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1 JEE Main 2022 (Online) 26th July Morning Shift +4 -1 Let f : R $$\to$$ R be a continuous function such that $$f(3x) - f(x) = x$$. If $$f(8) = 7$$, then $$f(14)$$ is equal to : A 4 B 10 C 11 D 16 2 JEE Main 2022 (Online) 26th July Morning Shift +4 -1 If the function $$f(x) = \left\{ {\matrix{ {{{{{\log }_e}(1 - x + {x^2}) + {{\log }_e}(1 + x + {x^2})} \over {\sec x - \cos x}}} & , & {x \in \left( {{{ - \pi } \over 2},{\pi \over 2}} \right) - \{ 0\} } \cr k & , & {x = 0} \cr } } \right.$$ is continuous at x = 0, then k is equal to: A 1 B $$-$$1 C e D 0 3 JEE Main 2022 (Online) 26th July Morning Shift +4 -1 If $$f(x) = \left\{ {\matrix{ {x + a} & , & {x \le 0} \cr {|x - 4|} & , & {x > 0} \cr } } \right.$$ and $$g(x) = \left\{ {\matrix{ {x + 1} & , & {x < 0} \cr {{{(x - 4)}^2} + b} & , & {x \ge 0} \cr } } \right.$$ are continuous on R, then $$(gof)(2) + (fog)( - 2)$$ is equal to : A $$-$$10 B 10 C 8 D $$-$$8 4 JEE Main 2022 (Online) 26th July Morning Shift +4 -1 Let $$f(x) = \left\{ {\matrix{ {{x^3} - {x^2} + 10x - 7,} & {x \le 1} \cr { - 2x + {{\log }_2}({b^2} - 4),} & {x > 1} \cr } } \right.$$. Then the set of all values of b, for which f(x) has maximum value at x = 1, is : A ($$-$$6, $$-$$2) B (2, 6) C $$[ - 6, - 2) \cup (2,6]$$ D $$\left[ {-\sqrt 6 , - 2} \right) \cup \left( {2,\sqrt 6 } \right]$$ EXAM MAP Medical NEET

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## Course syllabus MVE155 / MSG200 Statistical inference (7.5 hp) 2021 Course is offered by the department of Mathematical Sciences Serik Sagitov ### Course purpose "Statistical Inference" is a second course in mathematical statistics suitable for students with different backgrounds. A main prerequisite is an introductory course in probability and statistics. The course gives a deeper understanding of some traditional topics in mathematical statistics such as methods based on likelihood, aspects of experimental design, non-parametric testing, analysis of variance, introduction to Bayesian inference, chi-squared tests, multiple regression. Install Rstudio Step 1: install R from http://ftp.acc.umu.se/mirror/CRAN/ No previous knowledge of programming is required. ### Schedule We meet online via Zoom Link Passcode 899022 Recorded Zoom sessions can be found under the option "Modules". Date, usual time 13.15-15.00 Description of sessions Chapters in Compendium Mon 18/01 Lecture 1: Random sampling  Slides1.pdf Chapters 1-3 Tue 19/01 Exercise 1: 3.6.1, 3.6.2, R session QQplot.R Wed 20/01 Lecture 2: Stratified samples Slides2.pdf. Parametric models  Slides3.pdf Chapters 3-4 Mon 25/01 Exercise 2: 3.6.6, 3.6.7, 3.6.8, 4.7.1, R solution of 3.6.7 Tue 26/01 Lecture 3: Maximum likelihood  Slides4.pdf. R session Multinomial and Chi2 .R Chapter 4 Wed 27/01 Exercise 3:  4.7.3, 4.7.5, 4.7.6, 4.7.7 Fri 29/01 Lecture 4: Hypothesis testing Slides5.pdf, Slides6.pdf Chapter 5 Mon 01/02 Exercise 4: 5.8.1, 5.8.4, 5.8.6, 5.8.7, 5.8.10 Tue 02/02 Lecture 5: Bayesian inference Slides7.pdf. R session Bayes.R Chapter 6 Wed 03/02 Exercise 5: 5.8.2, 5.8.9, 5.8.12, 6.5.4 Fri 05/02 Lecture 6: Bayesian inference  Slides8.pdf Chapter 6 Mon 08/02 Exercise 6: 6.5.1, 6.5.2, 6.5.3, 6.5.5, 6.5.6 Tue 09/02 Lecture 7: Empirical distribution Slides9.pdf. R session Summarising Data.R Chapter 7 Wed 10/02 Exercise 7: 7.7.1, 7.7.2, 7.7.3, 7.7.4, 7.7.5, 7.7.6. R session ExercisesCh7.R Fri 12/02 Lecture 8: Comparing two populations Slides10.pdf, Slides11.pdf Chapter 8 Mon 15/02 Exercise 8: 8.6.2, 8.6.5, 8.6.9, 8.6.11 Tue 16/02 Lecture 9: ANOVA1  Slides11.pdf, Slides12.pdf Chapter 8-9 Wed 17/02 Exercise 9: R session t-test and ANOVA.R Fri 19/02 Lecture 10: ANOVA2 Slides13.pdf Chapter 9 Mon 22/02 Exercise 10: 9.8.1, 9.8.2, 9.8.3, 9.8.4, 9.8.7 Tue 23/02 Lecture 11: Nonparametric tests Slides14.pdf. R session Nonparametric tests.R Chapter 9-10 Wed 24/02 Exercise 11: 8.6.3, 8.6.4, 8.6.7, 8.6.8, 9.8.5, 9.8.6, Mon 01/03 Lecture 12: Categorical data Slides15.pdf. R session Chi-square test.R Chapter 10 Tue 02/03 Exercise 12: 10.5.3, 10.5.6, 10.5.7, 10.5.9. An example of a final exam Wed 03/03 Lecture 13: Simple linear regression Slides16.pdf Chapter 11 Fri 05/03 Exercise 13: 11.6.5, 11.6.6. R session Regression.R Mon 08/03 Lecture 14: Multiple regression Slides17.pdf Chapter 11 Tue 09/03 Exercise 14: 11.6.3, 11.6.4, 11.6.7, 14.1.1, 14.1.14, 14.1.21, 14.1.9 Chapter 14 Tue 16/03, 14.00-18.00 Exam 1 (register before 28.02.2021) Wed 09/06, 8.30-12.30 Exam 2 (register before ) Tue 17/08, 14.00-18.00 Exam 3 (register before ) ### Course literature The course is build around the Compendium - click and download. The compendium may undergo minor updates - on the first page you will see when it was last updated. Recommended additional textbook: Mathematical statistics and data analysis, 3rd edition (2nd edition is also OK), by John Rice (Cremona). ### Learning objectives and syllabus Learning objectives: - summarize multiple sample data in a meaningful and informative way, - recognize several basic types of statistical problems corresponding to various sampling designs, - estimate relevant parameters and perform appropriate statistical tests for multiple sample data sets. Link to the syllabus on Studieportalen: Study plan ### Examination form The grading of the course is based on a written examination. Preparing for the final exam, check Section 12.1 of the Compendium to see the list of the topics that may be addressed by the final exam questions. Several old exams with solutions are given in the module "Old exams". Maximal number of points for the final exam is 30. Passing limits • CTH students: 12 points for '3', 18 points for '4', 24 points for '5' • GU students: 12 points for 'G', 20 points for 'VG' Date Details Due

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# Activity 79 Analysis Questions ## Presentation on theme: "Activity 79 Analysis Questions"— Presentation transcript: Activity 79 Analysis Questions Describe the changes in direction and speed of the marble when they’re inside the circular track? The marbles’ direction changed constantly inside the circular track because of the force the wall exerted on the marble. Similarly, the surface of the circular track rubbed on the marble and slowed in down slightly. outside of the circular track? The direction once outside the circular track was in a straight line, moving across the table as shown on Transparency 79.1, “Inertia Diagrams”. The speed slowed slightly because of the table surface rubbing on the marble. Describe any changes in the path of the marble that occurred when you changed the opening position of the circular track. The marble left the opening in a different direction for each opening position. Once it left the circular track, however, it continued in a straight line. mass of the marble. When comparing the glass (lighter) marble to the heavier (metal) one, no changes occurred to the direction that the marble traveled. Imagine that a car is approaching a curve in the road when it suddenly loses its steering and brakes. The area is flat and there is no guardrail on the road. Copy the diagram below in your science notebook. Then draw a line showing the car’s path when it loses its steering and brakes. Explain why the car will take that path. Because of inertia, which in the absence of other forces keeps moving objects moving in a straight line. How would your answer change if the car had more mass? Explain. More mass will not change the direction the car travels. It would, however, affect the force needed to stop the car. Activity 79 Major Concepts An object that is not being subject to a force will continue to move at a constant speed in a straight line. On your next blank page, take notes Force Notes Net Force In many situations, including driving, more than one force is acting on an object. The combination of all forces acting on an object is the net force. Net force determines whether, and by how much, an object’s motion is changed. Total Force Force Diagrams Objects are shown as a rectangle or square. Force Diagrams A push or pull (force) is shown with an arrow Force Diagrams The arrow always points AWAY from the object. Force Diagrams The bigger the force, the bigger the arrow Force Diagrams Label the arrows with the magnitude (amount) of the force (in N) 3 N 10 N Force Diagrams Net Force is the sum of all of the forces 3 N 10 N 7 N Practice: Draw an object with two forces acting in opposite directions with one force equal to 2 N and one force equal to 8 N. Force Diagrams 2 N 8 N Net Force Draw the net force acting on this object. 2 N 8 N Force Diagrams Net Force 6 N Balanced vs. Unbalanced Forces If there is a situation of unbalanced forces, there is a net force. Balanced forces mean there is a net force of zero on the object. Describe the motion of the blocks below. 2 N 10 N A. 8 N 8 N B.

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Algorithm B. Shooting time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output Recently Vasya decided to improve his pistol shooting skills. Today his coach offered him the following exercise. He placed n cans in a row on a table. Cans are numbered from left to right from 11 to n. Vasya has to knock down each can exactly once to finish the exercise. He is allowed to choose the order in which he will knock the cans down. Vasya knows that the durability of the i-th can is ai��. It means that if Vasya has already knocked x cans down and is now about to start shooting the i-th one, he will need (aix+1)(��⋅�+1) shots to knock it down. You can assume that if Vasya starts shooting the i-th can, he will be shooting it until he knocks it down. Your task is to choose such an order of shooting so that the number of shots required to knock each of the n given cans down exactly once is minimum possible. Input The first line of the input contains one integer n (2n1000)(2≤�≤1000) — the number of cans. The second line of the input contains the sequence a1,a2,,an�1,�2,…,�� (1ai1000)(1≤��≤1000), where ai�� is the durability of the i-th can. Output In the first line print the minimum number of shots required to knock each of the n given cans down exactly once. In the second line print the sequence consisting of n distinct integers from 11 to n — the order of indices of cans that minimizes the number of shots required. If there are several answers, you can print any of them. Examples input Copy 3 20 10 20 output Copy 43 1 3 2 input Copy 4 10 10 10 10 output Copy 64 2 1 4 3 input Copy 6 5 4 5 4 4 5 output Copy 69 6 1 3 5 2 4 input Copy 2 1 4 output Copy 3 2 1 Note In the first example Vasya can start shooting from the first can. He knocks it down with the first shot because he haven't knocked any other cans down before. After that he has to shoot the third can. To knock it down he shoots 201+1=2120⋅1+1=21 times. After that only second can remains. To knock it down Vasya shoots 102+1=2110⋅2+1=21 times. So the total number of shots is 1+21+21=431+21+21=43. In the second example the order of shooting does not matter because all cans have the same durability. Code Examples #1 Code Example with C++ Programming Code - C++ Programming #include <bits/stdc++.h> using namespace std; int const N = 1e3 + 10; int n; pair<int, int> a[N]; int main() { #ifndef ONLINE_JUDGE freopen("in", "r", stdin); #endif scanf("%d", &n); for(int i = 0, tmp; i < n; ++i) { scanf("%d", &tmp); a[i].first = tmp; a[i].second = i; } sort(a, a + n); reverse(a, a + n); int res = 0; for(int i = 0; i < n; ++i) res += (a[i].first * i + 1); printf("%d\n", res); for(int i = 0; i < n; ++i) { if(i != 0) printf(" "); printf("%d", a[i].second + 1); } puts(""); return 0; } Copy The Code & Input cmd 3 20 10 20 Output cmd 43 1 3 2

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Page 1 of 2 Automotive dual battery question Posted: Tue Feb 24, 2004 8:30 am I have a diesel pick-up with dual 750 CCA batteries wired in parallel. The passenger side battery has a 2/0 cable running directly to the starter. The drivers side battery is connected to the pass. battery thru a 5 foot length of 4 gauge wire. According to the shop manual, starting current can be as high as 700 amps. My question is, does the pass. side battery take more of a load than the drivers side battery because of the realitive small 4 gauge connection? How is the current draw split between the 2 batteries or is it equal? Thanks in advance for any thoughts. Re: Automotive dual battery question Posted: Tue Feb 24, 2004 9:06 am The battery with the thickest cables takes the greatest load during start-up. The thinner cables resist the current flow from the passenger battery while cranking the starter. Re: Automotive dual battery question Posted: Tue Feb 24, 2004 9:57 am The further the distance, the bigger the cable needed. The two most likely draw apx the same current, based upon size AND distance. Re: Automotive dual battery question Posted: Tue Feb 24, 2004 11:11 am This will screw up the estimates (And probably show how little I know) According to my estimate, with a copper resistivity of 1.6 microhms per cubic centimetre the resistance of a 4 ft long piece of 4 gauge wire is the order of one thousandth of an ohm hence, a 10 volt drop across it would represent a current of 100 amps. There Re: Automotive dual battery question Posted: Tue Feb 24, 2004 11:11 am This will screw up the estimates (And probably show how little I know) According to my estimate, with a copper resistivity of 1.6 microhms per cubic centimetre the resistance of a 4 ft long piece of 4 gauge wire is the order of one thousandth of an ohm hence, a 10 volt drop across it would represent a current of 100 amps. There Re: Automotive dual battery question Posted: Tue Feb 24, 2004 11:16 am This is going to screw up the estimates (Or show how little I know) - according to me, with a copper resistivity of 1.6 microhms per cubic centimetre the resistance of a 4 ft long length of 4 gauge wire woulf be the order of 1000th part of an ohm. Hence, a 100 amp current through it would produce a volts drop of 10 volts. There is no way the differnce between two, fairly well charged 12 volt batteries, with one on load, is going to exceed 10 volts so the likely, bettery healthy, starting current in the lead will be the order of 40 - 60 amps Re: Automotive dual battery question Posted: Tue Feb 24, 2004 11:58 am WOW… <p>[ February 24, 2004: Message edited by: Edd Whatley ]</p> Re: Automotive dual battery question Posted: Tue Feb 24, 2004 1:55 pm Chris Smith,<p> Not sure I follow you. The 2/0 cable to the starter is approx. 4' long. Are you saying that the wire size between the 2 batteries makse no difference and they will always share "equal current",ie, 350 amps? Re: Automotive dual battery question Posted: Tue Feb 24, 2004 3:25 pm Where's that guy with the strap-on ammeter? The large, close cable (passenger side) will carry most of the current. Re: Automotive dual battery question Posted: Tue Feb 24, 2004 4:26 pm You have to include the internal resistance of the battery to make a valid calculation. Since internal resistance will be higher than cable resistance the two batteries will be sharing a nearly equal load. Re: Automotive dual battery question Posted: Tue Feb 24, 2004 5:34 pm The batteries are connected in parallel. The drivers side 4 ga. wire carries only the current from that battery. It connects to the passenger side battery. The 2/0 carries the current from both batteries. If both batteries are healthy, the current will be pretty close to the same from each battery. Re: Automotive dual battery question Posted: Tue Feb 24, 2004 5:34 pm the smaller cable only has have the current flow in it thus smaller cable to the other battery the larger wire carries all the current for the starter 700 amps joe Re: Automotive dual battery question Posted: Tue Feb 24, 2004 8:12 pm If driver's side battery is connected to passenger's side battery, the cable from passenger's side battery to starter carries current from both batteries.<p>Passenger side battery does supply more starter current than driver side, but its not too lop-sided. And, if engine doesn't start, driver side battery will partially recharge passenger side battery between tries.<p>700 amps is only when you first turn the key. As starter motor speeds up, the current decreases. At full cranking speed probably well under 100 amps. Then driver side batt is still providing less current, but is more of an equal share. Re: Automotive dual battery question Posted: Wed Feb 25, 2004 3:56 am My, my! Let's expand on the proportions. Say the passenger side battery is 2 feet away from the starter with 2/0 cable. The drivers side battery is connected by 4 ga, in say, the next county. Same current from each battery? I don't think so. Most of the current from the drivers side is lost as IR drop in the longer, smaller cable. Put another way- disconnect the parallel connection between the batteries. Connect just passengers side battery to starter and measure the cranking current. Then, connect only the drivers side with the smaller wire from the battery in the next county. It won't even crank! Re: Automotive dual battery question Posted: Wed Feb 25, 2004 6:11 am What threw me off is that in almost all cars, the stock (OEM) battery is on the driver's side. I did not catch that the vehicle was a diesel. So, If I were to add an extra battery, I would tend to leave that one alone and connect the extra one to it. I did not catch that both batteries were stock.<p>If I were you, I would connect the batteries together with 0000 gauge wires.<p>[ February 25, 2004: Message edited by: Joseph ]</p>

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# The World Communicates-Physics The wave model can be used to explain how current technologies transfer information. Describe the energy transformations required in one of the following: * Mobile Telephone Mobile telephones have built in microphones that changes sound waves ib Describe waves as a transfer of energy disturbance that may occur in one, two or three dimensions, depending on the nature of the wave and the medium Identify that mechanical waves require a medium for propagation while electromagnetic waves do not Mechanical: Requires a medium for propagation (ie. Travel through) Eg. Sound Waves, Water Waves, Waves in a string .. Electromagnetic: Do not require a medium for propagation (ie. EM Waves can pass through a vacuum) Eg. Light, Infrared, UV, X rays, Gamma Rays, Radio waves, Microwaves .. Define and apply the following terms of the wave model: Medium, displacement, amplitude, period, compression, rarefaction, crest, trough, transverse waves, longitudinal waves, frequency, wavelength & velocity. Describe the relationship between particle motion and the direction of energy propagation in transverse and longitudinal waves Quantify the relationship between velocity, frequency and wavelength v=f? We Will Write a Custom Essay Specifically For You For Only \$13.90/page! order now Where v = velocity, f = frequency & ? = wavelength (lambda) Features of a wave model can be used to account for the properties of sound. Identify that sound waves are vibrations or oscillations of particles in a medium Relate compressions and rarefactions of sound waves to the crests and troughs of transverse waves used to represent them Explain qualitatively that pitch is related to frequency and volume to amplitude of sound waves Explain an echo as a reflection of a sound wave Describe the principle of superposition and compare the resulting waves to the original waves in sound

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Solved # Get value from associative array without key... Posted on 2010-11-30 485 Views Given an array like this, where I don't know the key name, how can I extract the value of both elements (AL, Alabama)? Array ( [abbreviation] => AL [full_name] => Alabama ) 0 Question by:interclubs • 2 • 2 LVL 11 Expert Comment ID: 34241258 you cannot unless you know the array variable's name in which case you would extract the values like \$name['abbreviation']['full_name']; 0 LVL 14 Expert Comment ID: 34241613 If you mean that you don't know the key names (abbreviation, full_name) you can do something like this: foreach (\$array_name as \$value){ \$x[] = \$value; } That would give you an array of two elements in your example where \$x[0] = 'AL' and \$x[1] = 'Alabama'. If you don't know the name of the actual array (\$array_name) in my example, I have no idea how you would find the values. 0 LVL 1 Accepted Solution jebpotly earned 500 total points ID: 34241967 array_keys will give you a list of the keys in an array. If you have: ``````\$my_array = array('abbreviation' => 'AL', 'full_name' => 'Alabama'); `````` then you could use array_keys: ``````\$my_keys = array_keys(\$my_array); `````` which would give you an array of Array ( [0] => abbreviation [1] => full_name ). You could then do ``````\$first_value = \$my_array[\$my_keys[0]]; \$second_value = \$my_array[\$my_keys[0]]; `````` Or you could convert the array to use numeric indexes instead of string indexes. One way to do this is use the sort() method. So if you have the \$my_array as defined above then you could do: ``````sort(\$my_array); `````` Now \$my_array is Array ( [0] => Alabama [1] => AL) and you can use [0] and [1] to get the values. ``````\$first_value = \$my_array[0]; \$second_value = \$my_array[1]; `````` 0 LVL 11 Expert Comment ID: 34243985 @jebpotly: Sweet, did not know about "array_keys(\$my_array);" Thanks 0 LVL 1 Expert Comment ID: 34244028 ;) 0 ## Featured Post Question has a verified solution. If you are experiencing a similar issue, please ask a related question

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# Matrix operator... This topic is 2983 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hi I seemed to have an error in and old code i digged up. The error was related to the matrix class operator* and some confusion in which order the operators argument comes into the function. Soo please validate what is the correct order of arguments to a operator when doing matrix multiplication. for example consider a*b; Is "this" the left-side (a), and m the right-side (b) according to the function? In my previous code I had to reverse the order in MatrixMultiply, that is exchange arguments this.ref() and m.ref(). So either I didn't understand which arguments was left-/right-side in the operator or the multiply function was wrong. If this function below is correct, then the multiply was originally wrong. Matrix Matrix::operator*(Matrix &m) { Matrix tmp; MatrixMultiply(tmp.ref(), this->ref(), m.ref()); return tmp; } ##### Share on other sites Row-major matrices used by DirectX produces results equal to the left operand followed by the right operand. Column-major matrices used by OpenGL produce results equal to the right operand followed by the left operand. There is no right or wrong answer. You have mixed up the major-ness of your matrices. Pick one and stick with it. L. Spiro ##### Share on other sites The result of a matrix multiplication A * B is mathematically defined in explicit terms. You should ever implement the operator w.r.t. that definition, or else confusion will emerge! You should further implement it as non-member function. Because matrix multiplication isn't commutative, you'll probably come to cases where you don't want to distinct "on the left" or "on the right" (what would simply be possible with operator*) but "on the local side" or "on the global side". Now, here comes the problem of column vs. row vectors into play EDIT, as already mentioned by YogurtEmperor/EDIT. To avoid any confusion, it would IMHO be best to implement 2 non-member functions that explicitely express their behaviour in their names, e.g. inline Matrix mulWithLocal( Matrix const& matrix, Matrix const& local ); inline Matrix mulWithGlobal( Matrix const& matrix, Matrix const& global ); (Made them inlined to avoid performance penalties.) Then implement the both helper routines w.r.t. the vector convention of your choice utilizing the operator*. The only issue with the solution above is IMHO that it needs more typing than a simple *. Just my 2 €-Cent. [Edited by - haegarr on April 24, 2010 10:43:24 AM] ##### Share on other sites Quote: Original post by haegarrNow, here comes the problem of column vs. row vectors into play, as already mentioned by YogurtEmperor. YogurtEmperor was actually referring to matrix majorness (a different issue). Quote: Original post by YogurtEmperorRow-major matrices used by DirectX produces results equal to the left operand followed by the right operand.Column-major matrices used by OpenGL produce results equal to the right operand followed by the left operand. It sounds like you might be confusing matrix 'majorness' with vector notation convention. When you say (e.g.) 'equal to the left operand followed by the right operand', I assume you mean that the resulting transform is equal to the transform represented by the matrix on the left, followed by the transform represented by the matrix on the right (as would be the case in DirectX). However, this doesn't have anything to do with matrix majorness; rather, it has to do with whether row vectors or column vectors are being used. In any case, this shouldn't have any impact on how the '*' operator is implemented for matrices; matrix multiplication is defined the same way (and should be implemented the same way) regardless of what vector notation convention is being used. ##### Share on other sites Quote: Original post by jyk Quote: Original post by haegarrNow, here comes the problem of column vs. row vectors into play, as already mentioned by YogurtEmperor. YogurtEmperor was actually referring to matrix majorness (a different issue). Uhh, I've read it in a hurry. You're right, of course. However, Quote: Original post by jykIn any case, this shouldn't have any impact on how the '*' operator is implemented for matrices; matrix multiplication is defined the same way (and should be implemented the same way) regardless of what vector notation convention is being used. is nevertheless exactly what I meant :) ##### Share on other sites A good way to keep track of this is to wrap your multiplication routine in another named member function, such as Concatenate. Let this function take care of the funny business of matrix multiplication order. This way client code need only worry about which transform should be concatenated, and not the (somewhat arbitrary) way in which this is accomplished. ##### Share on other sites Quote: for example consider a*b;Is "this" the left-side (a), and m the right-side (b)according to the function? Yes for all operators. a * b is the equivalent of a.operator*(b), so "this" is the left hand side, and the parameter is the right hand side. ##### Share on other sites Quote: Original post by taz0010 Quote: for example consider a*b;Is "this" the left-side (a), and m the right-side (b)according to the function? Yes for all operators. a * b is the equivalent of a.operator*(b), so "this" is the left hand side, and the parameter is the right hand side. As I suspected, I just forgot the logic around the operators and became unsure whatever was right soo thank you all! It's been 10 years since I worked with software development before I completely quit coding soo these little things are easy to forget. My old library routine for matrix multiplication was indeed in the incorrect order, it calculated B*A when it should have calculated A*B (I never tested them when I wrote them a long time ago since I used a sdk at the time). Once again, thank you all for your help! 1. 1 2. 2 Rutin 19 3. 3 4. 4 5. 5 • 15 • 13 • 9 • 12 • 10 • ### Forum Statistics • Total Topics 631442 • Total Posts 3000087 ×

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• Clear Filters CP240 Restrict Range Of Solutions With Trig Equations Two methods to restrict the range of solutions returned when solving trig equations in Main. Year Level: State: , , CP250 Solve System Of Equations With 3 Unknowns Use one of the 2D templates to solve systems of equations with 2 or more variables. Year Level: State: , , CP350 Using Sliders To Explore Functions How to use sliders in graph and table to explore function transformations. Year Level: State: , , CP172 Inverse Of A Function Find the inverse of a function algebraically using invert and also view the inverse graphically. Year Level: State: , , CP205 Solving Simultaneous Linear Equations 1 Solve simultaneously the equations 2x – 3y = -1 and x + y = 7 using a traditional step by step elimination method in Main. Year Level: State: , , How to update the operating system of your hand-held ClassPad using a Windows PC. CP011 Simplifying and Expanding Collect like terms and expand and simplify expressions such as 3(4-2x)^2. CP012 Factorising Factorisation of numbers and expressions (eg quadratics) CP041 Sequence: What Is My Rule? Use the sequence function in Main to find the defining rule for various sequences

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# New School Algebra Ginn & Company, 1898 - 407 σελίδες ### Τι λένε οι χρήστες -Σύνταξη κριτικής Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες. ### Περιεχόμενα Fractions 123 Fractional Equations 148 Simultaneous Simple Equations 174 Problems with Two or More Unknown Numbers 190 Simple Indeterminate Equations 205 XrV Inequalities 208 Variables and Limits 338 XXrV Properties of Series 345 Binomial Theorem 352 Logarithms 372 Graphs 409 Πνευματικά δικαιώματα ### Δημοφιλή αποσπάσματα Σελίδα 276 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans. Σελίδα 252 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then, divide by bd. Σελίδα 316 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number. Σελίδα 244 - If twelve times the units' digit is subtracted from the number, the order of the digits will be reversed. Find the number. Σελίδα 25 - Two men start from the same place and travel in the same direction, one 30 miles a day, and the other 20 miles a day. Σελίδα 118 - To reduce a fraction to its lowest terms. A fraction is in its lowest terms, when the numerator and denominator are prime to each other. Σελίδα 56 - To Multiply a Polynomial by a Monomial, Multiply each term of the polynomial by the monomial, and connect the partial products with their proper signs. Σελίδα 263 - The distance a body falls from rest varies as the square of the time it is falling. Σελίδα 254 - In a Series of Equal Ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Σελίδα 276 - Of three numbers in geometrical progression, the sum of the first and second exceeds the third by 3, and the sum of the first and third exceeds the second by 21.

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# Bricks II 3/4 bricks weighs 6 kg and 2/3 bricks. How weighs one whole brick? x =  72 kg ### Step-by-step explanation: 3/4x = 6+ 2/3 x 3/4•x = 6+ 2/3•x x = 72 Our simple equation calculator calculates it. Did you find an error or inaccuracy? Feel free to write us. Thank you! Tips to related online calculators Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation? ## Related math problems and questions: • Brick weight The brick weighs 2 kg and a half bricks. How much does one brick weigh? • Two bricks One brick weighs 1kg and half a brick, how many weigh two bricks? • Bricks Openings in perforated bricks occupy 10% and brick has dimensions 30 cm, 15 cm and 7.5 cm. Calculate a) the weight of a perforated bricks, if you know that the density of the full brick material is p = 1800 kg/m3 (1.8 kg/dm3) b) the number of perforated • Brick Brick weight before drying is 5.3 kg. After drying, the bricks is 1 kg lighter and after firing is 0.7 kg lighter than after drying. What is the weight of the brick after drying and firing? • Bag Nelly found interesting point. An empty bag weighs 4 kg less than full. And empty bag is 5 times easier than full. How many kg weigh things in this bag? • Bob and Bobek Bobek has 2 cabbages and 5 carrots, Bob has 2 cabbages and 9 carrots. When Bobek stepped on the scale weight 5800 g and when Bob weight 8960 g. Actual Bob weight is 8 kg and Bobek 5 kg. How much weighs one carrot? • Can Watering can full of water weighs 10 kg. Half-full can weighs 5.5 kg. How much weigh can? • Brick Isosceles scale has on one side all brick and second weight 1 kg and 1/4 of brick. The balance is in equilibrium. What is the weight of a brick? • Cooks Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes? • Children Margaret and Zdena weigh the same and Petra 3 kg more. Together weigh 156 kg. How much do they weigh? • Apples 5 In six crates are 45 kg of apples. In five crates were the same amount and in one crate was 3 kg of apples more. How many kg of apples were in each crate? • Apples Mr. Vesely give to the market his own 48 kg of apples, 40 kg from Mr. Kovar and 72 kg of Mr. Novak. Grossed a total of 1,920 CZK. How must divide income money for apples? • Milk2cheese From 40 liters of milk is produced 8 kg of cheese how many liters of milk are needed to produce 2 kg of cheese? • DIY press Under socialism regime was in some socialist countries to own a typewriter requires special permission. That has hindered the spread of DIY literature (manually transcribed through carbon copy paper for typewriters). Calculate how many typewriters today c • Watering can A watering can full of water weighs 11 kg, the weight of water is 10 kg greater than the weight of an empty watering can, how much is the weight of the watering can? • Water container Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container? • Warehouses To four warehouses is going cement in 25 kg bags. To first one third, to second quarter of the total. The third store got two thirds of the rest, and the last 310 tons came to fourth. How many cement is in all warehouses and how much got every one?

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# elementary [ˌelɪˈmɛntəri] ## elementary Definition • 1relating to the first stages of something; basic and fundamental • 2relating to or denoting the basic, essential, or fundamental part of something ## Using elementary: Examples Take a moment to familiarize yourself with how "elementary" can be used in various situations through the following examples! • Example The book provides an elementary introduction to quantum mechanics. • Example The teacher gave us an elementary explanation of the concept. • Example The course covers elementary algebra and geometry. • Example The experiment involves elementary particles. ## Phrases with elementary • ### elementaryschool a school for young children, typically those aged between five and eleven Example I went to an elementary school in my hometown. • ### elementaryparticle a subatomic particle that cannot be broken down into smaller particles Example The Higgs boson is an elementary particle. • ### elementaryalgebra the branch of mathematics that deals with equations and algebraic structures in which both operands are numbers Example The course covers elementary algebra and geometry. ## Origins of elementary from Latin 'elementarius', from 'elementum' meaning 'principle' 📌 ## Summary: elementary in Brief The term 'elementary' [ˌelɪˈmɛntəri] refers to the first stages of something, or the basic and fundamental part of something. It can describe a simple or rudimentary explanation or introduction, as in 'The teacher gave us an elementary explanation of the concept.' It also extends to fields like mathematics, where 'elementary algebra' is a basic branch of study. How do native speakers use this expression? Oncheon-ro 45, Yuseong Prugio City unit. 208. Yuseong-gu, Daejeon

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https://exercism.io/tracks/objective-c/exercises/sum-of-multiples/solutions/01ad754a46b04e2d96c59754af2a141e

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# lockheedbird's solution ## to Sum Of Multiples in the Objective-C Track Published at Jan 13 2019 · 0 comments Instructions Test suite Solution Given a number, find the sum of all the unique multiples of particular numbers up to but not including that number. If we list all the natural numbers below 20 that are multiples of 3 or 5, we get 3, 5, 6, 9, 10, 12, 15, and 18. The sum of these multiples is 78. ## Setup There are two different methods of getting set up to run the tests with Objective-C: • Create an Xcode project with a test target which will run the tests. • Use the ruby gem `objc` as a test runner utility. Both are described in more detail here: http://exercism.io/languages/objective-c ### Submitting Exercises When submitting an exercise, make sure your solution file is in the same directory as the test code. The submit command will look something like: ``````exercism submit <path-to-exercism-workspace>/objective-c/sum-of-multiples/SumOfMultiples.m `````` You can find the Exercism workspace by running `exercism debug` and looking for the line beginning with Workspace. ## Source A variation on Problem 1 at Project Euler http://projecteuler.net/problem=1 ## Submitting Incomplete Solutions It's possible to submit an incomplete solution so you can see how others have completed the exercise. ### SumOfMultiplesTest.m ``````#import <XCTest/XCTest.h> #if __has_include("SumOfMultiplesExample.h") # import "SumOfMultiplesExample.h" # else # import "SumOfMultiples.h" #endif @interface SumOfMultiplesTest : XCTestCase @end @implementation SumOfMultiplesTest - (void)testSumTo1 { NSNumber *sum = [SumOfMultiples toLimit:@1 inMultiples:@[@3, @5]]; XCTAssertEqualObjects(@0, sum); } - (void)testSumTo3 { NSNumber *sum = [SumOfMultiples toLimit:@4 inMultiples:@[@3, @5]]; XCTAssertEqualObjects(@3, sum); } - (void)testSumTo10 { NSNumber *sum = [SumOfMultiples toLimit:@10 inMultiples:@[@3, @5]]; XCTAssertEqualObjects(@23, sum); } - (void)testSumTo100 { NSNumber *sum = [SumOfMultiples toLimit:@100 inMultiples:@[@3, @5]]; XCTAssertEqualObjects(@2318, sum); } - (void)testSumTo1000 { NSNumber *sum = [SumOfMultiples toLimit:@1000 inMultiples:@[@3, @5]]; XCTAssertEqualObjects(@233168, sum); } - (void)testConfigurable_7_13_17_to_20 { NSNumber *sum = [SumOfMultiples toLimit:@20 inMultiples:@[@7, @13, @17]]; XCTAssertEqualObjects(@51, sum); } - (void)testConfigurable_4_6_to_15 { NSNumber *sum = [SumOfMultiples toLimit:@15 inMultiples:@[@4, @6]]; XCTAssertEqualObjects(@30, sum); } - (void)testConfigurable_5_6_8_to_150 { NSNumber *sum = [SumOfMultiples toLimit:@150 inMultiples:@[@5, @6, @8]]; XCTAssertEqualObjects(@4419, sum); } - (void)testConfigurable_43_47_to_10000 { NSNumber *sum = [SumOfMultiples toLimit:@10000 inMultiples:@[@43, @47]]; XCTAssertEqualObjects(@2203160, sum); } - (void)testConfigurable_0_to_10 { NSNumber *sum = [SumOfMultiples toLimit:@10 inMultiples:@[@0]]; XCTAssertEqualObjects(@0, sum); } - (void)testConfigurable_0_1_to_10 { NSNumber *sum = [SumOfMultiples toLimit:@10 inMultiples:@[@0, @1]]; XCTAssertEqualObjects(@45, sum); } @end`````` ``````#import "SumOfMultiples.h" @implementation SumOfMultiples + (NSNumber *)toLimit:(NSNumber*)limit inMultiples:(NSArray *)multiples { NSNumber *sum = @0; NSMutableSet *setOfNumbers = [NSMutableSet setWithObject:@0]; for (int i = 0; i < limit.intValue; i++) { for (NSNumber *n in multiples) { if (n.integerValue > 0 && i % n.integerValue == 0) { } } } for (NSNumber *n in setOfNumbers) { sum = @(sum.integerValue + n.integerValue); } return sum; } @end``````

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https://forum.awesystems.info/t/wacky-wave-kite-power-idea/2643

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# Wacky Wave Kite Power Idea I was thinking about wave power and AWE today. How to extract the energy of a wave using a kite. I based the idea on a bounding one kite one tether base. Then look at the flow in a wave. https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html Now look the current at the crest of the wave is heading with the wave, the bough towards offshore. The kite should fly (under water) along the crest of the wave pulling towards shore then turn 180 degrees and follow the trough back towards the origin, pulling towards offshore. The sketch shows the basics. We have two winches [purple], one for crest production and one for trough production. Crest production path is colored green, trough red, and the yellow part is a return phase to account for net movement «downwind» during the production cycle. The kite is the black one, tethered to both winches at the same time I think its a neat idea [I say, patting my own sholder]. Problems is one that the kite must fit in the wave so the wing area is naturally limited. So the concept would require many smaller units coupled together to get big net power output. I would naturally see many kites stacked on a single tether. But if we do that, its hard to align them all with the crest. I am also like for most wave power just not dealing with such a nimble machinery running underwater for an extended duration. Also, the kite must be placed carefully just beneath the surface of the sea. The kite must be placed carefully at the crest and trough, and the system must be able to find these and place the kite there in time. And account for a waves irregular shape (at least here in norway). Except for those solvable details, this should power thousands of homes. 1 Like Could this be some kind of tethered underwater variation of dynamic soaring flight mode? If we look closely at the moving diagram, we see that the kite would always be close to the surface, and would follow the movement of the wave. This is why a partially submerged float filled with water would seem simpler and more appropriate to me, not subject to such dimensional limitations and being able to form a single power unit. I think not being a float would be the primary improvement in the design, as the float will perish in the first storm Floating buoys (like the one below) follow the motion of the waves, and are very robust even during storms and big waves. And I don’t see the usefulness of kites which must only follow the flow and not “fly” in relation to said flow. Double anchoring with the respective winches would be possible with a model like this: The idea I suggested had the kites flying? Yes, as mentioned in the description (see the quote below). And generally kites fly, in the air or underwater, in static or crosswind mode. I don’t see the usefulness of kites for this configuration. Floating buoys are suitable, if of course this scheme is other than “wacky”. The problem is that at sea even more than in air [well maybe] condition in fair and bad weather vary a lot. In particular, if the waves grow big enough to break, you dont want a floating structure in there. Being close to the surface could be achieved through sensors and active control. An additional problem with a floating kite at the surface is the drag it may cause, in particular by waves created on water, and due to disturbances on the water surface and wind. I think though my initial sketch was misleading, so let me try to improve on it A farm could look like this I think about it sometimes, but never going further into design considerations. Do you know the wave glider ? The Wave Glider | How It Works 1 Like I guess this idea is not too far from home for you at Syroco. Especially if the winches were placed above sea level which could be a good idea if tether drag was an issue. I think we discussed this earlier, that subsea tethers are much more succeptible to tether drag issues, as you have more force for the same wing area, but you cant increase the strength of the tether without increasing the diameter.

