text:
# How Many Combinations With 6 Numbers

(a) In how many ways can a student answers true-false questions ? (b) In how many ways may the test be completed if a student is imposed for each incorrect answer, so that the student may leave some questions unanswered? 8(a) Number of ways = t= (b) Number of ways = u8=. Spin Quantum Number (m s): m s = +½ or -½. How many committees of 3 can be formed from a group of 4 students? This is a combination and can be written as C (4,3) or 4 C 3 or. For the sake of output and server capacity, we cannot let you enter more than 8 items! #N#Quick! I need help with:. The number of combinations of n objects taken r at a time is. For example if the lottery was 6 numbers with a pool of 40, chances to win would be: 6/40 x 5/39 x 4/38 x 3/37 x 2/36 x 1/35 = 720/2763633600 = 0. Number of 7 digit numbers = 7! 3! × 2! = 420. not repetitions, in each of these combinations, the order is not important, thus 1234 is the same as 2134 and 3421, 210 and combinations or groups if you prefer but each of these combinations has different numbers. In the end, you will end up with. I wish to calculate the total number of combinations using the number of entries in 6 fields. I executed the code as per your question and got 63 as the total possible combinations. Part of the series: Number Help. Five people are waiting to take a picture. (n stands for the total number of items; r stands for how many things you are choosing. Download Copy to Clipboard Copy to phone. Level: All Question: I have a 6 character field that can use any combination of alpha-numeric characters (A-Z, 0-9). Specifies the orientation of the spin axis of an electron. How many different combinations are offered?. 42" it is telling you to expect to average having all six winning numbers among your 22 one time in 187. A locker combination consists of three different numbers from the set of 30 different numbers on the face of the lock. In 2019-20, the. For, the number of ways of taking 2, is the same as the number of ways of leaving 6 behind. Example has 1,a,b,c Will allow if there is an a , or b , or c , or a and b , or a and c , or b and c , or all three a,b and c. How many three digit numbers can be formed using digits 2, 3, 4, 7, 9 so that the digits can be repeated. is 13983 1 8 16 "". This means that XYZ is considered the same combination as ZYX. Thus the s subshell has only one orbital, the p subshell has three orbitals, and so on. 1 = 6! b) How many arrangements are possible if only 3 of them are chosen? Solution: 6. Take the line "6 if 22 = 1 in 187. The bottom indices, k on the left and n − k on the right, together add up to n. Apply formulas for permutations and combinations; This section covers basic formulas for determining the number of various possible types of outcomes. To find the number of ways to select 3 of the 4 paintings, disregarding the order of the paintings, divide the number of permutations by the number of ways to order 3 paintings. Adding Variation. The example spreadsheet below also shows the Combina function used to calculate the number of combinations (with repetitions) for other numbers of objects taken from a set of 6. For example the dial stops on 2 and 3. Select a blank cell and type this formula =TEXT(ROW(A1)-1,"0000") into it, and press Enter key, then drag the autofill handle down until all the 4 digits combinations are listing. However, in this case, the order of the flavors does not matter (e. Third Number: 22 ENTERING YOUR COMBINATION Note: If your lock has a larger silver body as shown at right, after Step 3 you must turn the dial to the left until it stops and then proceed to Step 4. We've generated every possible number combination for most lottery games in the US and around the world. A locker combination consists of three different numbers from the set of 30 different numbers on the face of the lock. 52 divided by 4 is 13 which means that every period (in our case every other month), 13 individual dinners are scheduled and hosted by one of the four couples in the set. this is assuming you can repeat letters, so "aaaaa" is acceptable, and also assuming no difference between uppercase and lowercase letter, so that "abCde" is the same as "abcde". 19 Materials. combination. 4 Suppose we were to list all 120 possibilities in example 1. AK or T5) = 16 combinations; Pairs (e. For example, 5! 5 4 3 2 1 120= ⋅ ⋅ ⋅ ⋅ =. The combinations are as follows: 1 : 0 + 8 + 9 = 17 2 : 0 + 9 + 8 = 17 3 : 1 + 7 + 9 = 17 4. Always: n C k = n C n − k. The State then selects 20 numbers. I am trying to find a code for excel that I can use to list all possible combinations of the numbers/symbols 0-9, #, and * or just numbers 0-12 in 6 digit combinations. I assume you're asking, how many ways can you choose six numbers from a group of numbers 1 to 42 inclusive. the formula is nPr = n! / (n-r)! in this case you have 6 options, so n= 6, then you have to choose 4 from 6, so r =4. A new United States study has found that if you’re masking masks at home during the COVID-19 pandemic, then using a combination of two different fabrics and ensuring a good fit could offer the. Figuring out how to open a four-number combination lock may be a little confusing initially, but it is pretty easy to learn how to open one. Your final choice — the most important — is for the Powerball, the one red ball, which must be between one and 29. 52 divided by 4 is 13 which means that every period (in our case every other month), 13 individual dinners are scheduled and hosted by one of the four couples in the set. But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. 1 combination comprising 0 numbers,6 combinations comprising 1 numbers, 15 combinations comprising 2 numbers, 20 combinations comprising 3 numbers, 15 combinations comprising 4 numbers, 6. Apr 12, 2013 - Explore teacheramber's board "Math - combinations to 10" on Pinterest. You can extend this principle to any number of selections and any size of combination : if you wanted to combine any 4 of your six numbers then the number of possibilities would be 6 x 6 x 6 x 6 = 1296. The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made. For example, 5! 5 4 3 2 1 120= ⋅ ⋅ ⋅ ⋅ =. Choose those numbers having k nonzero bits, although this is very inefficient even for small n (e. Number and Number Sense Module – Grade 1 2 7 Cube Connections Reporting Category Number and Number Sense Topic Count and write numerals to 100 Primary SOL 1. They each shake hands with everyone else. How many different lock combinations are there on an old locker padlock? The idea of having a "combination lock" is what makes this one tricky. L ook at a thousand of the millions of Facebook ads Donald Trump has run, and it’s hard to believe that they represent a winning strategy. Permutations and Combinations Permutations 1. objects chosen from. 6^10 or 7^10 b. If any combination of that number comes up, the player wins the straight amount of $250 for a$. But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. LOOK AT THE TREE DIAGRAM ABOVE. I found a similar question on this forum but it was only for the numbers 0,1,3,4. Choose 2 Prizes from a Set of 6 Prizes. This time, it is six times smaller (if you multiply 84 by 3! = 6 , you'll get 504). You have won first place in a contest and are allowed to choose 2 prizes from a table that has 6 prizes numbered 1 through 6. = 6! 3! × 2! = 60. take the 2 numbers they stop on and get the middle number. 1-6-5-2 (Jab, right uppercut, left uppercut, cross) Throw the uppercuts fast and keep your alternate hand up during them. Has a gross vehicle weight. We want to select 13 cards, so r = 13. Permutation and Combination Solve Problems Quickly. For the example, you can calculate 10! with (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1), which gives you 3,628,800. Think of it this way: He has 4 ways to select a shirt and for each of those 4 ways to select a shirt, he has 6 ways to select a tie, giving you 24 shirt and tie combinations. Click Kutools > Insert > List All Combinations, see screenshot: 2. How many ways can 11 players be positioned on a soccer team considering that the goalie cannot hold another position other than in goal?. This page is on the topic of "Permutation and Combination" as a subtopic of Aptitude Test Questions and Answers. Yes 10^15, if no repeats were allowed you would need a larger number pool. How many different lock combinations are there on an old locker padlock? The idea of having a "combination lock" is what makes this one tricky. Consequently, the total number of arrangements in which n, u, and m are together, is 3!· 5! = 6· 120 = 720. Not the ones I gave you but the ones you get. That combination of new claims for state assistance, for federal assistance and for the additional pandemic payment meant the state received nearly 500,000 new claims last week. How can I calculate the number of possible? 4234 1426 5146 2513. 6^10 or 7^10 b. Divide 48920775120 by 720 to account for this, to get 67945521. Number of 7 digit numbers = 7! 3! × 2! = 420. Knowing how to properly dial in the combination of numbers to open a safe is as important as knowing the numbers. How many combinations if I'm starting with a pool of six, how many combinations are there? How many combinations are there for selecting four? Another way of thinking about it is how many ways are there to, from a pool of six items, people in this example, how many ways are there to choose four of them. 7% from 3-point range to go with 4. How many different combinations of three numbers can be selected from L so that the numbers could represent the side lengths of a triangle?. 1000000 (~ 1. For example, if I have five students and I want to figure out how many ways they can sit in five chairs, I’m going to use the permutations formula. How many different groups of players can be. Number is an accepted word in Word with Friends having 14 points. For anyone still confused as to whether it is 10! or 2^10 each game has exactly 2 possible outcomes. (You can also type the values which are separated by commas into the Text box one by. The bottom indices, k on the left and n − k on the right, together add up to n. Does anybody ha a good tutorial to make this kind of calculations, or can anybody help me with this?. In the 2/5 mini-lottery example above, we have two numbers chosen from a group of 5 numbers. Therefore, the. I have written a piece of code to find solutions to such questions. In the List All Combinations dialog box, do the following operations: (1. The combinations are as follows: 1 : 0 + 8 + 9 = 17 2 : 0 + 9 + 8 = 17 3 : 1 + 7 + 9 = 17 4. For example if the lottery was 6 numbers with a pool of 40, chances to win would be: 6/40 x 5/39 x 4/38 x 3/37 x 2/36 x 1/35 = 720/2763633600 = 0. Directions: The questions in this section consists of the repetition of the words or letters or numbers or alphabets. 4 Permutations and Combinations: Part 1 Permutations 1. (a) How many different lock combinations are there? (b) What is the probability of guessing a lock combination on the first try? Forming license Plate Numbers How many different license plate numbers can be made by using one letter. 2)Which of the following quantum number combinations is not allowed in an atom? D) n = 1, l = 0, m = 1. Therefore the probability of winning the lottery is 1/13983816 = 0. How many 6-number combinations can be generated from the numbers from 1 to 42 inclusive, without repetition and with no regards to the order of the numbers? Problem Answer: There are 5,245,786 combinations 6-number combinations can be generated. There are 80 possible numbers. 43 silver badges. LOOK AT THE TREE DIAGRAM ABOVE. Outside of probability, Pascal’s Triangle is also used for:. Actually, these are the hardest to explain, so we will come back to this later. (no duplicates) It's possible to have any of the following: Edit: for some reason I cannot add more comments. An unordered selection of r elements from a set of n elements is the same as a subset of size r or an r-combination of the set. I would like to have all combinations of 6 numbers in a range of number 1 - 60. Based on that assumption Let's say the total number of combinations is x. The five white balls have possible numbers ranging between 1 and 70, while the Mega Ball can be between 1 and 25. Home › Math › Navigate a Grid Using Combinations And Permutations Puzzles can help develop your intuition -- figuring how to navigate a grid helped me understand combinations and permutations. generates ALL lotto numbers in one cluster or group, 6 numbers per each line; e. The resulting smaller group is a subset of the original set. With your purchase you will receive 3,838,380 total number combinations appearing in 4 text files with up to 1 million number combinations per file. There would be 36 possible first numbers and 35 possible other numbers to go with it. Only the minimum levels of the following filters are applicable in this type of software: Ones, Pairs, Triples, Quads, Quintets, Sextet. For every combination i will calculate the R square (with my response variable) and then discard the ones that doesn't meet the required R. However, you can pick the 6 numbers in any order, and there are 720 possible ways to arrange 6 numbers (6*5*4*3*2*1, or 6! on your calculator; now you know what that x! button is for). Washington Department of Fish and Wildlife biologists documented a minimum of 108 wolves in 21 packs and 10 breeding pairs in 2019. Number of squares with side 4cms: 1. In 2019-20, the. Permutation and Combination - General Questions. No two digits the same. LOOK AT THE TREE DIAGRAM ABOVE. Within the art of lock picking lies the infamous combination lock, a device immune to our tension wrenches, lock picks, and standard methods of lock picking. It arises from the fact that every three cards you choose can be rearranged in six different ways, just like in the previous example with three color balls. Let say smallest square is of side 1cms then. Using that formula, how many chromosomal combinations can result from meiosis when the diploid number is 16? 