(-\Delta)^\alpha u=f$$ or $$\partial_tu+(-\Delta)^\alpha u=0$$ satisfy a maximum principle. You get immediately an $L^p$ estimate for every $1\le p\le\infty$. If the equation is quasi-linear instead, it is likely that you have a $BV$-estimate for free. This helps a lot in proving well-posedness of the Boundary-value problem or the Cauchy problem. - I discovered a two-sided fractional derivative similar to the Grunwald-Letnikov derivative and defined for orders greater than -1. If the absolute value of the order is less than one, there is an inverse given by the same formulae. I proved that this derivative is equal to the Riesz potential, but does not have its problems. You can see the papers: Ortigueira, M. D., “Riesz Potentials and Inverses via Centred Derivatives” International Journal of Mathematics and Mathematical Sciences, Volume 2006 (2006), Article ID 48391, pages 1-12. Ortigueira, M. D., “Fractional Central Differences and Derivatives”, Journal of Vibration and Control , 14(9–10): 1255–1266, 2008. Prof. I. Podlubny made an implementation for this derivative that is in the site of Matlab. If you need you can contact me mdo@fct.unl.pt - thanks for your useful reference! – user23078 Apr 23 '12 at 13:28	782	3,020	{"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}	2.765625	3	CC-MAIN-2016-30	latest	en	0.86207
https://www.teacherspayteachers.com/Product/Division-Scoot-ActivityTask-Cards-4-digit-by-1-digit-With-Remainders-1331719	1,537,715,387,000,000,000	text/html	crawl-data/CC-MAIN-2018-39/segments/1537267159470.54/warc/CC-MAIN-20180923134314-20180923154714-00371.warc.gz	886,368,565	21,796	# Division Scoot Activity/Task Cards - 4 digit by 1 digit - With Remainders Subject Resource Type Common Core Standards Product Rating File Type PDF (Acrobat) Document File 446 KB\|10 pages Share Product Description Division Scoot Activity/Task Cards - 4 digit by 1 digit - With Remainders Scoot, scoot, scoot! Don't your kids just love to scoot!! This Division Scoot Activity gives 4th, 5th and 6th graders a fantastic opportunity to move around while learning. This will really help your students who NEED to move. In this scoot activity, students will find the answer to a 4 digit by 1 digit division problem. This is fantastic for practice or a review. Directions, student recording sheet, 30 cards, and answer sheet are all included. These scoot activity cards may also be used as task cards with any of my game boards. Click on the FREE game board template down below to view all my themed game boards. Check out my other scoot activities! ULTIMATE Class Scoot Activity/Task Card Bundle – SAVE Over \$20!!! Decimal Scoot Activity/Task Card Bundle – SAVE \$2 Place Value Scoot Activity/Task Card Bundle Decimal Place Value Scoot Activity/Task Cards Decimals Number Line Scoot Activity/Task Cards Comparing & Ordering Decimals Scoot Activity/Task Cards Converting Decimals to Fractions and Fractions to Decimals Scoot Activity/Task Cards Fraction Number Lines Scoot Activity/Task Cards Converting Improper Fractions and Mixed Numbers Scoot Activity/Task Cards Comparing & Ordering Fractions Scoot Activity/Task Cards Fraction Scoot Activity/Task Card Bundle – SAVE \$2 Related Data in a Table Scoot Activity/Task Cards Area, Perimeter, & Volume Scoot Activity/Task Card Bundle – SAVE \$1.50 Telling Time Scoot – 5 Minute Increments ULTIMATE Measurement Conversion Scoot Activity/Task Cards Bundle (U.S. Customary & Metric System) – SAVE \$2 Measurement Conversions Scoot Activity/Task Cards Bundle (U.S. Customary) – SAVE \$ Capacity Conversions Scoot Activity/Task Cards (U.S. Customary) Length Conversions Scoot Activity/Task Cards (U.S. Customary) Weight Conversions Scoot Activity/Task Cards (U.S. Customary) Measurement Conversions Scoot Activity/Task Cards Bundle (Metric System) – SAVE \$ Length Conversions Scoot Activity/Task Cards (Metric System) Mass Conversions Scoot Activity/Task Cards (Metric System) Capacity Conversions Scoot Activity/Task Cards (Metric System) Geometry Scoot Activity/Task Cards (Lines & Angles) Geometry Scoot Activity/Task Cards (Transformations & Symmetry) Geometry Scoot Activity/Task Cards (2D & 3D Figures) Multiplication & Division Scoot Activity/Task Card Multipack – SAVE \$5 Multiplication Scoot Activity/Task Card Bundle – SAVE \$2 Multiplication Scoot Activity/Task Cards (x10 and x100) Multiplication Scoot Activity/Task Cards (2 digit by 1 digit) Multiplication Scoot Activity/Task Cards (2 digit by 2 digit) Multiplication Scoot Activity/Task Cards (3 digit by 1 digit) Multiplication Scoot Activity/Task Cards (4 digit by 1 digit) Division Scoot Activity/Task Card Bundle – SAVE \$2 Division Scoot Activity/Task Cards (2 digit by 1 digit – No Remainders) Division Scoot Activity/Task Cards (2 digit by 1 digit – With Remainders) Division Scoot Activity/Task Cards (3 digit by 1 digit – No Remainders) Division Scoot Activity/Task Cards (3 digit by 1 digit – With Remainders) More scoot activities to come later! ********************************************************************************* Multiplication and Division Problem Solving Cards that match the Alpine Game Board theme Alpine Game Board Template SAVE \$5 with the set of 10 Game Board Templates Multipack SAVE \$2 with the set of 5 Adventure Game Board Templates Multipack SAVE \$2 with the set of 5 Sports Game Board Templates Multipack Click on any of the links above to view more game boards. ********************************************************************************* Check out these other FREE classroom resources! FREE Game Board Template FREE Scoot Template FREE QR Code Template FREE Jeopardy Game Template FREE Partial Quotient Division Poster FREE Lattice Multiplication Poster Total Pages 10 pages Included Teaching Duration N/A Report this Resource \$1.00 List Price: \$2.00 You Save: \$1.00 More products from Teaching With Heart in Texas Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials.	1,018	4,396	{"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-2018-39	latest	en	0.81135
https://www.jiskha.com/display.cgi?id=1235601999	1,516,568,954,000,000,000	text/html	crawl-data/CC-MAIN-2018-05/segments/1516084890874.84/warc/CC-MAIN-20180121195145-20180121215145-00188.warc.gz	936,494,159	4,475	# algebra posted by . In the magic square shown (I'll type it out), the sum of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by v,w,x,y, and z. Find y + z. Here's what the magic square looked like. I'll type semi-colons to separate each "square." v; 24; w 18; x; y 25; z; 21 I don't know how to solve this at all. Considering that all of the other problems on this worksheet had to do with systems of 3 equations with 3 variables, I'm assuming I'll have to make a system of equations. How would I find this information in the magic square? • algebra - last row = second column 25 + z + 21 = 24 + x + z x = 22 second row = last row (we now know x=22) 18+22+y = 25+z+21 y = z + 6 #1 first row = third colums v+24+w = w+y+21 y=v+3 #2 first row = right diagonal v+24+w = 25+x+w v+24 = 25+22 v = 23 then in #2 y = 23 + 3 = 26 we now know the sum of each row from the second row: 18+22+26 = 66 so what do we have so far ? 23 24 w 18 22 26 25 z 21 from that w = 66-23-24 = 19 z = 66-25-21 = 20 check: 23 24 19 18 22 26 25 20 21 OK! • algebra - There was really no method to what I did I noticed that the last row was a good one to use, since it contained only one variable from there it was just "hit or miss" there may very well be a better way. ## Similar Questions 1. ### Math A magic square is a square of numbers with each row, column, and diagonal of the square adding up to the same sum, called the magic sum. Arrange the numbers, -1,0,1,2,3,4,5,6,and 7 into a magic square. How does the average of these … 2. ### Math A magic square is a square of numbers with each row, column, and diagonal of the square adding up to the same sum, called the magic sum. Arrange the numbers, -1,0,1,2,3,4,5,6,and 7 into a magic square. How does the average of these … 3. ### pre-algebra In a number square, the sum of the numbers in each row, column, and main diagonal is the same. Find the sum of the number square. a 7 2 1 5 b 8 c 4 4. ### math justify that15 is the sum of eachrow of a 3X3 magic square using the number 0-9. Find the sume of all the numbers. What is the of eachrow in a 4X4 magic square that uses the numbers 1-16. 5. ### math if you have 3 rows and three columns and you have to find the hidden numbers. each number is less than 100,the sum of the digits of each number in column 2 is 10,the sum of the numbers in column 1 is 30,row 1 contains odd multiples … 6. ### Math - Magic Square??? My daughter is in 2nd grade and has a worksheet called Magic 26. It wants her to use the numbers 1 -12. Each row, column, and diagonal must equal 26. The four corners and four center numbers must equal 26 too. (example of puzzle below) … 7. ### math the frist grid is not a magic square. Change some of the numbers so the sum of each row, column and diagonal is the same number. Change no more than two numbers. 8. ### Math I have to do a 4x4 magic square with the digits 2011 so that each row column and diagonal contains one 2 one 0 and two 1s. But the hard part is that the sum of each row column and diagonal has to be 4. Please help if you can i've been … 9. ### math use all digits from 1 - 9 inclusively to make a 3 by 3 magic square.each row ,column and diagonal has the same total 10. ### MCA arrange the decimals 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8 and 5.9 in the square grid with 3 colums and 3 rows pattern to make the sum of the numbers in each row, column, and diagonal equal. More Similar Questions	1,064	3,495	{"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-2018-05	latest	en	0.929171
http://www.mywordsolution.com/question/write-single-matlab-statements-to-create-these/91246	1,488,179,513,000,000,000	text/html	crawl-data/CC-MAIN-2017-09/segments/1487501172649.58/warc/CC-MAIN-20170219104612-00121-ip-10-171-10-108.ec2.internal.warc.gz	522,420,057	9,815	+1-415-315-9853 info@mywordsolution.com ## Engineering Civil Engineering Chemical Engineering Electrical & Electronics Mechanical Engineering Computer Engineering Engineering Mathematics MATLAB Other Engineering Digital Electronics Biochemical & Biotechnology problem 1: Practice Vector Manipulation prepare single MATLAB statements to create these vectors from any vector Z. You can use vector Z shown as a sample input. Create a single m-file script (non-function) to containing all the statements. Comment each problem 'a' through 'e' in your m-file. Z = [4 5 2 8 4 7 2 64 2 57 2 45 7 43 2 5 7 3 3 6523 3 4 3 0 -65 -343]; a) Create a new vector vecA that is the odd numbered elements of Z (not the odd values, the elements with odd indexes). b) Count how many elements of Z are less than or equal to 10. c) Create a new vector vecC that is the same as Z except all the odd values of Z are changed to even by adding 1 to them. d) prepare a single MATLAB statement to generate 100 random integers with values -1 or 0 or 1. e) Create a new vector vecE that contains all the elements of Z that are a multiple of 3 f) Create a new vector vecF that is the same as Z except the first and last elements are swapped and nothing else is changed. g) find out how many elements of Z are within 10 of the max element in Z (include the max element(s) in your count). h) Create a new vector vecH that has the sum of the first and second elements of Z in the first position of vecH, the sum second and third elements of Z in the second position of vecH, the sum third and fourth elements of Z in the third position of vecH, etc. The last element of vecHis just the last elementof Z. problem 2: Create m-file functions to solve some basic vector problems in MATLAB. For each problem complete the following steps: A) Draw a picture or prepare pseudocode for solving the problem using composition (you do not have to hand this in) B) By hand, make an estimate of roughly the scale of the answer (you do not have to hand this in). C) prepare an m-file function to solve the problem. D) Test your m-file function using MATLAB in "calculator" mode with the diary on to save all your work in a command history file. It is fine to include errors in your command history file, as long as you eventually compute correctly. If you discover mistakes in your program, correct them and execute again. Please format the results to significant digits that are correct for the problem and data given. How to create a command history file?? >> diary BauerLab6.txt . . . >> diary off Problems: A) You are asked to determine the most efficient solid shape (defined by the shape with largest ratio of volume to its surface area) for a large hot air balloon. prepare a matlab script m-file named Efficient.m (function not necessary) to create a vector containing the ratios of the volume of a sphere to the surface area for a sphere for radius "r" values ranging from 50 to 100 by 2s. Do the same thing for the volume and surface area of a cube with side length "r" values ranging from 50 to 100 by 2s Do the same thing for the volume and surface area of a tetrahedron (equilateral triangle based pyramid) with side length "r" values ranging from 50 to 100 by 2s. Finally, plot the three vectors of ratios on the same graph, x-axis is the "r" vector, y-axis is the ratio of volume to surface area vector. Use different colors or symbols for each plot, label the axes, and add a legend. Which solid shape shape is most efficient (most volume per surface area)? B) A vector 'v' stores for the letter grades ('A', 'B', 'C', 'D', 'E') for a student's classes for a term. A student can have from 1 to 6 classes. Assume every class is a 3 credit hour class and assume each grade is worth this many grade points. A = 4, B = 3, C = 2, D = 1, E = 0 prepare a function call myGPA that has a single vector argument of grades as described above, and find outs and returns the GPA for the term. NO IF STATEMENTS ARE NEEDED, use vector conditions/manipulations) Sample call and result: >> GPA = myGPA(['B' 'A' 'A' 'C' 'B']) GPA = 3.2000 MATLAB, Engineering • Category:- MATLAB • Reference No.:- M91246 Have any Question? ## Related Questions in MATLAB ### Matlabproject descriptionwrite a mileage per gallons and MATLAB Project description: Write a mileage per Gallons and miles per dollar calculator program using two functions, one to calculate MPG and one to calculate MPD. The application will prompt the user to type the odm rea ... ### Question 1backgroundyou have been asked to manage a project QUESTION 1 Background You have been asked to manage a project to install a pipeline from an offshore gas platform to an onshore gas processing plant, and to find the cheapest design that is possible. The platform is Q km ... Problem 1 [10pts.]: The CSU-CHILL radar made observations of the Ponnequin Wind Farm located on the boarder of Wyoming and Colorado near I-25. The wind farm is approximately 62 km away from the radar. Complex valued digi ... ### Plotting and computer animation in matlabinstructions for Plotting and computer animation in MATLAB Instructions: For each of the following exercise, create an M-file to store the MATLAB commands. Copy and paste the M-file into a text document. For problems 1 and 2, include in ... ### 1 calculate the following for the function f x e-3x - 1) Calculate the following for the function f (x) = e -3x - 2x a. Calculate the derivative of the function by hand. Write a MATLAB function that calculates the derivative of this function and calculate the derivative at ... ### Use matlab to solve the following equations please i plot Use Matlab to solve the following equations. Please (i) plot the solution as a function of t for t ∈ [0, 100]. (ii) draw the phase diagram of the ODE. 1. dy/dt = y 2 + y with y(0) = 1 dy 1 /dt = y 2 2. ... ### Question 1backgroundclimate change is a change in global or QUESTION 1 Background Climate change is a change in global or regional climate patterns, in particular a change apparent from the mid to late 20th century onwards and attributed largely to the increased levels of atmosph ... ### Reports of projectproblem design a fourbar grashof REPORTS OF PROJECT PROBLEM: Design a fourbar Grashof crank-rocker to give? (Everyone will determine the terms given by professor) of rocker rotation with equal time forward and back, from a constant speed motor input. 1- ... ### Question 1 a what is the period of the forced oscillation Question 1. (a) What is the period of the forced oscillation? What is the numerical value (modulo 2Π) of the angle α defined by? (b) In this question you are asked to modify the file LAB06ex1.m in order to plot the compl ... ### Problem -tom cat is chasing jerry mouse the initial Problem - Tom cat is chasing Jerry mouse the initial distance between them is S 0 = 100m. Tom runs V c = 4-at m/s (negative accident) Jerry's velocity depends on the distance between Tom& Jerry V = Vmax - Ks (3-0.025 m/s ... • 13,132 Experts ## Looking for Assignment Help? Start excelling in your Courses, Get help with Assignment Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time. ### Section onea in an atwood machine suppose two objects of SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless ### Part 1you work in hr for a company that operates a factory Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl ### Details on advanced accounting paperthis paper is intended DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac ### Create a provider database and related reports and queries Create a provider database and related reports and queries to capture contact information for potential PC component pro ### Describe what you learned about the impact of economic Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen	1,921	8,180	{"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}	3.203125	3	CC-MAIN-2017-09	longest	en	0.855344
https://iitutor.com/proof-by-contradiction/	1,718,311,328,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198861488.82/warc/CC-MAIN-20240613190234-20240613220234-00081.warc.gz	273,907,377	28,082	$\textbf{Introduction to Proof by Contradiction}$ The basic idea of $\textit{Proof by Contradiction}$ is to assume that the statement that we want to prove is $\textit{false}$, and then show this assumption leads to nonsense. We then conclude that it was wrong to assume the statement was $\textit{false}$, so the statement must be $\textit{true}$. As an example of $\textit{Proof by Contradiction}$, consider the following proposition and its proof. A $\textit{rational number}$ is a number that can be written in the form $\dfrac{p}{q}$, where $p$ and $q$ are integers, $q \ne 0$. It has been proven that a rational number has a decimal expansion which either terminates or recurs. If we begin to write the decimal expansion of $\sqrt{2}$ , there is no indication that it will terminate or recur, and we might therefore suspect that $\sqrt{2}$ is irrational. $$1.414\ 213\ 562\ 373\ 095\ 048\ 801\ 688\ 724\ 209\ 698\ 078\ 569\ 671\ 875\ 376\ 948\ 073 \cdots$$ However, we cannot $\textit{prove}$ that $\sqrt{2}$ is rational by writing out its decimal expansion, as we would have to write an infinite number of decimal places. We might therefore $\textit{believe}$ that $\sqrt{2}$ is irrational, but it may also seem impossible to $\textit{prove}$ it. In fact, we can quite easily prove that $\sqrt{2}$ is rational by using a method called $\textit{Proof by Contradiction}$. In this method we suppose that the opposite is true of what we want to show is true, and follow a series of logical steps until we arrive at a contradiction. The contradiction confirms that our original supposition must be false. It is ready to use contradiction to prove that $\sqrt{2}$ is irrational. The first line of the proof must be “Suppose that the statement is not true that $\sqrt{2}$ is irrational. $\textit{Proof by Contradiction Example 1}$ $\textit{Proposition}$ The number $\sqrt{2}$ is irrational. Suppose for the sake of contradiction that it is not true that $\sqrt{2}$ is irrational. Then $\sqrt{2}$ is rational, so $\sqrt{2} = \dfrac{p}{q}$ for some (positive) integers $p$ and $q$, $q \ne 0$. We assume this fraction has been in lowest terms which means that this fraction is fully reduced, so $p$ and $q$ have no common factors. \begin{align} \displaystyle 2 &= \dfrac{p^2}{q^2} &\ \textit{squaring both sides}\\ p^2 &= 2q^2 \cdots (1) \\ \end{align} $p^2$ is even, and so $p$ must be even. Thus $p = 2k$, for some $k \in \mathbb{Z}^{+}$ \begin{align} \displaystyle 4k^2 &= 2q^2 &\ &\ \textit{substituting into } (1)\\ q^2 &= 2k^2 \\ \end{align} Thus $q^2$ is even, and so $q$ must be even. Here we have a contradiction, so $p$ and $q$ have no common factors. Therefore our original supposition is false, and $\sqrt{2}$ is irrational. $\textit{Proof by Contradiction Example 2}$ $\textit{Proposition}$ The sum of two even numbers is always even. Let’s $\textit{negate}$ this proposition. The sum of two even numbers is $\textit{not}$ always even. That means that there are two even numbers somewhere that will give us an odd number when they are added. $2x+2y=z, \ \ x,y,z \in \mathbb{Z}^{+}$, where $z$ is an odd number. Even and odd numbers are always positive integers, so we know $2x$ and $2y$ are positive integers, which means $x$ and $y$ are also positive integers. If these even numbers are divided by $2$, we get a positive integer. It is also known that $z$ is an odd number, which means it is not evenly divisible by $2$. \begin{align} \displaystyle 2x+2y &= z \\ x+y &= \dfrac{z}{2} \\ \end{align} $x+y$ is a positive integer, but $\dfrac{z}{2}$ is not a positive integer, because $z$ is assumed as an odd number. The left-hand side can’t possibly equal the fraction on the right. That’s a $\textit{contradiction}$! Because the sum of two even numbers $2x$ and $2y$ should always be positive integers that are divisible by $2$, this contradicted the proposition. Therefore the original proposition is true: the sum of two even numbers is always even. Discover more enlightening videos by visiting our YouTube channel! ## Induction Made Simple: The Ultimate Guide “Induction Made Simple: The Ultimate Guide” is your gateway to mastering the art of mathematical induction, demystifying a powerful tool in mathematics. This ultimate guide… ## Simplified Method for Calculating First Term and Common Ratio in Infinite Geometric Series Hello, math enthusiasts! Today, we’re delving into the captivating realm of infinite geometric series and discovering how to easily determine the “First Term” and the… ## Induction Magic: Your Ticket to Inequality Triumph Welcome to the world of mathematical induction, where we unravel the secrets of inequalities. Inequalities can be quite intimidating, but fear not! We have a… ## Domain and Range: Top Tips for Quick Learning Understanding Domain and Range: A Comprehensive Guide Domain and range are fundamental mathematical concepts that help us understand the behaviour and characteristics of relations and… ## Index Notation A convenient way to write a product of $\textit{identical factors}$ is to use $\textbf{exponential}$ or $\textbf{index notation}$.Rather than writing \$5 \times 5 \times 5 \times… #### Responses 1. Great explanation! Just one little thing though, I would recommend mentioning that for the statement in the first example that, p^2 or q^2 being even means that p and q is even, only works when the number (p or q) is an integer. 1. Great comment! We will make sure to consider your valuable points in future video lessons.	1,463	5,533	{"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": 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}	4.15625	4	CC-MAIN-2024-26	latest	en	0.925685
https://newbedev.com/how-to-draw-circles-in-an-arbitrary-plane	1,713,662,048,000,000,000	text/html	crawl-data/CC-MAIN-2024-18/segments/1712296817699.6/warc/CC-MAIN-20240421005612-20240421035612-00265.warc.gz	396,532,657	6,694	# How to draw circles in an arbitrary plane \documentclass[tikz,border=3.14mm]{standalone} \usetikzlibrary{3d,decorations.markings,calc} \usepackage{tikz-3dplot} \makeatletter % https://tex.stackexchange.com/a/48776/121799 \tikzoption{canvas is xy plane at z}[]{% \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}% \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}% \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}% \tikz@canvas@is@plane } \makeatother \begin{document} \foreach \X in {-50} {\tdplotsetmaincoords{110}{\X} \begin{tikzpicture} %\path[use as bounding box] (-6,-3) rectangle (6,5); %\node[anchor=north west] at (-6,5) {\X,\xtest,\ytest}; \begin{scope}[tdplot_main_coords] % ray in the back \draw [thick,blue,postaction={decorate,decoration={markings,mark=at position 0.2 with {\arrow{stealth};}}}] (-6,0,0) -- (0,0,0); % back \filldraw[cyan,fill opacity=0.3] (-0.5,-2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (-0.5,-2,2) -- cycle; % bottom \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,2,-2) -- (0,2,-2) -- cycle; % right \filldraw[cyan,fill opacity=0.1] (0,2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (0,2,2) -- cycle; % left \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,-2,2) -- (0,-2,2) -- cycle; % top \filldraw[cyan,fill opacity=0.1] (0,-2,2) -- (-0.5,-2,2) -- (-0.5,2,2) -- (0,2,2) -- cycle; %front \filldraw[cyan,fill opacity=0.1] (0,-2,-2) -- (0,2,-2) -- (0,2,2) -- (0,-2,2) -- cycle; % ray in front \draw[thick,blue] (0,0,0) -- (8,0,0); \begin{scope}[canvas is yz plane at x=8,xscale=-1,transform shape] \draw[gray] (-4,0) -- (4,0); \draw[gray] (0,-4) -- (0,4); \draw[red,thick] (0,0) circle (2); \node[circle,fill,red,inner sep=2pt] (A) at (45:2){}; \node[circle,fill,red,inner sep=2pt] (B) at (-135:2){}; \draw[gray] (A) circle (4.5pt) (B) circle (4.5pt); \draw[gray,shorten >=1.5pt,shorten <=1.5pt] (A)--(B); \end{scope} \draw[red] (A) -- (0,0,0) (B) -- (0,0,0); \end{scope} \end{tikzpicture}} \foreach \X in {-50} {\tdplotsetmaincoords{110}{\X} \begin{tikzpicture} %\path[use as bounding box] (-6,-3) rectangle (6,5); %\node[anchor=north west] at (-6,5) {\X,\xtest,\ytest}; \begin{scope}[tdplot_main_coords] % ray in the back \draw [thick,blue,postaction={decorate,decoration={markings,mark=at position 0.2 with {\arrow{stealth};}}}] (-6,0,0) -- (0,0,0); % back \filldraw[cyan,fill opacity=0.3] (-0.5,-2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (-0.5,-2,2) -- cycle; % bottom \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,2,-2) -- (0,2,-2) -- cycle; % right \filldraw[cyan,fill opacity=0.1] (0,2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (0,2,2) -- cycle; % left \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,-2,2) -- (0,-2,2) -- cycle; % top \filldraw[cyan,fill opacity=0.1] (0,-2,2) -- (-0.5,-2,2) -- (-0.5,2,2) -- (0,2,2) -- cycle; %front \filldraw[cyan,fill opacity=0.1] (0,-2,-2) -- (0,2,-2) -- (0,2,2) -- (0,-2,2) -- cycle; % ray in front \draw[thick,blue] (0,0,0) -- (8,0,0); \begin{scope}[canvas is yz plane at x=8,xscale=-1,transform shape] \draw[gray] (-5,0) -- (5,0); \draw[gray] (0,-4) -- (0,4); \draw[red,thick] (1,0) circle (2); \draw[red,thick] (-1,0) circle (2); \node[circle,fill,red,inner sep=2pt] (A) at ($(1,0)+(45:2)$) {}; \node[circle,fill,red,inner sep=2pt] (B) at ($(-1,0)+(-135:2)$) {}; \draw[gray] (A) circle (4.5pt) (B) circle (4.5pt); \draw[gray,shorten >=1.5pt,shorten <=1.5pt] (A)--(B); \end{scope} \draw[red] (A) -- (0,0,0) (B) -- (0,0,0); \end{scope} \end{tikzpicture}} \foreach \X in {-50} {\tdplotsetmaincoords{110}{\X} \begin{tikzpicture} %\path[use as bounding box] (-6,-3) rectangle (6,5); %\node[anchor=north west] at (-6,5) {\X,\xtest,\ytest}; \begin{scope}[tdplot_main_coords] % ray in the back \draw [thick,blue,postaction={decorate,decoration={markings,mark=at position 0.2 with {\arrow{stealth};}}}] (-6,0,0) -- (0,0,0); % back \filldraw[cyan,fill opacity=0.3] (-0.5,-2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (-0.5,-2,2) -- cycle; % bottom \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,2,-2) -- (0,2,-2) -- cycle; % right \filldraw[cyan,fill opacity=0.1] (0,2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (0,2,2) -- cycle; % left \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,-2,2) -- (0,-2,2) -- cycle; % top \filldraw[cyan,fill opacity=0.1] (0,-2,2) -- (-0.5,-2,2) -- (-0.5,2,2) -- (0,2,2) -- cycle; %front \filldraw[cyan,fill opacity=0.1] (0,-2,-2) -- (0,2,-2) -- (0,2,2) -- (0,-2,2) -- cycle; % ray in front \draw[thick,blue] (0,0,0) -- (8,0,0); \begin{scope}[canvas is yz plane at x=8,xscale=-1,transform shape] \draw[gray] (-5,0) -- (5,0); \draw[gray] (0,-4) -- (0,4); \draw[red,thick] (2,0) circle (2); \draw[red,thick] (-2,0) circle (2); \node[circle,fill,red,inner sep=2pt] (A) at ($(2,0)+(45:2)$) {}; \node[circle,fill,red,inner sep=2pt] (B) at ($(-2,0)+(-135:2)$) {}; \draw[gray] (A) circle (4.5pt) (B) circle (4.5pt); \draw[gray,shorten >=1.5pt,shorten <=1.5pt] (A)--(B); \end{scope} \draw[red] (A) -- (0,0,0) (B) -- (0,0,0); \end{scope} \end{tikzpicture}} \foreach \X in {-50} {\tdplotsetmaincoords{110}{\X} \begin{tikzpicture} %\path[use as bounding box] (-6,-3) rectangle (6,5); %\node[anchor=north west] at (-6,5) {\X,\xtest,\ytest}; \begin{scope}[tdplot_main_coords] % ray in the back \draw [thick,blue,postaction={decorate,decoration={markings,mark=at position 0.2 with {\arrow{stealth};}}}] (-6,0,0) -- (0,0,0); % back \filldraw[cyan,fill opacity=0.3] (-0.5,-2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (-0.5,-2,2) -- cycle; % bottom \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,2,-2) -- (0,2,-2) -- cycle; % right \filldraw[cyan,fill opacity=0.1] (0,2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (0,2,2) -- cycle; % left \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,-2,2) -- (0,-2,2) -- cycle; % top \filldraw[cyan,fill opacity=0.1] (0,-2,2) -- (-0.5,-2,2) -- (-0.5,2,2) -- (0,2,2) -- cycle; %front \filldraw[cyan,fill opacity=0.1] (0,-2,-2) -- (0,2,-2) -- (0,2,2) -- (0,-2,2) -- cycle; % ray in front \draw[thick,blue] (0,0,0) -- (8,0,0); \begin{scope}[canvas is yz plane at x=8,xscale=-1,transform shape] \draw[gray] (-5,0) -- (5,0); \draw[gray] (0,-4) -- (0,4); % \draw[red,thick] (1,0) circle (2); % \draw[red,thick] (-1,0) circle (2); \node[circle,fill,red,inner sep=2pt] (A) at (2.5,0) {}; \node[circle,fill,red,inner sep=2pt] (B) at (-2.5,0) {}; \draw[gray] (A) circle (4.5pt) (B) circle (4.5pt); %\draw[gray,shorten >=1.5pt,shorten <=1.5pt] (A)--(B); \end{scope} \draw[red] (A) -- (0,0,0) (B) -- (0,0,0); \end{scope} \end{tikzpicture}} \end{document} And the nowadays mandatory animation can't be missing. \documentclass[tikz,border=3.14mm]{standalone} \usetikzlibrary{3d,decorations.markings,calc} \usepackage{tikz-3dplot} \makeatletter % https://tex.stackexchange.com/a/48776/121799 \tikzoption{canvas is xy plane at z}[]{% \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}% \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}% \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}% \tikz@canvas@is@plane } \makeatother \begin{document} \foreach \Z in {0,0.075,...,4} {\pgfmathsetmacro{\X}{min(\Z,2)} \pgfmathsetmacro{\Y}{min(4-\Z,2)} \tdplotsetmaincoords{110}{-50} \begin{tikzpicture} %\path[use as bounding box] (-6,-3) rectangle (6,5); %\node[anchor=north west] at (-6,5) {\X,\xtest,\ytest}; \begin{scope}[tdplot_main_coords] % ray in the back \draw [thick,blue,postaction={decorate,decoration={markings,mark=at position 0.2 with {\arrow{stealth};}}}] (-6,0,0) -- (0,0,0); % back \filldraw[cyan,fill opacity=0.3] (-0.5,-2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (-0.5,-2,2) -- cycle; % bottom \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,2,-2) -- (0,2,-2) -- cycle; % right \filldraw[cyan,fill opacity=0.1] (0,2,-2) -- (-0.5,2,-2) -- (-0.5,2,2) -- (0,2,2) -- cycle; % left \filldraw[cyan,fill opacity=0.3] (0,-2,-2) -- (-0.5,-2,-2) -- (-0.5,-2,2) -- (0,-2,2) -- cycle; % top \filldraw[cyan,fill opacity=0.1] (0,-2,2) -- (-0.5,-2,2) -- (-0.5,2,2) -- (0,2,2) -- cycle; %front \filldraw[cyan,fill opacity=0.1] (0,-2,-2) -- (0,2,-2) -- (0,2,2) -- (0,-2,2) -- cycle; % ray in front \draw[thick,blue] (0,0,0) -- (8,0,0); \begin{scope}[canvas is yz plane at x=8,xscale=-1,transform shape] \draw[gray] (-5,0) -- (5,0); \draw[gray] (0,-4) -- (0,4); \draw[red,thick] (\X,0) circle (\Y); \draw[red,thick] (-\X,0) circle (\Y); \node[circle,fill,red,inner sep=2pt] (A) at ($(\X,0)+(45:\Y)$) {}; \node[circle,fill,red,inner sep=2pt] (B) at ($(-\X,0)+(-135:\Y)$) {}; \draw[gray] (A) circle (4.5pt) (B) circle (4.5pt); \draw[gray,shorten >=1.5pt,shorten <=1.5pt] (A)--(B); \end{scope} \draw[red] (A) -- (0,0,0) (B) -- (0,0,0); \end{scope} \end{tikzpicture}} \end{document}	4,047	8,675	{"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}	2.59375	3	CC-MAIN-2024-18	latest	en	0.409957
http://www.enotes.com/homework-help/what-value-grpah-ax-2-2x-4-intercepts-line-y-x-6-302771	1,462,076,754,000,000,000	text/html	crawl-data/CC-MAIN-2016-18/segments/1461860114285.32/warc/CC-MAIN-20160428161514-00055-ip-10-239-7-51.ec2.internal.warc.gz	509,861,234	11,888	# What is the value of a if the graph of y = ax^2 + 2x + 4 intercepts the line y + x = 6 at only one point. Posted on The graph of the curve y = ax^2 + 2x + 4 and the line y + x = 6 intersect at only one point. From y + x = 6, the value of the dependent variable is y = 6 - x. Equating this to y = ax^2 + 2x + 4 gives: 6 - x = ax^2 + 2x + 4 => ax^2 + 3x - 2= 0 Any quadratic equation ax^2 + bx + c = 0 has two equal roots if `b^2 - 4ac = 0` . Substitute the values for a, b and c from ax^2 + 3x - 2 = 0. `3^2 + 4a2 = 0 => a = -9/8` The curve y = -9x^2/8 + 2x + 4 intersects the line y + x = 6 once. The required value of a = -9/8	260	643	{"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}	4.125	4	CC-MAIN-2016-18	longest	en	0.797668
https://answersingenesis.org/genetics/mutations/mutations-yes-evolution-no/	1,511,568,047,000,000,000	text/html	crawl-data/CC-MAIN-2017-47/segments/1510934809160.77/warc/CC-MAIN-20171124234011-20171125014011-00212.warc.gz	556,830,383	32,487	2.5 Mutations, Yes; Evolution, No Darwin and Biologic Change on Share: The answer seems to be: “Mutations, yes; evolution, no.” In the last analysis, mutations really don’t help evolutionary theory at all. There are three major problems or limits (and many minor ones) that prevent scientific extrapolation from observed mutational change to hypothetical evolutionary change. (1) Mathematical challenges. Problem number one is the mathematical. I won’t dwell on this one, because it’s written up in many books and widely acknowledged by evolutionists themselves as a serious problem for their theory.1 Fortunately, mutations are very rare—or are they? They occur on an average of perhaps once in every ten million duplications of a DNA molecule (107, a one followed by seven zeroes). That’s fairly rare. On the other hand, it’s not that rare. Our bodies contain nearly 100 trillion cells (1014). So the odds are quite good that we have a couple of cells with a mutated form of almost any gene. A test tube can hold millions of bacteria, so, again, the odds are quite good that there will be mutant forms among them. The mathematical problem for evolution comes when you want a series of related mutations. The odds of getting two mutations that are related to one another is the product of their separate probabilities: one in 107 x 107, or 1014. That’s a one followed by 14 zeroes, 100 trillion! Any two mutations might produce no more than a fly with a wavy edge on a bent wing. That’s a long way from producing a truly new structure, and certainly a long way from changing a fly into some new kind of organism. You need more mutations for that. So, what are the odds of getting three mutations in a row? That’s one in a billion trillion (1021). Suddenly, the ocean isn’t big enough to hold enough bacteria to make it likely for you to find a bacterium with three simultaneous or sequential related mutations. What about trying for four related mutations? One in 1028. Suddenly, the earth isn’t big enough to hold enough organisms to make that very likely, and we’re talking about only four mutations. It would take many more than that to change a fish into a philosopher, or even a fish into a frog. It was at this level (just four related mutations) that microbiologists gave up on the idea that mutations in asexual lines could explain why some bacteria are resistant to four diﬀerent antibiotics at the same time. The odds against the mutation explanation were simply too great, so they began to look for another mechanism—and they found it. First of all, using cultures that are routinely kept for long periods of time, they found out that bacteria were resistant to antibiotics, even before commercial antibiotics were “invented.” Resistant bacteria were even found in the bodies of explorers frozen more than a century before medical antibiotic use. Genetic variability was “built right into” the bacteria. Did the nonresistant varieties get resistant by mutation? No. Resistant forms were already present. Furthermore, certain bacteria have little rings of DNA, called plasmids, that they trade around among themselves, and they passed on their resistance to antibiotics in that way. It wasn’t mutation and asexual reproduction at all, just ordinary recombination and variation within kind. Bacteria can be made antibiotic resistant by mutation, but such forms are “evolutionary cripples.” The mutation typically damages a growth factor, so that the mutationally crippled bacteria can scarcely survive outside the lab or hospital. The antibiotic resistance carried by plasmids results from enzymes produced to break down the antibiotic. Such bacteria do not have their growth crippled by mutation. Their resistance is by design. But why, you might well ask, would God create antibiotic resistance? It’s possible God designed antibiotic resistance in bacteria, and antibiotic production by fungi, to balance the growth of these prolific organisms in the soil. Only after the corruption of creation did some bacteria become disease causers, making antibiotic resistance “inadvertently” a medical problem. Contrary to popular opinion, drug resistance in bacteria does not demonstrate evolution. It doesn’t even demonstrate the production of mutations that add information for new categories of protein to the bacterial genome. It does demonstrate natural selection (or a sort of artificial selection, in this case), but only selection among already existing variations within a kind. It also demonstrates that when the odds that a particular process will produce a given eﬀect get too low, good scientists normally look for a better explanation, such as the plasmid explanation for resistance to multiple antibiotics. At this point, evolutionists often say that “time is the hero of the plot.” That’s what I used to say to my students. “Sure, the odds are low, but there’s all that time, nearly five billion years!” Five billion years is only about 1017 seconds, and the whole universe contains fewer than 1080 atoms. So even by the wildest “guesstimates,” the universe isn’t old enough or big enough to reach odds like the 1 in 103,000,000 that Huxley, an evolutionist, estimated as the odds against the evolution of the horse. Evolutionists like Huxley do believe in miracles; they just don’t believe in the Miracle Worker. In his chapter “Beyond the Reach of Chance,” Denton2 discusses attempts to simulate evolutionary processes on computers. He concludes with these strong words: If complex computer programs cannot be changed by random mechanisms, then surely the same must apply to the genetic programs of living organisms. The fact that systems in every way analogous to living organisms cannot undergo evolution by pure trial and error [i.e., by mutation and selection] and that their functional distribution invariably conforms to an improbable discontinuum comes, in my opinion, very close to a formal disproof of the whole Darwinian paradigm of nature. By what strange capacity do living organisms defy the laws of chance which are apparently obeyed by all analogous complex systems? (emphasis added). Most gratifyingly, Denton seems to look beyond the merely negative insuﬃciency of chance to glimpse a solution to “The Puzzle of Perfection,” as he calls it, in the “design hypothesis”: It is the sheer universality of perfection, the fact that everywhere we look, we find an elegance and ingenuity of an absolutely transcending quality, which so mitigates against the idea of chance. . . . In practically every field of fundamental biological research ever-increasing levels of design and complexity are being revealed at an ever accelerating rate. The credibility of natural selection is weakened, therefore, not only by the perfection we have already glimpsed but by the expectation of further as yet undreampt of depths of ingenuity and complexity (p. 342). In God’s handiwork, unlike man’s, the closer we look, the more marvelous is the perfection we see. Unfortunately, we also have evidence that the transcendent ingenuity and design Denton sees has been marred and scarred. In that sense, mathematics isn’t even the most serious challenge to using mutations as the basis for evolution. (2) Upward or downward? Even more serious is the fact that mutations are “going the wrong way” as far as evolution is concerned. Almost every mutation we know is identified by the disease or abnormality that it causes. Creationists use mutations to explain the origin of parasites and disease, the origin of hereditary defects, and the loss of traits. In other words, time, chance, and random changes do just what we normally expect: tear things down and make matters worse. Using mutations to explain the breakdown of existing genetic order (creation-corruption) is quite the opposite of using mutations to explain the build up of genetic order (evolution). Clearly, creation-corruption is the most direct inference from the eﬀects of mutations that scientists actually observe. By producing defects or blocking the normal function of certain genes, mutations have introduced numerous genetic abnormalities into the human population. The hemophilia (bleeders’ disease) that aﬄicted the royal houses of Europe may have arisen as a mutant of a clotting-factor gene in Queen Victoria, for example; and the dreaded Tay-Sach’s Disease may have arisen in Czechoslovakia in the 1920s as a mutation in the gene for producing an enzyme crucial to brain function. Some people like to call mutations “the means of creation,” but mutations don’t create; they corrupt! Both logically and often observationally, as in the examples above, the ordered state must come before mutations can disorder it. Mutations are real, all right, but they point to a corruption of the created order by time and chance. As a matter of fact, human beings are now subject to over 5,000 mutational disorders. Fortunately, we don’t show as many defects as we carry. The reason they don’t show up is that we each have two sets of genes, one set of genes from our mothers and another set from our fathers. The “bad genes” we inherit from our mothers’ side are usually covered up by our fathers’ genes, and vice versa. We can see what is likely to happen when an animal is born with only one set of genes. Figure 17, based on a description in a genetics textbook, represents the rare case of a turkey that was hatched from an unfertilized egg, so it had just one set of chromosomes. The poor bird couldn’t hold its head up; instead, it bobbed up and down from a neurological disorder. The feathers were missing in patches, and it finally had to be transferred to a germ-free chamber because its resistance to disease was so low. Figure 17. Mutations are mostly harmful, and, as time goes on, they impose an increasingly heavy “genetic burden” on a species. The turkey above, lacking a second set of genes to mask its hereditary defects, could scarcely survive. Creationists use mutations to help explain the origin of parasites and disease. Some evolutionists still believe that time, chance, and occasional favorable mutations provide the raw material for “upward-onward” progress, but the “post-neo-Darwinists” are looking for other means to explain evolution. Now here’s the basis for a good horror story. Picture a mirror at the end of a dark hall. You claw your way through the spider webs to reach the mirror, and then you press a button. The mirror then splits you in two halves, so you can see what you would look like if you had only those genes you inherited from your mother’s genes or only those from your father. In the next scene, you’re writhing there in agony, your hair turning white as you fall over backward and die of fright! Unfortunately, that picture exaggerates only slightly what mutations have done to human beings and to the various kinds of plants and animals as well. If it weren’t for having two sets of genes, few of us would be able to survive. Evolutionists recognize, of course, the problem of trying to explain “onward and upward” evolution on the basis of mutations that are harmful at least 1,000 times more often than they are helpful. No evolutionist believes that standing in front of x-ray machines would eventually improve human beings. No evolutionist argues that destruction of the earth’s ozone layer is good because it increases mutation rates and, therefore, speeds up evolution. Evolutionists know that decrease in the ozone layer will increase mutation rates, but they, like everyone else, recognize that this will lead only to increased skin cancer and to other harmful changes. Perhaps a helpful change might occur, but it would be drowned in the sea of harmful changes. Because harmful mutations so greatly outnumber any supposed helpful ones, it’s considered unwise nowadays (and illegal in many states) to marry someone too closely related to you. Why? Because you greatly increase the odds that bad genes will show up. By the way, you also increase the odds of bringing out really excellent trait combinations. But did you ever hear anybody say, “Don’t marry your first cousin or you’ll have a genius for a child?” They don’t usually say that, because the odds of something bad happening are far, far, far, far, far greater. That would not have been a problem, by the way, shortly after creation (no problem for Cain and his wife, for example). Until mutations had a chance to accumulate in the human population, no such risk of bad combinations existed. Mutations are often carried as “hidden genes”(recessives) that are diﬃcult to eliminate by selection, so they tend to build up in populations. The buildup of mutations with time poses a serious problem for plants and animals, as well as for human beings, and time, evolution’s “hero,” only worsens the problem of mutational decay. Geneticists, even evolutionary geneticists, refer to the problem as “genetic load” or “genetic burden,” terms meant to imply a burden that “weighs down” a species and lowers its genetic quality. In his article “The Mechanisms of Evolution” in the Scientific American book Evolution, Francisco Ayala3 defines a mutation as “an error” in DNA. Then he explains that inbreeding has revealed that mutations in fruit flies have produced “extremely short wings, deformed bristles, blindness, and other serious defects.” Does that sound like “the raw material for evolution?” It’s not that beneficial mutations are theoretically impossible. Bacteria that lose the ability to digest certain sugars, for example, can regain that ability by mutation. That’s no help to evolution, however, since the bacterium only gets back to where it started, but at least the mutation is helpful. A classic example used for decades to illustrate a beneficial mutation is sickle-cell anemia. Sickle-cell anemia is a disease of red blood cells. Why would anyone call that a beneficial mutation? Well, in certain parts of Africa, the death rate from malaria is quite high. Malaria is caused by a tiny, one-celled organism that gets inside the red blood cells and eats up the hemoglobin. Now, that particular germ doesn’t like sickle-cell hemoglobin. Carriers of one sickle-cell gene produce about half normal and half sickle-cell hemoglobin, and the malaria germ leaves them alone, too. So, carriers don’t get malaria. But the cost is high: 25 percent of the children