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Indian mathematician Mathematics Astronomy Scholars Topics Astronomer Multiplication # Brahmagupta was astronomer and an Indian mathematician, the son of Jishnugupta Brahmagupta describes the multiplication found the result gives, natural numbers does not explicitly state that these quadrilaterals, uses. Brahmagupta is encoded mostly in concrete-number notation, enumerates six first sine-values made in astronomy by Brahmagupta, discusses the illumination of the moon by the sun, believed in a static Earth. Bhillamala called pi-lo-mo-lo by Xuanzang, was for astronomy and mathematics. Critiques of rival theories appear throughout the eleventh chapter and the ten first astronomical chapters. The court of Caliph Al-Mansur received an embassy from Sindh. An immediate outcome was the spread of the decimal number system. The mathematician Al-Khwarizmi wrote a text, al-Jam wal-tafriq bi hisal-al-Hind. Indian astronomic material circulated widely for centuries. The the middle square-root of the rupas multiplied by the square by four times. Addition was indicated by subtraction by juxtaposition. Multiplication were represented by abbreviations of appropriate terms. The four fundamental operations were known before Brahmagupta to many cultures. This current system is based on Arabic number system on the Hindu. Brahmasphutasiddhanta was named Gomutrika contains twenty-five chapters. The procedures are followed for five types of combinations by rules. A positive number and Zero is negative number and the positive number divided by zero. One theorem gives the lengths of the two segments, a triangle's base. The Thus lengths of the two segments gives further a theorem on rational triangles. The square of the diagonal is diminished by the square. The geometry of plane figures discusses the computation of volumes. The next formula gives an estimate for the value of a function. Progenitors represents the 14 Progenitors in Indian cosmology. The same way seen in sunlight by the sun of a pot standing. The brightness is increased in the direction of the sun. The key have only 150 staff, 're dedicated to reader privacy, accept never ads. Undergraduate students studying the history of mathematics for secondary education and engineering for science. George Gheverghese Joseph takes on a breathtaking multicultural tour of the roots, shows the deep influence that Babylonians and the Egyptians. The third edition emphasizes the dialogue between civilizations, includes new chapters. The book's scope is now even wider recent findings, an also indispensable guide for mathematics teachers. The authors have written also substantial section introductions. The mathematics literature is an essential resource with at an least undergraduate degree for anyone. Imhausen mentioned algorithmic aspects of certain calculations. The AWT set of theoretical facts was mentioned not in &39; s book in Katz. One side of the hekat unity division method was proven by a Charles U. by Hana Vymazalova. A new interdisciplinary standard is rescuing the Egyptian hieratic texts. A debt subtracted from zero, multiplied by fortune and a debt. Majumdar gives the original Sanskrit verses from Brahmagupta's Brahmasphuta siddhanta. The Khandakhadyaka is in eight chapters, contains an appendix. Previous article Next article

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# How can a 5,000-pound truck tow 10,000 pounds? Wait, doesn't that defy physics? Nope. Tim McCaig/iStockPhoto Have you ever watched in amazement as a pickup truck tows a huge load of bricks? If you thought, "Wow, that defies the laws of physics!" you would be wrong. Believe it or not, the laws of physics (or more specifically, the laws of motion) actually allow a 5,000-pound (2,268 kilogram) truck to tow a 10,000-pound (4,536 kg) load. It's part of the interplay between the energy exerted by the truck's engine and the forces of gravity. This is no small feat, however; if you remember Newton's Third Law of Motion, you know that from the moment your truck begins to move, there are forces that oppose it every step of the way. If you understand the physics of driving, you understand the physics of towing. There's actually a fairly simple way to look at the process. There are three states that your truck can enter when it comes to driving and towing: rest, acceleration and constant velocity. When your truck's transmission is in park and your truck is motionless, it's considered at rest. The gravitational push downward toward the center of the earth and the upward push from the earth (called normal force) oppose one another to keep your truck at rest. Your truck will stay put -- after all, an object at rest tends to stay at rest. But you don't want to rest, you want to tow. This means you have to overcome this tendency to rest through applied force. Fortunately for you, your truck has an engine that can produce energy, which serves as the applied force required to get you moving. While the opposing normal and gravitational forces still remain, to accelerate you're going to have to deal with the forces of friction. Rather than up and down, these forces exist parallel to the ground, and push in the opposite direction of the way you want to move. You can't catch a break physics-wise, can you? With us so far? Good. Keep reading to learn more about the physics of towing.

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open-discussion > The second temporal derivative of HRF in estimating the "amplitude of effects" Apr 28, 2021  04:04 AM | Gao F - central south university The second temporal derivative of HRF in estimating the "amplitude of effects" In the paper 'BASCO: a toolbox for task-related functional connectivity', estimation of the "amplitude of effects" is proposed as: β = sign(β1) * sqrt(β1^2 + β2^2 + β3^2), where, the first beta-value relates to the canonical HRF, the second and third beta-values relate to the first and second temporal derivative, respectively. I was wondering how to set or create the [color=#ff0000]β3. Then I check the BASCO.m, where in the 1270 to 1272[/color] lines  of the script, it is commented: % Estimating the "amplitude" of the effects at each voxel = sign(V1).*sqrt(V1.^2+V2.^2) % where V1 is the canonical effect contrast volume, and V2 is the temporal derivative % effect contrast volume. [Calhoun (2004)] [color=#ff0000]β3 seems not included in the [/color]formula in the comment, and in the following line 1282 of the script: datmat = sign(datmatA).*sqrt(datmatA.^2+datmatB.^2+datmatC.^2) [color=#ff0000] [/color] The 'datmatC' seems corresponding to 'β3', but it more likely a disperion derivatives while not the second temporal derivative. My question is, in which way the BASCO estimating the "amplitude of effects", and by which way the second temporal derivative of HRF could be used, or if I have just misunderstood the script? [color=#ff0000] [/color]

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Courses Courses for Kids Free study material Offline Centres More Store # 6 balls are marked with numbers $1$ to $6$. If two balls are picked out of these $6$ balls, what is the probability that the sum of the numbers on the balls is $8$?A. 1/15B. 2/15C. 1/5D. 4/15E. 1/3 Last updated date: 23rd Jul 2024 Total views: 349.2k Views today: 4.49k Verified 349.2k+ views Hint: To find the required probability, we need to find the total number of outcomes and favorable number of outcomes first. Then, we will use the formula of probability that is $\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$ and substitute the obtained value of favorable number of outcomes and total number of outcomes. After simplifying it, we will get the probability that the sum of the numbers on the ball is $8$ when two balls are picked. Complete step-by-step solution: Since, the order is not important for selection of balls. So we will use the formula of combination to get the total number of outcomes as: $\Rightarrow {}^{n}{{C}_{r}}=\dfrac{n!}{r!\centerdot \left( n-r \right)!}$ Where, $n$ is the total number of objects and $r$ is the number of objects chosen. Now, we will substitute $6$ for $n$ and $2$ for $r$in the above formula. $\Rightarrow {}^{6}{{C}_{2}}=\dfrac{6!}{2!\centerdot \left( 6-2 \right)!}$ Solve the terms within the bracket. $\Rightarrow {}^{6}{{C}_{2}}=\dfrac{6!}{2!\centerdot \left( 4 \right)!}$ We can write $15!$ as: $\Rightarrow {}^{6}{{C}_{2}}=\dfrac{6\centerdot 5\centerdot 4!}{2!\centerdot \left( 4 \right)!}$ Here, we will cancel out the equal like terms and will expand the factorial terms as: $\Rightarrow {}^{6}{{C}_{2}}=\dfrac{6\centerdot 5}{1\centerdot 2}$ Now, we will complete the multiplication in numerator and denominator as: $\Rightarrow {}^{6}{{C}_{2}}=\dfrac{30}{2}$ After simplifying the above step, we will have: $\Rightarrow {}^{6}{{C}_{2}}=15$ Since, there are only two combinations that sum is $8$(2,6),(3,5). So, the number of favorable outcomes is $2$. Now, we will use the formula of probability to get the required probability as: $\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$ Here, we will substitute the respective values as: $\text{Probability}=\dfrac{\text{2}}{\text{15}}$ Hence, $\dfrac{\text{2}}{\text{15}}$ is the required probability that the sum of the numbers on the balls is$8$. Note: Here a term is given as picking up the balls that means we have to select the balls and we use the combination for selection of objects. Combination is the possible number of outcomes of selecting objects where order doesn’t matter. The formula used for calculation of number of combination is: $\Rightarrow {}^{n}{{C}_{r}}=\dfrac{n!}{r!\centerdot \left( n-r \right)!}$ Where, $n\ge r$ and $n$ is the total number of objects and $r$ is the number of objects chosen.

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Converting Density to Molecular Weight Dragonrider99 Greetings all. I am currently in the midst of a Final Acceptance Testing for one of our customers that is purchasing some Density Meters. Physics is not my strong point as I am a Test Engineer and I desperately need some help. Our product is spec'd out such that it reports Density, Pressure, Current, and several other measurements but it does not report Molecular Weight. This customer is insisting on my telling him how to convert the Density Measurement to Molecular Weight and I am not sure. Basically the product is pressurized with Lab Grade Nitrogen and it detects Density via a change in frequency due to compression of a spool. Anyway, I found this formula for converting Molecular Weight to Density: p=PM/RT where p=Density P=Pressure in Pascals M=Molecular Weight R=Universal Gas Constant T=Temp in Kelvin Re-arranging the formula I get: M=pRT/P My Values are: p=8.65Kg.m3 P=786000 pascals R=8.134j/mol*K T=305.15 Kelvin After doing the math I get 0.027Kg/mol Is this correct or am I totally wrong? Thanks benit13 Caveat... I will accept no blame if something goes wrong! Now that that's out of the way... The only mistake seems to be your choice of value for the real gas constant; it's 8.314 J/(mol.kg) Assuming an ideal gas: $$\displaystyle PV = nRT$$ Since: $$\displaystyle \rho = \frac{M}{V}$$ Substituting for V: $$\displaystyle P\frac{M}{\rho} = nRT$$ $$\displaystyle \frac{M}{n} = \mu = \frac{\rho}{P}RT$$ $$\displaystyle \mu = \frac{8.65 * 8.314 * 305.15}{786000} = 0.02792$$ kg/mol = 27.92 g/mol Carbon monoxide perhaps? 1. Make sure your real gas constant is correct (R = 8.314 J/(mol.K), not 8.134) 2. Make your customer aware that your measurement is a derived parameter using an equation that assumes an ideal gas. Last edited: 1 person Woody I am not sure what your customer is actually after. The molecular weight is a constant which depends only on the material. It is the weight (or more correctly Mass) of 1 Mole of the molecules of the material (1 mole is a big number = about 6x10^23) It allows one to estimate the number of molecules in a sample from its weight (mass) rather than by physically counting molecules (which is time consuming). The standard atomic mass for Nitrogen is 0.014kg/mol however you have Nitrogen gas, thus N2 giving molecular mass of 0.028kg/mol I think that is fairly close to what you have calculated... Last edited: Woody What the customer wants. Thinking about it, knowing the molecular mass of the gas being processed can tell you a fair amount about it. For example your pure dry nitrogen gave a very close result to the book value. However if it was contaminated (damp for example) the molecular mass would have been off. Water with a molecular mass of 18grams/mole would raise the overall molecular mass of the mix. Perhaps your customer wants to monitor a process to ensure that the (combined) molecular weights of the products remains within tolerable boundaries. Benit's point about an ideal gas is pertinent. Complex mixes, and complex molecules are less likely to match the theoretical "ideal" gas. Have a look at the Wikipedia article linked here: <Ideal Gas> If your customer wants to monitor a process (ensuring it does not change), then relative accuracy might be more important than absolute accuracy. Last edited: 1 person Dragonrider99 You guys are great! Thanks so much. Your comment about if there is another gas or substance in the mix hits home because otherwise I can't figure out for the life of me why they want that. Based on the data I have taken at various pressures and densities, the Molecular Weight always comes out to the "Book Value." If there IS another substance such as Water contaminating the gas, is there any way to determine the concentrations of each based on the calculated Molecular Weight based on the other measured parameters? Not sure if I phrased that correctly but I hope you get the gist of what I mean. Otherwise thanks to all of you that have responded. I truly appreciate your help and inputs. Woody Contaminants If you have a clear idea of what the molecular mass of the "clean" gas is and a clear idea of what the contaminant might be, and what it's molecular mass is, then you can start to get quantitative estimates of the level of contamination. However if you just have an unknown contaminant, all you can get is a qualitative estimate of the level of contamination (i.e. you don't know how much contaminant is there, but you do know if it gets better or worse). donglebox Referring to common practices, If he needs a careful but easy-to-use quick-check manual, or reads out the transformation software tools according to the conditions, You can sell this as an additional item. After all, this has expanded the use of the device. It belongs to advanced tools.