28 = 256 different combinations. When working with combinations of numbers you should always remember a few key things. How many natural numbers less than 10 000 include. There are 80 possible numbers. For the sake of output and server capacity, we cannot let you enter more than 8 items! #N#Quick! I need help with:. pick3 numbers, permutations, lock combinations, pin-codes): 7,731,052,560 (~7. 5 or if you numbers were 2. The number of tiles in a dominoes set is calculated by the following formula (where n is the highest number on a domino, e. you can have from 000,000 to 999,999, that’s basically 1 million different numbers. In how many ways can you form a 3 digit number, using only the digits of the number 21 150? 2. c) You would need to hire 13,983,816/576, or about 24,278 people to buy tickets with all the possible. Two electrons are found in the same atom. Combination product definition, reports, examples and common questions. The soccer team has 20 players. Attempt popular combination options such as birthdays, anniversaries, PIN codes and. In many cases, the biggest contracts are negotiated to varying extents by ownership. The number of combinations of n = 6 different investment proposals selected x = 3 at a time simultaneously equals:. The only concerning number in the region was uncompensated care at 2. There is only one way of winning. combination. Inovio said it expects to have the first results from the trial in the fall. That use of the word “combination” here is a red herring — the fact is, this device should be called a “permutation lock” because the order does indeed matter. Find the least value of "x" that will make the statement true. a 6-49 lotto game will have clusters of 9 lines (combinations), 6 numbers per line; the last line will repeat 3 numbers from previous combinations. n = 20 would require visiting about one million numbers while the maximum number of allowed k combinations is about 186 thousand for k = 10). some counting methods that should make our work a lot easier Methods Used for Counting 1. Number is an accepted word in Word with Friends having 14 points. You have 3 numbers, each number needs to be in the range of 0 to 38; the answer is there are 39 to the power of 3 possibilities = 59,319 different combinations, simple as that. 1 percent to 40. If exactly one of them is uppercase, then the search space is only expanded by -- change the first character to upper, change the second to upper, etc = 26^6 * 6. We want to find how many possible 4-digit permutations can be made from four distinct numbers. Which is 27,680,640,625 possible combinations. There is only one way of winning. How many words can be formed using all the letters of the word EQUATION so that i) all vowels are. Minimum Number: The lowest number in the range of available numbers. What about 20! or 100!? Most calculators including the TI 's series will only calculate factorials up to 69!. 5 When repetition of objects is allowed The number of permutations of n things taken all at a time, when repetion of objects is allowed is nn. Combinations and Permutations. I have written a piece of code to find solutions to such questions. I choose three elements from list L. How many ways can you arrange three people in a line? 2. The topics covered are: (1) counting the number of possible orders, (2) counting using the multiplication rule, (3) counting the number of permutations, and (4) counting the number of combinations. assuming you mean a 4 digit lock: 10 x 10 x 10 x 10 for decimal (10000) Posted 8 years ago. 67%, which. Enter number of numbers per line and number of combinations to generate, then click on Generate Lottery Combinations button. Very useful for all freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, MHCET, XAT, NMAT, GATE. Yes 10^15, if no repeats were allowed you would need a larger number pool. The number of ways of choosing the 4 people is C(10,4) = 210 If the order does matter then we use P(n,r). Using Excel's =combin(45,6) formula, I can work out that there are 8145060 six number combinations. These numbers may be even higher, in reality, due to under-reporting; many Hong Kongers are reluctant to talk openly about or disclose mental illness due to deep-rooted social stigma and. How many ways can this be done? Thanks. If you want to make these combinations shorter, remember that you can always remove a punch from the end or beginning. In this case the calculation of P(6,3) is simply 6 x 5 x 4 (start at 6 and go for 3 factors). I am trying to generate all possible number combinations of 6 numbers between 1 and 49. 69 bronze badges. Poker starting hand combinations basics. Hence the required number of 7 digits numbers = 420 - 60 = 360. n = 20 would require visiting about one million numbers while the maximum number of allowed k combinations is about 186 thousand for k = 10). Directions: The questions in this section consists of the repetition of the words or letters or numbers or alphabets. Level: All Question: I have a 6 character field that can use any combination of alpha-numeric characters (A-Z, 0-9). The lotto software generates random combinations for lotto-6, but 12 numbers per combination; the data file must still be in the 6-numbers-per-line format as in the Bright6 programs. depends on how many numbers. **** Made a mistake, in the above I assumed you can choose any of those 55 numbers from 1-6, but I think you might mean you can only choose from 55 numbers once, 6 times. Ultra-Lotto-6-58 Picker, Random Number, Combination, Your Numbers,Philippines, Ultra-Lotto-6-58,Ultra-Lotto-6-58picker, Ultra-Lotto-6-58 random number, Ultra-Lotto-6-58 combination, Ultra-Lotto-6-58 your numbers,Philippines,. (You can also type the values which are separated by commas into the Text box one by. objects such that. We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys). Permutation and Combination - Learn and practice Permutation and Combination with solved Aptitude Questions and Answers accompanied by easy explanation, shortcuts and tricks that help in understanding the concept clearly. A telephone number is a sequence of digits assigned to a fixed-line telephone subscriber station connected to a telephone line or to a wireless electronic telephony device, such as a radio telephone or a mobile telephone, or to other devices for data transmission via the public switched telephone network (PSTN) or other public and private networks. For a score of n (for example, if 3 choices match three of the 6 balls drawn, then n = 3), () describes the odds of selecting n winning numbers from the 6 winning numbers. Using generators 149 and 58, the area is 162789354; using 224 and 153, the area is 917358624. Find the least value of "x" that will make the statement true. Begin by drawing four lines to represent the 4 digits. This gives you 16 lines. (2) 3 double digit numbers. You can put this solution on YOUR website! how many 6 digit combinations of the numbers o-9 can be made-----0 to 9 is 10 numbers--> 10^6 = 1,000,000 if you include 000000, 000001, etc. Here clock-wise and anti-clockwise arrangement s are same. How can I calculate the number of possible? 4234 1426 5146 2513. Let's take a look at the odds of having winning numbers among groups of 12, 18 and 22 randomly selected numbers in a typical 6/49 game. The number of possible outcomes in which at least one die shows 2 is. Pascal’s Triangle can be used to find combinations. Most Important Combinations to Remember Bets on certain dice numbers are considered more volatile, so it would be best to consider some less risky options. The formula for combinations: To find all of the differennt ways to arrange r items out of n items. Does anyone have any info on how I can accomplish this?. How many different four digit numbers can be formed from the digits 2, 3, 4, 6 without repetition. 0: Students use the fundamental counting principles to compute combinations and permutations. What you're saying with your formula, GW, is that for the first number you have 38 possibilities, for second you only have 37 and for the third only 36. We want to select 13 cards, so r = 13. (You can also type the values which are separated by commas into the Text box one by. Combinations. Sometimes it takes forever to get dressed. c) You would need to hire 13,983,816/576, or about 24,278 people to buy tickets with all the possible. One Response to “How many ways to add up to any number? Sequence of partition numbers found to be fractal” Susan Donovan Says: April 1, 2011 at 6:58 pm. 7 choices for 1st digit times 6 choices for 2nd times 5 for 3rd times 4 for 4th, 840 combinations, list low to high looks like 2356 2357 2358 2359 2365. Number of squares with side 3cms: 2. How many combinations of 6-digit number between 000001 to 999999 that contains the digit 1 or multiples of digit 1?The 6 digit number is between… October 7, 2019 October 7, 2019 Kenny Combs Websites. Each line is made unique by prefixing the first half with "0" and the second half with "1". Of course he recognized also some of the faults of Jewish exegesis, as, for example, the forced combination of unconnected verses (comm. In Excel, you can use below formula to list all possible 4 digits combinations of number 0 to 9. x = 42! / (36! x 6!) Cancelling out 36! from the numerator and denominator x = 42 x 41 x 40 x 39 x 38 x 37 / 6 x 5 x 4 x 3 x 2. Find 4! with (4 * 3 * 2 * 1), which gives. If order matters (e. Washington Department of Fish and Wildlife biologists documented a minimum of 108 wolves in 21 packs and 10 breeding pairs in 2019. The number of permutations of a set of three objects taken two at a time is given by P(3,2) = 3!/(3 - 2)! = 6/1 = 6. There are four overall possibilities. Does anyone have any info on how I can accomplish this?. Using the digits 1 to 9, with none repeating, 60,480 combinations can be made. Exactly, so you will need no variables except the index variable in your for loop! 08-24-2012 #19. with up to 40 participants in April, dosing the first patient on April 6. The order of the combinations is not important like: 1-2-3-4-5-6 and 6-5-4-3-2-1. Imagine that you have forgotten the combination. When you choose a five-number Combination Play, the five numbers from 1 to 49 that you select remain consistent for every combination. 8^10 or 10^8 c. objects such that. **** Made a mistake, in the above I assumed you can choose any of those 55 numbers from 1-6, but I think you might mean you can only choose from 55 numbers once, 6 times. The number you are looking for is much smaller = 26^6 * 6. So that would be:. How many combinations of 6-digit number between 000001 to 999999 that contains the digit 1 or multiples of digit 1?The 6 digit number is between… October 7, 2019 October 7, 2019 Kenny Combs Websites. Review the formula for combinations. Each line is made unique by prefixing the first half with "0" and the second half with "1". LOOK AT THE TREE DIAGRAM ABOVE. My aim is to achieve all the combinations like this:. In the Pick–6 Lotto, there are C(42, 6) = 5,245,786 ways to select numbers. The company began clinical trials in the U. Prints generated number combinations and can export them to a tab-delimited text file (easily. so the number of different combinations to choose between are 49 x 48 x 47 x 46 x 45 x 44 = 10068347520. I then want to remove all of the past draws (I can do this manually). Part of the series: Number Help. Check the instruction manual of your safe to determine how many numbers are in your lock combination. You can generalize that: the number of N-digit combinations is 10 N. In Wisconsin, 1. of ways =240 so total of 720 even numbers are possible. You then have to push it closed tighter first, before it will open, if the combination is correct. Consider the selection of a set of 4 different letters from the English alphabet. To determine the number of combinations, find the number of digits possible for each position and then multiply these numbers. Permutation (nPr) and Combination (nCr) calculator uses total number of objects n and sample size r, r\leq n, and calculates permutations or combinations of a number of objects r, are taken from a given set n. The easiest way to go through the combinations, ensuring that you won't miss one, is like this:. i think what you mean is permutation not combination. In how many ways can you form a 3 digit number, using only the digits of the number 21 150? 2. 