of carriers can die of sickle-cell anemia, and another 25 percent are subject to malaria. If you want to call that a good mutation, you’re welcome to it! It seems doubtful to me that real improvement of human beings would result from accumulating that kind of “beneficial” mutation, and certainly hemoglobin’s ability to carry oxygen was not improved. The gene for sickle-cell anemia has built up to high levels in certain African populations, not because it is “beneficial” in some abstract sense, but simply because the death rate from anemia in those areas is less than the death rate from malaria. Natural selection is a “blind” process that automatically accumulates genes for short-term survival, even if it reduces the long-term survival of the species. For that reason, evolutionists recognize that natural selection can occasionally lead to “mischievous results” detrimental to genetic quality. That’s the eﬀect I think we’re seeing with sickle-cell anemia (Figure 18). Figure 18. “Sickle-cell anemia” is often given as an example of a favorable mutation, because people carrying sickle-cell hemoglobin in their red blood cells(Ss) are resistant to malaria. But the price for this protection is high: 25 percent of the children of carriers may die of the anemia (ss), and another 25 percent (SS) are subject to malaria. The gene will automatically be selected where the death rate from malaria is high, but evolutionists themselves admit that short-term advantages—all that natural selection can ever favor—can produce “mischievous results” detrimental to long-term survival. What do you think? Is sickle-cell anemia a “mischievous result,” or a good example of evolutionary progress? (Drawing from Parker, Reynolds, and Reynolds,Heredity,2ndedition [Chicago, IL: Educational Methods, Inc., 1977]). Furthermore, when the frequency of the sickle-cell gene reaches 18 percent, natural selection for it “stops.” That’s the point at which the death rates from sickle-cell anemia and malaria balance, demonstrating conclusively that sickle-cell anemia is not a suitable model for the continuous genetic expansion that evolutionists seek. Suppose I told you I had found a way to make cars run uphill without using gasoline. Then, as you watched in eager anticipation, I showed you how applying the brakes would make the car run downhill more slowly. Would you believe I had discovered a means for getting cars to run uphill without fuel? Similarly, natural selection can and does slow the rate of genetic decay produced by accumulating mutations (as it does with sickle-cell hemoglobin), but that hardly proves that mutation-selection produces upward and onward progress! A better example of favorable mutation might be found in a change from teosinte into corn, but the mutation was favorable to people, not to corn, which has been described as a “biological monstrosity” that could not survive on its own without man’s special care. There are many other examples of mutations “beneficial” to people: seedless grapes, short-legged sheep, hairless dogs, but these would all be harmful to the organism in its own environment and, hence, harmful in evolutionary perspective. While taking a graduate course in evolution on his way to a master-of-science degree in biology, one of my graduates asked his professor a simple question during a lecture on mutations as the raw material for evolution: “Would you please give us some examples of beneficial mutations?” After an uncomfortably long pause, the professor finally replied, “I can’t think of any right now, but there must be hundreds of them.” He did not come back to the next class with a list—but, to his credit, he didn’t try to use sickle-cell anemia to illustrate helpful mutations. Once again, let me say that it’s not that good mutations are theoretically impossible; rather, the price is too high. To explain evolution by the gradual selection of beneficial mutations, one must also put up with the millions of harmful mutations that would have to occur along the way. Even though he has been one of the “old guard” defenders of classic neo-Darwinian evolution, Ayala faces the problem squarely in his article in the Scientific American book Evolution. He is talking about variation within species (not kind, but species, the smallest possible unit). He says that variation within species is much greater than Darwin postulated. He speaks of such variation as “enormous” and “staggering.” Yet when he gets to the actual figures, the variation is less than I, as a creationist, would have expected. (Ayala did say his figures underestimated the real variation.) For creationists, all this variation poses no problem at all. If living things were created to multiply and fill the earth, then great variation within kind is simply good design. There would be no price to pay for created variability, since it would result from creation, not from time, chance, struggle, and death (natural selection). (Mutations have introduced further variability since creation was corrupted, but it’s the kind of variability a bull introduces into a china shop!) What problem did Ayala, as an evolutionist, see with all this staggering variability? Just this: For each beneficial mutation a species accumulated, the price would be a thousand or more harmful mutations. When genetic burden gets too great, oﬀspring are so likely to have serious hereditary defects that the ability of the species to survive is threatened. Take the Florida panther, for example, which is considered an endangered species. What endangers it? Highway traﬃc? No. Hunting? No. Habitat destruction? No. It’s endangered by too much “evolution,” i.e., the accumulation of mutations that have riddled the reproductive and circulatory systems with so much “evolutionary progress” (read that “genetic burden”) that the small, inbred population of panthers was unable to produce a cub that could survive and reproduce. I told my students that Florida oﬃcials should import panthers from out West to cross with the Florida panther to dilute the eﬀects of these harmful mutations. To my surprise, that’s what happened! The Florida panther is now making a comeback—except that as it becomes a healthier panther, it is less a “Florida” panther (which was never a true species anyway). Unfortunately, there are other cases where “endangered” sickly subspecies with multiple mutational defects are “protected” from good health by preventing their interbreeding with others of their kind. Time only makes this evolutionary problem worse. Thanks to our accumulated genetic burden, serious hereditary defects are present in perhaps 5 percent of all human births, and that percentage greatly increases among the children of closely related parents. All of us have some genetic shortcomings, and it’s really only by common consent that most of us agree to call each other “normal.” Natural selection cannot save us from this awful situation either. Selection can and does eliminate or reduce the worst mutations—but only when these mutants come to visible (phenotypic) expression. Most mutations “hide” as recessives, “invisible” to selection, and continue to build up in secret at multiple loci, somewhat like a “genetic cancer” slowly but steadily eating away at genetic quality. If early evolutionists had known what we know now about mutations, it’s most unlikely that mutations would ever have been proposed as the pathway to evolutionary progress. (3) Mutations point back to creation. Mathematics and genetic load are huge problems for evolution, but the biggest reason mutations cannot lead to evolution is an extremely simple one. It’s so simple, I’m almost afraid to say it. But really, mutations presuppose creation. After all, mutations are only changes in genes that already exist. Most mutations are caused by radiation or replication errors. What do you have to have before you can have a mutation? Obviously, the gene has to be there first, before the radiation can hit it or before it can make a copying mistake. In one sense, it’s as simple as that: the gene has to be there before it can mutate. All you get as a result of mutation is just a varied form of an already-existing gene, i.e., variation within kind (Figure 19). Figure 19. The most logical inference from our scientific observations of mutation, selection, and genetic recombination would seem to be variation within created kinds. There’s no “genetic burden” to bear if variety is produced by creation instead of time, chance, and mutation. But could there be enough variation in each created kind to produce all the diversity we see today? Creationists now have some promising answers to that question. (Drawing from Bliss, Origins: Two Models, 2nd edition [Green Forest, AR: Master Books, 1978]). Uncritical acceptance of evolution has so stunted scientific thinking that people give mutations god-like qualities. They act as if a cosmic ray striking a cell can cause a “mutation” that somehow assembles over 1,500 DNA bases into a brand new gene, regulators and all, that suddenly begins producing a brand new protein responsible for a brand new trait, raising the lucky mutated organism to the next higher rung on the evolutionary ladder! NOTHING remotely like that has ever, or could ever, happen! Mutations are NOT genetic “script writers”; they are merely “typographic errors” in a genetic script that has already been written. Typically, a mutation changes only one letter in a genetic sentence averaging 1,500 letters long. To make evolution happen—or even to make evolution a theory fit for scientific discussion—evolutionists desperately need some kind of “genetic script writer” to increase the quantity and quality of genetic INFORMATION. Mutations have no ability to compose genetic sentences, no ability to produce genetic information, and, hence, no ability to make evolution happen at all. That simple, absolutely foundational fact completely stumped Richard Dawkins, the world’s leading spokesman for evolution as of this writing. Ina video production featuring several evolutionist and creationist leaders and skeptics,4 Dawkins argued eloquently that millions of years of mutation and natural selection would serve as a “blind watchmaker,”5 producing all appearance of design among living things without any help from some supernatural Designer. Then in a quiet, non-threatening voice, not knowing what the answer would be, the narrator asked Dawkins to give an example of a mutation that adds information. The usually eﬀusive Dawkins gestured, opened his mouth, but stopped before he spoke. With his eyes shifting back and forth as if searching for some answer, he started to speak several times, but always checked himself. Finally, after a long embarrassing silence, the program resumed with Dawkins speaking on a diﬀerent subject—leaving unanswered the ultimate question, the origin of genetic information. Yet, molecules-to-man evolution is all about phenomenal expansion of genetic information. It would take thousands of information-adding mutations to change “simple cells” into invertebrates, vertebrates, and mankind. If there were any scientific merit at all to mutation-selection as a mechanism for evolution, Dawkins’ reply should have been enthusiastic and overwhelming, “My three favorite examples of mutations adding information are. . . . Excellent examples among plants are . . . among insects are . . . among bacteria are . . . .” His answer, instead, was silence, and with no mechanism to add genetic information, the “evolutionary tree” can’t grow. The problem with evolution is not some shortcoming in Dawkins, however. The problem is with the fundamental nature of information itself. The information in a book, for example, cannot be reduced to, nor derived from, the properties of the ink and paper used to write it. Similarly, the information in the genetic code cannot be reduced to, nor derived from, the properties of matter nor the mistakes of mutations; its message and meaning originated instead in the mind of its Maker. As cogently presented by two of the world’s leading information theorists,6 information comes only from pre-existing information.7 Information systems have the “exherent,” created kind of design, which can be logically inferred from our scientific observations as explained earlier (Figure 1). Although mutations may corrupt it and selection may sort variations into diﬀerent environments, it was not a “blind watchmaker” that composed the genetic script for each kind of organism, but a Creator with a plan and purpose and eyes wide open. If the evidence and logic is so convincingly clear, why is evolution still so popular? Laying aside personal biases and spiritual concerns, there is a serious semantic problem that could cause honest confusion. After all, evolution is about the continual production of new and diﬀerent genes, and mutations are continually producing new and diﬀerent genes—or are they? Genes of the same kind, like those for straight and curly hair or those for yellow and green seeds, are called alleles. There are over 300 alleles of the hemoglobin gene. That’s a lot of variation, but all those alleles produce hemoglobin, a protein for carrying oxygen in red blood cells (none better than the normal allele). By concept and definition, alleles are just variants of a given gene, producing variation in a given trait. Mutations produce only alleles, which means they can produce only variation within kind (creation), not change from one kind to others (evolution). Genes of the same kind can be defined objectively as segments of DNA that occupy corresponding positions (loci; sing. locus) on homologous chromosomes. Homologous chromosomes are pairs that look alike, but come from two diﬀerent parents, so their genetic content is similar but not identical. They pair up and then separate in the kind of cell division (meiosis) required for sexual reproduction. Genes that pair up in meiotic cell division, therefore, can be identified as genes of the same kind. Genes of the same kind are also turned on and oﬀ by the same gene regulators. Notice, it is not subjective human opinion that is telling us which genes are the same kind; it is objective, observable cellular processes. Mutations, random changes in the genetic code, do produce “new genes” not present at creation, but the so-called “new genes” are still found at the same locus, still pair the same way in meiosis, and are still turned on and oﬀ by the same regulators, so they are really only genes of the same kind as the original, and represent only variation within kind (usually harmful variation in the case of mutations). Notice the terms “new genes” or “different genes” can have two radically different meanings. As geneticists normally do, we have been calling genes of the same kind alleles. The genes for tongue rolling and non-rolling are “different genes” in one sense, but only variations of the same kind of gene—aﬀecting the same trait, found in corresponding positions (loci) on homologous chromosomes, pairing up in meiosis, and turned on and oﬀ by the same regulators. They are NOT diﬀerent genes in the sense that genes for tongue rolling, and genes for making sickle cell hemoglobin are! Similarly, the sickle cell gene is a “new gene” in the sense that it was not present at creation, but it is only a new (and harmful!) version of a pre-existing gene, one that occupies the same chromosomal position, pairs the same way, and is turned on and oﬀ by the same regulators as the gene for making normal hemoglobin. In fact, the gene for sickle cell hemoglobin diﬀers in base sequence at only one position out of several hundred in the normal gene for making hemoglobin, again just variation within kind or allelic variation. We need a new and diﬀerent term to describe genes that are truly new and different—genes with information aﬀecting a different category of trait—not just information on varieties of shirts, for example, but information on motorcycles! To refer to genes that do NOT occupy corresponding loci on homologs, that do NOT pair in meiosis, and that DO contain information on distinctive categories of traits, we will use the word genon. Genes for tongue rolling and non-rolling are diﬀerent alleles, for example, but genes for tongue rolling and genes for making hemoglobin are diﬀerent genons, with genes for normal and sickle cell hemoglobin as alleles of the hemoglobin genon. The complete set of DNA specifying a kind is called its genome. The human genome includes at least 30,000 diﬀerent genons, each of which could have been created in four diﬀerent allelic varieties (two in each parent). Genetic defects and diseases occurring since the corruption of creation have introduced many new alleles, but no new genons. All the genes in one generation available to be passed on to the next are called the gene pool. Members of the same kind may also be defined as organisms that share the same gene pool. The number of genes for diﬀerent kinds of traits (genons) can be called the depth of the gene pool. Using earlier examples, we could say the human gene pool is 30,000 genons deep, the E. coli bacterial gene pool about 5,000, while the gene pool of a small virus may be only a dozen genons deep. The width of the gene pool refers to the amount of its “horizontal” allelic variation. Among dogs, for example, the width of a greyhound’s gene pool is very narrow; crossing pure bred greyhounds just gives you more greyhounds, all very similar in speed, color, intelligence, hair length, nose length, etc. Crossing two “mongrels,” however, can give you big dogs and small dogs, dark and light and splotchy colored dogs, dogs with long and short hair, yappy and quiet dogs, mean and aﬀectionate dogs, etc., etc.! The width of the mongrel’s gene pool (its allelic variability) is quite large compared to the greyhound’s, but the depth of the gene pool (the number of genons) is the same for both dogs. Kind” is defined in terms of depth of the gene pool, the total number of diﬀerent genons in a genome and a list of the traits they influence. Variation within kind is defined in terms of the width of the gene pool, the number of alleles at each gene site (locus or genon). Creation: Facts of Life Dr. Parker, a leading creation scientist and former AiG speaker, presents the classic arguments for evolution used in public schools, universities, and the media, and refutes them in an entertaining and easy-to-read style. A must for students and teachers alike! This is a great book to give to a non-Christian as a witnessing tool. Footnotes 1. Paul S. Moorehead and Martin M. Kaplan, Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, Wistar Symposium No. 5 (Philadelphia, PA: Wistar Institute Press, 1967). 2. Denton, Evolution: A Theory in Crisis. 3. Francisco Ayala, “The Mechanisms of Evolution,” Scientific American (and Scientific American book Evolution) (September 1978). 4. Gillian Brown, From a Frog to a Prince, video, Keziah Productions. 5. Dawkins, The Blind Watchmaker. 6. Werner Gitt, In the Beginning Was Information (Green Forest, AR: Master Books, 2006). 7. Lee Spetner, Not By Chance (New York: Judaica Press, 1997). Answers in Genesis is an apologetics ministry, dedicated to helping Christians defend their faith and proclaim the gospel of Jesus Christ. • Customer Service 800.778.3390	7,139	33,845	{"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}	2.984375	3	CC-MAIN-2017-47	longest	en	0.937936
http://heli-air.net/2016/02/25/three-dimensional-wings-in-steady-subsonic-flow/	1,548,096,265,000,000,000	text/html	crawl-data/CC-MAIN-2019-04/segments/1547583804001.73/warc/CC-MAIN-20190121172846-20190121194846-00502.warc.gz	100,698,439	14,122	# Three-Dimensional Wings in Steady, Subsonic Flow 7- 1 Compressibility Corrections for Wings This chapter deals with the application to finite, almost-plane wings of the linearized, small-perturbation techniques introduced in Chapter 5. By way of introduction, we first review the similarity relations which govern variations in the parameter M, the flight Mach number. In the light of the asymptotic expansion procedure, the principal unknown, from which all other needed information can be calculated, is the first-order term* Ф? in the outer expansion for the velocity potential. The term Ф)’ is connected to the more familiar perturbation velocity potential <p(x, y, z) by (5-28). The latter is governed by the differential equations and boundary conditions (5-29)-(5-30), which we reproduce here (see also Fig. 5-1): (1 M )<Pxx “b <Pyy “f" <Pzz ——– 0, for (x, y) on S. (5-30) The pressure coefficient at any point in the field, including the upper and lower wing surfaces z = 0±, is found from Cp — 2 <px. Extending a procedure devised by Prandtl and Glauert for two-dimensional airfoils (see Fig. 7-1), Gothert (1940) introduced a transformation of independent and dependent variables which is equivalent to * The zeroth-order term is, of course, the free stream Фо = x. 124 Where /3 = /l — M2, as in Chapter 5. Equation (7-1) converts (5-29) into the constant-density perturbation equation (<Po)x0x0 + (‘Po)y0Vo + (<Po)z0zo = 0. (7-2) Some care must be observed when interpreting the transformed boundary condition at the wing surface. Thus, for example, the first of (5-30) states that just above the wing’s projection on the x, у-plane the vertical velocity component produced by the sheet of singularities representing the wing’s disturbance must have certain values, say Fu(x, y). After transformation, we obtain (<Po)z0 = Fu(0x о, у о) s FUo(x0, Vo) at z0 = 0—f—, for (x0, y0) on »S’o, where <S0 is an area of the x0, уо-ріапе whose lateral dimensions are the same as the original planform projection S, but which is stretched chordwise by a factor l/13. (See Fig. 7-2.) Equation (7-3) and the equivalent form for the lower surface state, however, that the “equivalent ” wing in zero-M, constant-density flow has (at corresponding stations) the same thickness ratio t, fractional camber в, and angle of attack a as the origi – ——– nal wing in the compressible stream. _____ Fig. 7-2. Equivalent wing planform in zero-Mach-number flow. If sweep is present, tanAo = (1 //3) tan A. The aspect ratio is А о = /ЗА. The similarity law might be abbreviated where the semicolon is used to separate the independent variables from the parameters. By way of physical explanation,[6] Gothert’s extended Prandtl-Glauert law states that to every subsonic, compressible flow over a thin wing there exists an equivalent flow of constant density liquid (at the same flight speed and free-stream ambient conditions) over a second wing, obtained from the first by a chordwise stretching 1//3 without change of surface slope distribution. It is obvious from (5-31) that pressure coefficients at corresponding points in the two flows are related by (7-5) Since they are all calculated from similar dimensionless chordwise and spanwise integrations of the Cp-distribution, quantities like the sectional lift and moment coefficients Ci(y), Cm{y), the total lift and moment coefficients Cl, Cm, and the lift-curve slope дСь/да are found from their constant-density counterparts by the same factor 1//3 as in (7-5). It is of interest in connection with spanwise load distribution, however, that the total lift forces and running lifts per unit //-distance are equal on the two wings, because of the increased chordwise dimensions at M = 0. Unfortunately, when one is treating a given three-dimensional configuration, the foregoing transformation requires that a different planform be analyzed (or a different low-speed model be tested) for each flight Mach number at which loading data are needed. This is not true for two-dimensional airfoils, since then the chordwise distortion at fixed a, etc., is no more than a change of scale on an otherwise identical profile; we have already seen (Section 1-4) that such a change has no effect on the physical flow quantities at fixed M. Measurements like those of Feldman (1948) correlate with the Gothert – Prandtl-Glauert law rather well up to the vicinity of critical Mach number, where sonic flow first appears at the wing surface. They also verify what we shall see later theoretically, that the coefficient of induced drag should be unaffected by M-changes below Afcrit. There exist, of course, more accurate compressibility corrections based on nonlinear considerations which are successful up to somewhat higher subsonic M. Inasmuch as (5-29) applies also to small-perturbation supersonic flow, M > 1, one might suspect that the foregoing considerations could be extended directly into that range. This is an oversimplification, however, since the boundary conditions at infinity undergo an essential change— disturbances are not permitted to proceed upstream but may propagate only downstream and laterally in the manner of an outward-going sound wave. (The behavior is connected with a mathematical alteration in the nature of the partial differential equation, from elliptical to hyperbolic or “wavelike.”) What one does discover is the existence of a convenient reference Mach number, M = /2, which plays a role similar to M = 0 in the subsonic case. When M = /2, the quantity В = y/M2 – 1 becomes unity and all flow Mach lines are inclined at 45° to the flight direction. Repetition of the previous reasoning leads to a supersonic similarity law <p(x, V, 2; M, А, г, 0, a) = <P (jj ‘ V, 2; M’ = л/2, BA, T, 0, a) . (7-6) Pressure coefficients at corresponding points, lift coefficients, etc., are related by CP = (Cp)_ (7-7) Once more the equivalent planform at M = /2 is obtained from the original by chordwise distortion, but now this involves a stretching if the original M < /2 and a shrinking if M > y/2. The process has been likened to taking hold of all Mach lines and rotating them to 45°, while chordwise dimensions vary in affine proportion. Clearly, Eqs. (7-5), (7-7), and the associated transformation techniques fail in the transonic range where M ^ 1. It has been speculated, because the equivalent aspect ratio approaches zero as M —> 1 and slender-body – theory results for lift are independent of Mach number (Chapter 6), that linearized results for three-dimensional wings might be extended into this range. This is, unfortunately, an oversimplification. Starting from the proper, nonlinear formulation of transonic small-disturbance theory, Chapter 12 derives the actual circumstances under which linearization is permissible and gives various similarity rules. It is found, for instance, that loading may be estimated on a linearized basis whenever the parameter At1/3 is small compared to unity.	1,685	7,001	{"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}	2.921875	3	CC-MAIN-2019-04	longest	en	0.861265
https://scholar.archive.org/work/xlpzs6re3nbm3jkgm2gren7ihu	1,632,044,098,000,000,000	text/html	crawl-data/CC-MAIN-2021-39/segments/1631780056752.16/warc/CC-MAIN-20210919065755-20210919095755-00308.warc.gz	563,784,629	5,799	### Demographics and the Politics of Capital Taxation in a Life-Cycle Economy Xavier Mateos-Planas 2010 The American Economic Review This appendix considers a more general case for the model in Section 3 of the paper. Here I denote periods t = 1, 2. The population is divided into two types of agents, i, old and young, with sizes µ old and 1 − µ old respectively. Agents own productive inputs in the form of capital k i t and one unit of labour, which earn an interest rate R t and a wage rate w t respectively. The income from the two inputs is taxed at rates τ k t and τ l t respectively. The individual after-tax income can be more » ... tax income can be divided between current consumption, c i t , and capital next period, k i t+1 . Firms produce output in each period with a Cobb-Douglass production function of labour and capital, with a capital share α ∈ (0, 1). The government uses the tax revenues to fund an amount of government spending equivalent to a share g of output. Assume 1 − g ≥ α. Markets for inputs and output are competitive. In the first period, the endowments of capital across types, k i 1 , as well as the tax rates, τ k 1 and τ l 1 , are given. Individuals choose investment and consumption to maximise their utility. In period 1, next-period tax rates will be chosen by an individual of a designated group i in order to maximise her own utility. An agent's utility depends only on her lifetime consumption, and is represented by log c t + β log c t+1 , with β > 0. Define the after-tax current income for an individual in group i at time t as Similarly, for the aggregate economy the after-tax income is y t ≡ (1−τ k t )R t k t +(1−τ l t )w t . In equilibrium, factor markets clear so k t = i µ i k i t , the government constraint holds so g = ατ k t + (1 − α)τ l t , and factor prices equal their marginal products so w t = (1 − α)k α t and R t = αk α−1 t . Then it follows that these measures of disposable income can be written as and Consider first the equilibrium determination of capital at t = 2 for an already given tax rate on capital τ k t , and initial incomes y t−1 and y i t−1 . The individual decision problem 1	536	2,157	{"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-2021-39	latest	en	0.911587
spmbiology.blog.onlinetuition.com.my	1,722,824,022,000,000,000	text/html	crawl-data/CC-MAIN-2024-33/segments/1722640427760.16/warc/CC-MAIN-20240805021234-20240805051234-00079.warc.gz	439,842,730	10,496	# Experiment 12.1 (Form 5 Biology Textbook Exercise and Answer) Continuous and Discontinuous Variation in Humans: Problem statement: Is the height, body weight and fingerprint of each pupil different? Aim: To study continuous variation and discontinuous variation in humans Hypothesis: Height, body weight and fingerprint of each pupil is different. Materials Graph paper, white papers Apparatus Height measuring equipment, weighing machine, ink pad Procedure A. Height 1. Measure and record height of each pupil in the class in the results table. 2. Plot a graph of number of pupils against height range. B. Body weight 1. Weigh and record body weight of each pupil in the class in the results table. 2. Plot a graph of number of pupils against body weight range. C. Fingerprint 1. Use the fingerprint patterns shown in page 259 for this activity. 2. Place a thumb surface of each pupil on an ink pad, then press the thumb on a piece of white paper. 3. Record the thumbprint pattern of each pupil in the results table. 4. Build a bar chart based on the results obtained. Results Discussion 1. What are the shapes of the graphs plotted for height and body weight? 2. Give inferences for distribution of height, body weight and thumbprint pattern of the pupils in your class. Conclusion Is the hypothesis accepted? Suggest a suitable conclusion.	296	1,356	{"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}	2.578125	3	CC-MAIN-2024-33	latest	en	0.872893
https://staging-pubs.nctm.org/browse?access=all&pageSize=10&sort=datedescending&t_0=grades_6-8_2&t_3=reasoning-sense-making	1,670,384,893,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446711126.30/warc/CC-MAIN-20221207021130-20221207051130-00706.warc.gz	574,221,215	30,568	# Browse ## You are looking at 1 - 10 of 14items for : • Eighth • Reasoning/Sense Making/Proof • Refine by Access: All content Clear All Restricted access ## Using Scaffolding to Scale-up Justifications Encouraging students to justify earlier as they attempt to solve an open-ended task can lead to greater understanding and engagement. Restricted access ## Patterns on a Calendar ### big solutions to little problems Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored. Restricted access ## Mathematical Explorations: A New Twist on Collaborative Learning Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997). Restricted access ## Mathematical Explorations: Find the Distance: No Formula Necessary This activity involves finding the distance between two points in a coordinate plane and emphasizes reasoning from repeated calculations, which is one of the mathematical practices specified by the Common Core State Standards for Mathematics. Restricted access ## Math for Real: Shaking Things Up with the Richter Scale ### “when will I ever use this?” This problem ties into the real-life measurement found in the Richter scale. Restricted access ## Algebra Homework: A Sandwich! Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning. Restricted access ## Connecting the “Missing Words” to the Common Core A sixth-grade teacher's word task uncovers higher-level thinking and engages her students in the Standards for Mathematical Practice. Restricted access ## Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs. Restricted access ## If Only Clairaut Had Dynamic Geometry Tools Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry. Restricted access	593	3,158	{"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-2022-49	latest	en	0.919082
https://wiki.iac.isu.edu/index.php?title=Lab_13_RS&diff=next&oldid=58531	1,660,001,033,000,000,000	text/html	crawl-data/CC-MAIN-2022-33/segments/1659882570879.1/warc/CC-MAIN-20220808213349-20220809003349-00299.warc.gz	556,915,107	7,201	# Difference between revisions of "Lab 13 RS" DC Bipolar Transistor Curves Data sheet for transistors. Using 2N3904 is more srtaight forward in this lab. # Transistor circuit 1.) Identify the type (n-p-n or p-n-p) of transistor you are using and fill in the following specifications. Value Description Collector-Base breakdown voltage Emitter-Base Breakdown Voltage Maximum Collector Voltage Maximum Collector Current Transistor Power rating() DC current gain 2.) Construct the circuit below according to the type of transistor you have. Let . variable power supply . Find the resistors you need to have , , and 3.) Measure the emitter current for several values of by changing such that the base current A is constant. V_{CC} V_B V_{BB} V_ {EC} V_ E R_E R_B I_E I_B mV mV V mV mV k mA \muA 4.) Repeat the previous measurements for A. Remember to keep so the transistor doesn't burn out V_{CC} V_B V_{BB} V_ {EC} V_ E R_E R_B I_E I_B mV mV V mV mV k mA \muA 5.) Graph -vs- for each value of and above. (40 pnts) 6.) Overlay points from the transistor's data sheet on the graph in part 5.).(10 pnts) # Questions 1. Compare your measured value of or for the transistor to the spec sheet? (10 pnts) 2. What is for the transistor?(10 pnts) 3. The base must always be more _________(________) than the emitter for a npn (pnp)transistor to conduct I_C.(10 pnts) 4. For a transistor to conduct I_C the base-emitter junction must be ___________ biased.(10 pnts) 5. For a transistor to conduct I_C the collector-base junction must be ___________ biased.(10 pnts) # Extra credit Measure the Base-Emmiter breakdown voltage. (10 pnts) I expect to see a graph and a linear fit which is similar to the forward biased diode curves. Compare your result to what is reported in the data sheet.	474	1,801	{"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}	2.75	3	CC-MAIN-2022-33	latest	en	0.786911
https://measurementstuff.com/how-many-days-is-100-hours/	1,701,787,143,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679100551.2/warc/CC-MAIN-20231205140836-20231205170836-00410.warc.gz	441,191,656	25,308	# How many days is 100 hours? I recently dropped a comment on Quora asking how many days is 100 hours. I wasn’t surprised to find that, while there are some fascinating insights, the answer is the prime source of confusion and disagreement. For whatever task that you need to complete within 100 hours, you should know it will take you 4.16667 days. If you are working based on the mentioned hour, you should be able to complete any task given within 4 days. However, you can choose to get the task done in a short time, depending on some factors. ## What is the meaning of 100 hours? To be honest, it depends on who you ask. But if you’re asking about the meaning of 100 hours in general, it’s just a number that represents how long something takes to complete. It doesn’t mean anything more than that. Also, 100 hours is a unit of measurement for work. It’s usually used when you’re talking about the number of hours that someone spent working on something. So if a person works 100 hours in one week, it means that they have worked for 4 days in a week. Also read: Different types of Measuring cups sizes ## How many days is 100 hours? There are exactly 24 hours in a day, but each hour has 60 minutes (60 minutes = 1 hour). So that means there are approximately 86,400 seconds per day (1 second = 1/3600th of an hour). So, there are about 360000 seconds in 100 hours, and that’s 4.16667 days in 100 hours. ## How many hours is 4 days? A 4 days work week means you’ll be working for four days in a row. That’s 96 hours per week. So, it all depends on how you choose to designate the time for the task you have. The bottom line is that you have 96 hours in a week to complete any given task. ## Is studying 100 hours a week good? At any given time, almost everyone is looking for a way to improve their focus, productivity, and overall work ethic. Whether it’s the brainpower of ultra-productive people who can complete 100 tasks in an hour or less or those with great attention-focusing skills that can see the big picture and get things done fast, there are many ways to build a stronger work ethic. So, if you’re serious about getting into college, then yes, 100 hours of study time per week is good because it means you’ll be putting in the hours necessary to get into your dream school. You can also find ways to reduce your study time later in order to maintain focus on other parts of life. If you’re not sure about college or have other goals in mind, then keep in mind that most people need less than 100 hours of study time per week to be successful at school. Try to find out what works best for you and make those changes. Read:: How wide is a 65 inch tv? ## Conclusion The length of a day is measured in hours. So, how many days is 100 hours? On this page, we were able to let you know that 100 hours makes 4.1 days. The length of a day is 24 hours or 86,400 seconds. A day consists of 24 hours, and each unit of time is called an hour. The length of a week is measured in days. The length of a week is seven days or 168 hours. Each unit of time is called a day; for example, Sunday is one day long, and Monday is another day long.	758	3,166	{"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}	3.34375	3	CC-MAIN-2023-50	longest	en	0.959873
https://www.jiskha.com/display.cgi?id=1315278852	1,511,067,970,000,000,000	text/html	crawl-data/CC-MAIN-2017-47/segments/1510934805362.48/warc/CC-MAIN-20171119042717-20171119062717-00639.warc.gz	834,503,607	3,739	# Algebra posted by . Tell whether the sum is positive, negative, or zero. Explain n is positive and m is negative. n + (-m) is ? • Algebra - See my last response to your problem. ## Similar Questions 1. ### math Instructions: Tell whether each expression represents a positive number or a negative number when m and n are negative. problem: -n/-m If both m and n are negative, then both -m and -n (numerator and denominator) are positive. What … 2. ### Decartes Rule of Signs Could you explain to me decartes Rule of signs? 3. ### Algebra Tell whether the sum is positive, negative, or zero. Explain n is positive and m is negative. n + (-m) is ? 4. ### algebra Could someone please help me with this? (1) If x is a nonzero real number, is x–2 always positive, always negative, or positive or negative depending on whether x is positive or negative? 5. ### algebra ) If x is a nonzero real number, is x–2 always positive, always negative, or positive or negative depending on whether x is positive or negative? 1) For a reaction delta Go is more negative than delta Ho. What does this mean? 7. ### phsics throughout a time interval, while the speed of a particle increases as it moves along the x-axis, its velocity and acceleration might be: a) positive and negative B) negative and negative c) negative and positive D) negative and zero … 8. ### math Which statement is true? A.The sum of two positive integers is sometimes positive, sometimes negative. B.The sum of two negative integers is always negative. C.The sum of a positive integer and a negative integer is always positive. 9. ### Math We are adding positive and negative numbers. The question is State positive or negative or it depends along with my answers. Are these correct? 10. ### Algebra II PLEASE HELPPPPPP What are the possible numbers of positive, negative, and complex zeros of f(x) = x4 + 3x3 − 2x2 + 1? More Similar Questions	453	1,920	{"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-2017-47	latest	en	0.85078
https://oeis.org/A200228	1,579,794,802,000,000,000	text/html	crawl-data/CC-MAIN-2020-05/segments/1579250610919.33/warc/CC-MAIN-20200123131001-20200123160001-00526.warc.gz	586,081,013	3,907	The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Thanks to everyone who made a donation during our annual appeal! To see the list of donors, or make a donation, see the OEIS Foundation home page. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A200228 Decimal expansion of greatest x satisfying 3x^2 - cos(x) = 4sin(x). 3 1, 1, 6, 4, 7, 2, 0, 1, 3, 2, 6, 0, 0, 0, 8, 6, 5, 4, 8, 1, 4, 4, 1, 7, 3, 6, 0, 3, 9, 1, 7, 6, 2, 9, 3, 4, 2, 8, 3, 8, 8, 5, 9, 8, 2, 9, 2, 3, 6, 1, 6, 8, 4, 5, 0, 1, 3, 9, 9, 2, 3, 7, 8, 1, 6, 7, 5, 4, 2, 8, 8, 0, 2, 7, 2, 0, 0, 6, 5, 0, 9, 7, 8, 3, 9, 7, 1, 5, 4, 7, 9, 2, 5, 5, 4, 8, 9, 5, 0 (list; constant; graph; refs; listen; history; text; internal format) OFFSET 1,3 COMMENTS See A199949 for a guide to related sequences. The Mathematica program includes a graph. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 EXAMPLE least x: -0.21220726159791829897823740501037540... greatest x: 1.164720132600086548144173603917629... MATHEMATICA a = 3; b = -1; c = 4; f[x_] := ax^2 + bCos[x]; g[x_] := cSin[x] Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}] r = x /.FindRoot[f[x] == g[x], {x, -.22, -.21}, WorkingPrecision -> 110] RealDigits[r] ( A200227 ) r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110] RealDigits[r] ( A200228 ) PROG (PARI) a=3; b=-1; c=4; solve(x=1, 2, ax^2 + bcos(x) - csin(x)) \\ G. C. Greubel, Jun 30 2018 CROSSREFS Cf. A199949. Sequence in context: A164293 A141796 A105160 * A309710 A241297 A021611 Adjacent sequences: A200225 A200226 A200227 * A200229 A200230 A200231 KEYWORD nonn,cons AUTHOR Clark Kimberling, Nov 14 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 January 23 10:50 EST 2020. Contains 331171 sequences. (Running on oeis4.)	874	2,063	{"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}	3.453125	3	CC-MAIN-2020-05	latest	en	0.629447
http://majortests.com/gre/problem_solving_test04	1,472,541,525,000,000,000	text/html	crawl-data/CC-MAIN-2016-36/segments/1471982974951.92/warc/CC-MAIN-20160823200934-00059-ip-10-153-172-175.ec2.internal.warc.gz	160,230,544	5,222	# GRE Math Problem Solving Practice Test 04 1. If a² = 12, then a4 = A. 144 B. 72 C. 36 D. 24 E. 16 2. If n is even, which of the following cannot be odd? Select all that apply. A. n + 3 B. 3n C. n² - 1 D. 2(n + 3) 3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle? Select ALL that apply. A. 24 B. 20 C. 5 4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds? A. 12 B. 11 C. 10 D. 9 E. 8 5. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube? A. 8p B. pq C. pq + 27 D. -p E. (p - q)6 6. Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop? A. 128 B. 64 C. 32 D. 16 E. 8 7. n is an integer chosen at random from the set {5, 7, 9, 11 } p is chosen at random from the set {2, 6, 10, 14, 18} What is the probability that n + p = 23 ? A. 0.1 B. 0.2 C. 0.25 D. 0.3 E. 0.4 8. A dress on sale in a shop is marked at \$D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ? A. 0.75D B. 0.76D C. 0.765D D. 0.775D E. 0.805D 9. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ? A. 2 B. 2√2 C. 3 D. √10 E. √20 10. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ? A. 9 B. 10 C. 11 D. 12 E. 13 ### Test information 10 questions 12 minutes This is just one of 12 free GRE math problem solving tests available on majortests.com. See the problem solving page for directions, tips and more information. * GRE is a registered trademark of Educational Testing Service (ETS). This website is not endorsed or approved by ETS. All content of site and tests copyright © 2016 Study Mode, LLC.	786	2,389	{"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}	3.703125	4	CC-MAIN-2016-36	latest	en	0.918584
https://cs.stackexchange.com/questions/129460/show-l-w-in-a-b-for-every-u-substring-of-w-5-leu-a%E2%88%92u-b-l/129476	1,719,270,635,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198865490.6/warc/CC-MAIN-20240624214047-20240625004047-00186.warc.gz	163,743,919	41,394	Show $L =$ { w $\in (a,b) ^$\| for every u substring of w, $-5\le\|u\|_a−\|u\|_b\le5\}$ is regular I try to show that this language is regular: $$L =$$ { w $$\in \ (a,b) ^ $$\| for every u substring of w, $$-5\le\|u\|_a−\|u\|_b\le5\}$$ If I build a NFA and run on it every substring of w (skip other letters every time) - and only if they are all accepted (follows the condition) then accept w. Is it possible in NFA? Is there other way to show the regularity of the language? • You can look at the residual sets: for each $w$, let $R(w) = \{u\| wu \in L\}$. For $L$ to be regular, the number of such sets ($R(w)$ for all $w$) must be finite. You can show that it's the case by noting that the only thing that matters for $R(w)$ is $\min$ and $\max$ of $#(a) - #(b)$ for all suffixes of $w$, and they can only be between $-5$ and $5$. – user114966 Commented Aug 21, 2020 at 21:08 • @Dmitry I started writing that down as the answer before I saw your comment. Commented Aug 22, 2020 at 16:07 Nice question! This is a very nontrivial problem involving regular languages. First of all: no, you cannot run an automaton on every substring of a string skipping other letters, you are supposed to run the automaton only once on the target string. In this case it is simpler to reason on the complementary of the given language, namely on $$L^C = \{ w \in (a,b) ^ * \mid \text{ there is a substring } u \text{ of } w \text{ such that } \|u\|_a−\|u\|_b>5 \text{ or } \|u\|_a−\|u\|_b<-5\}$$ The language $$L^C$$ is regular, as it is recognized by the following NFA: (each state name is the difference $$\|u\|_a−\|u\|_b$$, the first letter of the substring $$u$$ is "found" nondeterministically by the NFA). So, as $$L^C$$ is regular, also $$L=(L^C)^C$$ is. Following Hendrick's suggestion, I tried to determinize the NFA and to draw its complement, and I get this nice DFA that recognize $$L$$: Each name of an accepting state name is an interval: when, running the automaton, we are in state $$[x_1,x_2]$$ and we have read the string $$z$$ this means that for all $$x\in [x_1,x_2]$$ there is a suffix $$u$$ of $$z$$ such that $$\|u\|_a−\|u\|_b=x$$. Otherwise said, following Dmitry's suggestion, the automaton calculate the residual set of $$z$$. In a sense, as Hendrick says, it is like we are running the automaton on each substring, but this do not mean that we can directly use a DFA that recognize strings such that the difference between the $$a$$s and the $$b$$s is in $$[-5,5]$$ (which would be easy to realize) and run this automaton on each substring of a given one, and in this way prove that the language is regular. Lastly, I would write a trivial generalization of the result (I think that this is folklore, but I couldn't find a reference). Let $$T$$ be a regular language on an alphabet $$\Sigma$$ and let $$L$$ be the language defined as follows: $$L= \{ w \in \Sigma^* \mid \text{ for every substring } u \text{ of } w,\ u\in T\}$$ then also $$L$$ is regular. Indeed, as above, consider $$L^C$$, the complement of $$L$$, namely $$L^C = \{ w \in \Sigma^* \mid \text{ there is a substring } u \text{ of } w \text{ such that } u\not\in T\}$$ Then $$L^C=\Sigma^T^C\Sigma^$$, and therefore $$L=(\Sigma^T^C\Sigma^)^C$$ is regular, as the family of regular languages is closed under concatenation and complementation. Cleary the result is still true for every family of languages closed under concatenation and complementation, but this is not a necessary condition. Indeed, the family of finite languages it is not closed under complementation, but clearly if $$T$$ is finite, then also $$L$$ is (as it is always the case that $$L\subseteq T$$). On the other hand, this is not true for all classes of languages. Consider the family NR of non-regular languages, then $$T=\{1^p\mid p\text{ is prime}\}\in\$$NR, but in this case we have $$L=\varnothing$$, which is regular. • I like your solution using the complement! But contrary to what you suggest, it is possible to run the automaton on each substring, spawning after each letter a new computation. The point here is that there are only finitely many states, so if any of the parallel computations reach the same state they can be fused, so there will always be a bounded number of runs in parallel. Commented Aug 22, 2020 at 14:58 • Also it is very funny (I mean instructive) to see what happens if you actually determinise the NFA from your solution. The DFA states will always contain sets of states that form an interval. The letters move the interval up and down, but the interval will never loose $0$. Commented Aug 22, 2020 at 15:02 • Comment to self: I now realize that adding state zero every step of the computation (when making the NFA deterministic because of the loop at state zero) is actually the same as starting a computation in parallel for every next letter of the input. So my comments kind-of match. Commented Aug 22, 2020 at 15:52 • @HendrikJan, thanks for noticing the error, clearly you are right, as the automaton was not deterministic! Commented Aug 23, 2020 at 9:17 • @tas1 You are right, but in this case we started with a nondet automaton and we explicitly were trying to make a deterministic one. That last DFA had some extra edges that are now removed. Commented Aug 25, 2020 at 15:04	1,502	5,272	{"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": 35, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.640625	4	CC-MAIN-2024-26	latest	en	0.919435