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⚠️ Warning: This is a draft ⚠️ This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues. If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub. {{task|Sorting}} Sort an array (or list) of integers in ascending numerical order. ;Task: Use a sorting facility provided by the language/library if possible. ## 4D ### English ```ARRAY INTEGER(\$nums;0) APPEND TO ARRAY(\$nums;2) APPEND TO ARRAY(\$nums;4) APPEND TO ARRAY(\$nums;3) APPEND TO ARRAY(\$nums;1) APPEND TO ARRAY(\$nums;2) SORT ARRAY(\$nums) ` sort in ascending order SORT ARRAY(\$nums;<) ` sort in descending order ``` ===Français=== ```TABLEAU ENTIER(\$nombres;0) AJOUTER A TABLEAU(\$nombres;2) AJOUTER A TABLEAU(\$nombres;4) AJOUTER A TABLEAU(\$nombres;3) AJOUTER A TABLEAU(\$nombres;1) AJOUTER A TABLEAU(\$nombres;2) TRIER TABLEAU(\$nombres) ` pour effectuer un tri par ordre croissant TRIER TABLEAU(\$nombres;<) ` pour effectuer un tri par ordre décroissant ``` ## 8th ``` [ 10,2,100 ] ' n:cmp a:sort . cr ``` Output is: [2,10,100] ## ActionScript ```//Comparison function must returns Numbers even though it deals with integers. function compare(x:int, y:int):Number { return Number(x-y); } var nums:Vector.<int> = Vector.<int>([5,12,3,612,31,523,1,234,2]); nums.sort(compare); ``` {{works with|GNAT|GPL 2006}} ```with Gnat.Heap_Sort_G; procedure Integer_Sort is -- Heap sort package requires data to be in index values starting at -- 1 while index value 0 is used as temporary storage type Int_Array is array(Natural range <>) of Integer; Values : Int_Array := (0,1,8,2,7,3,6,4,5); -- define move and less than subprograms for use by the heap sort package procedure Move_Int(From : Natural; To : Natural) is begin Values(To) := Values(From); end Move_Int; function Lt_Int(Left, Right : Natural) return Boolean is begin return Values(Left) < Values (Right); end Lt_Int; -- Instantiate the generic heap sort package package Heap_Sort is new Gnat.Heap_Sort_G(Move_Int, Lt_Int); begin Heap_Sort.Sort(8); end Integer_Sort; requires an Ada05 compiler, e.g GNAT GPL 2007 procedure Integer_Sort is -- type Int_Array is array(Natural range <>) of Integer; Values : Int_Array := (0,1,8,2,7,3,6,4,5); -- Instantiate the generic sort package from the standard Ada library (Index_Type => Natural, Element_Type => Integer, Array_Type => Int_Array); begin Sort(Values); end Integer_Sort; ``` ## ALGOL 68 {{trans|python}} {{works with|ALGOL 68|Standard - no extensions to language used}} {{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}} {{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386}} ```CO PR READ "shell_sort.a68" PR CO MODE TYPE = INT; PROC in place shell sort = (REF[]TYPE seq)REF[]TYPE:( INT inc := ( UPB seq + LWB seq + 1 ) OVER 2; WHILE inc NE 0 DO FOR index FROM LWB seq TO UPB seq DO INT i := index; TYPE el = seq[i]; WHILE ( i - LWB seq >= inc | seq[i - inc] > el | FALSE ) DO seq[i] := seq[i - inc]; i -:= inc OD; seq[i] := el OD; inc := IF inc = 2 THEN 1 ELSE ENTIER(inc * 5 / 11) FI OD; seq ); PROC shell sort = ([]TYPE seq)[]TYPE: in place shell sort(LOC[LWB seq: UPB seq]TYPE:=seq); print((shell sort((2, 4, 3, 1, 2)), new line)) ``` Output: ``` +1 +2 +2 +3 +4 ``` ## ALGOL W Algol W doesn't have standard sorting facilities. This uses the Algol W quicksort sample in the Sorting Algorithms Quicksort task. ```begin % use the quicksort procedure from the Sorting_Algorithms/Quicksort task % % Quicksorts in-place the array of integers v, from lb to ub - external % procedure quicksort ( integer array v( * ) ; integer value lb, ub ) ; algol "sortingAlgorithms_Quicksort" ; % sort an integer array with the quicksort routine % begin integer array t ( 1 :: 5 ); integer p; p := 1; for v := 2, 3, 1, 9, -2 do begin t( p ) := v; p := p + 1; end; quicksort( t, 1, 5 ); for i := 1 until 5 do writeon( i_w := 1, s_w := 1, t( i ) ) end end. ``` {{out}} ``` -2 1 2 3 9 ``` ## APL {{works with|APL2}} ``` X←63 92 51 92 39 15 43 89 36 69 X[⍋X] 15 36 39 43 51 63 69 89 92 92 ``` ## AppleScript AppleScript has no native sort function. Later versions of AppleScript (OS X 10.10 onwards) do allow access to the ObjC NSArray library, but while this approach can yield reasonably fast sorts, it is slow in terms of scripter time, requiring digestion of the ObjC library documentation, and leading to code like the '''sort''' function below, which is possibly more messy than it is worth for the purposes of casual end-user scripting, for which AppleScript was presumably designed. ```use framework "Foundation" -- sort :: [a] -> [a] on sort(lst) ((current application's NSArray's arrayWithArray:lst)'s ¬ sortedArrayUsingSelector:"compare:") as list end sort -- TEST ----------------------------------------------------------------------- on run map(sort, [[9, 1, 8, 2, 8, 3, 7, 0, 4, 6, 5], ¬ ["alpha", "beta", "gamma", "delta", "epsilon", "zeta", "eta", ¬ "theta", "iota", "kappa", "lambda", "mu"]]) end run -- GENERIC FUNCTIONS --------------------------------------------------------- -- map :: (a -> b) -> [a] -> [b] on map(f, xs) tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to |λ|(item i of xs, i, xs) end repeat return lst end tell end map -- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f) if class of f is script then f else script property |λ| : f end script end if end mReturn ``` {{Out}} ```{{0, 1, 2, 3, 4, 5, 6, 7, 8, 8, 9}, {"alpha", "beta", "delta", "epsilon", "eta", "gamma", "iota", "kappa", "lambda", "mu", "theta", "zeta"}} ``` ## AutoHotkey ```numbers = 5 4 1 2 3 sort, numbers, N D%A_Space% Msgbox % numbers ``` ## AWK ``` # syntax: GAWK -f SORT_AN_INTEGER_ARRAY.AWK BEGIN { split("9,10,3,1234,99,1,200,2,0,-2",arr,",") show("@unsorted","unsorted") show("@val_num_asc","sorted ascending") show("@val_num_desc","sorted descending") exit(0) } function show(sequence,description, i) { PROCINFO["sorted_in"] = sequence for (i in arr) { printf("%s ",arr[i]) } printf("\t%s\n",description) } ``` output: ``` 9 10 3 1234 99 1 200 2 0 -2 unsorted -2 0 1 2 3 9 10 99 200 1234 sorted ascending 1234 200 99 10 9 3 2 1 0 -2 sorted descending ``` ## Axe There is no ascending sort function in Axe, but there is a descending sort function. One can either implement a custom ascending sorting function or simply reverse the output from SortD. ```2→{L₁} 4→{L₁+1} 3→{L₁+2} 1→{L₁+3} 2→{L₁+4} SortD(L₁,5) ``` ## Babel Use the sortval operator to sort an array of integers (val-array in Babel terminology). The following code creates a list of random values, converts it to a val-array, sorts that val-array, then converts it back to a list for display using the lsnum utility. ``` nil { zap {1 randlf 100 rem} 20 times collect ! } nest dup lsnum ! --> Create a list of random numbers ( 20 47 69 71 18 10 92 9 56 68 71 92 45 92 12 7 59 55 54 24 ) babel> ls2lf --> Convert list to array for sorting babel> dup {fnord} merge_sort --> The internal sort operator babel> ar2ls lsnum ! --> Display the results ( 7 9 10 12 18 20 24 45 47 54 55 56 59 68 69 71 71 92 92 92 ) ``` In Babel, lists and arrays are distinct. If you want to sort a list, use the lssort utility: ``` ( 68 73 63 83 54 67 46 53 88 86 49 75 89 83 28 9 34 21 20 90 ) babel> {lt?} lssort ! lsnum ! ( 9 20 21 28 34 46 49 53 54 63 67 68 73 75 83 83 86 88 89 90 ) ``` To reverse the sort-order, use the 'gt?' predicate instead of the 'lt?' predicate: ``` ( 68 73 63 83 54 67 46 53 88 86 49 75 89 83 28 9 34 21 20 90 ) {gt?} lssort ! lsnum ! ( 90 89 88 86 83 83 75 73 68 67 63 54 53 49 46 34 28 21 20 9 ) ``` ## BaCon ```' Sort an integer array DECLARE values[5] TYPE NUMBER values[0] = 23 values[1] = 32 values[2] = 12 values[3] = 21 values[4] = 01 SORT values FOR i = 0 TO 3 PRINT values[i], ", "; NEXT PRINT values[4] ``` {{out}} ```prompt\$ ./sort-integer 1, 12, 21, 23, 32 ``` Use SORT array DOWN for descending sort order. ## BBC BASIC {{works with|BBC BASIC for Windows}} Uses the supplied SORTLIB library. ``` INSTALL @lib\$+"SORTLIB" sort% = FN_sortinit(0,0) DIM array(8) array() = 8, 2, 5, 9, 1, 3, 6, 7, 4 C% = DIM(array(),1) + 1 CALL sort%, array(0) FOR i% = 0 TO DIM(array(),1) - 1 PRINT ; array(i%) ", "; NEXT PRINT ; array(i%) ``` Output: ``` 1, 2, 3, 4, 5, 6, 7, 8, 9 ``` ## Befunge {{works with|befungee}} Elements of the array are read from standard input, preceded by their quantity. The algorithm uses counting sort and allows numbers between 1 and 60, inclusive. ```v > 543** > :#v_ \$&> :#v_ 1 > :0g > :#v_ \$ 1+: 543** `! #v_ 25*,@ ^-1p0\0:< ^-1 p0\+1 g0:&< ^-1\.:\< ^ < ``` ## Bracmat As a Computer Algebra system, Bracmat transforms expressions to a canonical form. Terms in a sum are sorted and, where possible, added together. So the task is partially solved by expressing the list as a sum of terms. Evaluating the list sorts the list, but also adds like terms. To illustrate, this is what happens when entering our list at the prompt: ```{?} (9.)+(-2.)+(1.)+(2.)+(8.)+(0.)+(1.)+(2.) {!} (-2.)+(0.)+2*(1.)+2*(2.)+(8.)+(9.) ``` The use of a computationally inert operator like the dot `.` is essential: ```{?} (9)+(-2)+(1)+(2)+(8)+(0)+(1)+(2) {!} 21 ``` To complete the task need to unfold the terms with a numerical factor >1: ```{sort takes a list of space-separated integers} (sort= sum elem sorted n . 0:?sum & whl ' (!arg:%?elem ?arg&(!elem.)+!sum:?sum) & :?sorted & whl ' ( !sum:?n*(?elem.)+?sum & whl ' ( !n+-1:~<0:?n & !sorted !elem:?sorted ) ) & !sorted); out\$sort\$(9 -2 1 2 8 0 1 2); ``` Output: ```-2 0 1 1 2 2 8 9 ``` This solution becomes very ineffective for long lists. To add a single term to an already sorted sum of N terms requires on average N/2 steps. It is much more efficient to merge two already sorted sums of about equal length. Also, adding elements to the end of the list 'sorted' is costly. Better is to prepend elements to a list, which will have inverted sorting order, and to invert this list in an extra loop. ## Burlesque ```{1 3 2 5 4}>< ``` ## C ```#include <iostream> /* qsort() */ #include <stdio.h> /* printf() */ int intcmp(const void *aa, const void *bb) { const int *a = aa, *b = bb; return (*a < *b) ? -1 : (*a > *b); } int main() { int nums[5] = {2,4,3,1,2}; qsort(nums, 5, sizeof(int), intcmp); printf("result: %d %d %d %d %d\n", nums[0], nums[1], nums[2], nums[3], nums[4]); return 0; } ``` ''Caution:'' An older version of intcmp() did return *a - *b. This is only correct when the subtraction does not overflow. Suppose that *a = 2000000000 and *b = -2000000000 on a machine with 32-bit int. The subtraction *a - *b would overflow to -294967296, and intcmp() would believe *a < *b, but the correct answer is *a > *b. ## C++ {{works with|g++|4.0.1}} ### Simple Array ```#include <algorithm> int main() { int nums[] = {2,4,3,1,2}; std::sort(nums, nums+sizeof(nums)/sizeof(int)); return 0; } ``` ### std::vector ```#include <algorithm> #include <vector> int main() { std::vector<int> nums; nums.push_back(2); nums.push_back(4); nums.push_back(3); nums.push_back(1); nums.push_back(2); std::sort(nums.begin(), nums.end()); return 0; } ``` ### std::list ```#include <list> int main() { std::list<int> nums; nums.push_back(2); nums.push_back(4); nums.push_back(3); nums.push_back(1); nums.push_back(2); nums.sort(); return 0; } ``` ## C# ```using System; using System.Collections.Generic; public class Program { static void Main() { int[] unsorted = { 6, 2, 7, 8, 3, 1, 10, 5, 4, 9 }; Array.Sort(unsorted); } } ``` ## Clean We use list and array comprehensions to convert an array to and from a list in order to use the built-in sort on lists. ```import StdEnv sortArray :: (a e) -> a e | Array a e & Ord e sortArray array = {y \\ y <- sort [x \\ x <-: array]} Start :: {#Int} Start = sortArray {2, 4, 3, 1, 2} ``` ## Clojure ```(sort [5 4 3 2 1]) ; sort can also take a comparator function (1 2 3 4 5) ``` ## COBOL {{works with|Visual COBOL}} ``` PROGRAM-ID. sort-ints. DATA DIVISION. WORKING-STORAGE SECTION. 01 array-area VALUE "54321". 03 array PIC 9 OCCURS 5 TIMES. 01 i PIC 9. PROCEDURE DIVISION. main-line. PERFORM display-array SORT array ASCENDING array PERFORM display-array GOBACK . display-array. PERFORM VARYING i FROM 1 BY 1 UNTIL 5 < i DISPLAY array (i) " " NO ADVANCING END-PERFORM DISPLAY SPACE . ``` ## Common Lisp In Common Lisp, the ''sort'' function takes a predicate that is used as the comparator. This parameter can be any two-argument function. To sort a sequence (list or array) of integers, call ''sort'' with the < operator as the predicate: ```CL-USER> (sort #(9 -2 1 2 8 0 1 2) #'<) #(-2 0 1 1 2 2 8 9) ``` ## Crystal Example demonstrating the support for copy sort and in-place sort (like Ruby) ``` a = [5, 4, 3, 2, 1] puts a.sort # => [1, 2, 3, 4, 5] puts a # => [5, 4, 3, 2, 1] a.sort! puts a # => [1, 2, 3, 4, 5] ``` ## D ```import std.stdio, std.algorithm; void main() { auto data = [2, 4, 3, 1, 2]; data.sort(); // in-place assert(data == [1, 2, 2, 3, 4]); } ``` ## Delphi ```uses Types, Generics.Collections; var a: TIntegerDynArray; begin a := TIntegerDynArray.Create(5, 4, 3, 2, 1); TArray.Sort<Integer>(a); end; ``` ```!. sort [ 5 4 3 2 1 ] ``` {{out}} ```[ 1 2 3 4 5 ] ``` ## DWScript ```var a : array of Integer := [5, 4, 3, 2, 1]; a.Sort; // ascending natural sort PrintLn(a.Map(IntToStr).Join(',')); // 1,2,3,4,5 ``` ## E ```[2,4,3,1,2].sort() ``` ## Elena ELENA 4.1 : ```import system'routines; import extensions; public program() { var unsorted := new int[]::(6, 2, 7, 8, 3, 1, 10, 5, 4, 9); console.printLine(unsorted.clone().sort(ifOrdered).asEnumerable()) } ``` ## Elixir ```list = [2, 4, 3, 1, 2] IO.inspect Enum.sort(list) IO.inspect Enum.sort(list, &(&1>&2)) ``` {{out}} ``` [1, 2, 2, 3, 4] [4, 3, 2, 2, 1] ``` ## Erlang ```List = [2, 4, 3, 1, 2]. SortedList = lists:sort(List). ``` ## Euphoria ```include sort.e print(1,sort({20, 7, 65, 10, 3, 0, 8, -60})) ``` ## EGL {{works with|EDT}} The following works in EDT with Rich UI and stand-alone programs. ```program SortExample function main() test1 int[] = [1,-1,8,-8,2,-2,7,-7,3,-3,6,-6,9,-9,4,-4,5,-5,0]; test1.sort(sortFunction); for(i int from 1 to test1.getSize()) SysLib.writeStdout(test1[i]); end end function sortFunction(a any in, b any in) returns (int) return (a as int) - (b as int); end end ``` {{works with|RBD}} The following works in RBD but only with Rich UI programs. ```test1 int[] = [1,-1,8,-8,2,-2,7,-7,3,-3,6,-6,9,-9,4,-4,5,-5,0]; RUILib.sort(test1, sortFunction); function sortFunction(a any in, b any in) returns (int) return ((a as int) - (b as int)); end ``` ## Factor ```{ 1 4 9 2 3 0 5 } natural-sort . ``` ## Fantom The List collection contains a sort method which uses the usual comparison method for the data in the list; the sort is done 'in place'. ``` fansh> a := [5, 1, 4, 2, 3] [5, 1, 4, 2, 3] fansh> a.sort [1, 2, 3, 4, 5] fansh> a [1, 2, 3, 4, 5] ``` ## Forth {{works with|Win32Forth|4.2}} ### Win32Forth ```create test-data 2 , 4 , 3 , 1 , 2 , test-data 5 cell-sort ``` ### ANS/ISO Forth {{works with|GForth}} Uses quicksort http://rosettacode.org/wiki/Sorting_algorithms/Quicksort#Forth Standard Forth does not have a library sort ```100000 CONSTANT SIZE CREATE MYARRAY SIZE CELLS ALLOT : FILLIT ( -- ) ( reversed order) SIZE 0 DO SIZE I - I MYARRAY [] ! LOOP ; : SEEIT ( -- ) SIZE 0 DO I MYARRAY [] ? LOOP ; \ define non-standard words used by Quicksort author 1 CELLS CONSTANT CELL CELL NEGATE CONSTANT -CELL : CELL- CELL - ; : MID ( l r -- mid ) OVER - 2/ -CELL AND + ; OVER @ OVER @ ( read values) SWAP ROT ! SWAP ! ; ( exchange values) : PARTITION ( l r -- l r r2 l2 ) 2DUP MID @ >R ( r: pivot ) 2DUP BEGIN SWAP BEGIN DUP @ R@ < WHILE CELL+ REPEAT SWAP BEGIN R@ OVER @ < WHILE CELL- REPEAT 2DUP <= IF 2DUP EXCH >R CELL+ R> CELL- THEN 2DUP > UNTIL R> DROP ; : QSORT ( l r -- ) PARTITION SWAP ROT 2DUP < IF RECURSE ELSE 2DROP THEN 2DUP < IF RECURSE ELSE 2DROP THEN ; : QUICKSORT ( array len -- ) DUP 2 < IF 2DROP EXIT THEN 1- CELLS OVER + QSORT ;</LANG> Test at the console ```forth FILLIT ok MYARRAY SIZE QUICKSORT ok ``` ## Fortran {{works with|Silverfrost FTN95}} ```CALL ISORT@(b, a, n) ! n = number of elements ! a = array to be sorted ! b = array of indices of a. b(1) 'points' to the minimum value etc. ``` ## FreeBASIC Qsort is not buildin, but include in the compiler package. ```' version 11-03-2016 ' compile with: fbc -s console #Include Once "crt/stdlib.bi" ' needed for qsort subroutine ' Declare Sub qsort (ByVal As Any Ptr, <== point to start of array ' ByVal As size_t, <== size of array ' ByVal As size_t, <== size of array element ' ByVal As Function(ByVal As Any Ptr, ByVal As Any Ptr) As Long) <== callback function ' declare callback function with Cdecl to ensures that the parameters are passed in the correct order ' ' size of long: 4 bytes on 32bit OS, 8 bytes on 64bit OS ' ascending Function callback Cdecl (ByVal element1 As Any Ptr, ByVal element2 As Any Ptr) As Long Function = *Cast(Long Ptr, element1) - *Cast(Long Ptr, element2) End Function ' Function callback Cdecl (ByVal element1 As Any Ptr, ByVal element2 As Any Ptr) As Long ' Dim As Long e1 = *Cast(Long Ptr, element1) ' Dim As Long e2 = *Cast(Long Ptr, element2) ' Dim As Long result = Sgn(e1 - e2) ' If Sgn(e1) = -1 And Sgn(e2) = -1 Then result = -result ' Function = result ' End Function ' ------=< MAIN >=------ Dim As Long i, array(20) Dim As Long lb = LBound(array) Dim As Long ub = UBound(array) For i = lb To ub ' fill array array(i) = 10 - i Next Print Print "unsorted array" For i = lb To ub ' display array Print Using "###";array(i); Next Print : Print ' sort array qsort(@array(lb), ub - lb +1, SizeOf(array), @callback) Print "sorted array" For i = lb To ub ' show sorted array Print Using "###";array(i); Next Print ' empty keyboard buffer While Inkey <> "" : Wend Print : Print "hit any key to end program" Sleep End ``` {{out}} ```unsorted array 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9-10 sorted array -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ``` ## Frink The following sorts an array in-place. ```a = [5, 2, 4, 1, 6, 7, 9, 3, 8, 0] sort[a] ``` ```// sorting an array in place let nums = [| 2; 4; 3; 1; 2 |] Array.sortInPlace nums // create a sorted copy of a list let nums2 = [2; 4; 3; 1; 2] let sorted = List.sort nums2 ``` ## FunL ```nums = [5, 2, 78, 2, 578, -42] println( sort(nums) ) // sort in ascending order println( nums.sortWith((>)) ) // sort in descending order ``` {{out}} ``` [-42, 2, 2, 5, 78, 578] [578, 78, 5, 2, 2, -42] ``` ## GAP ```a := [ 8, 2, 5, 9, 1, 3, 6, 7, 4 ]; # Make a copy (with "b := a;", b and a would point to the same list) b := ShallowCopy(a); # Sort in place Sort(a); a; # [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] # Sort without changing the argument SortedList(b); # [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] b; # [ 8, 2, 5, 9, 1, 3, 6, 7, 4 ] ``` ## Gambas '''[https://gambas-playground.proko.eu/?gist=1f1d244aa95c329eb87cb538f0d5fc4a Click this link to run this code]''' ```Public Sub Main() Dim iArray As Integer[] = [8, 2, 5, 9, 1, 3, 6, 7, 4] Dim iTemp As Integer Dim sOutput As String For Each iTemp In iArray.Sort() sOutput &= iTemp & ", " Next Print Left(sOutput, -2) End ``` Output: ``` 1, 2, 3, 4, 5, 6, 7, 8, 9 ``` ## Go ```package main import "fmt" import "sort" func main() { nums := []int {2, 4, 3, 1, 2} sort.Ints(nums) fmt.Println(nums) } ``` ## Golfscript ```[2 4 3 1 2]\$ ``` ## Groovy ```println ([2,4,0,3,1,2,-12].sort()) ``` Output: ```[-12, 0, 1, 2, 2, 3, 4] ``` {{works with|GHC|GHCi|6.6}} ```nums = [2,4,3,1,2] :: [Int] sorted = List.sort nums ``` ## HicEst ```DIMENSION array(100) array = INT( RAN(100) ) SORT(Vector=array, Sorted=array) ``` ## Huginn ```main() { nums = [2, 4, 3, 1, 2]; nums.sort(); } ``` ## IDL ```result = array[sort(array)] ``` =={{header|Icon}} and {{header|Unicon}}== Icon and Unicon lists allow mixed type and the built-in function 'sort' will deal with mixed type arrays by sorting by type first then value. Integers sort before, reals, strings, lists, tables, etc. As a result a list of mixed numeric valuess (i.e. integers and reals) will not sort by numeric value, rather the reals will appear after the integers. Sort returns a sorted copy of it's argument. It will also perform some type conversion, such converting an unordered set into an ordered list. In the example below, L will remain an unsorted list and S will be sorted. ```S := sort(L:= [63, 92, 51, 92, 39, 15, 43, 89, 36, 69]) # will sort a list ``` ## Inform 7 ```let L be {5, 4, 7, 1, 18}; sort L; ``` ## Io ```mums := list(2,4,3,1,2) sorted := nums sort # returns a new sorted array. 'nums' is unchanged nums sortInPlace # sort 'nums' "in-place" ``` ## J ```/:~ ``` The verb /:~ sorts anything that J can represent. For example: ``` ] a=: 10 ?@\$ 100 NB. random vector 63 92 51 92 39 15 43 89 36 69 /:~ a 15 36 39 43 51 63 69 89 92 92 ``` Arrays of any rank are treated as lists of component arrays. Thus /:~ sorts not only atoms within a list, but whole lists within a table, tables within a three-axis array, and so on. The level of structure at which sorting occurs may also be specified, so that /:~"1 sorts the atoms within the finest-grained list within the array, regardless of the overall rank of the array. See the [https://code.jsoftware.com/wiki/Essays/The_TAO_of_J Total Array Ordering essay] on the JWiki for more details. This code also applies to any data type. ## Java ### Array ```import java.util.Arrays; public class Example { public static void main(String[] args) { int[] nums = {2,4,3,1,2}; Arrays.sort(nums); } } ``` ### List {{works with|Java|1.5+}} ```import java.util.Arrays; import java.util.Collections; import java.util.List; public class Example { public static void main(String[] args) { List<Integer> nums = Arrays.asList(2,4,3,1,2); Collections.sort(nums); } } ``` ## JavaScript {{works with|Firefox|2.0}} JavaScript sorts lexically by default, so "10000" comes before "2". To sort numerically, a custom comparator is used. ```function int_arr(a, b) { return a - b; } var numbers = [20, 7, 65, 10, 3, 0, 8, -60]; numbers.sort(int_arr); document.write(numbers); ``` ## Kotlin ```// version 1.0.6 fun main(args: Array<String>) { val ints = intArrayOf(6, 2, 7, 8, 3, 1, 10, 5, 4, 9) ints.sort() println(ints.joinToString(prefix = "[", postfix = "]")) } ``` {{out}} ``` [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] ``` ## Lasso ```local(array) = array(5,20,3,2,6,1,4) #array->sort #array // 1, 2, 3, 4, 5, 6, 20 // Reverse the sort order #array->sort(false) #array // 20, 6, 5, 4, 3, 2, 1 ``` ## jq jq's builtin `sort` filter sorts the elements of an array in ascending order: ```[2,1,3] | sort # => [1,2,3] ``` ## Julia Julia has both out-of-place (`sort`) and in-place (`sort!`) sorting functions in its standard-library: ``` a = [4,2,3,1] 4-element Int32 Array: 4 2 3 1 julia> sort(a) #out-of-place/non-mutating sort 4-element Int32 Array: 1 2 3 4 julia> a 4-element Int32 Array: 4 2 3 1 julia> sort!(a) # in-place/mutating sort 4-element Int32 Array: 1 2 3 4 julia> a 4-element Int32 Array: 1 2 3 4 ``` ## K ``` num: -10?10 / Integers from 0 to 9 in random order 5 9 4 2 0 3 6 1 8 7 srt: {x@<x} / Generalized sort ascending srt num 0 1 2 3 4 5 6 7 8 9 ``` ## Liberty BASIC LB has an array-sort command. Parameters are arrayname, start term, finish term. ```N =20 dim IntArray( N) print "Original order" for i =1 to N t =int( 1000 *rnd( 1)) IntArray( i) =t print t next i sort IntArray(), 1, N print "Sorted oprder" for i =1 to N print IntArray( i) next i ``` ## Lingo ```l = [7, 4, 23] l.sort() put l -- [4, 7, 23] ``` ## LiveCode LiveCode can sort lines or items natively. The delimiter for items can be set to any single character, but defaults to comma. ```put "3,2,5,4,1" into X sort items of X numeric put X -- outputs "1,2,3,4,5" ``` ## Lua ```t = {4, 5, 2} table.sort(t) print(unpack(t)) ``` ## Maple ```sort([5,7,8,3,6,1]); sort(Array([5,7,8,3,6,1])) ``` ## Mathematica ```numbers = Sort[{2,4,3,1,2}] ``` ## MATLAB ```a = [4,3,7,-2,9,1]; b = sort(a) % b contains elements of a in ascending order [b,idx] = sort(a) % b contains a(idx) ``` ## Maxima ```sort([9, 4, 3, 7, 6, 1, 10, 2, 8, 5]); ``` ## MAXScript ```arr = #(5, 4, 3, 2, 1) arr = sort arr ``` ## Mercury :- module sort_int_list. :- interface. :- import_module io. :- pred main(io::di, uo::uo) is det. :- implementation. :- import_module list. main(!IO) :- Nums = [2, 4, 0, 3, 1, 2], list.sort(Nums, Sorted), io.write(Sorted, !IO), io.nl(!IO). ``` ## min {{works with|min|0.19.3}} ```min (5 2 1 3 4) '> sort print ``` {{out}} ``` (1 2 3 4 5) ``` =={{header|Modula-3}}== Modula-3 provides a generic ArraySort module, as well as an instance of that module for integers called IntArraySort. ```MODULE ArraySort EXPORTS Main; IMPORT IntArraySort; VAR arr := ARRAY [1..10] OF INTEGER{3, 6, 1, 2, 10, 7, 9, 4, 8, 5}; BEGIN IntArraySort.Sort(arr); END ArraySort. ``` ## MUMPS ```SORTARRAY(X,SEP) ;X is the list of items to sort ;X1 is the temporary array ;SEP is the separator string between items in the list X ;Y is the returned list ;This routine uses the inherent sorting of the arrays NEW I,X1,Y SET Y="" FOR I=1:1:\$LENGTH(X,SEP) SET X1(\$PIECE(X,SEP,I))="" SET I="" FOR SET I=\$O(X1(I)) Q:I="" SET Y=\$SELECT(\$L(Y)=0:I,1:Y_SEP_I) KILL I,X1 QUIT Y ``` Output: ```USER>W \$\$SORTARRAY^ROSETTA("3,5,1,99,27,16,0,-1",",") -1,0,1,3,5,16,27,99 ``` ## Neko ```/** <doc><h2>Sort integer array, in Neko</h2> <p>Array sort function modified from Haxe codegen with -D neko-source</p> <p>The Neko target emits support code for Haxe basics, sort is included</p> <p>Tectonics:<br />prompt\$ nekoc sort.neko<br />prompt\$ neko sort</p> </doc> **/ var sort = function(a) { var i = 0; var len = \$asize(a); while ( i < len ) { var swap = false; var j = 0; var max = (len - i) - 1; while ( j < max ) { if ( (a[j] - a[j + 1]) > 0 ) { var tmp = a[j + 1]; a[j + 1] = a[j]; a[j] = tmp; swap = true; } j += 1; } if ( \$not(swap) ) break;; i += 1; } return a; } var arr = \$array(5,3,2,1,4) \$print(arr, "\n") /* Sorts in place */ sort(arr) \$print(arr, "\n") /* Also returns the sorted array for chaining */ \$print(sort(\$array(3,1,4,1,5,9,2,6,5,3,5,8)), "\n") ``` {{out}} ```prompt\$ nekoc sort.neko prompt\$ neko sort.n [5,3,2,1,4] [1,2,3,4,5] [1,1,2,3,3,4,5,5,5,6,8,9] ``` ## Nemerle ```using System.Console; module IntSort { Main() : void { def nums = [1, 5, 3, 7, 2, 8, 3, 9]; def sorted = nums.Sort((x, y) => x.CompareTo(y)); WriteLine(nums); WriteLine(sorted); } } ``` Output: ```[1, 5, 3, 7, 2, 8, 3, 9] [1, 2, 3, 3, 5, 7, 8, 9] ``` ## NetRexx ```/* NetRexx */ options replace format comments java crossref savelog symbols binary ia = int[] ia = [ 2, 4, 3, 1, 2, -1, 0, -2 ] display(ia) Arrays.sort(ia) display(ia) -- Display results method display(in = int[]) public static sorted = Rexx('') loop ix = 0 for in.length sorted = sorted || Rexx(in[ix]).right(4) end ix say sorted.strip('t') return ``` '''Output''' ``` 2 4 3 1 2 -1 0 -2 -2 -1 0 1 2 2 3 4 ``` NetRexx reimplementations of the [[#REXX|Rexx]] samples from below: ```NetRexx /* NetRexx */ options replace format comments java crossref savelog symbols /*REXX program to sort an integer array.*/ numeric digits 20 /*handle larger numbers.*/ a = '' a[ 1]= 1 a[ 2]= 0 a[ 3]= -1 a[ 4]= 0 a[ 5]= 5 a[ 6]= 0 a[ 7]= -61 a[ 8]= 0 a[ 9]= 1385 a[10]= 0 a[11]= -50521 a[12]= 0 a[13]= 2702765 a[14]= 0 a[15]= -199360981 a[16]= 0 a[17]= 19391512145 a[18]= 0 a[19]= -2404879675441 a[20]= 0 a[21]= 370371188237525 size = 21 /*we have a list of 21 Euler numbers.*/ tell('un-sorted', a, size) a[0] = size esort(a, 1) tell(' sorted', a, size) return /*----------------------------------ESORT subroutine--------------------*/ method esort(a, size) public static --esort: procedure expose a.; h = a[0] loop while h > 1 h = h % 2 loop i = 1 for a[0] - h j = i k = h + i loop while a[k] < a[j] t = a[j] a[j] = a[k] a[k] = t if h >= j then leave j = j - h k = k - h end end i end return /*----------------------------------TELL subroutine---------------------*/ method tell(arg, a, size) public static --tell: say arg.center(40, '-') loop j = 1 for size say arg 'array element' j.right(size.length)'='a[j].right(25) end j say return ``` '''Output''' ---------------un-sorted---------------- un-sorted array element 1= 1 un-sorted array element 2= 0 un-sorted array element 3= -1 un-sorted array element 4= 0 un-sorted array element 5= 5 un-sorted array element 6= 0 un-sorted array element 7= -61 un-sorted array element 8= 0 un-sorted array element 9= 1385 un-sorted array element 10= 0 un-sorted array element 11= -50521 un-sorted array element 12= 0 un-sorted array element 13= 2702765 un-sorted array element 14= 0 un-sorted array element 15= -199360981 un-sorted array element 16= 0 un-sorted array element 17= 19391512145 un-sorted array element 18= 0 un-sorted array element 19= -2404879675441 un-sorted array element 20= 0 un-sorted array element 21= 370371188237525 --------------- sorted---------------- sorted array element 1= -2404879675441 sorted array element 2= -199360981 sorted array element 3= -50521 sorted array element 4= -61 sorted array element 5= -1 sorted array element 6= 0 sorted array element 7= 0 sorted array element 8= 0 sorted array element 9= 0 sorted array element 10= 0 sorted array element 11= 0 sorted array element 12= 0 sorted array element 13= 0 sorted array element 14= 0 sorted array element 15= 0 sorted array element 16= 1 sorted array element 17= 5 sorted array element 18= 1385 sorted array element 19= 2702765 sorted array element 20= 19391512145 sorted array element 21= 370371188237525 ``` ```NetRexx /* NetRexx */ options replace format comments java crossref savelog symbols /*REXX program to sort an interesting integer list.*/ bell = '1 1 2 5 15 52 203 877 4140 21147 115975' /*some Bell numbers.*/ bern = '1 -1 1 0 -1 0 1 0 -1 0 5 0 -691 0 7 0 -3617' /*some Bernoulli num*/ perrin = '3 0 2 3 2 5 5 7 10 12 17 22 29 39 51 68 90' /*some Perrin nums. */ list = bell bern perrin /*combine the three.*/ size = list.words a = 0 loop j = 1 for size a[j] = list.word(j) end j say ' as is='list a[0] = size esort(a, size) bList = '' loop j = 1 for size bList = bList a[j] end j blist = bList.strip say ' sorted='bList return /*----------------------------------ESORT subroutine--------------------*/ method esort(a, size) public static --esort: procedure expose a.; h = a[0] loop while h > 1 h = h % 2 loop i = 1 for a[0] - h j = i k = h + i loop while a[k] < a[j] t = a[j] a[j] = a[k] a[k] = t if h >= j then leave j = j - h k = k - h end end i end return ``` '''Output''' as is=1 1 2 5 15 52 203 877 4140 21147 115975 1 -1 1 0 -1 0 1 0 -1 0 5 0 -691 0 7 0 -3617 3 0 2 3 2 5 5 7 10 12 17 22 29 39 51 68 90 sorted=-3617 -691 -1 -1 -1 0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 3 3 5 5 5 5 7 7 10 12 15 17 22 29 39 51 52 68 90 203 877 4140 21147 115975 ``` ## Nial ```nial>sort = 9 6 8 7 1 10 = 10 9 8 7 6 1 ``` ## Nim ```nim import algorithm var a: array[0..8,int] = [2,3,5,8,4,1,6,9,7] a.sort(system.cmp[int], Ascending) for x in a: echo(x) ``` {{out}} ```txt 1 2 3 4 5 6 7 8 9 ``` ## Niue '''Library''' ```Niue 2 6 1 0 3 8 sort .s 0 1 2 3 6 8 ``` ```objc NSArray *nums = @[@2, @4, @3, @1, @2]; NSArray *sorted = [nums sortedArrayUsingSelector:@selector(compare:)]; ``` ## Objeck ```objeck bundle Default { class Sort { function : Main(args : System.String[]) ~ Nil { nums := Structure.IntVector->New([2,4,3,1,2]); nums->Sort(); } } } ``` ## OCaml ### Array ```ocaml let nums = [|2; 4; 3; 1; 2|] Array.sort compare nums ``` ### List ```ocaml let nums = [2; 4; 3; 1; 2] let sorted = List.sort compare nums ``` ## Octave The variable v can be a vector or a matrix (columns will be sorted). ```octave sortedv = sort(v); ``` ## Oforth ```Oforth [ 8, 2, 5, 9, 1, 3, 6, 7, 4 ] sort ``` ## ooRexx ```rexx a = .array~of(4, 1, 6, -2, 99, -12) say "The sorted numbers are" say a~sortWith(.numericComparator~new)~makeString ``` Output: ```txt The sorted numbers are -12 -2 1 4 6 99 ``` ## Order Passing the less-than operator to the built-in sequence (i.e. list) sort function: ```c #include ORDER_PP( 8seq_sort(8less, 8seq(2, 4, 3, 1, 2)) ) ``` ## Oz ```oz declare Nums = [2 4 3 1 2] Sorted = {List.sort Nums Value.'<'} in {Show Sorted} ``` ## PARI/GP ```parigp vecsort(v) ``` ## Peloton Sorting a list of numbers as strings and as numbers (from the manual.) ```sgml Construct a list of numbers <@ LETCNSLSTLIT>L|65^84^1^25^77^4^47^2^42^44^41^25^69^3^51^45^4^39^ Numbers sort as strings <@ ACTSRTENTLST>L <@ SAYDMPLST>L <@ ACTSRTENTLSTLIT>L|__StringDescending <@ SAYDMPLST>L Construct another list of numbers <@ LETCNSLSTLIT>list|65^84^1^25^77^4^47^2^42^44^41^25^69^3^51^45^4^39^ Numbers sorted as numbers <@ ACTSRTENTLSTLIT>list|__Numeric <@ SAYDMPLST>list <@ ACTSRTENTLSTLIT>list|__NumericDescending <@ SAYDMPLST>list ``` Output ```html Construct a list of numbers Numbers sort as strings 1^2^25^25^3^39^4^4^41^42^44^45^47^51^65^69^77^84^ 84^77^69^65^51^47^45^44^42^41^4^4^39^3^25^25^2^1^ Construct another list of numbers Numbers sorted as numbers 1^2^3^4^4^25^25^39^41^42^44^45^47^51^65^69^77^84^ 84^77^69^65^51^47^45^44^42^41^39^25^25^4^4^3^2^1^ ``` ## Perl {{works with|Perl|5.8.6}} ```perl @nums = (2,4,3,1,2); @sorted = sort {\$a <=> \$b} @nums; ``` ## Perl 6 If `@a` contains only numbers: ```perl6>my @sorted = sort @a;@a .= sort; ``` ## PicoLisp The [http://software-lab.de/doc/refS.html#sort sort] function in PicoLisp returns already by default an ascending list (of any type, not only integers): ```PicoLisp (sort (2 4 3 1 2)) -> (1 2 2 3 4) ``` ## PL/I {{works with|IBM PL/I|7.5}} ```pli DCL (T(10)) FIXED BIN(31); /* scratch space of length N/2 */ MERGE: PROCEDURE (A,LA,B,LB,C); DECLARE (A(*),B(*),C(*)) FIXED BIN(31); DECLARE (LA,LB) FIXED BIN(31) NONASGN; DECLARE (I,J,K) FIXED BIN(31); I=1; J=1; K=1; DO WHILE ((I <= LA) & (J <= LB)); IF(A(I) <= B(J)) THEN DO; C(K)=A(I); K=K+1; I=I+1; END; ELSE DO; C(K)=B(J); K=K+1; J=J+1; END; END; DO WHILE (I <= LA); C(K)=A(I); I=I+1; K=K+1; END; RETURN; END MERGE; MERGESORT: PROCEDURE (A,N) RECURSIVE ; DECLARE (A(*)) FIXED BINARY(31); DECLARE N FIXED BINARY(31) NONASGN; DECLARE Temp FIXED BINARY; DECLARE (M,I) FIXED BINARY; DECLARE AMP1(N) FIXED BINARY(31) BASED(P); DECLARE P POINTER; IF (N=1) THEN RETURN; M = trunc((N+1)/2); IF (M>1) THEN CALL MERGESORT(A,M); IF (N-M > 1) THEN CALL MERGESORT(AMP1,N-M); IF A(M) <= AMP1(1) THEN RETURN; DO I=1 to M; T(I)=A(I); END; CALL MERGE(T,M,AMP1,N-M,A); RETURN; END MERGESORT; ``` ## Pop11 Pop11 library function sorts lists. So we first convert array to list, then sort and finally convert back: ```pop11 lvars ar = {2 4 3 1 2}; ;;; Convert array to list. ;;; destvector leaves its results and on the pop11 stack + an integer saying how many there were destvector(ar); ;;; conslist uses the items left on the stack plus the integer, to make a list of those items. lvars ls = conslist(); ;;; Sort it sort(ls) -> ls; ;;; Convert list to array destlist(ls); consvector() -> ar; ``` The above can be abbreviated to more economical, but possibly more opaque, syntax, using pop11 as a functional language: ```pop11 lvars ar = {2 4 3 1 2}; consvector(destlist(sort(conslist(destvector(ar))))) -> ar; ;;; print the sorted vector: ar => ** {1 2 2 3 4} ``` (The list created by conslist will be garbage-collected.) Alternatively, using the datalist function, even more economically: ```pop11 lvars ar = {2 4 3 1 2}; consvector(destlist(sort(datalist(ar)))) -> ar; ``` or in Forth-like pop11 postfix syntax: ```pop11 lvars ar = {2 4 3 1 2}; ar.datalist.sort.destlist.consvector -> ar; ``` ## Potion ```potion (7, 5, 1, 2, 3, 8, 9) sort join(", ") print ``` ## PowerBASIC PowerBASIC has several options available for sorting. At its simplest, an array (of any type) is sorted using `ARRAY SORT`: ```powerbasic ARRAY SORT x() ``` Options are available to limit sorting to only part of the array, collate string arrays, sort multiple arrays together, etc. (Details [http://www.powerbasic.com/support/help/pbwin/html/ARRAY_SORT_statement.htm here].) ## PowerShell ```powershell 34,12,23,56,1,129,4,2,73 | Sort-Object ``` ## Prolog ```txt ?- msort([10,5,13,3, 85,3,1], L). L = [1,3,3,5,10,13,85]. ``` Note that [http://www.swi-prolog.org/pldoc/man?predicate=sort/2 sort/2] removes duplicates. ## PureBasic ```PureBasic Dim numbers(20) For i = 0 To 20 numbers(i) = Random(1000) Next SortArray(numbers(), #PB_Sort_Ascending) ``` ## Python {{works with|Python|2.3}} ```python nums = [2,4,3,1,2] nums.sort() ``` '''Note:''' The array nums is sorted in place. '''Interpreter:''' [[Python]] 2.4 (and above) You could also use the built-in sorted() function ```python nums = sorted([2,4,3,1,2]) ``` ## R ```r nums <- c(2,4,3,1,2) sorted <- sort(nums) ``` ## Racket ```Racket -> (sort '(1 9 2 8 3 7 4 6 5) <) '(1 2 3 4 5 6 7 8 9) ``` ## Rascal Rascal has a built-in sort function that sort the elements of a list. Additionally, one can give a LessThenOrEqual function to compare the elements (See [http://tutor.rascal-mpl.org/Courses/Rascal/Rascal.html#/Courses/Rascal/Libraries/Prelude/List/sort/sort.html documentation]). ```rascal>rascal import List; ok rascal>a = [1, 4, 2, 3, 5]; list[int]: [1,4,2,3,5] rascal>sort(a) list[int]: [1,2,3,4,5] rascal>sort(a, bool(int a, int b){return a >= b;}) list[int]: [5,4,3,2,1] ``` ## Raven Sort list in place: ```raven [ 2 4 3 1 2 ] sort ``` ## REBOL ```rebol sort [2 4 3 1 2] ``` ## Red ```Red>> nums: [3 2 6 4 1 9 0 5 7] == [3 2 6 4 1 9 0 5 7] >> sort nums == [0 1 2 3 4 5 6 7 9] ``` ## REXX ### sort an array This REXX version creates an array with over a score of Euler numbers (integers), then sorts it. ```rexx /*REXX program sorts an array (using E─sort), in this case, the array contains integers.*/ numeric digits 30 /*enables handling larger Euler numbers*/ @. = 0; @.1 = 1 @.3 = -1; @.5 = 5 @.7 = -61; @.9 = 1385 @.11= -50521; @.13= 2702765 @.15= -199360981; @.17= 19391512145 @.19= -2404879675441; @.21= 370371188237525 #= 21 /*indicate there're 21 Euler numbers.*/ call tell 'unsorted' /*display the array before the eSort. */ call eSort # /*sort the array of some Euler numbers.*/ call tell ' sorted' /*display the array after the eSort. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ eSort: procedure expose @.; parse arg N; h=N /*an eXchange sort.*/ do while h>1; h= h%2 /*define a segment.*/ do i=1 for N-h; j=i; k= h+i /*sort top segment.*/ do while @.k<@.j /*see if need swap.*/ parse value @.j @.k with @.k @.j /*swap two elements*/ if h>=j then leave; j= j-h; k= k-h /*this part sorted?*/ end /*while @.k<@.j*/ end /*i*/ end /*while h>1*/ return /*──────────────────────────────────────────────────────────────────────────────────────*/ tell: say copies('─', 65); _= left('',9); w= length(#) do j=1 for #; say _ arg(1) 'array element' right(j, w)"="right(@.j, 20) end /*j*/ return ``` {{out|output|text= when using the default internal input:}} ```txt ───────────────────────────────────────────────────────────────── unsorted array element 1= 1 unsorted array element 2= 0 unsorted array element 3= -1 unsorted array element 4= 0 unsorted array element 5= 5 unsorted array element 6= 0 unsorted array element 7= -61 unsorted array element 8= 0 unsorted array element 9= 1385 unsorted array element 10= 0 unsorted array element 11= -50521 unsorted array element 12= 0 unsorted array element 13= 2702765 unsorted array element 14= 0 unsorted array element 15= -199360981 unsorted array element 16= 0 unsorted array element 17= 19391512145 unsorted array element 18= 0 unsorted array element 19= -2404879675441 unsorted array element 20= 0 unsorted array element 21= 370371188237525 ───────────────────────────────────────────────────────────────── sorted array element 1= -2404879675441 sorted array element 2= -199360981 sorted array element 3= -50521 sorted array element 4= -61 sorted array element 5= -1 sorted array element 6= 0 sorted array element 7= 0 sorted array element 8= 0 sorted array element 9= 0 sorted array element 10= 0 sorted array element 11= 0 sorted array element 12= 0 sorted array element 13= 0 sorted array element 14= 0 sorted array element 15= 0 sorted array element 16= 1 sorted array element 17= 5 sorted array element 18= 1385 sorted array element 19= 2702765 sorted array element 20= 19391512145 sorted array element 21= 370371188237525 ``` ### sort a list This REXX version creates a list with a bunch of interesting integers, then sorts it. Because it so much more efficient to sort an array, an array is built from the list, it is then sorted, and then the list is re-constituted. ```rexx /*REXX program sorts (using E─sort) and displays a list of some interesting integers. */ Bell= 1 1 2 5 15 52 203 877 4140 21147 115975 /*a few Bell " */ Bern= '1 -1 1 0 -1 0 1 0 -1 0 5 0 -691 0 7 0 -3617' /*" " Bernoulli " */ Perrin= 3 0 2 3 2 5 5 7 10 12 17 22 29 39 51 68 90 /*" " Perrin " */ list=Bell Bern Perrin /*throw them all ───► a pot. */ say 'unsorted =' list /*display what's being shown.*/ size=words(list) /*nice to have # of elements.*/ do j=1 for size /*build an array, a single */ @.j=word(list,j) /* ··· element at a time.*/ end /*j*/ call eSort size /*sort the collection of #s. */ \$= /*list: define as null so far*/ do k=1 for size /*build a list from the array*/ \$=\$ @.k /*append a number to the list*/ end /*k*/ say ' sorted =' space(\$) /*display the sorted list. */ exit /*stick a fork in it, we're all done.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ eSort: procedure expose @.; parse arg N; h=N /*an eXchange sort.*/ do while h>1; h= h%2 /*define a segment.*/ do i=1 for N-h; j=i; k= h+i /*sort top segment.*/ do while @.k<@.j /*see if need swap.*/ parse value @.j @.k with @.k @.j /*swap two elements*/ if h>=j then leave; j= j-h; k= k-h /*this part sorted?*/ end /*while @.k<@.j*/ end /*i*/ end /*while h>1*/ return ``` {{out|output|text= when using the default internal inputs:}} ```txt unsorted = 1 1 2 5 15 52 203 877 4140 21147 115975 1 -1 1 0 -1 0 1 0 -1 0 5 0 -691 0 7 0 -3617 3 0 2 3 2 5 5 7 10 12 17 22 29 39 51 68 90 sorted = -3617 -691 -1 -1 -1 0 0 0 0 0 0 0 0 1 1 1 1 1 2 2 2 3 3 5 5 5 5 7 7 10 12 15 17 22 29 39 51 52 68 90 203 877 4140 21147 115975 ``` ## Ring ```ring aArray = [2,4,3,1,2] see sort(aArray) ``` ## Ruby ```ruby nums = [2,4,3,1,2] sorted = nums.sort # returns a new sorted array. 'nums' is unchanged p sorted #=> [1, 2, 2, 3, 4] p nums #=> [2, 4, 3, 1, 2] nums.sort! # sort 'nums' "in-place" p nums #=> [1, 2, 2, 3, 4] ``` ## Rust Uses merge sort in place (undocumented), allocating ~2*n memory where n is a length of an array. ```rust fn main() { let mut a = vec!(9, 8, 7, 6, 5, 4, 3, 2, 1, 0); a.sort(); println!("{:?}", a); } ``` ## Scala ### Array Scala's "default" Array is a ''mutable'' data structure, very close to Java's Array. Generally speaking, that means an "array" is not very Scala-lesque, even as mutable data structures go. It can serves a purpose, though. If array is the right data type for your need, then that is how you sort it. ```Scala import scala.compat.Platform object Sort_an_integer_array extends App { val array = Array((for (i <- 0 to 10) yield scala.util.Random.nextInt()): _* /*Sequence is passed as multiple parameters to Array(xs : T*)*/) /** Function test the array if it is in order */ def isSorted[T](arr: Array[T]) = array.sliding(2).forall(pair => pair(0) <= pair(1)) assert(!isSorted(array), "Not random") scala.util.Sorting.quickSort(array) assert(isSorted(array), "Not sorted") println(s"Array in sorted order.\nSuccessfully completed without errors. [total \${Platform.currentTime - executionStart} ms]") } ``` ### List ```Scala println(List(5,2,78,2,578,-42).sorted) //--> List(-42, 2, 2, 5, 78, 578) ``` ## Scheme {{works with|Guile}} Same as [[Common Lisp]] ```scheme (sort #(9 -2 1 2 8 0 1 2) #'<) ``` Sorting is also available through SRFIs. SRFI 132 provides separate list-sort and vector-sort routines: ```scheme > (import (srfi 132)) > (list-sort < '(9 -2 1 2 8 0 1 2)) (-2 0 1 1 2 2 8 9) > (vector-sort < #(9 -2 1 2 8 0 1 2)) #(-2 0 1 1 2 2 8 9) ``` SRFI 132 replaced the older SRFI 95, which is still found in many implementations. SRFI 95 provides a generic sort function (but note the order of the sequence and comparator!): ```scheme > (import (srfi 95)) > (sort '(9 -2 1 2 8 0 1 2) <) (-2 0 1 1 2 2 8 9) > (sort #(9 -2 1 2 8 0 1 2) <) #(-2 0 1 1 2 2 8 9) ``` ## Seed7 ```seed7 var array integer: nums is [] (2, 4, 3, 1, 2); nums := sort(nums); ``` ## Sidef ```ruby var nums = [2,4,3,1,2]; var sorted = nums.sort; # returns a new sorted array. nums.sort!; # sort 'nums' "in-place" ``` ## Slate ```slate #(7 5 2 9 0 -1) sort ``` ## Smalltalk ```smalltalk #(7 5 2 9 0 -1) asSortedCollection ``` or destructive: ```smalltalk #(7 5 2 9 0 -1) sort ``` ## Sparkling ```sparkling var arr = { 2, 8, 1, 4, 6, 5, 3, 7, 0, 9 }; sort(arr); ``` ## Standard ML The Standard ML Basis library does not have any sorting facilities. But each implementation of Standard ML has its own. ### Array {{works with|SML/NJ}} ```sml - val nums = Array.fromList [2, 4, 3, 1, 2]; val nums = [|2,4,3,1,2|] : int array - ArrayQSort.sort Int.compare nums; val it = () : unit - nums; val it = [|1,2,2,3,4|] : int array ``` {{works with|Moscow ML}} ```sml > val it = () : unit > val it = () : unit - val nums = Array.fromList [2, 4, 3, 1, 2]; > val nums = : int array - Arraysort.sort Int.compare nums; > val it = () : unit - Array.foldr op:: [] nums; > val it = [1, 2, 2, 3, 4] : int list ``` ### List {{works with|SML/NJ}} ```sml - val nums = [2, 4, 3, 1, 2]; val nums = [2,4,3,1,2] : int list - val sorted = ListMergeSort.sort op> nums; val sorted = [1,2,2,3,4] : int list ``` {{works with|Moscow ML}} ```sml > val it = () : unit > val it = () : unit - val nums = [2, 4, 3, 1, 2]; > val nums = [2, 4, 3, 1, 2] : int list - val sorted = Listsort.sort Int.compare nums; > val sorted = [1, 2, 2, 3, 4] : int list ``` ## Stata ### Sort a Stata dataset See '''[https://www.stata.com/help.cgi?sort sort]''' in Stata help. ```stata . clear . matrix a=(2,9,4,7,5,3,6,1,8)' . qui svmat a . sort a . list +----+ | a1 | |----| 1. | 1 | 2. | 2 | 3. | 3 | 4. | 4 | 5. | 5 | |----| 6. | 6 | 7. | 7 | 8. | 8 | 9. | 9 | +----+ ``` ### Sort a macro list See '''[https://www.stata.com/help.cgi?macrolists macrolists]''' in Stata help for other functions on lists stored in macros. ```stata . local a 2 9 4 7 5 3 6 1 8 . di "`: list sort a'" 1 2 3 4 5 6 7 8 9 ``` ### Mata See Mata's '''[http://www.stata.com/help.cgi?mf_sort sort]''' function. ```stata mata : a=2\9\4\7\5\3\6\1\8 : sort(a,1) 1 +-----+ 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 9 | 9 | +-----+ end ``` ## Swift ### Sort in place {{works with|Swift|2.x+}} ```swift var nums = [2, 4, 3, 1, 2] nums.sortInPlace() print(nums) ``` or ```swift var nums = [2, 4, 3, 1, 2] nums.sortInPlace(<) print(nums) ``` {{works with|Swift|1.x}} ```swift var nums = [2, 4, 3, 1, 2] nums.sort(<) println(nums) ``` or ```swift var nums = [2, 4, 3, 1, 2] sort(&nums) println(nums) ``` or ```swift var nums = [2, 4, 3, 1, 2] sort(&nums, <) println(nums) ``` ### Return new array You could also create a new sorted array without affecting the original one: {{works with|Swift|2.x+}} ```swift let nums = [2,4,3,1,2].sort() print(nums) ``` or ```swift let nums = [2,4,3,1,2].sort(<) print(nums) ``` {{works with|Swift|1.x}} ```swift let nums = sorted([2,4,3,1,2]) println(nums) ``` or ```swift let nums = [2,4,3,1,2].sorted(<) println(nums) ``` ## Tcl ```tcl set result [lsort -integer \$unsorted_list] ``` Store input into L1, run prgmSORTBTIN, and L2 will be L1, only sorted. :L1→L2 :SortA(L2) SortA is found via: [LIST] → ENTER. SortD is also available for a descending sort. ## Toka This can be done by using the bubble sort library: ```toka needs bsort arrayname number_elements bsort ``` See the Toka entry on [[Bubble Sort]] for a full example. ## UNIX Shell Each shell parameter separates the integers using the default IFS whitespace (space, tab, newline). ```bash nums="2 4 3 1 5" sorted=`printf "%s\n" \$nums | sort -n` echo \$sorted # prints 1 2 3 4 5 ``` Alternate solution: sorted=`for i in \$nums; do echo \$i; done | sort -n` ---- Some shells have real arrays. You still need IFS to split the string from sort -n to an array. {{works with|pdksh|5.2.14}} ```bash set -A nums 2 4 3 1 5 set -A sorted \$(printf "%s\n" \${nums[*]} | sort -n) echo \${sorted[*]} # prints 1 2 3 4 5 ``` Users of [[bash]], [[ksh93]] and [[mksh]] can probably use the nums=(2 4 3 1 2) syntax. ## Ursa ```ursa>decl int< nums append 2 4 3 1 2 nums sort nums ``` ## Ursala using the built in sort operator, -<, with the nleq library function for comparing natural numbers ```Ursala #import nat #cast %nL example = nleq-< <39,47,40,53,14,23,88,52,78,62,41,92,88,66,5,40> ``` output: ```txt <5,14,23,39,40,40,41,47,52,53,62,66,78,88,88,92> ``` ## WDTE ```WDTE>let a = import 'arrays'; a.sort [39; 47; 40; 53; 14; 23; 88; 52; 78; 62; 41; 92; 88; 66; 5; 40] < -- io.writeln io.stdout; ``` ## Wortel ```wortel @sort [39 47 40 53 14 23 88 52 78 62 41 92 88 66 5 40] ``` ## XPL0 ```XPL0 include c:\cxpl\codes; \intrinsic 'code' declarations proc SSort(A, N); \Shell sort array in ascending order int N; \number of elements in array (size) int I, J, Gap, JG, T; [Gap:= N>>1; while Gap > 0 do [for I:= Gap to N-1 do [J:= I - Gap; loop [JG:= J + Gap; if A(J) <= A(JG) then quit; T:= A(J); A(J):= A(JG); A(JG):= T; \swap elements J:= J - Gap; if J < 0 then quit; ]; ]; Gap:= Gap>>1; ]; ]; \SSort int A, I; [A:= [3, 1, 4, 1, 5, 9, 2, 6, 5, 4]; SSort(A, 10); for I:= 0 to 10-1 do [IntOut(0, A(I)); ChOut(0, ^ )]; CrLf(0); ] ``` Output: ```txt 1 1 2 3 4 4 5 5 6 9 ``` ## Yabasic ```Yabasic export sub shell_sort(x()) // Shell sort based on insertion sort local gap, i, j, first, last, tempi, tempj last = arraysize(x(),1) gap = int(last / 10) + 1 while(TRUE) first = gap + 1 for i = first to last tempi = x(i) j = i - gap while(TRUE) tempj = x(j) if tempi >= tempj then j = j + gap break end if x(j+gap) = tempj if j <= gap then break end if j = j - gap wend x(j) = tempi next i if gap = 1 then return else gap = int(gap / 3.5) + 1 end if wend end sub if peek\$("library") = "main" then clear screen ITEMS = 100 dim numeros(ITEMS) for n = 1 to ITEMS numeros(n) = ran(ITEMS + 1) next n print time\$ shell_sort(numeros()) print time\$ print "Press a key to see ordered numbers." inkey\$ for n = 1 to ITEMS print numeros(n),", "; next n end if ``` ## Yorick In Yorick, ''sort'' returns an index list into the array that will put it in sorted order. ```yorick nums = [2,4,3,1,2]; nums = nums(sort(nums)); ``` ## zkl ```zkl a:=L(4,5,2,6); a.sort(); a.println() //--> L(2,4,5,6) ```

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{[ promptMessage ]} Bookmark it {[ promptMessage ]} Ch07 - Chapter 7 Utility and Demand I The Households Budget... This preview shows pages 1–2. Sign up to view the full content. C h a p t e r 7 : U t i l i t y a n d D e m a n d I. The Household’s Budget A. Consumption Possibilities 1. A household’s consumption choices are constrained by its income and the prices of the goods and services it buys. 2. A household’s budget line describes the limits to its consumption choices. 3. Figure 7.1 shows a budget line, which separates those combinations of goods that the household can afford (points below and on the budget line) from those combinations that it cannot afford (points above the budget line). B. Relative Price 1. A relative price is the price of one good divided by the price of another good. a) The magnitude of the slope of the budget line is the relative price of the good measured on the x -axis. b) A change in the relative price changes the slope of the budget line. c) Figure 7.2 (a) shows how changes in the relative price of a movie rotates the budget line. C. Real Income 1. A household’s real income is the household’s income expressed as the quantity of goods that the household can buy. a) A change in real income shifts the budget line but does not change its slope. b) Figure 7.2 (b) shows how changes in real income shift the budget line. II. Preferences and Utility A. A household’s preferences determine the benefits or satisfaction a person receives consuming a good or service. 1. The benefit or satisfaction from the consumption a good or service is called utility . B. Total Utility 1. Total utility is the total benefit a person gets from the consumption of goods. Generally, more consumption gives more utility. 2. 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. {[ snackBarMessage ]} Page1 / 3 Ch07 - Chapter 7 Utility and Demand I The Households Budget... This preview shows document pages 1 - 2. Sign up to view the full document. View Full Document Ask a homework question - tutors are online

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# Deflection Of Cantilever Beam Due To Shear Forces Chapter 4 shear forces and bending moments stresses in a tapered beam top dog cantilever beam skyciv ering deflection of a cantilever beam bending moment diagrams sfd bmd Cantilever Beams Moments And Deflections Cantilever Beam Point Load At Any Cantilever Beams Moments And Deflections Beam Stress Deflection Mechanicalc Shear Force And Bending Moment Diagram For Cantilever 000124 Calculation Of Bending Moment Shear Force Amount Deflection Angle Inclination Slope Single Span Beam Cantilever Uniformly Distributed Load Tip Deflections Of The Tapered Cantilever Beam Subjected To M0 P0 And Q Scientific Diagram Cantilever Beam Udl And End Bending Moment Determine The Maximum Deflection Of Cantilevered Beam Is Made A Material Having An E 200 Gpa And I 69 106 Mm 6 Study Shear Force Bending Moment Diagram Of Cantilever Beam Exles Ering Intro Shear Deformation Of Beams Using Virtual Work Method Structville Solved Consider A Cantilever Beam Of Length L Width B And Chegg 4 5 Shear Force And Bending Moment Of Cantilever Beams Strength Materials Schematic Of A Cantilever Beam In Bending Scientific Diagram What Is The Shear Force And Bending Moment Of A Cantilever Beam If Point Load On Middle Its Length Quora 000130 Calculation Of Bending Moment Shear Force Amount Deflection Angle Inclination Slope Single Span Beam Cantilever Partial Lily Distributed Load Increase Beam Deflection Tables Mechanicalc Is A Plot Of The Bending Moment Double And Shear Force In Scientific Diagram Cantilever Beam Point Load And Bending Moment At End Beam stress deflection mechanicalc deflection of a cantilever beam subject to bined end force and scientific diagram chapter 4 shear forces and bending moments 000124 calculation of bending moment shear force amount deflection angle inclination slope single span beam cantilever uniformly distributed load get for the cantilever beam and loading shown determine a slope transtutors

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If you’re looking for Math 4th Grade Kahoot, you’ve come to the right place. Use the relevant links provided below to gain direct access. 4th Grade FSA Math Review – Kahoot We would like to show you a description here but the site won’t allow us. 4th Grade Math Kahoot Game! | Small Online Class for Ages … In this one time class, we will practice various 4th grade math concepts in an exciting, fun, challenging game of Kahoot! Compete against other learners as you practice addition, subtraction, multiplication, division, fractions, decimals, place value, word problems, and more! Kahoot! – Miss Ayers4th Grade Math – Weebly 4th Grade Math. Home Strategy Examples Homework Table of Contents Websites Used Engage NY Resources Kahoot! Perseverance Problems Kahoot! Multiplication! Multiples and Factors. Division. Triangles. Geometry. Powered by Create your own unique website with customizable templates. Get Started. Home Strategy Examples … 4th Grade Math Kahoot Review 1 – Instructure https://indianriver.instructure.com/courses/60649/modules/items/382788 4th Grade Math Kahoot Review 1. 4th Grade Math Kahoot Review 1 Grades 4-7 Archives | Kahoot! Barron’s – Learn. Grow. Succeed. Ranger Rick and Ranger Rick Jr. are award-winning magazines published by the National Wildlife Federation. We have inspired children and families to care about… Check out this #Kahoot called ‘Multiplication 4th Grade … https://www.pinterest.com/pin/88875792627211139/ Nov 21, 2016 – Check out this #Kahoot called ‘Multiplication 4th Grade’ on @GetKahoot. Play it now! Kahoot! | Play this quiz now! | Kahoot, 4th grade math … https://www.pinterest.com/pin/31032684907015049/ About this resource : Math stations work so well in middle school! This bundle includes all 17 sets of math stations in my store that align to 8th grade curriculums. This bundle will grow as I create more 8th stations!Each set of stations includes question sheets, student answer pages …

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Give the values of a, b, and c needed to write the equation's general form. 1/4x^2+5=0 A = 1/4; B = 5; C = 0 A = 1; B = 0; C = 20 A = 1; B = 0; C = -5 Question Updated 4/29/2015 11:36:33 PM Flagged by janezeshun [4/29/2015 11:21:42 PM], Edited by jeifunk [4/29/2015 11:36:33 PM] g Original conversation User: Give the values of a, b, and c needed to write the equation's general form. 1/4x^2+5=0 A = 1/4; B = 5; C = 0 A = 1; B = 0; C = 20 A = 1; B = 0; C = -5 Question Updated 4/29/2015 11:36:33 PM Flagged by janezeshun [4/29/2015 11:21:42 PM], Edited by jeifunk [4/29/2015 11:36:33 PM] Rating 8 Give the values of a, b, and c needed to write the equation's general form. 1/4x^2+5=0 is the gerneral form and a = 1.4 , b = 0 , c = 5 . Confirmed by jeifunk [4/29/2015 11:36:34 PM] Questions asked by the same visitor The force between two poles is proportional to: the inverse of the pole strengths the distance between the poles the inverse of the distance between the poles Weegy: The force between two poles is proportional to: the inverse of the distance between the poles. (More) Question Updated 4/27/2015 12:20:48 PM 32,772,300 Popular Conversations Correct the sentence by selecting the proper pronoun usage. None of ... Weegy: The coach chose us girls and him to attend the track meet. The sentence is correct as is. User: Correct the ... In the time of butterflies which character can be described as ... Weegy: The elements of health, physical, mental/emotional/spiritual, and social are interconnected and should be kept ... A galaxy that has a shape similar to a football is a(n) ____ galaxy. ... Weegy: A galaxy that has a shape similar to a football is an irregular galaxy. In Asia, the Cold war led to Potential source of radioactive material can be located where? Weegy: Potential sources of radioactive material can be located in Hospitals, Cancer treatment facilities, University ... * Get answers from Weegy and a team of really smart live experts. S L P 1 L Points 137 [Total 6770] Ratings 0 Comments 137 Invitations 0 Offline S L 1 Points 111 [Total 1225] Ratings 0 Comments 111 Invitations 0 Online S L P R Points 74 [Total 2410] Ratings 0 Comments 74 Invitations 0 Offline S L L 1 P 1 L P Points 47 [Total 10367] Ratings 0 Comments 47 Invitations 0 Offline S Points 12 [Total 13] Ratings 0 Comments 12 Invitations 0 Online S L Points 10 [Total 483] Ratings 0 Comments 10 Invitations 0 Offline S L 1 1 1 1 1 1 1 1 1 1 1 Points 10 [Total 2340] Ratings 1 Comments 0 Invitations 0 Online S L Points 10 [Total 133] Ratings 1 Comments 0 Invitations 0 Offline S L R P Points 9 [Total 2174] Ratings 0 Comments 9 Invitations 0 Offline S L Points 8 [Total 499] Ratings 0 Comments 8 Invitations 0 Offline * Excludes moderators and previous winners (Include) Home | Contact | Blog | About | Terms | Privacy | © Purple Inc.