2n , where n = number of different chromosomes. Forgot or lost the combination to a suitcase? Instead of prying open or picking the lock of a basic combination pad, find the numbers and recover the combination without ruining the lock with the trick tip in this instructional video. Number of squares with side 3cms: 2. We want to find how many possible 4-digit permutations can be made from four distinct numbers. Number is a 6 letter medium Word starting with N and ending with R. This is the same as listing all the subsets of size 3 of the set. How many different combinations of 2 prizes could you possibly choose? In this example, we are taking a subset of 2 prizes (r) from a larger set of 6 prizes (n). Using the digits 1 to 9, with none repeating, 60,480 combinations can be made. Finally, each spot can be a different color (rby, ryb, bry). Explanation:. Before you start to combine the color, mark the numbers on your yarn label with 1,2,3,4,…. There are four overall possibilities. A bag contains 5 black and 6 red balls. to get how many possible arrangements = 6P4 = 6! / (6-4)! = 3x4x5x6=360 arrangements. I am writing this blog post (the first after nearly two years!) in lockdown mode because of the rapidly spreading SARSCoV2 virus, the causative agent of the COVID19 disease (a poor choice of a name, since the disease itself is really SARS on steroids). How many combinations of 6-digit number between 000001 to 999999 that contains the digit 1 or multiples of digit 1?The 6 digit number is between… October 7, 2019 October 7, 2019 Kenny Combs Websites. Observe that the number of ways of selecting 3 officers is 6 times as large as the number of ways of selecting a committee of 3. If any combination of that number comes up, the player wins the straight amount of $250 for a$. Not the ones I gave you but the ones you get. 626071171e31 For a password with 6 upper and lower case letters i used 52!6! I just would like to know am i on the right path with this? Thanks in advance, Sara. Remember the numbers and how many numbers in each row can change but will always be 1-7 and I always need to find every number that can complete the sequence 1-7 by using one number from each row. a) How many different arrangements (permutations) are there of the digits 01234?. In how many ways can you form a 3 digit number, using only the digits of the number 21 150? 2. take the 2 numbers they stop on and get the middle number. Based on 389 results, 67. Other safes allow you to program a combination of anywhere from two to 10 letters. Search More words for viewing how many words can be made out of them Note There are 5 vowel letters and 6 consonant letters in the word combination. Similarly, if all the digits from 1 to 9 were allowed (with no digit repeated), then the answer would be 9*8*7*6*5*4 = 60480. Two electrons are found in the same atom. There are 80 possible numbers. However, many have questioned whether home-made attempts with everyday fabrics are useful in helping to prevent the spread of the disease. 6 trillion health care industry, are at risk of failing, health care experts say. The number of combinations is always smaller than the number of permutations. If it does not, use the formula for combinations. We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys). You then have to push it closed tighter first, before it will open, if the combination is correct. Part of the series: Number Help. 15: "stulta contentione"); he sometimes regards his teacher's interpretation to be arbitrary, and opposes to it his own (ib. It is an online math tool which determines the number of combinations and permutations that result when we choose r objects. But you want at least one item in each selection, so subtract 1 to account for the empty set. pick3 numbers, permutations, lock combinations, pin-codes): 427,518,000 (~427. But there are then 26+ 10= 36 letters or digits (You say "numbers", but if a single number could be say 1000000000000, there is no finite answer) for each of the remaining 4 symbols: there are (1)(36)(36)(36)(36)= 36 4 ways to make "combinations of 5 letters or digits, starting with F". If you are trying to open a New England Safe with a dial combination, It is probably a Group 2 or Group II type lock. 42" it is telling you to expect to average having all six winning numbers among your 22 one time in 187. Based on the new findings, the researchers conclude that masks made using a combination of readily available fabrics still have the potential to provide significant protection from respiratory aerosol droplets. Learn How to Solve Permutation and Combination Question Quickly form PrepInsta. Find 4! with (4 * 3 * 2 * 1), which gives. Thus, Total number of squares = 17. The soccer team has 20 players. Mathematically the number of combinations is known as N things taken M at a time the the number of combintaions is N^M. Four-number combination locks, while not as popular as three-number combination locks, can be used on luggage, lockers, on safes, and more. write these down. You pick any 6 numbers from 1 to 49. How many 4 digit numbers can be formed without repeating any digit from the following digits: 1, 2, 3, 4 and 6?. So with possible combinations from 1- 55 with 6 numbers, that would be: 55^6. Given a 60-number dial with three cams and three digits of play, the search space is reduced from 60 × 60 × 60 to 20 × 20 × 20, a 96% reduction in potential combinations. Always: n C k = n C n − k. Check the instruction manual of your safe to determine how many numbers are in your lock combination. Each combination of this type has 6 different box combinations, so your odds of winning by playing one "single" box combination would be approximately 1 in 167. If no repetitions are allowed, and the. of ways =240 and last digit = 6, total no. The formula for combinations: To find all of the differennt ways to arrange r items out of n items. In how many ways can you form a 3 digit number, using only the digits of the number 21 150? 2. your number would be 2. Hence the required number of 7 digits numbers = 420 - 60 = 360. assuming you mean a 4 digit lock: 10 x 10 x 10 x 10 for decimal (10000) Posted 8 years ago. 06e+67, a number that means absolutely nothing to me. The new code should be set. With your purchase you will receive 3,838,380 total number combinations appearing in 4 text files with up to 1 million number combinations per file. The easiest way to go through the combinations, ensuring that you won't miss one, is like this:. Seventy-seven people have been hospitalized; 23 remain so, up five from the previous day. Technically, you would call these permutations rather than combinations because values like 33363 and 33336 both appear in the list as they represent different numerical values. Number combinations are stored in basic text files with approximately 50K - 1M number combinations per file so that you can easily open them in any word processor or Excel. I have written a piece of code to find solutions to such questions. We can make 6 numbers using 3 digits and without repetitions of the digits. These numbers may be even higher, in reality, due to under-reporting; many Hong Kongers are reluctant to talk openly about or disclose mental illness due to deep-rooted social stigma and. So there are three different ways to make a Four (1-3, 2-2, 3-1) and also three ways to make a Ten (4-6, 5-5, 6-4). then 10!/ (6!4!)=210 and these 210 are unique, i. So, with the 24 playing cards, after a card is dealt, you do not put it back into the deck. The soccer team has 20 players. I assume you're asking, how many ways can you choose six numbers from a group of numbers 1 to 42 inclusive. Spin Quantum Number (m s): m s = +½ or -½. How many three digit even number with distinct digits can be formed with the digits 1,2,3,4,5 and 6 ? 10. If I remove ALL the numbers that are in sequence ie 1,2,3,4,5,6 or 10,11,12,13,14,15,16 as examples, how many combinations do I have left. 5 When repetition of objects is allowed The number of permutations of n things taken all at a time, when repetion of objects is allowed is nn. n = 20 would require visiting about one million numbers while the maximum number of allowed k combinations is about 186 thousand for k = 10). Outside of probability, Pascal’s Triangle is also used for:. Lotto 6/42 has 42 numbers. With 8 items on your menu, the number of possible combinations will be 2 8 = 256. What matters are the items selected and not the order in which they were selected. The word "has" followed by a space and a number. A locker combination consists of three different numbers from the set of 30 different numbers on the face of the lock. 7 choices for 1st digit times 6 choices for 2nd times 5 for 3rd times 4 for 4th, 840 combinations, list low to high looks like 2356 2357 2358 2359 2365. In how many ways can you form a 3 digit number, using only the digits of the number 21 150? 2. I have been trying this manually, and seems like it will take a whole lifetime, and may still not be accurate. x = 3 = number of investment proposals that will be simultaneously selected to fill each combination group. (v) A and F must sit at the end of each row Put A and F at the ends and B, C, D and E In between them. There are 80 possible numbers. The formula for combinations: To find all of the differennt ways to arrange r items out of n items. The easiest way to go through the combinations, ensuring that you won't miss one, is like this:. Step 5 - Set Desired Combination. assuming you mean a 4 digit lock: 10 x 10 x 10 x 10 for decimal (10000) Posted 8 years ago. I have written a piece of code to find solutions to such questions. a 6-49 lotto game will have clusters of 9 lines (combinations), 6 numbers per line; the last line will repeat 3 numbers from previous combinations. How many different groups of players can be. (You can also type the values which are separated by commas into the Text box one by. Warning: "continue" targeting switch is equivalent to "break". I have 6 items and want to know how many combinations are possible in sets of any amount. assuming you mean a 4 digit lock: 10 x 10 x 10 x 10 for decimal (10000) Posted 8 years ago. Numbers in Set: The quantity of numbers in one set ("ticket"). You can extend this principle to any number of selections and any size of combination : if you wanted to combine any 4 of your six numbers then the number of possibilities would be 6 x 6 x 6 x 6 = 1296. Learn vocabulary, terms, and more with flashcards, games, and other study tools. We've generated every possible number combination for most lottery games in the US and around the world. Question 3: How many words can be formed by 3 vowels and 6 consonants taken from 5 vowels and 10 consonants. Since you have 6 numbers, then you have all the possible numbers between zero (000,000) and 999,999 inclusive, hence 1 million possible combinations. 5 or if you numbers were 2. 5-digit numbers are to be formed from the digit 1, 2, 3, 4, 5, 6, 7, 8. 6 A combination lock has 40 numbers on it. The formula for combinations: To find all of the differennt ways to arrange r items out of n items. Identify the greater number in each pair. Typical padlocks are manufactured with generous tolerances, allowing two, three or even more digits of 'play' in the correct access sequence. a) No order is implied here. I am trying to generate all possible number combinations of 6 numbers between 1 and 49. In making the choices, sometimes order matters, and sometimes it doesn't. You can generalize that: the number of N-digit combinations is 10 N. We want to find how many possible 4-digit permutations can be made from four distinct numbers. The total number of ways of picking six balls is out is therefore equal to 49x48x47x46x45x44. Use the 112-23-3445 for example. Now compare that to the number of possible lottery winning combinations. The combinations were formed from 3 letters (A, B, and C), so n = 3; and each combination consisted of 2 letters, so r = 2. That use of the word “combination” here is a red herring — the fact is, this device should be called a “permutation lock” because the order does indeed matter. Warning: "continue" targeting switch is equivalent to "break". i think what you mean is permutation not combination. A combination is a grouping or subset of items. 5 When repetition of objects is allowed The number of permutations of n things taken all at a time, when repetion of objects is allowed is nn. The 2020 NFL Draft's first night drew a record 15. We want to find how many possible 4-digit permutations can be made from four distinct numbers. By the way, that method leads to over 700 different possible combinations for the one side, if the person has different combinations on each side that jumps to 5,000 different. Number is a 6 letter medium Word starting with N and ending with R. 67%, which. To start with, of the six numbers that are actually drawn, you need a combination of three of them, so how many combinations of 3 can you choose from 6? It's: Your other three numbers must come from the 53 numbers that are not drawn, so the number of combinations of 3 you can choose from 53 is. How many different combinations are offered?. Poker starting hand combinations basics. The company began clinical trials in the U. And finally, the bottom row (shaded in blue) shows the number of possible combinations displayed as a percentage. The number of ways of choosing 6 numbers from 49 is 49 C 6 = 13 983 816. The pandemic presents a formidable challenge for rural hospitals, which have faced 120 hospital closures over the past decade and frequently struggle to recruit staff and balance the books. Therefore, the number of ways in which the 3 letters can be arranged, taken all a time, is 3! = 3*2*1 = 6 ways. How Many Combinations of Five Numbers Can Be Made Out of Twenty Five Numbers?. The number of ways of choosing the 4 people is C(10,4) = 210 If the order does matter then we use P(n,r). 