https://grammarlytutors.com/excel-chapter-6-grader-project-delta-paint/	1,679,946,876,000,000,000	text/html	crawl-data/CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00196.warc.gz	333,398,310	12,878	# Excel chapter 6 grader project – delta paint \| 1 Download and open the file named Exp19_Excel_Ch06_Cap_DeltaPaint.xlsx. Grader has automatically added your last name to the beginning of the filename. 2 Create appropriate range names for Total Production Cost (cell B18) and Gross Profit (cell B21) by selection, using the values in the left column. 3 Edit the existing name range Employee_Hourly_Wage to Hourly_Wages2021. Note, Mac users, in the Define Name dialog box, add the new named range, and delete the original one. 4 Use the newly created range names to create a formula to calculate Net Profit (in cell B22). Net Profit = Gross Profit – Total Production Cost. 5 Create a new worksheet labeled Range Names, paste the newly created range name information in cell A1, and resize the columns as needed for proper display. 6 On the Forecast sheet, start in cell E3. Complete the series of substitution values ranging from 10 to 200 at increments of 10 gallons vertically down column E. 7 Enter references to the Total_Production_Cost, Gross_Profit, and Net Profit cells in the correct locations (F2, G2, and H2 respectively) for a one-variable data table. Use range names where indicated. 8 Complete the one-variable data table in the range E2:H22 using cell B4 as the column input cell, and then format the results with Accounting Number Format with two decimal places. 9 Apply custom number formats to make the formula references appear as descriptive column headings. In F2, Total Costs; in G2, Gross Profit, in H2, Net Profit. Bold and center the headings and substitution values. 10 Copy the number of gallons produced substitution values from the one-variable data table, and then paste the values starting in cell E26. 11 Type \$15 in cell F25. Complete the series of substitution values from \$15 to \$40 at \$5 increments. 12 Enter the reference to the net profit formula in the correct location for a two-variable data table. 13 Complete the two-variable data table in the range E25:K45. Use cell B6 as the Row input cell and B4 as the Column input cell. Format the results with Accounting Number Format with two decimal places. 14 Apply a custom number format to make the formula reference appear as a descriptive column heading Wages. Bold and center the headings and substitution values where necessary. 15 Create a scenario named Best Case, using Units Sold, Unit Selling Price, and Employee Hourly Wage (use cell references). Enter these values for the scenario: 200, 30, and 15. 16 Create a second scenario named Worst Case, using the same changing cells. Enter these values for the scenario: 100, 25, and 20. 17 Create a third scenario named Most Likely, using the same changing cells. Enter these values for the scenario: 150, 25, and 15. 18 Generate a scenario summary report using the cell references for Total Production Cost and Net Profit. 19 Load the Solver add-in if it is not already loaded. Set the objective to calculate the highest Net Profit possible. 20 Use the units sold as changing variable cells. 21 Use the Limitations section of the spreadsheet model to set a constraint for raw materials (The raw materials consumed must be less than or equal to the raw materials available). Use cell references to set constraints. 22 Set a constraint for labor hours. Use cell references to set constraints. 23 Set a constraint for maximum production capability. Units sold (B4) must be less than or equal to maximum capability per week (B7). Use cell references to set constraints. 24 Solve the problem. Generate the Answer Report and Keep Solver Solution. 25 Create a footer on all four worksheets with your name on the left side, the sheet name code in the center, and the file name code on the right side. 26 Save and close Exp19_Excel_Ch06_Cap_DeltaPaint.xlsx. Exit Excel. Submit the file as directed. Calculate your essay price (550 words) Approximate price: \$22 ## How it Works 1 It only takes a couple of minutes to fill in your details, select the type of paper you need (essay, term paper, etc.), give us all necessary information regarding your assignment. 2 Once we receive your request, one of our customer support representatives will contact you within 24 hours with more specific information about how much it'll cost for this particular project. 3 After receiving payment confirmation via PayPal or credit card – we begin working on your detailed outline, which is based on the requirements given by yourself upon ordering. 4 Once approved, your order is complete and will be emailed directly to the email address provided before payment was made!	1,132	4,782	{"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-2023-14	latest	en	0.697671
https://www.scribd.com/presentation/125262526/Presentation-Krog-s-Metalfab	1,563,338,235,000,000,000	text/html	crawl-data/CC-MAIN-2019-30/segments/1563195525046.5/warc/CC-MAIN-20190717041500-20190717063500-00398.warc.gz	821,256,873	47,381	You are on page 1of 9 Krogs MetalFab Group -4 CASE FACTS Two Plants One at Chicago and other at Moline Fire destroyed Chicago plant Production affected , expenses incurred due to shifting of work force Insurance coverage : To compensate for lost profit Calculation Sales in 2003 \$5,079,094 \$5,434,630 \$3,845,499 (A) Lost Sales (B)Profit in 2003 as a apercent of 2003 sales(\$111,928/5,079,094) \$1,589,131 Lost profit(A*B) \$34,961 \$0.0220 500000 450000 400000 350000 300000 250000 200000 150000 100000 50000 0 30000 Sales Expense 25000 20000 15000 10000 5000 200000 400000 Sales \$ 600000 800000 0 0 COGS \$ Statement 40000 35000 30000 25000 20000 15000 10000 5000 0 0 Sales \$ Sales \$ Estimating Profit -Account Analysis Method COGS and Sales Expense treated as variable cost. Administrative Expense treated as fixed cost. Calculations COGS/\$ Sale S. Expense/\$ Sale Variable Cost Fixed Cost / Month Fixed Cost / Year \$0.89 \$0.04 \$0.93 \$20,250.00 \$243,000.00 Estimated Sales-2004 Estimated Cost Estimated Profit Actual Profit \$5,434,630.58 \$5,297,857.62 \$136,772.96 (\$724,210.00) Lost Profit \$860,982 Estimating Profit- High Low Method Time Period Highest Sales Lowest Sales Aug-03 Apr-03 Sales Cost \$602,210 \$485,120 Variable Cost/ \$ Sales \$0.44 Fixed Cost /Month \$220,660.00 Estimated Profit \$400,096.00 Lost Profit \$1,124,306.00 \$302,685 \$353,584 Estimating Profit Regression Method Scatter Plot of Sales and Cost 600000 500000 Total Cost 400000 300000 y = 0.3651x + 259418 R = 0.6036 200000 100000 Estimating Profit Using Least Squares Regression -Without Removing Outlier Total Cost = 259,418+0.3651xSales Fixed Component \$259,418.00 Variable Component 2003 Sales Predicted 2004 Sales Estimated Cost Estimated Profit Actual Profit \$0.37 \$5,079,094.00 \$5,434,630.58 \$5,097,199.62 \$337,430.96 (\$724,210.00) Lost Profit \$1,061,640.96 0 0 Sales Estimating ProfitRegression Method -II Scatter Plot of Sales and Cost (Removing Outlier) 600000 Total Cost 500000 Estimating Profit Using Least Squares Regression -After Removing Outlier Total Cost = 220338+0.437xSales 400000 Fixed Component \$220,338.00 300000 y = 0.437x + 220338 R = 0.9915 200000 100000 0 100000 200000 300000 400000 500000 600000 700000 Sales Variable Component 2003 Sales Predicted 2004 Sales Estimated Cost Estimated Profit Actual Profit Loss Profit \$0.44 \$5,079,094.00 \$5,434,630.58 \$5,018,989.56 \$415,641.02 (\$724,210.00) \$1,139,851.02 Recommendation Accountants analysis incorrect because of large proportion of fixed cost Use regression method to estimate costs as it is more accurate. Data check is necessary before applying regression	927	2,730	{"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-2019-30	latest	en	0.592138
http://www.velocityreviews.com/forums/t590127-beginners-help.html	1,397,721,055,000,000,000	text/html	crawl-data/CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00334-ip-10-147-4-33.ec2.internal.warc.gz	750,971,278	10,401	Velocity Reviews > beginners help # beginners help Guido van Brakel Guest Posts: n/a 02-07-2008 Hello I totally new to python and i'm doing a python course now. Maybe someone could help me a little bit here: I need to create this script. If i enter a center digit like 5 for example i need to create two vertical and horzitonal rows that looks like this. If i enter 6 it shows 6 six starts. How can i do this, because i don't have any clue. ***** * * * * * * *** Kind Regards, -- Guido van Brakel -- Guilherme Polo Guest Posts: n/a 02-07-2008 2008/2/7, Guido van Brakel <(E-Mail Removed)4all.nl>: > Hello > > I totally new to python and i'm doing a python course now. Maybe someone > could help me a little bit here: > > I need to create this script. > > If i enter a center digit like 5 for example i need to create two > vertical and horzitonal rows that looks like this. If i enter 6 it shows > 6 six starts. How can i do this, because i don't have any clue. > > *** > * * > * * > * * > *** > This would totally ruin the purpose of your course. Did you try anything at all ? > Kind Regards, > > -- > Guido van Brakel > -- > > -- > http://mail.python.org/mailman/listinfo/python-list > -- -- Guilherme H. Polo Goncalves Diez B. Roggisch Guest Posts: n/a 02-07-2008 Guido van Brakel wrote: > Hello > > I totally new to python and i'm doing a python course now. Maybe someone > could help me a little bit here: > > I need to create this script. > > If i enter a center digit like 5 for example i need to create two > vertical and horzitonal rows that looks like this. If i enter 6 it shows > 6 six starts. How can i do this, because i don't have any clue. > > *** > * * > * * > * * > *** This list is not there to provide you with solutions to your homework. If you try and show us your efforts, or have otherwise concrete questions you Diez Steve Holden Guest Posts: n/a 02-07-2008 Guido van Brakel wrote: > Hello > > I totally new to python and i'm doing a python course now. Maybe someone > could help me a little bit here: > > I need to create this script. > > If i enter a center digit like 5 for example i need to create two > vertical and horzitonal rows that looks like this. If i enter 6 it shows > 6 six starts. How can i do this, because i don't have any clue. > > *** > * * > * * > * * > *** > Welcome to c.l.py. We have a tradition here of helping people with classwork by asking them to make an attempt to solve their problem. Then we will point out what We wouldn't be helping you very much if we just gave you an answer that you had no understanding of, and it would be embarrassing if your teacher asked you to explain it. It doesn't matter how awful your code is, people here are generally kind to those making an honest first attempt. regards Steve -- Steve Holden +1 571 484 6266 +1 800 494 3119 Holden Web LLC http://www.holdenweb.com/ Matimus Guest Posts: n/a 02-07-2008 On Feb 7, 7:53 am, Guido van Brakel <guidovb1@invalid> wrote: > Hello > > I totally new to python and i'm doing a python course now. Maybe someone > could help me a little bit here: > > I need to create this script. > > If i enter a center digit like 5 for example i need to create two > vertical and horzitonal rows that looks like this. If i enter 6 it shows > 6 six starts. How can i do this, because i don't have any clue. > > *** > * * > * * > * * > *** > > Kind Regards, > > -- > Guido van Brakel > -- If you turn this in you will be rewarded for your effort Code: ```side = input("How many stars on a side?:") if side == 5: print "**" print " " print " " print " " print "**" elif side == 6: print "***" print " " print " " print " " print " " print "****"``` Dennis Lee Bieber Guest Posts: n/a 02-07-2008 On Thu, 07 Feb 2008 13:53:48 +0100, Guido van Brakel <guidovb1@invalid> declaimed the following in comp.lang.python: > > If i enter a center digit like 5 for example i need to create two No idea of what "center digit" means (to me it implies a digit in the middle of a multi-digit number: 123, 73837, 04377 [2, 8, 3, respectively]). > vertical and horzitonal rows that looks like this. If i enter 6 it shows > 6 six starts. How can i do this, because i don't have any clue. > Attempting to paraphrase, you are supposed to produce an ASCII art (okay, maybe ISO-Latin-1, or some other set -- but is pretty common in all) box whose sides are the length (call it "n") entered. You need only a few things... Line 1 is "n" copies of * Lines 2..n-1 are , 2..n-1 copies of space, Line n is "n" copies of * Brute force mode (not optimized) would be a loop for line 1; a loop for lines 2..n-1 that contains a loop for spacing the , and a final loop for line n. Python is high-level enough that it can be done with one loop containing an if/else block. -- Wulfraed Dennis Lee Bieber KD6MOG http://www.velocityreviews.com/forums/(E-Mail Removed) (E-Mail Removed) HTTP://wlfraed.home.netcom.com/ (Bestiaria Support Staff: (E-Mail Removed)) HTTP://www.bestiaria.com/ Steven D'Aprano Guest Posts: n/a 02-07-2008 On Thu, 07 Feb 2008 13:53:48 +0100, Guido van Brakel wrote: > Hello > > I totally new to python and i'm doing a python course now. Maybe someone > could help me a little bit here: > > I need to create this script. > > If i enter a center digit like 5 for example i need to create two > vertical and horzitonal rows that looks like this. If i enter 6 it shows > 6 six starts. How can i do this, because i don't have any clue. > > **** > * * > * * > * * > ***** Start by writing some Python code that draws a horizontal line of stars. (Hint: "print '' draws one star.) Now write some code that draws a column of stars. Now combine them to draw a square. Come back when you have some more specific questions. Regards, -- Steven Tim Chase Guest Posts: n/a 02-07-2008 > If i enter a center digit like 5 for example i need to create two > vertical and horzitonal rows that looks like this. If i enter 6 it shows > 6 six starts. How can i do this, because i don't have any clue. > > **** > * * > * * > * * > *** Well we start by introducing the neophite programmer to unit-testing: import unittest class Tester(unittest.TestCase): def testFive(self): """ digit like 5 for example i need to create two vertical and horzitonal rows that looks like this *** * * * * * * *** """ assert five() == "**\n \n \n \n***" def testSix(self): """If i enter 6 it shows 6 six starts""" assert six() == "start" 6 def five(): return "****\n \n \n \n***" def six(): return "start" 6 if __name__ == "__main__": unittest.main() works for me... -tkc Steve Holden Guest Posts: n/a 02-07-2008 Tim Chase wrote: >> If i enter a center digit like 5 for example i need to create two >> vertical and horzitonal rows that looks like this. If i enter 6 it shows >> 6 six starts. How can i do this, because i don't have any clue. >> >> ***** >> * * >> * * >> * * >> *** > > Well we start by introducing the neophite programmer to unit-testing: > > import unittest > > class Tester(unittest.TestCase): > def testFive(self): > """ digit like 5 for example i need to > create two vertical and horzitonal > rows that looks like this > *** > * * > * * > * * > *** > """ > assert five() == "**\n \n \n \n***" > > def testSix(self): > """If i enter 6 it shows 6 six starts""" > assert six() == "start" 6 > > def five(): > return "****\n \n \n \n***" > > def six(): > return "start" 6 > > if __name__ == "__main__": > unittest.main() > > > works for me... I think you've scared him away, Tim! regards Steve -- Steve Holden +1 571 484 6266 +1 800 494 3119 Holden Web LLC http://www.holdenweb.com/	2,311	7,756	{"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-2014-15	latest	en	0.833175
http://www.ck12.org/algebra/Horizontal-and-Vertical-Asymptotes/?by=all&difficulty=all	1,485,228,177,000,000,000	text/html	crawl-data/CC-MAIN-2017-04/segments/1484560283689.98/warc/CC-MAIN-20170116095123-00114-ip-10-171-10-70.ec2.internal.warc.gz	384,163,474	18,414	<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> # Horizontal and Vertical Asymptotes ## Guidelines that graphs approach based on zeros and degrees in rational functions. Levels are CK-12's student achievement levels. Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work. At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter. Advanced Students matched to this level are ready for material that requires superior performance and mastery. ## Horizontal and Vertical Asymptotes Find the horizontal and vertical asymptotes of rational functions. MEMORY METER This indicates how strong in your memory this concept is 0 ## Horizontal and Vertical Asymptotes Identifying and understanding asymptotes of rational functions. MEMORY METER This indicates how strong in your memory this concept is 0 ## Horizontal and Vertical Asymptotes Find the horizontal and vertical asymptotes of rational functions. MEMORY METER This indicates how strong in your memory this concept is 0 ## Horizontal and Vertical Asymptotes Identifying and understanding asymptotes of rational functions MEMORY METER This indicates how strong in your memory this concept is 0 ## Horizontal and Vertical Asymptotes Identifying and understanding asymptotes of rational functions MEMORY METER This indicates how strong in your memory this concept is 0 ## SLT 23: Identifying Effects of Transformations on Rational Functions MEMORY METER This indicates how strong in your memory this concept is 0 • Video ## Determining Vertical and Horizontal Asymptotes of Rational Functions Explains how to determine horizontal and vertical asymptotes of a rational function without using limits. MEMORY METER This indicates how strong in your memory this concept is 1 • Video ## Horizontal and Vertical Asymptotes: A Sample Application This video demonstrates a sample use of horizontal and vertical asymptotes. MEMORY METER This indicates how strong in your memory this concept is 0 • Video ## Horizontal and Vertical Asymptotes: An Explanation of the Concept This video provides an explanation of the concept of horizontal and vertical asymptotes. MEMORY METER This indicates how strong in your memory this concept is 0 • 0 • Real World Application ## A Shot in the Arm Find out how the incidence of tetanus in the United States can be modeled with a rational function. MEMORY METER This indicates how strong in your memory this concept is 0 • Study Guide	581	2,790	{"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}	3.5625	4	CC-MAIN-2017-04	longest	en	0.846177
http://kwiznet.com/p/takeQuiz.php?ChapterID=10671&CurriculumID=42&Method=Worksheet&NQ=6&Num=1.27&Type=C	1,558,829,521,000,000,000	text/html	crawl-data/CC-MAIN-2019-22/segments/1558232258453.85/warc/CC-MAIN-20190525224929-20190526010929-00159.warc.gz	113,643,707	3,186	Name: ___________________Date:___________________ Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs! ### Middle/High School Algebra, Geometry, and Statistics (AGS)1.27 Linear Equations Review Test Q 1: X and Y axis are divided the place into ____ regions.threeFoursixTwo Q 2: Solve 1/x + 1/y = 9 and 3/x + 2/y = 22.x = 1/4 and y = 1/5x = 4 and y = 5x = 1/5 and y = 1/4x = 5 and y = 4 Q 3: Solve x + y = 21 and x - y = 9.x = 16 and y = 4x = 8 and y = 7x = 12 and y = 8x = 15 and y = 6 Q 4: The equations ax+by+c = 0 and kax + kby + kc = 0 are known as ______.inconsistent equationsdependent equationsindependent equations Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only! #### Subscription to kwizNET Learning System costs less than \$1 per month & offers the following benefits: • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets • Instant scoring of online quizzes • Progress tracking and award certificates to keep your student motivated • Unlimited practice with auto-generated 'WIZ MATH' quizzes © 2003-2007 kwizNET Learning System LLC. All rights reserved. This material may not be reproduced, displayed, modified or distributed without the express prior written permission of the copyright holder. For permission, contact info@kwizNET.com For unlimited printable worksheets & more, go to http://www.kwizNET.com.	402	1,475	{"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	3	CC-MAIN-2019-22	longest	en	0.85332
https://leetcode.ca/2017-01-22-419-Battleships-in-a-Board/	1,719,082,274,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198862410.56/warc/CC-MAIN-20240622175245-20240622205245-00544.warc.gz	311,446,997	7,577	# 419. Battleships in a Board ## Description Given an m x n matrix board where each cell is a battleship 'X' or empty '.', return the number of the battleships on board. Battleships can only be placed horizontally or vertically on board. In other words, they can only be made of the shape 1 x k (1 row, k columns) or k x 1 (k rows, 1 column), where k can be of any size. At least one horizontal or vertical cell separates between two battleships (i.e., there are no adjacent battleships). Example 1: Input: board = [["X",".",".","X"],[".",".",".","X"],[".",".",".","X"]] Output: 2 Example 2: Input: board = [["."]] Output: 0 Constraints: • m == board.length • n == board[i].length • 1 <= m, n <= 200 • board[i][j] is either '.' or 'X'. Follow up: Could you do it in one-pass, using only O(1) extra memory and without modifying the values board? ## Solutions • class Solution { public int countBattleships(char[][] board) { int m = board.length, n = board[0].length; int ans = 0; for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { if (board[i][j] == '.') { continue; } if (i > 0 && board[i - 1][j] == 'X') { continue; } if (j > 0 && board[i][j - 1] == 'X') { continue; } ++ans; } } return ans; } } • class Solution { public: int countBattleships(vector<vector<char>>& board) { int m = board.size(), n = board[0].size(); int ans = 0; for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { if (board[i][j] == '.') continue; if (i > 0 && board[i - 1][j] == 'X') continue; if (j > 0 && board[i][j - 1] == 'X') continue; ++ans; } } return ans; } }; • class Solution: def countBattleships(self, board: List[List[str]]) -> int: m, n = len(board), len(board[0]) ans = 0 for i in range(m): for j in range(n): if board[i][j] == '.': continue if i > 0 and board[i - 1][j] == 'X': continue if j > 0 and board[i][j - 1] == 'X': continue ans += 1 return ans • func countBattleships(board [][]byte) int { m, n := len(board), len(board[0]) ans := 0 for i := 0; i < m; i++ { for j := 0; j < n; j++ { if board[i][j] == '.' { continue } if i > 0 && board[i-1][j] == 'X' { continue } if j > 0 && board[i][j-1] == 'X' { continue } ans++ } } return ans } • function countBattleships(board: string[][]): number { const m = board.length; const n = board[0].length; let ans = 0; for (let i = 0; i < m; ++i) { for (let j = 0; j < n; ++j) { if (board[i][j] === '.') { continue; } if (i && board[i - 1][j] === 'X') { continue; } if (j && board[i][j - 1] === 'X') { continue; } ++ans; } } return ans; }	861	2,505	{"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}	3.203125	3	CC-MAIN-2024-26	latest	en	0.607614
https://www.shaalaa.com/question-bank-solutions/write-the-truth-value-of-the-following-statement-n-n-n2-n-is-even-number-while-n2-n-is-an-odd-number-truth-value-of-statement_142654	1,653,755,934,000,000,000	text/html	crawl-data/CC-MAIN-2022-21/segments/1652663016949.77/warc/CC-MAIN-20220528154416-20220528184416-00494.warc.gz	1,137,866,065	10,497	# Write the truth value of the following statement: ∀ n ∈ N, n2 + n is even number while n2 – n is an odd number. - Mathematics and Statistics Sum Write the truth value of the following statement: ∀ n ∈ N, n2 + n is even number while n2 – n is an odd number. #### Solution Let p: ∀ n ∈ N, n2 + n is an even number. q: ∀ n ∈ N, n2 − n is an odd number. Then the symbolic form of the given statement is p∧q. The truth values of p and q are T and F respectively. ∴ The truth value of p∧q is F. ..........[T∧F ≡ F]. Concept: Truth Value of Statement Is there an error in this question or solution? #### APPEARS IN Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 1 Mathematical Logic Miscellaneous Exercise 1 \| Q 3.2 \| Page 33	224	790	{"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}	3.734375	4	CC-MAIN-2022-21	latest	en	0.836921
http://uk.mathworks.com/help/symbolic/airy.html?requestedDomain=uk.mathworks.com&nocookie=true	1,475,323,704,000,000,000	text/html	crawl-data/CC-MAIN-2016-40/segments/1474738662856.94/warc/CC-MAIN-20160924173742-00105-ip-10-143-35-109.ec2.internal.warc.gz	270,645,202	15,599	Documentation This is machine translation Translated by Mouse over text to see original. Click the button below to return to the English verison of the page. airy Syntax • ``airy(x)`` example • ``airy(0,x)`` • ``airy(1,x)`` example • ``airy(2,x)`` example • ``airy(3,x)`` example • ``airy(n,x)`` • ``airy(___,1)`` Description example ````airy(x)` returns the Airy function of the first kind, Ai(x), for each element of `x`.``` ````airy(0,x)` is the same as `airy(x)`.``` example ````airy(1,x)` returns the derivative of Ai(x).``` example ````airy(2,x)` returns the Airy function of the second kind, Bi(x).``` example ````airy(3,x)` returns the derivative of Bi(x).``` ````airy(n,x)` uses the values in vector `n` to return the corresponding Airy functions of elements of vector `x`. Both `n` and `x` must have the same size.``` ````airy(___,1)` returns the Scaled Airy Functions following the syntax for the MATLAB® `airy` function.``` Examples Find the Airy Function of the First Kind Find the Airy function of the first kind, Ai(x), for numeric or symbolic inputs using `airy`. Approximate exact symbolic outputs using `vpa`. Find the Airy function of the first kind, Ai(x), at `1.5`. Because the input is double and not symbolic, you get a double result. `airy(1.5)` ```ans = 0.0717``` Find the Airy function of the values of vector `v` symbolically, by converting `v` to symbolic form using `sym`. Because the input is symbolic, `airy` returns exact symbolic results. The exact symbolic results for most symbolic inputs are unresolved function calls. ```v = sym([-1 0 25.1 1+1i]); vAiry = airy(v)``` ```vAiry = [ airy(0, -1), 3^(1/3)/(3gamma(2/3)), airy(0, 251/10), airy(0, 1 + 1i)]``` Numerically approximate the exact symbolic result using `vpa`. `vpa(vAiry)` ```ans = [ 0.53556088329235211879951656563887, 0.35502805388781723926006318600418,... 4.9152763177499054787371976959487e-38,... 0.060458308371838149196532978116646 - 0.15188956587718140235494791259223i] ``` Find the Airy function, Ai(x), of the symbolic input `x^2`. For symbolic expressions, `airy` returns an unresolved call. ```syms x airy(x^2)``` ```ans = airy(0, x^2)``` Find the Airy Function of the Second Kind Find the Airy function of the second kind, Bi(x), of the symbolic input `[-3 4 1+1i x^2]` by specifying the first argument as `2`. Because the input is symbolic, `airy` returns exact symbolic results. The exact symbolic results for most symbolic inputs are unresolved function calls. ```v = sym([-3 4 1+1i x^2]); vAiry = airy(2, v)``` ```vAiry = [ airy(2, -3), airy(2, 4), airy(2, 1 + 1i), airy(2, x^2)]``` Use the syntax `airy(2,x)` like `airy(x)`, as described in the example Find the Airy Function of the First Kind. Plot Airy Functions Plot the Airy Functions, and , over the interval `[-10 2]` using `fplot`. ```syms x fplot(airy(x), [-10 2]) hold on fplot(airy(2,x), [-10 2]) legend('Ai(x)','Bi(x)','Location','Best') title('Airy functions Ai(x) and Bi(x)') grid on ``` Plot the absolute value of over the complex plane. ```syms y z = x + 1iy; figure(2) fsurf(abs(airy(z))) title('\|Ai(z)\|') a = gca; a.ZLim = [0 10]; caxis([0 10]) ``` Find Derivatives of Airy Functions Find the derivative of the Airy function of the first kind, Ai′(x), at `0` by specifying the first argument of `airy` as `1`. Then, numerically approximate the derivative using `vpa`. ```dAi = airy(1, sym(0)) dAi_vpa = vpa(dAi)``` ```dAi = -(3^(1/6)gamma(2/3))/(2pi) dAi_vpa = -0.2588194037928067984051835601892``` Find the derivative of the Airy function of the second kind, Bi′(x), at `x` by specifying the first argument as `3`. Then, find the derivative at x = 5 by substituting for `x` using `subs` and calling `vpa`. ```syms x dBi = airy(3, x) dBi_vpa = vpa(subs(dBi, x, 5))``` ```dBi = airy(3, x) dBi_vpa = 1435.8190802179825186717212380046``` Solve Airy Differential Equation for Airy Functions Show that the Airy functions Ai(x) and Bi(x) are the solutions of the differential equation `$\frac{{\partial }^{2}y}{\partial {x}^{2}}-xy=0.$` ```syms y(x) dsolve(diff(y, 2) - xy == 0)``` ```ans = C1airy(0, x) + C2airy(2, x)``` Differentiate Airy Functions Differentiate expressions containing `airy`. ```syms x y diff(airy(x^2)) diff(diff(airy(3, x^2 + xy -y^2), x), y)``` ```ans = 2xairy(1, x^2) ans = airy(2, x^2 + xy - y^2)(x^2 + xy - y^2) +... airy(2, x^2 + xy - y^2)(x - 2y)(2x + y) +... airy(3, x^2 + xy - y^2)(x - 2y)(2x + y)(x^2 + xy - y^2) ``` Expand Airy Function using Taylor Series Find the Taylor series expansion of the Airy functions, Ai(x) and Bi(x), using `taylor`. ```aiTaylor = taylor(airy(x)) biTaylor = taylor(airy(2, x))``` ```aiTaylor = - (3^(1/6)gamma(2/3)x^4)/(24pi) + (3^(1/3)x^3)/(18gamma(2/3))... - (3^(1/6)gamma(2/3)x)/(2pi) + 3^(1/3)/(3gamma(2/3)) biTaylor = (3^(2/3)gamma(2/3)x^4)/(24pi) + (3^(5/6)x^3)/(18gamma(2/3))... + (3^(2/3)gamma(2/3)x)/(2pi) + 3^(5/6)/(3gamma(2/3))``` Fourier Transform of Airy Function Find the Fourier transform of the Airy function Ai(x) using `fourier`. ```syms x aiFourier = fourier(airy(x))``` ```aiFourier = exp((w^31i)/3)``` Numeric Roots of Airy Function Find a root of the Airy function Ai(x) numerically using `vpasolve`. ```syms x vpasolve(airy(x) == 0, x)``` ```ans = -226.99630507523600716771890962744``` Find a root in the interval `[-5 -3]`. `vpasolve(airy(x) == 0, x, [-5 -3])` ```ans = -4.0879494441309706166369887014574``` Input Arguments collapse all Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression. Type of Airy function, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, or multidimensional array. The values of the input must be `0`, `1`, `2`, or `3`, which specify the Airy function as follows. n Returns `0` (default) Airy function, Ai(x), which is the same as `airy(x)`. `1` Derivative of Airy function, Ai'(x). `2` Airy function of the second kind, Bi(x). `3` Derivative of Airy function of the second kind, Bi'(x). collapse all Airy Functions The Airy functions Ai(x) and Bi(x) are the two linearly independent solutions of the differential equation `$\frac{{\partial }^{2}y}{\partial {x}^{2}}-xy=0.$` Ai(x) is called the Airy function of the first kind. Bi(x) is called the Airy function of the second kind. Scaled Airy Functions The Airy function of the first kind, Ai(x), is scaled as `${e}^{\left(\frac{2}{3}{x}^{\left(3/2\right)}\right)}\text{Ai}\left(x\right).$` The derivative, Ai'(x), is scaled by the same factor. The Airy function of the second kind, Bi(x), is scaled as `${e}^{-\|\frac{2}{3}\text{Re}\left({x}^{\left(3/2\right)}\right)\|}\text{Bi}\left(x\right).$` The derivative, Bi'(x), is scaled by the same factor. Tips • When you call `airy` for inputs that are not symbolic objects, you call the MATLAB `airy` function. • When you call `airy(n, x)`, at least one argument must be a scalar or both arguments must be vectors or matrices of the same size. If one argument is a scalar and the other is a vector or matrix, `airy(n,x)` expands the scalar into a vector or matrix of the same size as the other argument with all elements equal to the scalar. • `airy` returns special exact values at `0`.	2,419	7,375	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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-2016-40	latest	en	0.609306
http://cook-style.net/arran/example-of-ratio-for-grade-7-pdf.php	1,618,332,541,000,000,000	text/html	crawl-data/CC-MAIN-2021-17/segments/1618038073437.35/warc/CC-MAIN-20210413152520-20210413182520-00251.warc.gz	20,581,079	9,169	Grade for of 7 ratio pdf example 7th Proportions Unit of Study Putting Children First Grade 7 Equivalent Ratios Lesson and Resources. free math worksheets preview resource ratio and proportion recipes download this web page as a pdf with answer key proportionately speaking is proportions worksheet, Grade 7 В» Ratios & Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. For example, if. Seventh grade Lesson Ratio & Proportion Lesson 1 Grade 7 Equivalent Ratios Lesson and Resources. Find Ratios in Maths - Grade 7 Maths a ratio is used to compare quantities. Example 1: Grade 7 Math Questions With Detailed Solutions; Grade 7 Math word, Some examples of ratios are 3 4, 4 2.. 2 1,, 3 5.6, and 10 1 0. Ratios are treated just like fractions. 6.7 Applications of Ratios and Proportions (6-43) 345 6.7. TIPS4RM: Grade 7: Unit 9 вЂ“ Ratio and Rate 1 Unit 9 Grade 7 Ratio and Rate Relating to Ratios Grade 7 5 to 7 Non-Examples 15 Proportional Relationships [7th grade] Sabrina Bennett o Ratios and Rates can be used to describe proportional вЂњExample/Non-ExampleвЂќ in which the w/c ratio and a certain minimum grade of concrete for that particular exposure. C= 41.7 to 46.6 MPa B= 36.8 to 41.7 MPa. Workability of Concrete. Placing condition Percent Word Problems Ratio and proportion method an electrician, worked 7 months out of the year. A student earned a grade of 80% on a math test that had 7th Grade Math Ratio & Proportion Ratio & Proportion Lesson 7 Ratio & Proportion Lesson 8; -Do next example together where percent is missing. 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Ratios Word Problems The volume of water in two containers is in the ratio of 6 to 7. If the volume of first container is 36 liters, find the 7th Grade Math Worksheets Ratio Worksheets. Ratio and proportion is an important concept in both math as well as science. A few real-life examples of when we use ratio 7:2. How much of each type of content will be needed to make a book of 450 pages? 2. 30 girls and boys have planned for a picnic. There is a ratio of Ratio Problems And Answers Grade 7 tables example 1 В· Solving ratio problems with tables example 2 7. Read the PDF document for Ratio PRACTICE QUIZ Ratios/Unit Rates/Proportions A. Write each ratio in simplest form based on the following situation. 7 36 8 = x 11) 4 17 18 Another common example is the weight ratio of water to cement used in mortar, (Read this as вЂThe ratio of water to cordial is 7 to 2.вЂ™) In this example, a ratio into an equivalent ratio of integers in lowest terms. EXAMPLE 1 Finding equivalent ratios 6.7 Applications of Ratios and Proportions (6-47) 349 Ratio Worksheets. Compare two 6th Grade. Ratio Pets. Write ratios in the table to compare the number of each animal. 5th through 7th Grades. Ratio Marbles. 7th Curriculum Guide to the Alabama Course of Study: Mathematics 84 GRADE 7 . Students will: Ratios and Proportional Relationships . Analyze proportional r Improve your math knowledge with free questions in "Understanding ratios" and thousands of other math skills. IXL Learning Learning . Grade 7 L.1 Understanding ratios Grade 7 Equivalent Ratios Lesson and Resources on the overhead to illustrate an example of Grade 7 Equivalent Ratios Lesson and Resources 7th Grade Math Ratio & Proportion Ratio & Proportion Lesson 7 Ratio & Proportion Lesson 8; -Do next example together where percent is missing. Grade 7 This task 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: Seventh Grade вЂ“ 2003 PRACTICE QUIZ Ratios/Unit Rates/Proportions A. Write each ratio in simplest form based on the following situation. 7 36 8 = x 11) 4 17 18 Solve free ratio worksheets online and learn the concept with fun. Download the PDF and get started! Grade 7 В» Ratios & Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. For example, if Here are some practice examples to show you what the questions on the real test are like. Practice Example 1 5 and sand in the ratio 3 Test Page 7 Question 21 MARS Tasks Grade 7. ratio and proportion problems can be to achieve success at this level students need to work confidently with non-integer ratios such as 2.7 : for example, practice writing and using ratios to compare two quantities with these printable worksheets.). w/c ratio and a certain minimum grade of concrete for that particular exposure. C= 41.7 to 46.6 MPa B= 36.8 to 41.7 MPa. Workability of Concrete. Placing condition To understand the concept of ratio and use ratio language to describe a ratio relationship between two quantities. Plan your 90-minute lesson in Math or Number Sense Lesson Plan The Cafeteria Grade 7 Equivalent Ratios on the overhead to illustrate an example of The Cafeteria Grade 7 Equivalent Ratios When printing the PDF files for the three The Assessment Structure and example items can be found on the Mathematics Grade 8 Page 7 GO ON TO THE NEXT Ratio word problems with solutions and detailed explanations for grade 9. Free The measures of the two acute angles of a right triangle are in the ratio 2:7. Grade 7 В» Ratios & Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. For example, if The measures of the two acute angles of a right triangle are in the ratio 2:7. . What are the measures of the two angles? Math Word Problems with Answers - Grade 9; the sequence converges; we must know that the limit of this ratio is less than 1. Example 3. Does the series n 1 10n so the series converges by the Ratio Test. 7. 1:5 say вЂњ1 to 5вЂќ 3:9 say вЂњ3 to 9вЂќ 2:7 say вЂњ2 to 7 Fill in the table below with your own examples of ratios. Simple Ratios Worksheet Author: a ratio into an equivalent ratio of integers in lowest terms. EXAMPLE 1 Finding equivalent ratios 6.7 Applications of Ratios and Proportions (6-47) 349 Grade 7 Equivalent Ratios Lesson and Resources on the overhead to illustrate an example of Grade 7 Equivalent Ratios Lesson and Resources Grade 7 Proportional Relationships Unit Rates and Proportions Unit of Study Proportional вЂў The ratio of two quantities remains constant as the When printing the PDF files for the three The Assessment Structure and example items can be found on the Mathematics Grade 8 Page 7 GO ON TO THE NEXT Example Correct Answer Incorrect Answer . Write an equivalent ratio as a fraction in simplest form. Grade 7, Ratio, Proportion, Percent, Ratios- Author: 7th Grade Math Understanding Ratios Seventh grade Lesson Ratio & Proportion Lesson 1. the best source for free ratio worksheets. easier to grade, 4 version 5 version 6 version 7 version 8 version 9 version 10 writing an example of a ratio., when printing the pdf files for the three math the assessment structure and example items can be found on the math grade 7 page 11 go on to the next). 6. Mr. Jeff divided his money in the ratio 42 between Jon Math Common Core Sample Questions Grade 6. ratio and proportion handout 7 to 30 finding common units: ratios should be written in the same units or measure look at the second example b) \$2.80 7 lbs. \$2.00, when printing the pdf files for the three math the assessment structure and example items can be found on the math grade 7 page 11 go on to the next). 7th Proportions Unit of Study Putting Children First Seventh Grade Project Based Lessons Teacher Summer Dreamers. grade 7 ratio and proportional relationships a resource in which students use ratio and proportional reasoning to mix paint, grade 7 math here is a list of all of the math skills students learn in grade 7! these skills are organized into categories, and you can move your mouse). Printable Seventh Grade (Grade 7) Tests Worksheets and 6. Mr. Jeff divided his money in the ratio 42 between Jon. w/c ratio and a certain minimum grade of concrete for that particular exposure. c= 41.7 to 46.6 mpa b= 36.8 to 41.7 mpa. workability of concrete. placing condition, printable seventh grade (grade 7) worksheets, tests, and activities. print our seventh grade (grade 7) worksheets and activities, or administer them as online tests.). Ratio and Proportion Handout 7 to 30 Finding common units: Ratios should be written in the same units or measure Look at the second example b) \$2.80 7 lbs. \$2.00 When printing the PDF files for the three Math The Assessment Structure and example items can be found on the Math Grade 7 Page 11 GO ON TO THE NEXT When printing the PDF files for the three Math The Assessment Structure and example items can be found on the Math Grade 7 Page 11 GO ON TO THE NEXT PRACTICE QUIZ Ratios/Unit Rates/Proportions A. Write each ratio in simplest form based on the following situation. 7 36 8 = x 11) 4 17 18 Find Ratios in Maths - Grade 7 Maths a ratio is used to compare quantities. Example 1: Grade 7 Math Questions With Detailed Solutions; Grade 7 Math word When printing the PDF files for the three The Assessment Structure and example items can be found on the Mathematics Grade 8 Page 7 GO ON TO THE NEXT 1 http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf A Story of Ratios Curriculum Overview Grade 6 Grade 7 For example, вЂњThe ratio of wings For example, вЂњThis recipe has a ratio of 3 cups Note: In Grade 6, the focus is on ratios, equivalent ratios, and rates. In Grade 7, students will study When printing the PDF files for the three Math The Assessment Structure and example items can be found on the Math Grade 7 Page 11 GO ON TO THE NEXT Printable worksheets and online practice tests on Ratio and Proportion for Grade 6. This template covers a mix of questions from the topic of Ratio and Proportions Improve your math knowledge with free questions in "Understanding ratios" and thousands of other math skills. IXL Learning Learning . Grade 7 L.1 Understanding ratios Proportional Reasoning number of boys to girls as in the example above (ratio of 7. If 1 football player weighs 115 kg, Ratio and Rates Word Problems - Independent Practice Worksheet 3. 11 16 22 32 48 44 64 55 80 9 7 18 14 27 21 36 28 4 6 8 12 16 24 Grade 7 Math Skill Test Questions and problems, games, What is the smallest part of the ratio? Grade 7 Numbers and Arithmetic In order to earn an A, Grade 7 This task 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: Seventh Grade вЂ“ 2003 Some examples of ratios are 3 4, 4 2.. 2 1,, 3 5.6, and 10 1 0. Ratios are treated just like fractions. 6.7 Applications of Ratios and Proportions (6-43) 345 6.7 Free worksheets for ratio word problems Homeschool Math	3,615	14,586	{"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-2021-17	latest	en	0.896696
https://www.websiteperu.com/search/how-to-insert-fraction-in-graphing-calculator	1,679,383,195,000,000,000	text/html	crawl-data/CC-MAIN-2023-14/segments/1679296943637.3/warc/CC-MAIN-20230321064400-20230321094400-00712.warc.gz	1,214,372,208	14,704	# Keyword Analysis & Research: how to insert fraction in graphing calculator ## Keyword Research: People who searched how to insert fraction in graphing calculator also searched How to put base log on graphing calculator? “logBase (” is the name of the operation on your calculator that allows you to calculate any base logarithm (If you are only interested in calculating base 10 logs, you can just use the [log] button). To access it, press [alpha] , [window], and select the fifth option from the menu, logBase (. How to convert percentages into fractions using a calculator? Convert Percents to Fractions To convert a Percent to a Fraction follow these steps: Step 1: Write down the percent divided by 100 like this: percent 100 Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point. (For example, if there is one number after the decimal, then use 10, if there are two then use 100, etc.) How to use calculator for fractions? You can use the LCD Calculator to find the least common denominator for a set of fractions For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator Multiply the numerator and denominator of your first fraction by that number Repeat Steps 3 and 4 for each fraction	287	1,341	{"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}	3.5	4	CC-MAIN-2023-14	latest	en	0.860231
https://turkishlifeforums.com/qa/how-does-an-artist-use-math.html	1,618,979,317,000,000,000	text/html	crawl-data/CC-MAIN-2021-17/segments/1618039508673.81/warc/CC-MAIN-20210421035139-20210421065139-00563.warc.gz	686,989,599	8,680	# How Does An Artist Use Math? ## Are art schools hard to get into? Hoping to get into a college art program. Many of the best art programs are highly competitive, and, even if your portfolio is strong, it can be difficult to stand out from the crowd.. ## What is the number 1 art school in America? Yale UniversityJerry’s Top 10 Fine Art Schools USA1Yale UniversityUS2Rhode Island School of Design (RISD)US3University of California-Los Angeles (UCLA)US4Virginia Commonwealth University School of the Arts (VCU)US7 more rows ## How does the Mona Lisa use the golden ratio? One very famous piece, known as the Mona Lisa, painted by Leonardo Da Vinci, is drawn according to the golden ratio. … If we divide that rectangle with a line drawn across her eyes, we get another golden rectangle, meaning that the proportion of her head length to her eyes is golden. ## Is math a science or art? Mathematics is inherently different from other disciplines. While it is wildly creative, it is not art. While it can be used to model natural phenomena, it is not science. There are elements of both art and science in the field, but it isn’t a subset of either. The biggest similarity between math and music is patterns. For example, music has repeating verses and choruses while math uses patterns to explain the unknown. You can use different mathematical phenomena in music. These include geometry, signal processing, differential calculus, and even trigonometry. ## How did Leonardo da Vinci use math in his art? Da Vinci used the mathematical principles of linear perspective – parallel lines, the horizon line, and a vanishing point – to create the illusion of depth on a flat surface. In The Annunciation, for example, he uses perspective to emphasise the corner of a building, a walled garden and a path. ## Does art help in learning math? Using art can help students lagging behind Fortunately, research shows that when art is used to teach mathematics, it can impact students’ understanding and retention of key concepts and vocabulary. ## Is Mona Lisa perfect? There is no doubt that the Mona Lisa is a very good painting. It was highly regarded even as Leonardo worked on it, and his contemporaries copied the then novel three-quarter pose. The writer Giorgio Vasari later extolled Leonardo’s ability to closely imitate nature. Indeed, the Mona Lisa is a very realistic portrait. ## How do you do math drawings? Here are three ways math and drawing go hand-in-hand.Measurement. It’s no secret students struggle using rulers. … Ratio and Proportion. Using math to calculate scale is another opportunity to advance interdisciplinary skills. … X/Y Axis. Another technique allowing artists to scale up a drawing is the well-known grid method. ## Do artists need math? In art, mathematics is not always visible, unless you are looking for it. But there is much symmetry, geometry, and measurement involved in creating beautiful art. As well, many artists take advantage of mathematical findings, such as the golden ratio to make their artwork realistic and beautiful. ## Who used math in drawing? Some famous artists that use mathematical principles in their art include Leonardo da Vinci and M.C. Escher. The Mona Lisa by da Vinci involves the use of the golden ratio, which is approximately 1.618 and is represented by the Greek letter phi. In his famous drawings, M.C. ## Is math an art? Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. ## Is it worth going to art school? In a word, yes, it’s worth it. If it’s a good school with an accredited art program. It will teach you things in technique and in what to expect in the business world of art that could otherwise take a lot longer to learn. It will also teach you discipline and show you that art is hard work, even if you do love it. ## What is the geometric form found in the Mona Lisa? Notice: The Earth Circle fits exactly inside the Mona Lisa Square because of their matching dimensions. The Mona Lisa Square can thus also be called the Earth Square. ## How many students have interest in art and mathematics? Answer: 1509 people are interested in Art an mathematics. ## Do grades matter for art school? Grades and SAT scores still matter. Art schools want to know that their students are serious about education. By looking at your grades, colleges can tell what kind of student you’ll be if you attend their school. Even the best portfolio can’t win over an admissions committee if the student’s grades are sub-par. ## Why Math is a language? In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. … Math is a universal language. The symbols and organization to form equations are the same in every country of the world. ## What are the four branches of mathematics? The main branches of mathematics are algebra, number theory, geometry and arithmetic.	1,070	5,164	{"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}	2.8125	3	CC-MAIN-2021-17	longest	en	0.91843