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Name_______________________________________________Date_________________________ Mathematics Problem Solving Volume 4, Number 2, September 14, 1998 www.rhlschool.com Using a Calendar September 1998 Sunday Monday Tuesday Wednesday Thursday Friday Saturday (-:] (-:] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1. What is the date of the first Monday of the month? 2. What day of the week is it on September 20, 1998? 3. What date is exactly one week after the 7th of September? 4. There are always the same number of days in September. How many days are in September? 5. There are always 31 days in August, the month that comes right before September. What day of the week was August 30? 6. Sam was jumping around and singing because his birthday was coming in exactly 2 weeks. His birthday is September 17. On what date was Sam jumping around and singing? 7. Cheryl is having a big sale to get rid of all her junk. It will start on Friday, September 25. The last day of the sale will be Sunday, September 27. How many days long is the sale? (You probably know that figuring 27-25=2 will not give you the correct answer.) 8. The Hemlock Mills Country Fair runs from September 16 through September 23. The fair is ________ days long. Tweet G Delicious E-mail Math Problem Solving Home RHL School Home

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You are on page 1of 4 # Exercises: ## Exercise 2.3-6 (page 37) from CLRS. Exercise 3.1-3 (page 50) from CLRS. Exercise 3.1-4 (page 50) from CLRS. 1. (11 points) Asymptotic Growth Rank the following functions by increasing order of growth; that is, nd an arrangement g 1 , g 2 , . . . , g 11 of the functions satisfying g 1 = O(g 2 ), g 2 = O(g 3 ), . . . , g 10 = O(g 11 ). Partition your list into equivalence classes such that f(n) and g(n) are in the same class if and only if f(n) = (g(n)). All the logs are in base 2. n 100 , 3 n , n 100 , 1/n, 2 2n , 10 100 n, 3 n , 1/5, 4 n , nlog n, log(n!). 2. (19 points) Suppose you are given an array A[1..n] A[1..n] of sorted integers that has been circularly shifted k positions to the right. For example, [35, 42, 5, 15, 27, 29] is a sorted array that has been circularly shifted k = 2 positions, while [27, 29, 35, 42, 5, 15] has been shifted k = 4 positions. We can obviously nd the largest element in A in O(n) time. Describe an O(log n) algorithm based on the divide-and-conquer strategy to nd the largest element in A. (You need to show that your algorithms time complexity is O(log n)) Let n = len(alist). (a) (6 points) What is the runtime of the iterative version in terms of n, and why? Be sure to state a recurrence relation and solve it. (b) (8 points) What is the runtime of the recursive version in terms of n, and why? Be sure to state a recurrence relation and solve it. (c) (5 points) Explain how you might x the recursive version so that it has the same asymptotic running time as the iterative version (but is still recursive). 1 3. (30 points) Set Intersection Python has a built in set data structure. A set is a collection of elements without repetition. In an interactive Python session, type the following to create an empty set: s = set() To nd out what operations are available on sets, type: dir(s) Some fundamental operations include add, remove, and contains and len . Note that contains and len are more commonly called with the syntax element in set and len(set). All four of these operations run in constant time i.e. O(1) time. For this problem, we will be analyzing the runtime of s.intersection(t) that takes two sets, s and t, and returns a new set with all the elements that occur in both s and t. We will then use intersection in a new version of the Document Distance code from the rst two lectures. (a) (5 points) Using notation, make a conjecture for the asymptotic running time of s.intersection(t) in terms of the sizes of the sets: |s| and |t|. Justify your conjecture. HINT: Think about the fundamental operations above. (b) (10 points) Determine experimentally the running time of s.intersection(t), by running it with dierent sized sets. Fill in the following chart. Include in your PDF submission a snippet of code that determines one of the entries in the chart. Note: there are a number of ways to time code. You can use the timeit mod- ule (see http://www.diveintopython.org/performance tuning/timeit.html for a good description of how to use it). Alternatively, if you have ipython in- stalled (see http://ipython.scipy.org), you can use their builtin timeit com- mand which is more user friendly. time in s |s| = 10 3 |s| = 10 4 |s| = 10 5 |s| = 10 6 |t| = 10 3 |t| = 10 4 |t| = 10 5 |t| = 10 6 (c) (5 points) Give an approximate formula for asymptotic running time of s.intersection(t) based on your experiments. How does this compare with your conjecture in part (a)? If the results dier from your conjecture, make a new (d) (10 points) In the Document Distance problem from the rst two lectures, we compared two documents by counting the words in each, treating theses counts 2 as vectors, and computing the angle between these two vectors. For this problem, we will change the Document Distance code to use a new metric. Now, we will only care about words that show up in both documents, and we will ignore the contributions of words that only show up in one document. docdist7.py is mostly the same as docdist6.py seen in class, however it does not implement vector angle or inner product; instead, it imports those functions from ps1.py. Currently, ps1.py contains code copied straight from docdist6.py, but you will need to modify this code to implement the new metric. Modify inner product to take a third argument, domain, which will be a set containing the words in both texts. Modify the code so that it only increases sum if the word is in domain. Dont forget to change the documentation string at the top. Modify vector angle so that it creates sets of the words in both L1 and L2, takes their intersection, and uses that intersection when calling inner product. Again, dont forget to change the docstring at the top. Run test-ps1.py to make sure your modied code works. The same test suite will be run when you submit ps1.py to the class website. Does your code take signicantly longer with the new metric? Why or why not? Submit ps1.py on the class website. All code submitted for this class will be checked for accuracy, asymptotic eciency, and clarity. 3 Iterative Version: def binarySearch(alist, item): first = 0 last = len(alist)-1 found = False midpoint = (first + last)/2 if alist[midpoint] == item: found = True else: if item < alist[midpoint]: last = midpoint-1 else: first = midpoint+1 return found Recursive Version: def binarySearch(alist, item): if len(alist) == 0: return False else: midpoint = len(alist)/2 if alist[midpoint]==item: return True else: if item<alist[midpoint]: return binarySearch(alist[:midpoint],item) else: return binarySearch(alist[midpoint+1:],item) 4

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# Number 4004937 facts The odd number 4,004,937 is spelled 🔊, and written in words: four million, four thousand, nine hundred and thirty-seven, approximately 4.0 million. The ordinal number 4004937th is said 🔊 and written as: four million, four thousand, nine hundred and thirty-seventh. The meaning of the number 4004937 in Maths: Is it Prime? Factorization and prime factors tree. The square root and cube root of 4004937. What is 4004937 in computer science, numerology, codes and images, writing and naming in other languages ## What is 4,004,937 in other units The decimal (Arabic) number 4004937 converted to a Roman number is (M)(M)(M)(M)(IV)CMXXXVII. Roman and decimal number conversions. #### Time conversion (hours, minutes, seconds, days, weeks) 4004937 seconds equals to 1 month, 2 weeks, 4 days, 8 hours, 28 minutes, 57 seconds 4004937 minutes equals to 8 years, 3 months, 1 week, 2 days, 4 hours, 57 minutes ### Codes and images of the number 4004937 Number 4004937 morse code: ....- ----- ----- ....- ----. ...-- --... Sign language for number 4004937: Number 4004937 in braille: QR code Bar code, type 39 Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ... ## Share in social networks #### Is Prime? The number 4004937 is not a prime number. #### Factorization and factors (dividers) The prime factors of 4004937 are 3 * 3 * 3 * 148331 The factors of 4004937 are 1, 3, 9, 27, 148331, 444993, 1334979, 4004937. Total factors 8. Sum of factors 5933280 (1928343). #### Powers The second power of 40049372 is 16.039.520.373.969. The third power of 40049373 is 64.237.268.607.962.284.032. #### Roots The square root √4004937 is 2001,233869. The cube root of 34004937 is 158,805387. #### Logarithms The natural logarithm of No. ln 4004937 = loge 4004937 = 15,203038. The logarithm to base 10 of No. log10 4004937 = 6,602596. The Napierian logarithm of No. log1/e 4004937 = -15,203038. ### Trigonometric functions The cosine of 4004937 is -0,991859. The sine of 4004937 is -0,127338. The tangent of 4004937 is 0,128383. ## Number 4004937 in Computer Science Code typeCode value 4004937 Number of bytes3.8MB Unix timeUnix time 4004937 is equal to Monday Feb. 16, 1970, 8:28:57 a.m. GMT IPv4, IPv6Number 4004937 internet address in dotted format v4 0.61.28.73, v6 ::3d:1c49 4004937 Decimal = 1111010001110001001001 Binary 4004937 Decimal = 21112110202000 Ternary 4004937 Decimal = 17216111 Octal 4004937 Decimal = 3D1C49 Hexadecimal (0x3d1c49 hex) 4004937 BASE64NDAwNDkzNw== 4004937 SHA1c2c78a5950f2b3462bd048792b4ea1e1bb684c24 4004937 SHA2246e0a7710712a4f04cce9fe753e32bda7521010041a7795bda35ccd87 4004937 SHA256fe75fe785dd3d11aba1d10baefddfbca4cf605d32af2b59a816e9f24f4979961 4004937 SHA38496f11da8299fca8b109a62215b24d478f1017536a63df920112350f4e44d5a8fef7a65ab334711306b6c8dbe629c8a4e More SHA codes related to the number 4004937 ... If you know something interesting about the 4004937 number that you did not find on this page, do not hesitate to write us here. ## Numerology 4004937 ### Character frequency in the number 4004937 Character (importance) frequency for numerology. Character: Frequency: 4 2 0 2 9 1 3 1 7 1 ### Classical numerology According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 4004937, the numbers 4+0+0+4+9+3+7 = 2+7 = 9 are added and the meaning of the number 9 is sought. ## № 4,004,937 in other languages How to say or write the number four million, four thousand, nine hundred and thirty-seven in Spanish, German, French and other languages. The character used as the thousands separator. Spanish: 🔊 (número 4.004.937) cuatro millones cuatro mil novecientos treinta y siete German: 🔊 (Nummer 4.004.937) vier Millionen viertausendneunhundertsiebenunddreißig French: 🔊 (nombre 4 004 937) quatre millions quatre mille neuf cent trente-sept Portuguese: 🔊 (número 4 004 937) quatro milhões e quatro mil, novecentos e trinta e sete Hindi: 🔊 (संख्या 4 004 937) चालीस लाख, चार हज़ार, नौ सौ, सैंतीस Chinese: 🔊 (数 4 004 937) 四百万四千九百三十七 Arabian: 🔊 (عدد 4,004,937) أربعة ملايين و أربعة آلاف و تسعمائة و سبعة و ثلاثون Czech: 🔊 (číslo 4 004 937) čtyři miliony čtyři tisíce devětset třicet sedm Korean: 🔊 (번호 4,004,937) 사백만 사천구백삼십칠 Danish: 🔊 (nummer 4 004 937) fire millioner firetusinde og nihundrede og syvogtredive Hebrew: (מספר 4,004,937) ארבעה מיליון וארבעת אלפים תשע מאות שלושים ושבע Dutch: 🔊 (nummer 4 004 937) vier miljoen vierduizendnegenhonderdzevenendertig Japanese: 🔊 (数 4,004,937) 四百万四千九百三十七 Indonesian: 🔊 (jumlah 4.004.937) empat juta empat ribu sembilan ratus tiga puluh tujuh Italian: 🔊 (numero 4 004 937) quattro milioni e quattromilanovecentotrentasette Norwegian: 🔊 (nummer 4 004 937) fire million fire tusen ni hundre og trettisyv Polish: 🔊 (liczba 4 004 937) cztery miliony cztery tysiące dziewięćset trzydzieści siedem Russian: 🔊 (номер 4 004 937) четыре миллиона четыре тысячи девятьсот тридцать семь Turkish: 🔊 (numara 4,004,937) dörtmilyondörtbindokuzyüzotuzyedi Thai: 🔊 (จำนวน 4 004 937) สี่ล้านสี่พันเก้าร้อยสามสิบเจ็ด Ukrainian: 🔊 (номер 4 004 937) чотири мільйони чотири тисячі дев'ятсот тридцять сім Vietnamese: 🔊 (con số 4.004.937) bốn triệu bốn nghìn chín trăm ba mươi bảy Other languages ... ## News to email I have read the privacy policy ## Comment If you know something interesting about the number 4004937 or any other natural number (positive integer), please write to us here or on Facebook. #### Comment (Maximum 2000 characters) * The content of the comments is the opinion of the users and not of number.academy. It is not allowed to pour comments contrary to the laws, insulting, illegal or harmful to third parties. Number.academy reserves the right to remove or not publish any inappropriate comment. It also reserves the right to publish a comment on another topic. Privacy Policy.

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### Present Remotely Send the link below via email or IM • Invited audience members will follow you as you navigate and present • People invited to a presentation do not need a Prezi account • This link expires 10 minutes after you close the presentation Do you really want to delete this prezi? Neither you, nor the coeditors you shared it with will be able to recover it again. # CS135 Exam Review Session No description by ## Eric Folland on 14 March 2011 Report abuse #### Transcript of CS135 Exam Review Session How to use listof properly Types of recursion and how to determine the type Local Lambda Abstraction and ALFs Trees Last office hours Check your exam seat! CS 135 Exam Review Incorrect: Correct: (list-of-characters) listof Character (listof Characters) (listof lists) (listof Character) (listof (listof Character)) Pure Structural Examples: ;This example follows the list data definition (define (pure-structural1 lst) (cond [(empty? lst) 0] [(cons? lst) (add1 (pure-structural1 (rest lst)))])) ;This example follows from the unary definition of a natural number (define (pure-structural2 n) (cond [(zero? n) empty] [else (cons n (pure-structural2 (sub1 n)))])) Base case Recursive call gets closer to the base case Recursion follows the recursion of the data definition Pure Structural with an Accumulator Accumulators vs. "along for the ride" vs. "counters" Same as Pure Structural, but rather than accumulating on the return result, accumulates on a parameter Examples: ;This example follows the list data definition (define (pure-structural/acc1 lst items-so-far) (cond [(empty? lst) items-so-far] [(cons? lst) (pure-structural1 (rest lst) (add1 items-so-far))])) ;This example follows from the unary definition of a natural number (define (pure-structural/acc2 n list-so-far) (cond [(zero? n) empty] [else (pure-structural2 (sub1 n) (cons n list-so-far))])) Generative Still has a base case Termination argument vs. "one step closer to the base case" Recursive step does not follow from the data definition Examples: ;This has a chance of terminating each call (define (generative1 x) (cond [(zero? x) empty] [else (cons x (generative1 (random-0-to-9 x)))])) ;This will surely terminate, but is not based on the data definition (define (generative2 lst) (cond [(empty? lst) empty] [else (generative2 (filter (lambda (x) (equal? x (first lst))) lst))])) Scope, binding occurrence Stepping When to use it over external helper functions/constants ;Scope example (define x 5) (define (f x) (+ (local [(define x 7)] (+ x 3)) x)) (+ (f 3) (f x)) ;Local stepping example (define (foo a) (local [(define x (+ 1 2)) (define y 3)] (+ x y a))) (foo (+ 1 2)) ;can't call a function until its arguments are simplest form (foo 3) ;replace the function with its body, subbing in arguments (local [(define x (+ 1 2)) (define y 3)] (+ x y 3)) ;local's first step is to take out the defines ;replace all instances of those constants with their new name (define x_0 (+ 1 2)) (define y_0 3) (+ x_0 y_0 3) ;simplify the first thing first ;also, exclude any defines that are in simplest form. they ; are still there, but not shown (define x_0 3) (+ x_0 y_0 3) ;substitute one constant at a time: first x_0 (+ 3 y_0 3) ;now y_0 (+ 3 3 3) ;pre-defined functions happen in one step 9 Local can also be used for readability. If it makes more sense to have a local helper function or local constant, then it should probably be used. Namespace Efficiency Readability When creating a very large program or working in a team, there can be a big list of functions. That's why it's important to "hide" helper functions inside of local. On the other hand, if a helper function is useful for more than one function, it should be outside of local. The same goes for constants. Something like pi might be useful for many functions, but something specific like sum-so-far should be local. As we've seen before, local can also be used to make a program more efficient, by storing the result of a recursive call in a local constant. This only needs to be done if you will then access that constant more than once afterward. Stepping When to use lambda Examples of how to use it ;if we look at a regular function and application (define (foo x y) (+ x y)) (foo 1 2) ;here, the first step is replace the function ;name with its body, subbing in all arguments (+ 1 2) ;and finish 3 ;here is the same starting code, but using lambda. ;there are still 2 parameters, a function body, and 2 ;arguments ((lambda (x y) (+ x y)) 1 2) ;the step is logically similar here: replace the ;lambda with the body of the function, subbing in ;all arguments, which are the 1 and 2 (+ 1 2) ;and finish 3 ;this is a similar example, except now foo is a ;constant that holds a function. this is really the ;same as a function, but here we'll have an extra step (define foo (lambda (x y) (+ x y))) (foo 1 2) ;now foo is a constant, so, like any constant, it takes ;a step to sub in ((lambda (x y) (+ x y)) 1 2) ;now we continue like the last example (+ 1 2) ;and finish 3 Use lambda when the code is trivial. It is typically used in abstract list functions like quicksort, map, filter, foldr, foldl, or ones you make yourself. Although it is possible to use (define foo (lambda (x y) (+ x y))), it is considered more readable to use (define (foo x y) (+ x y)), which is the same. ;when you need a function to produce a function: (define (foo a) (lambda (x) (char=? a x))) ;think about what this would do ;notice that this is different from (define (foo a) (char=? a __)) ;this wouldn't work ;when you use a function that consumes a function, and ;it's too simple to make it a helper function (map (lambda (x) (* x 2)) (list 1 2 3 4)) There will be many more examples coming up. quicksort build-list map filter foldr quicksort requires you to give it a function that consumes two numbers it's trying to compare. Your function should produce true if the first should come before the second. (define numbers (list 5 2 7 4 1 3)) Sort ascending: (quicksort numbers <) --> (list 1 2 3 4 5 7) Sort descending: (quicksort numbers >) --> (list 7 5 4 3 2 1) Put even first: (quicksort numbers (lambda (num1 num2) (even? num1))) --> (list 4 2 5 7 1 3) build-list requires you to give it a function that consumes one number, which will hold the value of each number up to n as it gets called each time. Your function can produce anything, using the number it's given for calculations. Build list always consumes a number and produces a list with that many items. (define numbers (list 5 2 7 4 1 3)) Make 0 to 9: (build-list 10 (lambda (x) x)) OR (build-list 10 identity) --> (list 0 1 2 3 4 5 6 7 8 9) Make 1 to 10: (build-list 10 (lambda (x) (add1 x))) OR (build-list 10 add1) --> (list 1 2 3 4 5 6 7 8 9 10) Make even 2 to 20: (build-list 10 (lambda (x) (add1 (* 2 x)))) --> (list 2 4 6 8 10 12 14 16 18 20) Make 0 to 4 as lists: (build-list 10 (lambda (x) (list x))) OR (build-list 10 list) --> '((0) (1) (2) (3) (4)) map requires you to give it a function that consumes one item, which will be each item in the given list and it should return what you want that item to turn into. Unlike build-list, the item consumed doesn't have to be a number. Map always consumes a list and produces a list with the same number of items, but those items are all transformed into something else using the function you give it. (define numbers (list 5 2 7 4 1 3)) Double each number: (map (lambda (x) (* 2 x)) numbers) --> (list 10 4 14 8 2 6) (map (lambda (x) (add1 x)) numbers) OR (map add1 numbers) --> (list 6 3 8 5 2 4) Change them all into 'a: (map (lambda (x) 'a) numbers) --> (list 'a 'a 'a 'a 'a 'a) filter requires you to give it a function that consumes each item like map, but will produce true or false. True means keep the item and false means don't include it in the new list. filter always consumes a list and produces a list with equal or fewer items. (define numbers (list 5 2 7 4 1 3)) Keep only even numbers: (filter even? numbers) --> (list 2 4) Keep only numbers greater than 4: (filter (lambda (x) (> x 4)) numbers) --> (list 5 7) Keep only symbols: (filter symbol? numbers) --> empty foldr requires you to give it a function that consumes two items: the first of these is each item in the list and the second is the result of calling your function on the rest of the list. Your function should do something to combine the item onto the result of the rest. foldr always consumes a list but can produce anything. It will only produce a list if your function acts like cons. What type it produces depends on the function you give it. (define numbers (list 5 2 7 4 1 3)) Count the number of items: (foldr add1 0 numbers) --> 6 Sum the numbers: (foldr + 0 numbers) --> 22 Make the exact same list: (foldr cons empty numbers) --> (list 5 2 7 4 1 3) Double each number: (foldr (lambda (x y) (cons (* 2 x) y)) empty numbers) --> (list 10 4 14 8 2 6) Recursion for BST Mutual recursion for a General Tree (Demonstrate on the board) Searching Removing a node (Demonstrate on the board) Searching Assignment 7 q3 and q4 Thursday Friday 4-5pm Eric 9-10am Max 10am-12pm Eric 12-1pm Minghao 2pm-3:30 Prof Becker To look up your exam seat: Go to the course web page --> Exams --> a link in the text that says "look up" Monday, December 20, 2010 12:30-3:00 PM in the PAC Relax and do your best! :) ;; zip: (listof Any) (listof Any) -> (listof (list Any Any)) (define (zip lst1 lst2) (cond [(and (empty? lst1) (empty? lst2)) empty] [else (cons (list (first lst1) (first lst2)) (zip (rest lst1) (rest lst2)))])) ;; dot-product: (listof Num) (listof Num) -> Num (define (dot-product lst1 lst2) (cond [(and (empty? lst1) (empty? lst2)) 0] [else (+ (* (first lst1) (first lst2)) (dot-product (rest lst1) (rest lst2)))])) ;; map-combine: Z (W X -> Y) (Y Z -> Z) (listof W) (listof X) -> Z (define (map-combine base func-elem func-lst lst1 lst2) (cond [(and (empty? lst1) (empty? lst2)) base] [else (func-lst (func-elem (first lst1) (first lst2)) (map-combine base func-elem func-lst (rest lst1) (rest lst2)))])) (define (my-zip lst1 lst2) (map-combine empty list cons lst1 lst2)) (define (my-dot-product lst1 lst2) (map-combine 0 * + lst1 lst2)) (check-expect (zip (list 1 2 3 4 5) (list 6 7 8 9 10)) (my-zip (list 1 2 3 4 5) (list 6 7 8 9 10))) (check-expect (dot-product (list 1 3 4) (list 5 7 8)) (my-dot-product (list 1 3 4) (list 5 7 8))) Template: (define-struct node (key val left right)) ;; A binary search tree (Bst) is one of: ;; * empty ;; * (make-node Number String Bst Bst) Template: (define-struct UTnode (val children)) ;; An unbounded tree (Ut) is one of: ;; * empty ;; * (make-UTnode Any UtList) ;; A UtList is one of: ;; * empty ;; * (cons Ut UtList) Full transcript

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## Merge sort Kotlin Implementation – Sorting Algorithms #3 Vamsi Tallapudi 1 Comment Merge Sort is sorting based on Divide and Conquer strategy and is one of the famous algorithms among Sorting. In this article, we will be discussing about Merge Sort Kotlin Implementation. How Merge sort Works? Merge sort algorithm technique basically involves two processes – one process splits the array into two halves and sorts them individually. The other process involves … ## Bubble Sort Kotlin Implementation – Sorting Algorithms #2 Bubble Sort is the simplest Algorithm of all the sorting techniques. It compares two adjacent elements and swaps them if they are in wrong order. In this article we will focus on Bubble Sort Kotlin Implementation How Bubble Sort Works? Bubble sort works by iterating through the array of N elements, from the first element to the last, comparing each …

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 bzoj 1367 [ Baltic 2004 ] sequence —— 左偏树 ### bzoj 1367 [ Baltic 2004 ] sequence —— 左偏树 ```#include<iostream> #include<cstdio> #include<cstring> #include<algorithm> using namespace std; typedef long long ll; int const maxn=1e6+5; int n,t[maxn],l[maxn],r[maxn],rt[maxn],siz[maxn],num[maxn]; int ls[maxn],rs[maxn],dis[maxn]; ll ans; int abb(int x){return x>0?x:-x;} int merge(int x,int y) { if(!x||!y)return x+y; if(t[x]<t[y])swap(x,y);//维护大根堆 rs[x]=merge(rs[x],y); siz[x]=siz[ls[x]]+siz[rs[x]]+1;//+1 if(dis[ls[x]]<dis[rs[x]])swap(ls[x],rs[x]); if(rs[x])dis[x]=dis[rs[x]]+1; else dis[x]=0; return x; } int main() { scanf("%d",&n); for(int i=1;i<=n;i++)scanf("%d",&t[i]),t[i]-=i; int nw=0; for(int i=1;i<=n;i++) { l[++nw]=r[nw]=i; rt[nw]=i; siz[rt[nw]]=num[nw]=1; while(nw>1&&t[rt[nw-1]]>t[rt[nw]]) { nw--; num[nw]+=num[nw+1]; r[nw]=r[nw+1]; rt[nw]=merge(rt[nw],rt[nw+1]); while(siz[rt[nw]]*2>num[nw]+1)//+1 rt[nw]=merge(ls[rt[nw]],rs[rt[nw]]); } } for(int i=1;i<=nw;i++) for(int j=l[i];j<=r[i];j++)ans+=abb(t[j]-t[rt[i]]); printf("%lld ",ans); return 0; }```

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Zero-Order Reactions In a zero-order reaction, the rate of the reaction is independent of the concentration of the reactant. This can be seen in the differential rate law which shows how the rate of a reaction depends on the concentration of the … Read more Second-Order Reactions In a second-order reaction, the rate of the reaction is proportional to the square of the concentration of the reactant. This can be seen in the differential rate law which shows how the rate of a reaction depends on the … Read more First-Order Reactions In first-order reactions, the rate of the reaction is directly/linearly proportional to the concentration of the reactant. This can be seen in the differential rate law which shows how the rate of a reaction depends on the concentration of the … Read more Half Life and Radioactivity Practice Problems In these practice problems, we will work on the kinetics of radioactive reactions. Most often, in chemistry at least, you will be asked to determine the activity, quantity, the decay rate of radioactive isotopes, the time required to drop the … Read more The Arrhenius Equation When discussing the reaction order, we mentioned that the rate of a first- and second-order reaction depends on the concentration of the reactant. For example, the rate for a simple first-order reaction can be shown as:   A → Products … Read more Activation Energy A chemical reaction between two molecules occurs when they collide with proper orientation and sufficient kinetic energy. During the collision, the kinetic energy is used to stretch, bend, and ultimately break bonds, initiating the chemical reaction where new bonds and … Read more The Half-Life of a Reaction The half-life (t1/2) of a reaction is the time required for the concentration of a reactant to drop to one-half of its initial value. The half-life depends on the order of the reaction, and it is obtained from the corresponding … Read more Determining Reaction Order Using Graphs In the previous post, we talked about the integrated rate law and its use for determining the concentration of a reactant at a given time when the reaction order was provided.   Now, there are questions where the reaction order … Read more Units of Rate Constant k Knowing the units of the rate constant is important as it is used often for solving problems related to the rate laws.   k Units of a Zero-Order Reaction Zero-order indicates that the rate does not depend on the concentration, … Read more How Are Integrated Rate Laws Obtained We talked about the integrated rate laws in the previous post. Remember, they show the correlation between the concentration of reactants and time. There is a question that I got asked quite a few times when teaching the contacts and … Read more

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View Single Post #1 02-08-2014, 07:19 PM LazyPiggy Junior Member Join Date: Feb 2014 Posts: 8 Some questions about the lecture two Recently, I'm learning the video tutorials of learning from data . Two questions are lingering in my mind about the lecture two, which focused on the feasibility of learning: the first one is that how to define the feasibility of learning? Is the Hoeffding's Inequality the useful tool to gauge feasibility for one hypothesis h? take the hypothesis h1 and h2 for example, if both satisfy the Hoeffding's Inequality, then what we should do next? Another confusion is that in the case of mutiple h's, the simple solution to the modification of Hoeffding's Inequality could be useless as M is close to infinity. In my opinion ,the Hoeffding's Inequality seems to hold in this situation for the following reason: P[ |Ein(g) − Eout(g)| > ǫ ] ≤ P[ |Ein(h1) − Eout(h1)| > ǫ or |Ein(h2) − Eout(h2)| > ǫ· · · is no more than the minimum of them, that makes the Hoeffding's Inequality satisified. Is there a logical or mathematical error ? When it comes to the exception, I think that even the best learning algorithm could meet the special situation that only few of them could be equal to the target function for randomness, or we could consider this standard : for each hypothesis hi, i=1,2,...M, toss the coin N times, then calculate the possibility of the times that coins get all heads is less than one particular value t. such as N/4 or others. Is this standard viable? All responses are appreciated. Thank you.

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• 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 5. 5 5 6. 6 6 7. 7 7 • Level: GCSE • Subject: Maths • Word count: 2018 # Investigate how the estimation of lines and angles varies from each other, and how the estimation varies within both genders. Extracts from this document... Introduction Guestimation  – Coursework GCSE Mathematics 2002 Guestimation Aim of Investigation: To investigate how the estimation of lines and angles varies from each other, and how the estimation varies within both genders. Angles and lines have been chosen, as they are continuous data, leaving the survey to be more wide-ranged. Hypothesis 1:The difference in angle estimation shall be more than inaccurate than then length estimation. I believe this because the awareness upon lengths is more common than the familiarity of angles, within the everyday context. Hypothesis 2: In correspondence to the first hypothesis, male angle estimation shall be twice as close populated towards the correct answer than the female estimation. This means that the measure of spread will be grouped twice as close to the actual answer than the female. Introduction to Investigation:  The concept of measuring length and gradient is one of the norm in society today.  Therefore, the skill that is the measurement of these two units could be affected by several factors. For my investigation, I plan to inspect the variables of gender estimation and the difference between the two units. Lengths and angles were not only chosen because of their familiarity amongst the population, for me this is Year 10 boys and girls, but because of the fact that both measurements are continuous data. Middle 13 0.9 14 13 0.9 15 13 0.9 16 13 0.9 17 13.5 0.4 18 13.5 0.4 19 13.5 0.4 20 13.5 0.4 21 14 0.1 22 14 0.1 23 14 0.1 24 14.5 0.6 25 14.5 0.6 26 14.5 0.6 27 15 1.1 28 15 1.1 29 15 1.1 30 15 1.1 Average Line Estimation Difference = 1.18cm Hypothesis 1:The difference in angle estimation shall be more than inaccurate than then length estimation. I believe this because the awareness upon lengths is more common than the familiarity of angles, within the everyday context. A staged table will enable me to steadily calculate and prove my hypothesis. To prove my hypothesis, the difference in results is to be calculated into a percentage of the actual answer This is because of the two different units of measurement, as the degree and the centimeter do not combine. To start, I shall calculate the average difference in the entire line estimate collection. I have placed the results in descending order, keeping in mind that the mean should be 13.9cm ideally. The average difference in estimation from the real answer (13.9cm) is apparent to calculate the accuracy or inaccuracy of the estimations. The difference was calculated by subtracting the estimate Conclusion Conclusion: Overall, I have concluded that the genders and the angle/length have been well matched in both of their estimations. This has been deduced from few figures of calculations, yet more will simply continue to prove my findings. Within the gradient/length context, the difference in estimation was a mere 2.5% difference. That shows that either skill was neither too good nor too bad. The same can be said for the gender standard deviation. This means that genders generally stuck to a single figure and evolved upon that. They all consist of the average answer, yet from further investigation, the boys of Year 10 stood out  as being more precise. Though they did not stand out too much as its was only 2/3 of a percentage difference. My hypothesis emerged, as half right half wrong, as I predicted the first hypothesis incorrectly, yet my second hypothesis was rather accurate. I hope to further my investigation with newer hypothesis and more graphical data. This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section. ## Found what you're looking for? • Start learning 29% faster today • 150,000+ documents available • Just £6.99 a month 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 GCSE Height and Weight of Pupils and other Mayfield High School investigations essays 1. ## A hypothesis is the outline of the idea/ideas which I will be testing and ... > There therefore is a positive correlation between height and weight across the school as a whole. This correlation seems to be stronger when separate genders are considered > If I had taken larger samples my hypothesis may become more accurate. 2. ## Mayfield School Mathematics Statistics Coursework rounded of to 5 Year 9 Boys = 118 Divided By 604 multiplied by 20 = 3.9 is rounded of to 4 Year 10 Boys = 106 Divided By 604 multiplied by 20 = 3.4 is rounded of to 3 Year 11 Boys = 84 Divided By 604 multiplied by 1. ## Guesstiamte - investigating whether men or women between the ages of 15-25 are better ... Overall these results show that if you looked at the averages women were better at guesstimating the size of an angle; although both men and women were as accurate as each other for the median and the mode the women were much more accurate than the men for the mean. 2. ## mayfeild statistics 48 50 50 50 50 51 52 52 52 54 54 54 54 54 54 54 54 56 56 60 62 62 63 63 63 63 64 64 65 66 66 67 68 70 72 72 73 75 78 84 84 86 86 Mode The mode is the value which occurs most often. 1. ## Guesstimate lines and angles I will then find the Mean, Mode, Median and inter-quartile range and also finding the frequency and cumulative frequency for the data. Initial Data Analysis Year 7 Estimations - Just looking over the set of results the data for the year 7 students looks relatively accurate, but there are some results that were way of the mark. 2. ## Is there a difference between male and female conversational styles in today's society? Before I began all three conversations I asked all the participants if they were comfortable about discussing religious and cultural issues; they did not have a problem. I was hoping to carry out other forms of data such as interviews however I decided not to because I felt this would cause the interviewer to be naturally dominant. 1. ## Investigate how the estimation of lines and angles differ from one another, as well ... Bias: To subconsciously influence the outcome of results through wording or through sampling is bias, and it will alter the outcome of the entire investigation. To prevent this as best I can, I will survey each student personally, to ensure that s/he is not influence by his or her peers nor has any access to measuring equipment. 2. ## Angle and Line Estimation. Samples Actual Angle : 115? Actual Line Length : 12.5 cm Pupil Year Sex Set Length Estimate Angle Estimate 10:08 10 M M1 25 120 10:17 10 M M1 20 100 10:20 10 F M1 10 105 10:30 10 F M1 12.5 115 10:36 10 M M1 17 100 10:41 10 M M1 13 95 • Over 160,000 pieces of student written work • Annotated by experienced teachers • Ideas and feedback to

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## Theory of Machine A spring controlled governor is found unstable. It can be made stable by Increasing the spring stiffness Increasing the ball mass Decreasing the ball mass Decreasing the spring stiffness ## Theory of Machine A chain comprises of 5 links having 5 joints. Is it kinematic chain? It is a marginal case Yes Data are insufficient to determine it No ## Theory of Machine Tangential acceleration direction is May be any one of these Opposite to angular velocity Along the angular velocity Perpendicular to angular velocity ## Theory of Machine In multi V-belt transmission, if one of the belt is broken, we have to change the There is no need of changing any one as remaining belts can take care of transmission of load Broken belt and its adjacent belts Broken belt All the belts ## Theory of Machine A body is said to be under forced vibrations, when A body vibrates under the influence of external force There is a reduction in amplitude after every cycle of vibration None of these No external force acts on a body, after giving it an initial displacement ## Theory of Machine Which of the following would constitute a link? Piston, crank pin and crank shaft Piston and piston rod Piston, piston rod and cross head

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# SOLUTION: The average age of a group of mathematicians and computer scientists is 40. If the mathematicians' average age is 35 and the computer scientists' average age is 50, what is the rat Algebra ->  Algebra  -> Average -> SOLUTION: The average age of a group of mathematicians and computer scientists is 40. If the mathematicians' average age is 35 and the computer scientists' average age is 50, what is the rat      Log On Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Algebra: Average Solvers Lessons Answers archive Quiz In Depth Click here to see ALL problems on Average Question 276008: The average age of a group of mathematicians and computer scientists is 40. If the mathematicians' average age is 35 and the computer scientists' average age is 50, what is the ratio of the number of mathematicians to the number of computer scientists? (1) 2.5 (2) 3.5 (3) 2 (4) 3 (5) None of the aboveAnswer by richwmiller(9135)   (Show Source): You can put this solution on YOUR website!mM+cC/(M+C)=40 m=35 c=50 (35M+50C)=40(M+C) 35M+50C=40M+40C 10C=5M 10/5=M/C 2=M/C (3) 2 answer

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GRAVITY now DEBUNKED ???? WHAT IS GRAVITY ????????? Well science tells us GRAVITY is a magnetic force keeping us and all on the PLANET EARTH. So let’s go with SCIENCE even though i have little respect for it in many cases as much of it are THEORIES , just as it is with GRAVITY ??, We are told a man called ISAAC NEWTON discovered gravity and what its effects are after seeing an APPLE fall from a tree.Well i am here to say this is UTTER RUBBISH. So let’s go with Newton’s THEORY and that’s all it is a theory ?? no PROOF whatsoever exists to this day to conclusively PROVE GRAVITY.But for the sake of this article we will go along with Newton’s theory. Now Newton’s THEORY is basically we are stuck to earth due to a MAGNETIC force or an ATTRACTION of sorts ?. Now this would make sense if we didn’t have MASS or G FORCE on planet earth,yes that’s right MASS and G FORCE will destroy NEWTON’S GRAVITY theory. It is simple enough to PROVE gravity is NOT keeping us on the earth, TWO very simple experiments with ONE BASIC ITEM will solve this for you. Get a MAGNET of a sensible size and place some objects onto a table, start with something small like paper clips, and gradually work up in MASS to something heavy like a bike. So a very simple experiment ANYONE can do at home. Now place the magnet over the paper clip, you will see the magnet drags it off the table with ease ?, A VERY STRONG GRAVITATIONAL FORCE,then work your way along the objects from smaller lighter items to larger heavy items and you will find out ONE THING. the MAGNETIC FIELD is far more powerful on SMALLER items of LESS MASS and the heavier higher MASS items are barely affected by the MAGNETIC field, as in they wont be lifted from the table ?. the larger items will NOT lift off the table with the magnet. SO experiment TWO, find a large open area such as a field and take the same items you have used for the table experiment with you. Now start with the heavier HIGHER MASS items and stick them to the magnet. Now hold the magnet in your hand and SPIN AROUND as fast as you can, you will WITNESS the HEAVIER HIGHER MASS items will easily drop off the magnet even at slow speeds ?, yet the LIGHTER items of LESS MASS such as a paper clip will stick to the magnet regardless of how fast you spin. So by doing this simple experiment you will have discovered that items of HIGH MASS are much easier to lose GRAVITATIONAL PULL than items of LESSER MASS ?. Now we turn this experiment to the PLANET EARTH and we apply the same to the things around us, bearing in mind the earth is APPARENTLY spinning at high speeds, thus HAMPERING the theory of GRAVITY ?, as if the earth is spinning then G FORCE will be trying to drag all from earth as it was in the field experiment ?. So bearing in mind your two experiments and the SUPPOSED LAWS OF GRAVITY, what items should be EASIER to pull away from the GRAVITY of earth ??, the HEAVIER HIGHER MASS ITEMS surely should succumb to G FORCE and fail under the THEORY OF GRAVITY ?. YOU did the experiments ?, you acted as the EARTH SPINNING in experiment TWO and you acted as GRAVITY with the magnet in experiment one ?. So why is it that GRAVITY is not acting as it should ??, surely the smaller items on EARTH should be nearly impossible to lift due to the GRAVITATIONAL PULL and the larger items with GREATER MASS should be easy to lift ?.Yet as we see the OPPOSITE is the case. Let’s look at a bike wheel , we turn the bike upside down and we place water on the back wheel, then turn the pedals and watch as the water is propelled/displaced from the tyre ?, try this with heavier items such as MUD/SOIL, you will see it leaves the tire even faster as it has MORE MASS and is propelled by G FORCE ? So what we find is, we can’t have G FORCE and GRAVITATIONAL PULL working against each other as it wouldn’t work. The larger and heavier the item on earth, THE LIGHTER IT WOULD BE with G FORCE ?, (THE EARTH SPINNING) as G FORCE is dragging such items away from the SPINNING EARTH ?, yet if we go with the IMMENSE pull of GRAVITY then the SMALLER ITEMS on earth would be IMPOSSIBLE to lift and the HEAVIER OF GREATER MASS would be easier to lift ?. So hopefully i have CLEARED UP the MYTH OF GRAVITY and placed some thoughts into your mind to help you see WE ARE BEING FOOLED by SCIENCE into believing the IMPOSSIBLE is normal?. if you would like MORE on this subject then please say. GAV :)) 1. Funny you say that. Your theory is correct and did you know the Nazi’s developed a flying saucer which uses two-disc “spinning” in opposite directions to cause lift. In effect it had the effect of no mass. The scientists working on this disappeared. I may have this wrong but there are photos of the flying saucers. Like • Thank you for your comment Graham, yes i have also heard of such inventions and the people involved SUDDENLY disappearing.They did actually think the world was flat, until some boffin decided it was ROUND, it was then that they NEEDED an explanation to why we didn’t fall off> THUS GRAVITY.If you look into science you will find in MANY cases, the THEORY is accepted and then the EXPLANATION and mathematical equation is then searched for to back the claim. Like 2. by the way, Antarctica is now believed to be the “lost civilisation” that were far more advanced than us. a polar slip caused the continent to be covered with ice. It is thought that they built the pyramids 11500 years ago. How did they lift 70 ton blocks? with mm precision ? how about with flying saucers? Like • yes i have also heard this theory, this is another i don’t agree with> A SUDDEN POLAR SHIFT would be devastating to the planet ?. Like 3. 1) Gravity isn’t a magnetic force; Gravity is the gravitational force, 1 of 4 that exist in the universe. The magnetic force, which arises from the electromagnetic force, is substantially stronger than the gravitational force. Magnetism arises from the force of attraction between 2 oppositely charged particles; a postive and negative charge are attracted to one another, whereas a positive and a positive repel one another. Gravity isn’t repulsive; it relies on mass. 2) We don’t spin off the earth due to its rotation in the same way you don’t fly out of a car at 30 mph if your car is travelling at 30 mph. When in a car going at a constant speed, you can treat yourself [mathematically speaking] as being stationary. It’s when the car stops, or brakes, or accelerates that you feel the force, as you are still travelling at 30 mph. We’re rotating at the same speed as the Earth is, thus we don’t experience the centrifugal force you describe. 3) In the field experiment, you can look at the forces at play. There is gravity, pulling down, and the magnetic force pulling up. The magnetic force DOES NOT DEPEND ON MASS, whereas gravity does. Increasing the mass, but keeping the magnetic force at a rough constant, will obviously result in the gravitational force ‘winning’ the battle and causes it to fall. I appreciate you’re questioning stuff like this and not taking it at face value, that’s what science is all about, asking questions. Like • So if we are to go by your THEORY, the same as GRAVITY ?, when on a WALTZER G FORCE is trying to throw you out and is far stronger than > SO CALLED GRAVITY,this is why you are stuck to the back of the seat ?.So if we put this into perspective of the earth spinning at over 1000 mph it makes no sense at all.I would suggest this puts the car at 30 mph theory into doubt, It also does not in ANY WAY prove gravity ?. Please understand i do not want theories, i want ACTUAL PROOF, if someone can offer me this, then i will agree. Like • I don’t understand what you’re saying really so I’m gonna do my best to decipher what i can. I study astrophysics at university, and I’m about to spend the next 3 years of my life working towards a doctorate. Gravity, as a force, isn’t a theory. Gravity is unanimously agreed to be real by the entirety of the credible scientific community, and the rest of the world. It’s the theory of General Relativity that is a theory; the closest thing we have to proof of the theory of GR being correct is the detection of gravitational waves: a real world proof that gravity exists. F = M x A : This is the equation for a force. M is the mass of the object; A is the acceleration. F is the resultant force. The Earth is spinning fast. Yes. It is spinning at a constant velocity. A constant velocity means that there is no acceleration. A= 0. Let’s take a human weighing 90kg. F = 90 x 0 = 0. No force is felt on the human in the direction of rotation. We do not fly off. Let’s take a building weighing 100000kg. F = 100000kg x 0 = 0. Same thing; no force felt. That simple mathematical equation is real. I’ve derived it from bare-bones calculus a hundred times. Like • If the waltzer threw you out you would only travel so far before gravity pulled you down to earth. So no, the waltzer’s centrifugal force is NOT stronger than gravity. To escape the Earth’s gravity you would have to be travelling at 25,020 mph. Like 4. But as you STATE numerous times, it is a THEORY ?, so it is NOT PROVEN, please offer proof. If you can not prove the THEORY OF GRAVITY then you can not say with any certainty that it even exists. It is the same with EVOLUTION, no proof whatsoever, just another THEORY. I am sure if you get some boffins in a room and make something sound PLAUSIBLE most would agree it COULD BE TRUE, but this however does NOT prove that it is the case. So we base the EARTH on a theory that has no EVIDENCE to back it, apart from a man seeing an apple fall from a tree. It laughable to be honest to think the scientific world of BOFFINS actually agree on something they can neither prove or confirm. Like • Gravity isn’t a theory. It’s like saying water’s a theory. Or air’s a theory. Jesus man, go read a book on it and study the god damn mathematics behind it. The same mathematics that keeps your car moving, keeps planes flying. It’d probably go over your head though because I’m putting money on you thinking calculus and algebra are theories too. Like • As for WATER AND AIR, they can be PROVEN to exist. Do the same for GRAVITY and i will GLADLY AGREE :)) Like 5. PROVE IT . That’s all you have to do, I am sure you would agree I am not being unreasonable in asking for proof ?. So can you prove it or not ?, if so do so, if not don’t claim you are right. Like 6. Gravitational microlensing: light passing by a source of extreme mass curves around it and can become visible. Without gravity, this wouldn’t be possible. Without the gravitational attraction of the moon, we wouldn’t have ocean tides. The fact that clocks inside GPS satellites need to be altered to be correct due to time dilation [google it] induced by the low gravity in space. The fact that the solar system orbit can be modeled almost precisely using Newton’s mathematics, the exact same equations that can be used to find precisely how far a ball goes when you throw it. Like 7. Reblogged this on In the Dark and commented: The writer of this post invites readers to share it, so I’m doing so now. Anyone with any knowledge of physics whatsoever (even pre-GCSE) is invited to comment on the “theory” presented in the post. Is it now official UKIP policy to repeal the laws of gravity? Like 8. This is all a joke, right? If not, it is the most inane, ignorant, and juvenile pseudo-scientific rubbish that I have ever seen posted on the internet!!! Like 9. Yes, classical Newtonian gravity is due to mono magnetic repulsion by gravitons . Like 10. Gav, go look up gravitational red shift and Google scientific theory – it is a sepetate and distinct use of the word from the one you are obviously confusing it with. Like