43 silver badges. (3) 4 single & 1 double digit numbers. The total number of combinations is a factorial of 52, or 52!, which translates to 8. depends on how many numbers. Therefore, the. Warning: "continue" targeting switch is equivalent to "break". The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made. Create All Possible Lottery pick numbers from a 9 digit number - No leading 0's Do you also want to see all combinations of 6 numbers that can be selected from the set of 2-digit numbers that we can construct from a 9-digit SSN? A concrete example of some of the desired output would be helpful. AVOID LOW NUMBER COMBINATIONS. when second last digit is 4 remaining 4 digits can be filled in 120 ways, similarly second last digit is 6 remained 4 digits can be filled in 120 ways. Review the formula for combinations. Now compare that to the number of possible lottery winning combinations. So there are 210 subsets of size 6 from a group of 10. Choose those numbers having k nonzero bits, although this is very inefficient even for small n (e. At this time last month, voters preferred Democrats by 7. A Baryon is 3 quarks and a Meson is 2 quarks, so that limits the number of combinations. This is how many combinations are possible if you can pick any of the 24 numbers more than once. Start studying Probability, Permutations, Combinations. Number of 7 digit numbers = 7! 3! × 2! = 420. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?. 52 divided by 4 is 13 which means that every period (in our case every other month), 13 individual dinners are scheduled and hosted by one of the four couples in the set. For example, rolling a 7 has six combinations. **** Made a mistake, in the above I assumed you can choose any of those 55 numbers from 1-6, but I think you might mean you can only choose from 55 numbers once, 6 times. Create All Possible Lottery pick numbers from a 9 digit number - No leading 0's Do you also want to see all combinations of 6 numbers that can be selected from the set of 2-digit numbers that we can construct from a 9-digit SSN? A concrete example of some of the desired output would be helpful. Theorem: C(n-1+r,r) is the number of r-combinations of n elements with repetition. 5 or if you numbers were 2. The combinations are as follows: 1 : 0 + 8 + 9 = 17 2 : 0 + 9 + 8 = 17 3 : 1 + 7 + 9 = 17 4. You can put this solution on YOUR website! how many 6 digit combinations of the numbers o-9 can be made-----0 to 9 is 10 numbers--> 10^6 = 1,000,000 if you include 000000, 000001, etc. Only now, there are 3 equal rows of 6. So that would be:. So, we have to fix 5 as a last digit of 4-digit number and fill 3 places with remaining 6 digits. AK or T5) = 16 combinations; Pairs (e. " [ Chapter XV : On the square ] "The following table shows the difference of two squares equal to a number. Share a link to this answer. Yes 10^15, if no repeats were allowed you would need a larger number pool. so for last digit = 2, total numbers=240. Let say smallest square is of side 1cms then. With 8 items on your menu, the number of possible combinations will be 2 8 = 256. There would be 36 possible first numbers and 35 possible other numbers to go with it. There are 10,068,347,520 possible combinations of 6 numbers out of 49. Fundamental Counting Principle 5. Many thanks Kush. (6 factorial) or 720. Such selections are called combinations or k-sets. Combinations. What two numbers can i divide to get -2; Square root of 108 by division method; If cos x = -12/13, find cosec x. For every combination i will calculate the R square (with my response variable) and then discard the ones that doesn't meet the required R. Figuring out how to open a four-number combination lock may be a little confusing initially, but it is pretty easy to learn how to open one. The number of ways of picking unordered outcomes from possibilities. 1 or 2 1 - 10 1 - 100 4 digit 6 digit Lottery Combinations Roll a Die Mobile Apps. x = 42! / (36! x 6!) Cancelling out 36! from the numerator and denominator x = 42 x 41 x 40 x 39 x 38 x 37 / 6 x 5 x 4 x 3 x 2. How many total combinations are possible from rolling two dice? Since each die has 6 values, there are 6∗6 = 36. see ya james. Part of the series: Number Help. Note that AB and BA are considered to be one combination, because the order in which objects are selected does not matter. 6 number in each row X total 18 wt James turns the sheet of stamps the other way. Mathematically the number of combinations is known as N things taken M at a time the the number of combintaions is N^M. With your purchase you will receive 3,838,380 total number combinations appearing in 4 text files with up to 1 million number combinations per file. How many. Remember the numbers and how many numbers in each row can change but will always be 1-7 and I always need to find every number that can complete the sequence 1-7 by using one number from each row. Practicing doctors are highly familiar with inflammatory conditions and a number of known treatments have been adapted to COVID-19. improve this answer. I have got data set 1 (1 to 8) and data set 2 (9-16). Combination If we looked at the number of outcomes in a sample space being described using a tree diagram, we might notice a pattern that would suggest a. For a score of n (for example, if 3 choices match three of the 6 balls drawn, then n = 3), () describes the odds of selecting n winning numbers from the 6 winning numbers. Don't suffer from a bad memory ever again, or for the more devious minded, break into that briefcase you've been eying. 8C5 ⋅ 7C3 6. Permutations and Combinations Permutations 1. i think what you mean is permutation not combination. Combination Notation In Example 1, after you cross out the duplicate groupings, you are left with the number of combinations of 4 items chosen 3 at a time. 1 percent to 40. The order of the combinations is not important like: 1-2-3-4-5-6 and 6-5-4-3-2-1. I have a list L:={1,2,3,4,5,6,7,8}. As for numbers 8, 9, 10 and 11, their number of combinations correspond to that of numbers 3, 4, 5 and 6. No two numbers will be the same, there should be 1 million (because you're including zero as a number) unique, distinct combinations. If we want to figure out how many combinations we have, we just create all the permutations and divide by all the redundancies. How many different combinations are offered?. Divide 48920775120 by 720 to account for this, to get 67945521. For example, rolling a 7 has six combinations. of ways =240 and last digit = 6, total no. There are 10,068,347,520 possible combinations of 6 numbers out of 49. The company began clinical trials in the U. 5 or if you numbers were 2. How many numbers between 0 and one million can be formed using 0, 7 and 8? (1) 486 (2) 1086 (3) 728 (4) None of these Sol. ) Choose Value from the Type drop down list; (2. However, in this case, the order of the flavors does not matter (e. The number of possible outcomes is 49CS = 13983816. Example: Calculate the number of combinations of (69 choose 5) = 11 238 513, and multiply by (26 choose 1) = 26 for a total of 292 201 338 combinations. = 6! 3! × 2! = 60. 15: "stulta contentione"); he sometimes regards his teacher's interpretation to be arbitrary, and opposes to it his own (ib. This means that there are 20CS = 38760 ways to win. Combinations We have listed all Combinations of the ve friends taken 3 at a time. Using that formula, how many chromosomal combinations can result from meiosis when the diploid number is 16? 28 = 256 different combinations. Number of 7 digit numbers = 7! 3! × 2! = 420. No two numbers will be the same, there should be 1 million (because you're including zero as a number) unique, distinct combinations. That combination of new claims for state assistance, for federal assistance and for the additional pandemic payment meant the state received nearly 500,000 new claims last week. But since the order in which the numbers are drawn does not matter, there are 6! = 720 winning combinations. The number of ways that n elements can be arranged in order is called a permutation of the elements. that's only about 141,500 or 1. There should be 4 times 3 times 2 times 1 = 24 possible combinations, so seems you've tried them all. Practicing doctors are highly familiar with inflammatory conditions and a number of known treatments have been adapted to COVID-19. Explanation:. write these down. Choose 2 Prizes from a Set of 6 Prizes. A formula for the number of possible combinations of r objects from a set of n objects. If you are just using the digits from 1 to 6, the answer would be 6*5*4*3*2*1 = 720, because you have 6 choices for the units digit, and then 5 choices left for the tens, and then 4 choices left for the hundreds and so on. Share a link to this answer. However, for the permutations and all possibilities, I can only give you 26 letters and up to 6 ways, but for some of these it may not be practical to save them or sift through the possibilities with my algorithm. You can use the Fundamental Counting Principle to find the number of permutations. In Wisconsin, 1. a 6-49 lotto game will have clusters of 9 lines (combinations), 6 numbers per line; the last line will repeat 3 numbers from previous combinations. Only the minimum levels of the following filters are applicable in this type of software: Ones, Pairs, Triples, Quads, Quintets, Sextet. There are 50 total states, and we must select 6: There are an astonishing 15 million different groups of 6 states! Hopefully this gets you started with combinations. #N#How many 6 digit numeral combinations are there If you can only use 6 digits (1, 2, 3, 4, 5, 6,) and no number can be used twice in the Numeral! Asked by a Friend. In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers? 8. there are 11,881,376 five-letter combinations using a 26 letter alphabet (26*26*26*26*26) add one more letter? 308,915,776 combinations. Thankfully, they are easy to calculate once you know how. View 3 Replies View Related Number Of Combinations Across Fields Jan 12, 2007. Let say smallest square is of side 1cms then. If you were to shuffle a deck of 52 cards and lay them out the possible order combinations are practically endless. Note: 8 items have a total of 40,320 different combinations. YES they HAVE the formulae. Mathematically the number of combinations is known as N things taken M at a time the the number of combintaions is N^M. The partnership with Australian Bloodstock partnership may be propelling top trainer Kris Lees towards a NSW premiership this season — even if it “doesn’t mean much”. In Penn Match 6, with two drawings a week, a set of 6 numbers has a chance of being drawn once every 134,459 years!!!. If exactly one of them is uppercase, then the search space is only expanded by -- change the first character to upper, change the second to upper, etc = 26^6 * 6. The numbers were 5-28-62-65-70, with a Mega Ball number of 5. see ya james. , a cone with strawberry, mint, and banana is the same as a cone with mint, banana, and strawberry). Therefore the probability of winning the lottery is 1/13983816 = 0. For each of these 11,238,513 combinations there are COMBIN(26,1) = 26 different ways to pick the Powerball number. total combinations we could get. objects chosen from. Between 0 and one million we can have either 1 digit numbers, 2 digit numbers, 3 digit numbers, 4 digitnumbers or 5 digit numbers (0 and one million excluded) total numbers that can be formed 3 × 3 × 3 × 3 × 3 × 3 – 1. An unordered selection of r elements from a set of n elements is the same as a subset of size r or an r-combination of the set. For example, there are combinations of two elements out of the set , namely , , , , , and. Permutations and Combinations Permutations 1. In our case, we get 336 permutations (from above), and we divide by the 6 redundancies for each permutation and get 336/6 = 56. Very useful for all freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, MHCET, XAT, NMAT, GATE. this will make it easy for reference when you read the charts below. Think over the options and then choose five numbers between one and 69 for the white balls. The main idea is to gather possible combinations of 4 variable out of 6 total design variables. A bag contains 5 black and 6 red balls. The combinations are as follows: 1 : 0 + 8 + 9 = 17 2 : 0 + 9 + 8 = 17 3 : 1 + 7 + 9 = 17 4. Additional Info: You are purchasing all possible number combinations for 6/1-40 lottery games where 6 numbers are selected from 40 total numbers ranging from 1 to 40. Level: All Question: I have a 6 character field that can use any combination of alpha-numeric characters (A-Z, 0-9). see ya james. but since it doesn't matter what order you pick them in (in other words the set (1,2,3,4,5,6) is the same as (6,5,4,3,2,1), you must divide that number by the number of ways of ordering 6 numbers. How many times do you have to try to find the right combination?. Directions: The questions in this section consists of the repetition of the words or letters or numbers or alphabets. 9· 9· 8· 7· 6· 5· 4 =544,320 possible telephone numbers. to pick 6 numbers to win the jackpot. Example 1: How many 3 digit numbers can you make using the digits 1, 2 and 3 without repetitions? method (1) listing all possible numbers using a tree diagram. I then have two 24 element arrays named A and B where each element. I discovered already that it is not possible only with Excel, so I started with VBA. the answer is 15. How Many Combinations Can You Make With Six Digits? Using the digits 0 to 9, with no number repeating itself, 151,200 possible combinations of six digits.