https://cstheory.stackexchange.com/questions/9008/forbidden-minors-for-bounded-treewidth-graphs/9012	1,718,804,722,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198861825.75/warc/CC-MAIN-20240619122829-20240619152829-00498.warc.gz	157,971,830	41,501	# Forbidden minors for bounded treewidth graphs This question is similar to one of my previous questions. It is known that $K_{t+2}$ is a forbidden minor for graphs of treewidth at most $t$. Is there a nicely-constructed, parameterized, infinite family of graphs (other than complete graphs and grid graphs) that are minimal forbidden minors for graphs of every treewidth. In other words, is there an explicit graph $G_r$ on $r$ vertices (which is not a complete graph) such that $G_r$ is a forbidden minor for graphs of treewidth at most $r$, where $r$ is a function of $t$ ? The complete sets of forbidden minors are known for graphs of treewidth at most three. See this Wikipedia article for more details. Is the complete set of forbidden minors of graphs of treewidth at most four known ? • In the first question, with "forbidden minor" you mean "minimal forbidden minor", don't you? if not the grid graphs are an example. Commented Nov 17, 2011 at 19:11 • Yes. I meant minimal forbidden minor. Commented Nov 17, 2011 at 19:13 • You've made two comments augmenting your question, one here and one under an answer; it would be preferable to include the changes in the question itself so people don't have to read through various comment threads to understand the question. Commented Nov 18, 2011 at 7:53 • @joriki I updated the question. Commented Nov 18, 2011 at 15:18 ## 2 Answers If G is formed from a smaller graph H that is not a clique by adding two vertices x and y, such that x and y are not adjacent to each other but adjacent to all other vertices of G, then $tw(G)=tw(H)+2$. For, in any tree decomposition of $G$, either $x$ and $y$ have disjoint subtrees or they have overlapping subtrees. If they have disjoint subtrees, all the other subtrees have to include the shortest path between the trees for $x$ and $y$, from which it follows that the treewidth is $n-2$; the assumption that $H$ is not a clique can then be used to show that $n-2\ge tw(H)+2$. Alternatively if $x$ and $y$ have overlapping subtrees, every other vertex has to have a subtree that touches the intersection of the two subtrees of $x$ and $y$, and we can restrict the tree decomposition to that intersection, giving a tree decomposition in which $x$ and $y$ participate in every tree node. This implies that the hyperoctahedral graph $K_{2,2,2,\dots}$ with $2k$ nodes is a minimal forbidden minor for width $2k-3$. For, the octahedral graph $K_{2,2,2}$ is a minimal forbidden minor for width three, from which the argument above shows that the hyperoctahedral graph has width $2k-2$. And if any edge contraction or edge deletion is performed in the hyperoctahedral graph, the symmetries of the graph allow us to assume that the operation is happening to one of the twelve edges in the base octahedron, causing its width and the width of all the hyperoctahedra built from it to decrease. (The other class of graphs you should be including in your question along with the complete graphs are the grid graphs. An $r\times r$ grid has treewidth $r$. It's separate from the complete graph minors because its planar and therefore has no complete minor with more than four vertices. It's not a minimal forbidden minor, though, because some small changes (such as contracting the corner vertices) don't change its treewidth.) • Yes. Lets exclude grid graphs. Commented Nov 17, 2011 at 20:07 In Sparse obstructions and exact treewidth determination, Lucena states that in the PhD thesis of Sanders, "75 or so minimal forbidden minors for treewidth $\leq 4$ are given, and it is believed though not proven that this may constitute the entire obstruction set."	888	3,647	{"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}	3.109375	3	CC-MAIN-2024-26	latest	en	0.943157
http://www.markedbyteachers.com/university-degree/biological-sciences/elodea-plant-lab.html	1,590,855,983,000,000,000	text/html	crawl-data/CC-MAIN-2020-24/segments/1590347409337.38/warc/CC-MAIN-20200530133926-20200530163926-00187.warc.gz	184,664,116	21,119	• Join over 1.2 million students every month • Accelerate your learning by 29% • Unlimited access from just £6.99 per month Page 1. 1 1 2. 2 2 3. 3 3 4. 4 4 # Elodea Plant Lab Extracts from this document... Introduction Aquatic Photosynthesis of Elodea Leaves Lab Design Problem: What is the effect of temperature (warm, cool, room temperature) on the rate of photosynthesis in Elodea leaves measured by the levels of dissolved oxygen in the flask solutions? Hypothesis: If temperature is related to the rate of photosynthesis (levels of dissolved oxygen) then increasing the temperate will increase the rate of photosynthesis up to an optimal temperature. Variables: Independent: temperature of the water bath which the Elodea plant is immersed in Dependent: the rate of photosynthesis measured by the level of oxygen dissolved in the flask solution Constants: Relative size of the Elodea leaf, relative surface area of the Elodea leaves, (around 3 cm each), volume of water in all beakers, amounts of light exposure to the plants, and type of light source. Method: Materials: Light Source Elodea. Keep this warm and illuminated before you use it, 3 small flasks, 10g/L sodium bicarbonate (NaHCO3) solution, oxygen sensor Lab Quest data logger. Graduated cylinder Hot Plate 3 Large beaker (1 for warm water, 1 for cool water, 1 room temp) ...read more. Middle Conclusion Thermometer: �0.5 (Degrees Celsius) Data Processing Sample Calculation: Presentation of Processed Data: Graphs: Conclusion/Evaluation Conclusion: Based on my data collection and processed calculations, my hypothesis was correct in the sense that temperature is related to the rate of photosynthesis (levels of dissolved oxygen) and thus, increasing the temperate increased the rate of photosynthesis up to an optimal temperature. According to my previous knowledge of limiting factors on photosynthesis, I would have expected both hot water and cold water rates of photosynthesis to be lower than that of the room temperature as when looking at a typical graph of the effect of temperature on the rate of photosynthesis we see a bell shaped curve in which too cold of a temperature as well as too hot of a temperature will inhibit/denature photosynthesis, thought a moderate temperature will be optimal with a high rate of photosynthesis. One possible explanation for the higher rate of photosynthesis of the hot water bath could be the fact that we had not yet reached the optimal temperature before it starts to denature and decrease in the rate of photosynthesis. ...read more. The above preview is unformatted text This student written piece of work is one of many that can be found in our University Degree Marine & Freshwater Biology section. ## Found what you're looking for? • Start learning 29% faster today • 150,000+ documents available • Just £6.99 a month ## Here's what a teacher thought of this essay Overall this is a fairly poor piece of work. The student has completed the experiment and collected data, but has made a fundamental error of understanding and so drawn the wrong conclusions. This demonstrates how important it is to pay attention to what is actually being plotted on a graph. I would also expect an undergraduate to be able to elaborate on null and alternative hypotheses.In a first year practical this write up might get 2/5, as the demonstrators should have cleared up the misunderstanding. Marked by teacher Rebecca Lewis 02/05/2012 Not the one? Search for your essay title... • Join over 1.2 million students every month • Accelerate your learning by 29% • Unlimited access from just £6.99 per month # Related University Degree Marine & Freshwater Biology essays 1. ## Plankton - Marine Biology,Scientific Paper 3 star(s) Nitrogen exists in the marine environment as NO3-, NO2-, or NH4+. Organic compounds are found in the waters and also play a key role in maintaining the food web. Organisms feed on this as a food source. The most significant source of dissolved organic carbon is from phytoplankton. 2. ## An investigation into the abundance of freshwater invertebrates in pools and riffles at six ... + (0.5 � n) (n + 1) - ?R1 = (6 � 6) + (0.5 � 6) (6 + 1) - 25 = 32 The lowest value of U is that of U1 which is 4, therefore I have to use this value when looking up the critical value. 1. ## A comparison of marine organisms on shale &amp; limestone coasts. Doolin, Ireland. Bio-diversity of marine organisms will also be greater with decreasing distance from the shoreline. In terms of rock pool characteristics it is predicted that species diversity will increase with increasing pool size (depth & pool diameter). It is also thought that sheltered rock pools will have a greater bio-diversity than rock pools which are exposed to wind and wave action. 2. ## Do patients with chronic low back pain have proprioceptive deficits in their lumbar spine? and reproducing a pre determined position (Gill 1998). Although no significant results were found, both authors recognised that differences in proprioception do exist and that their studies provide vital background information to this area. Alternative methods have produced significant results, including O'Sullivan (2003) 1. ## Abundance, Distribution and Species Diversity of Invertebrates Collected By Commercial Trawler From Near Shore ... Hence subtidal fauna remains little stidied. Compared to the subtidal and benthic marine studies, investigation of the intertidal fauna, flora and their biology are many in number as shown in Ataur-Rahim, (1986). For instance, Ahmed (1977) dealt with the distribution of marine organisms on some rocky, sandy and muddyshores of Karachi region in relation to pollution. 2. ## Moreton Bay Marine Ecology as fish stock population and health will be evaluated to determine the impact of the green zone on Saint Helena Island and to determine the factors that influence the fish stock populations in both areas. There will be two main arguments that will be covered in this report including the • Over 160,000 pieces of student written work • Annotated by experienced teachers • Ideas and feedback to improve your own work	1,358	6,162	{"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-2020-24	latest	en	0.885689
https://math-faq.com/category/finite-mathematics-ebook/	1,722,882,636,000,000,000	text/html	crawl-data/CC-MAIN-2024-33/segments/1722640454712.22/warc/CC-MAIN-20240805180114-20240805210114-00360.warc.gz	307,642,517	16,643	# What is factorial notation? Certain patterns occur often when applying the multiplication principle. As we saw in Example 2, the factors that result from choices are often the same. In this case, we can use exponents to abbreviate the product: You may see the factors written with exponents instead of factors so it is important to recognize that they are the same. Another pattern that results from the multiplication principle can be written using factorial notation. Suppose a production line requires six workers to carry out six different jobs. Each worker can only do one job at a time. Once a worker is selected for a job, the other jobs must be carried out by the remaining workers. To find the number of ways we can assign workers to jobs, calculate the product The number of ways to make each choice drops by one in each factor since each worker can only do one job. In effect, we can’t choose the same worker twice. This is often indicated by saying that we want to assign workers without repetition. This type of product occurs so often that it is assigned its own symbol. ### Factorial Notation For any positive integer n, n! = n (n-1) (n-2) … 3 · 2 · 1 The value of 0! is defined to be 1. When we read an expression with factorial notation, a symbol like n! is read “n factorial”. ### Example 3 Use Factorial Notation Compute the value of each expression involving factorial notation. a. 6! Solution Use the formula above to get 6! = 6 · 5 · 4 · 3 · 2 · 1 b. 9! Solution It is tedious to multiply the factors out for larger numbers. Instead, use a calculator’s factorial command to find the product. On a TI graphing calculator, start by typing 9. Then press . Choosing 4 inserts the factorial symbol ! from the PRB menu. The value is displayed on the screen. c. Solution It is not practical to multiply all of the factors in the numerator and denominator. In addition, each of the factors in the fraction may not be calculated individually. If we try to do this the calculator will return an overflow error. Instead, write down some of the factor to see if any patterns emerge: Every factor in the denominator is also in the numerator. These factors may be reduced to give # How do you count choices using the multiplication principle? A small cellular provider gives its customers 2 choices of phones to use. They may use an iPhone or a phone that uses the Android operating system. In addition, the company offers three different calling plans: Budget plan, Regular plan, and the Deluxe plan. How many different choices of phone and calling plan does a customer have? To answer this question, we can use a decision tree and list out all of the choices a customer may make. A decision tree show the different choice a customer makes when choosing a phone and plan. If we move left to right through the tree, we can list out each of the possibilities: By listing out each of the possibilities, we see that there are six possible phone/plan choices. The decision tree helps us to list out these possibilities. However, if we only need to know how many choices, we can multiply the number of choices for phones and plans. This strategy is useful for determining the total number of choices even when there are a larger number of choices. ### Multiplication Principle Suppose we wish to know the number of ways to make n choices where there are d1 ways to make choice 1 d2 ways to make choice 2 dn ways to make choice n Then the total number of ways to make all of the choices is d1 · d2 · … · dn ### Example 1 Multiplication Principle An online custom bicycle seller wishes to count the total number of different types of bicycles that are available through its website. The seller offers 4 different frame styles, 8 different fender colors, 10 different tire colors, 8 different wheel colors, 6 different pedal colors, and 12 different accessory colors. How many different bicycles can a customer order? Solution Each choice the customer must make leads to a different factor in the multiplication principle. There are 184,320 different bicycles that can be ordered. ### Example 2 Multiplication Principle As the number of cars on the road has increased, so has the number of license plates. The format of the license plate determines how many different license plates there are. For each of the formats below, find the number of different license plates that are available. a. Three numbers Solution We use the multiplication principle and choose each number. There are ten choices for numbers 0 through 9 giving b. Three letters followed by three numbers Solution In this type of license plate, we have six choices to make. For each of the first three choices, there are 26 letters to choose from. For the last three choices, there are 10 numbers to choose from. This gives leads to the total number of license plates, c. Six characters where each character may be a letter or number Solution Since the character can be a letter or a number, there are 36 choices for each character. This gives a total number of license plates, # How is Bayes’ Rule used to compute conditional probability? In Question 2, we learned that the likelihood of an event A occurring given that an event has already occurred is We can also use the same basic expression to find the likelihood of an event B occurring given that an event A has already occurred, Each of these expressions may be solved for the joint probability in the numerator to give The joint event A and B is exactly the same event as the joint event B and A. This means their probabilities are also the same. Setting the left sides of these expressions equal gives We can solve for either conditional probability, but if we solve for P(B \| A) we get the most basic form of Bayes’ Rule. ### Bayes’ Rule If A and B are events, the conditional probability P(B \| A) may be computed in terms of using This expression allows us to compute one conditional probability in terms of the “reverse” conditional probability. In practice, the most challenging part of using Bayes’ Rule is identifying the events and computing the probabilities on the right side. We can simplify this task using a tree diagram. For instance, let’s return to the tax return tree diagram we developed in Question 4. This tree diagram is defined in terms of the marginal probabilities P(E) and P(E’), as well as the conditional probabilities P(R \| E), P(R’ \| E), P(R \| E’), and P(R’ \| E’). If we want to find the likelihood of one of these conditional probabilities reversed such as P(E \| R), we apply Bayes’ Rule to give ### Example 6 Bayes’ Rule The tree diagram for tax returns is shown below. Using the events E: return is selected for further examination E’: return is not selected for further examination R: return results in a refund of taxes paid R’: return does not result in a refund of taxes paid find the probability that a return was examined if we already know it resulted in a refund. Solution We want to find P(E \| R). Since the tree diagram is drawn to correspond to events given E or E’, we’ll apply Bayes’ Rule to “reverse” the conditional probabilities. For this conditional probability, Bayes’ Rule gives us We can locate and highlight these probabilities on the tree diagram. The probabilities in the numerator are located along the green branch. The probability in the denominator is found using the red and green branches which all terminate at R. Put the numbers in to yield If a return results in a refund, it is unlikely the return was examined. # What is the product rule for probability? The rule for computing conditional property can be interpreted different. In Question 2, we defined the conditional probability . If we multiply both side of this equation by P(B), we get We can also apply this strategy to the conditional probability to obtain a similar expression, These expressions give the joint probability of A and B as a product of a conditional probability and a marginal probability. ### Product Rule for Probability The probability of the event A and B is P( A and B) = P(A \| B) P(B) or P(A and B) = P(B \| A) P(A) Note that we have used the fact collection of outcomes in A and B is the same as the collection of outcomes in B and A. This rule is very useful when we work with tree diagrams. Let’s return to the consumer cell phone survey. We constructed the tree diagram for this survey shown below. In this tree diagram, a branch passing through the event M, “consumer is male”, and the event B, “consumer owns a basic phone”, is colored red. The first part of the branch ending at male is labeled with the probability 0.551. This is the probability that the consumer is male, P(M) = 0.551. The part of the branch beginning with male and ending at basic phone is labeled with the probability 0.316. This is the probability that the consumer owns a basic phone given that the consumer is male, P(B \| M) = 0.316. Using the Product Rule for Probability, we may multiply these values to give In words, the product of the probabilities along the branch gives us the likelihood that a consumer owns a basic phone and is male. ### Product Rule for Tree Diagrams The product of all probabilities along a branch on a tree diagram is the likelihood of all events occurring that are on the branch. ### Example 5 Product Rule for Tree Diagrams In 2008, 1.01% of all individual tax returns were selected for further examination. Of those examined, 3.59% received a refund on taxes paid. Of the returns that were not examined, 86.44% received a refund on taxes paid. Use this information to answer the parts below. a. Label the branches on the tree diagram below. Solution To make it easier to work with the events, define the events below: E: return is selected for further examination E’: return is not selected for further examination R: return results in a refund of taxes paid R’: return does not result in a refund of taxes paid Using complements allows us to limit the number of letters used to represent the different events. Using these events and the fact that 1.01% of returns are selected for further examination, we write P(E) = 0.0101. In addition, we can use the fact that the sum of probabilities from any event must be 1 (P(E) + P(E’) = 1 ). This tells us that P(E’) = 0.9899 . Label these branches on the tree diagram. Now let’s look at the statement, “Of those examined, 3.59% received a refund on taxes paid.” This tells us that P(R \| E) = 0.0359. The other branch originating at E is the complement, so P(R’ \| E) = 1 – 0.0359 = 0.9641. A similar strategy gives us the probabilities originating at E’, This gives the completed tree diagram below. b. Find the likelihood that a return is not selected for examination and the return does not result in a refund. Solution The event we are interested in is E’ and R’. These individual events are highlighted in the tree diagram below. The joint probability is the product of the probabilities along the highlighted branch, c. Find the probability that a return results in no refund. Solution Two branches along the tree terminate at returns that result in no refund. As we saw in part b, returns along the lower branch are not examined and result in no refund (E’ and R’). Returns along the upper branch are examined and result in no refund (E and R’). Together, these branches give all returns that result in no return. In effect, the returns in R’ are the same as the returns in (E’ and R’) or (E and R’). Since there are no returns that correspond to both branches, we can find the likelihood of a return resulting in no refund by applying the product rule to each branch and then add the results: In general, there are no outcomes in common to branches corresponding joint probabilities in a tree diagram. This means we may add probabilities from these branches to create other events that are compound events created with “or”. This strategy will be useful for computing other marginal probabilities for Bayes’ Rule in Question 5. # What are independent events? When computing conditional probabilities, you might be curious to know whether the fact that an event has occurred has any effect on the probability of another event. For instance, earlier in this section we computed the probability of a consumer owning a smartphone as P(S) ≈ 0.60 . We also computed the likelihood of a consumer owning a smartphone given the fact that the consumer is male, P(S \| M) ≈ 0.684. The fact that the consumer is male changes the likelihood of the consumer owning a smartphone. These events are an example of dependent events since one event occurring changes the likelihood of another event occurring. When two events are independent, one event occurring has no effect on the likelihood of the other event occurring. Independent Events If one event occurring does not change the likelihood of another event occurring, the two events are independent. This means that for events A and B, P(A \| B) = P(A) and P(B \| A) = P(B ### Example 4 Are the Events Independent? In Example 1, we calculated the conditional probabilities where F and B represent the events, F: consumer is female B: consumer owns a basic phone Are F and B independent events? Solution We already have the conditional events. To determine if P(B \| F) = P(B) and P(F \| B) = P(F), we need to compute P(B) and P(F). The information for these events are given in the table below. The likelihood of “consumer is female” is calculated by dividing the number of female consumers by the number of consumers surveyed, Since , the likelihood of F changes if B has occurred. Therefore, F and B are dependent. Similarly, the likelihood that the “consumer owns a basic phone” is This is different from the conditional probability . To prove that two events like B and F are dependent, we only need to show that P(F \| B) ≠ P(F) or P(B \| F) ≠ P(B). However, to prove that the events are independent, we must prove that both P(F \| B) = P(F) and P(B \| F) = P(B) .	3,091	14,083	{"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}	4.8125	5	CC-MAIN-2024-33	latest	en	0.907295
https://www.jackpotmobilecasino.co.uk/blog/how-to-predict-roulette-numbers/	1,718,977,032,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198862125.45/warc/CC-MAIN-20240621125006-20240621155006-00827.warc.gz	732,895,016	69,794	1. / 2. Blog 3. / 4. Predicting Roulette Numbers: How... Predicting Roulette Numbers: How Easy or Difficult Is It? Roulette is a casino table game that involves a ball, a wheel, and a set of Roulette numbers. You can hope to defeat the game and win more money by betting on Roulette if you are good with Roulette numbers. It is, however, difficult to bet a casino at a Roulette table. For decades, players have attempted to find ways to solve Roulette, and in some cases, they have succeeded by talent rather than chance. In any casino game, depending on chance is not the only way to achieve an advantage. Despite the various “systems” that have been suggested, there are only two profitable ways to play Online Roulette. You may either take advantage of an unbalanced wheel or the necessarily deterministic aspect of both the ball and the wheel’s spin. The first form of hack would be resisted at all times by casinos. Since betting on the result is generally not allowed until after the ball and wheel have started spinning, the second exploit is probable. That is, before making a wager, one should track the motion of both the ball and the wheel. There have been many strategies used to achieve an advantage in the game, including: • Dealer signatures • Visual prediction • Pocket computers • Discovering & taking benefits of biased wheels • Accept the Gambler’s Fallacy Each approach has one thing in common: it attempts to uncover the next Roulette numbers in such a manner that the house edges, which are 5.26 percent on the American double-zero wheel and 2.7 percent on the European single-zero wheel, are solved. 1. Each dealer has its unique signature. Few dealers are better at hitting a single part of the wheel than others, and some prefer odd numbers over even numbers. The goal is to locate a certain dealer’s signature and use it to achieve an advantage in the game. In theory, this method functions and can help you forecast future Roulette numbers; however, implementing it into operation is difficult. Even the dealers agree that controlling or even predicting where the ball will stop on the wheel is impossible. There are even times where even the dealer is unaware of a particular move he or she is making. If a dealer, for example, employs the same form of moving the ball around the wheel every time, the production numbers create a pattern. You should try to foresee the system to gain an advantage in the game. 2. Is it possible for a Roulette player to determine the next number by watching the rotation of the ball on the wheel? This technique was popular in the 1990s, but it hasn’t done as well since then. Even though the visual prediction system rarely succeeds, many Roulette players are eager to give it a shot. However, merely analyzing the ball’s rotating speed and the wheel’s speed is not enough to predict a number or the direction where the ball will strike. Here’s a smarter way of thinking about it. To make better forecasts, you must first study the ball’s pace and movement to decide how many bounces it takes in each pocket and in which direction. You should try and work out the Roulette numbers in the portion where the ball is most likely to fall based on this. Then you can put a wager on those estimates. Of necessity, it seems to be a near-impossible mission, and making an accurate forecast is incredibly challenging. This is why it’s referred to as gambling. 3. Casinos deem the use of pocket computers or some other digital devices to change the outcome of an online casino game to be unethical and could result in prison time. If you want to use a Roulette machine, you must exercise extreme caution. A Roulette machine measures the speed of the ball at the end of the track to help you determine the winning figure. It is based on the assumption that the ball’s speed remains constant at the end of the track. The tool also considers the angle at which the ball descends before predicting the pocket where the ball would most likely strike. It automates all a player might have to do manually in method two. Bear in mind that even this approach can’t guarantee the precise position of the ball’s landing. It automates all a player might have to do manually in method two. Bear in mind that even this approach can’t guarantee the precise position of the ball’s landing. 4. This isn’t a very normal mechanism these days since the forecast on biassed wheels was entirely reliant on the presence of biassed or off wheels. This system worked particularly well in the days when Roulette was played with mechanical wheels. It was possible to spot a wheel that was malfunctioning and exhibiting a certain number or sequence of Roulette numbers more often than others back then. However, in today’s computerized Roulette sports, where there are no biassed wheels, it is hardly used. 5. I can tell you that this approach for forecasting the next Roulette number will not succeed, but we’ll discuss it anyway. If you assume that something that is about to happen has been conditioned by something that has already happened, you are committing the Gambler’s Fallacy. Consider the following scenario: We all know that seeing a red result eight times in a row on the Roulette wheel is impossible. If the ball has landed on red for seven spins in a row, we can safely assume that it will land on black on the next spin. That isn’t mathematically right. However, you can opt to accept it and use it to guide your betting decisions. It won’t help in the long term, but it’s just as successful as any other tactic. There are five common approaches for estimating Roulette numbers. So, how effective are these methods? I’m not sure that any of these strategies should be used reliably to win money in a modern casino, but you can give them a shot. Except for the machine, that is. Share your stories in the comments whether you have had some results – or even if you haven’t.	1,232	5,936	{"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}	2.75	3	CC-MAIN-2024-26	latest	en	0.936213
http://stackoverflow.com/questions/11252669/new-function-does-not-have-access-to-arguments	1,464,402,005,000,000,000	text/html	crawl-data/CC-MAIN-2016-22/segments/1464049277286.69/warc/CC-MAIN-20160524002117-00170-ip-10-185-217-139.ec2.internal.warc.gz	275,984,498	19,495	I try to use `new Function()` in a calculator and I find it does not have access to the arguments I'm passing to the function it's in. I'm using it like this: ``````function go(a, b, c) { return new Function('return a + b + c')(); } go(4, '/', 2); `````` But it is not working because it says that a is undefined. Is there any way to get around this? - Why are you returning a function to return a function? – Madara Uchiha Jun 28 '12 at 20:52 Why not `return function() { return a + b + c; };` - that'll work. – Pointy Jun 28 '12 at 20:53 @Truth: I think it's a silly example to illustrate the issue :/ – Matchu Jun 28 '12 at 20:53 What is this even supposed to do? – Hans Z Jun 28 '12 at 20:54 Pointy is correct. If you're going to write a function that returns a function ... then the least you can do is actually return a "function()" ;) – paulsm4 Jun 28 '12 at 20:54 You probably want: ``````function go(a, b, c) { return new Function('return ' + a + b + c + ';')(); } go(4, '/', 2); `````` But this isn't the correct way to go. Make a distinct function for each action you're supporting. - perhaps this? ``````var add = function (a, b, c) { return a + b + c; }; `````` then invoke as such: ``````var sum = add(3, 4, 5); // sum is 12 `````` - That's not what he's trying to do. Note that one of the arguments given to go is an operator. – johusman Jun 28 '12 at 21:05 This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. – OptimusCrime Nov 14 '12 at 20:27 I believe @Truth is correct in his assessment of what you are trying to achieve. However, I was curious as to why `a` was undefined. As it turns out, the specification states that when `Function` is used as a constructor, the scope for the evaluated function body is the global environment: Section 15.3.2.1 This is unlike `eval()` which uses the current scope. -	561	1,924	{"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}	2.796875	3	CC-MAIN-2016-22	latest	en	0.923978
https://cindyticknor.com/tag/fraction-division/	1,576,156,719,000,000,000	text/html	crawl-data/CC-MAIN-2019-51/segments/1575540543850.90/warc/CC-MAIN-20191212130009-20191212154009-00225.warc.gz	316,187,228	16,477	## Guide for Parents & Teachers This guide has activities and prompts for math journals that illuminate all the math in Newton’s Nemesis and how it… ## Keep, Change, Flip: Are Algorithms our Frenemies? In our zest to have children learn math deeply and creatively, professional math educators sometimes give the impression that algorithms are the enemy. In my opinion, nothing could be further from the truth. ## From Fractions To Board Games I recently stumbled upon the work of Robert Siegler, a professor of cognitive psychology at Carnegie Mellon University who is… ## A Fraction-Algebra Sandwich Peck and Matassa (2016) recently published a research paper that reinforced why fraction division and multiplication is such an important… ## Analogies in Teaching Fractions: Lessons from Hong Kong and Japan In Newton’s Nemesis, I wanted to provide a nice variety of visual and mental images of division with both whole… ## Connecting Whole Number & Fraction Division In Newton’s Nemesis, I created Theo’s precocious little sister Leah not only because I was like that to my older sister (yes, I regret that a little bit now) but because I wanted to connect division with whole numbers and fractions. There is some evidence that the difficulties with fraction division are rooted in understanding division… ## Starting a Research Blog on Dividing by Fractions When I first envisioned using a comic book to teach fractions, I naturally went online to see if anyone had thought of the idea yet. There were plenty of resources on teaching the concept of a fraction, and even adding and subtracting. But when I searched…	325	1,631	{"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-2019-51	longest	en	0.928527
https://www.percentcalc.net/decimal/0.36-as-a-percent	1,708,940,953,000,000,000	text/html	crawl-data/CC-MAIN-2024-10/segments/1707947474659.73/warc/CC-MAIN-20240226094435-20240226124435-00471.warc.gz	944,633,469	12,274	## Convert Percent to decimal The answer: 0.36 as a percentage? = 36 % Input Fields Buttons section Output Fields Formula: 0.36 × 100 = 36 % ## 0.36 decimal as a percent What is 0.36 decimal in percentage? and what are the steps to follow to convert 0.36 to percent?. We will answer all these questions today. And Find out why 0.36 decimal converted to 36% . Use the calculator above to calculate a value other than 0.36 . ### Solution for 0.36 decimal as a percent: To convert 0.36 decimal to percent; use the next formula. Formula: Decimal value × 100 Step 1 0.36 × 100 To convert 0.36 decimal to percent; we multiply 0.36 by 100 . Step 2 = 36% 0.36 multiply by 100 equals 36 . The result 0.36 decimal as a percent? equals 36% In words: point three six as a percent? equals thirty six percent. ### Similar calculation 0.36 as a percent?= 36% 0.37 as a percent?= 37% 0.38 as a percent?= 38% 0.39 as a percent?= 39% 0.4 as a percent?= 40% 0.41 as a percent?= 41% 0.42 as a percent?= 42% 0.43 as a percent?= 43% 0.44 as a percent?= 44% 0.45 as a percent?= 45% 0.46 as a percent?= 46% 0.47 as a percent?= 47% 0.48 as a percent?= 48% 0.49 as a percent?= 49% 0.5 as a percent?= 50% 0.51 as a percent?= 51% 0.52 as a percent?= 52% 0.53 as a percent?= 53% 0.54 as a percent?= 54% 0.55 as a percent?= 55% 0.56 as a percent?= 56% 0.57 as a percent?= 57% 0.58 as a percent?= 58% 0.59 as a percent?= 59% 0.6 as a percent?= 60% 0.61 as a percent?= 61% 0.62 as a percent?= 62% 0.63 as a percent?= 63% 0.64 as a percent?= 64% 0.65 as a percent?= 65%	536	1,550	{"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-2024-10	latest	en	0.941324
http://www.informit.com/articles/article.aspx?p=32090&seqNum=6	1,579,337,899,000,000,000	text/html	crawl-data/CC-MAIN-2020-05/segments/1579250592394.9/warc/CC-MAIN-20200118081234-20200118105234-00214.warc.gz	233,069,041	13,562	# Process Control: Understanding Dynamic Behavior • Print This chapter is from the book ## 3.6 Integrating System We found in the previous chapter that material balances on liquid surge vessels or gas drums often yielded models with the following form: Equation 3.32 In the Laplace domain, this is Equation 3.33 Consider an integrating process initially at steady state, with y(0) = 0. #### Step Response If a step input change of Du is made at t = 0, and we find the time-domain value Equation 3.34 That is, the output ramps with a constant slope of kDu. #### Impulse Response If an impulse input of magnitude P is made at t = 0, then the output immediately changes to a new steady-state value of #### Example 3.5: Tank-Height Problem The mathematical model for a liquid surge tank is (see Example 1.3) where h is the liquid height, A is the constant cross-sectional area of the tank, F1 is the inlet flow rate, and F2 is the outlet flow rate. Assume that the outlet flow rate remains constant at a steady-state value of F2s. Defining the output and input in deviation variable form as For a constant cross-sectional area of 10 m2, the model is #### Step Response For a step input change of 0.25 m3/min, the output response is which is shown in Figure 3-7. If the steady-state height is 2 meters, then the height as a function of time is Figure 3-7. Step response of a liquid surge tank. Deviation variables. #### Impulse Response For an impulse input of 1 m3, the output response is which makes sense, because the cross-sectional area is 10 m3.	390	1,572	{"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}	3.5625	4	CC-MAIN-2020-05	latest	en	0.874269
https://fabricebaudoin.wordpress.com/2013/03/25/lecture-26-lyons-continuity-theorem-proof/	1,532,097,251,000,000,000	text/html	crawl-data/CC-MAIN-2018-30/segments/1531676591683.78/warc/CC-MAIN-20180720135213-20180720155213-00525.warc.gz	643,085,416	19,585	## Lecture 26. Lyons’ continuity theorem: Proof We now turn to the proof of Lyons’ continuity theorem. Theorem: Let $\gamma > p \ge 1$. Assume that $V_1, \cdots, V_d$ are $\gamma$-Lipschitz vector fields in $\mathbb{R}^n$. Let $x_1,x_2 \in C^{1-var}([0,T], \mathbb{R}^d)$ such that $\\| S_{[p]}(x_1) \\|^p_{p-var,[0,T]}+\\| S_{[p]}(x_2) \\|^p_{p-var,[0,T]} \le K$ with $K \ge 0$. Let $y_1,y_2$ be the solutions of the equations $y_i(t)=y(0)+\sum_{j=1}^d \int_0^t V_j(y_i(s)) dx_i^j(s), \quad 0 \le t \le T, \quad i=1,2$ There exists a constant $C$ depending only on $p,\gamma$ and $K$ such that for $0 \le s \le t \le T$, $\\|( y_2(t) -y_2(s)) - (y_1(t)-y_1(s))\\| \le C \\| V \\|_{\text{Lip}^{\gamma}} e^{ C \\| V \\|^p_{\text{Lip}^{\gamma}}} d_{p-var,[0,T]} ( S_{[p]}(x_1), S_{[p]}(x_2)) \omega(s,t)^{1/p} ,$ where $\omega$ is the control $\omega(s,t)=\left( \frac{d_{p-var,[s,t]} ( S_{[p]}(x_1), S_{[p]}(x_2)) }{d_{p-var; [0,T]}(S_{[p]}(x_1), S_{[p]}(x_2)) } \right)^p+\left( \frac{ \\| S_{[p]}(x_1) \\|_{p-var,[s,t]}}{\\| S_{[p]}(x_1) \\|_{p-var,[0,T]} } \right)^p+\left( \frac{ \\| S_{[p]}(x_2) \\|_{p-var,[s,t]}}{\\| S_{[p]}(x_2) \\|_{p-var,[0,T]} } \right)^p.$ Proof: We may assume $p < \gamma < [p]+1$, and for conciseness of notations, we set $\varepsilon = d_{p-var,[0,T]} ( S_{[p]}(x_1), S_{[p]}(x_2))$. Let $g_i=\Delta_{\frac{1}{\omega(s,t)^{1/p}}} ( S_{[p]}(x_i)(s)^{-1} S_{[p]}(x_i)(t)), \quad i=1,2.$ We have, $d(g_1,g_2) =\frac{1}{\omega(s,t)^{1/p}} d(S_{[p]}(x_1)(s)^{-1} S_{[p]}(x_1)(t) , S_{[p]}(x_2)(s)^{-1} S_{[p]}(x_2)(t))$ $\le \frac{1}{\omega(s,t)^{1/p}}d_{p-var,[s,t]} ( S_{[p]}(x_1), S_{[p]}(x_2))$ $\le \varepsilon$ and, in the same way, $d(0,g_i) =\frac{1}{\omega(s,t)^{1/p}} d ( S_{[p]}(x_i)(s), S_{[p]}(x_i)(t))$ $=\frac{1}{\omega(s,t)^{1/p}} \\| S_{[p]} (x_i) \\|_{p-var,[s,t]} \le K.$ Therefore, there exist $x^{s,t}_1,x^{s,t}_2 \in C^{1-var}([s,t], \mathbb{R}^d)$ and a constant $C_1=C_1([p],K)$ such that $S_{[p]}(x^{s,t}_i)(s)^{-1} S_{[p]}(x^{s,t}_i)(t) =S_{[p]}(x_i)(s)^{-1} S_{[p]}(x_i)(t) , i=1,2$ and $\\| x^{s,t}_1\\|_{1-var,[s,t]} +\\| x^{s,t}_2\\|_{1-var,[s,t]} \le C_1\omega(s,t)^{1/p}$ and $\\| x^{s,t}_1-x^{s,t}_2 \\|_{1-var,[s,t]} \le \varepsilon C_1\omega(s,t)^{1/p}.$ We define then $x_i^{s,t,u}$ as the concatenation of $x_i^{s,t}$ and $x_i^{t,u}$. As in the proof of Davie’s lemma, we denote by $y_i^{s,t}$ the solution of the equation $y^{s,t}_i(r)=y_i(s)+\sum_{j=1}^d \int_s^r V_j(y^{s,t}_i(v)) dx_i^j(v), \quad s \le r \le t, \quad i=1,2$ and consider the functionals $\Gamma^i_{s,t}=(y_i(t)-y_i(s))-(y^{s,t}_i(t) -y^{s,t}_i(s))= y_i(t)-y^{s,t}_i(t),$ and $\bar{\Gamma}_{s,t} =\Gamma^1_{s,t}-\Gamma^2_{s,t}$ From the proof of Davie’s estimate, it is seen that $\\| \Gamma^i_{s,t} \\| \le \frac{1}{2} C_2 \left( \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p} \right)^{[p]+1},$ and thus $\\| \bar{\Gamma}_{s,t} \\| \le C_2 \left( \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p} \right)^{[p]+1}.$ On the other hand, by estimating $\bar{\Gamma}_{s,u}- \bar{\Gamma}_{s,t}- \bar{\Gamma}_{t,u},$ as in the proof of Davie’s lemma, that is by inserting $y_i^{s,t,u}$ which is the solution of the equation driven by the concatenation of $x_i^{s,t}$ and $x_i^{t,u}$, and then by using the two lemmas of the previous lecture, we obtain the estimate $\\| \bar{\Gamma}_{s,u} \\|$ $\le \\| \bar{\Gamma}_{s,t} \\| e^{C_3 \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,u)^{1/p}} + \\| \bar{\Gamma}_{t,u} \\|+C_3( \\| y_1-y_2\\|_{\infty, [s,t]} +\varepsilon)\left( \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,u)^{1/p} \right)^\gamma e^{C_3 \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,u)^{1/p}}$ $\le \left( \\| \bar{\Gamma}_{s,t} \\| + \\| \bar{\Gamma}_{t,u} \\|+C_3( \\| y_1-y_2\\|_{\infty, [s,t]} +\varepsilon) \left( \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,u)^{1/p} \right)^{\gamma} \right) e^{C_3 \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,u)^{1/p}}.$ It remains to bound $\\| y_1-y_2\\|_{\infty, [s,t]}$. For this let us observe that $\\| (y_1(t)-y_2(t))-(y_1(s)-y_2(s))-\bar{\Gamma}_{s,t} \\| =\\|( y^{s,t}_1(t) -y^{s,t}_2(t) )-( y^{s,t}_1(s) -y^{s,t}_2(s) )\\|.$ $\\|( y^{s,t}_1(t) -y^{s,t}_2(t) )-( y^{s,t}_1(s) -y^{s,t}_2(s) )\\|$ can then be estimated by using classical estimates on differential equations driven by bounded variation paths. This gives, $\\|( y^{s,t}_1(t) -y^{s,t}_2(t) )-( y^{s,t}_1(s) -y^{s,t}_2(s) )\\| \le C_4 \left( \\| y_1(s) -y_2(s) \\| +\varepsilon \right) \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p} e^{ C_4\\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p}}.$ By denoting $z=y_1-y_2$, we can summarize the two above estimates as follows: $\\| \bar{\Gamma}_{s,u} \\| \le \left( \\| \bar{\Gamma}_{s,t} \\| + \\| \bar{\Gamma}_{t,u} \\|+C_3( \\| z\\|_{\infty, [s,t]} +\varepsilon) \left( \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,u)^{1/p} \right)^{\gamma} \right) e^{C_3 \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,u)^{1/p}}$ and $\\| z(t)-z(s) -\bar{\Gamma}_{s,t} \\| \le C_4 \left( \\| z \\|_{\infty,[0,s]} +\varepsilon \right) \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p} e^{ C_4\\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p}}.$ From a lemma already used in the proof of Davie’s estimate, the first estimate implies $\\| \bar{\Gamma}_{s,t} \\| \le C_5 \left( \varepsilon + \\| z \\|_{\infty,[0,t]} \right) \left( \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p} \right)^{\gamma} e^{ C_5 \\| V \\|_{\text{Lip}^{\gamma}} \omega(s,t)^{1/p}}.$ Using now the second estimate we obtain that for any interval $[a,b]$ included in $[0,T]$, $\sup_{s,t \in [a,b]} \\| z(t)-z(s) \\| \le C_6 (\varepsilon + \\| z \\|_{\infty, [0,b]} ) \\| V \\|_{\text{Lip}^{\gamma}} \omega(a,b)^{1/p} e^{C_6 \\| V \\|_{\text{Lip}^{\gamma}} \omega(a,b)^{1/p}}.$ Using the fact that $z(0)=0$ and picking a subdivision $0 = \tau_0 \le \tau_1 \le \cdots \le \tau_N \le T$ such that $C_6 \\| V \\|_{\text{Lip}^{\gamma}} e^{C_6 \\| V \\|_{\text{Lip}^{\gamma}} } \omega(\tau_i , \tau_{i+1} )^{1/p} \le 1/2$ we see that it implies $\\| z \\|_{\infty,[0,T]} \le C_7 \varepsilon e^{C_7 \\| V \\|^p_{\text{Lip}^{\gamma}} }.$ Coming back to the estimate $\sup_{s,t \in [a,b]} \\| z(t)-z(s) \\| \le C_6 (\varepsilon + \\| z \\|_{\infty, [0,b]} ) \\| V \\|_{\text{Lip}^{\gamma}} \omega(a,b)^{1/p} e^{C_6 \\| V \\|_{\text{Lip}^{\gamma}} \omega(a,b)^{1/p}}.$ concludes the proof $\square$ This entry was posted in Rough paths theory. Bookmark the permalink.	2,887	6,265	{"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": 62, "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-2018-30	latest	en	0.37761