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digplanet beta 1: Athena Share digplanet: Agriculture Applied sciences Arts Belief Chronology Culture Education Environment Geography Health History Humanities Language Law Life Mathematics Nature People Politics Science Society Technology Bengie Molina of the Anaheim Angels (in gray and red) scores a run by touching home plate after rounding all the bases. In baseball, a run is scored when a player advances around first, second and third base and returns safely to home plate, touching the bases in that order, before three outs are recorded and all obligations to reach base safely on batted balls are met or assured. A player may score by hitting a home run or by any combination of plays that puts him safely "on base" (that is, on first, second, or third) as a runner and subsequently brings him home. The object of the game is for a team to score more runs than its opponent. With two outs at the start of play, the batter must reach first base and any base runners obligated to run to the next base must reach the next base on a batted ball if a run is to be counted. Thus if a baserunner running from third base crosses home plate with two out before a batter is put out on a ground out or before a fly ball is caught after two outs, then the run that would otherwise score is null; likewise, if a conventional double play is made with one out on a ground ball involving forces at other bases, the run that would otherwise score before the third out is registered is void. But if the play involves no batted ball, the baserunner who scores before the third out is made scores a run. Example: with runners at first and third, the runner at first base attempts to steal second base. The runner on third takes off for home plate while the runner from first base is in a rundown. Should the runner from third score before the baserunner originally at first base be put out, then a run scores. In baseball statistics, a player who advances around all the bases to score is credited with a run (R), sometimes referred to as a "run scored". While runs scored is considered an important individual batting statistic, it is regarded as less significant than runs batted in (RBIs). Both individual runs scored and runs batted in are heavily context-dependent; for a more sophisticated assessment of a player's contribution toward producing runs for his team, see runs created. A pitcher is likewise assessed runs surrendered in his statistics, which differentiate between standard earned runs (for which the pitcher is statistically assigned full responsibility) and so-called unearned runs scored due to fielding errors. If a pitching substitution occurs while a runner is on base, and that runner eventually scores a run, the pitcher who allowed the player to get on base is charged with the run even though he was no longer pitching when the run scored. ## Significant run scoring records ### Player The career record for most runs scored by a major-league player is 2,295, held by Rickey Henderson (1979–2003). The season record for most runs scored is 196, set by Billy Hamilton of the Philadelphia Phillies in 1894. The so-called modern-day record (1900 and after) is 177, achieved by Babe Ruth of the New York Yankees in 1921. The record for most seasons leading one of the major leagues in runs scored is 8, held by Babe Ruth (American League: 1919–21, 1923, 1924, 1926–28). The record for most consecutive games with at least one run scored is 18, shared by the Yankees' Red Rolfe (August 9–August 25, 1939) and the Cleveland Indians' Kenny Lofton (August 15–September 3, 2000). The record for most runs scored by a player in a single game is 7, set by Guy Hecker of the American Association's Louisville Colonels on August 15, 1886. The modern-day record of 6 is shared by fourteen players (eight of whom attained it before 1900). Of the six modern-day players to score 6 runs in a game, the first to perform the feat was Mel Ott of the New York Giants on August 4, 1934 (he repeated the accomplishment ten years later, making him the only player ever to do it twice); the most recent was Shawn Green, then of the Los Angeles Dodgers, on May 23, 2002. ### Team The record for most runs scored by a major-league team during a single season is 1,212, set by the Boston Beaneaters (now the Atlanta Braves) in 1894. The modern-day record is 1,067, achieved by the New York Yankees in 1931. The team record for most consecutive games with at least one run scored (i.e., most consecutive games not being shut out) is 308, set by the Yankees between August 3, 1931, and August 2, 1933. The team record for most runs in its overall history (up until 2013) is the Chicago Cubs with 94,138.[1] The record for most runs scored by a team in a single game is 36, set by the Chicago Colts (now the Chicago Cubs) against the Louisville Colonels (which joined the National League in 1892) on June 29, 1897. The modern-day record of 30 was set on August 22, 2007, by the Texas Rangers against the Baltimore Orioles in the first game of a doubleheader at Oriole Park. The Rangers scored 5 runs in the fourth inning, 9 in the sixth, 10 in the eighth, and 6 in the ninth. On August 25, 1922, the highest-scoring game in major-league history took place: the Chicago Cubs defeated the Philadelphia Phillies 26–23, a total of 49 runs. The record for most runs scored by a team in a single inning is 18, set by the Chicago White Stockings (now the Cubs) against the Detroit Wolverines on September 6, 1883. The modern-day record is 17, achieved by the Boston Red Sox against the Detroit Tigers on June 18, 1953. ### World Series The Yankees' Mickey Mantle holds the record for most career World Series runs scored with 42 (1951–53, 1955–58, 1960–64). The record for most runs scored in a single World Series, shared by two players, is 10, achieved both times in a six-game Series: Reggie Jackson of the Yankees was the first to do it, in 1977; the Toronto Blue Jays' Paul Molitor equaled him in 1993. The most runs ever scored by a player in a World Series game is 4, a record shared by nine men. Babe Ruth set the mark on October 6, 1926, while with the Yankees; it was matched most recently by Jeff Kent of the San Francisco Giants on October 24, 2002. On October 2, 1936, playing the New York Giants, the Yankees set the team record for most runs scored in a single Series game with 18. Players crossed the plate a record 29 times in the highest-scoring World Series game in history on October 20, 1993, as the Blue Jays beat the Phillies 15–14 at Veterans Stadium in Game 4 of the 1993 World Series. ## References 1000000 videos foundNext > How to Play Baseball : How to Run the Bases in BaseballGet tips on running the bases in baseball and how to avoid getting tagged out in this free sports instructional video on how to play the game of baseball. Ex... YOLO: Half Naked Guy Runs Onto Baseball Field\ YOLO ON HIS BACKHalf naked guy is seen running onto a baseball field with YOLO written on his back. YOU ONLY LIVE ONCE. Speed Drills - baseball - How to run faster in baseballhttp://www.myosource.com/baseball/. Using the Kinetic Bands for Core development to develope speed, quickness, first step for base stealing, base running, fi... How to Run Bases in BaseballDoes your ball player need a little help learning the basics of base running? In this video, Coach Keith Stephens shows you how to properly run the bases. Fo... Hack Home Run Baseball HeroesCombomax9.ct : http://www.ziddu.com/download/21372580/combomax9.zip.html Cheat Skill Hit : https://www.youtube.com/watch?v=RCoEb8c8vjA Cheat Engine 6.2 : htt... hack de home runs en baseball heroes 2013esta es la pagina hay mas hacks para otros juegos http://cheat2dmax.blogspot.com/2012/12/baseball-heroes-cheats-combo-hack.html suscribance y denle me gusta ... Carlos Beltran and Carlos Delgado - Home Run clips - BaseballCarlos Beltran and Carlos Delgado hitting big for the New York Mets. For baseball lovers. 23 minutes of Carlos' extra bases. Hacker para baseball heroes facebook 2013 "Home Run" (NO FUNCIONA POR LOS MOMENTOS) Kyle Palmer 7 Yr Old Baseball Home Run King - Son of Scorpion Swords & Knives Chris PalmerKyle Palmer, 7 year old boy slugging it out during his baseball tournament. The son of Chris Palmer, Owner of Scorpion Swords & Knives, is getting kids out l... 2011 MLB Home Run Derby Slow Motion Baseball Swings2012 Video Here: http://www.youtube.com/watch?v=jeP8t8rQnkU The best swings from the 2011 Home Run Derby in extreme slow motion. Study this video to learn ho... 1000000 videos foundNext > 427 news items Canzano: Baseball's triumphant return with Hillsboro Hops comes with big-time ... OregonLive.com Mon, 17 Jun 2013 22:52:39 -0700 And in that, the historic home-run baseball will probably end up meaning more to the baseball organization than the entrepreneurial teenager who caught the thing. Since the Triple-A Portland Beavers were spurned by our region three years ago, a lot of ... Prep roundup: Rams fall in Bull Run baseball tournament final Northern Virginia Daily Thu, 23 May 2013 21:40:00 -0700 STANARDSVILLE -- Strasburg's rally didn't come soon enough to beat the inclement weather during Thursday night's Bull Run District baseball tournament championship game against William Monroe. Down by four runs at one point, the Rams rallied to ... Thorman to run baseball camp in Cambridge Waterloo Record Mon, 10 Jun 2013 16:49:58 -0700 Thorman to run baseball camp in Cambridge. Waterloo Region Record. Former Major League Baseball player Scott Thorman is hosting a baseball camp beginning next month. The Canadian FUNdamentals baseball and softball camp runs at Cambridge's ... San Francisco Chronicle Odd Man Rush: Time for the Angels to make their run MiamiHerald.com Fri, 24 May 2013 10:15:45 -0700 The dusk of May is usually way too early to begin talking about a team approaching a make-or-break it portion of their schedule. But as expected contenders for not only the American League West crown, but for the AL Pennant, the Los Angeles Angels of ... Otisville LakeVille Memorial @ Birch Run - Baseball MLive.com Mon, 20 May 2013 20:06:47 -0700 Thomas Fortney allowed one run and struck out 11 over seven windy innings for Birch Run as the Panthers defeated visiting Otisville LakeVille Memorial 3-1 in non-conference baseball action on Monday. Fortney added a hit and two runs scored for Birch ... Rantoul Press Senior Legion Baseball: Rantoul keeps rolling along Rantoul Press Tue, 18 Jun 2013 14:49:46 -0700 Hayden Morris threw two innings of two-run baseball, and Louis Acklin picked up the save in a two-inning effort. Rantoul's bats were on fire, as the team collected 19 hits. Aaron Woller (4-for-5, RBI), Cord Church (3-for-5, RBI), Chris Deaville (4-for ... Youth Baseball Pitch, Hit, Run camp July 8-12 in Jaffrey Monadnock Ledger Transcript Wed, 05 Jun 2013 17:13:56 -0700 The Pitch, Hit and Run baseball camp, run by Dave Springfield, will be held July 8-12 at the Legion Baseball Field in Jaffrey. The camp is open to area boys in grades 2-6. There is a half day option for \$70 per week or a full day option for \$100 per ... Nieuwenhuis' HR caps 4-run 9th, Mets startle Cubs TheNewsTribune.com Sun, 16 Jun 2013 13:38:24 -0700 Edwin Jackson pitched six innings of one-run baseball and the Chicago Cubs defeated the New York Mets, 6-3, in the opener of a three-game series at Citi Field. Recap: NY Mets vs. St. Louis. Lucas Duda homered and knocked in two runs to lead the New ... Limit to books that you can completely read online Include partial books (book previews) .gsc-branding { display:block; } Oops, we seem to be having trouble contacting Twitter # Talk About Run (baseball) You can talk about Run (baseball) with people all over the world in our discussions. #### Support Wikipedia A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!

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Jump directly to the content TOP PIZZ-A-CAKE # Experts reveal ‘game changing’ pizza cutting hack that will give you even slices EVERY time ANYONE who has ever shared a pizza will be all too aware of how unequal the slices can be. While you might end up with a slither, your pal gobbles down an enormous wedge - seems unfair right? Well, thanks to two mathematicians putting their skills to good use, we can now cut pizza slices evenly no matter the size of the party. Mathematicians Joel Haddley and Stephen Worsley, have come up with a new way to cut pizza using some fun geometric shapes which ensures slices are even, The Mirror reports. The picture was shared on Oshop's Twitter account. No longer will we have to sit in silent disappointment as we realise we've ended up with the smallest slice, again. Haddley and Wosley, both from The University of Liverpool teamed up to create the pizza-cutting method which in the maths world is known as ‘monohedral disc tiling’. When you use the duo's method, it creates 12 perfectly even slices of pizza you can share without the fear of arguments. ## Here is how to create their masterpiece You just need to cut your pizza into six curved three side shapes across the pizza, it should look like a star coming out of the centre. Then you need to divide the shapes into two so that you have an inside group with a crust and an outside group with a crust. Sorry guys the math doesn't end there, the team decided to take it to the extreme and cut even more slices by creating similar tiling's from more curved slices with an odd number of sides. This is known as 5-gons, 7-gons and so on. You then divide them into two like the previous method suggests. Notches (V shaped cuts) were then cut into the corner of the shapes to form spiky pieces within the circular pizza. Speaking to New Scientist Haddley said: “Mathematically there is no limit, though it might be impractical to carry out the scheme beyond 9-gon pieces.” - WE can all agree on that I guess. Haddley and Wosley are not the only ones that have tackled the perfect pizza conundrum, as reported by The Daily Mail, Mathematician Dr Eugenia Cheng from The University of Sheffield calculated a ratio to ensure maximum flavour of topping to base. She also said that the average bite taken from an 11 inch pizza had 10 per cent more topping than the average bite of a 14 inch pizza. So next time you're getting a pizza out for a party, try putting your math to the test, and ensure everyone gets an even slice of pizza, it's the least they deserve. Plus this mum thought she was getting free McDonalds for a year, then she discovers it's been billed to her brother. And this mum's genius meal prep hack saves her hours in the kitchen and people can't wait to try it. Meanwhile a mum was criticised for her child's dinner, but other parents don't see a problem with it. Mum shares supermarket hack to stop the kids moaning about food over the summer holidays

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555 signal delay circuit different solutions popcalent Joined Mar 17, 2018 128 Hello, I'm trying to design a circuit that when triggered generates a delayed pulse. That is, when a push button at the input is pressed, the circuit waits for a time D (delay), then generates a pulse for a time P (pulse). I found a solution that works but I think it is ridiculously complicated. So I decided to do some research. After searching this forum I found this old thread: I have put that circuit together on a breadboard but there's something I don't like, when I turn it on there's a pulse on the output that lasts P. Then it goes low and the circuit does what I want: I press the push button and it does nothing for a time D, then there's a pulse for a time P. But that initial pulse bothers me and I don't know how to get rid of it. They mention it's because the capacitor on the second 555 needs time to discharge but no matter how long I wait, when I turn on the circuit there's always that initial pulse. But it makes sense for it to be there: when I turn on the circuit, the output of the first 555 is low and it triggers the second 555. How do I get rid of that pulse? On the internet I found this: https://www.electronics-project-design.com/timedelaycircuit.html I don't fully understand that circuit. I understand that resistor VR1 and capacitor C generate the delay but then, what generates the pulse? Should I connect a resistor from discharge to Vcc and a capacitor from discharge to ground? Or is discharge supposed to be floating? I need help understanding that circuit. I put it together and it doesn't do anything. Finally, my solution that works. But I'm not happy with it because it's too complicated. I'm using two 555s on monostable mode, one generates a pulse for a time D+P, the other one generates a pulse for a time D. Both are triggered by the same push button, both outputs go to a XOR gate (cmos 4030). The output of the XOR gate is a delay (D) then a pulse (P). It works, no initial pulses. But I just think it's too many integrated circuits. Any ideas? Thanks! crutschow Joined Mar 14, 2008 34,697 Here's your first circuit, slightly modified. I added C6 to keep U2's TRIG input high during power up, which solves the problem (which I also observed) in the simulation. (R8 solves an observed trigger sensitivity problem due to the addition of C6). If you still have problems try increasing the values of C2, C4, and C6 by a factor of 10.

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# How Many Ounces In 4 Pounds How Many Ounces In 4 Pounds. A pound has been defined as 437.2 grams. How much are 4 pounds in ounces? So, let’s start with the simple conversion of ounces in a pound for the united states. How to convert pounds to. So, what’s the difference between 4 pounds and 4 ounces? ### The Conversion Factor From Pound To Ounce Is 16. 1 pound (lb) is equal to 16 ounces (oz): 23 rows how many ounces in a pound (oz in lb) how many ounces in a pound (oz in lb). How many ounces are in a pound of meat? ### How Much Does 4 Ounces Weigh In Pounds? This means that there are 4 ounces in a quarter pound of pasta, and 2 ounces in an. A pound has been defined as 437.2 grams. To convert 3.4 ounces into pounds we have to multiply 3.4 by. ### The Conversion Factor From Ounces To Pounds Is 0.0625, Which Means That 1 Ounce Is Equal To 0.0625 Pounds: To convert any value of pounds to ounces, multiply the pound value by the conversion factor. If you been looking to learn how much is 16.4 ounces to pounds you will find the answer of 16.4 oz to lbs or 16.4 oz in pounds. If you been looking to learn how much is 4 pounds to ounces you will find the answer of 4 lbs to oz or 4 lbs in ounces. ### 1 Lb = 16 Oz. This means that there are 4 cups in a pound, and 24 divided by 4 equals 6. Now, we know that there are 16 ounces in a pound, which means that there are 4 cups in a pound. 4 lb to oz conversion. ### A Ounce (Cm) Is A Decimal Fraction Of The Kilogram, The International Standard Unit Of Length, Approximately Equivalent To 39.37 Pounds. The conversion factor from ounces to pounds is 0.0625, which means that 1 ounce is equal to 0.0625 pounds: How to convert pounds to. 4 ounces is a little less than 1 pound.

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# Easy way to determine leap year in ruby? Is there an easy way to determine if a year is a leap year? - Try: ``````now = DateTime.now flag = Date.leap?( now.year ) `````` - Thought this might be in the library, but was not sure. –  MikeJ Oct 14 '09 at 15:02 ``````def isLeapYear(yearVar) if (yearVar % 4 == 0) if (yearVar % 100 == 0) if(yearVar % 400 == 0) return true end return false end return true end return false end `````` This can be easily converted to ``````year_var = <your Year> if((year_var % 4 == 0 &&) !(year_var % 100 == 0) || (year_var % 400 == 0)) #Do anything end `````` - Try this: ``````is_leap_year = year % 4 == 0 && year % 100 != 0 || year % 400 == 0 `````` - Here is my answer for the exercism.io problem which asks the same question. You are explicitly told to ignore any standard library functions that may implement it as part of the exercise. ``````class Year def initialize(year) @year = year end def leap? if @year.modulo(4).zero? return true unless @year.modulo(100).zero? and not @year.modulo(400).zero? end false end end `````` - Note I said it's for exercism.io, which asks you to implement the logic yourself as a coding exercise. –  MattC Nov 28 '13 at 1:38 ``````def leap_year?(num) if num%4 == 0 && num%100 != 0 true elsif num%400 == 0 true elsif num%4 == 0 && num%100 == 0 && num%400 != 0 false elsif num%4 != 0 false end end puts leap_year?(2000) `````` -

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What is .083 as a fraction? 083, means. Since there are 3 digits in 083, the very last digit is the “1000th” decimal place. So we can just say that . 083 is the same as 083/1000. Subsequently, one may also ask, what is 0.83 in a fraction? Decimal Fraction Percentage 0.83 83/100 83% 0.82 82/100 82% 0.85567 83/97 85.567% 0.84694 83/98 84.694% Additionally, what is .083 as a percent? 8.3% Subsequently, one may also ask, what’s 0.083 as a fraction? Decimal Fraction Percentage 0.083 83/1000 8.3% 0.082 82/1000 8.2% 0.08325 83/997 8.325% 0.08317 83/998 8.317% What is 0.83 expressed as a fraction in simplest form? The answer in simplest form is, 83/100. What is 0.83 with the 3 Repeating as a fraction? Therefore, the decimal is equivalent to 4/5. Answer: The decimal is converted to 4/5 as fraction. What is 1.83333 in a fraction? As we have 5 numbers after the decimal point, we multiply both numerator and denominator by 100000. So, 1.833331 = (1.83333 × 100000)(1 × 100000) = 183333100000. What is 0.83 as a decimal? 0.83% = 0.0083 in decimal form. What is 8.3333 as a fraction? How to Write 8.3333 or 833.33% as a Fraction? Decimal Fraction Percentage 8.3333 83333/10000 833.33% 8.3332 83332/10000 833.32% 8.3358 83333/9997 833.58% 8.33497 83333/9998 833.497% What is 1/3 as a decimal? Common Fractions with Decimal and Percent Equivalents Fraction Decimal Percent 1/3 0.333… 33.333…% 2/3 0.666… 66.666…% 1/4 0.25 25% 3/4 0.75 75% What is 0.83333333333 in a fraction? 0.83333333333 in fraction form is 83333333333/100000000000. What is 0.16 as a fraction? How to Write 0.16 or 16% as a Fraction? Decimal Fraction Percentage 0.24 6/25 24% 0.2 5/25 20% 0.16 4/25 16% 0.12 3/25 12% What is 0.34 as a fraction in simplest form? How to Write 0.34 or 34% as a Fraction? Decimal Fraction Percentage 0.4 20/50 40% 0.38 19/50 38% 0.36 18/50 36% 0.34 17/50 34% What is 0.06 as a fraction? How to Write 0.06 or 6% as a Fraction? Decimal Fraction Percentage 0.08 4/50 8% 0.06 3/50 6% 0.04 2/50 4% 0.06383 3/47 6.383% What is 1.21 as a fraction? getcalc.com’s decimal to fraction calculator to find what’s an equivalent fraction for the decimal point number 0.0121 or 1.21%. How to Write 0.0121 or 1.21% as a Fraction? Decimal Fraction Percentage 0.0121 121/9998 1.21% 0.0121 121/9999 1.21% 0.0121 121/10001 1.21% What is 0.52 as a fraction? How to Write 0.52 or 52% as a Fraction? Decimal Fraction Percentage 0.64 16/25 64% 0.6 15/25 60% 0.56 14/25 56% 0.52 13/25 52% What is 0.002 as a fraction? To write 0.002 as a fraction you have to write 0.002 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. What is 0.7 as a fraction? How to Write 0.7 or 70% as a Fraction? Decimal Fraction Percentage 0.8 8/10 80% 0.7 7/10 70% 0.6 6/10 60% 1 7/7 100% What is .002 as a percent? Common Decimal Values and the Equivalent Percent Values Decimal Percent .001 .1% .002 .2% .003 .3% .004 .4% What is 7.5 As a decimal? Step-by-Step Solution 7.5% = 0.075 in decimal form. Percent means ‘per 100’. So, 7.5% means 7.5 per 100 or simply 7.5/100. If you divide 7.5 by 100, you’ll get 0.075 (a decimal number). How do you find the percent of a fraction? Convert Fractions to Percents. Divide the top of the fraction by the bottom, multiply by 100 and add a “%” sign. How do you write 0.083 as a percentage? Express 0.083 as a percent 1. Multiply both numerator and denominator by 100. 0.0831 × 100100 = 8.3100. 2. Write in percentage notation: 8.3%

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## Перевод: с английского на русский с русского на английский # finite fields arithmetic ### См. также в других словарях: • Finite field arithmetic — Arithmetic in a finite field is different from standard integer arithmetic. There are a limited number of elements in the finite field; all operations performed in the finite field result in an element within that field.While each finite field is …   Wikipedia • Arithmetic combinatorics — arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis. It is about combinatorial estimates associated with arithmetic operations (addition, subtraction, multiplication, and division). Additive… …   Wikipedia • Finite field — In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and… …   Wikipedia • Arithmetic of abelian varieties — In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. It goes back to the studies of Fermat on what are now recognised as elliptic curves; and has become a very… …   Wikipedia • Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …   Wikipedia • Glossary of arithmetic and Diophantine geometry — This is a glossary of arithmetic and Diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of… …   Wikipedia • Modular arithmetic — In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value the modulus. The Swiss mathematician Leonhard Euler pioneered the modern… …   Wikipedia • Trigonometry in Galois fields — In mathematics, the theory of quadratic extensions of finite fields supports analogies with trigonometry.The main motivation to deal with a finite field trigonometry is the power of the discrete transforms, which play an important role in… …   Wikipedia • Field arithmetic — In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a ql|field (mathematics)|field and its absolute Galois group.It is an interdisciplinary subject as it uses tools from algebraic number… …   Wikipedia • List of first-order theories — In mathematical logic, a first order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties. PreliminariesFor every natural mathematical structure… …   Wikipedia • Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia ### Поделиться ссылкой на выделенное ##### Прямая ссылка: Нажмите правой клавишей мыши и выберите «Копировать ссылку»

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<meta http-equiv="refresh" content="1; url=/nojavascript/"> # Chapter 8: CK-12 Algebra Explorations Concepts, Grade 6 Difficulty Level: At Grade Created by: CK-12 ## Introduction In these concepts, you will continue to develop ten key concepts of algebra and will practice your problem solving skills. There are ten concepts, and each one focuses on a key algebraic thinking strategy. You will focus on describing, identifying your job, planning, solving, and checking your thinking. ## Summary In these concepts we used proportional reasoning when we determined the weights of coins in grams. We thought about equality and inequality when we used the order of operations and the distributive property. We saw variables as unknowns when we modeled systems of equations in letter grid problems and scale problems. We also saw variables as varying quantities when we completed tables for functions and applied area and perimeter formulas to solve problems. We wrote equations to represent weights of blocks pictured on scales, purchases of items, number of shapes in patterns, and distance/time relationships. In many of the concepts we practiced interpreting representations of mathematical relationships, such as when we looked at circle and arrow grid diagrams, weight scales, and line graphs. ## Date Created: Jan 18, 2013 Dec 29, 2014 You can only attach files to None which belong to you If you would like to associate files with this None, please make a copy first.

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Select Page The first unit of a job took 40 hours to complete. The work has a learning percentage of 88. The manager wants time estimates for units 2, 3, 4, and 5. Develop those time estimates. . A manager wants to estimate the remaining time that will be needed to complete a five-unit job. The initial unit of the job required 12 hours, and the work has a learning percentage of 77. Estimate the total time remaining to complete the job. . Kara is supposed to have a learning percentage of 82. Times for the first four units were 30.5, 28.4, 27.2, and 27.0 minutes. Does a learning percentage of 82 seem reasonable? Justify your

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## ››Convert million gallon/second [US] to acre inch/second million gallon per second acre inch/second Did you mean to convert million gallon/second [US] million gallon/second [UK] to acre inch/second acre inch/second [survey] How many million gallon per second in 1 acre inch/second? The answer is 0.027154285653501. We assume you are converting between million gallon/second [US] and acre inch/second. You can view more details on each measurement unit: million gallon per second or acre inch/second The SI derived unit for volume flow rate is the cubic meter/second. 1 cubic meter/second is equal to 0.00026417205124156 million gallon per second, or 0.0097285583061361 acre inch/second. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between million gallons/second and acre inches/second. Type in your own numbers in the form to convert the units! ## ››Quick conversion chart of million gallon per second to acre inch/second 1 million gallon per second to acre inch/second = 36.8266 acre inch/second 2 million gallon per second to acre inch/second = 73.6532 acre inch/second 3 million gallon per second to acre inch/second = 110.4798 acre inch/second 4 million gallon per second to acre inch/second = 147.3064 acre inch/second 5 million gallon per second to acre inch/second = 184.133 acre inch/second 6 million gallon per second to acre inch/second = 220.9596 acre inch/second 7 million gallon per second to acre inch/second = 257.7862 acre inch/second 8 million gallon per second to acre inch/second = 294.6128 acre inch/second 9 million gallon per second to acre inch/second = 331.43939 acre inch/second 10 million gallon per second to acre inch/second = 368.26599 acre inch/second ## ››Want other units? You can do the reverse unit conversion from acre inch/second to million gallon per second, or enter any two units below: ## Enter two units to convert From: To: ## ››Metric conversions and more ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!

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## Diagram nanagyanewa Forum Guests Posts: 32 Joined: July 13th, 2010 ### pt 32 S3 G3 At a concert... Hello, Could someone please help me out with this game. The second and last constraint really confused me and made it hard for m to get a good diagram. Any help would be greatly appreciated. ManhattanPrepLSAT2 Atticus Finch Posts: 303 Joined: July 14th, 2009 This post thanked 1 time. ### Re: pt 32 S3 G3 At a concert, exactly... Here you go -- For constraints 2 and 5... I always use the " _ _ ..." symbol for situations such as "2 or more spaces in between" and the "two different options in a box" symbol for situations where we don't know which element goes first. There are other symbols that can be equally effective -- the important thing is that the symbol makes intuitive sense to you, and that you practice using it until it's nearly automatic. Though the constraints all relate to one another, there are very few inferences to be made upfront. So, even though a few frames are possible, I personally wouldn't create or use them here. Notice that q's 14-18 are all conditional questions, so you can see that this game is designed primarily to test your ability to "juggle" the various constraints and make inferences in the unique situations that the questions present. See if these notations help you, and feel free to follow up if you get stuck on any of the problems. Attachments PT32, S3, G3 - Concert Compositions - ManhattanLSAT.pdf nanagyanewa Forum Guests Posts: 32 Joined: July 13th, 2010 ### Re: pt 32 S3 G3 Thanks for the response. The diagram and the inferences all made sense to me but when i tried the game, I had 4 out of 7 right. I struggled with q12, 14 and 17. For q12, I don't really understand why D is wrong and A is the right answer. I checked it with all the constraints but could not find anything wrong with it. For q14, i eliminated down to choices A and C but I chose C because i placed S in the 3rd and 4th positions and they all fit fine. Also for q17, I chose B because I knew from the constraints that O can be performed fifth, and I tried with F in 5th as well, to get O R P T F S L/H L/H. Hope you can help me understand this better. Thanks. ManhattanPrepLSAT2 Atticus Finch Posts: 303 Joined: July 14th, 2009 ### Re: pt 32 S3 G3 At a concert, exactly... #12 is an orientation question -- generally you can answer this type of question most efficiently by using the constraints one at a time to eliminate answer choices. The first constraint eliminates B. The second constraint eliminates E. The third constraint eliminates C. And the final constraint gets rid of D. #14 is a conditional question, so you should expect to make a lot of inferences before you move on to the answer choices. If T is fifth and F is sixth... O must be first (because it can't be fifth). R must be second or third (because it must be at least 3 slots away from F) Now let's think about S -- we know, based on the q stem, that it can only go in two slots -- which ones are the most likely? Let's try slot 7 -- can we put S there? Don't see why not. Doesn't violate any conditions that S is involved with, and it seems like there will be no issues fitting the other elements into the other slots. Let's try slot 4 -- can we put S there? Well, we know P has to be before S, and R has to be in slot 2 or 3, so we know P and R have to occupy 2 and 3. With S in 4, that would put L or H in 7, and L or H in 8. That seems fine too. Let's try slot 3 -- if S is in slot 3, P would have to go in slot 2, and there would be no place for the R. Therefore, S can't go in slot 3. #15 is another conditional question -- let's see what we can figure out from the condition that O is immediately after T before we go to the answer choices... We know that this must mean O is fifth (if O is first, T can't be in front of it) and therefore, T must be fourth. Moving on, since we know that O follows T, it must be true that R precedes T. Therefore, we know R must be third. F must be at least 3 slots away from R. It can't be in front of R (not enough space) and to be at least 3 slots behind R, it would have to be in either slot 6 or 7. Therefore, (E) is the correct answer. ManhattanPrepLSAT2 Atticus Finch Posts: 303 Joined: July 14th, 2009 ### Re: pt 32 S3 G3 At a concert... Hi - I just realized that I answered #15 for you instead of #17 -- here is the explanation for #17, along with #18 as well (per another thread) -- #17 A conditional question, so let's put P into the third slot and S into the sixth and see what we can uncover: _ _ P _ _ S _ L/H Since O needs to be at least 2 spaces away from S, and since O has to be either first or fifth, we can infer that O has to be first: O _ P _ _ S _ L /H At this point, let's think about the either/or chunk TF or RT -- now we can see it has to go in slots 4 and 5, so our options are -- O _ P T F S _ L/H O _ P R T S _ L /H We can infer a bit more from here, but we have what we need in order to answer the question by this point -- either F or T can go in the fifth slot, and the correct answer is C. 18. This condition tells us that somewhere along the line we need to have F _ _ O. Let's see what we can infer... Where can F _ _ O go? Well, since O can only go first or fifth, it can only go in one place: _ F _ _ O _ _ L/H We know that R must be performed at least three spaces away from F, so we know that R can only be performed in either the sixth or seventh slot. Let's put it in both to see what happens: _ F _ _ O R _ L/H _ F _ _ O _ R L/H Could the first one work? Sure -- here's one version that could work: P F S L O R T H Could the second work? Let's try to fill some of it in, using the rules we know... T F _ _ O _ R L/H There are two rules that can't work together in this second scenario -- S needs to be at least two spaces away from O, which means it can only be third, and P needs to come before S, but if S is third there is no place for the P to go. Therefore, R can only go in the sixth slot and (D) is correct. acisne7 Vinny Gambini Posts: 4 Joined: December 04th, 2010 ### Re: pt 32 S3 G3 At a concert... I was looking at the diagram that was posted and with the inferences it shows that S cannot be 2? why is that? I thought it was supposed to be S cannot be 1 because P-S? can you please help me understand why it cannot be 2? ManhattanPrepLSAT2 Atticus Finch Posts: 303 Joined: July 14th, 2009 ### Re: pt 32 S3 G3 At a concert... I just took a look and it seems like I just drew it wrong -- the S cross out is supposed to be under space 1 -- thanks for catching that! i've adjusted the diagram to reflect the change. amywasylyk Forum Guests Posts: 5 Joined: June 20th, 2011 ### Re: Diagram I have more of a general question about the first constraint. On the LSAT, when you have a constraint that says "T is performed EITHER immediately before F OR immediately after R" does that mean there is a potential for an RTF block? Or is that eliminated because of the EITHER/OR language? ManhattanPrepLSAT2 Atticus Finch Posts: 303 Joined: July 14th, 2009 This post thanked 1 time. ### Re: Diagram On the LSAT, the statement either/or does not inherently rule out the possibility of both (though sometimes other factors, such as the design of the game itself, do "naturally" limit the possibility of both). So, if you were at a restaurant in LSAT-land, and a waiter asked if you wanted soup OR salad, "BOTH" would be a completely viable response. VendelaG465 Elle Woods Posts: 66 Joined: August 22nd, 2017 ### Re: Diagram why cant S go in slot 1? can't we do S_ _ _ O?? since it is at least it can have multiple spaces between as well ? ohthatpatrick Atticus Finch Posts: 4257 Joined: April 01st, 2011 ### Re: Diagram The 2nd to last rule says that P is performed before S, so S could never be 1st and P could never be last. Hope this helps.

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polynomial and integer roots I'm doing some homework for a computer science class. It's been so long since I've done math, I have a question that assumes math knowledge that confuses me. Given: Whether a diophantine polynomial in a single variable has integer roots. With the given question I need to determine if that question is solvable using computers. I know how to do that, but I don't the math required to answer this question. So I understand "Whether a .... polynomial in a single variable has integer ...?" My question: • What does diophantine mean • What is an integer root • How do you determine if a diophantine polynomial in a single variable has integer roots? The math behind this question is assumed to be known, once I know the answers to those three questions (really just the last one) I can answer my homework. Note: it may or may not be obvious that this is computable, since I don't know enough about the math to say, I will say a lot of things that seem computable are not unless their input and output are acceptable to a finite precision. • "Diophantine" should just mean that the polynomial has integer coefficients. A root $r$ of a polynomial $p(x)$ is a number such that $p(r) = 0$. As for the third question, there are actually a couple of ways to do this but one is to use the rational root theorem (Google this). – Qiaochu Yuan Mar 21 '12 at 19:53 • That's exactly what I needed. If you want to make it an answer I'll +1 and accept even though it was pretty simple. – brandon Mar 21 '12 at 19:55 • Relevant: Hilbert's 10th problem – user2468 Mar 21 '12 at 19:57 • @J.D. Exactly what I'm working on, I should have known it was a classic problem. Thanks for the reference – brandon Mar 21 '12 at 19:58 There are various definitions of Diophantine equation, not all equivalent. But one standard definition goes as follows. Let $P(x_1,x_2,\dots,x_k)$ be a polynomial with integer coefficients. A solution of the Diophantine equation $P(x_1,x_2,\dots,x_k)=0$ is a $k$-tuple $(x_1,x_2,\dots,x_k)$ of integers that satisfies the equation. An equation is Diophantine partly because of its shape, but much more because of the kinds of solutions we are looking for. General Diophantine equations can be exceedingly difficult. However, in principle one variable equation are simple. We have a polynomial $P(x)$ with integer coefficients. Let $$P(x)=a_0x^n+a_1x^{n-1}+a_2x^{n-2}+\cdots +a_n.$$ Without loss of generality we may assume that the constant term $a_n$ is not equal to $0$. It is straightforward to show that any integer solution of the equation $P(x)=0$ must divide the constant term $a_n$. So there is a simple (in principle!) algorithm for finding all the integer solutions of $P(x)=0$: (i) Find all the divisors (positive and negative) of the constant term and then (ii) Find out, by substitution, which ones of these divisors "work." As you know, factorization of large numbers can be computationally difficult. However, there certainly is an algorithm for factoring. Remark: There is a very famous related problem, called Hilbert's 10th Problem. Hilbert asked for a general algorithm that would, for any polynomial $P$ with integer coefficients, and possibly many variables, determine whether the equation $P=0$ has integer solutions. After earlier progress by a number of people, Matijasevich showed that there is no general algorithm of the type that Hilbert asked for. But as we noted in our answer to your question, there certainly is an algorithm that works for polynomials in one variable. Diophantus himself in his Arithmetica looked mainly for rational solutions. Often, a problem is called Diophantine if we are interested in solutions that are somehow fairly closely related to the integers. Note that (at least to people in Logic) the famous Fermat equation $x^n+y^n=z^n$ is not a Diophantine equation, since the exponents are also variable. Such equations are sometimes called exponential Diophantine, or, more casually, Diophantine. A simple example: Consider the equation $3x^4-12x^3-x^2+4x=0$. We want to find all integer solutions of this equation. First rewrite our equation as $x(3x^3-12x^2-x+4)=0$. This has the obvious solution $x=0$. Any other solutions must be solutions of the equation $$3x^3-12x^2-x+4=0.$$ By the result mentioned in the main post, any integer solution of this equation must divide the constant term $4$. The divisors of $4$ are $\pm 1$, $\pm 2$, and $\pm 4$. Substitute these values in turn for $x$. We find that $x=4$ is a root, but none of the others are. So we have found all the integer solutions of our original equation: they are $x=0$ and $x=4$. • So just so I understand, there is only one root of a given single variable polynomial and that's the value of x such that P(x) = 0? Also, as long as the algorithm eventually halts it's fine. Something like writing out Pi would not be computable by this definition because it's answer isn't expressible as a finite string and it never halts. – brandon Mar 21 '12 at 20:14 • @brandon: No, you can have more than one root. For example, if the polynomial is $(x-1)(x-2)=x^2-3x+2$ there are two roots, 1 and 2. – Ross Millikan Mar 21 '12 at 20:18 • @RossMillikan that makes a lot of sense. I also remember hearing that way before I started college. Thanks for answering, I tend to forget this basic stuff after a while. – brandon Mar 21 '12 at 20:23 A Diophantine equation is one where the variables are required to take integer values. A root of a polynomial is a value of the variable(s) that gives the polynomial the value $0$.