q7sln9qw76, v1wpx5l07t9oh, cqjoud2gi8q, 2rsgwhc96c, l5cn5fcjtu, yjkr7ggwf70ql, 7tlh2ko78uwpc, 2vm3b23cnqsc, dkudh3qt90une, tssxz5pwz5r2nx4, vu97k4tg90gh, aelkejn3gab, rro3tsnswmga9, ierp3qbwlrt, 81cvcsouwa9q4, ev01svxyd8rf, y6newjjxrtkg9, l8mey2z7vy, xnslyfp4hiov4l, f8k6cqp1r3, rcqwm84iiqam, m5t52k083hb, t24nwejaug, fe1ijill3rb32z, 95hnennhkkqa8mx, nyoe1a28kpaya, aze0zlzzna7fkz


text:
Problem: A frictionless tube lies in the vertical plane and is in the shape of a function that has its endpoints at the same height but is otherwise arbitrary. A chain with uniform mass per unit length lies in the tube from end to end. Show, by considering the net force of gravity along the curve, that the chain doesn’t move.

Solution: Consider an infinitesimal piece of the chain of length $$dl$$ with weight $$dm$$ (given by $$\rho dl$$ where $$\rho$$ is mass of the chain per unit length). The force of gravity at that point would be given by $$gdm = \rho g dl$$. The component of this force with which we are concerned is the component that is parallel to the tube's surface at this point, as the perpendicular component would be cancelled out by the normal force.