https://analyticsindiamag.com/activation-functions-in-neural-network/	1,670,202,593,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446711001.28/warc/CC-MAIN-20221205000525-20221205030525-00806.warc.gz	127,294,744	54,471	# Activation Functions in Neural Networks: An Overview In this article, I’ll discuss the various types of activation functions present in a neural network. Neural networks have a similar architecture as the human brain consisting of neurons. Here the product inputs(X1, X2) and weights(W1, W2) are summed with bias(b) and finally acted upon by an activation function(f) to give the output(y). The activation function is the most important factor in a neural network which decided whether or not a neuron will be activated or not and transferred to the next layer. This simply means that it will decide whether the neuron’s input to the network is relevant or not in the process of prediction. For this reason, it is also referred to as threshold or transformation for the neurons which can converge the network. Activation functions help in normalizing the output between 0 to 1 or -1 to 1. It helps in the process of backpropagation due to their differentiable property. During backpropagation, loss function gets updated, and activation function helps the gradient descent curves to achieve their local minima. #### THE BELAMY ##### Sign up for your weekly dose of what's up in emerging technology. In this article, I’ll discuss the various types of activation functions present in a neural network. Linear Linear is the most basic activation function, which implies proportional to the input. Equation Y = az, which is similar to the equation of a straight line. Gives a range of activations from -inf to +inf. This type of function is best suited to for simple regression problems, maybe housing price prediction. Demerits – The derivative of the linear function is the constant(a) thus there’s no relation with input. Thus it should not be an ideal choice as it would not be helpful in backpropagation for rectifying the gradient and loss functions. ReLU Rectified Linear Unit is the most used activation function in hidden layers of a deep learning model. The formula is pretty simple, if the input is a positive value, then that value is returned otherwise 0. Thus the derivative is also simple, 1 for positive values and 0 otherwise(since the function will be 0 then and treated as constant so derivative will be 0). Thus it solves the vanishing gradient problem. The range is 0 to infinity. Demerits – Dying ReLU problem or dead activation occurs when the derivative is 0 and weights are not updated. Cannot be used anywhere else than hidden layers. ELU Exponential Linear Unit overcomes the problem of dying ReLU. Quite similar to ReLU except for the negative values. This function returns the same value if the value is positive otherwise, it results in alpha(exp(x) – 1), where alpha is a positive constant. The derivative is 1 for positive values and product of alpha and exp(x) for negative values. The Range is 0 to infinity. It is zero centric. Demerits – ELU has the property of becoming smooth slowly and thus can blow up the activation function greatly. It is computational expensive than ReLU, due to the exponential function present. LeakyReLU LeakyReLU is a slight variation of ReLU. For positive values, it is same as ReLU, returns the same input, and for other values, a constant 0.01 with input is provided. This is done to solve the dying ReLu problem. The derivative is 1 for positive and 0.01 otherwise. Demerit – Due to linearity, it cannot be used in complex problems such as classification. PReLU Parameterized Rectified Linear Unit is again a variation of ReLU and LeakyReLU with negative values computed as alphainput. Unlike Leaky ReLU where the alpha is 0.01 here in PReLU alpha value will be learnt through backpropagation by placing different values and the will thus provide the best learning curve. Demerits – This is also a linear function so not appropriate for all kinds of problems Sigmoid Sigmoid is a non-linear activation function. Also known as the Logistic function. It is continuous and monotonic. The output is normalized in the range 0 to 1. It is differentiable and gives a smooth gradient curve. Sigmoid is mostly used before the output layer in binary classification. Demerits – Vanishing gradient problem and not zero centric, which makes optimisation become harder. Often makes the learning slower. Tanh Hyperbolic tangent activation function value ranges from -1 to 1, and derivative values lie between 0 to 1. It is zero centric. Performs better than sigmoid. They are used in binary classification for hidden layers. Demerits – Vanishing gradient problem Softmax Softmax activation function returns probabilities of the inputs as output. The probabilities will be used to find out the target class. Final output will be the one with the highest probability. The sum of all these probabilities must be equal to 1. This is mostly used in classification problems, preferably in multiclass classification. Demerits – Softmax will not work for linearly separable data Swish Swish is a kind of ReLU function. It is a self-grated function single it just requires the input and no other parameter. Formula y = x sigmoid(x). Mostly used in LSTMs. Zero centric and solves the dead activation problem. Has smoothness which helps in generalisation and optimisation. Demerits – High computational power and only used when the neural network has more than 40 layers. Softplus Finding the derivative of 0 is not mathematically possible. Most activation functions have failed at some point due to this problem. It is overcome by softplus activation function. Formula y = ln(1 + exp(x)). It is similar to ReLU. Smoother in nature. Ranges from 0 to infinity. Demerits – Due to its smoothness and unboundedness nature softplus can blow up the activations to a much greater extent. ## More Great AIM Stories ### 8 Fullstack Frameworks Every Developer Must Master Machine learning and data science enthusiast. Eager to learn new technology advances. A self-taught techie who loves to do cool stuff using technology for fun and worthwhile. ## Our Upcoming Events Conference, in-person (Bangalore) Machine Learning Developers Summit (MLDS) 2023 19-20th Jan, 2023 Conference, in-person (Bangalore) Rising 2023 \| Women in Tech Conference 16-17th Mar, 2023 Conference, in-person (Bangalore) Data Engineering Summit (DES) 2023 27-28th Apr, 2023 Conference, in-person (Bangalore) MachineCon 2023 23rd Jun, 2023 Conference, in-person (Bangalore) Cypher 2023 20-22nd Sep, 2023 ### Whatsapp group Discover special offers, top stories, upcoming events, and more. ### Discord Server Stay Connected with a larger ecosystem of data science and ML Professionals	1,459	6,638	{"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-2022-49	latest	en	0.916898
https://za.pinterest.com/explore/damping-ratio/	1,500,981,858,000,000,000	text/html	crawl-data/CC-MAIN-2017-30/segments/1500549425144.89/warc/CC-MAIN-20170725102459-20170725122459-00468.warc.gz	857,780,734	74,092	An Introduction To System Dynamics – First and Second Order Linear Systems #control #systems, #system #dynamics, #transfer #function, #time #constant, #dc #gain, #damping #ratio, #natural #frequency, #time #domain, #response, #differential #equations, #laplace #transforms http://poland.nef2.com/an-introduction-to-system-dynamics-first-and-second-order-linear-systems-control-systems-system-dynamics-transfer-function-time-constant-dc-gain-damping-ratio-natural-frequency/ # An Introduction To… STIFFNESS AND VISCOUS DAMPING OF THE HUMAN LEG – k=28,500 N/m. damping ratio ζ= d / 2 / (mk)^1/2 Using Damping ratios and eigenvalues to specify racecar damping \| ChassisSim Dynamic moduli and damping ratios for cohesive soils / Sun, Joseph I. 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https://stats.libretexts.org/Courses/Taft_College/PSYC_2200%3A_Elementary_Statistics_for_Behavioral_and_Social_Sciences_(Oja)/Unit_3%3A_Relationships/15%3A_Regression/15.02A_Regression_Line_Equation	1,669,914,752,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446710829.5/warc/CC-MAIN-20221201153700-20221201183700-00229.warc.gz	565,802,170	31,612	15.2: Regression Line Equation $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\\| #1 \\|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$ The goal of regression is the same as the goal of ANOVA: to take what we know about one variable ($$X$$) and use it to explain our observed differences in another variable ($$Y$$). In ANOVA, we talked about – and tested for – group mean differences, but in regression we do not have groups for our explanatory variable; we have a continuous variable, like in correlation. Because of this, our vocabulary will be a little bit different, but the process, logic, and end result are all the same. Regression Equation In regression, we most frequently talk about prediction, specifically predicting our outcome variable $$Y$$ from our explanatory variable $$X$$, and we use the line of best fit to make our predictions. Let’s take a look at the equation for the line, which is quite simple: $\widehat{\mathrm{Y}}=\mathrm{a}+\mathrm{bX} \nonumber$ In which $$\mathrm{bX}$$ mean beta times X. The terms in the equation are defined as: • $$\widehat{\mathrm{Y}}$$: the predicted value of $$Y$$ for an individual person • $$a$$: the intercept of the line • $$b$$: the slope of the line • $$X$$: the observed value of $$X$$ for an individual person What this shows us is that we will use our known value of $$X$$ for each person to predict the value of $$Y$$ for that person. The predicted value, $$\widehat{\mathrm{Y}}$$, is called “$$y$$-hat” and is our best guess for what a person’s score on the outcome is. The equation has only two parameter estimates: an intercept (where the line crosses the Y-axis) and a slope (how steep – and the direction, positive or negative – the line is). I bet when you took geometry in high school, you never thought that you'd use that again! But here we are, talking about slopes. The intercept and slope are parameter estimates because, like everything else in statistics, we are interested in approximating the true value of the relation in the population but can only ever estimate it using sample data. We will soon see that one of these parameters, the slope, is the focus of our hypothesis tests (the intercept is only there to make the math work out properly and is rarely interpretable). The formulae for these parameter estimates use very familiar values. $\mathrm{a}=\overline{X_y}- (\mathrm{b} \times \overline{X_x}) \nonumber$ We have seen each of these before. $$\overline{X_y}$$ and $$\overline{X_x}$$ are the means of $$Y$$ and $$X$$, respectively. Next, the slope: $\dfrac{\sum(Diff_{x} \times Diff_{y})}{\sum({Diff_{X}}^2)} \nonumber$ In which "Diff" means the difference of each score from the mean. Thus, just like with standard deviations, we must subtract the mean from each score. The numerator of this formula means that, for each person, we multiply their score on the first variable minus the means of that variable times their score on the second variable minus the mean of that variable. When we do that for each participant, then we sum all of those products (scores that were multiplied). The denominator is the squaring of each of those differences score (each person's score minus the mean) for the first variable, then summing all of those squared into one number, It is very important to point out that the $$Y$$ values in the equations for $$a$$ and $$b$$ are our observed $$Y$$ values in the dataset, NOT the predicted $$Y$$ values ($$\widehat{\mathrm{Y}}$$) from our equation for the line of best fit. You may be asking why we would try to predict $$Y$$ if we have an observed value of $$Y$$, and that is a very reasonable question. The answer is that we first need a group with all of the values (observed X and observed Y) to create the intercept and slope. Then, we can use that on samples in which we don't have values for the Y variable. In other words, we need to use known values of $$Y$$ to calculate the parameter estimates in our equation, and we use the difference between our observed values and predicted values ($$Y – \widehat{\mathrm{Y}}$$) to see how accurate our equation is. Then, we can use regression to create a predictive model that we can then use to predict values of $$Y$$ for other people for whom we only have information on $$X$$. Example Let’s look at this from an applied example. Businesses often have more applicants for a job than they have openings available, so they want to know who among the applicants is most likely to be the best employee. There are many criteria that can be used, but one is a personality test for conscientiousness, with the belief being that more conscientious (more responsible) employees are better than less conscientious employees. A business might give their employees a personality inventory to assess conscientiousness and existing performance data to look for a relation. In this example, we have known values of the predictor ($$X$$, conscientiousness) and outcome ($$Y$$, job performance), so we can estimate an equation for a line of best fit and see how accurately conscientious predicts job performance, then use this equation to predict future job performance of applicants based only on their known values of conscientiousness from personality inventories given during the application process. The key to assessing whether a linear regression works well is the difference between our observed and known $$Y$$ values and our predicted $$\widehat{\mathrm{Y}}$$ values. We use subtraction to find the difference between them ($$Y – \widehat{\mathrm{Y}}$$) in the same way we use subtraction for deviation scores and sums of squares. The value ($$Y – \widehat{\mathrm{Y}}$$) is our residual, which, as defined before, is how close our line of best fit is to our actual values. We can visualize residuals to get a better sense of what they are by creating a scatterplot and overlaying a line of best fit on it, as shown in Figure $$\PageIndex{1}$$. In Figure $$\PageIndex{1}$$, the triangular dots represent observations from each person on both X (Conscientiousness scores) and Y (job performance ratings). The dashed red line is the line of best fit estimated by the equation $$\widehat{\mathrm{Y}}= a + (b * X)$$. For every person in the dataset, the line represents their predicted score. The red bracket between a few of the triangular dots and the predicted scores on the line of best fit are our residuals (they are only drawn for four observations for ease of viewing, but in reality there is one for every observation); you can see that some residuals are positive and some are negative, and that some are very large and some are very small. This means that some predictions are very accurate and some are very inaccurate, and the some predictions overestimated values and some underestimated values. Across the entire dataset, the line of best fit is the one that minimizes the total (sum) value of all residuals. That is, although predictions at an individual level might be somewhat inaccurate, across our full sample and (theoretically) in future samples our total amount of error is as small as possible. We call this property of the line of best fit the Least Squares Error Solution. This term means that the solution – or equation – of the line is the one that provides the smallest possible value of the squared errors (squared so that they can be summed, just like in standard deviation) relative to any other straight line we could draw through the data. Ack, that was a lot. It's okay if you don't totally understand what's going on here. This is the foundation of the equation and the interpretation, but, just like with null hypothesis significance testing, you can figure out how to interpret the results without completely understanding the conceptual underpinnings. Predicting Scores and Explaining Variance The purpose of regression is twofold: we want to predict scores based on our line and, as stated earlier, explain variance in our observed $$Y$$ variable just like in ANOVA. These two purposes go hand in hand, and our ability to predict scores is literally our ability to explain variance. That is, if we cannot account for the variance in $$Y$$ based on $$X$$, then we have no reason to use $$X$$ to predict future values of $$Y$$. We know that the overall variance in $$Y$$ (job performance in this example) is a function of each score deviating from the mean of $$Y$$ (as in our calculation of variance and standard deviation). So, just like the red brackets in Figure $$\PageIndex{1}$$ representing residuals, given as ($$Y – \widehat{\mathrm{Y}}$$), we can visualize the overall variance as each score’s distance from the overall mean of $$Y$$, given as ($$Y – \overline{X_y}$$). This is shown in Figure $$\PageIndex{2}$$. In Figure $$\PageIndex{2}$$, the solid blue line is the mean of $$Y$$ (job performanc), and the blue brackets are the deviation scores between our observed values of $$Y$$ and the mean of $$Y$$. This represents the overall variance that we are trying to explain. Thus, the residuals and the deviation scores are the same type of idea: the distance between an observed score and a given line, either the line of best fit that gives predictions or the line representing the mean that serves as a baseline. Here's why math is so cool: The difference between these two values, which is the distance between the lines themselves, is our model’s ability to predict scores above and beyond the baseline mean; that is, it is our model's ability to explain the variance we observe in $$Y$$ (job performance) based on values of $$X$$ (conscientiousness). If we have no ability to explain variance, then our line will be flat (the slope will be 0.00) and will be the same as the line representing the mean, and the distance between the lines will be 0.00 as well. Summary We now have three pieces of information: the distance from the observed score to the mean, the distance from the observed score to the prediction line, and the distance from the prediction line to the mean. These are our three pieces of information needed to test our hypotheses about regression. They are our three Sums of Squares, just like in ANOVA. Our distance from the observed score to the mean is the Sum of Squares Total, which we are trying to explain. Our distance from the observed score to the prediction line is our Sum of Squares Error, or residual, which we are trying to minimize. Our distance from the prediction line to the mean is our Sum of Squares Model, which is our observed effect and our ability to explain variance. Each of these will go into the ANOVA table to calculate our test statistic. This page titled 15.2: Regression Line Equation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Michelle Oja.	2,784	11,702	{"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}	4.40625	4	CC-MAIN-2022-49	latest	en	0.566702
https://chemistry.stackexchange.com/questions/142611/why-is-the-change-in-enthalpy-computation-for-a-change-of-state-done-like-this/142612#142612	1,632,602,785,000,000,000	text/html	crawl-data/CC-MAIN-2021-39/segments/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00330.warc.gz	217,765,304	38,891	# Why is the change in enthalpy computation for a change of state done like this? Suppose that a system whose initial state is Pressure = $$P_1$$, Volume = $$V_1$$; and it is taken through a process after which final pressure and volume are $$P_2$$ and $$V_2$$ respectively. Now change in enthalpy is defined as $$\Delta H= \Delta U +P\Delta V+V\Delta P$$ The thing which I am confused with is which pressure and which volume do we hold constant for their respective parts in the calculation? Till now I had dealt only with problems involving the $$P\Delta V$$ part, and it was calculated as $$P_2(V_2-V_1)$$, same as irreversible work. But when I came across a problem in which Pressure also varied with volume, the second part needed to be taken as $$V_1(P_2-P_1)$$.Why do we take $$P_2$$ as constant in one case and $$V_1$$ in the other? One reason which I thought of was that in an irreversible process, The pressure is first changed by a finite amount and then the volume varies. Thus the pressure throughout the process was $$P_2$$. This can be a rationale for the $$P\Delta V$$ part, but I am not sure if it is reasonable to say that the volume at start of the process was $$V_1$$, which resulted in this method of calculation. So.. what is the reason? • The expression you should use for a finite change is $\Delta H = \Delta U + \Delta (pV)$ Nov 11 '20 at 13:49 • $d(pV)=p.dV + V.dp + dp.dV$, $\Delta(pV) = p.\Delta V + V . \Delta p + \Delta p . \Delta V$. But dp.dV can be neglected with infinitely small error, so it is never explicitly mentioned nor used. $\Delta p . \Delta V$ cannot be neglected. Draw it as geometrical scenario of 1 rectangle consisting of 4 rectangles to see it. Nov 11 '20 at 14:33 • @Pournik See my answer. Nov 11 '20 at 14:59 • @ChetMiller thanks, I have seen it. Nov 11 '20 at 15:16 You're confused because the equation is incorrect. It should read $$\Delta H=\Delta U+\Delta (PV)$$If you insist on writing it the way you did, then P should be $$\frac{P_1+P_2}{2}$$ and V should be $$\frac{V_1+V_2}{2}$$. That will give the same result as the first equation I wrote.	595	2,106	{"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": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.953125	4	CC-MAIN-2021-39	latest	en	0.945349
https://www.lessonup.com/en/lesson/aig2CfZaHM2PkYpuR	1,632,169,487,000,000,000	text/html	crawl-data/CC-MAIN-2021-39/segments/1631780057091.31/warc/CC-MAIN-20210920191528-20210920221528-00508.warc.gz	885,267,962	42,391	# reference position Sept 21, 2020 Reference position Sept 21, 2020 Ms.Famin 1 / 15 Slide 1: Slide Science Secondary Education This lesson contains 15 slides, with interactive quizzes, text slides and 1 video. ## Items in this lesson Reference position Sept 21, 2020 Ms.Famin #### Slide 1 -Slide INSTRUCTIONS Mute your mics do not on unless instructed No discussions with each other only with teacher unless instructed Write your names in the chat section Raise your hands before talking #### Slide 2 -Slide unscramble THE WORDS #### Slide 3 -Open question objectives 1. Describe the reference direction in two dimensions 2. Compare distance and displacement #### Slide 4 -Slide Sometimes direction is described using the words positive or negative. The reference direction is the positive (+) direction. The opposite direction is the negative (-) direction. #### Slide 5 -Slide Locate your classmate's home [use directions ] #### Slide 7 -Slide If East is the reference direction, the museum is in _________ direction from the bus stop A positive B up C down D negative #### Slide 8 -Quiz If East is the reference direction, the library is in _________ direction from the bus stop A up B positive C negative D down #### Slide 10 -Video Observe the image Which line represents distance and which represents displacement? Give reason #### Slide 11 -Slide ANALYZE The boy wants to move from point A to Point C. How much is the displacement? How much is the distance? #### Slide 13 -Link From 6:35 to 7:15, the tip of which hand of the clock experiences greater displacement? A the hour hand B the minute hand C both experience the same displacement D it depends on the reference point	429	1,708	{"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-2021-39	latest	en	0.79846
https://startups.mathsgee.com/49386/contains-balls-green-balls-ball-drawn-random-probability-that	1,679,881,673,000,000,000	text/html	crawl-data/CC-MAIN-2023-14/segments/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00039.warc.gz	603,344,220	19,357	0 like 0 dislike 67 views A bag contains 3 red balls and 4 green balls. If one ball is drawn at random, what is the probability that it is red? \| 67 views 0 like 0 dislike The probability that the ball drawn is red would be $\dfrac{3}{7}$. This is because there are 3 red balls out of a total of 3+4=7 balls in the bag, so the probability of drawing a red ball is $\dfrac{3}{7}$. by Diamond (88,926 points) 1 like 0 dislike 0 like 0 dislike 0 like 0 dislike 1 like 0 dislike 1 like 0 dislike 0 like 0 dislike 0 like 0 dislike 1 like 0 dislike 1 like 0 dislike 0 like 0 dislike 3 like 0 dislike 0 like 0 dislike 0 like 0 dislike 0 like 0 dislike	204	646	{"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}	3.21875	3	CC-MAIN-2023-14	latest	en	0.91755
https://dfc-org-production.my.site.com/forums/ForumsMain?id=906F00000008wK7IAI	1,721,915,517,000,000,000	text/html	crawl-data/CC-MAIN-2024-30/segments/1720763858305.84/warc/CC-MAIN-20240725114544-20240725144544-00805.warc.gz	172,143,143	54,779	Starting November 20, the site will be set to read-only. On December 4, 2023, forum discussions will move to the Trailblazer Community. ShowAll Questionssorted byDate Posted # Comparing dates elapsed time I am trying to use the following formula but I am getting a syntax error. Can someone tell me what I am doing wrong? if(First_Report_Due_Date__c > 30, "2", if(First_Report_Due_Date__c > 60, "3", "1")) i am trying to populate a text field to fill in the number of elapsed months. thanks, Mirko JPClark3 ( YEAR(TODAY() ) + MONTH( TODAY() ) ) - ( YEAR(First_Report_Due_Date__c ) + MONTH( First_Report_Due_Date__c ) ) Hello, I've created a custom text field whose sole purpose is to calculate the number of elapsed month. I need to use an existing First_Report_Due_Date (date field) and compare against the current date to get elapsed time in month. thanks, Mirko Navatar_DbSup Hi, You are getting the error because First_Report_Due_Date__c is a date type field and you compare that value with a number. So firstly you have to convert that into a number and then use <,< these operators. I have taken formula field return type as number and CustomDate__c as date type custom field. Below is the Formula for the same: Value(if( DAY( CustomDate__c) > 30, "2", if(DAY(CustomDate__c )> 60, "3", "1"))) Well I want to suggest that you can simply use month function to get the current month from that date type field like this: MONTH(CustomDate__c) Did this answer your question? If not, let me know what didn't work, or if so, please mark it solved. JPClark3 ( YEAR(TODAY() ) + MONTH( TODAY() ) ) - ( YEAR(First_Report_Due_Date__c ) + MONTH( First_Report_Due_Date__c ) ) This was selected as the best answer	473	1,741	{"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}	2.609375	3	CC-MAIN-2024-30	latest	en	0.859912
https://www.coursehero.com/file/6717334/notes6/	1,490,662,556,000,000,000	text/html	crawl-data/CC-MAIN-2017-13/segments/1490218189583.91/warc/CC-MAIN-20170322212949-00392-ip-10-233-31-227.ec2.internal.warc.gz	878,012,065	23,030	notes6 # notes6 - Notes 6 Model Specification : Overall strategy -... This preview shows pages 1–2. Sign up to view the full content. 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: Notes 6 Model Specification : Overall strategy - Box Jenkins Approach: 1. To decide a reasonable - but tentative - values for p,d,q . 2. Estimate φ,θ and σ 2 a , for that model. 3. Check the model’s adequacy. 4. If the model appears inadequate, consider the nature of the inadequacy to select another model. 5. Estimate the new model and check it for accuracy. To obtain a tentative order d (based on the graphical approach) A basic rule: The first (and most important) step in fitting an ARIMA model is to determine the value of d (i.e. the order of differencing). Normally, the correct amount of differ- encing is the lowest order of differencing that yields a time series which fluctuates around a well-defined mean value and whose autocorrelation function (ACF) plot de- cays fairly rapidly to zero. If the series still exhibits a long-term trend, or otherwise lacks a tendency to return to its mean value, or if its autocorrelations are positive out to a high number of lags, say 10 or more, then a higher order of differencing is needed. Properties of the sample autocorrelation function Theorem : Suppose that Z t = μ + ∞ X j =0 ψ j a t- j where a t iid ∼ (0 ,σ 2 a ) , < σ 2 a < ∞ . Assume ∑ ∞ j =0 \| ψ j \| < ∞ and ∑ ∞ j =0 ψ 2 j < ∞ . (This will be satisfied by any stationary ARMA model). Then, for any fixed m , the joint distribution of √ n ( r 1- ρ 1 ) , √ n ( r 2- ρ 2 ) ,..., √ n ( r m- ρ m ) approaches, as n → ∞ , a joint normal distribution with zero means, variances c ii and... View Full Document ## This note was uploaded on 01/20/2012 for the course STA 4005 taught by Professor ? during the Spring '08 term at CUHK. ### Page1 / 5 notes6 - Notes 6 Model Specification : Overall strategy -... This preview shows document pages 1 - 2. Sign up to view the full document. View Full Document Ask a homework question - tutors are online	579	2,200	{"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-2017-13	longest	en	0.843305
https://ededgames.com/betting/frequent-question-what-is-the-probability-of-throwing-one-7-with-two-dice.html	1,642,476,426,000,000,000	text/html	crawl-data/CC-MAIN-2022-05/segments/1642320300722.91/warc/CC-MAIN-20220118032342-20220118062342-00609.warc.gz	298,744,342	15,864	# Frequent question: What is the probability of throwing one 7 with two dice? Contents ## What is the probability of rolling a total of 7 with two dice at least once in 10 rolls? With the help of a calculator we find that we will not get a total of 7 on any of the first 10 rolls approximately 16.15% of the time. This implies that we will get a total of 7 on at least one of the first 10 rolls 100%−16.15%=83.85% of the time. ## What is the probability of not getting a 7 when rolling two standard six sided dice? Probability : Example Question #1 The sample space for rolling two six-sided dice is 36. We can get 7 six different ways: 1,6 2,5 3,4 4,3 5,2 6,1 so the probability of getting a 7 is or . The probability of NOT getting a 7 is . We can add up all the things we want or we can subtract from 1 what we don’t want. ## How many times can you roll a 7? As the chart shows the closer the total is to 7 the greater is the probability of it being thrown. Probabilities for the two dice. Total Number of combinations Probability 6 5 13.89% 7 6 16.67% 8 5 13.89% 9 4 11.11% ## How many ways can you roll 7? For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6. THIS IS FUNNING: What does OV mean in betting? ## What is the probability of rolling 2/3 or 12? Using Probability to Calculate the Odds in the Game of Craps Roll Target Outcomes Probability 8 5 5/36 9 4 4/36 = 1/9 10 3 3/36 = 1/12 11 2 2/26 = 1/18 ## What’s the odds of rolling a 7? Two (6-sided) dice roll probability table Roll a… Probability 5 10/36 (27.778%) 6 15/36 (41.667%) 7 21/36 (58.333%) 8 26/36 (72.222%)	560	1,830	{"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-2022-05	latest	en	0.890902
http://boardgames.stackexchange.com/questions/2339/do-you-need-to-buy-a-card-when-playing-treasures-in-dominion?answertab=active	1,462,231,592,000,000,000	text/html	crawl-data/CC-MAIN-2016-18/segments/1461860117914.56/warc/CC-MAIN-20160428161517-00041-ip-10-239-7-51.ec2.internal.warc.gz	34,503,376	17,414	# Do you need to buy a card when playing treasures in Dominion? So I ran into a situation where I had a single treasure, the Loan card. I wanted to play the Loan card but I did not want to buy any cards. So can you play treasure cards and not buy anything? I believe I read in the rules that you play treasures first, then buy cards. So I believe that means I can play treasures and not buy any cards. Thanks. Edit I just re-read my question and I failed to mention that I want to make sure I can use the "powers" of the treasure cards even if I don't buy anything. So in the example above I want to use the powers of the Loan card, but not buy any cards. - Upvoted because this is the first Dominion question in a while that made me go "Ooh, that's quite a good question", rather than "obviously the answer to that is written in plain English in the appropriate section of the rulebook, why didn't you just look there in the first place?" ;) – thesunneversets Jan 27 '11 at 23:37 That's fine. From the Dominion rules: The cost of a card is in its lower left corner. The player may play some or all of the Treasure cards from his hand to his play area and add to their value the coins provided by Action cards played this turn. The player may then gain any card in the Supply of equal or lesser value. He takes the purchased card from its Supply pile and places it face-up on his Discard pile. He my not use the ability of the card when it is gained. (bolded for emphasis by me) EDITED, to answer Chris' edit: Yes, it's fine to use Loan's "power" and then not buy anything. As stated in the rules above, you play a Treasure card from your hand, in this case the Loan: at which point the Loan card's abilities kick in, and you carry out all the revealing, discarding and trashing. Now you have (at least) 1 coin in your pool that you could spend on a Buy: but the rules make it clear that actually buying something is always optional, no matter how much cash or how many Buys you are entitled to! - Just to add something minor to the other two answers, you can also play treasure without buying anything to gain the benefits of other cards, e.g. Alchemist. - No, you do not have to buy a card. You are free to use the power of Loan or any other treasure played during your turn. There is no obligation to buy anything just because you used the power of a treasure. From the rulebook pg7, emphasis mine: The player may play some or all of the Treasure cards from his hand to his play area and add to their value the coins provided by Action cards played this turn. The player may then gain any card in the Supply of equal or lesser value and later on Players do not have to use any or all of their Buys -	632	2,722	{"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-2016-18	latest	en	0.985933
http://www.stat.umn.edu/macanova/htmlhelp/node49.htm	1,708,729,304,000,000,000	text/html	crawl-data/CC-MAIN-2024-10/segments/1707947474470.37/warc/CC-MAIN-20240223221041-20240224011041-00115.warc.gz	68,333,499	2,228	Next: chplot() Up: MacAnova Help File Previous: changestr() Contents # cholesky() Usage: ```cholesky(x [,pivot:T or force:T , nonposok:T]), x a positive definite square REAL matrix with no MISSING values ``` Keywords: matrix algebra ```cholesky(A) returns the Cholesky decomposition of the positive definite REAL symmetric matrix A. Its value is the REAL upper triangular matrix r of the same size as A such that r' %% r = A. It is an error if A is not positive definite. cholesky(A, nonposok:T) does the same, except that a non positive definite A is not considered to be an error, but results a value of NULL being returned. This makes it possible for a macro to take corrective action when a matrix is not positive definite. See topics 'macros' and 'NULL'. cholesky(A,pivot:T [,nonposok:T]) reorders the rows and columns as the computation proceeds so as to obtain the most stable computation. It returns a structure with components 'r', a REAL upper triangular matrix, and 'pivot', a REAL vector of integers describing the reordering. After result <- cholesky(A,pivot:T), result\$r' %% result\$r should equal A[result\$pivot, result\$pivot] except for rounding error. cholesky(A,force:Vec [,nonposok:T]), where Vec is a REAL vector whose length is nrows(A), enables pivoting, but allows some control on reordering. The elements of Vec should be 1, -1, or 0, since only the signs are used. Before factoring, rows and columns of A, if any, with index j such that Vec[j] > 0 are moved to rows and columns 1, 2, ..., (initial columns) but are not further moved. All rows and columns with Vec[j] < 0 are moved to rows and columns nrows(A), nrows(A) - 1, ..., (final columns) but are not further moved. Rows and columns, if any, with Vec[j] == 0 (pivoted columns), are free to be reordered, but will follow the initial columns and precede the final columns. Again the result is a structure with components 'r' and 'pivot'.	517	1,942	{"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-2024-10	latest	en	0.801486
http://gmatclub.com/forum/if-8-k-8-is-k-46914.html	1,466,839,797,000,000,000	text/html	crawl-data/CC-MAIN-2016-26/segments/1466783392159.3/warc/CC-MAIN-20160624154952-00040-ip-10-164-35-72.ec2.internal.warc.gz	127,150,092	47,199	Find all School-related info fast with the new School-Specific MBA Forum It is currently 25 Jun 2016, 00:29 ### 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 # If –8 < k < 8, is k <2> 0 Author Message Manager Joined: 07 May 2007 Posts: 178 Followers: 2 Kudos [?]: 39 [0], given: 0 If –8 < k < 8, is k <2> 0 [#permalink] ### Show Tags 10 Jun 2007, 13:04 00:00 Difficulty: (N/A) Question Stats: 0% (00:00) correct 0% (00:00) wrong based on 0 sessions ### HideShow timer Statistics This topic is locked. If you want to discuss this question please re-post it in the respective forum. If –8 < k < 8, is k <2> 0 (2) 1/k > 1/2 Manager Joined: 07 May 2007 Posts: 178 Followers: 2 Kudos [?]: 39 [0], given: 0 ### Show Tags 10 Jun 2007, 13:06 Not sure why the questions did post correctly, retrying If –8 < k < 8, is k <2> 0 2. 1/k > 1/2 SVP Joined: 01 May 2006 Posts: 1798 Followers: 9 Kudos [?]: 132 [0], given: 0 ### Show Tags 10 Jun 2007, 13:08 U should try to check the checkbox "Disable HTML in this post" just under the area to tape your question Manager Joined: 07 May 2007 Posts: 178 Followers: 2 Kudos [?]: 39 [0], given: 0 ### Show Tags 10 Jun 2007, 13:09 OK, final attempt If -8<k<8, is k<2> 0 2. 1/k > 1/2 Manager Joined: 07 May 2007 Posts: 178 Followers: 2 Kudos [?]: 39 [0], given: 0 ### Show Tags 10 Jun 2007, 13:11 Thanks Fig, final final... If –8 < k < 8, is k < –2 ? (1) k^2 – 7k – 18 > 0 (2) 1/k > 1/2 SVP Joined: 01 May 2006 Posts: 1798 Followers: 9 Kudos [?]: 132 [0], given: 0 ### Show Tags 10 Jun 2007, 13:47 (A) for me We have : \|k\| < 8 k < -2 ? From 1 k^2 – 7k – 18 > 0 If k = -2, then (-2)^2 -7(-2) - 18 = 18 - 18 = 0. -2 is a root. k^2 – 7k – 18 > 0 <=> (k+2)(k-9) > 0 Outside of the roots, ax^2 + bx + c is of the signt of a. Here, we have so: (k+2)(k-9) > 0 <=> k > 9 or k < -2. As \|k\| < 8, we are sure that -8 < k < -2. SUFF. From 2 1/k > 1/2 > 0... So, k > 0. Thus, k < 2. INSUFF. Senior Manager Joined: 03 Jun 2007 Posts: 384 Followers: 2 Kudos [?]: 11 [0], given: 0 ### Show Tags 11 Jun 2007, 13:28 I feel it is B. 1/K > 1/2 => k is between 0 and 2 (both excluded) In stmt 1 K > 9 or k < -2 so insufficient Manager Joined: 22 May 2007 Posts: 121 Followers: 1 Kudos [?]: 4 [0], given: 0 ### Show Tags 11 Jun 2007, 13:50 Looks like D to me. 1 is explained by Fig 2. 1/k>1/2 --->>> k must be positive so it has to be more than -2 in any case. What is the OA? VP Joined: 10 Jun 2007 Posts: 1459 Followers: 7 Kudos [?]: 207 [0], given: 0 ### Show Tags 11 Jun 2007, 18:25 If –8 < k < 8, is k < –2 ? (1) k^2 – 7k – 18 > 0 (2) 1/k > 1/2 ________________________________________ Rephase the question: The question is really asking if -8<k<-2? (1) k^2 - 7k -18 >0 is the same as (k-9)(k+2) > 0 From this, we know that the critical points are k=9 and k=-2. The range of k where (k-9)(k+2) > 0 are k<-2 and k>9. INSUFFICIENT. (2) 1/k > 1/2 From this, we know that 0<k<2. This is SUFFICIENT since k will never be between -8 and -2. VP Joined: 10 Jun 2007 Posts: 1459 Followers: 7 Kudos [?]: 207 [0], given: 0 ### Show Tags 11 Jun 2007, 18:33 Fig wrote: Here, we have so: (k+2)(k-9) > 0 <k> 9 or k < -2. As \|k\| < 8, we are sure that -8 < k < -2. No, this is incorrect. \|k\|<8 is the same as -8<k<8. We don't know for sure that k is between -8 and 8. The answer only say k<-2. If k=-13, then k will NOT be between -8 and 8. GMAT Club Legend Joined: 07 Jul 2004 Posts: 5062 Location: Singapore Followers: 28 Kudos [?]: 276 [0], given: 0 ### Show Tags 11 Jun 2007, 18:36 St1: (k-9)(k+2) > 0 valid range: k <2> 9 Insufficient. St2: k<2. Sufficient. Because k must be at positive but not 0. Ans B SVP Joined: 01 May 2006 Posts: 1798 Followers: 9 Kudos [?]: 132 [0], given: 0 ### Show Tags 11 Jun 2007, 23:38 Hayabusa wrote: Looks like D to me. 1 is explained by Fig 2. 1/k>1/2 --->>> k must be positive so it has to be more than -2 in any case. What is the OA? U are right... (D) it is ... The second statment is 0 < k < 2 SVP Joined: 01 May 2006 Posts: 1798 Followers: 9 Kudos [?]: 132 [0], given: 0 ### Show Tags 11 Jun 2007, 23:44 bkk145 wrote: Fig wrote: Here, we have so: (k+2)(k-9) > 0 <k> 9 or k < -2. As \|k\| < 8, we are sure that -8 < k < -2. No, this is incorrect. \|k\|<8 is the same as -8<k<8. We don't know for sure that k is between -8 and 8. The answer only say k<-2. If k=-13, then k will NOT be between -8 and 8. We analyse the inequation without constraint and then we add \|k\| < 8 to conclude.... So, no, we do not say k = -13 Manager Joined: 17 Oct 2006 Posts: 52 Followers: 0 Kudos [?]: 1 [0], given: 0 ### Show Tags 12 Jun 2007, 00:49 [u]Statement 1[/u] k^2-7k-18>0 (k-9)(k+2)>0 it implies that either k-9 and k+2 both are positive or negative. If they are positive then, k>9 (which is not possible according to the stem), and if they are negative, then k<2. Since, k<2 does not clearly tells us whether k<2>1/2 This statement tell us two things. 1) that K is positive and 2) that k<2. Since K is positive and smaller than 2, so this statement definitely tells us that K cannot be <-2. So it is SUFFICIENT. VP Joined: 09 Jan 2007 Posts: 1045 Location: New York, NY Schools: Chicago Booth Class of 2010 Followers: 10 Kudos [?]: 160 [0], given: 3 ### Show Tags 12 Jun 2007, 02:13 Tricky one... D for me: 1) The inequality gives us as already stated: (K-9)(K+2)>0 So K<2>9; As -8<k<8 only the "left side" of the inequality counts giving us -8<k<2>1/2 The result is k<2, k must be positive, , so 0<k<2; SUF Director Joined: 06 Sep 2006 Posts: 743 Followers: 1 Kudos [?]: 24 [0], given: 0 ### Show Tags 12 Jun 2007, 08:59 If (k+2)(k-9) > 0 does not that means either k+2>0 or k-9>0 either k>-2 OR k>9 How did you get k < -2? VP Joined: 09 Jan 2007 Posts: 1045 Location: New York, NY Schools: Chicago Booth Class of 2010 Followers: 10 Kudos [?]: 160 [0], given: 3 ### Show Tags 12 Jun 2007, 09:09 [quote="asaf"]If (k+2)(k-9) > 0 does not that means either k+2>0 or k-9>0 either k>-2 OR k>9 How did you get k <2>0... So for K<2>9, both are positive.... VP Joined: 09 Jan 2007 Posts: 1045 Location: New York, NY Schools: Chicago Booth Class of 2010 Followers: 10 Kudos [?]: 160 [0], given: 3 ### Show Tags 12 Jun 2007, 09:10 asaf wrote: If (k+2)(k-9) > 0 does not that means either k+2>0 or k-9>0 either k>-2 OR k>9 How did you get k < -2? Take care, is not "or", but "and" (K+2) "and" (k-9)>0... So for K<-2 both terms are negative, and the product is positive, also for k>9, both are positive.... Manager Joined: 07 May 2007 Posts: 178 Followers: 2 Kudos [?]: 39 [0], given: 0 ### Show Tags 12 Jun 2007, 21:29 OA is D 2) 1/k > 1/2 means K must be positive and less than 2 ==> Suff 1) (k-9)(k+2) > 0 implies either (K-9) > 0 AND (k+2) > 0 -----> Both positive -- (a) or (K-9) < 0 AND (k+2) < 0 -----> Both negative -- (b) But since \|k\| < 8, (k-9) can never be > 0. This rules out (a) from (b) we can conclude k < -2 Hence 2) alone is sufficient Senior Manager Joined: 27 Jul 2006 Posts: 298 Followers: 1 Kudos [?]: 10 [0], given: 0 ### Show Tags 12 Jun 2007, 22:47 D a tells us that K is either -2 or 9. 9 is out since we already know that it is less than 8. Sufficient B tells us that K is positive. It could be a fraction, but in all cases it will be larger then -2 also sufficient Display posts from previous: Sort by	3,082	7,891	{"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-2016-26	longest	en	0.824098
https://www.studypool.com/discuss/1058382/geometric-shapes-amp-angles-7th-grade-algebra-1?free	1,508,832,223,000,000,000	text/html	crawl-data/CC-MAIN-2017-43/segments/1508187828189.71/warc/CC-MAIN-20171024071819-20171024091819-00681.warc.gz	1,013,223,862	14,306	##### geometric shapes & Angles 7th Grade Algebra. label Algebra account_circle Unassigned schedule 1 Day account_balance_wallet \$5 Jun 30th, 2015 Hi ! Angle YQZ = 5x + 72 Angle ZQP = 13x Now from the figure we can see that Angle YQZ + Angle ZQP = 180 degree So (5x + 72) + (13x) = 180 5x + 13x + 72 = 180 18x + 72 = 180 18x = 180 - 72 18x = 108 x = 108/18 x = 6 So Angle YQZ = 5x + 72 = 5(6) + 72 = 30 + 72 = 102 degree & Angle ZQP = 13x = 13(6) = 78 degree Hence Angle YQZ = 102 degree Angle ZQP = 78 degree Hope you get it. Thanks :) Jun 30th, 2015 Omg your amazing, thanks so much! Jun 30th, 2015 My Pleasure! Jun 30th, 2015 ... Jun 30th, 2015 ... Jun 30th, 2015 Oct 24th, 2017 check_circle	303	723	{"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-2017-43	latest	en	0.757531
http://en.wikipedia.org/wiki/Locus_(mathematics)	1,438,116,609,000,000,000	text/html	crawl-data/CC-MAIN-2015-32/segments/1438042982502.13/warc/CC-MAIN-20150728002302-00114-ip-10-236-191-2.ec2.internal.warc.gz	78,199,153	14,077	# Locus (mathematics) Each curve in this example is a locus defined as the conchoid of a circle centered at point P and the line l. In this example, P is 7cm from l. In geometry, a locus (plural: loci) is a set of points whose location satisfies or is determined by one or more specified conditions.[1][2] ## Commonly studied loci Examples from plane geometry include: • The set of points equidistant from two points is a perpendicular bisector to the line segment connecting the two points.[3] • The set of points equidistant from two lines which cross is the angle bisector. • All conic sections are loci:[4] • Parabola: the set of points equidistant from a single point (the focus) and a line (the directrix). • Circle: the set of points for which the distance from a single point is constant (the radius). The set of points for each of which the ratio of the distances to two given foci is a positive constant (that is not 1) is referred to as a Circle of Apollonius. • Hyperbola: the set of points for each of which the absolute value of the difference between the distances to two given foci is a constant. • Ellipse: the set of points for each of which the sum of the distances to two given foci is a constant. The circle is the special case in which the two foci coincide with each other. ## Proof of a locus In order to prove that a geometric shape is the correct locus for a given set of conditions, one generally divides the proof into two stages:[5] • Proof that all the points that satisfy the conditions are on the given shape. • Proof that all the points on the given shape satisfy the conditions. ## Examples (distance PA) = 3.(distance PB) ### First example We find the locus of the points P that have a given ratio of distances k = d1/d2 to two given points. In this example we choose k= 3, A(-1,0) and B(0,2) as the fixed points. P(x,y) is a point of the locus $\Leftrightarrow \|PA\| = 3 \|PB\|$ $\Leftrightarrow \|PA\|^2 = 9 \|PB\|^2$ $\Leftrightarrow (x+1)^2+(y-0)^2=9(x-0)^2+9(y-2)^2$ $\Leftrightarrow 8(x^2+y^2)-2x-36y+35 =0$ $\Leftrightarrow \left(x-\frac18\right)^2+\left(y-\frac94\right)^2=\frac{45}{64}$ This equation represents a circle with center (1/8,9/4) and radius $\frac{3}{8}\sqrt{5}$. It is the circle of Apollonius defined by these values of k, A, and B. ### Second example Locus of point C A triangle ABC has a fixed side [AB] with length c. We determine the locus of the third vertex C such that the medians from A and C are orthogonal. We choose an orthonormal coordinate system such that A(-c/2,0), B(c/2,0). C(x,y) is the variable third vertex. The center of [BC] is M( (2x+c)/4, y/2 ). The median from C has a slope y/x. The median AM has slope 2y/(2x+3c). The locus is a circle C(x,y) is a point of the locus $\Leftrightarrow$ The medians from A and C are orthogonal $\Leftrightarrow \frac{y}{x} \cdot \frac{2y}{2x+3c} = -1$ $\Leftrightarrow 2 y^2 + 2x^2 + 3c x = 0$ $\Leftrightarrow x^2 + y^2 + (3c/2) x = 0$ $\Leftrightarrow (x + 3c/4)^2 + y^2 = 9c^2/16$ The locus of the vertex C is a circle with center (-3c/4,0) and radius 3c/4. ### Third example The intersection point of the associated lines k and l describes the circle A locus can also be defined by two associated curves depending on one common parameter. If the parameter varies, the intersection points of the associated curves describe the locus. In the figure, the points K and L are fixed points on a given line m. The line k is a variable line through K. The line l through L is perpendicular to k. The angle $\alpha$ between k and m is the parameter. k and l are associated lines depending on the common parameter. The variable intersection point S of k and l describes a circle. This circle is the locus of the intersection point of the two associated lines. ### Fourth example A locus of points need not be one-dimensional (as a circle, line, etc.). For example,[1] the locus of the inequality 2x+3y–6<0 is the portion of the plane that is below the line 2x+3y–6=0.	1,130	3,997	{"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": 12, "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}	4.71875	5	CC-MAIN-2015-32	latest	en	0.902938