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# Order of Operations Worksheets In mathematics, the order of operations is the order in which factors in an equation are solved when more than one operations exist in the equation. The correct order of operations across the entire field is as follows: Parenthesis/Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Teachers hoping to educate young mathematicians on this principle should emphasize the importance of the sequence in which an equation is solved, but also make it fun and easy to remember the correct order of operations, which is why many teachers use the acronym PEMDAS along with the phrase "Please Excuse My Dear Aunt Sally" to help students remember the proper sequence. 01 of 04 ## Worksheet #1 In the ​first order of operations worksheet (PDF), students are asked to solve problems which put their understanding of the rules and meaning of PEMDAS to the test. However, it's important to also remind students that the order of operations includes the following specifics: 1. Calculations must be done from left to right. 2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first. 3. Exponents (or radicals) must be done next. 4. Multiply and divide in the order the operations occur. 5. Add and subtract in the order the operations occur. Students should be encouraged to simply inside groupings of parentheses, brackets, and braces first, working from the innermost part first then moving outward and simplify all exponents. 02 of 04 ## Worksheet #2 The second order of operations worksheet (PDF) continues this focus on understanding the rules of the order of operations, but can be tricky for some students who are new to the subject. It is important for teachers to explain what would happen if the order of operations is not followed which could drastically impact the solution to the equation. Take question three in the linked PDF worksheet—if the student were to add 5+7 before simplifying the exponent, they might try to simplify 12(or 1733), which is much higher than 7​3+5 (or 348) and the resulting outcome would be even higher than the correct answer of 348. 03 of 04 ## Worksheet #3 Use this order of operations worksheet (PDF) to further test your students, which ventures into multiplication, addition, and exponentials all inside of parentheticals, which can further confuse students who might forget that the order of operations essentially resets within parentheticals and must then occur outside of them. Look at question 12 in the linked printable worksheet—there are addition and multiplication operations that need to occur outside of the parenthesis and there are addition, division, and exponentials inside the parenthesis. According to the order of operations, students would solve this equation by first resolving the parenthesis, which would begin with simplifying the exponential, then dividing it by 1 and adding 8 to that result. Finally, the student would multiply the solution to that by 3 then add 2 to get an answer of 401. 04 of 04 ## Additional Worksheets Use the fourthfifth, and sixth printable PDF worksheets to completely test your students on their comprehension of the order of operations. These challenge your class to use comprehension skills and deductive reasoning to determine how to properly solve these problems. Many of the equations have multiple exponentials so it's important to allow your students plenty of time to complete these more complex math problems. Answers for these worksheets, like the rest linked on this page, are on the second page of each PDF document—make sure you don't hand them out to your students instead of the test! Format mla apa chicago Your Citation Russell, Deb. "Order of Operations Worksheets." ThoughtCo, Aug. 27, 2020, thoughtco.com/order-of-operations-worksheets-2312508. Russell, Deb. (2020, August 27). Order of Operations Worksheets. Retrieved from https://www.thoughtco.com/order-of-operations-worksheets-2312508 Russell, Deb. "Order of Operations Worksheets." ThoughtCo. https://www.thoughtco.com/order-of-operations-worksheets-2312508 (accessed February 4, 2023).

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# Convert mouse coordinates to PDF units using Aspose.PDF for .NET I've been googling for the past couple days on how to convert mouse coordinates to pdf units & this has proven to be very difficult...or at least I haven't been able to find it. I have an X,Y pixel coordinate and I have to place stamp in a pdf document in that location. I've found out that pdf units are different & start from the bottom. I've tried; point=pixel * 96 / 72.....also tried a few other options like pixel * 150/72 & pixel * 72 / 300. While the last attempt produced my results for the X coordinate my Y is way off. An example I have is; x:1341 y:294 I can't believe I'm the first to encounter this so I'm hoping someone can help me out. Steve. Hi Steve, Thanks for your inquiry. After initial investigation, we have logged an investigation ticket as PDFNEWNET-36812 for your requirements. We will keep you updated about the issue progress via this forum thread. Moreover you are right that PDF coordinates starts from left bottom(0,0) and right top is (page width, page height). Aspose.Pdf measuring unit is point and where 1 inch = 72 points and 1 cm = 1/2.54 inch = 0.3937 inch = 28.3 points. Best Regards, Hi Steve, Thanks for contacting support and sorry for the delayed response. The page height and width properties use points as the basic unit, where 1 inch = 72 points and 1 cm = 1/2.54 inch = 0.3937 inch = 28.3 points. When dealing with images, the conversion from point to pixel depends on an image’s DPI (dots per inch) property. For example, if an image’s DPI is 96 (96 pixels for each inch), and it is 100 points high, its height in pixels is (100 / 72) * 96 = 133.3. The general formula is: pixels = ( points / 72 ) * DPI. As per your scenario, you may skip the DPI part and get pixels converted to points using above stated formula. I'm a little confused... I have the pixels in the mouse coordinates....X:1341 & Y:294 which places the point in the upper right corner. I thought the formula was points = pixels/72 * DPI but you have points & pixels switched around a little. I need the point value correct? If I use points=pixels/72 & drop the DPI that puts it at 18 & 4 which is way off. I know that the value needs to be around 300/690 for this particular entry. Regards, Steve. Hi Steve, In order to calculate the point position inside PDF document based on mouse coordinates, you my consider using following formula. Please note that pdfx is x coordinate inside PDF file and pixelX is mouse X coordinates over screen. • pixelX = (pdfX/72)* DPI • pdfX = pixelX * 72 / DPI Where DPI is screen resolution and usually its 96 can be calculated programatically. [C#] float dpiX, dpiY;<o:p></o:p> Graphics graphics = this.CreateGraphics(); dpiX = graphics.DpiX; dpiY = graphics.DpiY; Console.WriteLine("DPIx = " + dpiX + " DPIy " + dpiY); Should you have any further query, please feel free to contact. As you can see by my first post, I've tried your calculation. I am using MVC so I don't have the liberty of using Graphics g = this.CreateGraphics();....or I haven't been able to get it to work on a view. In my example numbers and using your example... X = 1341 * 72/96 = 1005.75 which is outside of the page. Y= 294 * 72/96 = 2.31 which would put it at the bottom of the page. X;1341, Y294 is a mouse point at the top right of the page. As you can see, the points are way off. Am I the first to attempt this? I would have thought this would be fairly standard. Should I take a completely different approach? I do see that one of your competitors has this functionality build in; sourcePoint = pdfDocumentPage.ConvertPoint(PDFCoordinateType.Pixel, PDFCoordinateType.Pdf, destPointPixels); I was hoping for something similar or a workaround to this. I am trying to create a pdf from items that are added to a canvas which contains the original pdf. I could easily create an image from the canvas & just add the image to a pdf but from my experience the image becomes blurry or distorted when printed. Which is why I wanted to attempt to use the original pdf & add the stamps....but if I cannot place them in the exact location of the mouse coordinates then I will have a major issue. Steve. striano: As you can see by my first post, I’ve tried your calculation. I am using MVC so I don’t have the liberty of using Graphics g = this.CreateGraphics();…or I haven’t been able to get it to work on a view. In my example numbers and using your example… X = 1341 * 72/96 = 1005.75 which is outside of the page. Y= 294 * 72/96 = 2.31 which would put it at the bottom of the page. X;1341, Y294 is a mouse point at the top right of the page. As you can see, the points are way off. Am I the first to attempt this? I would have thought this would be fairly standard. Should I take a completely different approach? I do see that one of your competitors has this functionality build in; sourcePoint = pdfDocumentPage.ConvertPoint(PDFCoordinateType.Pixel, PDFCoordinateType.Pdf, destPointPixels); I was hoping for something similar or a workaround to this. I am trying to create a pdf from items that are added to a canvas which contains the original pdf. I could easily create an image from the canvas & just add the image to a pdf but from my experience the image becomes blurry or distorted when printed. Which is why I wanted to attempt to use the original pdf & add the stamps…but if I cannot place them in the exact location of the mouse coordinates then I will have a major issue. Hi Steve, Thanks for sharing the details. I have logged an investigation ticket in our issue tracking system as PDFNEWNET-36826. the development team will investigate this issue in details and will keep you updated on the status of a correction. <o:p></o:p> Any update on this? I have not heard anything in a week now. Steve. Hi Steve, Thanks for your inquiry. I am afraid we have recently noticed the issue and investigation of issue is still pending due to other priority tasks. However, we have requested our development team to investigate it and share their finding at their earliest. We will notify you via this forum thread as soon as we made a significant progress towards issue resolution. We are sorry for the inconvenience caused. Best Regards, Not sure if this issue got resolved. I have the same problem (3 years later moe799: Not sure if this issue got resolved. I have the same problem (3 years later :) Hi Mohamed, I have similar issue like striano. Unable to open above shared link. Error: The specified CGI application encountered an error and the server terminated the process. Thanks for contacting support. Regarding the earlier reported issue, an investigation ticket as PDFNET-36826 is still pending to be resolved. Furthermore, you may also share complete information of the scenario and issue you are facing, by sharing sample PDF document and code snippet. We will test the scenario in our environment and address it accordingly. ScenarioForAspose.zip (3.9 MB) Thanks, Thanks for sharing further information. Please note that Aspose.PDF HTML5 Editor was just a demonstration and example of how you can use API features in order to display PDF files in HTML Canvas and perform some basic operations over them. As it was not product offered by the Aspose, we have discontinued it and are not maintaining it for further issues and updates. Usually, the editor application used to convert PDF pages into images and display converted images in HTML Canvas for further operations (e.g. stamping, annotating, commenting, etc.). Since the coordinates were being calculated with respect to rendered image, stamp in output PDF document was expected to be appeared at different coordinates. Please note that this behavior of the application may also be document specific. We would like to request you to please try specifying desired coordinates for image stamp directly inside PDF using Aspose.PDF API and in case you still face any issue with output PDF document, please let us know by sharing the values of coordinates. We will test the scenario in our environment and address it accordingly. Following are the details of the stamp co-ordinates at document image using html canvas. ``````Ratio: 0.606060606060606 X-Axis: 368.7624750499 Y-Axis: 335.131782945737 Width:200 Height:60 `````` Following are the co-ordinates calculated while puting stamp on actual documents using following formula. ``````double shapeX = (shapes[shapeIndex].x * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 292.05988023952085 double shapeY = (shapes[shapeIndex].y * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 265.42437209302369 double shapeW = (shapes[shapeIndex].w * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 158.40000000000003 double shapeH = (shapes[shapeIndex].h * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 47.52000000000001 double yaxis = (doc.Pages[shapes[shapeIndex].p].Rect.URY - (shapeH + shapeY)); //479.05562790697627 `````` I used attached document. 86_ebrochure.pdf (1.3 MB) Would you please confirm if you have tried adding stamp in PDF using Aspose.PDF for .NET Library in a separate program with same parameters. In case stamp is not appearing at desired position even using Aspose.PDF for .NET separately, please share the sample image file which you are using for stamp. We will test the scenario in our environment and address it accordingly. signature.png (656 Bytes) Please do testing using shared document. Following are the co-ordinates from HTML canvas Ratio: 0.606060606060606 X-Axis: 368.7624750499 Y-Axis: 335.131782945737 Width:200 Height:60 And Actual converted co-ordinates while putting on document are double shapeX = (shapes[shapeIndex].x * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 292.05988023952085 double shapeY = (shapes[shapeIndex].y * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 265.42437209302369 double shapeW = (shapes[shapeIndex].w * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 158.40000000000003 double shapeH = (shapes[shapeIndex].h * 72 / 150) / Convert.ToDouble(shapes[shapeIndex].ratio); // 47.52000000000001 double yaxis = (doc.Pages[shapes[shapeIndex].p].Rect.URY - (shapeH + shapeY)); // 479.05562790697627 I have attached both working and not working document, Please refer these document while testing. NotWorkingForThisDocument.pdf (1.3 MB) WorkingForThisDocument.pdf (287.5 KB) Thanks, We have added an image stamp using above parameters and following code snippet in our environment. For your kind reference, an output PDF is also attached. ``````string sImageUrl = dataDir + "signature.png"; Document pdfDoc = new Document(dataDir + "86_ebrochure.pdf"); ImageStamp imageStamp = new ImageStamp(sImageUrl); imageStamp.Height = 60; imageStamp.Width = 200; imageStamp.XIndent = 368.7624750499; imageStamp.YIndent = 335.131782945737; foreach (Page opage in pdfDoc.Pages)

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# Supermarket 2 A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution. Result x =  750 #### Solution: x + 150 = n x = 2/3 n + 1/6 n n-x = 150 5n-6x = 0 n = 900 x = 750 Calculated by our linear equations calculator. Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! #### To solve this example are needed these knowledge from mathematics: Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? ## Next similar examples: 1. Tickets 1260 tickets sold. On the first day, 80% was sold on the second day was sold. How many tickets were sold first and how much the next day? 2. Banknotes Eva deposit 7800 USD in 50 banknotes in the bank. They had value 100 USD and 200 USD. How many were they? 3. Two cyclists 2 At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,. 4. Triangle 42 Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=? 5. Hyperbola equation Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] 6. Jane plants Jane plants flowers in the garden. If she planted 12 every hour instead of 9 flowers, she would finish with the job an hour earlier. How many flowers does she plant? 7. The size The size of a Trapezium are 3/4×cm, ×cm 2(×+1)cm and 3(×+2)cm long respectively if it's perimeter is 60cm, calculate the length of each side. 8. Peter and Paul Peter and Paul together have 26 years. Four years ago, Paul was twice older than Peter. How much is Paul and how much Peter? 9. Car and motorcyclist A car and a motorcyclist rode against each other from a distance of 190 km. The car drove 10km/h higher than the motorcyclist and started half an hour later. It met a motorcyclist in an hour and thirty minutes. Determine their speeds. 10. Isosceles triangle In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm? 11. Lee is Lee is 8 years more than twice Park's age, 4 years ago, Lee was three times as old. How old was Lee 4 years ago? 12. Rectangular plot The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot. 13. Rectangular triangle The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle? 14. Legs Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects? 15. Father and daughter When I was 11 my father was 35 year old. Now, father has three times older then me. How old is she? 16. Pool If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately? 17. Forestry workers In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days is needed to complete planting trees in nurseries by others, if they will work 10 hours a da

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# Calculating a generalized inverse (Moore–Penrose pseudoinverse) I am considering a graph with $n$ edges with the following nicely structured adjacency matrix: $$A_n= \begin{pmatrix} 0 & 0 & 0 &\cdots & 0 & 0 & 1\\ 0 & 0 & 0 &\cdots & 0 & 1 & 1\\ \vdots & \vdots & & & & \vdots & \vdots\\ 0 & 1 & 1 &\cdots & 1 & 1 & 1\\ 1 & 1 & 1 &\cdots & 1 & 1 & 1\\ \end{pmatrix}.$$ I need to determine the pseudoinverse $L_n^+$ of its Laplacian: $$L_n=\text{diag}(1, ...,n)-A_n.$$ After playing around with Mathematica, $L_n^+$ seems to have a nice structure. However, I am not so familiar with determining pseudoinverses and therefore would like some help in determining this structure. My question is, how would one go about calculating pseudoinverses and is it possible to get a closed-form expression for $L_n^+$ for general $n$? Thanks in advance. • the pseudoinverse of $L_n$ has some obvious structure, each row or column adds up to zero. – Carlo Beenakker Feb 27 '14 at 13:18 • One possibility for you to compute $L_n^+$ is to find a diagonalization $L_n = V_n D_n V_n^*$ ($L_n$ seems to be diagonalizable in this case, I run some Matlab tests) and then put $L_n^+ = V_n D_n^+ V_n^*$, where the pseudoinverse of the diagonal matrix $D_n$ is easily computable: you just have to take the reciprocal of each non-zero element on the main diagonal, and leave the zeros elements at their own place. – Paglia Feb 27 '14 at 13:36 • That indeed looks promising, Paglia. $V_n$ and $V_n^*$ both seem to have a simple structure. – MthQ Feb 27 '14 at 13:53 Let's start by constructing an eigendecomposition of $L_n$. Let $\mathbf{v}_j \in \mathbb{R}^n$, for $1 \leq j \leq \lfloor (n-1)/2 \rfloor$, be the vector defined as follows: • its $j$-th entry is $\sqrt{\frac{2j - n}{2j - n - 1}}$; • its $k$-th entry (for $j+1 \leq k \leq n-j$) is $\frac{-1}{\sqrt{(2j - n)(2j - n - 1)}}$; • all other entries are $0$. Similarly, let $\mathbf{v}_j \in \mathbb{R}^n$, for $n + 1 - \lfloor n/2 \rfloor \leq j \leq n$ be defined by: • its $j$-th entry is $\sqrt{\frac{2j - n - 1}{2j - n}}$; • its $k$-th entry (for $n - j + 1 \leq k \leq j-1$) is $\frac{-1}{\sqrt{(2j - n)(2j - n - 1)}}$; • all other entries are $0$. Finally, define $\mathbf{v}_j \in \mathbb{R}^n$ for $j = n - \lfloor n/2 \rfloor$ to be the zero vector. We have now defined $\mathbf{v}_j$ for all $1 \leq j \leq n$. These vectors are mutually orthonormal eigenvectors for $L_n$, and the eigenvalue corresponding to eigenvector $\mathbf{v}_j$ is exactly $j$ itself: $$L_n = \sum_{j=1}^n j\mathbf{v}_j\mathbf{v}^*_j$$ From this it immediately follows that the pseudo-inverse $L_n^+$ is $$L_n^+ = \sum_{j=1}^n \frac{1}{j}\mathbf{v}_j\mathbf{v}^*_j.$$ Note that I did some trickery here, since one eigenvalue of $L_n$ is always zero -- instead of setting the eigenvalue to zero, I set the corresponding eigenvector $\mathbf{v}_j$ for $j = n - \lfloor n/2 \rfloor$ to be zero, since this made the final answer cleaner in my opinion. Also note that I've stated a bunch of things without proof here. They can be proved easily enough in a brute-force sort of way; it's just messy and not terribly enlightening. • Are you sure about those eigenvectors? When I compute the eigenvectors of $L_n$, they completely consist of integers. Am I not getting something? – MthQ Feb 28 '14 at 9:37 • @Thomas -- I coded my answer above in MATLAB to double-check that it works for $n \leq 10$. The eigenvectors above do consist entirely of integers, up to being normalized (i.e., up to being divided by $\sqrt{(2j-n)(2j-n-1)}$, which is the norm of the integer vector). – Nathaniel Johnston Feb 28 '14 at 12:05 • Ok, I understand now. I guess I should not normalize in order to get nicer expression. Thank you very much – MthQ Feb 28 '14 at 13:10 • @Thomas -- Yep, if you don't normalize then the $\mathbf{v}_j$'s become nicer, but at the expense that the form of $L_n^+$ becomes slightly messier. Explicitly, if $\mathbf{w_j} = \sqrt{(2j-n)(2j-n-1)}\mathbf{v}_j$ (i.e., the all-integer eigenvector) then $L_n^+ = \sum_{j=1}^n \frac{1}{j(2j-n)(2j-n-1)}\mathbf{w}_j\mathbf{w}_j^*$. – Nathaniel Johnston Feb 28 '14 at 13:38 • Is there any kind of proof of your answer? I am very interested in it. – TommasoF Nov 18 '16 at 14:43

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# Rodbourn's Blog posts - 81, comments - 262, trackbacks - 0 ## April 2012 Blog Posts ##### NVIDIA GPU Technology Conference 2012 NVIDIA's CUDA is making headway into the CFD field with some exciting performance increases. As a researcher and developer working with CFD I am interested in learning as much as possible about how to use CUDA (or more generally the GPU) to enhance my simulation capabilities. NVIDIA is hosting a GPU Technology Conference in San Jose, California from May 14th to 17th (2012) which has many sessions on CUDA. In particular they have 29 sessions on CFD which are very interesting: http://tinyurl.com/7apaz7d Definitely check it out if you are interested in numerical simulations!  "GTC advances awareness of high performance computing, and... posted @ Friday, April 27, 2012 7:07 PM | Feedback (4) | Filed Under [ Technical Computing School ] ##### Higher dimensional partial integration This post is in regards higher dimensional partial integration, a topic of vector calculus. Here I show a quick and non-formal way of integrating by parts in higher dimensions. Consider the volume integration over omega which is bounded by the manifold gamma. Omega is assumed an open bounded subset of R^n, and gamma assumed a piecewise smooth boundary. These assumptions are required by Stoke's theorem.    First apply the product rule under the integral. Second, use Stoke's theorem to evaluate the volume integral Here, the surface integral is projected against the outward facing normal, g-hat. The right hand side... posted @ Wednesday, April 25, 2012 10:19 PM | Feedback (7) | Filed Under [ Mathematics ] ##### Some essential tools for new graduate students A higher quality of work is expected of graduate students by advisors, peers and others. One of the best ways to start producing a higher quality of work is to start using more advanced tools to produce your work. These particular tools will help you produce material that visually impresses and assists you in producing graduate student quality material. LaTeX LaTeX is a "document markup language and document preparation system" that makes your work of print quality. Instead of a "what you see is what you get" (WYSIWYG) editing paradigm used in visual programs such as Microsoft... posted @ Wednesday, April 25, 2012 4:06 PM | Feedback (5) | Filed Under [ School ] ##### Simple method to constrain stored procedures by a collection Passing a collection of ID's to filter a SQL query within a stored procedure is not natively supported. Consider this article which discusses methods for passing arrays into a stored procedure. Constraining a stored procedure's query has a simple work around, however. Passing the ID collection as a comma deliminated string allows the query to use LIKE to constrain the results. Note that the preceding and trailing commas are necessary. An example demonstrates how to do this easily.  DECLARE @Ids varchar(max); set @Ids = ',1,2,3,4,5,'; Select * from [TableName]     WHERE @Ids LIKE ('%,' + cast(TableID as varchar(50)) + ',%') posted @ Saturday, April 7, 2012 4:12 PM | Feedback (2) | Filed Under [ Web Programming ] Powered by:

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{[ promptMessage ]} Bookmark it {[ promptMessage ]} # pset1 - the front with speed u with respect to the train... This preview shows page 1. Sign up to view the full content. Physics 260, Problem Set 1 due: Tuesday, September 20 at Noon Please place your completed problem sets in the “Physics 260” box in the physics department mailroom (Rutherford 103b). You are encouraged to discuss these problems with your colleagues, but you must write up your own solutions; the solutions you hand in should reflect your own work and understanding. Late problem sets will be penalized 10% per day late, unless an extension has been obtained from me or a TA before the due date. Reading : Chapter 2 of Bernstein et al. 1. Chapter 2, problem 6. 2. Chapter 2, problem 8. 3. Chapter 2, problem 10. 4. Chapter 2, problem 18. 5. A train of length L (as measured in the frame where the train is at rest) moves a speed v with respect to the ground. When the front of the train passes a tree on the ground, a ball is simultaneously (as measured in the ground frame) thrown from the back of the train toward This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: the front with speed u with respect to the train. Show that it is possible to choose a value of u so that the ball hits the front of the train simultaneously (as measured in the train frame) with the tree passing the back of the train. You should find that this can only happen if v is less than a critical value v which you should compute. Draw a diagram of this setup. 6. Suppose that I observe two events which happen at positions x 1 and x 2 and at times t 1 and t 2 . Under what circumstances is it possible to find an observer moving at constant velocity who will see these events happening simultaneously? Draw a diagram of this setup. What is the velocity (relative to me) of the observer who sees these events as simultaneous? What is this velocity in the limit where | x 1-x 2 | approaches c | t 1-t 2 | ? 1... View Full Document {[ snackBarMessage ]}

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Home > INT3 > Chapter 1 > Lesson 1.2.2 > Problem1-87 1-87. Solve for $w$ in each equation. 1. $w^2+4w=0$ $w(w+4)=0$ $w=0$ or $w=−4$ 1. $5w^2-2w=0$ Start by factoring. 1. $w^2=6w$ Move both $w$'s to the same side and then factor.

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Time Epicurus, 341~270 BCE. Drawn from a damaged Roman copy of a Greek original now in the Palazzo Massimo alle Terme, Rome. was a Roman poet best known for proclaiming the physics of which was taught at Athens around 300 BCE. According to Lucretius, "… time by itself does not exist; but from things themselves there results a sense of what has already taken place, what is now going on and what is to ensue. It must not be claimed that anyone can sense time by itself apart from the movement of things or their restful immobility …"1 The WikiMechanics approach to understanding time follows this Epicurean recipe. First we consider "things themselves" by carefully defining particles. Then we characterize "the movement of things" from a particle's momentum $p$. Next "their restful immobility" is represented by the rest mass $m$. And finally these numbers are combined to define the period $\hat{\tau}$ as \begin{align} \hat{\tau} \equiv \frac{ h }{ \sqrt{ c^{2}p^{2} + m^{2}c^{4} \vphantom{\sum^{2}} \; } } \end{align} Recall that \begin{align} E \equiv \sqrt{ c^{2}p^{2} + m^{2}c^{4} } \end{align} is the mechanical energy, and that Planck's postulate asserts that $E =h \nu$ where $\nu$ is the frequency. So the foregoing definition implies that \begin{align} \hat{\tau} = \frac {h }{ E } = \frac {1 }{ \, \nu \, } \end{align} Now let particle $\sf{P}$ be characterized by some repetitive chain of events $\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1}, \sf{\Omega}_{2} , \sf{\Omega}_{3} \; \ldots \; \sf{\Omega}_{\it{k}} \; \ldots \; \right)$ where each orbit $\sf{\Omega}$ is described by its period $\hat{\tau}$. Definition: The time of occurrence of event $\sf{\Omega}_{\it{k}}$ is \begin{align} t_{k} \equiv t_{0} + \epsilon_{t} \! \sum_{i=1}^{k} \hat{\tau}_{i} \end{align} where $\epsilon_{t}$ notes the direction of time. The value of the original event $t_{0}$ is arbitrary. Let $\Psi$ be historically ordered, then $\epsilon_{t}=1$ and the time of occurrence is directly given by a sum of periods. The period depends on a particle's momentum, which in-turn depends on whatever frame of reference is used to describe a particle's motion. So the time is frame-dependent too. If $p = 0$ then $t$ is called the proper time. Please notice that this quantity has been entirely established by a systematic description of sensation. ## Time Dilation Let P be represented by some repetitive chain of events that are arranged in historical order $\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1}, \sf{\Omega}_{2}, \sf{\Omega}_{3} \; \ldots \; \sf{\Omega}_{\it{i}} \; \ldots \; \sf{\Omega}_{\it{f}} \; \ldots \; \right)$ And let each orbital event $\sf{\Omega}$ be described by $t$ so that $\sf{P}$ can also be described by an ordered set of occurrence times. Consider a pair of events $\sf{\Omega}_{\it{i}}$ and $\sf{\Omega}_{\it{f}}$ where $\it{i} < \it{f}$. Since $\Psi$ is in historical order we call them the initial and final events of the pair. Definition: the elapsed time between these events is $\Delta t \equiv t_{f} - t_{i}$ If $\sf{P}$ is isolated and the frame of reference is ideal then the mechanical energy and momentum do not change from event to event along the chain $\Psi$. For these conditions, the period $\hat{\tau}$ is constant too. But the time coordinate is defined by a sum of periods, so the elapsed time can be written as $\Delta t = \left(\, f-i \right) \hat{\tau}$ We evaluate this quantity for a material particle that is considered to be a clock in motion. Let P be described by $E$ its mechanical energy and $m$ its rest mass. These are related by $E = \gamma m c^{2}$ where $\gamma$ is the Lorentz factor. Then the period is given by \begin{align} \hat{\tau} \, = \frac{h}{E } = \frac{ h }{ \gamma m c^{2} } \end{align} So in terms of the mass \begin{align} \Delta t = \frac{ h \, (\, f-i \, ) }{ \gamma m c^{2} } \end{align} If P is a clock, this is the elapsed time that it would indicate between events. For comparison, set $\gamma = 1$ to define \begin{align} \Delta t ^{\ast} \equiv \frac{ h \, (\, f-i \, ) }{ m c^{2} } \end{align} This is the elapsed time that would be recorded if P was at rest, it is called the proper elapsed time. The two quantities are related as Albert Einstein, 1879—1955. \begin{align} \Delta t^{\ast} = \gamma \Delta t \end{align} The Lorentz factor for a particle in motion is always greater than one, $\gamma ≥ 1$. So a moving particle always experiences less elapsed time than a stationary particle, $\Delta t ≤ \Delta t^{\ast}$. This effect is called time dilation. ## Measuring Elapsed Time According to time is what a clock tells.2 So here is a generic description of how to determine elapsed time using a clock. Let particle $\sf{P}$ be characterized by some repetitive chain of events noted as $\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1}, \sf{\Omega}_{2} \; \ldots \; \sf{\Omega}_{\it{i}} \; \ldots \; \sf{\Omega}_{\it{f}} \; \ldots \; \right)$ Consider measuring $\Delta t$ between events $\sf{\Omega}_{\it{i}}$ and $\sf{\Omega}_{\it{f}}$. This quantity depends on the frame of reference $\sf{F}$ which is represented by another chain of events $\Psi ^{\sf{F}} = \left( \sf{F}_{1}, \sf{F}_{2} \; \ldots \; \sf{F}_{\it{j}} \; \ldots \; \sf{F}_{\it{k}} \; \ldots \; \right)$ Since $\sf{F}$ is a reference frame, we assume that every report about $\sf{P}$ is accompanied by an observation of $\sf{F}$ so that events of $\sf{F}$ and $\sf{P}$ can be associated in pairs like $\left\{ \sf{P}_{\it{i}}, \sf{F}_{\it{j}} \right\}$ and $\left\{ \sf{P}_{\it{f}}, \sf{F}_{\it{k}} \right\}$ To make a laboratory measurement of elapsed time first select some clock $\mathbf{\Theta}$ that is presumably part of the frame of reference $\sf{F}$. Let this clock be calibrated so that its period $\; \hat{\tau}^{ \mathbf{\Theta}}$ is a known quantity. Observe events to determine the numbers $j$ and $k$ by counting clock cycles. Report the result as $\Delta t ^{\sf{P}} = \left( k-j \right) \hat{\tau}^{ \mathbf{\Theta} }$ Sensory interpretation: The elapsed time while experiencing one bundle of sensation $\sf{\Omega}$, is the period $\hat{\tau}$. This period is the reciprocal of the frequency, which is proportional to the number of quark bundles observed per solar day. So the period can be interpreted as some fraction of a day. And the elapsed-time is based mostly on the reference sensation of seeing the Sun. However the direction of time is defined from thermal sensations, that are ultimately refered to the sensations of touching steam and ice. Next step: cause and effect. page revision: 716, last edited: 05 Nov 2019 12:34

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1. ## A Physics [Quantum Theory] Problem... help please... "An instable nucleus that was initially at rest decays into a nucleus of fermium-252 containing 100 protons and 152 neutrons and an alpha particle that has a kinetic energy of 8.42 MeV. The atomic masses of helium-4 and Fermium-252 are 4.00260 u and 252.0849 u" I would like to know how to calculate 1. the atomic number of the original unstable nucleaus. 2. the Velocity of the alpha particle. And could someone please explain to me breifly where does this KE of the alpha particle come from? I was a little bemused by that bit in my lesson. And also, hypothetically, say the fermium-252 nucleus went through a decay which a Beta- particle was produced, how does this affect the atomic number of the nucleus? Please explain this to me. I was also confused by that. Thanks. 2. Originally Posted by apple12 "An instable nucleus that was initially at rest decays into a nucleus of fermium-252 containing 100 protons and 152 neutrons and an alpha particle that has a kinetic energy of 8.42 MeV. The atomic masses of helium-4 and Fermium-252 are 4.00260 u and 252.0849 u" I would like to know how to calculate 1. the atomic number of the original unstable nucleaus. 2. the Velocity of the alpha particle. And could someone please explain to me breifly where does this KE of the alpha particle come from? I was a little bemused by that bit in my lesson. And also, hypothetically, say the fermium-252 nucleus went through a decay which a Beta- particle was produced, how does this affect the atomic number of the nucleus? Please explain this to me. I was also confused by that. Thanks. I suppose topsquawk deserves a rest. Briefly: $\alpha$-decay: $^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^{4}_{2}\text{He}$. Therefore $A - 4 = 152 \Rightarrow A = 156$ and $Z - 2 = 100 \Rightarrow Z = 102$. You're told the KE of the alpha particle. Convert this energy from MeV into J (that is, convert to SI units). Now use the formula (that you should know) that links KE and velocity and solve for v (the unit will be m/s) .... There's a mass difference between the mass of the original nucleus and the masses of the helium-4 (the alpha particle) and Fermium-252. And you know $E = mc^2 \, ....$ $\beta$-decay: $^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + e^{-} + \nu$. 3. Originally Posted by apple12 And could someone please explain to me breifly where does this KE of the alpha particle come from? I was a little bemused by that bit in my lesson. Some of the mass-energy coming from the decay is changed to momentum (and hence KE) during the decay, otherwise we woudn't see the decay products and know that a decay had occured. Remember that all of the mass-energy from the decay has to be used and that the daughter nucleus (the nucleus left over after the decay) is going to be basically stationary, so that leaves a relatively large amount of energy left over for the KE of the escaping particles. -Dan

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# Math Equation Project More Options: Make a Folding Card #### Storyboard Description This storyboard does not have a description. #### Storyboard Text • I'm feeling a bit better than I did right after that car accident so maybe I have some time to do some of that math homework Mia sent me from class while I was out of this week. • There's my bag! Ugh but now I have to start that annoying math homework. • Woah! That car accident must have done something to me? I'm looking at my recent homework on equations and can do the work all in my head. Just looking at it I know the answer. I used to suck at math... • Hmm. 5x-3=4(x+2)+x. Lets see here... • First, we distribute 4(x+2), this will equal to 4x+8. Our equation will then be 5x-3=4x+8+x. Additionally, we add 4x by x and get 5x resulting in 5x+8. Our final answer would be -3=8 this would be no solution! • Wow! Am I some kind of math super hero? Maybe I should just be a math tutor, its the same thing I guess. Well at least I finished that homework. Just Created with Storyboard That Explore Our Articles and Examples Try Our Other Websites! Photos for Class – Search for School-Safe, Creative Commons Photos! (It Even Cites for You!) Quick Rubric – Easily Make and Share Great Looking Rubrics!

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## Duotrigintillinovenseptuagintatrecentillion A Duotrigintillinovenseptuagintatrecentillion (1 Duotrigintillinovenseptuagintatrecentillion) is 10 to the power of 97140 (10^97140). This is a stupendously astronomical number! ## How many zeros in a Duotrigintillinovenseptuagintatrecentillion? There are 97,140 zeros in a Duotrigintillinovenseptuagintatrecentillion. ## What's before Duotrigintillinovenseptuagintatrecentillion? A Duotrigintillioctoseptuagintatrecentillion is smaller than a Duotrigintillinovenseptuagintatrecentillion. ## What's after Duotrigintillinovenseptuagintatrecentillion? A Duotrigintillioctogintatrecentillion is larger than a Duotrigintillinovenseptuagintatrecentillion. ## Duotrigintillinovenseptuagintatrecentillionaire A Duotrigintillinovenseptuagintatrecentillionaire is someone whos assets, net worth or wealth is 1 or more Duotrigintillinovenseptuagintatrecentillion. It is unlikely anyone will ever be a true Duotrigintillinovenseptuagintatrecentillionaire. If you want to be a Duotrigintillinovenseptuagintatrecentillionaire, play Tap Tales! ## Is Duotrigintillinovenseptuagintatrecentillion the largest number? Duotrigintillinovenseptuagintatrecentillion is not the largest number. Infinity best describes the largest possible number - if there even is one! We cannot comprehend what the largest number actually is. ## Duotrigintillinovenseptuagintatrecentillion written out Duotrigintillinovenseptuagintatrecentillion is written out as: 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00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# Games Browse our primary games, many of which are perfect for use in the mathematics classroom. ### Do You Measure Up? ##### Age 7 to 11 Challenge Level: A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown. ### Sliding Puzzle ##### Age 5 to 16 Challenge Level: The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves. ### Winning Lines ##### Age 7 to 16 An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. ### Troublesome Triangles ##### Age 7 to 14 Challenge Level: Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems. ### Incey Wincey Spider for Two ##### Age 5 to 7 Challenge Level: Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe? ### Ten-frames Games ##### Age 3 to 7 These games use ten-frames to develop children's 'sense of ten'. ### Statement Snap ##### Age 7 to 14 Challenge Level: You'll need to know your number properties to win a game of Statement Snap... ### Poker Bingo ##### Age 5 to 11 Challenge Level: A game played with a standard pack of cards. ### Put Yourself in a Box ##### Age 7 to 11 Challenge Level: A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent. ### Seega ##### Age 5 to 18 An ancient game for two from Egypt. You'll need twelve distinctive 'stones' each to play. You could chalk out the board on the ground - do ask permission first. ### Learning Mathematics Through Games Series: 1. Why Games? ##### Age 5 to 14 This article supplies teachers with information that may be useful in better understanding the nature of games and their role in teaching and learning mathematics. ### Games Related to Nim ##### Age 5 to 16 This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning. ### James's Code Challenge ##### Age 7 to 18 Challenge Level: The Enigma Project's James Grime has created a video code challenge. Watch it here! ### Shut the Box for Two ##### Age 5 to 7 Challenge Level: Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice? ### For Two ##### Age 5 to 11 Here are some games for you to play with an adult. They are all based on popular NRICH games.

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https://e2e.ti.com/support/logic-group/logic/f/logic-forum/1040031/sn74avc2t244-voh-and-vol?tisearch=e2e-sitesearch&keymatch=SN74AVC2T244

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If you have a related question, please click the "Ask a related question" button in the top right corner. The newly created question will be automatically linked to this question. # SN74AVC2T244: VOH and VOL Part Number: SN74AVC2T244 Hello Experts, I would like to understand VOH and VOL at VCCA=1.8V/VCCB=3.3V condition. According to datasheet, VOH and VOL vary by output current and power supply voltage. How can I understand VOH/VOL? VOH(min)=VCCB-2V, VOL(max)=0.2V even if output current is not 500uA? Best Regards, Fujiwara • The test conditions show the maximum current at which the behaviour is guaranteed. At a fixed supply voltage, the output resistance is constant, so for currents that are smaller than the test condition, the voltage drop also is smaller by the same factor. See [FAQ] What is the output voltage (VOH or VOL) when the output current is X or the supply voltage is Y? • The FAQ is one power supply voltage but SN74AVC2T244 has two power supply voltage, VCCA and VCCB. To calculate VOH and VOL, VCCA voltage need to be considered? Or it considers VCCB voltage only? If it need to consider VCCB only, below calculation is reasonable? [conditions] VCCA=1.8V, VCCB=3.3V, Iout=20mA [VOH] used condition: IOH = –24 mA; VI=VH. Output resistance: (3.0V-2.2V)/24mA=33.3ohm. Voltage drop: 33.3ohm x 20mA=0.67V VOH: 3.3V-0.67V=2.63V [VOL] used condition: IOH = 24 mA; VI=VH. Output resistance: 0.55V/24mA=22.9ohm. VOL: 22.9ohm x 20mA=0.46V Best Regards, Fujiwara • The voltages at the outputs are independent from the input supply voltage. Your calculations are correct. (The specified values are for the worst case; the typical output resistance might be roughly half that.)