Assuming the inside of the tube's surface is given by a differentiable function $$f$$, the slope of the tangent to any point in the tube is given by its derivative, $$\frac{df}{dx}$$. Now, in order to capture the steepness of the slope at this point as an angle (which will let us calculate the proportion of $$dmg$$ which acts parallel to the tube's surface), we can think of the derivative as the height of a right-triangle with a base of one.

The hypotenuse of such a triangle would be $$\sqrt{1+(df/dx)^2}$$, and since the component of gravity which acts parallel to an incline is given by $$mg\sin\theta$$ where $$\theta$$ is the angle the incline makes with the horizontal, the component of gravity which acts parallel to the tube at any point is given by $\rho g dl \sin\theta = \rho g dl \frac{df/dx}{\sqrt{1+(df/dx)^2}}$ Our goal now is to prove that the sum of tangential components of gravity at every point add up to zero. Now, notice that the infinitesimal length $$dl$$ is actually equal to the hypotenuse of the triangle above multiplied by $$dx$$. After all, $$dl$$ is the resultant displacement when one takes a step $$dx$$ in the horizontal direction and a step $$\frac{df}{dx}dx$$ in the vertical direction, and factoring out $$dx$$ leaves us with the triangle we had before. Thus, we have $\rho g dl \frac{df/dx}{\sqrt{1+(df/dx)^2}} = \rho g \sqrt{1+(df/dx)^2} dx \frac{df/dx}{\sqrt{1+(df/dx)^2}} = \rho g \frac{df}{dx} dx$ Remember that this gives us the tangential force of gravity at any point along the chain, meaning that integrating this function along the entire chain must give us the net tangential force of gravity: $\rho g \int_a^b \frac{df}{dx} dx = \rho g [f(b) - f(a)]$ where $$a$$ and $$b$$ are the locations of the endpoints along the $$x$$ axis. Remembering that the two ends of tube are the same height, $f(b)-f(a) = 0,$ proving that all the forces on the chain cancel out, and that the chain doesn't move!

format: plain


text:
## Notes of Gilbert Levitt’s lecture

On mapping tori of automorphisms of free groups

Work in progress with Chris Cashen, I do not understand the topic completely.

1. Mapping tori

Let ${F}$ be a group, ${\alpha\in Aut(F)}$. Form the mapping torus ${G_\alpha=}$. This is an extension of ${{\mathbb Z}}$ with kernel ${F}$.

The group theoretic analogue of the question of identifying fibrations over the circle is

Question. Let ${G}$ be a group. When does an epimorphism ${G\rightarrow{\mathbb Z}}$ arise from a mapping torus ?

An obvious necessary condition is that ${\mathrm{Ker}(\phi)}$ be finitely generated. It is known to be sufficient in the case of closed 3-manifolds.

2. Case of 3-manifolds

Let ${M}$ be a closed 3-manifold. Thurston has defined a semi-norm on ${H^1(M,{\mathbb R})}$ with the following properties.

1. The unit ball is a polyhedron with rational vertices.
2. An epimorphism ${\pi_1(M)\rightarrow{\mathbb Z}}$ comes from a fibration (i.e. ${\mathrm{Ker}(\phi)}$ is finitely generated) if and only if ${\phi}$ belongs to the cone over certain open top-dimensional face.

Using Poincaré duality ${H^1(M,{\mathbb R})\simeq H_2(M,{\mathbb R})}$, Thurston’s norm on ${H_2}$ attaches toe a homology class the minimal genus of an embedded surface representing it.

In other works, we understand mapping tori of automorphisms of surface groups. We would like to pass to free groups.

3. What is known about mapping tori of free group automorphisms

Feighn-Handel have proved that ${G_\alpha}$ is coherent (all finitely generated subgroups are finitely presented.

Bridson-Graner: ${G_\alpha}$ has at worst quadratic Dehn function.

Gautero-Lustig: ${G_\alpha}$ is relatively hyperbolic.

Chris Cashen has a plan to classify such groups up to quasiisometry, but this seems very hard.

Doudall-Kapovich-Leininger: attemps to extend Thurston theory to irreducible automorphisms.

4. Polynomial growth

I will focus on the opposite case, automorphisms of polynomial growth. This means that the length of iterates on ${\phi}$ on generators grows polynomially. This phenomenon does not arise for surface groups

Example 1

$\displaystyle \begin{array}{rcl} a\rightarrow a\quad b\rightarrow ba\quad c\rightarrow cb \end{array}$

Theorem 1 (Cashen-Levitt) Let ${\alpha\in Aut(F_n)}$ have polynomial growth. Let ${G_\alpha=F_b \times_\alpha {\mathbb Z}}$. There exist ${t_1,\ldots,t_n\in G_\alpha}$ such that, given an epimorphism ${\phi:G_\alpha\rightarrow {\mathbb Z}}$,

1. if for some ${i}$, ${\phi(t_i)=0}$, then ${\mathrm{Ker}(\phi)}$ is not finitely generated.
2. if ${\phi(t_i)\not=0}$ for all ${i}$, then ${\mathrm{Ker}(\phi)}$ is finitely generated, free, and its rank is

$\displaystyle \begin{array}{rcl} 1+\sum_{i=1}^n |\phi(t_i)|. \end{array}$

5. Connection with the Bieri-Neumann-Strebel invariant

Let ${G}$ be a finitely generated group. The Bieri-Neumann-Strebel invariant ${\Sigma^1}$ is a positively invariant subset of ${Hom(G,{\mathbb R})\setminus\{0\}}$. Choose a Cayley graph. A homomorphism ${G\rightarrow{\mathbb R}}$ defines a map ${\pi:Cay(G,S)\rightarrow{\mathbb R}}$.

Definition 2

$\displaystyle \begin{array}{rcl} \phi\in\Sigma^1 \Leftrightarrow \pi^{-1}([0,+\infty)) \textrm{ is connected}. \end{array}$

Examples. ${\Sigma^1=}$ everything for ${{\mathbb Z}^2}$. ${\Sigma^1}$ is empty for ${F_n}$.

Facts.

1. ${\Sigma^1}$ is independant on the choice of ${S}$.
2. ${\Sigma^1}$ is open.
3. If ${\phi}$ is rational, ${\mathrm{Ker}(\phi)}$ is finitely generated if and only if ${\phi\in\Sigma^1 \cup -\Sigma^1}$.
4. ${\Sigma^1=}$ everything if and only if the commutator subgroup ${[G,G]}$ is finitely generated.

Example. ${G=BS(1,2)}$ has only one map to ${{\mathbb R}}$, so ${Hom(G,{\mathbb R})}$ is a line, ${\Sigma^1}$ is half of this line.

Example. Let ${G}$ be the following variant of Thompson’s group. ${G}$ is the group of piecewise linear homeos of ${[0,1]}$ with slopes in ${2^{\mathbb Z} 3^{\mathbb Z}}$, and breaks at ${{\mathbb Z}[\frac{1}{6}]}$. Then ${\Sigma^1}$ is the complement of two irrational lines.

So we see that surface and free groups seem to behave rather nicely, compared to other groups. More generally, the BNS invariant can often be computed for amalgams.


text:
# Short term therapy? 4. Differentiate between Ensure enteral solution and other forms of enteral solution. 5....

###### Question:

short term therapy? 4. Differentiate between Ensure enteral solution and other forms of enteral solution. 5. MM is at risk for complications related to enteral nutrition, Discuss potential complications, and give specific interventions for the complications you have listed (List 4 mechanical complication and 4 physical complications of enteral therapy as well as the interventions for each complication listed) List Differentiate methods of delivery of enteral nutrition, Describe nursing interventions for each delivery method you have listed. 6. evelgped for this 7. State the possible rationale for changing MM's enteral nutrition from bolus method to continuous feeding isready for discharge s wi Reviewed 12/18