http://mathhelpforum.com/advanced-algebra/154148-subgroup-test.html	1,480,707,113,000,000,000	text/html	crawl-data/CC-MAIN-2016-50/segments/1480698540409.8/warc/CC-MAIN-20161202170900-00068-ip-10-31-129-80.ec2.internal.warc.gz	179,371,429	10,464	1. ## Subgroup Test I want to use the "one step subgroup test". The identity is $e=I= \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}$ And $det(I)=1-0=1=(\sqrt{2})^0$ and $0 \in \mathbb{Z}$ Therefore H is not empty since $I \in H$. Now I have to show that for any two elements $x_1,x_2 \in H$, $x_1x_2^{-1}$ is in H. Let $\begin{bmatrix}a & b \\c & d\end{bmatrix}, \begin{bmatrix}a' & b' \\c' & d'\end{bmatrix} \in H$ $x_2^{-1}= \frac{1}{(\sqrt{2})^k} \begin{bmatrix}d' & -b' \\-c' & a'\end{bmatrix}$ So we have: $x_1x_2^{-1}= \begin{bmatrix}a & b \\c & d\end{bmatrix} \frac{1}{(\sqrt{2})^k} \begin{bmatrix}d' & -b' \\-c' & a'\end{bmatrix}$ $=\frac{1}{(\sqrt{2})^k} \begin{bmatrix}-d'a+-c'b & -b'a'+b'a' \\cd'+-c'd & -b'c+a'd\end{bmatrix}$ And $det (x_1x_2^{-1})=\frac{1}{(\sqrt{2})^k}(-d'a+-c'b)(b'c+a'd)-(-b'a'+b'a')(cd'+-c'd)$ If my working is correct so far, could anyone please show me how to manipulate this determinant to show that it satisfies the given condition, and $x_1x_2^{-1} \in H$. 2. You don't need any of that. $det(AB) = det(A)det(B)$ and $det(A^{-1}) = \frac{1}{det(A)}$ are all you need. 3. Thank you! So we have: $det(x_1x_2^{-1})= \frac{(ad-bc)}{(a'd'-c'b')}=\frac{(\sqrt{2})^{k_1}}{(\sqrt{2})^{k_2}}$ where $k_1,k_2 \in \mathbb{Z}$ So how could I now simplify this to show that the whole thing can be written as $(\sqrt{2})^k$?? 4. $det(x_1x_2^{-1}) = \frac{(\sqrt{2})^{k_1}}{(\sqrt{2})^{k_2}} = (\sqrt{2})^{k_1-k_2}$ and $k_1 - k_2 \in \mathbb{Z}$.	657	1,489	{"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": 0, "codecogs_latex": 19, "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-2016-50	longest	en	0.555814
http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=A673&l=en	1,532,248,197,000,000,000	text/html	crawl-data/CC-MAIN-2018-30/segments/1531676593142.83/warc/CC-MAIN-20180722080925-20180722100925-00453.warc.gz	495,917,746	4,544	Mathematical and Physical Journal for High Schools Issued by the MATFUND Foundation Already signed up? New to KöMaL? # Problem A. 673. (May 2016) A. 673. We have colour pearls placed on an $\displaystyle n\times n$ board; a square may contain more than one pearl. Altogether we used $\displaystyle 2n-1$ colours and $\displaystyle n$ pearls from each colour. The pearls are arranged in such a way that no row or column contains more than one pearl of the same colour. Prove that it is possible to select $\displaystyle n$ pearls with distinct colours such that no two of them are in the same row or column. (5 pont) Deadline expired on June 10, 2016. ### Statistics: 3 students sent a solution. 5 points: Williams Kada. 3 points: 1 student. 2 points: 1 student. Problems in Mathematics of KöMaL, May 2016	226	813	{"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	3	CC-MAIN-2018-30	latest	en	0.854811
http://www.britannica.com/EBchecked/topic/451499/perfect-rectangle	1,397,852,594,000,000,000	text/html	crawl-data/CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00348-ip-10-147-4-33.ec2.internal.warc.gz	330,762,723	14,801	× In Edit mode, you will be able to click anywhere in the article to modify text, insert images, or add new information. Once you are finished, your modifications will be sent to our editors for review. You will be notified if your changes are approved and become part of the published article! × × × In Edit mode, you will be able to click anywhere in the article to modify text, insert images, or add new information. Once you are finished, your modifications will be sent to our editors for review. You will be notified if your changes are approved and become part of the published article! × × Click anywhere inside the article to add text or insert superscripts, subscripts, and special characters. You can also highlight a section and use the tools in this bar to modify existing content: Editing Tools: We welcome suggested improvements to any of our articles. You can make it easier for us to review and, hopefully, publish your contribution by keeping a few points in mind: 1. Encyclopaedia Britannica articles are written in a neutral, objective tone for a general audience. 2. You may find it helpful to search within the site to see how similar or related subjects are covered. 3. Any text you add should be original, not copied from other sources. 4. At the bottom of the article, feel free to list any sources that support your changes, so that we can fully understand their context. (Internet URLs are best.) Your contribution may be further edited by our staff, and its publication is subject to our final approval. Unfortunately, our editorial approach may not be able to accommodate all contributions. # perfect rectangle Article Free Pass Thank you for helping us expand this topic! Once you are finished and click submit, your modifications will be sent to our editors for review. The topic perfect rectangle is discussed in the following articles: ## definition and properties • TITLE: number game SECTION: Geometric dissections ...theory. In this connection, a squared rectangle is a rectangle that can be dissected into a finite number of squares; if no two of these squares are equal, the squared rectangle is said to be perfect. The order of a squared rectangle is the number of constituent squares. It is known that there are no perfect rectangles of orders less than 9, and that there are exactly two perfect... Please select the sections you want to print MLA style: "perfect rectangle". Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc., 2014. Web. 18 Apr. 2014 <http://www.britannica.com/EBchecked/topic/451499/perfect-rectangle>. APA style:	561	2,620	{"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}	2.640625	3	CC-MAIN-2014-15	longest	en	0.88843
https://crypto.stackexchange.com/questions/71602/derive-operations-from-an-arbitrary-number	1,716,444,286,000,000,000	text/html	crawl-data/CC-MAIN-2024-22/segments/1715971058611.55/warc/CC-MAIN-20240523050122-20240523080122-00057.warc.gz	149,365,399	41,535	# Derive operations from an arbitrary number I don't really know how to phrase this question, so I'll just mention the idea. This is partially reminiscent (at least in spirit to white box crypto): Can one derive arithmetic operations from a number? Is there a formula to do that? So, the simplest example would be: a = 4 ops = get_operations(a) print(ops) /* output: * * b = 2 * c = 2 * return b + c */ The idea is to simply have a way to "derive" a mathematical operation from a value. There are obviously more than "one" operation that could be derived from the above example. The system does not have to be complete. The flow of such a "derivation" algorithm in my head is as such: 1. Get input (k) 2. Randomly choose an arithmetic operand (P) where y = k (P) x and store the operand (P) 3. Pick a random number (x) and store its value 4. Solve for (y) and store its value 5. Now, we have a combination of (P), (x), and (y) that, when solved, would yield the correct input (k). My question is this: did someone research this and make a way better algorithm that what I could muster up here? • "a way better algorithm" - define "better", that is, by what criteria are you comparing the various possible algorithms? Jun 27, 2019 at 6:33 • "way better" means if there is a name for this topic and has it been researched before by professional mathematicians Jun 27, 2019 at 6:45 Is there a formula to do that? Your example looks like a problem about Partitions to me. A partition is a way of representing a positive number as a sum of $$n$$ positive integers, for example: The partitions of the number $$5$$ are: • $$5 \space (+0)$$ • $$4 + 1$$ • $$3 + 2$$ • $$3 + 1 + 1$$ • $$2 + 2 + 1$$ • $$2 + 1 + 1 + 1$$ • $$1 + 1 + 1 + 1 + 1$$ Since partitions consider every possibility valid, the number for possible ways of any integer $$n$$ can grow very fast, i.e. the number of possible partitions of the number $$100$$ is $$190,569,292$$. There exist some formulas (some more complicated or faster than others and some are only approximations). In your example you only have an operator once, so here $$4 + 1$$ and $$3 + 2$$ would be a possiblity. Since you mentioned "more than one operation", a possibility would also be to represent numbers as their prime factors, for example: The prime factorization of the number 22 is: • $$2 \times 11$$ There's always only one possiblity to represent a number as it's prime factors (if you don't care about the way you write it ($$2 \times 11$$ is the same as $$11 \times 2$$)). There are a lot of factoring algorithms, since this is still a unsolved problem (Does P = NP ?) and this problem is important for cryptography. I assume that a problem occurs if you'd try to do this with the operators of division and subtraction, for example: There are infinite possibilities to represent a number as a subtraction, for example: For the number $$5$$: • $$6 - 1$$ • $$7 - 2$$ • $$8 - 3$$ • $$9 - 4$$ • $$\ldots$$ I could think of two things: Tweakable Block Cipher, and Tweakable Compression Function. 1. Tweakable Block Cipher: A Tweakable Block Cipher is defined with the prototype: $$f : D \times K \times T \rightarrow D$$ where $$D$$ is the block of data to be encrypted/decrypted with the key $$K$$ using the block cipher function $$f$$, that can be efficiently parameterized with $$T$$. 1. Tweakable Compression Function: I assume you mean binary operations when you say operation (binary in the sense that there are 2 operands). Basically, we just build a compression function from a tweakable block cipher using Davies–Meyer construct or any other method to turn a block cipher into a compression function. $$g : D \times D \times T \rightarrow D$$ f <- blockcipher(d, key, tweak); g <- compressionfunc(a, b, tweak){ return blockcipher(a, b, tweak) xor a; }	1,009	3,832	{"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": 29, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.96875	4	CC-MAIN-2024-22	latest	en	0.933077
http://qa.answers.com/Q/How_many_25_meter_laps_do_you_have_to_swim_to_equal_a_mile	1,532,194,980,000,000,000	text/html	crawl-data/CC-MAIN-2018-30/segments/1531676592650.53/warc/CC-MAIN-20180721164755-20180721184755-00536.warc.gz	304,742,372	41,508	# How many 25 meter laps do you have to swim to equal a mile? Would you like to merge this question into it? #### already exists as an alternate of this question. Would you like to make it the primary and merge this question into it? #### exists and is an alternate of . There are 1,609.344 meters in a mile. When 1 length = 1 lap, you would need to complete 64.3 laps to swim a mile. 4 people found this useful # How many 25 meter laps equal a mile? It will take 64.4 lengths (32.2 laps) to equal one mile. 29 # How many laps must you swim in a 25 meter pool to swim a mile? There is 1,609.344 metres in a mile, so to swim one mile in a 25 metre pool you would have to do 64.37 lengths or laps. # How many laps to swim a mile in 25 meter pool? 64 laps to swim a mile in a 25 meter pool # How many laps in a 25 meter pool must you swim to equal 500 yards? since 1 meter is equal to 1.094 yards, then one lap (one direction) in a 25 meter pool is really 27.35 yards. So then 500 yards at 27.35 yards a lap, you would need to complet # How many laps in a 25 meter pool to swim a mile? 64.37376 laps. So go for 64 or 65 laps, otherwise you'll be wallowing in the middle of the pool. # How many laps in 25 meters to make one mile in swimming pool? 1 mile = 1,609.334m 1 lap = 25m Therefore 1609.334 / 25 = 64.37336 laps 65 laps = (25*65) / 1609.334 = 1.01 miles 16 laps 35 # How many laps in a 25 meter pool must you swim to do 1.2 miles? Since a mile is 64 laps, (1600 meters) you would have to swim 84.8 laps. # How many laps is a 25 meter swim? I am a swimmer and there is only 1 lap in a 25 meter swim. Just down, not back. # How many laps in 25 meter to equal 1 mile? 1 mile = 1609.344 metres which is 64.4 laps of 25m. 65 lenghts of a 25 meter pool = 1 mile i do i quite regular # How many lap must you swim in a 25 meter pool to equal 2 miles? 2 miles = 3218.7 metres So, at 25 metres per lap, you would need to swim 3281.7/25 = 128.7 or 129 laps. # How many laps in a 50 meter pool do I need to swim to equal 2 miles? 32 laps Or to be exact, 32 laps plus 9.34 more meters into the 33rd lap. # How many laps equal .25 mile in a 25 meter pool? 0.25 mile = 402.3 metres So 402.3/25 = 16 laps (plus a tiny bit more). # How many laps in a 25 meter pool would equal the same effort not distance in running a mile which is much easier than swimming a mile what would your estimate be for a mile swim to equal a mile run? It so much depends on how fast you run and how fast you swim and what type of stroke, and your weight. But roughly, say you run a 10 minute mile you burn 100 calories; say you # How many laps to equal a mile swimming a 50 meter lap? A mile is 1600m, therefore you need to swim 32 laps of a 50m poolto equal 1 mile	824	2,767	{"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}	4.09375	4	CC-MAIN-2018-30	latest	en	0.970389
https://justaaa.com/statistics-and-probability/76104-test-the-claim-that-the-mean-gpa-of-night	1,713,997,745,000,000,000	text/html	crawl-data/CC-MAIN-2024-18/segments/1712296819971.86/warc/CC-MAIN-20240424205851-20240424235851-00059.warc.gz	295,048,210	9,824	Question # Test the claim that the mean GPA of night students is larger than 2.4 at the... Test the claim that the mean GPA of night students is larger than 2.4 at the 0.025 significance level. The null and alternative hypothesis would be: H0:p≤0.6H0:p≤0.6 H1:p>0.6H1:p>0.6 H0:μ≤2.4H0:μ≤2.4 H1:μ>2.4H1:μ>2.4 H0:p=0.6H0:p=0.6 H1:p≠0.6H1:p≠0.6 H0:p≥0.6H0:p≥0.6 H1:p<0.6H1:p<0.6 H0:μ≥2.4H0:μ≥2.4 H1:μ<2.4H1:μ<2.4 H0:μ=2.4H0:μ=2.4 H1:μ≠2.4H1:μ≠2.4 The test is: two-tailed right-tailed left-tailed Based on a sample of 75 people, the sample mean GPA was 2.43 with a standard deviation of 0.05 The p-value is: (to 2 decimals) Based on this we: • Reject the null hypothesis • Fail to reject the null hypothesis Can you please tell me how you get the answer on a TI 84 PLUS as well We were unable to transcribe this image t24 0.025 = 1.984 Decision Rule & 24 to 7 este then Beject to ot 0.025-1 2-0.5. tal = 0.5196 < ttable 21.989 0.5196 C 1.984 Accept Ho et o.o25 conclusion :- GPA of might student is u- 2.4 #### Earn Coins Coins can be redeemed for fabulous gifts.	447	1,082	{"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-2024-18	latest	en	0.816076
https://www.bodylanguageacadamy.us/guide-2/allin-with-aaxx-before-the-flop.html	1,566,544,770,000,000,000	text/html	crawl-data/CC-MAIN-2019-35/segments/1566027318011.89/warc/CC-MAIN-20190823062005-20190823084005-00429.warc.gz	745,607,941	5,750	## Allin with AAxx before the Flop Suppose you have \ - Av - V - > in the big blind, with the blinds at \$5-\$10. You have \$450 in front of you to start the hand, \$10 of i t i n the big blind already. S o the pot holds \$15 and the first two players t o act c all \$ 10 each, making it \$ 35. The button then calls the \$10 and raises t he s ize of t he pot—the raiser i s the t hird player t o call \$10 ( \$30) a nd t he two blinds are t ogether worth \$15, so he can call the \$10 and raise it \$ 45, making it \$55 to go—and the small blind calls the \$55 to go. Now you say, "I raise the size of t he pot." You announce this out l oud (verbal declarations stand in poker) partly so that the dealer or other players can tell you how much you can make it t o go. ( There i s always someone at t he table who is r eally sharp and fast t o say, "Fine, y ou can make it \$x to go.") I n this c ase, two players have put in \$55 each (the button and the small blind) and the two prior players had put i n \$10 each and you wiil have to call the \$55 before you raise the size of the pot. S o we have \$55 + \$55 + \$55 + \$10 + \$10, which equals \$185. So you call the \$55 and raise it \$185, making it \$240 to go. Whew! The math isn't all that complicated once you get used to it, and the dealer and other players are always there to help. Now that you have invested \$240 of your chips before the flop, it's time to bet the other \$210 on the flop no matter what c ards c ome up, i n order to protect your hand. That's one of the nice things about starting with A-A-x-x. You can miss the flop entirely and stiil have a hand that c an win. 0 0	464	1,650	{"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}	3.578125	4	CC-MAIN-2019-35	latest	en	0.946753
https://stacks.math.columbia.edu/tag/0DET	1,721,055,448,000,000,000	text/html	crawl-data/CC-MAIN-2024-30/segments/1720763514707.52/warc/CC-MAIN-20240715132531-20240715162531-00094.warc.gz	469,312,329	6,434	Lemma 37.48.1. Let $S$ be a scheme. Let $\{ S_ i \to S\} _{i \in I}$ be an fppf covering. Then there exist 1. an étale covering $\{ S'_ a \to S\}$, 2. surjective finite locally free morphisms $V_ a \to S'_ a$, such that the fppf covering $\{ V_ a \to S\}$ refines the given covering $\{ S_ i \to S\}$. Proof. We may assume that each $S_ i \to S$ is locally quasi-finite, see Lemma 37.23.6. Fix a point $s \in S$. Pick an $i \in I$ and a point $s_ i \in S_ i$ mapping to $s$. Choose an elementary étale neighbourhood $(S', s) \to (S, s)$ such that there exists an open $S_ i \times _ S S' \supset V$ which contains a unique point $v \in V$ mapping to $s \in S'$ and such that $V \to S'$ is finite, see Lemma 37.41.1. Then $V \to S'$ is finite locally free, because it is finite and because $S_ i \times _ S S' \to S'$ is flat and locally of finite presentation as a base change of the morphism $S_ i \to S$, see Morphisms, Lemmas 29.21.4, 29.25.8, and 29.48.2. Hence $V \to S'$ is open, and after shrinking $S'$ we may assume that $V \to S'$ is surjective finite locally free. Since we can do this for every point of $S$ we conclude that $\{ S_ i \to S\}$ can be refined by a covering of the form $\{ V_ a \to S\} _{a \in A}$ where each $V_ a \to S$ factors as $V_ a \to S'_ a \to S$ with $S'_ a \to S$ étale and $V_ a \to S'_ a$ surjective finite locally free. $\square$ In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).	526	1,574	{"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": 2, "x-ck12": 0, "texerror": 0}	2.9375	3	CC-MAIN-2024-30	latest	en	0.768557
https://voiceofwave.com/how-do-you-figure-out-the-amplitude-of-a-wave	1,660,149,472,000,000,000	text/html	crawl-data/CC-MAIN-2022-33/segments/1659882571198.57/warc/CC-MAIN-20220810161541-20220810191541-00790.warc.gz	541,158,778	10,288	How do you figure out the amplitude of a wave? 2 Asked By: Berniece Kiehn Date created: Wed, Jul 7, 2021 3:00 PM Date updated: Wed, Jul 13, 2022 6:14 AM Content Top best answers to the question «How do you figure out the amplitude of a wave» • Amplitude is generally calculated by looking on a graph of a wave and measuring the height of the wave from the resting position. The amplitude is a measure of the strength or intensity of the wave. For example, when looking at a sound wave, the amplitude will measure the loudness of the sound. FAQ Those who are looking for an answer to the question «How do you figure out the amplitude of a wave?» often ask the following questions: 👋 How do you double the amplitude of a wave? Any wave or short pulse can be thought of as a sum of harmonic waves (Fourier transform). Doubling the height of each point of a pulse, will double the amplitude of each fourier component, this means that also in a pulse the energy will become 4 times stronger. 👋 How do you find the amplitude of a harmonic wave? • For a harmonic wave, the energy amplitude is proportional to the frequency squared. However, the complex exponential formulations of Eq. (91) are very useful and convenient in calculating the time-averaged energy ⟨e⟩, which is calculated by taking the average of Eq. 👋 How do you find the amplitude of a light wave? If you know the intensity, then the amplitude can be found using this formula I=1/2pvwA^2 where p is density, v, w is angular velocity, v is speed of wave. Hence, if you measure the intensity in a a unit area, (W m^-2), you can find the amplitude inversely solving. 👋 How do you find the amplitude of a wave function? • Integration of the square of the wavefunction over the last quarter of the tube yields the final answer. The calculation is simplified by centering our coordinate system on the peak of the wavefunction. where A is the amplitude of the wavefunction and k = 2π / λ is its wavenumber. 👋 How do you find the peak amplitude of a wave? • Where A is the peak amplitude, k = 2π/λ is the wavenumber and ω = 2π f is the angular frequency of the wave. Consider another wave of the same frequency and amplitude but with a different phase travelling to the right. 👋 How do you write amplitude of a wave? 1. amplitude is A = 3. 2. period is 2π/100 = 0.02 π 3. phase shift is C = 0.01 (to the left) 4. vertical shift is D = 0. 👋 How many nodes does the standing wave in figure? This standing wave is called the fundamental frequency, with L = λ 2 L= \dfrac{\lambda}{2} L=2λL, equals, start fraction, lambda, divided by, 2, end fraction, and there are two nodes and one antinode. 👋 How to figure out the frequency of a sine wave? What is the formula for a sine wave? • The Sine wave is the graph that is formed if the function contains a sine function. The General Formula of the Sine wave is: y=AsinB(x-C)+D where x is the angle or theta. 👋 How to figure out the speed of a wave? The speed of a wave can be found using the equation v=λf, or velocity = wavelength x frequency. If an ocean wave has a frequency of 2 hertz and a speed of 4 meters per second, what is its wavelength? Speed = Wavelength x Wave Frequency. 1 other answer the equation for the amplitude of a wave is 1/2 the distance between the highest and lowest place. Your Answer We've handpicked 6 related questions for you, similar to «How do you figure out the amplitude of a wave?» so you can surely find the answer! How to work out the amplitude of a longitudinal wave? In a longitudinal wave, like this video, amplitude is measured by determining how far the molecules of the medium have moved from their normal rest position. The concept of measuring how far molecules move is difficult to measure, so amplitude is usually only discussed in terms of transverse waves. What does the amplitude of a wave tell you? The amplitude of a wave is a measure of the displacement of the wave from its rest position… For example, when looking at a sound wave, the amplitude will measure the loudness of the sound. The energy of the wave also varies in direct proportion to the amplitude of the wave. What happens to the amplitude of a wave as it spreads out? • A vibration of particles in the medium (push or pull). This wave requires particles to collide to transfer energy. Spreads out. Example: Sound gets quieter or light gets dimmer the further you are from the source, decreasing the amplitude as the wave spreads out. The wavelength period and frequency do not change. What wave has the largest amplitude? Gamma rays has the greatest amplitude among all electromagnetic waves. Which wave has the greatest amplitude? Gamma rays has the greatest amplitude among all electromagnetic waves. Which wave has the largest amplitude? Wave amplitude of a transverse wave is the difference in height between the crest and the resting position. The crest is the highest point particles of the medium reach. The higher the crests are, the greater the amplitude of the wave.	1,176	5,029	{"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}	4.125	4	CC-MAIN-2022-33	latest	en	0.91578
https://jp.maplesoft.com/support/help/maple/view.aspx?path=DataSeries%2FDatatype	1,642,482,997,000,000,000	text/html	crawl-data/CC-MAIN-2022-05/segments/1642320300722.91/warc/CC-MAIN-20220118032342-20220118062342-00131.warc.gz	404,609,877	31,741	Datatype - Maple Help DataSeries/Datatype obtain the data type of a DataSeries Calling Sequence Datatype(ds) Parameters ds - a DataSeries object Description • The Datatype command returns the data type of a DataSeries object. • The data type determines the values that can be stored in the data series. This is similar to the datatype option of an rtable. • Trying to set an entry of a DataSeries to a value that is not of the specified data type leads to an error. • The data type can be set using the datatype option in the DataSeries constructor call. • If no data type is specified in the constructor call, Maple uses the data type of the data argument if that is an rtable or DataSeries, or type anything otherwise. • If you want to store floating point data in a DataSeries, it will be advantageous to set the data type to float[8]. This uses less memory than the alternatives, and it can yield speed-ups in computations. • If you want to store true-or-false data in a DataSeries, it will be advantageous to set the data type to truefalse or truefalseFAIL. (FAIL is the third Boolean constant in Maple, signifying unknown or undetermined truth values.) This yields small speed-ups when used in DataSeries indexing or DataFrame indexing. Examples The default data type is anything. > $\mathrm{ds1}≔\mathrm{DataSeries}\left(\left[1,2,3\right]\right)$ ${\mathrm{ds1}}{≔}\left[\begin{array}{cc}{1}& {1}\\ {2}& {2}\\ {3}& {3}\end{array}\right]$ (1) > $\mathrm{Datatype}\left(\mathrm{ds1}\right)$ ${\mathrm{anything}}$ (2) > $\mathrm{v1}≔\mathrm{Vector}\left(\left[2.,3.\right]\right)$ ${\mathrm{v1}}{≔}\left[\begin{array}{c}{2.}\\ {3.}\end{array}\right]$ (3) > $\mathrm{ds2}≔\mathrm{DataSeries}\left(\mathrm{v1}\right)$ ${\mathrm{ds2}}{≔}\left[\begin{array}{cc}{1}& {2.}\\ {2}& {3.}\end{array}\right]$ (4) > $\mathrm{Datatype}\left(\mathrm{ds2}\right)$ ${\mathrm{anything}}$ (5) You can override the default in the DataSeries constructor. > $\mathrm{ds3}≔\mathrm{DataSeries}\left(\mathrm{v1},\mathrm{datatype}=\mathrm{float}\left[8\right]\right)$ ${\mathrm{ds3}}{≔}\left[\begin{array}{cc}{1}& {2.}\\ {2}& {3.}\end{array}\right]$ (6) > $\mathrm{Datatype}\left(\mathrm{ds3}\right)$ ${{\mathrm{float}}}_{{8}}$ (7) Alternatively, you can make sure that the data defining the DataSeries already has a specified data type. > $\mathrm{v2}≔\mathrm{Vector}\left(\left[2.,3.\right],\mathrm{datatype}=\mathrm{float}\left[8\right]\right)$ ${\mathrm{v2}}{≔}\left[\begin{array}{c}{2.}\\ {3.}\end{array}\right]$ (8) > $\mathrm{ds4}≔\mathrm{DataSeries}\left(\mathrm{v2}\right)$ ${\mathrm{ds4}}{≔}\left[\begin{array}{cc}{1}& {2.}\\ {2}& {3.}\end{array}\right]$ (9) > $\mathrm{Datatype}\left(\mathrm{ds4}\right)$ ${{\mathrm{float}}}_{{8}}$ (10) Compatibility • The DataSeries/Datatype command was introduced in Maple 2016.	892	2,851	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 20, "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-2022-05	longest	en	0.481107
https://gpuzzles.com/mind-teasers/math-symbols-teaser/	1,508,640,453,000,000,000	text/html	crawl-data/CC-MAIN-2017-43/segments/1508187825057.91/warc/CC-MAIN-20171022022540-20171022042540-00157.warc.gz	713,263,689	11,244	• Views : 70k+ • Sol Viewed : 20k+ # Mind Teasers : Math Symbols Teaser Difficulty Popularity Given with the numbers - 2, 3, 4 and 5, you have to make an equation that is mathematically correct. The challenge is that you can only use two signs i.e. + and =. Also, you can't repeat a number or sign. How will you do it? Discussion Suggestions • Views : 80k+ • Sol Viewed : 20k+ # Mind Teasers : Logic Math Problem Difficulty Popularity David and Albert are playing a game. There are digits from 1 to 9. The catch is that each one of them has to cut one digit and add it to his respective sum. The one who is able to obtain a sum of exact 15 will win the game? You are a friend of David. Do you suggest him to play first or second? • Views : 40k+ • Sol Viewed : 10k+ # Mind Teasers : Connect Nodes Puzzle Difficulty Popularity Can you connect the nodes between them based on the value of the node? Note: Inside the first node there is a value of 1 which means that this node is connected to just one node • Views : 70k+ • Sol Viewed : 20k+ # Mind Teasers : Picture Brain Teaser Difficulty Popularity You can see the figure or draw one of your own. The scenario is as shown. There are three houses represented with the triangle over the square. There are three utilities: W, G and E representing water, gas and electricity respectively. Can you draw a line and get each utility into every house (9) total lines without ever crossing any line? • Views : 70k+ • Sol Viewed : 20k+ # Mind Teasers : Unlock The Distance Puzzle Difficulty Popularity Distances from you to Man united is written below. CHELSEA and ARSENAL are 700 kms away SPURS 1800 kms away WOLVES 200 kms away Based on the system , How far should it be to MANCITY ? • Views : 40k+ • Sol Viewed : 10k+ # Mind Teasers : What Do you See - Brick Optical Illusion Riddle Difficulty Popularity What except brick can you see in the picture below? • Views : 70k+ • Sol Viewed : 20k+ # Mind Teasers : Eden Hazard And The Two Masked People Puzzle Difficulty Popularity Eden Hazard the famous Chelsea footballer leave home and then he makes three left turns and returns home where he found 2 people wearing the mask. Can you Identify the two masked people? • Views : 80k+ • Sol Viewed : 20k+ # Mind Teasers : Box Ball Logic Problem Difficulty Popularity There are three bags.The first bag has two blue rocks. The second bag has two red rocks. The third bag has a blue and a red rock. All bags are labeled but all labels are wrong.You are allowed to open one bag, pick one rock at random, see its color and put it back into the bag, without seeing the color of the other rock. How many such operations are necessary to correctly label the bags ? • Views : 80k+ • Sol Viewed : 20k+ # Mind Teasers : Two Men One Question Puzzle Difficulty Popularity Imagine that you are travelling to a village. You happen to reach a point in the road where there is a fork. There are two ways that you can go into but only one amongst them is correct and leads to the village. You happen to see two men standing on the fork and you can ask them for the direction. To your bad luck, one amongst the two men always lies and the other one always says the truth. But you do not know who is a liar and who is not. At that point of the situation you are allowed to ask only one question to any one of the men standing there. • Views : 50k+ • Sol Viewed : 20k+ # Mind Teasers : Logic Number Sequence Puzzle Difficulty Popularity Solve this logic number sequence puzzle by the correct digit 8080 = 6 1357 = 0 2022 = 1 1999 = 3 6666 = ? • Views : 80k+ • Sol Viewed : 20k+ # Mind Teasers : Smart Birbal Riddle Difficulty Popularity Akbar called Birbal and asked him to draw a line on the floor. He asked Birbal to make that line smaller without erasing it. Birbal smiled and did it before Akbar could blink his eyes. How did he managed to do it? ### Latest Puzzles 21 October Choose the correct shadow of the bird?... 20 October ##### Three Brothers Age Puzzle Three brothers Kylian Thorgan Eden lives... 19 October ##### Never See What Am I I am always ahead of you. You want me to... 18 October ##### Find Airplane Puzzle Can you find the airplane in the puzzle ... 17 October There is something that Adam and Eve do ... 16 October ##### Science - Physics Brain Teaser We have two identical balls in terms of ... 15 October ##### Nonsense Brain Teaser What is Lionel Messi(Soccer Player) favo...	1,131	4,484	{"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-2017-43	latest	en	0.92733
https://abc-pizza-cooking.com/qa/is-20-60-considered-legally-blind.html	1,606,314,512,000,000,000	text/html	crawl-data/CC-MAIN-2020-50/segments/1606141182794.28/warc/CC-MAIN-20201125125427-20201125155427-00406.warc.gz	177,360,247	8,307	# Is 20 60 Considered Legally Blind? ## What does 20/200 eyesight look like? Having a 20/200 visual acuity means the smallest letters that you’ll identify from the chart by standing 20 feet away from it will be equal to the size of the smallest letters a person with “normal vision” would be able to identify at a distance of 200 feet from the chart.. ## What does it mean to have 20 60 Vision? 20/20 vision describes visual acuity, or the sharpness of vision at 20 feet from an object. Having 20/60 vision means that you must be at 20 feet to see what a person with normal vision can see at 60 feet. ## Is 0.75 eye prescription bad? With -0.50 and -0.75, you should be able to pass the driver test. You will pass the driver even with -1.00, so you shouldn’t worry. Small refractive errors like -0.25 and -1.00 are negligible, even the distance vision isn’t blurry enough for you to need glasses. Most people will need them, however, at -1.25 or -1.50. Sph (Sphere) If you have a minus number, like -2.75, it means you’re short-sighted and find it more difficult to focus on distant objects. A plus number indicates long-sightedness, so objects up close appear more blurred or close vision is more tiring on the eyes. ## What does a person with 20 50 Vision See? A person with 20/50 vision can clearly see something 20 feet away that a person with normal vision can see clearly from a distance of 50 feet. Bad distance vision was considered “improved” if corrections boosted visual acuity to 20/40 or better. ## What is the legally blind limit? 20/200If a visual impairment limits vision to 20/200, or one-tenth of normal vision, a person is considered legally blind. ## What prescription strength is legally blind? Simply put, if your prescription is -2.5 or lower, this means that you are legally blind. Visual acuity of -2.5 is equivalent to 20/200 vision. Visual acuity of -3.0, for instance, means that you have 20/250 or 20/300 vision. ## Can you drive with 20 50 Vision? A person must have a minimum corrected (with glasses or contacts) visual acuity of 20/50 to qualify for a restricted license (drive with corrective lenses). Drivers with visual acuity of 20/60 are restricted to daytime driving only. … A person with one functional eye must have a field vision of 105 degrees. ## What’s the worst eyesight number? There’s blind and legally blind which are two different things. Legally blind in the US is best corrected vision (with glasses or contacts) that is 20/200 or worse OR visual field limited to 20 degrees (meaning loss of peripheral vision). Some cannot see light. ## How bad does your eyesight have to be to not drive? Minimum visual acuity standard Under California law, a driver must have a minimum visual acuity of at least 20/200 in one eye, with or without correction. Meeting the minimum visual acuity standard does not mean a driver will be approved to drive in California. ## What is considered bad vision? Few people are totally without sight. … 20/70 to 20/160, this is considered moderate visual impairment, or moderate low vision. 20/200 or worse, this is considered severe visual impairment, or severe low vision. 20/500 to 20/1000, this is considered profound visual impairment or profound low vision. ## Is 20 80 considered legally blind? Putting This Into Perspective… With 20/40 vision, a person can pass a driver’s license test. With 20/80 vision, a person still might be able to read a large newspaper headline. With 20/200 vision, a person is considered legally blind. ## What percentage of eyesight is legally blind? Someone who is legally blind has a corrected vision of 20/200 in their best seeing eye. ## What vision do I have out of 20? What is 20/20 vision? 20/20 vision means you have normal visual acuity (or sharpness and clarity) at a distance of 20 feet away. It doesn’t mean perfect vision, though. It only means you can see clearly at a distance. ## What is a 20 30 Vision? This means when you are 20 feet away from an object, you can comfortably see details that most people with normal vision can also see at 20 feet distance. If you have 20/30 vision, that means what you see comfortably at 20 feet, can be seen by a person with “normal” vision at 30 feet.	1,026	4,243	{"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-2020-50	latest	en	0.921287
http://homepages.inf.ed.ac.uk/stg/NOTES/node73.html	1,596,730,508,000,000,000	text/html	crawl-data/CC-MAIN-2020-34/segments/1596439736972.79/warc/CC-MAIN-20200806151047-20200806181047-00543.warc.gz	45,719,118	3,202	NEXT · UP · PREVIOUS · CONTENTS · INDEX # Delaying evaluation One form of delayed evaluation which we have already seen is conditional evaluation. In an if .. then .. else .. expression only two of the three sub-expressions are evaluated. The boolean expression will always be evaluated and then, depending on the outcome, one of the other sub-expressions will be evaluated. The effect of a conditional expression would be different if all three of the sub-expressions were always evaluated. This explains why there is no cond function [of type (bool * 'a * 'a) -> 'a] in Standard ML. Similarly, a recursive computation sometimes depends upon the outcome of evaluating a boolean expression [as with the takewhile function []]. In cases such as these, the evaluation of expressions can be delayed by placing them in the body of a function. By packaging up expressions in this way, we can program in a `non-strict' way in Standard ML and we can describe recursive computations and we can define infinite objects such as the list of all natural numbers or the list of all primes. Consider the following function. ```fun FIX f x = f (FIX f) x; ``` Exercise What is the type of FIX? The purpose of the FIX function is to compute fixed points of other functions. [Meaning: x is a fixed point of the function f if f (x) = x.] How is this function used? Consider the facbody function below. No derived forms are used here in order to make explicit that this is not a recursive function [not a val rec .. ]. ```val facbody = fn f => fn 0 => 1 \| x => x f (x - 1);``` If this function were to be given the factorial function as the argument f then it would produce a function as a result which was indistinguishable from the factorial function. That is, the following equivalence would hold. fac = facbody(fac) But this is just the equivalence we would expect to hold for a fixed point. What would then be the result if we defined the fac function as shown below. `val fac = FIX (facbody);` The fac function will then compute the factorials of the integers which it is given as its argument. Notice that neither the declaration of fac nor the declaration of facbody were recursive declarations; of the three functions which were used only FIX is a recursive function. This effect is not specific to computing factorials, it would work with any recursive function. The functions below use FIX to define the usual map function for lists. ```val mapbody = fn m => fn f => fn [] => [] \| h::t => f h :: m f t; fun map f l = (FIX mapbody) f l;``` This method of defining functions succeeds because the FIX function delays a part of the computation. In its definition the parenthesised sub-expression FIX f which appears on the right-hand side is an unevaluated function term [sometimes called a suspension] equivalent to fn x => FIX f x. Crucially, this is the role of x in the definition; to delay evaluation. Without it the function would compute forever. (* Always diverges when used *) `fun FIX' f = f (FIX' f);` Exercise What is the type of FIX'? This version of the function makes it much easier to see that the fixed point equation is satisfied--that f (FIX' f) = FIX' f--and in a lazy variant of the Standard ML language the FIX' function would be perfectly acceptable and would operate just as FIX does. NEXT · UP · PREVIOUS · CONTENTS · INDEX	773	3,369	{"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}	3.5625	4	CC-MAIN-2020-34	latest	en	0.910179
https://it.mathworks.com/matlabcentral/answers/1835973-problem-with-threshold-in-if-statement	1,722,988,551,000,000,000	text/html	crawl-data/CC-MAIN-2024-33/segments/1722640523737.31/warc/CC-MAIN-20240806224232-20240807014232-00051.warc.gz	260,703,448	29,146	# Problem with threshold in if statement 1 visualizzazione (ultimi 30 giorni) Siegmund Nuyts il 26 Ott 2022 Commentato: Siegmund Nuyts il 2 Nov 2022 My goal is to determine the difference between troughs and peaks, and select the troughs/peaks with a difference bigger than 35. Sometimes there is no difference bigger than 35. So now I'm writing an if statement that if there is no difference bigger than 35, that it can just be 0. The issue that I have is that there are multiple values varying below and above the threshold so it's not correctly identifying the threshold. It should select the first trough/peak with a difference bigger than 35 and if there is no difference bigger than 35, then it should just be 0. Here is the code that I have: Ps = P.Ps; threshold = 35; [mins, min_locs] = findpeaks(-Ps); [maxs, max_locs] = findpeaks(Ps); peaks = [maxs max_locs]; troughs = [mins min_locs]; sp = size (peaks); st = size (troughs); s = max(sp(1), st(1)); dif = [[peaks;zeros(abs([s 0] - sp))],[troughs;zeros(abs([s, 0]-st))]]; difs = [dif (dif(:,1)+dif(:,3))]; if difs(difs(:,5)>threshold,:); [idx, ~] = find(difs(:,5)>threshold); difs = difs(unique(idx),:); thresh = difs(1,4); else thresh = 0 end thresh = 0 ##### 3 CommentiMostra 1 commento meno recenteNascondi 1 commento meno recente Jeffrey Clark il 27 Ott 2022 @Siegmund Nuyts, hard to say from what you gave but please note that the conditional if difs(difs(:,5)>threshold,:) will be true as long as none of the difs(difs(:,5)>threshold,:) are zero. With floating point data it is unlikely that any column would be zero when column 5>threshold so the if may always be executing. Did tou intend if difs(:,5)>threshold which would execute the if part when any row with column 5>threshold was found? Siegmund Nuyts il 27 Ott 2022 The if statement should look for any data in column 5 that is above 35. If none of the data is above 35, then the result can be 0. Accedi per commentare. ### Risposta accettata Jeffrey Clark il 29 Ott 2022 Modificato: Jeffrey Clark il 29 Ott 2022 @Siegmund Nuyts, since you are negating the values input to Find local maxima - MATLAB findpeaks (mathworks.com) when looking for your valleys the mins returned will be negated values that you must then negate when used. Also since you are only interested in the first difference of the find indexed difs you should just have find return the first and eliminate some code. Along with my first comment the code would change to: Ps = P.Ps; threshold = 35; [mins, min_locs] = findpeaks(-Ps); [maxs, max_locs] = findpeaks(Ps); peaks = [maxs max_locs]; troughs = [-mins min_locs]; %negate values to match -Ps use sp = size (peaks); st = size (troughs); s = max(sp(1), st(1)); dif = [[peaks;zeros(abs([s 0] - sp))],[troughs;zeros(abs([s, 0]-st))]]; difs = [dif (dif(:,1)+dif(:,3))]; idx = find(difs(:,5)>threshold,1); %only need the first if ~isempty(idx) %saves doing the find twice thresh = difs(idx,4); else thresh = 0 end ##### 1 CommentoMostra -1 commenti meno recentiNascondi -1 commenti meno recenti Siegmund Nuyts il 2 Nov 2022 Thanks! That worked perfectly Accedi per commentare. ### Categorie Scopri di più su Descriptive Statistics in Help Center e File Exchange R2020b ### Community Treasure Hunt Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting! Translated by	976	3,362	{"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-2024-33	latest	en	0.787727
https://gmatclub.com/forum/abc-is-a-triangle-with-area-1-af-ab-3-be-bc-3-and-ed-101041.html?kudos=1	1,579,845,203,000,000,000	text/html	crawl-data/CC-MAIN-2020-05/segments/1579250615407.46/warc/CC-MAIN-20200124040939-20200124065939-00212.warc.gz	455,150,510	152,675	GMAT Question of the Day: Daily via email \| Daily via Instagram New to GMAT Club? Watch this Video It is currently 23 Jan 2020, 22:51 ### 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 # ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = Author Message TAGS: ### Hide Tags Senior Manager Joined: 02 Oct 2009 Posts: 355 GMAT 1: 530 Q47 V17 GMAT 2: 710 Q50 V36 ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = [#permalink] ### Show Tags Updated on: 09 Jul 2013, 06:50 2 12 00:00 Difficulty: 95% (hard) Question Stats: 43% (02:10) correct 57% (02:42) wrong based on 176 sessions ### HideShow timer Statistics ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = FD. Find the area of the shaded figure. Attachment: 1.JPG [ 5.35 KiB \| Viewed 14501 times ] A. 1/3 B. 13/16 C. 5/9 D. 1/2 Originally posted by RaviChandra on 14 Sep 2010, 23:58. Last edited by Bunuel on 09 Jul 2013, 06:50, edited 1 time in total. Renamed the topic and edited the question. Retired Moderator Joined: 02 Sep 2010 Posts: 714 Location: London ### Show Tags 15 Sep 2010, 02:03 2 RaviChandra wrote: In triangle ABC, D and E are points on AC and AB such DE \|\| BC and length of DE is one-third of BC. If the area of triangle ABC is 216 square units, find the area of the shaded triangle. a. 12 b. 18 c. 24 d. 16 Attachment: 2.PNG Note that AED is similar to ABC with each side as 1/3rd of the original => Area(AED) = 1/9 * Area(ABC) =24 Area(ABD) = Area(ACE) = 1/3 * Area(ABC) = 72 [same height, 1/3rd base] Area(ABD) = Area(ACE) => Area(ABD) - Area(AEDF) = Area(ACE) - Area(AEDF) => Area(BEF) = Area(CDF) = x (say) Finally note that DEF is similar to BFC with one side in the ratio of 1:3 Thus area(DEF) = 1/9 * area(BFC) = y (say) Area(EDC) = Area(EDF)+Area(DFC) = x + y ALSO Area(EDC) = Area(AEC) - Area(AED) =72 - 24 = 48 So x+y = 48 Area(BEDC) = Area(BEF) + Area(CDF) + Area(EDF) + Area(BFC) = x+x+y+9y ALSO Area(BEDC) = Area(ABC)-Area(AED)=216-24=192 So x+5y=96 Subtracting the 2 equations 4y=48 y=12 Hence, Area(DEF)=12 _________________ Senior Manager Joined: 02 Oct 2009 Posts: 355 GMAT 1: 530 Q47 V17 GMAT 2: 710 Q50 V36 ### Show Tags 14 Sep 2010, 23:59 1 In triangle ABC, D and E are points on AC and AB such DE \|\| BC and length of DE is one-third of BC. If the area of triangle ABC is 216 square units, find the area of the shaded triangle. a. 12 b. 18 c. 24 d. 16 Attachment: 2.PNG [ 2.36 KiB \| Viewed 14428 times ] Math Expert Joined: 02 Sep 2009 Posts: 60627 ### Show Tags 15 Sep 2010, 00:54 1 RaviChandra wrote: ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = FD. Find the area of the shaded figure. Attachment: The attachment 1.JPG is no longer available a. 1/3 b. 13/16 c. 5/9 d. 1/2 Rotate the triangle so that CA to be the base. Now, triangle CDA has the same base as CBA and half of its height ("read" the diagram for explanation), which means that area of CDA will be half of the area of CBA, so 1/2. Attachment: 7.PNG [ 5.36 KiB \| Viewed 14386 times ] RaviChandra these are not GMAT questions, so I wouldn't worry about them too much and definitely wouldn't spend much time on them. _________________ Manager Joined: 24 Jul 2011 Posts: 162 Location: India GMAT 1: 570 Q50 V19 GMAT 2: 650 Q49 V28 GMAT 3: 690 Q50 V34 WE: Information Technology (Investment Banking) Re: ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = [#permalink] ### Show Tags 28 Sep 2015, 06:38 1 Whoa!!! A tough one A small trick that helped me to solve it in 1:37 Imagine that the triangle ABC is an isosceles triangle with AB = BC. (Reason: All the mentioned conditions are satisfied so area ratio should also hold for Isosceles triangle) Redraw it in your notepad, you will find symmetry. D is just in middle of AF and DE. You will figure out that D is a mid-point so its height should be half. Now if height of triangle is reduced to half, area of triangle will also reduce to half of its original value (Area = 0.5* base * height). Hence D. _________________ Middle of nowhere! Intern Joined: 07 Sep 2010 Posts: 9 Location: Doha, Qatar Schools: INSEAD, Princeton, HKUST, Oxford, ISB, SP Jain WE 1: 5.5 ### Show Tags 15 Sep 2010, 01:39 Wht is answer of the 2nd question ??? 24 ? Intern Joined: 07 Sep 2010 Posts: 9 Location: Doha, Qatar Schools: INSEAD, Princeton, HKUST, Oxford, ISB, SP Jain WE 1: 5.5 ### Show Tags 15 Sep 2010, 05:02 Wow... thks a ton. I had guessed it to be 24 - Thinking T. EFD should be of area 1/9th of main traingle. If I knew T. AED = 1/9 T. ABC, 12 would have been my guess, as it (T. EFD) looks half the size of T. AED Non-Human User Joined: 09 Sep 2013 Posts: 14004 Re: ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = [#permalink] ### Show Tags 08 Jun 2018, 00:04 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: ABC is a triangle with area 1. AF = AB/3, BE = BC/3 and ED = [#permalink] 08 Jun 2018, 00:04 Display posts from previous: Sort by	1,934	5,804	{"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-2020-05	latest	en	0.896198