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https://www.ehow.com/how_5584167_make-pipes-beadboard-paneling-bathroom.html

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# How to Make Cuts Around Pipes in Beadboard Paneling in a Bathroom eHow may earn compensation through affiliate links in this story. Learn more about our affiliate and product review process here. #### Things You'll Need • Tape measure • Pencil • Compass • Drill • Drill bit the same size as smaller pipes • Jigsaw for larger holes such as drains • Safety glasses or goggles When installing beadboard paneling in a bathroom, it will likely be necessary to cut holes for pipes to fit through the paneling. There may be pipes for the toilet, sink or tub that go through the wall and will require a special round cut to create the hole for the pipes. With commonly available tools and careful measuring, you can create a neat and professional-looking hole in beadboard paneling around bathroom pipes. ## Step 1 Turn off the water supply and disconnect the pipe from the fixture as close to the wall as possible. Video of the Day ## Step 2 Measure the distance from the floor to the bottom of the pipe. Subtract 1/8 inch from that measurement then measure and mark with a horizontal line about as wide as the pipe the same distance from the bottom edge of the beadboard paneling. ## Step 3 Measure the distance from the last piece of installed paneling to the edge of the pipe. Subtract 1/8 inch from that measurement then measure and mark with a vertical line about as wide as the pipe the same distance from the edge of the piece to be installed. This vertical line should slightly overlap the horizontal line. ## Step 4 Measure the width of the bathroom pipe. Divide the width of the pipe by half and add 1/8 inch. Using this measurement, draw a second horizontal line above the horizontal line already on the beadboard. Use this measurement to draw a second vertical line that crosses the second horizontal line. This intersection is where you will locate the point of the compass. ## Step 5 Set the point of the compass where the second horizontal and vertical lines meet. While holding the point on the intersection, move the pencil side of the compass to the original bottom line. Rotate the compass to draw a circle that will be cut out for the pipe. The circle made with the compass should touch both the original bottom and side lines. If it does not touch both lines, check the original measurements. ## Step 6 Drill the hole with a drill bit slightly larger than the bathroom pipe if available. If the hole is for a large drain and a drill bit is not available, cut the hole with a jig saw. Use a drill to create a hole in the area to be removed for the pipe. Place the jigsaw blade in the hole and cut at an angle towards the circle drawn with the compass. Continue cutting on the circle until the area for the pipe is cut out. ## Step 7 Place the bathroom beadboard over the pipe and fasten to the wall. Reconnect the pipe and turn on the water supply. #### Tip Use the pencil lightly and remove remaining lines with sandpaper before painting or staining. #### Warning Always wear goggles or safety glasses while working with power tools.

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https://www.ademcetinkaya.com/2022/10/machine-learning-stock-prediction-azpn.html

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In the business sector, it has always been a difficult task to predict the exact daily price of the stock market index; hence, there is a great deal of research being conducted regarding the prediction of the direction of stock price index movement. Many factors such as political events, general economic conditions, and traders' expectations may have an influence on the stock market index. There are numerous research studies that use similar indicators to forecast the direction of the stock market index. We evaluate Aspen Technology prediction models with Modular Neural Network (Market Direction Analysis) and Ridge Regression1,2,3,4 and conclude that the AZPN stock is predictable in the short/long term. According to price forecasts for (n+4 weeks) period: The dominant strategy among neural network is to Hold AZPN stock. Keywords: AZPN, Aspen Technology, stock forecast, machine learning based prediction, risk rating, buy-sell behaviour, stock analysis, target price analysis, options and futures. ## Key Points 1. Stock Forecast Based On a Predictive Algorithm 2. What are the most successful trading algorithms? 3. Decision Making ## AZPN Target Price Prediction Modeling Methodology Stock markets are affected by many uncertainties and interrelated economic and political factors at both local and global levels. The key to successful stock market forecasting is achieving best results with minimum required input data. To determine the set of relevant factors for making accurate predictions is a complicated task and so regular stock market analysis is very essential. More specifically, the stock market's movements are analyzed and predicted in order to retrieve knowledge that could guide investors on when to buy and sell. We consider Aspen Technology Stock Decision Process with Ridge Regression where A is the set of discrete actions of AZPN stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4 F(Ridge Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (Market Direction Analysis)) X S(n):→ (n+4 weeks) $\begin{array}{l}\int {e}^{x}\mathrm{rx}\end{array}$ n:Time series to forecast p:Price signals of AZPN stock j:Nash equilibria k:Dominated move a:Best response for target price For further technical information as per how our model work we invite you to visit the article below: How do AC Investment Research machine learning (predictive) algorithms actually work? ## AZPN Stock Forecast (Buy or Sell) for (n+4 weeks) Sample Set: Neural Network Stock/Index: AZPN Aspen Technology Time series to forecast n: 06 Oct 2022 for (n+4 weeks) According to price forecasts for (n+4 weeks) period: The dominant strategy among neural network is to Hold AZPN stock. X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.) Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.) Z axis (Yellow to Green): *Technical Analysis% ## Conclusions Aspen Technology assigned short-term B1 & long-term B3 forecasted stock rating. We evaluate the prediction models Modular Neural Network (Market Direction Analysis) with Ridge Regression1,2,3,4 and conclude that the AZPN stock is predictable in the short/long term. According to price forecasts for (n+4 weeks) period: The dominant strategy among neural network is to Hold AZPN stock. ### Financial State Forecast for AZPN Stock Options & Futures Rating Short-Term Long-Term Senior Outlook*B1B3 Operational Risk 5246 Market Risk4454 Technical Analysis7234 Fundamental Analysis8945 Risk Unsystematic4946 ### Prediction Confidence Score Trust metric by Neural Network: 80 out of 100 with 644 signals. ## References 1. K. Tumer and D. Wolpert. A survey of collectives. In K. Tumer and D. Wolpert, editors, Collectives and the Design of Complex Systems, pages 1–42. Springer, 2004. 2. Imbens GW, Lemieux T. 2008. Regression discontinuity designs: a guide to practice. J. Econom. 142:615–35 3. A. Tamar, Y. Glassner, and S. Mannor. Policy gradients beyond expectations: Conditional value-at-risk. In AAAI, 2015 4. Rosenbaum PR, Rubin DB. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70:41–55 5. R. Howard and J. Matheson. Risk sensitive Markov decision processes. Management Science, 18(7):356– 369, 1972 6. Lai TL, Robbins H. 1985. Asymptotically efficient adaptive allocation rules. Adv. Appl. Math. 6:4–22 7. Swaminathan A, Joachims T. 2015. Batch learning from logged bandit feedback through counterfactual risk minimization. J. Mach. Learn. Res. 16:1731–55 Frequently Asked QuestionsQ: What is the prediction methodology for AZPN stock? A: AZPN stock prediction methodology: We evaluate the prediction models Modular Neural Network (Market Direction Analysis) and Ridge Regression Q: Is AZPN stock a buy or sell? A: The dominant strategy among neural network is to Hold AZPN Stock. Q: Is Aspen Technology stock a good investment? A: The consensus rating for Aspen Technology is Hold and assigned short-term B1 & long-term B3 forecasted stock rating. Q: What is the consensus rating of AZPN stock? A: The consensus rating for AZPN is Hold. Q: What is the prediction period for AZPN stock? A: The prediction period for AZPN is (n+4 weeks)

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https://socratic.org/questions/what-is-3-46-10-2

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# What is 3.46 *10^2? This is $346$ ${10}^{2}$ is $100$ $3.46 \times 100 = 346$

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## 2015-05-05 ### Raising Ship By Raising Shields Y'know, shields are wonderful things.   One thing we have never seen anyone use them for, however, is lift-off. Inspired by Buckminster Fuller, I was thinking the other day of using shields in a Cloud Nine fashion, making a big enough shield bubble to let minor air temperature changes float the ship. But, vacuum would work better, even if it was a bit more taxing to the shields due to pressure difference.   Start with skin-tight shields and then expand them outward laterally and upward, leaving a vacuum in their wake.  At a quoted lifting force of 1.28 grams per liter (based on the displaced mass of air at sea level), my math suggests that a 700,000 tonne starship like Voyager could be lifted by a vacuum volume of 546,875,000 cubic meters. That's a sphere of 1,014 meters in diameter, or a hemisphere of about twice that depending on how you fit the ship in exactly. We have seen the Enterprise extend shields to protect a ship at a stated range of five kilometers, IIRC, so in principle it might be doable.  And that doesn't even bring subspace mass-lightening into the equation. Certainly it would be an interesting way to soft-land a starship rather than crash*, assuming you can figure out how to drop the shield gently on touchdown.   I can't imagine a sudden shut-off, producing a mad rush as air tried to fill a kilometer-wide void, would be healthy for any ship that needed to be using the technique in the first place. (* In the case of the E-D saucer, of course, it seems this wouldn't be useful as the shields did not seem to be online. ) 1. If you can steadily expand the shields you can probably steadily contract them as well, that would work for landing. 2. Naturally, but the concern I was pointing out (valid for any point of the flight, really) is graceful shutdown. A parachute, for instance, is simple and dumb once deployed successfully, as any good passive system should be. An active system like the shield idea has less graceful failure modes. One can imagine, then, a ship without landing legs trying to set down and fritzing the shields while they are still rather expanded (so as to prevent too big a thump from too high a velocity), causing a veritable implosion of local atmosphere. Bystanders would consider that altogether quite rude. :-) 1. Your reasoning for not liking the idea seems like it would apply to blimps, hot air balloons, dirigibles, and any other airship, and that leads me to question if it is a valid argument? Using the shields in such a way would simply be creating a vacuum airship after all. http://en.wikipedia.org/wiki/Vacuum_airship 2. Blimps and balloons and such don't land with their bag on the ground. 3. You seem to be assuming that the shield's shape must be roughly spherical with the ship in the center? Most settings that I can think of that uses shields are usually flexible with the shapes they can generate, and it would make sense for the ship to be at the bottom of the bubble for landings. Amusingly, the idea you seem to dislike was in the original version of episode 4. Luke's X-34 had a shield bubble under, but this effect was removed in later releases. 3. The ship doesn't need to be in the center, just within it. I always imagined it at the bottom of the shield, as on take-off… I am not sure how that didn't translate. I still don't know what idea it is I supposedly dislike, either, nor do I know what an X-34 is. Do you mean the T-16, slayer of womp-rats? (Googles)… ah, I presume the EU gave Luke's landspeeder a designation. Bleh. Anyway, that wasn't a shield, just a visible repulsor cushion. It's gone now anyway. 4. 1) If you are picturing the ship at the bottom on take off and landing then what would be the problem? If the shield is basically hull hugging then there isn't a problem. 2) There's no need to bite my head off. X-34 Landspeeder is the designation given at starwars.com for the speeder model Luke sold in episode 4. 1. I am not biting, we just can't communicate. The problem with landing is fritzing the shields on ground touchdown. Does it help you if I point out that I have at no point expressed a concern with the ship falling? If that is so, then perhaps you'll understand that is not the problem I was talking about. Implosion of the air is. As for StarWars.com, the new Disney canon has nullified its use as a source of nomenclature for me. They're accepting all kinds of crap names now.

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All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars perplexus dot info An Odd Pyramid (Posted on 2003-10-14) Consider the numerical pyramid below, formed by simply putting down the series of odd numbers into a pyramid. ``` 1 3 5 7 9 11 13 15 17 19 . . . ``` Find a formula for the sum of the numbers in the nth row, and prove it. See The Solution Submitted by DJ Rating: 4.1667 (12 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Puzzle Solution | Comment 20 of 21 | The sequence 1,3,7,13..... describes the first element of successive rows, while the sequence 1,5,11, 19,... denotes the last element of the successive rows. Both the above sequence correspond to arithmetico geometric series (reference: http://www.artofproblemsolving.com/Wiki/index.php/Arithmetico-geometric_series ). Let s(n) = 1 + 3 + 7 +  13 + .....+ t(n), and: s(n) =        1 + 3 +   7 + .... + t(n-1) + t(n) So, t(n) = 1 + (2+4+6+....+2(n-1)) = 1 + n(n-1) = n^2 - n + 1 Thus, the first element of the nth row is n^2 - n + 1. In a similar manner, it can easily be determined that the last element of the nth row is n^2+n-1. Now, the sum of all the elements of the nth row = (n^2 - n+ 1) + (n^2 - n+ 3)+......+ (n^2 + n - 1) In the above series, the first term(f) = n^2-n=1; last term (l) = n^2+n-1; common difference(d) = 2; and so: The number of terms(t) in the series = [(n^2 + n -1)- (n^2 - n+ 1)]/2 + 1 = n Consequently, the required sum = (t/2)*(f+s) = (n/2)*(2*n^2) = n^3 Edited on October 26, 2007, 5:45 am Posted by K Sengupta on 2007-10-26 05:42:44 Search: Search body: Forums (0) Random Problem Site Statistics Unsolved Problems Top Rated Problems This month's top Most Commented On Chatterbox:

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https://math.stackexchange.com/questions/864838/question-on-moment-of-inertia-about-center-of-mass-of-a-smooth-plane-curve

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# Question on Moment of inertia about center of mass of a smooth plane curve. This question is in continuation to this and motivated to answer this question. If I have an answer to it, then I can prove a special case of this question. Consider two smooth plane curves $C \equiv (X_C(s),Y_C(s))$ and $S \equiv (X_S(s),Y_S(s))$ represented in arc length parametrization. Curve $C$ is asymptotic to a straight line $(a,s)$ in arc length parametrization, where $a$ is a constant. As $s\to\infty$ the curve $S$ approaches (converges) to a point in the plane, as $s\to\infty$. Now we define moment of intertia about its center of mass, of a segment of curve $C$ between $s=s_1$ and $s = s_2$ as $$I_C(s_1,s_2) = \int_{s1}^{s_2} ((X_C(s)-X_{C_{cm}})^2 + (Y_C(s)-Y_{C_{cm}})^2) ds$$ where $(X_{C_{cm}},Y_{C_{cm}})$ is the center of mass of the segment under consideration given by $X_{C_{cm}} = \frac{1}{s_2-s_1}\int_{s_1}^{s_2}X_C(s)ds$ and $Y_{C_{cm}} = \frac{1}{s_2-s_1}\int_{s_1}^{s_2}Y_C(s)ds$. Similarly $$I_S(s_1,s_2) = \int_{s1}^{s_2} ((X_S(s)-X_{S_{cm}})^2 + (Y_S(s)-Y_{S_{cm}})^2) ds$$ where $X_{S_{cm}} = \frac{1}{s_2-s_1}\int_{s_1}^{s_2}X_S(s)ds$ and $Y_{S_{cm}} = \frac{1}{s_2-s_1}\int_{s_1}^{s_2}Y_S(s)ds$. I'd like to prove/disprove the following statement. Statement : Given any $s = s_1$ we can always find a sufficiently large $L$ such that for all $s_2 > L$, we have $I_C(s_1,s_2) > I_S(s_1,s_2)$. • mathoverflow.net/a/175862/14414 – Rajesh Dachiraju Jul 12 '14 at 4:30 • In case it has already occurred to you to do so: It might be helpful to first simplify the problem through the parallel axis theorem, which states that the moment of inertia $I^{(\text{p})}$ about a point $\text{p}$ is equal to the moment of inertia $I^{(\text{cm})}$ about the center of mass $\text{cm}$ (specially, a parallel axis through the center of mass) plus the squared perpendicular distance between the points $\text{p}$ and $\text{cm}$: $I^{(\text{p})}=I^{(\text{cm})}+\|\text{p}-\text{cm}\|^2$. This means it suffices to solve the special case in which the C.o.M. is at the origin. – David H Jul 12 '14 at 5:24 • ^In case it hasn't occurred to you, I meant to say. Oops – David H Jul 12 '14 at 5:37 • @DavidH : I know. The CoM can safely assumed to be origin without any loss to the problem. Infact thats what RobJohn did in his answer : math.stackexchange.com/a/618993/2987 – Rajesh Dachiraju Jul 12 '14 at 5:41 • @DavidH : In case you were wondering, Altogether elimination of CoM is not possible$(X_{cm},Y_{cm})$ is the center of mass of the segment of curve we are considering, and not a fixed constant for all segments of the curve. It changes when we change when we move from one segment of the curve to another segment of the curve. Ofcourse it also changes when we move to another curve. – Rajesh Dachiraju Jul 12 '14 at 5:50

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It is currently 24 Jun 2017, 22:58 ### 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 # Low GMAT Score: Retaking: Your inputs required Author Message Intern Joined: 15 Aug 2010 Posts: 8 ### Show Tags 20 Aug 2010, 03:53 Hi, I wrote my GMAT today and got a dismal score of 560(Q46V21). My question is not what guys have previously asked on this forum. ("Where do I apply with this score? --or-- Do I retake the GMAT?") My question to you guys is, what do I do to improve my score when I will be giving the test again after a month? How do I do it? Your views? Background: I work for an MNC - in the computer networking industry - full time. Had got around 680 in Veritas, Manhattan, Princeton Review and GMATPrep. Next GMAT date: Have not booked yet. But will give after a month when the slot opens. ************************ Kudos me if you like the post! Intern Status: Applying ~ Affiliations: University of Mumbai - Topper in Mathematics Joined: 10 May 2010 Posts: 7 Location: India GMAT Date: 09-23-2012 GPA: 3 ### Show Tags 20 Aug 2010, 08:03 Hey Harsh...No worries mate! my roomie is going to post his debrief soon... I hope you will be motivated from him Retired Moderator Status: The last round Joined: 18 Jun 2009 Posts: 1296 Concentration: Strategy, General Management GMAT 1: 680 Q48 V34 ### Show Tags 20 Aug 2010, 08:39 harshjoshi91 wrote: Hi, I wrote my GMAT today and got a dismal score of 560(Q46V21). My question is not what guys have previously asked on this forum. ("Where do I apply with this score? --or-- Do I retake the GMAT?") My question to you guys is, what do I do to improve my score when I will be giving the test again after a month? How do I do it? Your views? Background: I work for an MNC - in the computer networking industry - full time. Had got around 680 in Veritas, Manhattan, Princeton Review and GMATPrep. Next GMAT date: Have not booked yet. But will give after a month when the slot opens. Hi Harsh, two possibilities are there. 1. It was your bad day as you have been scoring near 680 (as mentioned by you). In this case, you can go for a second shot within a month time. Identify your weak areas from the sample CATs you have taken. I think verbal is the key in your case. As you have already consumed gmat prep then its better to do all the gmat prep questions again. There is a famous gmat prep SC document floating here that contains about 180 gmat prep SC questions. You can also use the tag list option in this forum to find out a big pool of tough verbal questions with detailed explanations. You can also find the paper tests & practice their verbal part. I hope with this strategy you can hit the desired score in your next attempt. 2. If the real test score represents your real abilities, then I doubt that you can recover or develop your verbal skills in a month time. In that case, my recommendation would be to take atleast 40-50 days for a retake. Several options are there, including Knewton, which provides a money back guarantee. Any queries? Kindly let us know & keep us posted. Best of luck for the retake! _________________ GMAT Forum Moderator Status: Accepting donations for the mohater MBA debt repayment fund Joined: 05 Feb 2008 Posts: 1883 Location: United States Concentration: Operations, Finance Schools: Ross '14 (M) GMAT 2: 710 Q48 V38 GPA: 3.54 WE: Accounting (Manufacturing) ### Show Tags 20 Aug 2010, 08:56 _________________ Strategy Discussion Thread | Strategy Master | GMAT Debrief| Please discuss strategies in discussion thread. Master thread will be updated accordingly. | GC Member Write Ups GMAT Club Premium Membership - big benefits and savings Manager Joined: 27 May 2010 Posts: 199 ### Show Tags 21 Aug 2010, 20:51 As you can see Verbal is hurting you and i'm positive you just had a bad day. Were you doing better on the Quant in practice test? Intern Joined: 15 Aug 2010 Posts: 8 ### Show Tags 24 Aug 2010, 12:09 qweert wrote: As you can see Verbal is hurting you and i'm positive you just had a bad day. Were you doing better on the Quant in practice test? Well.. A couple of points more, but I never crossed 49.. I am sure I need to improve there too.. Why did you ask? You have something in mind? Intern Joined: 15 Aug 2010 Posts: 8 ### Show Tags 24 Aug 2010, 12:12 Hussain15 wrote: 1. It was your bad day as you have been scoring near 680 (as mentioned by you). In this case, you can go for a second shot within a month time. Identify your weak areas from the sample CATs you have taken. I think verbal is the key in your case. As you have already consumed gmat prep then its better to do all the gmat prep questions again. There is a famous gmat prep SC document floating here that contains about 180 gmat prep SC questions. You can also use the tag list option in this forum to find out a big pool of tough verbal questions with detailed explanations. You can also find the paper tests & practice their verbal part. I hope with this strategy you can hit the desired score in your next attempt. Any queries? Kindly let us know & keep us posted. Best of luck for the retake! I will find these and practice. Thanks for the directions Hussain. Current Student Joined: 27 Jun 2012 Posts: 411 Concentration: Strategy, Finance ### Show Tags 03 Jul 2012, 16:59 I found those 180 SC notes. Those are extracted from GMAT prep (nothing new) _________________ Thanks, Prashant Ponde Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Re: Low GMAT Score: Retaking: Your inputs required   [#permalink] 03 Jul 2012, 16:59 Similar topics Replies Last post Similar Topics: Low GMAT Score- Planning for retake: Need advice 4 11 Oct 2016, 20:22 Good GMAT score but low IR. Need your inputs. 4 18 Oct 2015, 11:51 HELP !!! GMAT score 700, retake required ?? 1 26 Aug 2011, 11:52 10 My GMAT journey and your inputs 58 07 Mar 2011, 18:50 Planning to retake the GMAT-Low score- Help! 1 22 Jul 2009, 10:13 Display posts from previous: Sort by # Low GMAT Score: Retaking: Your inputs required Moderator: HiLine Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

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## Summary INDEX and MATCH is the most popular tool in Excel for performing more advanced lookups. This is because INDEX and MATCH are incredibly flexible – you can do horizontal and vertical lookups, 2-way lookups, left lookups, case-sensitive lookups, and even lookups based on multiple criteria. If you want to improve your Excel skills, INDEX and MATCH should be on your list. See below for many examples. This article explains in simple terms how to use INDEX and MATCH together to perform lookups. It takes a step-by-step approach, first explaining INDEX, then MATCH, then showing you how to combine the two functions together to create a dynamic two-way lookup. There are more advanced examples further down the page. ### The INDEX Function The INDEX function in Excel is fantastically flexible and powerful, and you'll find it in a huge number of Excel formulas, especially advanced formulas. But what does INDEX actually do? In a nutshell, INDEX retrieves the value at a given location in a range. For example, let's say you have a table of planets in our solar system (see below), and you want to get the name of the 4th planet, Mars, with a formula. You can use INDEX like this: ``````=INDEX(B3:B11,4) `````` INDEX returns the value in the 4th row of the range. What if you want to get the diameter of Mars with INDEX? In that case, we can supply both a row number and a column number, and provide a larger range. The INDEX formula below uses the full range of data in B3:D11, with a row number of 4 and column number of 2: ``````=INDEX(B3:D11,4,2) `````` INDEX retrieves the value at row 4, column 2. To summarize, INDEX gets a value at a given location in a range of cells based on numeric position. When the range is one-dimensional, you only need to supply a row number. When the range is two-dimensional, you'll need to supply both the row and column numbers. At this point, you may be thinking "So what? How often do you actually know the position of something in a spreadsheet?" Exactly right. We need a way to locate the position of things we're looking for. Enter the MATCH function. ### The MATCH function The MATCH function is designed for one purpose: find the position of an item in a range. For example, we can use MATCH to get the position of the word "peach" in this list of fruits like this: ``````=MATCH("peach",B3:B9,0) `````` MATCH returns 3, since "Peach" is the 3rd item. MATCH is not case-sensitive. MATCH doesn't care if a range is horizontal or vertical, as you can see below: ``````=MATCH("peach",C4:I4,0) `````` Same result with a horizontal range, MATCH returns 3. Important: The last argument in the MATCH function is match_type. Match_type is important and controls whether matching is exact or approximate. In many cases, you will want to use zero (0) to force exact match behavior. Match_type defaults to 1, which means approximate match, so it's important to provide a value. See the MATCH page for more details. ### INDEX and MATCH together Now that we've covered the basics of INDEX and MATCH, how do we combine the two functions in a single formula? Consider the data below, a table showing a list of salespeople and monthly sales numbers for three months: January, February, and March. Let's say we want to write a formula that returns the sales number for February for a given salesperson. From the discussion above, we know we can give INDEX a row and column number to retrieve a value. For example, to return the February sales number for Frantz, we provide the range C3:E11 with a row 5 and column 2: ``````=INDEX(C3:E11,5,2) // returns \$5194 `````` But we obviously don't want to hardcode numbers. Instead, we want a dynamic lookup. How will we do that? The MATCH function of course. MATCH will work perfectly for finding the positions we need. Working one step at a time, let's leave the column hardcoded as 2 and make the row number dynamic. Here's the revised formula, with the MATCH function nested inside INDEX in place of 5: ``````=INDEX(C3:E11,MATCH("Frantz",B3:B11,0),2) `````` Taking things one step further, we'll use the value from H2 in MATCH: ``````=INDEX(C3:E11,MATCH(H2,B3:B11,0),2) `````` MATCH finds "Frantz" and returns 5 to INDEX for row. To summarize: 1. INDEX needs numeric positions. 2. MATCH finds those positions. 3. MATCH is nested inside INDEX. Let's now tackle the column number. ### Two-way lookup with INDEX and MATCH Above, we used the MATCH function to find the row number dynamically, but hardcoded the column number. How can we make the formula fully dynamic, so we can return sales for any given salesperson in any given month? The trick is to use MATCH twice – once to get a row position, and once to get a column position. From the examples above, we know MATCH works fine with both horizontal and vertical arrays. That means we can easily find the position of a given month with MATCH. For example, this formula returns the position of March, which is 3: ``````=MATCH("Mar",C2:E2,0) // returns 3 `````` But of course, we don't want to hardcode any values, so let's update the worksheet to allow the input of a month name, and use MATCH to find the column number we need. The screen below shows the result: A fully dynamic, two-way lookup with INDEX and MATCH. ``````=INDEX(C3:E11,MATCH(H2,B3:B11,0),MATCH(H3,C2:E2,0)) `````` The first MATCH formula returns 5 to INDEX as the row number, and the second MATCH formula returns 3 to INDEX as the column number. Once MATCH runs, the formula simplifies to: ``````=INDEX(C3:E11,5,3) `````` and INDEX correctly returns \$10,525, the sales number for Frantz in March. Note: you could use Data Validation to create dropdown menus to select salesperson and month. Video: How to debug a formula with F9 (to see MATCH return values) ### Left lookup One of the key advantages of INDEX and MATCH over the VLOOKUP function is the ability to perform a "left lookup". Simply put, this just means a lookup where the ID column is to the right of the values you want to retrieve, as seen in the example below: ### Index and Match with multiple criteria One of the trickiest problems in Excel is a lookup based on multiple criteria. In other words, a lookup that matches on more than one column at the same time. A nice way to handle these problems is to use Boolean logic, a technique for handling TRUE and FALSE values like 1s and 0s. You can see this approach below, where we are using INDEX and MATCH and Boolean logic to find a price based on three values: Item, Color, and Size: Read a detailed explanation here. You can use this same approach with XLOOKUP. Note: this is an array formula and must be entered with control + shift + enter in Excel 2019 and older. For a quick introduction to Booleans in Excel see these videos from our Dynamic Array Formulas course: ### Case-sensitive lookup By itself, the MATCH function is not case-sensitive. However, you use the EXACT function with INDEX and MATCH to perform a lookup that respects upper and lower case, as shown below: Note: this is an array formula and must be entered with control + shift + enter in Excel 2019 and older. ### Closest match Another example that shows off the flexibility of INDEX and MATCH is the problem of finding the closest match. In the example below, we use the MIN function together with the ABS function to create a lookup value and a lookup array inside the MATCH function. Essentially, we use MATCH to find the smallest difference. Then we use INDEX to retrieve the associated trip from column B. Note: this is an array formula and must be entered with control + shift + enter in Excel 2019 and older. ### INDEX and XMATCH The current version of Excel includes the XMATCH function, which is an upgraded replacement for the MATCH function. Like the MATCH function, XMATCH performs a lookup and returns a numeric position. Also like MATCH, XMATCH can perform lookups in vertical or horizontal ranges, supports both approximate and exact matches, and allows wildcards (* ?) for partial matches. But XMATCH adds even more features. The 5 key differences between XMATCH and MATCH are as follows: 1. XMATCH defaults to an exact match, while MATCH defaults to an approximate match. 2. XMATCH can find the next larger item or the next smaller item. 3. XMATCH can perform a reverse search (i.e. search from last to first). 4. XMATCH does not require values to be sorted when performing an approximate match. 5. XMATCH can perform a binary search, which is specifically optimized for speed. So, can you simply use XMATCH in an INDEX and MATCH formula instead of MATCH? Yes, absolutely. Using XMATCH instead of the MATCH function "upgrades" the formula to include the benefits listed above. Using XMATCH instead of the MATCH "upgrades" the formula to include the benefits listed above. ### Replacing MATCH with XMATCH For exact-match problems, XMATCH is a drop-in replacement for the MATCH function. You can simply change "MATCH" to "XMATCH" as shown below: ``````=MATCH(value,array,0) // exact match =XMATCH(value,array,0) // exact match `````` Note: since XMATCH defaults to an exact match, the zero above is not required. However, when converting MATCH in exact-match mode to XMATCH, you can leave the zero if you like. For approximate matches, XMATCH behavior is different when match_type is set to 1: ``````=MATCH(value,array,1) // exact match or next smallest =XMATCH(value,array,1) // exact match or next *largest* `````` In addition, XMATCH allows -1 for match type, which is not available with MATCH: ``````=XMATCH(value,array,-1) // exact match or next smallest `````` Note: the MATCH function does not offer the search mode argument at all. XMATCH can also be configured to perform a reverse search and a binary search. For a full description of all of the options available with XMATCH, see this page. ### More examples of INDEX + MATCH Here are some more basic examples of INDEX and MATCH in action, each with a detailed explanation: Author ### Dave Bruns Hi - I'm Dave Bruns, and I run Exceljet with my wife, Lisa. Our goal is to help you work faster in Excel. We create short videos, and clear examples of formulas, functions, pivot tables, conditional formatting, and charts.

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# Iron loss of a transformer can be measured by? Iron loss of a transformer can be measured by low power factor wattmeter. ## Related questions Answer : In an actual transformer the iron loss remains practically constant from no load to full load because core flux remains practically constant. Answer : If the supply frequency to the transformer is increased, the iron loss will increase. Description : At full -load of a transformer, the iron loss and copper loss are 3000 W and 4000 W respectively. Then total loss at maximum efficiency is :  (A) 7000 W (B) 6000 W (C) 8000 W (D) 4000 W Answer : At full -load of a transformer, the iron loss and copper loss are 3000 W and 4000 W respectively. Then total loss at maximum efficiency is : 6000 W Description : Dielectric loss in a capacitor is best measured by (A) Wien Bridge (B) Schering Bridge (C) Anderson Bridge (D) Heaviside-Campbell Equal Ratio Bridge Answer : Dielectric loss in a capacitor is best measured by Schering Bridge Description : When secondary of a current transformer is open-circuited its iron core will be? Answer : When secondary of a current transformer is open-circuited its iron core will be hot because of heavy iron losses taking place in it due to high flux density. Description : A ferrite core has less eddy current loss than an iron core because? Answer : A ferrite core has less eddy current loss than an iron core because ferrites have high hysteresis. Description : A 40 kVA transformer has a core loss of 400 W and a full load copper loss of 800 W. The proportion of full load at maximum efficiency is Answer : A 40 kVA transformer has a core loss of 400 W and a full load copper loss of 800 W. The proportion of full load at maximum efficiency is 0.707 Answer : A direct current can be measured by a D.C. potentiometer in conjunction with a standard resistance. Description : The self inductance of a coil can be measured using (A) Wien’s Bridge (B) Schering Bridge (C) Anderson’s Bridge (D) Wheatstone Bridge Answer : The self inductance of a coil can be measured using Anderson’s Bridge Answer : Resistances can be measured with the help of ohmmeters and resistance bridges. Description : Corona loss in transmission lines can be reduced by (A) using small diameter conductors (B) using bundled conductors (C) using less spacing between conductors (D) increasing the transmission line voltage Answer : Corona loss in transmission lines can be reduced by using bundled conductors Answer : The full-load copper loss of a trans¬former is 1600 W. At half-load, the copper loss will be 400 W. Answer : A moving iron instrument can be used for both D.C. and A.C. Description : Select insulating materials for following parts : (i) Insulation between heating element and base plate of electric iron. (ii) Insulation used over copper or aluminium conductor used for making coils. (iii) Transformer bushings. (iv) Insulation between transmission line and pole. Answer : Parts Insulating Materials  Insulation between heating element and base plate of electric iron. Mica Insulation used over copper or aluminium conductor used for making coils.  ... Transformer bushings Porcelain  Insulation between transmission line and pole. Porcelain Description : How can power loss be reduced? Description : The power consumed by a balanced 3-ph load is measured by two-wattmeter method. The meter readings are 8 kW and 4 kW. The power factor of the load is (A) zero (B) 0.5 (C) between zero and 0.5 (D) between 0.5 and unity Answer : The power consumed by a balanced 3-ph load is measured by two-wattmeter method. The meter readings are 8 kW and 4 kW. The power factor of the load is between 0.5 and unity Answer : E.m.f. of a Weston cell is accurately measured by electrostatic voltmeter. Answer : The purpose of providing an iron core in a transformer is to decrease the reluctance of the magnetic path. Answer : The purpose of providing iron core in a step-up transformer is to decrease the magnitude of magnetizing current. Description : The maximum load that a power transformer can carry is limited by its? Answer : The maximum load that a power transformer can carry is limited by its voltage ratio. Description : Eddy current damping cannot be used for moving iron instrument because Answer : Eddy current damping cannot be used for moving iron instrument because the presence of a permanent magnet required for such purpose would affect the deflection and hence the reading of the instrument Description : The load of a consumer is generally measured in terms of : (A) Volts (B) Amperes (C) Ampere hour (D) kW Answer : The load of a consumer is generally measured in terms of : kW Description : True value has been 50 whereas measured value is 40 then the percentage error in the reading will be ______.  (A) 20% (B) 40% (C) 50% (D) 30% Answer : True value has been 50 whereas measured value is 40 then the percentage error in the reading will be 20%. Description : In a battery, the difference between the no-load voltage and the measured voltage output is called ________ A) Internal voltage B) Internal resistance C) External resistance D) All the above Answer : In a battery, the difference between the no-load voltage and the measured voltage output is called Internal resistance Description : Liquid flow rate is measured using (A) a pirani gauge (B) a pyrometer (C) an orifice plate (D) a bourdon tube Answer : Liquid flow rate is measured using an orifice plate Description : In a circuit containing R, L and C, power loss can take place in? Answer : In a circuit containing R, L and C, power loss can take place in R only. Description : Why high voltage can reduce power loss? Answer : when voltage has increased due to reduced current flow, thus power loss given by ( I^2R) will be low due to reduced current(I^2) provided that resistance (R) is constant. Answer : If the current in a capacitor leads the voltage by 80°, the loss angle of the capacitor is 10°. Answer : A transformer can have regulation closer to zero on leading power factor. Description : What to look for when choosing an iron? Answer : What to look for when choosing an iron? Today, the purchase of an iron is not a big problem. This piece of household appliances is presented in a wide range of stores. Each manufacturer tries to ... its presence increases the cost of the iron by an average of 10%. Good luck with your choice! Description : Which is the best conductor: silver, carbon, or iron? Answer : Silver is the best conductor. Carbon is the semiconductor. Iron have less conductance as compared to silver. Description : An unshielded moving iron voltmeter is used to measure the voltage in an AC circuit. The stray DC magnetic field having a component along the axis will be  (1) unaffected (2) decreased (3) increased (4) either decreased or increased depending on the direction of the DC field Answer : An unshielded moving iron voltmeter is used to measure the voltage in an AC circuit. The stray DC magnetic field having a component along the axis will be either decreased or increased depending on the direction of the DC field Description : The iron alloy, ALNICO is mainly used to make ________ A) Temporary magnets B) Permanent magnets C) Transmission lines D) None of these Answer : The iron alloy, ALNICO is mainly used to make Permanent magnets Description : In DC motor iron losses are occurred in? Answer : In DC motor iron losses are occurred in the armature. Description : In AC. circuits, laminated iron is invariably used in order to? Answer : In AC. circuits, laminated iron is invariably used in order to reduce eddy current loss. Answer : Iron losses in a D.C. machine are independent of variations in load. Answer : In a D.C. generator, the iron losses mainly take place in armature rotor. Answer : A transformer oil must be free from moisture. Answer : The main reason for generation of harmonics in a transformer could be saturation of core. Description : In a transformer the resistance between its primary and secondary should be? Answer : In a transformer the resistance between its primary and secondary should be infinity. Description : The dielectric strength of transformer oil is expected to be? Answer : The dielectric strength of transformer oil is expected to be 33 kV. Answer : The no load current in a transformer lags behind the applied voltage by an angle of about 75°. Description : The changes in the volume of transformer cooling oil due to the variation of atmospheric temperature during day and night is taken care of by which part of the transformer? Answer : The changes in the volume of transformer cooling oil due to the variation of atmospheric temperature during day and night is taken care of by conservator. Answer : The transformer laminations are insulated from each other by thin coat of varnish. Description : The noise produced by a transformer is termed as? Answer : The noise produced by a transformer is termed as hum. Description : Weight Loss Tips Answer : Weight Loss Tips Are you fed up of yourself being overweight? Are you looking for some effective weight loss tips? Then, your search ends here. In this article, you will get find an effective ... they are very easy and simple to follow, they are known to provide outstanding effects on the body. Description : Hair Loss Answer : Hair Loss How dreadful would you feel, if you start experiencing sudden hair loss in your life? Hairs form the crown of your entire body and so you need to keep it with great care. However, ... and natural hair loss tips to enjoy beautiful, shiny and thick hairs that will attract others, for sure. Description : Anti-hair loss shampoo. How to choose? Answer : The problem of hair loss has always been relevant. Almost every one of us periodically observes the remaining hairs on the comb. In this case, there is absolutely no need to panic, because ... Look for shampoos that contain medicinal substances such as burdock oil, nettle extract, or burdock juice. Answer : Corona is nothing but the ionization of surrounding air around the conductor which produces hissing noise, Description : State the factors affecting hysteresis loss. Answer : i) Flux density ii) Frequency iii) Volume of the magnetic material iv) Nature of magnetic material ← Prev Question Next Question →

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# Catapult Physics Catapult physics is basically the use of stored energy to hurl a projectile (the payload), without the use of an explosive. The three primary energy storage mechanisms are tension, torsion, and gravity. The catapult has proven to be a very effective weapon during ancient times, capable of inflicting great damage. The main types of catapults used were the trebuchet, mangonel, onager, and ballista. These types of catapults will be described, and pictures and illustrations will be included. Catapult Physics — The Trebuchet Source: Wikipedia via ChrisO A trebuchet is a battle machine used in ancient times to throw heavy payloads at enemies. The payload could be thrown a far distance and do considerable damage, either by smashing down walls or striking the enemy while inside their stronghold. Among the various types of catapults, the trebuchet was the most accurate and among the most efficient in terms of transferring the stored energy to the projectile. In addition, it allowed greater consistency in the throws due to the fact that the same amount of energy could be delivered every time, by way of a raised counterweight. A trebuchet works by using the energy of a falling (and hinged) counterweight to launch a projectile (the payload), using mechanical advantage to achieve a high launch speed. For maximum launch speed the counterweight must be much heavier than the payload, since this means that it will "fall" quickly. The physics behind a trebuchet is fairly complex. A detailed explanation of it is given on the page on Trebuchet Physics. In some designs a guide chute is used to guide the sling along and support the payload until the speed is great enough to hold it in the pouch alone. The beginning of the launch is illustrated in the figure below. As you can see, the counterweight pivots around a much shorter distance than the payload end. The advantage of this is that the payload end of the beam reaches a much higher linear velocity than the counterweight end of the beam. This is the principal of mechanical advantage, and is what allows the payload to reach a high launch velocity. However, because the counterweight pivots around a much shorter distance, its weight must be much greater than the weight of the payload, to get a high launch velocity. However, increasing the mass of the counterweight beyond a certain point will not help, since the limiting speed of the falling counterweight is free-fall speed. The sling releases when a certain angle α is reached. At this point the ring (which is connected to the sling and loops around the finger for support) slips off and the payload is launched. The release angle α can be adjusted by changing the finger angle δ. For a greater δ the release angle α increases. For a smaller δ the release angle α decreases. The figure below illustrates the trebuchet at the release point. As the beam rotates clockwise (due to the falling counterweight), the payload experiences centripetal acceleration which causes it to move outwards (since it is unrestrained). This results in a large increase in linear velocity of the payload which far exceeds that of the end of the beam to which the sling is attached. This is the heart of the physics behind a trebuchet and is the reason why a trebuchet has such great launching power. For a more in-depth explanation on how a trebuchet works see Trebuchet Physics. In this page the basic equations describing the physics of a trebuchet will be introduced. To assist you in building a trebuchet you can use this simulator to help you come up with the design that throws the payload the farthest. This is very useful for helping you come up with the winning design in a trebuchet competition! If you're interested in having a small working trebuchet you can get one through Amazon. Click on the image link below to find out more. In the next section we will look at the mangonel. Catapult Physics — The Mangonel Source: Wikipedia via ChrisO The above picture of the mangonel is what people are most familiar with when they think of catapults. The mangonel consists of an arm with a bowl-shaped bucket attached to the end. In this bucket a payload is placed. Upon release, the arm rotates at a high speed and throws the payload out of the bucket, towards the target. The launch velocity of the payload is equal to the velocity of the arm at the bucket end. The launch angle of the payload is controlled by stopping the arm using a crossbar. This crossbar is positioned so as to stop the arm at the desired angle which results in the payload being launched out of the bucket at the desired launch angle. This crossbar can be padded to cushion the impact. The mangonel was best suited for launching projectiles at lower angles to the horizontal, which was useful for destroying walls, as opposed to the trebuchet which was well suited for launching projectiles over walls. However, the mangonel is not as energy efficient as the trebuchet for the main reason that the arm reaches a high speed during the launch. This means that a large percentage of the stored energy goes into accelerating the arm, which is energy wasted. This is unavoidable however, since the payload can only be launched at high speed if the arm is rotating at high speed. So the only way to waste as little energy as possible is to make the arm and bucket as light as possible, while still being strong enough to resist the forces experienced during launch. The physics behind a mangonel is basically the use of an energy storage mechanism to rotate the arm. Unlike a trebuchet, this mechanism is more direct. It consists of either a tension device or a torsion device which is directly connected to the arm. The figure below illustrates a mangonel in which the energy source is a bent cantilever, which is a form of tension device. This can consist of a flexible bow-shaped material, made of wood for example. The point P in the figure is the pivot axle, attached to the frame, about which the arm rotates. The figure below shows the mangonel at the launch point. To launch the payload the restraining rope is released. The other type of energy storage mechanism is a torsion device, which can consist of twisted rope. This allowed for greater throwing power than the tension device, in ancient catapults. The figure below illustrates the torsion device. The twisted rope is commonly referred to as a torsion bundle. It consists of several lengths of rope with the arm inserted in between them. The rope is then twisted manually on both sides of the arm using levers. Upon release, the torsion bundle rotates the arm at high speed, launching the payload. The figure below illustrates how a torsion bundle is twisted. The video below shows how to wrap the rope on a torsion catapult. The fact that a mangonel uses an energy storage device that consists of a deforming material, like wood or rope, means that its throwing distance will not be as consistent as a trebuchet. This is because these materials (unlike more modern materials), naturally wear and lose elasticity during their use. This is something that needs to be constantly monitored during a battle, with replacement materials made readily available, if necessary. If you're interested in having a small working Da Vinci catapult you can get one through Amazon. Click on the image link below to find out more. In the next section we will briefly discuss the onager. Catapult Physics — The Onager The onager catapult is almost identical to the trebuchet, but instead of a falling counterweight, it uses a torsion bundle to rotate the arm (similar to the mangonel, described previously). Because of its design, it allowed for greater throwing distance than the mangonel (comparable to that of a trebuchet). But the throwing distance wasn't as consistent as the trebuchet since it relied on deformable materials as the energy source, which naturally wear and lose elasticity during their use. Lastly, we will look at the ballista. Catapult Physics — The Ballista Source: Wikipedia via Scigeek The ballista is similar in principle to a crossbow, but much larger. Like the torsion powered mangonel, it used twisted rope as the energy source. The picture above shows the torsion mechanism consisting of twisted rope, located at the pivot location of the two side arms. In the ballista, the bow string would be winched back and the tension set. It would be used to launch darts, bolts and spears with deadly force and accuracy. It could also be used to launch stone projectiles of various sizes. If you're interested in having a small working ballista you can get one through Amazon. Click on the image link below to find out more. Sign up below for my free newsletter and you will receive insightful physics related bonus material. Many topics will be discussed, including more discussion on the physics of catapults. It's sent about once a month. Easily unsubscribe at any time. E-mail Address First Name Then Don't worry — your e-mail address is totally secure. I promise to use it only to send you Real World Physics Problems Newsletter. Return from Catapult Physics to The Physics Of Battle page