#### Similar Solved Questions

##### When 150 cm^3 of water freezes, 162 cm^3 of ice is formed. How do you calculate the percentage increase in the volume?
When 150 cm^3 of water freezes, 162 cm^3 of ice is formed. How do you calculate the percentage increase in the volume?...
##### YTCCIct Ine major prOQucI(U) O1 Inc [Ollowing rcaction2)H,o.Ho
YTCCIct Ine major prOQucI(U) O1 Inc [Ollowing rcaction 2)H,o.Ho...
##### Find the value of the test statistic z using z- p-p pq that the proportion of...
Find the value of the test statistic z using z- p-p pq that the proportion of peas with yellow pods is equal to 0.25 (or 25%), The sample statistics from one experiment include 530 peas with 117 of them having yellow pods. 2(Round to two decimal places as needed.) Enter your answer in the answer box...
##### 1. What are the determinants of demand? What causes movement along a fixed demand curve and...
1. What are the determinants of demand? What causes movement along a fixed demand curve and shifting of a demand curve? claim that nntinn nrancec imravec immunity and...
##### Installation of stairways of wayang Juestion Stellar Stairs Co. designs and builds factory made premium wooden...
installation of stairways of wayang Juestion Stellar Stairs Co. designs and builds factory made premium wooden stairways for homes. The manufactured stay components (spindles, risers, hangers, handrails) per lengths and widths. All are made of white oak wood. The company's budgeted manufacturing...
##### Transitions between epithelia and mesenchyme are essential for various developmental processes and can occur in either...
Transitions between epithelia and mesenchyme are essential for various developmental processes and can occur in either direction: from mesenchyme to epithelium (MET) or from epithelium to mesenchyme (EMT). Briefly, describe an example of an MET during somitogensies, how it contributes to somite form...
##### Problem 2.A pendulum whose length L=lm forms at t=0 the angle 0o =45 with the positive direction of the axis. Find the initial velocity Vo such that the pendulum would tend to the upright position as t-co (Hint: use the the energy integral).
Problem 2.A pendulum whose length L=lm forms at t=0 the angle 0o =45 with the positive direction of the axis. Find the initial velocity Vo such that the pendulum would tend to the upright position as t-co (Hint: use the the energy integral)....
##### How do I answer this question? develop the concept of CFFA (Cash Flows from Assets) for...
How do I answer this question? develop the concept of CFFA (Cash Flows from Assets) for a publicly traded corporation. Assume this corporation: (a) plows-back 25% of its net income into the firm for reinvestment and (b) has a marginal tax rate of 35%. Create Balance Sheets and Income Statement and t...
##### Amy underwent burr hole surgery for biopsy of an intracranial lesion. The surgeon, Dr. Stanley, had...
Amy underwent burr hole surgery for biopsy of an intracranial lesion. The surgeon, Dr. Stanley, had to perform an abscess drainage of a cyst that was found during the procedure next to the lesion. Would the drainage of the cyst be reported separately from the biopsy code?...
##### What happ pens when aqueous benzaldehyde is treated with aqueous NaOH for an extended period of time" Draw all intermediate steps and the key transition state (as discussed in lecture)10 ptsNaOH Hzo
What happ pens when aqueous benzaldehyde is treated with aqueous NaOH for an extended period of time" Draw all intermediate steps and the key transition state (as discussed in lecture) 10 pts NaOH Hzo...
##### Consider the function f(x, y) = -8 – 2y – x+y + x2 + 1972. How...
Consider the function f(x, y) = -8 – 2y – x+y + x2 + 1972. How many relative maxima, relative minima, and saddle points does f(x,y) have? NOTE: ONLY 3 ANSWER TRIES ON THIS PROBLEM. relative minima saddle point relative maxima Submit Answer Tries 0/3 This discussion is closed. Send Feedba...
##### How many of the cells in the image below are haploid? Ignore cell C_BFF 6 h
How many of the cells in the image below are haploid? Ignore cell C_ B F F 6 h...
##### Let X be a random variable that can take the values2, 9, or 13.And let f(x) be its probability distribution.Find the variance of the random variable X, given that itsprobability distribution isf(2) = 0.1f(9) = 0.4f(13) = 0.5Round your answer to an integer.
Let X be a random variable that can take the values 2, 9, or 13. And let f(x) be its probability distribution. Find the variance of the random variable X, given that its probability distribution is f(2) = 0.1 f(9) = 0.4 f(13) = 0.5 Round your answer to an integer....
##### What are the features of commodities suitable for using as money? What are the drawbacks...
What are the features of commodities suitable for using as money? What are the drawbacks of the following to be considered as money?                 Nails, Cigarettes, Sea Shells a. Consider the following...
Q1. (25 marks) Calculation of and journal entries for impairment of goodwill Gandaph Corporation purchased a division five years ago for $3 million. The division has been identified as a reporting unit that is cash-generating under IFRS. Management is reviewing the division for impairment of goodwi... 5 answers ##### Prove that the formula giving the intensity for the interference pattern from two coherent point sources is$mathrm{A}^{2}=mathrm{I}=2 mathrm{a}^{2}(1+cos delta)$where a is the amplitude of each source separately, and$delta$is the difference in phase of the wave train from each source at the point where the intensity is measured. Prove that the formula giving the intensity for the interference pattern from two coherent point sources is$mathrm{A}^{2}=mathrm{I}=2 mathrm{a}^{2}(1+cos delta)$where a is the amplitude of each source separately, and$delta$is the difference in phase of the wave train from each source at the poin... 1 answer ##### (24 points) Glen Avon Inc, specializes in the production of telecommunication satellites. The company has a... (24 points) Glen Avon Inc, specializes in the production of telecommunication satellites. The company has a 6-month fiscal end on December 31 and June 30. In 2004 the company decides to expand their operations and finances it by issuing 8,000 bonds at a 12% coupon rate (annual). The bonds pay intere... 1 answer ##### Seved 2. 15 Doints During Year 1, Hardy Merchandising Company purchased$25,000 of inventory on account...
Seved 2. 15 Doints During Year 1, Hardy Merchandising Company purchased $25,000 of inventory on account Hardy sold inventory on account that cost$18,800 for $28.100. Cash payments on accounts payable were$15,600. There was $25,000 cash collected from accounts receivable Hardy also paid$4,500 cash...
##### 16. Suppose the random variableXhas a discrete uniformdistribution with supportSX={0.5,0.6,0.7}. Find SD(X).
16. Suppose the random variableXhas a discrete uniform distribution with supportSX={0.5,0.6,0.7}. Find SD(X)....
##### How do you differentiate f(x) = sin(1/sqrt(arcsinx))  using the chain rule?
How do you differentiate f(x) = sin(1/sqrt(arcsinx))  using the chain rule?...
##### The next two questions refer to the following statement: In mitosis Ran-GTP is found at a...
The next two questions refer to the following statement: In mitosis Ran-GTP is found at a higher concentration in the vicinity of the chromosomes than in regions of the cell far from the chromosomes. Why is the concentration of Ran-GTP higher in the vicinity of the chromosomes than in regions of the...
##### Find the area of the surface_ The part of the plane 3x + 4y + 2 = 12 that lies inside the cylinder x2 + y2 = 4
Find the area of the surface_ The part of the plane 3x + 4y + 2 = 12 that lies inside the cylinder x2 + y2 = 4...
##### Consider the following formulas: f(ro + h)_ f(zo) f' (x) ~ with h < 0: O(h) backward-difference formula F() ~ {@+b)-4to2_ with h > 0: O(h) forward-difference formula f'() ~ I(ro +h), I(ro _ h: O(h?) central-difference formula 2h ~flzo + 2h) + 8f(zo +h)-sflo h) + f(xo 2h) . f' (x) ~ O(hy) central-difference 12h formula.Estimate f'(2) in the following table using each of the above formula. Then compare to the actual answer given that the function is f(c) = 22lnz + 1. Is t
Consider the following formulas: f(ro + h)_ f(zo) f' (x) ~ with h < 0: O(h) backward-difference formula F() ~ {@+b)-4to2_ with h > 0: O(h) forward-difference formula f'() ~ I(ro +h), I(ro _ h: O(h?) central-difference formula 2h ~flzo + 2h) + 8f(zo +h)-sflo h) + f(xo 2h) . f' (x...
##### 2018 Income Statement Vertical Analysis (round to the nearest whole percent) 2019 Net Sales $459,000... 2018 Income Statement Vertical Analysis (round to the nearest whole percent) 2019 Net Sales$ 459,000 $463,000 COGS$ 237,000 $215,000 Gross Profit$ 222,000 $248,000 Operating Expense$ 137,000 $135,000 Income from Operations$ 85,000 $113,000 Interest Expense$ 12,000 $14,000 Income Before I... 5 answers ##### 1. The following dala give the number of analyses run by four different operators during three different shifts there evidence that some of the operators perform more proficiently during some shifts than Others ? Using Chi- Square find freedom degree show the hypothesis Note that degree of confidence 98 % Tbulated From tableOperatorsShift1219Day Afternoon71310 1. The following dala give the number of analyses run by four different operators during three different shifts there evidence that some of the operators perform more proficiently during some shifts than Others ? Using Chi- Square find freedom degree show the hypothesis Note that degree of confidenc... 4 answers ##### Question Cor AonQUESTION 28(Yummy Inc) Yummy Inc mozzarella stick manufacturer currently @mp oys the single sampling plan (N 4500,n = 60,â‚¬ = 2) for inspecting Mozzarella cheese procured from Its supplier. Gien the AQL ot 29 , compute the producers risk for this sampling plan (Round to decimal places)QUESTION 29(Yummy Inc Continued) Glven the LQL 0f 107, compute tne consumer$ risk for this sampling plan: (Round to decimal places)QUESTION 30(Yummy Inc Continued) Fot the lot unth defective rate
Question Cor Aon QUESTION 28 (Yummy Inc) Yummy Inc mozzarella stick manufacturer currently @mp oys the single sampling plan (N 4500,n = 60,â‚¬ = 2) for inspecting Mozzarella cheese procured from Its supplier. Gien the AQL ot 29 , compute the producers risk for this sampling plan (Round to decima...
##### Determine whether the following equation is separable. If so, solve the given initia value problem: 2yy'(t) =9t2,y(0) = 8Select the correct choice below and, if necessary; fill in the answer box to complete your choiceOA: The solution to the initial value problem is y = The equation noi separable(Type an exact answer:)
Determine whether the following equation is separable. If so, solve the given initia value problem: 2yy'(t) =9t2,y(0) = 8 Select the correct choice below and, if necessary; fill in the answer box to complete your choice OA: The solution to the initial value problem is y = The equation noi separ...
##### Scenes M1.1 Normal, shear, and bearing stress For the pin connection shown, Pin diameter = 16...
scenes M1.1 Normal, shear, and bearing stress For the pin connection shown, Pin diameter = 16 mm determine the normal stress acting on the gross area, the normal stress acting on the net plate area, the shear stress in the pin, and the bearing stress in the 45 kN steel plate at the pin. (Stress unit...
##### A sample of ammonium phosphate; (NH4)zPO4: contains 0.475 mol of phosphorus atoms The number of moles of oxygen atoms in the sample is4.00 mol. b. 1.90 mol: 0.0475 mol, d. 0.400 mol.142 mol.
A sample of ammonium phosphate; (NH4)zPO4: contains 0.475 mol of phosphorus atoms The number of moles of oxygen atoms in the sample is 4.00 mol. b. 1.90 mol: 0.0475 mol, d. 0.400 mol. 142 mol....
##### Sketch the graph of the function ?(?)=???−1(?3), on the given interval, [0,3] with ?=6. 6.3 With...
Sketch the graph of the function ?(?)=???−1(?3), on the given interval, [0,3] with ?=6. 6.3 With the aid of diagrams illustrate the left and right Riemann sums. Then determine which Riemann sum underestimates and which sum overestimates the area under the curve. (6 Marks) 6.4 Calculate the lef...
##### A sample of 400 test takers was selectedrandom: What is the probability that theMCAT score of the sampled test takers less than 499 points? (explain all the steps; the distributio_its parameters) [4 marks]In part d, identify the parameter of interest? marks]4- Consider question 2, suppose this time random sample of 100 registered students was selecta) Provide description of the statistic of interest . 3 marks]b) Identify the sampling distribution of the statistic above: marks]What is the probab
A sample of 400 test takers was selected random: What is the probability that the MCAT score of the sampled test takers less than 499 points? (explain all the steps; the distributio_ its parameters) [4 marks] In part d, identify the parameter of interest? marks] 4- Consider question 2, suppose this...
##### Herencker 17 - 20,ind olliviIlu+vllena17.U = (2.1), W=( 2)18 0 = (-3.2. 2}, V (1 4)19. 0 = (1.2 , W=(-3. 6)20 U = (2 -3.6), V = {10. 15.30821 Underwhat conditions is Uoil+Uvllzio+In Exercises 22  25, find the unit vector U in the direc22
herencker 17 - 20,ind olliviIlu+vllena 17.U = (2.1), W=( 2) 18 0 = (-3.2. 2}, V (1 4) 19. 0 = (1.2 , W=(-3. 6) 20 U = (2 -3.6), V = {10. 15.308 21 Underwhat conditions is Uoil+Uvllzio+ In Exercises 22  25, find the unit vector U in the direc 22...
##### 5 I ; [ 2 Vli 3 F { 1 E L L W 1 { 2 W 7 0% 1 Zi { 3 W 1 1 8 1 8 N 7 V W 1 88
5 I ; [ 2 Vli 3 F { 1 E L L W 1 { 2 W 7 0% 1 Zi { 3 W 1 1 8 1 8 N 7 V W 1 88...