https://math.stackexchange.com/questions/2559556/equation-of-a-curve-along-the-surface-of-a-cylinder	1,566,703,750,000,000,000	text/html	crawl-data/CC-MAIN-2019-35/segments/1566027322170.99/warc/CC-MAIN-20190825021120-20190825043120-00148.warc.gz	553,702,963	30,460	# Equation of a Curve Along the Surface of a Cylinder? I find myself with a cylinder of radius r, positioned along the x-axis, with equation y^2 + z^2 = r^2. If I have two arbitrary points which lie on the surface of such a cylinder, is there a"two-point formula" which would give me some equation of a curve (which also curves along the surface of the cylinder) connecting the two points? I envision an equation similar to the two-point equation of a line in 2D or 3D, but I do not know if such an equation is possible or makes sense. My use case is wanting to render a curve connecting two points laying on such a cylinder, in a program I am writing in Python. I would like to render this curve but also understand the underlying mathematics. • There are infinitely many of such curves. Are you looking for one with the shortest path? – Dylan Dec 10 '17 at 5:38 • Hi, thank you for replying. I am looking for the shortest curve that connects the two points along the surface of the cylinder. If an insect were walking from one point on the surface of a cylinder to another point on the surface taking the shortest path, is there an equation that defines that segment? – kreeser1 Dec 10 '17 at 5:42 You can convert the problem into cylindrical coordinates $(x,y,z)\mapsto (x,\theta,r)$ $$x = x, \ y = r\cos\theta, \ z = r\sin\theta$$ The constant surface $r = r_0$ in this coordinates system is somewhat equivalent to a "plane" in traditional Cartesian, in that any point on the surface is only dependent on two coordinates $(x,\theta)$ Suppose our two points are described by $(x_1,\theta_1)$ and $(x_2,\theta_2)$, then the shortest path between them is the linear parametrization (equivalent to defining a line in Cartesian space) $$x(t) = x_1(1-t) + x_2t$$ $$\theta(t) = \theta_1(1-t) + \theta_2t$$ where the angles are picked so that $\|\theta_2-\theta_1\|\le \pi$ • Thank you for your help Dylan, I appreciate the insight. – kreeser1 Dec 10 '17 at 7:13	512	1,968	{"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}	3.890625	4	CC-MAIN-2019-35	latest	en	0.932862
http://slideplayer.com/slide/4393970/	1,519,329,340,000,000,000	text/html	crawl-data/CC-MAIN-2018-09/segments/1518891814249.56/warc/CC-MAIN-20180222180516-20180222200516-00559.warc.gz	310,355,735	20,489	# Katie Dagon and Diane Lambert CT DEP Recycling Office Preliminary Results & Findings. ## Presentation on theme: "Katie Dagon and Diane Lambert CT DEP Recycling Office Preliminary Results & Findings."— Presentation transcript: Katie Dagon and Diane Lambert CT DEP Recycling Office Preliminary Results & Findings  Target audience – municipal officials/employees ◦ How does your community manage disposal of used mattresses?  Preliminary data compiled from responses submitted March 23, 2011 to April 6, 2011  90 CT municipalities responded so far ◦ 53% of the state ◦ Good cross-section of small towns, suburban communities and larger cities 2 Very little, if any, residential recycling of mattresses (those that come through municipal facilities). 3 4  Survey Question: Give an estimate, or known number, of mattresses disposed every year at: a) Transfer Station b) Curbside  Analyzed by matching yearly totals with town population to generate per capita collection rates.  Preliminary data indicates the following: State Population (July 2009)3,518,288 Average Per Capita Rate (mattresses/person/year) 0.025 Total Collected Per Year Statewide (residential and through municipality) 88,050* 5  Approx. 10% of the population buys a new mattress every year.  Assumption is that this is equal to the number of mattresses that are to be disposed.  However, need to factor in that about 50% of those mattresses are given as hand-me-downs, donated to a non-profit shelter or illegally dumped, therefore never making it into the disposal stream. Population of CT = 3,518,288 (July 2009) 3,518,288 x 10% = est. 352,000 mattresses 352,000 mattresses x 50% = est. 176,000 mattresses Est. 176,000 mattresses available for recycling, every year Photo: Ohio Mattress Recovery and Recycling 6  “Cost of time & equipment to pick up illegally dumped materials and dispose of properly, not to mention lost dumping fees.”  “It causes blight, once residents see a mattress lying on the side of the road they start dumping other bulky items there.”  “It requires staff from public works to collect them and then transfer them to our transfer station. This time erodes into other projects.”  “As the economy flounders and disposal costs to individuals rise I fully expect that illegal dumping will escalate.” Photo: The Macarthur Chronicle 7  Product Stewardship ◦ “It would be nice if the manufacturers had a system of recycling the old ones.” ◦ “Our town would like to see a mattress take back program in place by all appropriate retailers/ manufacturers, without undue expense placed upon the resident.”  Other Concerns ◦ “[Mattresses] are problematic when processing them with landfill equipment, so we would prefer there to be alternative options.” ◦ “During evictions in our city, workers do not want to unload mattresses for health concerns and recent bed bug infestations.” ◦ “Residents are not happy about paying a separate fee for the disposal of mattresses & box springs.” 8 Download ppt "Katie Dagon and Diane Lambert CT DEP Recycling Office Preliminary Results & Findings." Similar presentations	726	3,114	{"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-2018-09	latest	en	0.905434
http://mathhelpforum.com/calculus/227246-how-solve-differential-equation-initial-conditions.html	1,481,273,382,000,000,000	text/html	crawl-data/CC-MAIN-2016-50/segments/1480698542687.37/warc/CC-MAIN-20161202170902-00190-ip-10-31-129-80.ec2.internal.warc.gz	178,043,908	9,954	# Thread: How to solve a a differential equation with initial conditions? 1. ## How to solve a a differential equation with initial conditions? I'm having trouble with this: Is my answer right? If not, which one works? :/ 2. ## Re: How to solve a a differential equation with initial conditions? This is correct. How did you solve it? All you need to do is integrate the original expression once. Solve for the constant using the initial condition of $y'$ Then integrate again and solve for the constant using the initial condition of $y$	117	544	{"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}	2.65625	3	CC-MAIN-2016-50	longest	en	0.942221
http://timng.ca/blog/2013/04/	1,521,810,016,000,000,000	text/html	crawl-data/CC-MAIN-2018-13/segments/1521257648226.72/warc/CC-MAIN-20180323122312-20180323142312-00582.warc.gz	297,708,883	14,601	# Challenges in Combinatorics on Words (Day 5) My knees were killing me, but that wouldn’t stop me from going to a talk that relates algebra and automata theory! • Kiran Kedlaya gave two talks on Christol’s theorem. Christol’s theorem says that a formal Laurent series is algebraic over the field $\mathbb F_q(t)$, where $q$ is a prime power, if and only if it is automatic. The second of his two talks was about a theorem of his which generalized Christol’s theorem to apply for general power series. • Eric Rowland gave a neat talk on characterizing $p$-automatic sequences using 1-dimensional cellular automata. There’s actually a lot more algebra to cellular automata than I would’ve expected was possible (and even some connections to Kedlaya’s talk on Christol’s theorem). Then again, I don’t really know much about cellular automata other than Conway’s Game of Life. So even though I didn’t really contribute at the workshop and I was kind of wandering around as a lone graduate student, it was a really interesting experience. At the very least, I got to meet some interesting people working on interesting things and I have a pile of interesting things to look up over the summer before I head to Kingston and ramp up into hardcore math research mode. And now, some miscellany. • Lunch notes: tried Mother’s Dumplings again and opted for a double order of dumplings this time around. I went with boiled again, because I couldn’t justify paying a bit more to get a bit less, even if the steamed dumplings were supposed to be amazing. Maybe that’ll happen if I’m there with other people in the future. • Commuting notes: I got a ride to and from Fields, since it probably wouldn’t be a good idea to be on the TTC for long periods of time with my knees in their current state. The morning trip involved going across Eglinton, which is an absurdly wide road and I don’t really know why people are mad about LRTs on that road when it’d essentially be replacing a lightly used HOV lane (or maybe even not). Once we hit the DVP, traffic got heavy and Bloor was pretty bad. We went down Sherbourne, where I saw the Minnan-Wong bike lanes and we continued on Carlton and College. • The evening commute was also interesting. My dad usually takes Lake Shore through to The Beaches and up Kingston, but apparently, there’s some construction going on there, so we went along Gerrard through the east end of old Toronto instead. We ended up cutting across to Southwest Scarborough on Danforth and back up to STC to pick up a new phone. This was a much better route than the one proposed by my dad, who wanted to go up to the DVP. • Replacement phone notes: Got a new phone and restoring service was pretty easy. The tough part was restoring from iCloud backups since, Apple, in their sometimes questionable wisdom, decided that you could only restore iCloud backups when you first set up your phone, which the Koodo lady zipped past while we were at the booth. So I had to reset the iPhone, which was baffling, since it required downloading the latest iOS update, which I’m pretty sure I’d already downloaded. But after all of that, my phone was in pretty much the same state as I had it in yesterday. # Challenges in Combinatorics on Words (Day 4): Bus theft edition So today was an adventure for reasons unrelated to exciting developments in combinatorics on words. • More talks and pretty proof heavy, which I thought I’d enjoy, but for someone who’s not in the field, it was kind of tedious. It was interesting to see that conjectures do get proven, I guess. • Theoreticians in CS love complexity measures, so we had two today! Antonio Restivo defined a complexity measure based on periodicity and Jörg Endrullis talked about comparing two different infinite words by using transducers. The transducer thing was pretty interesting because it’s more automata stuff and because there are so many natural questions that arise that haven’t been worked on very much yet. • Also, problems were getting solved during the workshop. Steffen Kopecki mentioned that him and others had solved some cases of Thomas Stoll’s problem, which asked if there are infinitely many odd $n$ such that $s_2(n^2) = s_2(n) = k$, where $s_2(n)$ is the sum of binary digits of $n$. • I finally got an experience of stereotypical Malvern life, in which my phone got stolen on the bus right as the hooligans were leaving the bus. I chased them down and I guess I was faster than I looked because they looked back and went “oh shit” and one of them decided they needed to stop me so they pushed me. • I chased them a bit longer but stopped because I was feeling tired and I realized my knee was actually bleeding really badly, which one guy who was walking home pointed out. That guy was good people and let me into his home to treat my wounds, provided wifi to see if I could track my phone down, and a phone for contacting people. • My dad picked me up a bit later and we decided the cut on the knee was pretty nasty so we went over to the hospital, which is my first experience with the Canadian healthcare system after being politically aware. Since my injuries weren’t that bad, I started keeping track of the dreaded wait times. It took about an hour before the doctor saw me and half an hour to treat and get stitches and maybe another half an hour for followup with cleaning and stuff, so it took almost two hours on the dot. That seemed reasonable but maybe I’ve been socially engineered by the communism. Also, didn’t pay anything. # Challenges in Combinatorics on Words (Day 3) A short day today, with interested persons off to a visit at the ROM. • Now that open problem presentations are over, it’s mostly just talks and problem solving time. I don’t know if it was intentional, but today’s talks (other than the plenary talk) dealt mostly with algorithmic aspects of strings, which aren’t really my thing. • There was one talk which was particularly interesting, which was Florin Manea’s talk on finding hidden repetitions, which introduced the idea and motivation behind “hidden” repetitions. We want to check for repetitions of a particular factor $x$ or $f(x)$, where $f$ is an involutive (anti-)morphism. This problem actually comes out of the DNA setting, where words are taken over $\{A,C,G,T\}$ and taking the Watson-Crick complement of a word is the involutive antimorphism we’re interested in. • Jason Bell gave two plenary talks, one yesterday and one today, on algebraic aspects of $k$-automatic sequences. I’d read about $k$-regular sequences before out of interest but didn’t really retain much of it and I’m glad that I got a chance to have someone actually explain how to derive them from the idea of $k$-automatic sequences and also what the $k$-kernel is. • For lunch, it was raining and I didn’t feel like walking all the way down Spadina to King’s Noodle so I decided to try Kom Jug Yuen. It was more expensive and not as great as I was expecting. I’ll just walk to King’s or Gold Stone again next time. • The Fields Institute keeps all of its mathematicians and visiting mathematicians very well caffeinated and fed throughout the day. I think they have a scheduled coffee break at 3pm-ish because a bunch of people that I didn’t recognize were always around the coffees and foods and talking about math that I didn’t recognize. For coffee, they’ve usually got some combination of Starbucks and Timothy’s. For food, they have a wide selection of fruits and cakes. For breakfast, they have a platter of baked goods. I have also seen a platter of pita wedges and some kind of nice bread with various delicious dips. # Challenges in Combinatorics on Words (Day 2) More open problems and talks! • There were two talks and a bunch of open problems by Aleksi Saarela and Juhani Karhumäki on $k$-abelian equivalence. So you have your alphabet $\Sigma = \{a_1,…,a_m\}$ and two words $u,v \in \Sigma^*$ and $u = v$ if they’re the same, which is obvious. We have this notion of abelian equivalence, where we have $u \equiv v$ if $\|u\|_a = \|v\|_a$ for every $a \in \Sigma$. That is, $u$ and $v$ have the same number of each letter ($aaabba$ and $ababaa$ are abelian equivalent since they both have 4 $a$s and 2 $b$s). We generalize abelian equivalence to $k$-abelian equivalence by saying that $u \equiv_k v$ if $\|u\|_x = \|v\|_x$ for every factor $x$ of length up to $k$. A lot of the problems that were posed were questions of how to extend properties that we know for the normal case and the abelian case to this new $k$-abelian setting. • The room that we’re in at the Fields Institute has a neat projector setup, where it uses two screens. The right screen displays whatever is currently displayed on the computer, while the left screen displays what was previously the current screen. This is really useful, because speakers tend to go through their slide decks a lot faster than I can write and often refer to definitions and theorems stated on the previous slide. However, the system has an interesting quirk: it somehow detects when the screen changes, which works for most presentations, since they’re static slides, but there was one presentation where the speaker had a slide with an animated gif or something on it and the left screen kept updating. • There was a problem from Štepán Starosta that dealt with extending things we know about palindromes to generalizations of palindromes. So instead of considering the mirror or reverse operation, what you’d do is consider a finite group of involutive morphisms and antimorphisms (an involutive function $\Theta$ has the property that $\Theta^2$ is the identity function). • I met a prof who happened to do his undergrad at Waterloo and is currently at a university overseas. We had a nice chat about various flavours of CS double majors and students chasing trends to make monies (as it turns out, CS/C&O wasn’t always popular). • I think I can articulate now why I feel useless in the problem solving sessions. While I know a bunch of results and definitions, combinatorics on words really is a pretty different field from automata theory or formal languages. So, since the basic “language” of the two fields is the same, if someone walked me through a proof or something, I’d be able to follow it. But when it comes to working on problems, even though the two are related, there’s an intuition to these kinds of problems that I haven’t developed yet nor do I really have a feel for how results are connected or what certain properties might imply. # Challenges in Combinatorics on Words (Day 1) Workshop blogging! Very exciting, since I’ll try to reconstruct some highlights from my awful note-taking for each day. • One of the neat things about this is that unlike a “real” conference, there aren’t many results presented. Instead, the focus is on open problems and working on those problems. Essentially, what you have is very smart people coming up and talking about a problem that they had trouble solving and all of the things they tried before they got frustrated and gave up or something. • Luca Zamboni presented an open problem involving factors of an aperiodic infinite word and palindromes. An interesting tidbit was when he described how to use palindromes to describe a word. Basically, you say that certain positions of a word are palindromes and you try and fill in those spots with letters. So the question that comes up is trying to figure out what is the fewest number of palindromes that’s necessary to describe a particular word. • Eric Rowland talked about $p$-automatic sequences and deriving an automaton from some polynomial which describes a $p$-automatic sequence. We know how to get the polynomial from an automaton, but coming up with an efficient algorithm for the other direction is tricky. • Neil Sloane gave a neat talk about curling numbers. If we have a word $S = XYYYY \cdots Y = XY^k$ with factors $X$ and $Y$ for some finite $k$, then the curling number of $S$ is $k$. We can define a sequence where the $n$th term of the sequence is the curling number of the previous $n-1$ terms. There are a bunch of interesting conjectures that arise from this sort of thing. • Also, he really likes sequences, which I guess is what you’d expect from the guy who started the Online Encyclopedia of Integer Sequences. I was in his group for dinner and he spent much of the time introducing various sequences to us and we spent a lot of it playing around with them. • I was pretty much useless during open problem solving sessions because of a number of reasons (tiredness, lack of experience in the field and problems, overheating from sitting in the sun). But, I did watch a group work on a problem having to do with unbordered words and factors and it was nice knowing that a bunch of international experts worked on problems in much of the same way I do: by writing stuff on the board and staring at it for a while. # How Toronto’s War on the Church™ ended up going I should start by noting that I’m by no means an expert on planning or urbanism at all and I’ve only been following this issue whenever it’s popped up. I’ve tried to go through whatever I can of the respective documents and files, but there’s only so much I can understand as an amateur. Basically, the best I can do is read and try to follow what happens at council so that’s what I’ll be focusing on. So a few months ago, I noticed this thing scary graphic being passed along on Facebook about how Toronto was declaring war on the church or some such thing. Basically the war was conducted on two fronts: 1. The harmonized zoning bylaw 2. The Toronto District School Board raising rents on religious groups by some inordinate amount I’ll be focusing on the harmonized zoning bylaw. First, a bit of history is necessary to put everything in context. As you may or may not remember, what we now know as the City of Toronto used to be a two-tier municipality consisting of six different cities (Scarborough, North York, East York, York, Etobicoke, and Toronto) and a regional layer of government on top called Metropolitan Toronto. Everyone was happy with this arrangement, so obviously, the provincial government needed to wreck it. Sometime during the first term of Mike Harris’ Common Sense Revolution™ Progressive Conservative provincial government, it was thought that Toronto (and a few other cities around the province) could run more efficiently as one giant city instead of a bunch of different cities. And so, in 1998, the Government of Ontario decided to smush all of these cities together even though no one wanted it to happen and here we are today, with one giant City of Toronto. Obviously, having to merge six different governments together into one giant government is not a trivial task and even now, 15 years later, we’re still trying to work out the kinks. One of those kinks is planning and zoning regulations. You see, because Toronto used to be six autonomous cities, this means that all of those cities each had their own sets of planning regulations. This is obviously not ideal. So in order to try and simplify things (or at least make them less unwieldy), the city tried to work on harmonizing the bylaw across the city. This has been a work in progress for many, many years and almost happened in 2010 but it kind of blew up and everyone went back to the drawing board and here we are again. Now a few months ago, someone found out that the newest version of the proposed draft zoning bylaw turned out to severely restrict the zones where places of worship could be established. Even though the immediate reaction was over the top spiritual war rhetoric, the concerns weren’t unjustified. Essentially, places of worship were limited to select commercial and institutional zones and that was all, no residential or industrial zones. Was it intentional? Was it a mistake? Who knows? But it’s helpful to remember that planning staff was trying to go through an incredibly complex set of regulations and trying to make everything somehow work together. For those of you who aren’t familiar with how City Council works, essentially, stuff starts out in the various committees before heading out to the council floor. And so, religious leaders and groups went and got in touch with their councillors with their concerns and went and deputed at Planning and Growth Committee meetings and the bylaw was revised into something much more reasonable before being shipped off to council. In other words, there was something that was overlooked by someone, interested and concerned parties gave input and worked with their representatives, changes were made, and civic governance worked as intended. With that done, we fast forward to the April 3 meeting of Toronto City Council. At this particular council meeting, the mayor made the zoning bylaw and Hero Burger at Nathan Phillips Square his two key items. Most people will remember the second one because councillors basically argued about whether to put a Hero Burger in Nathan Phillips Square for two or three hours and it featured the deputy mayor reading a selection of items from the menu of Hero Burger among other things. But before the Hero Burger shenanigans started, a pretty healthy chunk of time was spent dealing with the zoning bylaw and within that debate, there was a substantial amount of stuff dealing with places of worship. As was mentioned earlier, initially, places of worship really were significantly impacted negatively by the proposed changes. However, all of that got significantly reworked and when it hit the council floor, it was something much more reasonable. The proposed bylaw now allowed for places of worship in all residential and commercial zones, various institutional zones, and industrial office zones. This was mostly fine, except for some fighting over whether to allow places of worship in light industrial zones. The context behind this particular scrap is that a common thing for smaller churches to do is to rent or establish their church in areas which are zoned for industrial use because the cost of doing so is a lot cheaper. However, this puts them at odds with the city’s attempts at trying to preserve its industrial lands. What tends to happen is because the land value in these zones tends to be cheaper, condo developers often buy up these lands and try to get zoning changes on the lands. The result is that there are fewer and fewer places in the city where industry can set up operations. Of course, churches don’t tend to be huge developers or speculators buying up cheap land to flip over to developers, so what’s the problem with letting them on industrial lands? The problem is that places of worship still negatively impact the use of industrial lands for industry. The reason for this is because a place of worship is classified as a sensitive use under provincial regulations and so the surrounding industry has to restrict their industrial activities, even though they’re in an industrial zone. The particular motion (Motion 3, Part 3) to allow places of worship on light industrial zones was eventually lost and the initial recommendations from Planning and Growth Management were basically passed. Of course, this doesn’t meant that churches are suddenly getting booted from industrial lands. Most churches that are already there legally based on whatever bylaw was in effect before gets grandfathered and gets to stay there. It’s just new churches won’t be able to move into industrial zones. So tl;dr, everything worked out in the end and it’s going back to staff for one more go-over before being finalized for reals.	4,232	19,633	{"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}	2.546875	3	CC-MAIN-2018-13	latest	en	0.970817
https://www.thedonutwhole.com/how-many-cups-is-4-egg-whites/	1,708,957,006,000,000,000	text/html	crawl-data/CC-MAIN-2024-10/segments/1707947474660.32/warc/CC-MAIN-20240226130305-20240226160305-00773.warc.gz	1,026,633,525	28,593	# How many cups is 4 egg whites? 4 egg whites is approximately 1/2 cup or 4 fluid ounces (118 ml). The exact amount can vary slightly depending on the size of the eggs. ## Measuring Egg Whites by Volume When separating egg whites from the yolk, you can measure the whites in graduated measuring cups to determine the volume. Here are some general guidelines for expecting egg white yields: • 1 large egg white = about 2 tablespoons or 1 fluid ounce • 1 extra large or jumbo egg white = about 1/4 cup or 2 fluid ounces • 4 large egg whites = about 1/2 cup or 4 fluid ounces • 4 extra large or jumbo egg whites = about 1 cup or 8 fluid ounces As you can see, the size of the eggs impacts the expected volume of egg whites. Large eggs average about 1 ounce per egg white, while extra large or jumbo eggs average closer to 2 ounces per egg white. So for 4 large egg whites, you can expect around 1/2 cup or 4 fluid ounces. For 4 extra large or jumbo egg whites, expect around 1 cup or 8 fluid ounces. ## Measuring Egg Whites by Weight You can also measure egg whites by weight, using a kitchen scale. Here are some estimates: • 1 large egg white = about 30 grams • 1 extra large or jumbo egg white = about 40 grams • 4 large egg whites = about 120 grams • 4 extra large or jumbo egg whites = about 160 grams So 4 large egg whites weighs approximately 120 grams or 4 ounces. Four extra large egg whites would be around 160 grams or 5.5 ounces. The weight of egg whites gives you a more precise measurement compared to volume. But volume measurements in cups, tablespoons, or fluid ounces are still common and useful, especially for liquid ingredients. ## Tips for Measuring Egg Whites Here are some tips when measuring and working with egg whites: • Make sure eggs are thoroughly separated, with no traces of yolk in the whites. The yolk introduces fat which can impact whipping. • Crack eggs one at a time into a small bowl, then transfer the white to the measuring cup. This prevents losing whites. • Use a clear liquid measuring cup for easiest and most accurate reading. • To weigh egg whites, tare the weighing scale with an empty bowl on it, then add the egg whites. • Whipped egg whites will temporarily increase in volume before settling. For more accuracy, measure before whipping. • Any extra egg whites can be tightly covered and refrigerated for 3-4 days for later use. Follow these tips for best results when measuring out egg whites by volume or weight for recipes. ## Converting 4 Egg Whites to Whole Eggs In some recipes, you may need to substitute whole eggs for egg whites, or vice versa. Here is how to convert: • 1 whole large egg is equivalent to about 2 egg whites • 4 egg whites is equivalent to about 2 whole large eggs So in a recipe, you can substitute 4 egg whites for 2 whole eggs. For every 2 whole eggs, use 4 egg whites instead. Just keep in mind that whole eggs and egg whites function a bit differently in recipes. Whole eggs provide binding, richness, and moisture. Egg whites provide foaming, leavening, and structure. So substituting one for the other can impact the texture and rise of baked goods. Sometimes extra adjustments need to be made to the other ingredients when replacing whole eggs with egg whites, or vice versa. But for a 1:2 ratio, 4 egg whites is typically equivalent to about 2 large whole eggs. ## Typical Uses for 4 Egg Whites What can you make with 4 egg whites? Here are some ideas: • Meringues – The whites whip up into a light, airy foam perfect for meringues. Make individual meringue kisses or a pavlova. • Macarons – These French sandwich cookies use whipped egg whites in the batter to give them their signature chewy, crisp texture. • Mousses – Sweet or savory egg white mousses, like chocolate or avocado, rely on whipped whites for their airy texture. • Soufflés – The egg white foam helps soufflés achieve their dramatic rise. Make cheese, fruit, or chocolate soufflés. • Omelettes – For fluffier, lower-calorie omelettes, use 4 egg whites instead of 2-3 whole eggs. • Cocktails – Use 4 egg whites to make an airy, foamy cocktail like a whiskey sour or pisco sour. Whipped egg whites create lightness and volume in both sweet and savory dishes. With 4 egg whites on hand, let your creativity guide you! ## Nutrition Information for Egg Whites Egg whites are low in calories and fat while providing high-quality protein. Here are some nutrition facts: • Calories: About 17 calories per egg white • Protein: 3.6 grams per egg white • Fat: 0 grams per egg white • Carbs: 0.2 grams per egg white So 4 egg whites would contain about: • 68 calories • 14.4 grams protein • 0 grams fat • 0.8 grams carbs Egg whites are mostly water and protein. The protein offers a complete amino acid profile to support muscle tissue. Egg whites also contain antioxidants like ovalbumin. Using egg whites instead of whole eggs reduces calories, fat, and cholesterol for a healthier nutrition profile. But you still get high-quality protein. ## Cost of Egg Whites Egg whites are relatively inexpensive, especially when you separate and use your own eggs. But you can also buy cartons of egg whites: • Carton of 12 large egg whites – \$3 to \$5 • 1 large egg white – About \$0.25 to \$0.40 each So 4 egg whites would cost approximately \$1 to \$1.60 if buying pre-separated egg whites. Of course, costs vary based on the store, brand, source of the eggs (organic, free-range, etc), and location. But in general, egg whites are an affordable ingredient. Buying egg white cartons lets you skip the separating step for convenience. But you pay a little more than separating your own eggs. ## Should You Refrigerate Egg Whites? Proper storage of egg whites is important for food safety. Here are some guidelines: • Store egg whites in an airtight container in the refrigerator. The whites are very perishable once separated from the shell. • Use egg whites within 2-4 days for best quality and freshness. • Label the container with the date for easy tracking. • Don’t store at room temperature more than 2 hours. • Pasteurized cartoned egg whites can be stored in the fridge for 7-10 days before opening. The refrigerator temperature helps keeps egg whites safe and minimizes bacterial growth. For longest shelf life, freeze extra egg whites up to 1 year. Only leave egg whites out at room temperature once they are being used and incorporated into a cooked or baked recipe. Proper refrigeration prevents any foodborne illness. ## Can You Freeze Egg Whites? Yes, egg whites can be frozen for later use: • Place egg whites in a freezer-safe container or bag, allowing headspace for expansion. • Label with the number of egg whites and date. • Freeze for up to 1 year at 0°F or below. • Thaw in the refrigerator overnight before using. • Use thawed egg whites in recipes as you normally would. Frozen egg whites are great to have on hand for recipes down the road. Just make sure to freeze them promptly in an airtight container for best quality. ## Conclusion To summarize: • 4 large egg whites = About 1/2 cup or 4 fluid ounces • Measure egg whites precisely using volume (cups, tablespoons) or weight (grams, ounces). • Store egg whites refrigerated in an airtight container and use within 2-4 days, or freeze for longer storage. • 4 egg whites can make recipes like meringues, macarons, mousses and soufflés. • Egg whites provide protein with little fat or calories. Knowing how to measure and substitute egg whites gives you more flexibility when cooking and baking. With a little practice, you’ll have no problem using 4 egg whites equivalents in all kinds of delicious recipes.	1,782	7,667	{"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-2024-10	latest	en	0.908384
https://web2.0calc.com/questions/helpppp-6q-2-7qr-24r-2	1,548,315,661,000,000,000	text/html	crawl-data/CC-MAIN-2019-04/segments/1547584519382.88/warc/CC-MAIN-20190124055924-20190124081924-00074.warc.gz	672,603,535	6,308	+0 # helpppp!!! 6q^2 - 7qr - 24r^2 ????? 0 427 4 helpppp!!! 6q^2 - 7qr - 24r^2 Jul 20, 2017 #1 +20857 +1 6q^2 - 7qr - 24r^2 $$6q^2 - 7qr - 24r^2 = 6(q-\frac83r) (q+\frac32r)$$ Jul 20, 2017 #2 +1 How did you do it? Guest Jul 20, 2017 #3 +2 Factor the following: 6 q^2 - 7 q r - 24 r^2 6 q^2 - 7 q r - 24 r^2 = 6 q^2 - 7 q r - 24 r^2: 6 q^2 - 7 q r - 24 r^2 The coefficient of q^2 is 6 and the coefficient of r^2 is -24. The product of 6 and -24 is -144. The factors of -144 which sum to -7 are 9 and -16. So 6 q^2 - 7 q r - 24 r^2 = 6 q^2 - 16 q r + 9 q r - 24 r^2 = 3 q (2 q + 3 r) - 8 r (2 q + 3 r): 3 q (2 q + 3 r) - 8 r (2 q + 3 r) Factor 2 q + 3 r from 3 q (2 q + 3 r) - 8 r (2 q + 3 r): Answer: \| (2q + 3r ) (3q - 8r) Jul 20, 2017 #4 +94619 +1 6q^2 - 7qr - 24r^2 To factor this kind of problem, first multiply the first coefficient abd last coefficient = 6 * -24 = -144 Now....we're looking for 2 factors the multiply to 144 and sum to the midle coefficient, -7 A little trial and error produces -16 and 9 Now, we can write the middle term as a combo of these So we have 6q^2 - 16qr + 9qr - 24r^2 factoring each pair of terms, we have 2q (3q - 8r) + 3r (3q -8r ) and (3q -8r ) is common ro both terms......so write this and then the other two terms in a separate set of parentheses........so we have (3q -8r ) ( 2q + 3r ) Jul 20, 2017	653	1,384	{"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}	4.25	4	CC-MAIN-2019-04	latest	en	0.68624
https://affordableessaywritingservice.com/trayne-rice-has-3000-to-invest-for-three-years-he-wants-to-receive/	1,627,810,926,000,000,000	text/html	crawl-data/CC-MAIN-2021-31/segments/1627046154175.76/warc/CC-MAIN-20210801092716-20210801122716-00669.warc.gz	103,588,698	13,609	# Trayne rice has \$3,000 to invest for three years. he wants to receive 1. Trayne Rice has \$3,000 to invest for three years. He wants to receive \$5,000 at the end of the three years. What invest rate would his investment have to earn to achieve his goal? (Round to the nearest percent.) 2. Your mother is trying to choose one of the following bank CDs to deposit \$10,000. Which one will have the highest future value if she plans to invest for three years? a. 3.75% compounded annually. b. 3.5% compounded daily c. 3.4% compounded quarterly d. 3.25% compounded monthly 3. Hassan Ali has made an investment that will pay him \$11,455, \$16,376, and \$19,812 at the end of the next three years. His investment was to fetch him a return of 14 percent. What is the present value of these cash flows? (Round to the nearest dollar.) a. \$36,022 b. \$41,675 c. \$39,208 d. \$33,124 4. Genaro needs to capture a return of 40 percent for his one-year investment in a property. He believes that he can sell the property at the end of the year for \$150,000 and that the property will provide him with rental income of \$25,000. What is the maximum amount that Genaro should be willing to pay for the property? a. \$112,500 b. \$150,000 c. \$125,000 d. \$137,500	343	1,281	{"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-2021-31	latest	en	0.975518
https://welt.irza.info/28-cm-equals-how-many-inches/	1,670,079,022,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446710933.89/warc/CC-MAIN-20221203143925-20221203173925-00397.warc.gz	642,462,863	16,093	# 28 Cm Equals How Many Inches 28 Cm Equals How Many Inches. Learn how to convert from centimeters to inches and what is the conversion factor as well as the conversion formula. How to convert 28.7 centimeters to inches? 24 inches is equal to 1 00164041994750656 centimeters. A common question is how many centimeter in 28.5 inch? 24 inch how many cm. ### One Centimeter Equals 0.393701 Inches, To Convert 28.6 Cm To Inches We Have To Multiply The Amount Of Centimeters By 0.393701 To Obtain The Width, Height Or. How many inches is 28 centimeters. Cm is an abbreviation of centimeter. In the past many different distance. ### 24 Inches Is Equal To 1 00164041994750656 Centimeters. Convert 24 inches to centimeters. Here is the formula to calculate 28.28 cm to in: 28 centimeters (cm) equals to 11.0236 inches 28 inches to cm from www.howmanypedia.com so, 28 centimeters = 28 ×. ### Multiply The Value In Centimeters By The Conversion Factor '0.3937007874021'. [cm] = 200 / 2.54 = 78.74. The history of measurement scales has been quite varied. 28 inches are equal to 11.0236 centimeters. ### Convert 28.6 Cm To Inches. [cm] = inches / 2.54. 101 rows how tall is 28 cm in feet and inches? So, a better formula is. ### 28 Inches = 28 X 2.54. How to convert 28.5 centimeters to inches? Use this easy calculator to. In this case 1 centimeter is equal to 0.014060742407199 × 28 inches.	400	1,393	{"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	3	CC-MAIN-2022-49	latest	en	0.809003
https://www.easyelimu.com/kenya-secondary-schools-pastpapers/term-past-papers/form-4/item/3423-physics-paper-1-questions-and-answers	1,680,144,464,000,000,000	text/html	crawl-data/CC-MAIN-2023-14/segments/1679296949093.14/warc/CC-MAIN-20230330004340-20230330034340-00660.warc.gz	841,816,699	29,266	Physics Paper 1 Questions and Answers - Form 4 Mid Term 2 Exams 2021 PHYSICS PAPER 1 FORM 4 MID TERM 2 INSTRUCTIONS • This Paper has Section A nd B. Answer all questions in Section A nd B • Working must be clearly shown. SECTION A (25 marks) Answer all the questions in this section in the spaces provided 1. Figure 1 below shows a part of Vernier calipers used to determine the length of a metallic cube. If the cube has a mass of 1533g. Determine the density of the cubein g/cm3 (3marks) 2. Figure 2 below shows a mercury manometer. Some dry gas is trapped in one of the limbs. Given that the atmospheric pressure is 76cm of mercury. Determine the pressure of the gas in mmHg (3 marks) 3. When it is raining, it is advisable not to touch a canvas tent from inside. Explain. (1 mark) 4. State the reason why it is easier to separate water into drop than to separate a piece of solid into smaller pieces. (1 mark) 5. Figure 3 below shows a simple fire alarm. Explain how it works (2marks) 6. It feels hotter to sit on a metallic chair that has been left in the sun for a long time than wooden bench at the same temperature. Explain(2 marks) 7. State the principle of moments. (1 Mark) 8. A uniform meter rule of mass 10g is balanced by masses 24 g and 16g suspended at 0 cm mark and 100cm mark respectively. Determine the position of the pivot. (2 marks) 9. The figure below shows a compression spring, before and after a mass of 5kg was placed on it. Use it to answer questions 9, 10, and 11. Find the spring constant of the spring. (3marks) 10. Sketch a graph of force against length if different masses were used in the above set up. (1 mark) 11. Explain the shape of the graph above (1 mark) 12. State Bernoulli’s effect (1 mark) 13. 1. Water flows through a pipe of different cross-section areas as shown in the diagram below. Indicate in the diagram the levels of water in tubes A, B and C. (1 mark) 2. Give a reason for your answer in 13(a) above. (1 mark) 14. 1. An electric heater is placed at equal distances from two similar metal cans A and B filled with water at room temperature. The outer surface of can A is shiny while that of can B is dull black. State with reasons which can will be at a higher temperature after the heater is switched on for some time. (2marks) 2. Sketch a graph of temperature against time for can A and B after the heater is switched off. (1 mark) SECTION B: (55 marks) 1. 1. State Charles’ law. (1 mark) 2. The Set up below was used to verify Charles’ law. Use it to answer the following questions. 1. State two measurements taken from the above set up. (2marks) 2. Describe briefly how the set up above can be used to verify Charles’s law. (3marks) 3. State the function of sulphuric acid index. (1 mark) 4. Pressure of the trapped air remains unchanged throughout the experiment. Explain how this is possible. (2marks) 5. A mass of 1200 cm3 of oxygen at 270 C and a pressure 1.2 atmosphere is compressed until its volume is 600 cm3 and its pressure is 3.0 atmospheres. Find the temperature of the gas after compression (2 marks) 2. 1. Define the term heat capacity. (1 mark). 2. In experiment to determine the specific latent heat of vaporization Lv of water, steam was passed into cold water in a copper calorimeter. The following data was obtained: Mass of calorimeter 105.2g Mass of calorimeter + water =228.8 g Mass of calorimeter + water + steam= 231.2g Temperature of the cold water = 180C Final temperature of the water=290 C 1. Determine the amount of steam that condensed. (1 mark) 2. Calculate the amount of heat lost by the condensed steam. (specific heat capacity of water=4200J/Kg/K) (3 marks) 3. Calculate the amount of heat absorbed by water and the calorimeter (specific heat capacity of copper = 390J/kg/K) (3marks) 4. Calculate the specific latent heat of vaporization Lv of water. (2 marks) 5. Explain why cooling the water used in the calorimeter to below room temperature could have led to more accurate result. (1 mark) 3. 1. Distinguish between elastic collision and inelastic collision. (1 mark) 2. A van of mass 1500 kg travelling at a constant velocity of 72 km/h collides with a stationary car of mass 900kg. The impact takes 2 seconds before they move together at a constant velocity for 20 seconds. Calculate: 1. Their common velocity (3marks) 2. The distance moved after the impact.(2marks) 3. The impulsive force (3marks) 4. The change in kinetic energy (3marks) 5. Why is the kinetic energy not conserved in this collision (1 mark) 4. 1. Define angular velocity. (1 mark). 2. Figure 4 below shows a mass 500g moving in vertical circle having a radius of 35cm at a constant velocity. It makes 2 revolutions in one second. 1. Indicate on the diagram the direction of centripetal force. (1 mark) 2. Calculate the linear velocity of the mass. (3marks) 3. Calculate the centripetal acceleration of the object. (2marks) 4. Determine the centripetal force. (3marks) 5. Giving a reason, state the point at which the string is likely to snap. (2mark) 5. 1. State the law of conservation of energy. (1 mark) 2. Figures4 below shows a ball of mass of 5kg rolling along a frictionless path as shown. 1. Calculate the potential energy of the ball at point O. (2 marks) 2. Determine the velocity of the ball at point A (2 marks) 3. If the ball rolls back when it reaches point B, state the energy changes that takes place O to B. (1 mark) 4. It is observed that the efficiency of the machine increases when it is used to lift large loads. Give a reason for this (1 mark) MARKING SCHEME 1. Length= 5.35cm Volume= 5.35 x 5.35 x 5.35 = 28.6225cm3 p= m/v = 1533/28.6225 = 53.5593g/cm3 2. Total pressure = atm + ρgh = 760mmHg+20mmHg = 780mmHg 3. This breaks the surface tension of water running over the canvas tent hence increasing adhesive force so that the tent leaks. 4. Cohesive forces are stronger in solids than in liquids 5. • In case of fire outbreak, the temperature increases, brass expands more than iron. • The bimetallic strip bends towards the iron side and makes the contact. • This completes the circuit causing the electric bell to ring. 6. The metallic chair is a good conductor of heat and gains heat faster than the wooden bench, which is a poor conductor of heat 7. For a system in equilibrium, the sum of clockwise moments is equal to the sum of anticlockwise moments 8. (xx24) = (100-x)16+(x-50)10 24x=1600 - 16x+10x-500 24x=1100-6x x=36.67cm 9. F=ke 50=k x 0.2 K= 500/2 = 250N/M K=250 n/m 10. 11. The length of the spring reduces as the masses are added until it cannot reduce anymore 12. For a fluid that is non-viscous incompressible and the flow is streamline, then an increase in velocity causes a corresponding decrease in pressure it exerts. 13. 1. 2. Water level in manometer B is lower than the levels in manometer A and C. Water level in manometer A is the highest hence high pressure compared to B and C. 14. 1. B will have a higher temperature than the water in A. Dull surfaces are good obsorbers of heat 2. 15. 1. For a fixed mass of gas volume is directly propotional to absolute temperature provided pressure is kept constant. 2. 1. • Length of the air column trapped / volume of air (L) • Temperature of the water bath 2. • Temperature is varied and corresponding value of L and T are recorded • A grapgh of L vs absolute temperature T is then plotted • Straight line is obtained cutting the x-axis at OK(-273ºC) 3. • Sulphuric acid index acts as a pointer in the volume of the gas on the scale 4. Pressure of the trapped air is the same as the atmospheric pressure pluse pressure due to acid index which remains constant through the experiment 5. Vi=1200cm3 , T=27+273=3000K p=1.2atm p1V1 = p2v2 → 1.2 x 1200 = 3 x 600 T1 T2 300 t2 T2 → 375K or 102ºC 16. 1. A quantity of heat required to change the temperature of a given mass of a substance by 1Kelvin 2. 1. 231.2-228.8=2.4g 2. Steam condensed to water at 29ºC Steam 100ºC → water 100ºC → Water 29ºC Q=MLV+MCO =(0.003 x lv+894.6) 3. Heat absorbed = mc cc o + mw cw o =0.105 x 390 x (29-18)+0.1236x x 42.0x(29-18) =480.45+5710 32 =6190.77j 4. Heat lost - heat gained 0.003Lv + 894.6=6190.77 0.003Lv=Ω96.17 Lv= 1,765390 0r 1.765 x 106 j/kg 5. This balances the heat exchange between the calorimeter with its contents and the surrounding. 17. 1. • Elastic collision- both momentum and kinetic energy of colliding bodies is conserved • Inelastic collision- only momentum is conserved but not kinetic energy 2. Moment before collision = momentum after collision 1. (1500 x 20)+0=2400 x v 12.5m/s=v 2. s=ut=12.5m/s x 0=250m 3. ft=mv -mu fx2=1500(20-12.5) fx2=11250→f= 5625 or ft=mv-mu fx2=900x12.5 f-5625N 4. Initial KE=1/2 mu2 =1/x 1000x 202= 300,000 Final KE=1/2(m1m2)v2 =1/x 2400 x 12.52=187,500J KE change= 300000-187500= 112500J 5. This is the energy converted to sound and heat or energy used in doing work 18. 1. Rate of change of angular displacement 2. 1. 2. f=2Hz ω= 2πf = 2 x 3.142x2 = 12.56 V= r ω = 0.35 x 12.56 = 4.3982m/s 3. a=v2/r=(4.3982)2 0.35 =55.270m/s2 4. f=mv2/r=0.5 x 55.270 =27.635N 5. At point R. This is where tension is maximum in the string 19. 1. The sum of kinetic energy and potential energy of a system is constant 1. PE=mgh=5x10x20=1000J 2. PE=KE mgh=1/2 mv2 v2=2gh v2=2x10x20 v2=400 v=20m/s 3. PE →KE → PE + heat energy + sound 4. Efficiency increase because as the load increases energy used in overcoming frictionand lifitng the weight of the machine parts becomes insignificant. • MA advatage increase because friction and weight of the machine parts remain constant. 2. Download Physics Paper 1 Questions and Answers - Form 4 Mid Term 2 Exams 2021. • ✔ To read offline at any time. • ✔ To Print at your convenience • ✔ Share Easily with Friends / Students Read 513 times Last modified on Friday, 22 October 2021 13:21 . Subscribe now access all the content at an affordable rate or Buy any individual paper or notes as a pdf via MPESA and get it sent to you via WhatsApp	2,903	10,005	{"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-2023-14	latest	en	0.885761
https://schoollearningcommons.info/question/the-angle-measurement-of-a-quadrilateral-are-35-49-67-the-measure-of-fourth-angle-19765666-62/	1,631,925,484,000,000,000	text/html	crawl-data/CC-MAIN-2021-39/segments/1631780056120.36/warc/CC-MAIN-20210918002951-20210918032951-00343.warc.gz	551,886,735	13,442	## The angle measurement of a quadrilateral are 35°,49°,67°.The measure of fourth angle Question The angle measurement of a quadrilateral are 35°,49°,67°.The measure of fourth angle in progress 0 1 week 2021-09-10T02:15:51+00:00 2 Answers 0 views 0 ## Answers ( ) 209° is the answer of this question Step-by-step explanation: let the required angle be x x+35+49+67 = 360° x+151° = 360° x = (360 – 151)° x = 209° 209 ° Step-by-step explanation: 35°+49°+67°=151° 360°-151°=209°	175	490	{"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-2021-39	latest	en	0.772514
http://thefinancebase.com/calculate-proceeds-sales-bonds-2663.html	1,506,112,959,000,000,000	text/html	crawl-data/CC-MAIN-2017-39/segments/1505818689192.26/warc/CC-MAIN-20170922202048-20170922222048-00154.warc.gz	339,491,498	13,694	# How to Calculate Proceeds From Sales of Bonds by Ryan Menezes All bonds include a face value, which is the amount you will receive when the bond matures. The bond's total value, or the proceeds you will get from selling it, is the sum of this face value and the bond's added value from interest. Each bond's coupon states its interest rate. When a bond returns its dividends, the investor can reinvest the returns, compounding the bond's interest. The bond's total value takes into account its principle and its compounded interest. Add 1 to the bond's coupon rate. For example, if a bond offers a coupon of 0.06, adding 1 gives 1.06. Raise this value to the power of the number of years in the bond's term. For example, if the bond matures after five years, raising 1.06 to the power of 5 gives 1.338. Multiply this factor by the bond's face value. For example, if you are selling a \$5,000 bond, multiplying \$5,000 by 1.338 gives \$6,690. This selling price for the bond takes into account its future dividends. #### References • "The Strategic Bond Investor: Strategies and Tools..."; Anthony Crescenzi and Mohamed El-Erian; 2010 • "All About Bonds..."; Esme Faerber; 2008	292	1,185	{"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-2017-39	latest	en	0.87843
https://nrich.maths.org/4937&part=note	1,680,057,962,000,000,000	text/html	crawl-data/CC-MAIN-2023-14/segments/1679296948932.75/warc/CC-MAIN-20230329023546-20230329053546-00289.warc.gz	489,953,918	5,415	### In the Playground What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school? ### The Car That Passes What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas? ### Avalanche! Investigate how avalanches occur and how they can be controlled # Match the Matches ## Match the Matches Two football teams, Alpha United and Beta Rovers have each played fifteen games in their league. The data below show how many goals the teams scored in their matches. There are six different collections of data, three show the results for Alpha United and three show Beta Rovers' goals. Can you match the data to the teams? ### Why do this problem? This problem could be used at the start of a series of lessons on data handling, or as an assessment opportunity at the end of the unit. It will get children talking meaningfully about mathematics, presenting and justifying arguments. ### Possible approach As an introduction to this task, you may choose to ask general questions about the different forms of data. This might be most helpful in the case of the pie chart if the class is not so familiar with this method of representation. For example, you could ask questions such as: • Looking at the pie chart, in approximately what fraction of the total number of games did the team score one goal? • What does the tally chart show us? This activity would be ideal to tackle in pairs or threes. You could print off this Word document or this pdf containing the six different forms of data which could be cut up to create six cards. In this way, children would be encouraged to talk to each other as they interpret the data and the richness of their discussion will allow you to assess their understanding. In the plenary, you can focus on how pupils knew which forms of data go together. ### Key questions What is the total number of goals each team scored over the fifteen matches? Have you tried comparing two of the charts with each other? Do you think they represent the same team's goals? Why or why not? ### Possible extension You could challenge children to make their own version of this problem in pairs. ### Possible support It might be helpful for children to be encouraged to make jottings on the cards as they work on this task.	494	2,394	{"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-2023-14	latest	en	0.947407
http://www.mathworks.com/matlabcentral/answers/54614-add-numerical-array-as-column-or-in-cell-array	1,454,965,883,000,000,000	text/html	crawl-data/CC-MAIN-2016-07/segments/1454701154221.36/warc/CC-MAIN-20160205193914-00116-ip-10-236-182-209.ec2.internal.warc.gz	512,251,176	12,953	## add numerical array as column or in cell array ### Paul (view profile) on 23 Nov 2012 Accepted Answer by Jan Simon ### Jan Simon (view profile) How to add a numerical array ` a=[1 2 3 4]` as row into my cell ``` C = \|'a' 'b' 'c' 'd'\| \|'e' 'f' 'g' 'h'\| \|'i' 'j' 'k' 'l'\| \|'m' 'n' 'o' 'p'\|``` so, that ``` C = \|'1' '2' '3' '4'\| \|'a' 'b' 'c' 'd'\| \|'e' 'f' 'g' 'h'\| \|'i' 'j' 'k' 'l'\| \|'m' 'n' 'o' 'p'\|``` or as new column into cell C: ```C = \|'1' 'a' 'b' 'c' 'd'\| \|'2' 'e' 'f' 'g' 'h'\| \|'3' 'i' 'j' 'k' 'l'\| \|'4' 'm' 'n' 'o' 'p'\| ``` (the numerical values become strings). AND: How to transform for example a 2x4 cell into a 1x8 (or 8x1) cell: ``` C= \|'a' 'b' 'c' 'd'\| ----> C = \|'a' 'b' 'c' 'd' 'e' 'f' 'g' 'h'\| \|'e' 'f' 'g' 'h'\| or:----> C = \|'a'\| \|'e'\| \|'b'\| \|'f'\| \|'c'\| \|'g'\| \|'d'\| \|'h'\|``` I can solve these problems with for-loops, but imagine you have a huge size of the cell array, it is not very efficient. Is there an easier way? Thanks! ## Products No products are associated with this question. ### Jan Simon (view profile) Answer by Jan Simon ### Jan Simon (view profile) on 23 Nov 2012 Edited by Jan Simon ### Jan Simon (view profile) on 23 Nov 2012 ```C = {'a' 'b' 'c' 'd'; ... 'e' 'f' 'g' 'h'; ... 'i' 'j' 'k' 'l'; ... 'm' 'n' 'o' 'p'}; a = [1 2 3 4]; tmp = sprintf('%g', a); tmp(end) = []; aC = regexp(tmp, '', 'split'); C_row = cat(1, aC, C); % Insert as row C_col = cat(2, aC', C); % Insert as column ``` ```C2 = reshape(transpose(C), 1, []) C3 = reshape(C, [], 1) ``` ### Azzi Abdelmalek (view profile) Answer by Azzi Abdelmalek ### Azzi Abdelmalek (view profile) on 23 Nov 2012 Edited by Azzi Abdelmalek ### Azzi Abdelmalek (view profile) on 23 Nov 2012 ``` C = {'a' 'b' 'c' 'd' 'e' 'f' 'g' 'h' 'i' 'j' 'k' 'l' 'm' 'n' 'o' 'p'} a=[1 2 3 4]``` ` out=[num2cell(a); C]` %or ` out=[num2cell(a') C]` % for third case ` out=C(:)'` %or ` out=reshape(C,1,[])` Jan Simon ### Jan Simon (view profile) on 23 Nov 2012 @Azzi: Paul asked for "the numerical values become strings", but NUM2CELL replies {1,2,3,4} instead of the wanted {'1', '2', '3', '4'}. Azzi Abdelmalek ### Azzi Abdelmalek (view profile) on 23 Nov 2012 Ok Simon, ```outv=[arrayfun(@(x) cellstr(num2str(x)),a); C] ``` or ```outh=[arrayfun(@(x) cellstr(num2str(x)),a)' C] ``` MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi test ### Discover what MATLAB® can do for your career. Opportunities for recent engineering grads.	1,015	2,484	{"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-2016-07	latest	en	0.58035
http://www.sciforums.com/threads/on-the-idea-of-time-in-physics-relativity.133989/	1,550,267,443,000,000,000	text/html	crawl-data/CC-MAIN-2019-09/segments/1550247479159.2/warc/CC-MAIN-20190215204316-20190215230316-00454.warc.gz	441,717,211	14,386	# On the idea of time in physics-relativity Discussion in 'Physics & Math' started by ash64449, Mar 15, 2013. 1. ### ash64449Registered Senior Member Messages: 795 Hello friends, i am now reading Theory of relativity written by Albert Einstein.It described on the idea of time in physics by the use of simultaneity.Lightning struck on two extreme parts of the train.In order to test whether the two lightning is simultaneous,a person is made to sit in the middle and two mirrors to let him see two lightning at the same time,if it does,it is simultaneous.. but why is the observer kept at the middle of the train?? Won't those events to him be simultaneous even if he was not sitting in the middle?? 3. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member Messages: 10,676 Because the speed of light is not infinite. Let's say you are half way between the earth and the moon. A light is flashed on the moon and the earth at the same time - you would see them as simultaneous. If the same flashes of light were done again and you were on earth 10 feet away from the 'earth' light they would not appear simultaneous to you, would they? The flash on the moon would be more than a second after the earth flash. 5. ### rpennerFully WiredValued Senior Member Messages: 4,833 Light travels at a finite speed, so by staying at the center of the train, the physical observer assures that he will see the light from each flash reach him at the same time only if they were originally simultaneous -- at least from his perspective. Since he saw both flashes at the same time, that's a fact which cannot be changed by a change of perspective. Now for someone who doesn't have the train's state of motion, the observer still sees the flashes arrive to him at the same time, but that may be because the flashes started at different times, and the relative motion of the train moved the observer towards the direction of one of the flashes. So what is simultaneous and far-apart from one person's perspective may not be simultaneous to another, and the key factor that makes the difference is the relative motion between what those people consider "at rest." 7. ### ash64449Registered Senior Member Messages: 795 That means those events are simultaneous but because of the finite velocity of light,it is "appeared" that the events are not simultaneous?? Messages: 10,676 Yes. 9. ### ash64449Registered Senior Member Messages: 795 If observer moves in opposite direction to that of the train in the same velocity. for an observer outside he won't be moving.. But for that man in the train,he is moving. because he moves in direction opposite to the train,won't he perceive the simultaneous events to outside observer simultaneous to that man too? 10. ### ash64449Registered Senior Member Messages: 795 then why not the case of what i said?? Man was moving,so it "appeared" to him that events are not simultaneous... 11. ### rpennerFully WiredValued Senior Member Messages: 4,833 Physical observers in the same state of inertial motion conclude that events that to one are simultaneous are also simultaneous to the other. 12. ### ash64449Registered Senior Member Messages: 795 What?? I didn't understand.. Can you please tell in simple manner than just statements? I really want to understand... 13. ### rpennerFully WiredValued Senior Member Messages: 4,833 Origin was talking about the example of a situation of geometry when the observer is not at the midpoint. You put "appeared" in scare quotes because you knew that a reasonable observer would factor in the light-travel time and so by asking a leading question you shifted the topic of discussion to perception of light flashes, not simultaneity. When you changed the topic of discussion again, Origin learned a lesson about your intellectual honesty and the folly of answering leading questions as if they were simple questions. 14. ### ash64449Registered Senior Member Messages: 795 Oh!! I understood what you said.. Thank you! 15. ### Prof.Laymantotally internally reflectedRegistered Senior Member Messages: 982 I have heard people on the net act like there is some big connection with things being seen as simultaneous and time dilation. What is this big connection really? All observers measure the speed of light to be the same speed, but then each observer then recieves a flash of light at different times. I have read about this example before, but I never read about it really being used as an explanation for time dilation itself. If the train went 10% the speed of light, then he would measure it to travel 10% slower than an observer on the station. If he measured the beam of light to travel 10% slower then wouldn't they still observe the flash to reach them at the same time? Then wouldn't he measure a flash of light behind him to be 10% faster? To me, it seems like it would only be something true for lightning caused by electrons, that are not always measured to travel at the same speed. 16. ### ash64449Registered Senior Member Messages: 795 how it is explains time dialation is like this: imagine 3 clocks in the train. Two on extreme parts and one in the middle. It is set in such a way that their pointers are simultaneouly the same. So now we are able to explain the time of the event when it happened with the help of simultanity.. As a result we have arrivied on the idea of time in physics.. 17. ### ash64449Registered Senior Member Messages: 795 no.. U didn't understand relativity.. Speed of light is the same for all observers irrespective of their motion(uniform or rest). When we move in uniform motion along a straight line and light too move in same direction,we would have measured less. But this contradicts principle of relativity in restricted sense.so either principle of relativity or law of light is wrong. But relativity shows that both are correct.. If both are correct,the something should change.. That change is distance,time as a result simultaneous events. 18. ### Prof.Laymantotally internally reflectedRegistered Senior Member Messages: 982 That is what the guy said that I talked to, go figure. Small world? He seemed to believe that time doesn't actually slow down and it is just the flashes of light that just reaches us at different times. In every book I have read on relativity says that time actually slows down. Then goes on about things actually slowing down uniformly so that is how we could theoretically not notice time actually slowing down. So for me it was a hard thing to chew on. I only read this example once, and it only claimed that was one of Einsteins thought experiments that he used to develop his theory, not that it is the actual cause of time dilation itself. So it has been kind of gnawing at me for a while now, since I never cared to ask why it is viewed as only being a matter of simultaneity. 19. ### SyneSine qua nonValued Senior Member Messages: 3,515 No one here was talking about relativistic speeds (significant fraction of the speed of light), so this is an off-topic non sequitur. At non-relativistic speeds, time dilation does not have an appreciable effect on the time it takes a finite speed light signal to reach observers at different distances. Last edited: Mar 17, 2013 20. ### Prof.Laymantotally internally reflectedRegistered Senior Member Messages: 982 The M&M experiment was used to measure light traveling at the same speed in different directions, with no velocity relative to the Earth. You cannot assume that all observers will measure light to travel at the same speed, but that if it is a slow speed then that is okay. I was just wondering how people have taken one of Einsteins mind experiments, and then have proclaimed it to be the Holy Grail of physics. I wonder if Einstein new any better about the difference of the speed of photons and electrons at the time he came up with this, or if he did and that is why he used lightning in his example instead of flashes of light. It is the odd ball of theoretical physics writings, and then we have held it higher than any other one as though it has more significance. I wonder if it was even valid. Did Einstein even assume that the speed of light was constant at this time? Or was he dodging the question by saying that it was not light in the problem? 21. ### SyneSine qua nonValued Senior Member Messages: 3,515 Incomprehensible post. How does any of that justify your non sequitur introduction of a relativistic observer? 22. ### Prof.Laymantotally internally reflectedRegistered Senior Member Messages: 982 I have heard that relativity of simultaneity proves that time dilation doesn't actually slow down time, that is in contrary to what I have read about the subject, so then I question its validity. It doesn't assume the constant speed of light, if it doesn't assume the constant speed of light then I would agree that the relativity of simultaneity does not show that time actually slows down in effects of time dilation. I don't think it could ever show that there is time dilation becaue it doesn't assume the constant speed of light. It would more accuratly describe when lightning or electrons would arrive somewhere. I don't think this could be a cause of different observers, measuring particles to be at different locations at the same time either. So then by saying that it is lightning, Einstein has prevented himself from being wrong in this respect. 23. ### SyneSine qua nonValued Senior Member Messages: 3,515 You "heard" wrong. Time dilation is not significant for observers at non-relativistic velocities, but the relativity of simultaneity is calculated using Lorentz transformations, which necessarily includes even inappreciable time dilation. The relativity of simultaneity very much does assume the constant speed of light. This is the whole reason that time dilation and length contraction are evoked. The relativity of simultaneity is a direct consequence of the two postulates of SR, and as such necessarily assumes the constant speed of light, seeing how that is one of the postulates. And who said anything about "different observers, measuring particles to be at different locations at the same time"?	2,185	10,208	{"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-2019-09	latest	en	0.966335
https://mathematica.stackexchange.com/questions/81399/parametricplot3d-of-boys-surface/115652	1,576,184,375,000,000,000	text/html	crawl-data/CC-MAIN-2019-51/segments/1575540547165.98/warc/CC-MAIN-20191212205036-20191212233036-00377.warc.gz	448,792,619	32,387	# ParametricPlot3D of Boy's surface I'm trying to visualize Boy's surface using Bryant's parametrization, as per the MathWorld article. However, I'm not sure I understand the parametrization, and I don't know how to implement it when the parameter is complex. z := u + vI g1 := -(3/2) Im[(z (1 - z^4))/(z^6 + z^3 √5 - 1)] g2 := -(3/2) Re[(z (1 + z^4))/(z^6 + z^3 √5 - 1)] g3 := Im[(1 + z^6)/(z^6 + z^3 √5 - 1)] - 1/2 g = g1^2 + g2^2 + g3^2 ParametricPlot3D[{g1/g, g2/g, g3/g}, {u, 0, 0.5}, {v, 0, 0.5}] Now, I understand that $z=u+v\mathrm{i}$ is the parameter, and that it must range over the closed unit disc, so $u^2+v^2\leq1$. But I don't know how do do this! (I let $u,v$ range between 0 and 0.5, for good measure, but the graphic appears empty.) In the end, I want to end up with exactly this image, for which I've been unable to find the original code. Edit: The 3 solutions provided here worked like a charm (with the caveat that the one using polar coordinates was weirdly sharped, and I couldn't fix that, but I'm a Mathematica newb), and I found another method: ParametricPlot3D[Boys[u, v], {u, v} ∈ Disk[{0, 0}, 1]] I don't know why, but using RegionFunction the surface rendered ~30% slower, and, using Piecewise, about %5 slower. The only issue is that the mesh is now weirdly triangulated. Also, I compiled the actual parametric formula and performance increased threefold: Boys = Compile[{u, v}, {(-(3/2) Im[((u + v I) (1 - (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])/((-(3/2) Im[((u + v I) (1 - (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])^2 + (-(3/2) Re[((u + v I) (1 + (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])^2 + (Im[( 1 + (u + v I)^6)/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)] - 1/2)^2), (-(3/2) Re[((u + v I) (1 + (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])/((-(3/2) Im[((u + v I) (1 - (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])^2 + (-(3/2) Re[((u + v I) (1 + (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])^2 + (Im[( 1 + (u + v I)^6)/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)] - 1/2)^2), (Im[( 1 + (u + v I)^6)/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)] - 1/ 2)/((-(3/2) Im[((u + v I) (1 - (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])^2 + (-(3/2) Re[((u + v I) (1 + (u + v I)^4))/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)])^2 + (Im[( 1 + (u + v I)^6)/((u + v I)^6 + (u + v I)^3 Sqrt[5] - 1.)] - 1/2)^2)}, Parallelization -> True]; I also tried compiling each of $g1,g2,g3,g$ separately, but performance was a bit worse. • Hello! It's g = g1^2+g2^2+g3^2, right? – Ivan May 1 '15 at 20:25 • Yes! Will correct! – étale-cohomology May 1 '15 at 20:27 • Your first problem is that vI is a different variable name; you need v I with a space in between. – Rahul May 1 '15 at 20:41 • "that it must range over the closed unit disc" - that should have tipped you off to use polar coordinates. As I don't have Mathematica on hand, try this: ParametricPlot3D[With[{z = r Exp[I θ]}, (#/(#.#)) &[Re[{I z (1 - z^4), z (z^4 + 1), -(2 I/3) (z^6 + 1)}/(z^6 + Sqrt[5] z^3 - 1) + {0, 0, 1/2}]]], {r, 0, 9/10}, {θ, -π, π}, PlotPoints -> {20, 30}] – J. M. will be back soon May 2 '15 at 1:22 • Yes, I totally missed that!! Thanks! – étale-cohomology May 2 '15 at 17:21 z := u + v I g1 := -(3/2) Im[(z (1 - z^4))/(z^6 + z^3 Sqrt[5] - 1)] g2 := -(3/2) Re[(z (1 + z^4))/(z^6 + z^3 Sqrt[5] - 1)] g3 := Im[(1 + z^6)/(z^6 + z^3 Sqrt[5] - 1)] - 1/2 g = g1^2 + g2^2 + g3^2; You could use Piecewise here. When Abs[z] > 1, the function is undefined and plots nothing. ParametricPlot3D[Piecewise[{{{g1/g, g2/g, g3/g}, Abs[z] <= 1}}, Undefined], {u, -1, 1}, {v, -1, 1}] I'm not an expert on Graphics, but I hope that helps. • You could also add the option RegionFunction -> Function[{x, y, z, u, v}, u^2 + v^2 <= 1] instead of changing the function. – Rahul May 1 '15 at 20:42 • Ah, yes, both solutions worked!! Thanks so much! On a totally unrelated note, does anyone happen to know of this parametrization has 3-fold symmetry when viewed from the 'top'? – étale-cohomology May 1 '15 at 21:06 • @Diego, yes, my current Gravatar does display that feature you speak of... – J. M. will be back soon May 2 '15 at 0:33 Altho traditionally one should use polar coordinates as I suggested in a comment above, I found it amusing that ParametricPlot3D[] can actually support a region specification for specifying the domain of the parameters. Thus here is a way to plot the Bryant-Kusner parametrization of the Boy surface: ParametricPlot3D[With[{z = u + I v}, (#/(#.#)) &[Re[{0, 0, 1/2} + {I z (1 - z^4), z (z^4 + 1), -(2 I/3) (z^6 + 1)}/ (z^6 + Sqrt[5] z^3 - 1)]]], {u, v} ∈ Disk[], Axes -> None, Boxed -> False, Mesh -> True, PlotPoints -> {20, 30}, PlotStyle -> Opacity[2/3]] where I made the surface translucent to display the inner structure. Mathematically, the construction is an inversion of a certain minimal surface that is topologically equivalent to the projective plane, thrice-punctured. See the linked paper for more background.	2,000	5,037	{"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}	3.453125	3	CC-MAIN-2019-51	latest	en	0.728133
https://brainsanswers.co.uk/mathematics/consider-the-line-y7x1-find-the-equ-2991586	1,611,293,106,000,000,000	text/html	crawl-data/CC-MAIN-2021-04/segments/1610703529128.47/warc/CC-MAIN-20210122051338-20210122081338-00599.warc.gz	247,160,949	32,819	# Consider the line y=7x-1 find the equation of the line that is perpendicular to this line and passes through the point (-5,6) ### Another question on Mathematics Mathematics, 05.02.2019 00:41 On the way home from visiting his family, vincentâ€™s plane cruised at an altitude of 3.2 Ă— 104 feet. he had heard that a man named felix baumgartner skydived from an altitude of 1.28 Ă— 105 feet. vincent wants to know how much higher felix went on his skydiving trip. question 1 you have already seen how adding numbers works in either scientific notation or standard notation. but can you subtract numbers in scientific notation and get the same results as subtracting in standard notation? to find out, first solve vincentâ€™s problem in standard notation. part a write the cruising altitude of vincentâ€™s plane in standard notation.	207	834	{"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-2021-04	latest	en	0.942049
https://equationsworksheet.co/solving-linear-equations-variable-on-both-sides-worksheet/	1,656,283,339,000,000,000	text/html	crawl-data/CC-MAIN-2022-27/segments/1656103322581.16/warc/CC-MAIN-20220626222503-20220627012503-00432.warc.gz	301,959,203	10,668	# Solving Linear Equations Variable On Both Sides Worksheet Solving Linear Equations Variable On Both Sides WorksheetA worksheet can help students find out how to address formulas more quickly. These worksheets will aid students find out how to break down tough equations right into absorbable items. The more time you take into addressing an equation, the better off you will certainly remain in the long run. Academics as well as companies alike put a high importance on this ability. Browse through this site for further details on just how to use an algebra worksheet. This article will check out an algebraic formula. As long as the worksheet has numerous troubles, pupils will certainly discover it beneficial. A wide variety of equations having several variables will certainly be exercised by the students therefore. One step is all it takes to solve a linear equation. The second equation calls for using three variables. A slope intercept worksheet will require trainees to respond to a single-variable equation. The student needs to know with the appropriate variables. This worksheet is intended towards grade school trainees, although it can also be utilized by youngsters in intermediate school. If you’re seeking for math worksheets for pupils in qualities 5 with 8, the Web is your biggest option. Equation-solving worksheets can be discovered in numerous places online. The freebies are accessible in both PDF as well as HTML formats. Linear equations of one as well as 2 actions are accessible. On each web page, there are 10 concerns, as well as each worksheet has multiple-step problems in it. An excellent device for pupils in qualities 5 via 8 may be found right here. Solving Linear Equations Variable On Both Sides Worksheet Multiple-step problems can additionally be consisted of in this style of math worksheet. You will certainly first require to turn word issues right into formulas in order to fix for variables. In the “Back 9” of algebra, you will certainly be able to make use of these worksheets. It’s possible to download the complete material as a PDF by clicking on the photo below. Attempt using the on-line version if you’re having troubles with formulas. Solving Linear Equations Variable On Both Sides Worksheet Worksheets for several action formulas are likewise available. It’s ideal for students who are having difficulty learning on their own. Trainees will find out exactly how to use polynomials to resolve algebraic issues. Usually, a more meaningful collection of outcomes is the outcome of this approach. You can get an equations worksheet with responses from a Tpt store. There are several outstanding materials offered, however it is just one of the best. for understanding this ability. You’ll have the ability to much better recognize algebraic and also two-step mathematics expressions as a result of this. Worksheets for algebra are offered right here. If you’re having difficulty addressing algebraic problems, you can utilize these printables. These worksheets can be made use of to decode a myriad of significantly intricate formulas. Generally, with multivariable issues, there are additionally multiple-step troubles. These worksheets are perfect for trainees in grades five via 8. Solving Linear Equations Variable On Both Sides Worksheet	634	3,305	{"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-2022-27	latest	en	0.945749
https://learn.careers360.com/school/question-need-solution-for-rd-sharma-maths-class-12-chapter-18-indefinite-integrals-excercise-18-point-14-question-5/?question_number=5.0	1,686,404,827,000,000,000	text/html	crawl-data/CC-MAIN-2023-23/segments/1685224657720.82/warc/CC-MAIN-20230610131939-20230610161939-00065.warc.gz	412,385,251	42,699	Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.14 Question 5 Answer: $\frac{1}{2} \log \left\|x+\sqrt{x^{2}+\frac{1}{4}}\right\|+c$ Hint: To solve this integral, use special integral formula. Given: $\int \frac{1}{\sqrt{1+4 x^{2}}} d x$ Solution: Let \begin{aligned} &I=\int \frac{1}{\sqrt{1+4 x^{2}}} d x=\int \frac{1}{\sqrt{4\left(\frac{1}{4}+x^{2}\right)}} d x \\ &=\frac{1}{2} \int \frac{1}{\sqrt{x^{2}+\left(\frac{1}{2}\right)^{2}}} d x \end{aligned} \begin{aligned} &=\frac{1}{2} \log \left\|x+\sqrt{x^{2}+\left(\frac{1}{2}\right)^{2}}\right\|+c \quad\quad\quad\quad\quad\quad\quad\quad\left[\because \int \frac{1}{\sqrt{x^{2}+a^{2}}} d x=\log \left\|x+\sqrt{x^{2}+a^{2}}\right\|+c\right] \\ \\&=\frac{1}{2} \log \left\|x+\sqrt{x^{2}+\frac{1}{4}}\right\|+c \end{aligned}	344	818	{"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": 0, "codecogs_latex": 4, "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}	4.1875	4	CC-MAIN-2023-23	longest	en	0.270637
http://forums.trossenrobotics.com/tutorials/index.php?s=30592f141e0c422f0295642c60c4642d	1,575,635,381,000,000,000	text/html	crawl-data/CC-MAIN-2019-51/segments/1575540488620.24/warc/CC-MAIN-20191206122529-20191206150529-00174.warc.gz	59,595,490	8,639	## Tutorial Search Delta robot kinematics How can i use this code to generate the workspace of delta robot?I tried plotting the workspace... by mouradsme on 05-03-2017 06:24 PM Delta robot kinematics Can someone tell me how a1, a2, b1, b2 and d were found?I think there are some operations on... by mouradsme on 04-27-2017 08:44 PM Delta robot kinematics into the inverse kinematics, what is the ""?"" doing: "theta = 180.0*atan(-zj/(y1 - yj))/pi +... by Santiago on 12-05-2016 09:53 PM Delta robot kinematics I think I have found an error: In J'3 the x3 value should be with minus, beacuse for the same... by Gordon51 on 12-04-2016 10:19 AM Delta robot kinematics how the way I review how to simulate the delta robot in Matlab ? by adysetyo on 12-01-2016 03:25 AM 1. ## How To, DIY • Tutorials: 47 • Posts: 189 How I make Carbon... by rebel 03-29-2012 07:09 PM 2. ## Introduction • Tutorials: 36 • Posts: 155 by Nishi 01-20-2010 01:13 PM 3. ## Build Articles • Tutorials: 9 • Posts: 50 Build an... by Slugman 02-16-2012 08:46 PM 4. ## Product Feature, Demos • Tutorials: 2 • Posts: 3 Two Demos of the... by Matt 08-22-2008 12:49 PM 5. ## Mod, Hack • Tutorials: 4 • Posts: 18 by mannyr7 06-27-2009 09:00 PM 6. ## Published Product Reviews For finished product reviews. Tutorials entered here will be live and show up on various areas of the TRC Community. If you have a tutorial in progress, please start it in the TRC Tutorial Drafts. • Tutorials: 3 • Posts: 60 Crabfu's Review of... by crabfu 03-01-2009 01:19 PM Category Contains New Tutorials Category Contains No New Tutorials ## Random Entries 1. ### Calculating LED Resistor... Category: Introduction • Views: 59,278 • Replies: 4 06-21-2009 06:36 PM 2. ### Simple H-bridges Category: Introduction • Views: 39,193 • Replies: 6 08-11-2008 01:58 PM by ScuD 3. ### Choosing Wheels and... Category: Introduction • Views: 1,244,150 • Replies: 0 04-15-2009 08:01 PM by metaform3d 4. ### Sensor bot Category: Build Articles • Views: 121,067 • Replies: 3 05-31-2008 04:20 AM by 4mem8 5. ### Adding a Serial Port to... Category: Mod, Hack • Views: 1,207,843 • Replies: 9 05-21-2008 03:06 AM	754	2,169	{"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-2019-51	latest	en	0.710771
https://cs.stackexchange.com/questions/37135/couting-self-dual-functions	1,643,034,272,000,000,000	text/html	crawl-data/CC-MAIN-2022-05/segments/1642320304570.90/warc/CC-MAIN-20220124124654-20220124154654-00388.warc.gz	238,997,537	32,196	Couting Self dual functions The Dual of a Boolean function $F(x_1, x_2, ..., x_n)$, written as $F^D$ is the same expression as that of $F$ with $+$ and $.$ swapped. $F$ is said to be self dual if $$F=F^D$$ How can we count total number of self dual function with $n$ Boolean variables. I know For $n$ variables total $2^n$ minterms or maxterms are possible and any boolean function can be expressed as combination of minterms or maxterms. But what else is required to count all self dual functions of $n$ variable. Using de Morgan's laws, we get a more useful characterization of self-dual functions: those are functions satisfying $\lnot F(x_1,\ldots,x_n) = F(\lnot x_1,\ldots,\lnot x_n)$. Suppose that you knew the value of a self-dual function on all inputs in which $x_1$ is false. Can you recover the rest of $F$? Can you deduce the number of self-dual functions?	241	872	{"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}	3.171875	3	CC-MAIN-2022-05	latest	en	0.866797
https://www.numbersaplenty.com/63311808000	1,659,918,619,000,000,000	text/html	crawl-data/CC-MAIN-2022-33/segments/1659882570741.21/warc/CC-MAIN-20220808001418-20220808031418-00210.warc.gz	815,913,318	3,429	Search a number 63311808000 = 293537172163 BaseRepresentation bin111010111101101011… …011000011000000000 320001102022100002020210 4322331223120120000 52014130310324000 645030211434120 74400632326420 oct727553303000 9201368302223 1063311808000 1124939957471 121032abb5940 135c7c914cac 1430c8664480 1519a8389350 63311808000 has 960 divisors, whose sum is σ = 257117971968. Its totient is φ = 13536460800. The previous prime is 63311807963. The next prime is 63311808067. The reversal of 63311808000 is 80811336. It is a tau number, because it is divible by the number of its divisors (960). It is a Harshad number since it is a multiple of its sum of digits (30). It is a congruent number. It is an unprimeable number. It is a pernicious number, because its binary representation contains a prime number (17) of ones. It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 388415919 + ... + 388416081. Almost surely, 263311808000 is an apocalyptic number. 63311808000 is a gapful number since it is divisible by the number (60) formed by its first and last digit. It is an amenable number. It is a practical number, because each smaller number is the sum of distinct divisors of 63311808000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (128558985984). 63311808000 is an abundant number, since it is smaller than the sum of its proper divisors (193806163968). It is a pseudoperfect number, because it is the sum of a subset of its proper divisors. 63311808000 is a wasteful number, since it uses less digits than its factorization. 63311808000 is an odious number, because the sum of its binary digits is odd. The sum of its prime factors is 240 (or 197 counting only the distinct ones). The product of its (nonzero) digits is 3456, while the sum is 30. The spelling of 63311808000 in words is "sixty-three billion, three hundred eleven million, eight hundred eight thousand".	562	1,997	{"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-2022-33	latest	en	0.878335
http://metamath.tirix.org/mpeascii/ismndo1	1,720,967,869,000,000,000	text/html	crawl-data/CC-MAIN-2024-30/segments/1720763514580.77/warc/CC-MAIN-20240714124600-20240714154600-00696.warc.gz	25,831,380	2,145	Metamath Proof Explorer Theorem ismndo1 Description: The predicate "is a monoid". (Contributed by FL, 2-Nov-2009) (Revised by Mario Carneiro, 22-Dec-2013) (New usage is discouraged.) Ref Expression Hypothesis ismndo1.1 `\|- X = dom dom G` Assertion ismndo1 `\|- ( G e. A -> ( G e. MndOp <-> ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) )` Proof Step Hyp Ref Expression 1 ismndo1.1 ` \|- X = dom dom G` 2 1 ismndo ` \|- ( G e. A -> ( G e. MndOp <-> ( G e. SemiGrp /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) )` 3 1 smgrpmgm ` \|- ( G e. SemiGrp -> G : ( X X. X ) --> X )` ` \|- ( ( G e. A /\ ( G e. SemiGrp /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) -> G : ( X X. X ) --> X )` 5 1 smgrpassOLD ` \|- ( G e. SemiGrp -> A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) )` ` \|- ( ( G e. A /\ ( G e. SemiGrp /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) -> A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) )` 7 simprr ` \|- ( ( G e. A /\ ( G e. SemiGrp /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) -> E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) )` 8 4 6 7 3jca ` \|- ( ( G e. A /\ ( G e. SemiGrp /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) -> ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) )` 9 3simpa ` \|- ( ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) -> ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) ) )` 10 1 issmgrpOLD ` \|- ( G e. A -> ( G e. SemiGrp <-> ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) ) ) )` 11 9 10 syl5ibr ` \|- ( G e. A -> ( ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) -> G e. SemiGrp ) )` 12 11 imp ` \|- ( ( G e. A /\ ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) -> G e. SemiGrp )` 13 simpr3 ` \|- ( ( G e. A /\ ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) -> E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) )` 14 12 13 jca ` \|- ( ( G e. A /\ ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) -> ( G e. SemiGrp /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) )` 15 8 14 impbida ` \|- ( G e. A -> ( ( G e. SemiGrp /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) <-> ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) )` 16 2 15 bitrd ` \|- ( G e. A -> ( G e. MndOp <-> ( G : ( X X. X ) --> X /\ A. x e. X A. y e. X A. z e. X ( ( x G y ) G z ) = ( x G ( y G z ) ) /\ E. x e. X A. y e. X ( ( x G y ) = y /\ ( y G x ) = y ) ) ) )`	1,696	3,387	{"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-2024-30	latest	en	0.313913
https://community-forums.domo.com/main/discussion/60465/beast-mode-calculation-help-needed	1,718,264,069,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198861342.74/warc/CC-MAIN-20240613060639-20240613090639-00051.warc.gz	160,868,139	99,292	# Beast Mode Calculation Help Needed Options Member I need to create a new Column via Beast mode called % Sales Material based on the following calculation. (Sales Price - Actual Cost) / Sales Price I am struggling with the exact Beast Mode Code because Sales Price is on one Line Based on WTSTEP 000 And Actual Cost is on a Separate Line and is based on Beast Mode Where when WTSTEP = 010 it will take 'UnitCost' * 'QTY Ordered' • Coach Options I see in your example that the 3 entries share the same SO#, so would the % you're trying to calculate be at the SO# level? if that is the case if you display your card by SO# instead of WTSTEP a formula like the one below might get you what you need: ```SUM(`Sales Price`- `Actual Cost`)/SUM(`Sales Price`) ``` If for some reason you'd need to display things at the WTSTEP level but still need the same percentage to show on each line for the same SO#, you'd need to use a FIXED function to do this for you, something like: ```SUM(SUM(`Sales Price`- `Actual Cost`) FIXED (BY `SO#`))/SUM(SUM(`Sales Price`) FIXED (BY `SO#`)) ``` Hope this helps, (I'm guessing `Actual Cost` would be the addition of the 4 columns you have with the Cost word in them, so you'd need to put those in parenthesis and add them instead). • Contributor Options I think your beast mode calculation should be as below. 1. `(SUM``(`Sales Price`) - SUM(`Actual Cost`))/``SUM``(`Sales Price`)` Try and let us know. • Member edited August 2023 Options Update / FYI the Sale Price is a Single Line Field where as Actual Material Cost is multiple lines Summed within Card. This is what is causing me frustration / confusion. • Coach Options I see in your example that the 3 entries share the same SO#, so would the % you're trying to calculate be at the SO# level? if that is the case if you display your card by SO# instead of WTSTEP a formula like the one below might get you what you need: ```SUM(`Sales Price`- `Actual Cost`)/SUM(`Sales Price`) ``` If for some reason you'd need to display things at the WTSTEP level but still need the same percentage to show on each line for the same SO#, you'd need to use a FIXED function to do this for you, something like: ```SUM(SUM(`Sales Price`- `Actual Cost`) FIXED (BY `SO#`))/SUM(SUM(`Sales Price`) FIXED (BY `SO#`)) ``` Hope this helps, (I'm guessing `Actual Cost` would be the addition of the 4 columns you have with the Cost word in them, so you'd need to put those in parenthesis and add them instead). • Member Options I tried your first solution but the answer is not correct. I am getting 49% when I do the simple math in Excel. Here it is showing 39% ???? • Member Options Excel Calculation is not matching Calculation in DOMO. Used this calculation. ```SUM(SUM(`Sales Price`- `Actual Cost`) FIXED (BY `SO#`))/SUM(SUM(`Sales Price`) FIXED (BY `SO#`)) ``` • Contributor Options I think your beast mode calculation should be as below. 1. `(SUM``(`Sales Price`) - SUM(`Actual Cost`))/``SUM``(`Sales Price`)` Try and let us know. • Member Options Marcel, I found the issue on this. I had two different numbers labor and material being represented by a single field jt158_WTExtendedCost that are differentiated by the WT#. I created a Function in the ETL to break this out and I was able to get it to work with your second formula.	836	3,330	{"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}	2.9375	3	CC-MAIN-2024-26	latest	en	0.900168
https://discourse.julialang.org/t/tips-on-integrals-using-diffeqoperators/56769	1,653,485,932,000,000,000	text/html	crawl-data/CC-MAIN-2022-21/segments/1652662587158.57/warc/CC-MAIN-20220525120449-20220525150449-00030.warc.gz	257,362,077	5,656	# Tips on integrals using DiffEqOperators I’m trying to use DiffEqOperators to define the Kermack-McKendrick model, which is basically a PDE generalization of the simple SIR epidemiological model: The equation for I is a PDE, while that for S and R is an ODE with an integral of I over a at t. The declarations seem straightforward: @parameters t a β γ @variables S(…) I(…) R(…) @derivatives Dt’~t @derivatives Da’~a However, how does one describe integrals over one dimension (in this case, a)? You can’t yet. @zobot is going to start working on it though IIRC. You mean Feature request: add integro-differential equation support · Issue #572 · SciML/ModelingToolkit.jl · GitHub right? Kinda, but not quite. I was hoping to write down something like this for the equations (probably abusing all sorts of notation here): ``````@parameters t a β c γ @variables S(t) i(t,a) R(t) @derivatives Dt'~t @derivatives Da'~a Y(t) = sum(i[t,]) N(t) = S(t)+Y(t)+R(t) eqs = [Dt(S) ~ -βcY(t)S, Da(i) ~ -γi, Dt(R) ~ γ*Y] `````` (missing out the boundary conditions and domains right now), to be passed to DiffEqOperators to be solved by the method of lines, along the lines of this: https://europepmc.org/article/med/26337289 This involves integrating along the spatial dimension rather than the time dimension - the latter is the issue you refer to for integro-differential equation support. Yeah we can’t handle this in any of the discretizers right now. Lump it into the other requests. We’re getting to it, though a little slower than we hoped.	423	1,550	{"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-2022-21	latest	en	0.861387
https://www.jiskha.com/display.cgi?id=1264783570	1,503,516,798,000,000,000	text/html	crawl-data/CC-MAIN-2017-34/segments/1502886123359.11/warc/CC-MAIN-20170823190745-20170823210745-00162.warc.gz	910,243,253	3,993	# math posted by . wat is an equation of the line that passes through the point (4,-6) and has a slope of -3??? some one plzzz help me those are the choices y= 3x+6 y=3x+6 y=3x+10 y=3x+14 • math - None have a slope of three. Shouldn't the first one of the choices have a "minus" sign in front of the y? That would be the correct answer, if it did. ## Similar Questions 1. ### Equation of a straight line. 1. Find the equation of the line described in each case: a) Gradient 3, cuts through (0, 6). b) Steepness of 4, passes through (0, -2). c)Parallel to y = 5x - 1, cuts the y-axis at (0, 10). d)Cuts through (0, 7) and (5, 17) 2. Here … 2. ### Math(check) 1)Find the range of the relation [(-1,4)},(2,5),(3,5)}.Then determine whether the relation is a funtion. 4,5,5 is the range 4,5 is a function 2)Find f(-1),if f(x)= x^2-6x/x+2 (-1)^2-6(-1)/-1+2 1+6/-1+2 7/1 =7 3)Find f(a),if f(t)= 2t^2-t-2. … 3. ### math-slopes >wat is an equation of the line that passes through the point (4,-6) >and has a slope of -3? 4. ### math I have a few question so I will number them off. Please answer them for me I have a test tommorow and I am sure this can help other people too. 1.How do you make an equation that passes through a y-intercept and a certain point in … 5. ### Math 101 Find the equation for each of the following items below: a. A line that passes through (6,26) and has a slope of 3. b. A line that passes though the points (5,5) and (10,20) c. A line that passes through (9,25) and has a slope of -3. … 6. ### math i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation … 7. ### geometry I would love for someone to check my work on the seven problems that I did. I would be eternally grateful. I am going to list my problems and answers. Even if you only want to check one of them, that would be great. 1. Write an equation … 8. ### Algebra 1.Tell whether the sequence is arithmetic. If it is, what is the common difference? 9. ### Math What is the y-intercept of y = 2/3x + 2? I have to write it out but how?	703	2,207	{"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}	3.78125	4	CC-MAIN-2017-34	longest	en	0.912132

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