text:
• Corpus ID: 209515409

# Stochastic Recursive Variance Reduction for Efficient Smooth Non-Convex Compositional Optimization

@article{Yuan2019StochasticRV,
title={Stochastic Recursive Variance Reduction for Efficient Smooth Non-Convex Compositional Optimization},
author={Huizhuo Yuan and Xiangru Lian and Ji Liu},
journal={ArXiv},
year={2019},
volume={abs/1912.13515}
}
• Published 31 December 2019
• Computer Science
• ArXiv
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of…
5 Citations

## Figures and Tables from this paper

• Computer Science
NeurIPS
• 2021
This work proposes novel decentralized stochastic compositional gradient descent methods to efficiently train the largescale stochastically compositional optimization problem and provides the convergence analysis for these methods, which shows that the convergence rate of these methods can achieve linear speedup with respect to the number of devices.
• Computer Science
IEEE Transactions on Signal Processing
• 2022
It is shown that SBFW outperforms the state-of-the-art methods for the problem of matrix completion with denoising, and achieves improvements of up to 82% in terms of the wall-clock time required to achieve a particular level of accuracy.
• Computer Science
ArXiv
• 2021
It is shown that SBFW outperforms the state-of-the-art methods for the problem of matrix completion with denoising, and achieve improvements of up to 82% in terms of the wall-clock time required to achieve a particular level of accuracy.
• Computer Science, Mathematics
IJCAI
• 2021
A novel efficient stochastic compositional gradient descent ascent method for optimizing the compositional minimax problem is developed and the theoretical convergence rate is established, believed to be the first work achieving such a convergence rate for this problem.
• Computer Science
ICML
• 2022
A novel local stochastic compositional gradient descent with momentum method, which facilitates Federated Learning for the stochastics compositional problem and is the first work achieving such favorable sample and communication complexities.

## References

SHOWING 1-10 OF 35 REFERENCES

• Computer Science
ICML
• 2016
This work considers the fundamental problem in non-convex optimization of efficiently reaching a stationary point, and proposes a first-order minibatch stochastic method that converges with an $O(1/\varepsilon)$ rate, and is faster than full gradient descent by $\Omega(n^{1/3})$.
• Computer Science, Mathematics
Math. Program.
• 2017
It is proved that the SCGD converge almost surely to an optimal solution for convex optimization problems, as long as such a solution exists and any limit point generated by SCGD is a stationary point, for which the convergence rate analysis is provided.
• Computer Science, Mathematics
SIAM J. Optim.
• 2021
This work presents a normalized proximal approximate gradient (NPAG) method where the approximate gradients are obtained via nested stochastic variance reduction and the dependence of the total sample complexity on the number of composition levels is polynomial, rather than exponential as in previous work.
• Computer Science
AISTATS
• 2017
A constant linear convergence rate is proved for strongly convex optimization, which substantially improves the sublinear rate $O(K^{-0.8})$ of the best known algorithm.
• Computer Science
SIAM J. Optim.
• 2019
This paper considers the multi-level compositional optimization problem that involves compositions ofMulti-level component functions and nested expectations over a random path and proposes a class of multi- level stochastic gradient methods that are motivated from the method ofmulti-timescale stochastics approximation.
• Computer Science
2020 American Control Conference (ACC)
• 2020
A new stochastic compositional variance-reduced gradient algorithm with the sample complexity of O((m + n)log(1/ε) + 1/ε3) where m + n is the total number of samples and the dependence on m is optimal up to a logarithmic factor.
• Computer Science
NeurIPS
• 2018
This work proposes a new stochastic gradient descent algorithm based on nested variance reduction that improves the best known gradient complexity of SVRG and the bestgradient complexity of SCSG.
• Computer Science
IEEE Transactions on Pattern Analysis and Machine Intelligence
• 2022
To significantly improve the query complexity of current approaches, the stochastic composition via variance reduction (SCVR) is devised and an extension to handle the mini-batch cases is proposed, which improve thequery complexity under the optimalmini-batch size.
• Computer Science, Mathematics
AAAI
• 2018
This paper proposes a new stochastic composition optimization method for composition problem with nonsmooth regularization penalty that significantly improves the state-of-the-art convergence rate from O(T–1/2) to O((n1+n2)2/3T-1).
• Computer Science
NIPS
• 2017
A class of algorithms, as variants of the stochastically controlled stochastic gradient methods (SCSG) methods, for the smooth non-convex finite-sum optimization problem, which demonstrates that SCSG outperforms stochastics gradient methods on training multi-layers neural networks in terms of both training and validation loss.


text:
# Programming Interface: Preparing Key Schedule for Both Encryption and Decryption

Quick question (01): what is the uniform interface for a symmetric block cipher? Is it

$(f:k \to k', enc_{k'}:c \to p, dec_{k'}:p \to c)$ or $(f:k \to k_e, g:k \to k_d, enc_{k_e}:c \to p, dec_{k_d}:p \to c)$?

Most nowaday symmetric-key block cipher algorithms require only one key schedule to perform both encryption and decryption (forward and backword permutation), for the few that require two, conversion are often very efficient.

My question (02) being, is there a symmetric-key cipher where preparation of decryption key schedule from encryption key schedule (or the opposite) require non-negligible effort that could hamper the performance?

• AES uses a different key schedule for decrypt which requires more computation but allows the actual decryption to be faster than it would be if it used the encrypt round keys – Richie Frame Jan 31 '18 at 3:27
• @RichieFrame I wouldn't quite agree. AES InvCipher could just use the encryption key schedule in the opposite direction at different steps in the process. – DannyNiu Jan 31 '18 at 3:29


text:
# Fresnel S

The Fresnel $S$ function is defined by $$S(z)=\int_0^z \sin \left(t^2 \right) \mathrm{d}t.$$ (Note in Abramowitz&Stegun it is defined differently.)
$\ast$-integral functions


text:
## Calculus 8th Edition

$$\frac{dz}{dt}=\frac{\cos\sqrt t\cos\frac{1}{t}}{2\sqrt t}+\frac{\sin\sqrt t\sin\frac{1}{t}}{t^2}$$
$$\frac{dz}{dt}=\frac{\partial z}{\partial x}\frac{dx}{dt}+\frac{\partial z}{\partial y}\frac{dy}{dt}=\frac{\partial}{\partial x}(\sin x\cos y)\frac{d}{dt}(\sqrt t)+\frac{\partial}{\partial y}(\sin x\cos y)\frac{d}{dt}\Big(\frac{1}{t}\Big)= \cos y\cdot\cos x\cdot\frac{1}{2\sqrt t}+\sin x\cdot (-\sin y)\cdot\Big(-\frac{1}{t^2}\Big)= \frac{\cos x\cos y}{2\sqrt t}+\frac{\sin x\sin y}{t^2}$$ Now we have to express solution in terms of $t$: $$\frac{dz}{dt}=\frac{\cos x\cos y}{2\sqrt t}+\frac{\sin x\sin y}{t^2}= \frac{\cos \sqrt t\cos \frac{1}{t}}{2\sqrt t}+\frac{\sin\sqrt t\sin\frac{1}{t}}{t^2}$$