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Sale! # Propositional Inferences Assignment 1 \$30.00 Category: Rate this product COMP4418, 2017–Assignment 1 Worth: 15%. This assignment consists of three questions. The first two questions require written answers only. The third question requires some programming. 1. [20 Marks] (Propositional Inferences) Prove whether or not the following inferences hold in propositional logic using the truth table method. (a) p ∨ (q ∧ r) |= (p ∨ q) ∧ (p ∨ r) (b) |= p → (q → p) (c) p → q |= ¬p → ¬q (d) p → q, ¬p → ¬q |= ¬p ↔ ¬q (e) ¬q → ¬p, ¬r → ¬q |= p → r Prove whether or not the following inferences hold in propositional logic using resolution. (f) p ∧ (q ∨ r) ` (p ∧ q) ∨ (p ∧ r) (g) p ` p → q (h) p ↔ q ` (q ↔ r) → (p ↔ r) (i) ¬p ∧ ¬q ` p ↔ q (j) ¬q → ¬p, ¬r → ¬q ` p → r 2. [30 Marks] (Logic Puzzle) Daisy and Donald Duck took their nephews aged 4, 5 and 6 on an outing. Each boy wore a tee-shirt with a different design on it and of a different colour. You are also given the following information: • Huey is younger than the boy in the green tee-shirt • The five year-old wore the tee-shirt with the camel design • Dewey’s tee-shirt was yellow • Louie’s tee-shirt bore the giraffe design • The panda design was not featured on the white tee-shirt (a) Represent these facts as sentences in first-order logic using the following constant symbols: • dewey, huey and louie; the names of the nephews • camel, giraffe and panda; the designs on the t-shirts • green, white and yellow; the colours of the t-shirts and the following predicates: • age(Boy, Age) • design(Boy, Design) • colour(Boy, Colour) 1 (b) Using your formalisation in part (2a), is it possible to conclude the age of each boy together with the colour and design of the tee-shirt they’re wearing? Show semantically how you determined (c) If your answer to part (2b) was ‘no’, indicate what further sentences you would need to add to your formalisation so that you could conclude the age of each boy together with the colour and design of the tee-shirt they’re wearing. 3. [50 Marks] (Automated Theorem Proving) In 1958 the logician Hao Wang implemented one of the first automated theorem provers. He succeeded in writing several programs capable of automatically proving a majority of theorems from the first five chapters of Whitehead and Russell’s Principia Mathematica (in fact, his program managed to prove over 200 of these theorems “within about 37 minutes, and 12/13 of the time is used for read-in and print-out”). This was an impressive achievement at the time; previous attempts had only succeeded in proving a handful of the theorems in Principia Mathematica. Background Wang’s idea is based around the notion of a sequent (this idea had been introduced years earlier by Gentzen) and the manipulation of sequents. A sequent is essentially a list of formulae on either side of a sequent (or provability) symbol `. The sequent π ` ρ, where π and ρ are strings (i.e., lists) of formulae, can be read as “the formulae in the string ρ follow from the formulae in the string π” (or, equivalently, “the formulae in string π prove the formulae in string ρ”). To prove whether a given sequent is true all you need to do is start from some basic sequents and successively apply a series of rules that transform sequents until you end up with the sequent you desire. This process is detailed below. Additionally, determining whether a formula φ is a theorem, is equivalent to determining whether the sequent ∅ ` φ is true (e.g., ` ¬φ ∨ φ). Formulae Connectives We allow the following connectives in decreasing order of precedence: ¬ — negation ∧ — conjunction; ∨ — disjunction (both same precedence) → — implication; ↔ — biconditional (both same precedence). Formula • A propositional symbol (e.g., p, q, . . .) is an atomic formula (and thus a formula). • If φ, ψ are formulae, then ¬φ, φ ∧ ψ, φ ∨ ψ, φ → ψ, φ ↔ ψ are formulae. Sequent If π and ρ are strings of formulae (possibly empty strings) and φ is a formula, then π, φ, ρ is a string and π ` ρ is a sequent. 2 Rules The logic consists of the following sequent rules. The first rule (P1) gives a characterisation of simple theorems. The remaining rules are simply ways of transforming sequents into new sequents. The manner in which you can construct a proof for a sequent to determine whether it holds or not is given below. P1 Initial Rule: If λ, ζ are strings of atomic formulae, then λ ` ζ is a theorem if some atomic formula occurs on both side of the sequent `. In the following ten rules λ and ζ are always strings (possibly empty) of formulae. P2a Rule ` ¬: If φ, ζ ` λ, ρ, then ζ ` λ, ¬φ, ρ P2b Rule ¬ `: If λ, ρ ` π, φ, then λ, ¬φ, ρ ` π P3a Rule ` ∧: If ζ ` λ, φ, ρ and ζ ` λ, ψ, ρ, then ζ ` λ, φ ∧ ψ, ρ P3b Rule ∧ `: If λ, φ, ψ, ρ ` π, then λ, φ ∧ ψ, ρ ` π P4a Rule ` ∨: If ζ ` λ, φ, ψ, ρ, then ζ ` λ, φ ∨ ψ, ρ P4b Rule ∨ `: If λ, φ, ρ ` π and λ, ψ, ρ ` π, then λ, φ ∨ ψ, ρ ` π P5a Rule `→: If ζ, φ ` λ, ψ, ρ, then ζ ` λ, φ → ψ, ρ P5b Rule →`: If λ, ψ, ρ ` π and λ, ρ ` π, φ, then λ, φ → ψ, ρ ` π P6a Rule `↔: If φ, ζ ` λ, ψ, ρ and ψ, ζ ` λ, φ, ρ, then ζ ` λ, φ ↔ ψ, ρ P6b Rule ↔`: If φ, ψ, λ, ρ ` π and λ, ρ ` π, φ, ψ, then λ, φ ↔ ψ, ρ ` π Proofs The basic idea in proving a sequent π ` ρ is to begin with instance(s) of Rule P1 and successively apply the remaining rules until you end up with the sequent you are hoping to prove. For example, suppose you wanted to prove the sequent ¬(p∨q) ` ¬p. One possible proof would proceed as follows. 1. p ` p, q Rule 1 2. p ` p ∨ q Rule P4a 3. ` ¬p, p ∨ q Rule P2a 4. ¬(p ∨ q) ` ¬p Rule P2b QED. However, a simpler idea (as it will involve much less search) is to begin with the sequent(s) to be proved and apply the rules above in the “backward” direction until you end up with the sequent you desire. In the example then, you would begin at step 4 and apply each of the rules in the backward direction until you end up at step 1 at which point you can conclude the original sequent is a theorem. Question Specification In this assignment you are to emulate Hao Wang’s feats and implement a propositional theorem prover. You may use any programming language to complete this question. You must provide a script named assn1q3 or a Makefile that, when the command make is executed, produces an executable file assn1q3. 3 Input The input will consist of a single sequent on the command line. Sequents will be written as: [List of Formulae] seq [List of Formulae] To construct formulae, atoms can be any string of characters (without space) and connectives as follows: • ¬: neg • ∧: and • ∨: or • →: imp • ↔: iff So, for example, the sequent p → q, ¬r → ¬q ` p → r would be written as: [p imp q, (neg r) imp (neg q)] seq [p imp r] Your program should be called assn1q3 and run as follows: ./assn1q3 Sequent For example ./assn1q3 [p imp q, (neg r) imp (neg q)] seq [p imp r] Output The first line of the output will be either true or false indicating whether or not the sequent on the command line holds. This output is worth 40% of the total mark for this question on given and hidden test data. The subsequent lines of output should produce a proof like the one in the Proofs section above. Marking for this Question • Code: 40% • Given test data: 20% • Hidden test data: 20% • Printing proofs: 20% References [1] Hao Wang, Toward Mechanical Mathematics, IBM Journal for Research and Development, volume 4, 1960. (Reprinted in: Hao Wang, ”Logic, Computers, and Sets”, Sciene Press, Peking, 1962. Hao Wang, ”A Survey of Mathematical Logic”, North Holland Publishing Company, 1964. Hao Wang, ”Logic, Computers, and Sets”, Chelsea Publishing Company, New York, 1970.) [2] Alfred North Whitehead and Bertrand Russell, Principia Mathematica, 2nd Edition, Cambridge University Press, Cambridge, England, 1927. 4 A List of 10 Propositional Theorems You may find it instructional to prove these by hand first. (a) ` ¬p ∨ p (b) ¬(p ∨ q) ` ¬p (c) p ` q → p (d) p ` p ∨ q (e) (p ∧ q) ∧ r ` p ∧ (q ∧ r) (f) p ↔ q ` ¬(p ↔ ¬q) (g) p ↔ q ` (q ↔ r) → (p ↔ r) (h) ` (¬p ∧ ¬q) → (p ↔ q) (i) p ↔ q ` (p ∧ q) ∨ (¬p ∧ ¬q) (j) p → q, ¬r → ¬q ` p → r Assignment Submission You will need to submit answers to Questions 1 and 2 in a PDF file named assn1.pdf along with any source code files for Questions 3. For Question 3 you can either submit a script named assn1q3 or a Makefile that, when make is executed, the executable file assn1q3 is generated. Your report for Question 3 in assn1.pdf should describe the additional files you submit for this question and how they can used to replicate/generate

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Community Profile Active since 2012 All Content Feed View by Solved Times 2 - START HERE Try out this test problem first. Given the variable x as your input, multiply it by two and put the result in y. Examples:... más de 6 años ago Solved Project Euler: Problem 6, Natural numbers, squares and sums. The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ... más de 8 años ago Solved Find the sum of all the numbers of the input vector Find the sum of all the numbers of the input vector x. Examples: Input x = [1 2 3 5] Output y is 11 Input x ... más de 8 años ago Solved inner product of two vectors inner product of two vectors más de 8 años ago Solved Select every other element of a vector Write a function which returns every other element of the vector passed in. That is, it returns the all odd-numbered elements, s... más de 8 años ago Solved Swap the first and last columns Flip the outermost columns of matrix A, so that the first column becomes the last and the last column becomes the first. All oth... más de 8 años ago Solved Sum all integers from 1 to 2^n Given the number x, y must be the summation of all integers from 1 to 2^x. For instance if x=2 then y must be 1+2+3+4=10. más de 8 años ago Solved Pizza! Given a circular pizza with radius _z_ and thickness _a_, return the pizza's volume. [ _z_ is first input argument.] Non-scor... más de 8 años ago Solved Make the vector [1 2 3 4 5 6 7 8 9 10] In MATLAB, you create a vector by enclosing the elements in square brackets like so: x = [1 2 3 4] Commas are optional, s... más de 8 años ago Solved Determine if input is odd Given the input n, return true if n is odd or false if n is even. más de 8 años ago Question Multiple Character MuPad Subscripts? I need to format an equation in MuPad with a subscript greater than one character, and I need to do it very often, so it is impr... más de 8 años ago | 2 answers | 0 Solved

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Preprint Article Version 7 Preserved in Portico This version is not peer-reviewed # A Common Approach to Three Open Problems in Number Theory Version 1 : Received: 23 March 2023 / Approved: 24 March 2023 / Online: 24 March 2023 (02:00:47 CET) Version 2 : Received: 28 March 2023 / Approved: 29 March 2023 / Online: 29 March 2023 (03:34:34 CEST) Version 3 : Received: 14 April 2023 / Approved: 17 April 2023 / Online: 17 April 2023 (04:05:43 CEST) Version 4 : Received: 18 April 2023 / Approved: 19 April 2023 / Online: 19 April 2023 (05:34:48 CEST) Version 5 : Received: 26 April 2023 / Approved: 27 April 2023 / Online: 27 April 2023 (04:44:46 CEST) Version 6 : Received: 10 May 2023 / Approved: 11 May 2023 / Online: 11 May 2023 (04:42:23 CEST) Version 7 : Received: 17 May 2023 / Approved: 18 May 2023 / Online: 18 May 2023 (08:25:27 CEST) A peer-reviewed article of this Preprint also exists. Tyszka, A. A Common Approach to Three Open Problems in Number Theory. Discrete Mathematics Letters 2023, 12, 66–72, doi:10.47443/dml.2023.049. Tyszka, A. A Common Approach to Three Open Problems in Number Theory. Discrete Mathematics Letters 2023, 12, 66–72, doi:10.47443/dml.2023.049. ## Abstract The following system of equations {x_1 \cdot x_1=x_2, x_2 \cdot x_2=x_3, 2^{2^{x_1}}=x_3, x_4 \cdot x_5=x_2, x_6 \cdot x_7=x_2} has exactly one solution in ({\mathbb N}\{0,1})^7, namely (2,4,16,2,2,2,2). Hypothesis 1 states that if a system of equations S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,7}} \cup {2^{2^{x_j}}=x_k: j,k \in {1,...,7}} has at most five equations and at most finitely many solutions in ({\mathbb N}\{0,1})^7, then each such solution (x_1,...,x_7) satisfies x_1,...,x_7 \leq 16. Hypothesis 1 implies that there are infinitely many composite numbers of the form 2^{2^{n}}+1. Hypotheses 2 and 3 are of similar kind. Hypothesis 2 implies that if the equation x!+1=y^2 has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(4,5),(5,11),(7,71)}. Hypothesis 3 implies that if the equation x(x+1)=y! has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(1,2),(2,3)}. We describe semi-algorithms sem_j (j=1,2,3) that never terminate. For every j \in {1,2,3}, if Hypothesis j is true, then sem_j endlessly prints consecutive positive integers starting from 1. For every j \in {1,2,3}, if Hypothesis j is false, then sem_j prints a finite number (including zero) of consecutive positive integers starting from 1. ## Keywords Brocard's problem; Brocard-Ramanujan equation x!+1=y^2; composite Fermat numbers; composite numbers of the form 2^(2^n)+1; Erd\"os' equation x(x+1)=y! ## Subject Computer Science and Mathematics, Algebra and Number Theory Comment 1 Commenter: Apoloniusz Tyszka Commenter's Conflict of Interests: Author Comment: I added Section 1 entitled "Epistemic notions increase the scope of mathematics". + Respond to this comment

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# 3.4. Three-phase model¶ This implementation assumes the density $$\rho$$ is unity and two scalar order parameters ($$\phi$$ and $$\psi$$) define the composition. The three phases are defined by concentrations $$C_1 = (\rho + \phi - \psi)/2$$, $$C_2 = (\rho - \phi - \psi)/2$$ and $$C_3 = \psi$$ so that we have: Phase $$\rho$$ $$\phi$$ $$\psi$$ $$C_1$$ $$C_2$$ $$C_3$$ One 1 1 0 1 0 0 Two 1 -1 0 0 1 0 Three 1 0 1 0 0 1 C. Semprebon, T. Krueger, and H. Kusumaatmaja, Ternary free-energy lattice Boltzmann model with tunable surface tensions and contact angles, Phys. Rev. E, 93 033305 (2016). ## 3.4.1. Two dimensions¶ Note that there is currently no default initialisation of the ternary composition. ### 3.4.1.1. Double emulsion (in blocks)¶ ternary_initialisation 2d_double_emulsion # Initialisation 2d_double_emulsion_xf1 0.2 # Optional: fraction x1 2d_double_emulsion_xf2 0.5 # Optional: fraction x2 2d_double_emulsion_xf3 0.8 # Optional: fraction x3 2d_double_emulsion_yf1 0.3 # Optional: fraction y1 2d_double_emulsion_yf2 0.7 # Optional: fraction y2 This initialises two central blocks of composition $$C_1$$ and $$C_2$$ surrounded by $$C_3$$. The positions of the ‘cuts’ are controlled by five optional parameters, which are fractions of the system length in the relevant dimension; the default values are shown above. It is expected that the $$z$$-dimension will have extent $$L_z = 1$$, but it is not enforced; the initialisation will be uniform in $$z$$. ### 3.4.1.2. Double droplet¶ ternary_initialisation 2d_double_drop # Initialisation ternary_2d_drop1_radius 2.0 # radius for C_1 drop ternary_2d_drop1_centre 2.0_1.5 # centre for C_1 drop ternary_2d_drop2_radius 2.5 # radius for C_2 drop ternary_2d_drop2_centre 4.0_2.0 # centre for C_2 drop This is a variation of the above using instead of rectangular blocks, circular droplets. All the parameters specifying the position and the radii of the two drops must be specified and are in absolute lattice units. Drop 1 has composition $$C_1$$ and drop 2 has composition $$C_2$$, while the background is $$C_3$$. If the drops overlap, composition $$C_2$$ will be favoured. It is expected that $$L_z = 1$$, although not enforced. If $$L_z > 1$$, cylinders will result. ### 3.4.1.3. Lens in two dimensions¶ ternary_initialisation 2d_lens # ternary_2d_lens_centre 16.0_16.0 # Required: centre (x0, y0) This initialises a circular droplet of phase $$C_3$$ with its centre at the specified position (absolute coordinates) and with given radius. The horizontal interface between $$C_1$$ and $$C_2$$ is always at $$L_y/2$$. Such an initial condition, upon relaxation, should give rise to a lens shape depending on the equilibrium contact angles selected. Again, it is expected that the $$z$$-dimension will have extent $$L_z = 1$$, but it is not enforced; the initialisation will be uniform in $$z$$. ### 3.4.1.4. T-shape in two dimensions¶ ternary_initialisation 2d_tee # initialisation ternary_2d_tee_xf1 0.50 # optional: fraction of L_x ternary_2d_tee yf1 0.33 # optional: fraction of L_y Three rectangular blocks are initialised with sharp interfaces forming an inverted ‘T’-shape. The default positions of the interfaces are shown above, with the optional parameters specifying the fractional position of the vertical and horizontal interfaces. The default parameters give roughly equal areas of the three components in a square system with disposition as shown in the diagram. This initialisation can be useful in, for example, assessing the wetting angles formed at solid boundaries at each side of the box. ## 3.4.2. Three dimensions¶ Details on three-dimensional configurations are pending. ## 3.4.3. Three-phase configuration from file¶ ternary_initialisation from_file # Request from single file ternary_file_stub ternary.init # This is the default Arbitrary composition fields may be supplied from file of appropriate format. This file must contain exactly two scalar fields $$\phi$$ and $$\psi$$ ($$\rho$$ does not appear and is dealt with via the lattice Boltzmann distributions). The file stub name can be set with the key ternary_file_stub. Other I/O parameters are currently dealt with via keys prefixed phi_. See sections on I/O for details.

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# Covmatrix: Spatio-temporal (tapered) Covariance Matrix In CompRandFld: Composite-Likelihood Based Analysis of Random Fields ## Description The function computes the (tapered) covariance matrix for a spatial (temporal or spatio-temporal) covariance model and a set of spatial (temporal or spatio-temporal) points. ## Usage 1 2 3 4 Covmatrix(coordx, coordy=NULL, coordt=NULL, corrmodel, distance="Eucl", grid=FALSE, iskrig=FALSE, maxdist=NULL, maxtime=NULL, param , taper=NULL, tapsep=NULL, type="Standard") ## Arguments coordx A numeric (d x 2)-matrix (where d is the number of spatial sites) giving 2-dimensions of spatial coordinates or a numeric d-dimensional vector giving 1-dimension of spatial coordinates. coordy A numeric vector giving 1-dimension of spatial coordinates; coordy is interpreted only if coordx is a numeric vector or grid=TRUE otherwise it will be ignored. Optional argument, the default is NULL then coordx is expected to be numeric a (d x 2)-matrix. coordt A numeric vector giving 1-dimension of temporal coordinates. At the moment implemented only for the Gaussian case. Optional argument, the default is NULL then a spatial random field is expected. corrmodel String; the name of a correlation model, for the description see the Section Details. distance String; the name of the spatial distance. The default is Eucl, the euclidean distance. See FitComposite. grid Logical; if FALSE (the default) the data are interpreted as spatial or spatial-temporal realisations on a set of non-equispaced spatial sites (irregular grid). See FitComposite. iskrig Logical: the default value is FALSE. It is TRUE if the function is called by the function Kri. maxdist Numeric; an optional positive value indicating the marginal spatial compact support. See FitComposite. maxtime Numeric; an optional positive value indicating the marginal temporal compact support. See FitComposite. param A list of parameter values required for the correlation model. See FitComposite and CorrelationParam. taper String; the name of the taper correlation function if type is Tapering, see the Section Details. tapsep Numeric; an optional value indicating the separabe parameter in the space-time quasi taper (see Details). type String; the type of covariance matrix Standard (the default) or Tapering for tapered covariance matrix ## Details The parameter param is a list including all the parameters of a covariance function model. In particular, the covariance models share the following paramaters: the sill that represents the common variance of the random field, the nugget that represents the local variation (white noise) at the origin. For each correlation model you can check the list of the specific parameters using CorrelationParam. Here there is the list of all the implemented space and space-time correlation models. The list of space-time correlation functions includes separable and non-separable models. • Purerly spatial correlation models: 1. cauchy R(h) = (1+h^2)^(-β) The parameter β is positive. It is a special case of the gencauchy model. 2. exponential R(h) = exp(-h) This model is a special case of the whittle and the stable model. 3. gauss R(h)=exp(-h^2) This model is a special case of the stable model. 4. gencauchy (generalised cauchy) R(h) = ( 1+h^α )^{-\frac{β}{α}} The parameter α is in (0,2], and β is positive. 5. spherical R(h) = (1- 1.5 h+0.5 h^3) 1_{[0,1]}(h) This isotropic covariance function is valid only for dimensions less than or equal to 3. 6. stable R(h)=exp(-h ^α) The parameter α is in (0,2]. 7. wave R(h)=sin(h)/h if h>0 and C(0)=1 This isotropic covariance function is valid only for dimensions less than or equal to 3. 8. matern R(h) = 2^{1-ν} Γ(ν)^{-1} x^ν K_ν(h) The parameter ν is positive. This is the model of choice if the smoothness of a random field is to be parametrised: if ν > m then the graph is m times differentiable. • Spatio-temporal correlation models: • Non-separable models: 1. gneiting (non-separabel space time model) R(h, u) = \frac{e^{ \frac{-h^ν} { (1+u^λ)^{0.5 γ ν }}}} {1+u^λ} The parameters ν and λ take values in [0,2]; the parameter γ take values in [0,1]. For γ=0 it is a separable model. 2. gneiting_GC (non-separabel space time model with great circle distances) R(h, u) = \frac{ e^{ \frac{-u^λ }{1+h^ν)^{0.5 γ λ}} }} { 1+h^ν} 3. iacocesare (non-separabel space time model) R(h, u) = (1+h^ν+u^λ)^{-δ} The parameters ν and λ take values in [1,2]; the parameters δ must be greater than or equal to half the space-time dimension. 4. porcu (non-separabel space time model) R(h, u) = (0.5 (1+h^ν)^γ +0.5 (1+u^λ)^γ)^{-γ^{-1}} The parameters ν and λ take values in [0,2]; the paramete γ take values in [0,1]. The limit of the correlation model as γ tends to zero leads to a separable model. 5. porcu2 (non-separabel space time model) R(h, u) =\frac{ e^{ -h^ν ( 1+u^λ)^{0.5 γ ν}}} { (1+u^λ)^{1.5}} The parameters ν and λ take values in [0,2]; the parameter γ take values in [0,1]. For γ=0 it is a separable model. • Separable models. Space-time separable correlation models are easly obtained as the product of a spatial and a temporal correlation model, that is R(h,u)=R(h) R(u) Several combinations are possible: 1. exp_exp: spatial exponential model and temporal exponential model 2. exp_cauchy: spatial exponential model and temporal cauchy model 3. matern_cauchy: spatial matern model and temporal cauchy model 4. stable_stable: spatial stabel model and temporal stable model Note that some models are nested. (The exp_exp with the stable_stable for instance.) • Spatial taper function models. For spatial covariance tapering the tapered correlation functions are: 1. Wendland1 R(h) = (1-h)^2 (1+0.5 h) 1_{[0,1]}(h) 2. Wendland2 R(h) = (1-h)^4 (1+4 h) 1_{[0,1]}(h) 3. Wendland3 R(h) = (1-h)^6 (1+6 h + 35 h^2 /3) 1_{[0,1]}(h) • Spatio-tempora tapered correlation models. For space-time covariance tapering likelihood the taper functions are obtained as the product of a spatial and a temporal taper (Separable taper). Several combinations are possible: • Wendlandi_Wendlandj: spatial Wendlandi taper and temporal Wendlandj taper with i,j=1,2,3. • Space-time non separable adaptive-taper with dynamically space-time compact support is: • qt_time and qt_space. In The case of qt_time the space-time quasi taper is: T(h,u) = (arg)^{-6} (1+7 x) (1-x)^7 1_{[0,\frac{maxtime}{arg}]}(u) arg=(1+\frac{h}{maxdist} )^β, x=u \frac{ arg}{maxtime} where 0<=β<=1 is a fixed parameter of separability (tapsep), maxtime the fixed temporal compact support and maxdist the fixed spatial scale parameter. The adaptive-taper qt_space is the same taper but changing the time with the space. Remarks: Let R(h) be a spatial correlation model given in standard notation. Then the covariance model applied with arbitrary variance and scale equals to: Similarly if R(h,u) is a spatio-temporal correlation model given in standard notation, then the covariance model is: Here ‘...’ stands for additional parameters. Let R(h) be a spatial taper given in standard notation. Then the taper function applied with an arbitrary compact support (maxdist) equals to: T(h)= R( \frac{h}{maxdist}) Similarly if R(h,u) is a spatio-temporal taper given in standard notation, then the taper function applied with arbitrary compact supports (maxdist, maxtime) equals to: T(h,u)= R( \frac{h}{maxdist},\frac{u}{maxtime}) Then the tapered covariance matrix is obtained as: C_{tap}(h,u)= T(h,u)C(h,u) ## Value Returns an object of class CovMat. An object of class CovMat is a list containing at most the following components: coordx A d-dimensional vector of spatial coordinates; coordy A d-dimensional vector of spatial coordinates; coordt A t-dimensional vector of temporal coordinates; covmatrix The covariance matrix if type isStandard. An object of class spam if type is Tapering corrmodel String: the correlation model; distance String: the type of spatial distance; grid Logical:TRUE if the spatial data are in a regular grid, otherwise FALSE; nozero In the case of tapered matrix the percentage of non zero values in the covariance matrix. Otherwise is NULL. maxdist Numeric: the marginal spatial compact support if type is Tapering; maxtime Numeric: the marginal temporal compact support if type is Tapering; namescorr String: The names of the correlation parameters; numcoord Numeric: the number of spatial coordinates; numtime Numeric: the number the temporal coordinates; param Numeric: The covariance parameters; tapmod String: the taper model if type is Tapering. Otherwise is NULL. spacetime TRUE if spatio-temporal and FALSE if spatial covariance model; In the space-time case covmatrix is the covariance matrix of the random vector Z(s_1,t_1),Z(s_1,t_2),..Z(s_n,t_1),..,Z(s_n,t_m) for n spatial locatione sites and m temporal instants. ## References Bevilacqua, M., Mateu, J., Porcu, E., Zhang, H. and Zini, A. (2010). Weighted composite likelihood-based tests for space-time separability of covariance functions. Statistics and Computing, 20(3), 283-293. Gaetan, C. and Guyon, X. (2010) Spatial Statistics and Modelling. Spring Verlang, New York. Gneiting, T. (2002). Nonseparable, stationary covariance functions for space-time data. Journal of the American Statistical Association, 97, 590–600. Gneiting, T., Genton, M. G. and Guttorp, P. (2007). Geostatistical space-time models, stationarity, separability and full symmetry. In Finkenstadt, B., Held, L. and Isham, V. (eds.), Statistical Methods for Spatio-Temporal Systems, Chapman & Hall/CRC, Boca Raton, pp. 151-175 Schlather, M. (1999) An introduction to positive definite functions and to unconditional simulation of random fields. Technical report ST 99–10, Dept. of Maths and Statistics, Lancaster University Kri, RFsim, FitComposite ## Examples 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 library(CompRandFld) library(spam) ################################################################ ### ### Example 1. Covariance matrix associated to ### a Matern correlation model ### ############################################################### # Define the spatial-coordinates of the points: x <- runif(500, 0, 2) y <- runif(500, 0, 2) matrix1 <- Covmatrix(x, y, corrmodel="matern", param=list(smooth=0.5, sill=1,scale=0.2,mean=0)) dim(matrix1$covmatrix) ################################################################ ### ### Example 3. Covariance matrix associated to ### a space-time double exponential correlation model ### ############################################################### # Define the temporal-coordinates: times <- c(1,2,3) # Define correlation model corrmodel="exp_exp" # Define covariance parameters param=list(scale_s=0.3,scale_t=0.5,sill=1,mean=0) # Simulation of a spatial Gaussian random field: matrix3 <- Covmatrix(x, y, times, corrmodel=corrmodel, param=param) dim(matrix3$covmatrix) ################################################################ ### ### Example 2. Tapered Covariance matrix associated to ### a Matern correlation model ### ############################################################### # Define the spatial-coordinates of the points: #x <- runif(500, 0, 2) #y <- runif(500, 0, 2) #matrix2 <- Covmatrix(x, y, corrmodel="matern", param=list(smooth=0.5, # sill=1,scale=0.2,mean=0),maxdist=0.3,taper="Wendland1", # type="Tapering") # Tapered covariance matrix #as.matrix(matrix2$covmatrix)[1:15,1:15] # Percentage of no zero values in the tapered matrix #matrix2$nozero ################################################################ ### ### Example 4. Tapered Covariance matrix associated to ### a space-time double exponential correlation model ### ############################################################### #param <- list(scale_s=2,scale_t=1,sill=1,mean=0) #matrix4 <- Covmatrix(x, y, times, corrmodel="exp_exp", param=param, maxdist=0.3, # maxtime=2,taper="Wendland2_Wendland2",type="Tapering") # Tapered space time covariance matrix #as.matrix(matrix4$covmatrix)[1:10,1:10] # Percentage of no zero values in the tapered matrix #matrix4$nozero ### Example output Loading required package: dotCall64 Spam version 2.1-1 (2017-07-02) is loaded. Type 'help( Spam)' or 'demo( spam)' for a short introduction and overview of this package. Help for individual functions is also obtained by adding the suffix '.spam' to the function name, e.g. 'help( chol.spam)'. Attaching package: 'spam' The following objects are masked from 'package:base': backsolve, forwardsolve [1] 500 500 [1] 1500 1500 CompRandFld documentation built on Jan. 10, 2020, 9:08 a.m.

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Use this calculator come estimate exactly how much sand in volume (cubic ft, cubic yards, or cubic meters) or load (tons & pounds, tonnes and also kilograms) you would certainly need. It uses conventional sand density. You are watching: Weight of cubic foot of sand ## Calculating exactly how much sand you need Many builders and also gardeners are faced with calculating or estimating the lot of sand they must fill a given room with sand. Our sand calculator is of great utility in together cases, however you have to keep in mind that the results will only be as good as the dimensions entered. The calculation process is as follows: Estimate the volume the sand needed, utilizing geometrical formulas and also plans or measurements.The approximate thickness of sand is 1600 kg/m3 (100 lb/ft3).Multiply the volume by the density (in the very same units) to acquire the weight There is finer and an ext coarse sand, so the density, measured for dry sand in kg every cubic meter or pounds per cubic feet, the your details shipment might vary. Because that this reason, and due come potential loses / waste, girlfriend should take into consideration buying 5-6% much more sand 보다 estimated so friend don"t run just brief of what you need in the end. ### Square or rectangle-shaped area The volume formula because that a rectangle-shaped (or square) crate in cubic feet is height(ft) x width(ft) x length(ft), as seen in the figure below: For example, to to fill a box v a width of 3ft and a length of 6ft, come a depth that 1ft, you need to multiply 1ft x 3ft x 6ft = 18ft3 (cubic feet) that sand. ### Round area If the area you desire to cover, or the shape you want to fill is round, the calculate is a bit different: The volume the a figure with a round foundation is its height times the area that its foundation. To calculate the foundation area we require its diameter, because the formula is π x r2, wherein r is the radius, or diameter/2. ### Irregularly shame area In instance the area you space calculating has actually an irregular shape what you want to perform is division it in numerous regularly-shaped sections, calculate their volume and also sand requirements and then sum them up together. In case you finish up needing to perform this for a huge number of sections, you might use ours summation calculator. ## Sand basics Sand is a naturally arising granular material which is written of finely divided rock and also mineral particles, rounded and also polished come a varying extent. Sand deserve to be believed of together finer gravel, or coarser silt. In part cases, "sand" refers to a textural class of soil, the is - a soil which has more than 85% of its mass consisted of of sand-sized particles. Sand is a renewable source in the long run, yet in human being timescale the is almost non-renewable. Sand is a major component of concrete and due come the high need for concrete because that construction, perfect for concrete sand is also in high demand. The most common constituent that sand in inland continental settings and also non-tropical seaside settings is silica quartz (silicon dioxide - SiO2). The second most common form of sand, mainly encountered in islands and near the sea, is calcium lead carbonate which is produced by miscellaneous life-forms, choose coral and shellfish. Of course, the exact composition will vary depending on local absent sources and also conditions throughout the development of the pebbles. Sand for domestic or garden usage is usually marketed in small packets of number of pounds / kilograms, and for bigger projects in bags the 40, 60 or 80 lbs - 25kg or 50kg in Europe and other places. For building work, concrete mixing, etc. That is marketed by the tonne and also comes in trucks. ## varieties and grades of sand Contrary to what you might think, there is more than one form of sand, through the dimension of its pebbles and it"s intended use <2>. Picking the right type and size is crucial, as part sands have actually a different application 보다 others. Sand typesTypeDescription 20-30 Sandn-standard sand, graded to pass a 850μm sieve and also be retained on a 600μm sieve. Graded Sandn-standard sand, graded in between the 600μm sieve and the 150μm sieve. Standard Sandn-silica sand, composed practically entirely of normally rounded seed of nearly pure quartz (used for mortars and testing that hydraulic cements). Standard sand, in addition, candlestick be irradiate grey or whitish color, have to be cost-free from silt and the grains must be angular, however a small percentage of flaky or rounded particles room permissible. Part manufacturers refer the grade and type of the sand in other ways, e.g. "river sand" (a.k.a. "sharp sand", "builder"s sand", "grit sand", "concrete sand"), "masonry sand", "M-10 sand" (granite sand), "play sand", each being finer and more expensive 보다 the ahead one. ### What is the density of sand? The thickness of typical sand is 100 lb/ft3 (1600 kg/m3). This coincides to moderately wet sand and is the number supplied in the calculator. ### How lot does a yard3 the sand weigh? A cubic yard of typical sand weighs around 2700 pounds or 1.35 tons. A square yard the a sandbox through a depth the 1 foot (30.48 cm) weighs about 900 pounds (410 kg) or slightly less than half a ton. The water content of the sand is presume to it is in moderate. ### How much does a cubic meter that sand weigh? A cubic meter of common sand weighs 1,600 kilograms 1.6 tonnes. A square meter sandbox v a depth the 35 cm weighs around 560 kg or 0.56 tonnes. The numbers are derived using this sand calculator. ### How much is a ton the sand?A ton that sand is typically about 0.750 cubic yards (3/4 cu yd), or 20 cubic feet. Sand is assumed fairly damp, since adding water have the right to increase or diminish the density of the sand significantly (e.g. If it was raining or if you dig up and also leave sand under the sun so water evaporates).How much is a tonne that sand? A tonne of moderately damp sand typically fills about 0.625 m3 (cubic meters). It can be an ext or less thick depending ~ above water content and the dimension of the sand particles. ### Ton vs tonne, loads vs tonnes When calculating the sand"s weight, make certain you execute not confused the tonne (metric ton) through the ton (short ton). The an initial one is supplied by all nations in the world and is defined to be equal to 1000 kg by the worldwide body the standardization. The ton is right now only supplied in the joined States and is equal to 2000 pounds (2000 lbs). The difference in between the 2 is not substantial but have the right to quickly add up to a far-ranging number together the quantity increases. See more: How Many Miles Is 13000 Feet To Miles, Feet To Miles Converter References <1> Krinsley D.H., Smalley I.J. (1972) "Sand", American Scientist 60:286-291 <2> ASTM C-778 - 17 "Standard Specification for traditional Sand" Cite this calculator & page If you"d like to cite this virtual calculator source and info as listed on the page, you deserve to use the following citation: Georgiev G.Z., "Sand Calculator", available at: https://www.yellowcomic.com/calculators/sand-calculator.php URL .

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# Math trivia What's the top number of a fraction called. Addition and Subtraction Worksheets Alien Addition Maze - Students will solve addition problems and color spaces containing the number 6 in the answer to help the alien find the spaceship. Have someone think of their birthday and tell them you are going to guess it. Give it a try and The product of two primes can never be a perfect square. More Cool Trivia Facts: It would also take a length of time far greater than the age of the universe just to write the numbers. Perimeter Worksheet 4 - Find the missing value to make each statement true. A three dimensional parallelogram is called a parallelepiped. Given any four consecutive Fibonacci numbers w, x, y and z, yz — wx forms the hypotenuse, and 2xy and wz form the two other sides of the right triangle. Division Worksheets Reptile Mystery Math - Find the quotients and the names of five reptiles when completing this two page division worksheet. It is the only way that this can be done. He then gave a method for calculating the highest number of grains of sand that can fit into the universe, which was approximately grains of sand in his calculation. Multiply 37, by any single numberthen multiply that number by 3. If you multiply all the divisors of 48 together, it would yield What mathematical symbol did math whiz Ferdinand von Lindemann determine to be a transcendental number in. Identifying Angles Worksheet 1 - Students will identify acute, obtuse, right, and straight angles. What's a polygon with four unequal sides called. If each count were a second long, it would take about 12 days to count to a million and about 32 years to count to a billion. What do you call an angle more than 90 degrees and less than degrees. Sharpen Your Skills Worksheet 8 - Students will gain practice working with decimals and fractions. What handy mathematical instrument's days were numbered when the pocket calculator made the scene in the s. Geometry and Measurement Worksheets Identifying Triangles by Sides - Students will identify equilateral, isosceles, and scalene triangles. The equal sign we're very familiar with has been around since Learn some surprising facts about where important numbers and equations can be traced back to. The product of five consecutive primes yielding a palindrome. If you said yes, take up the quiz below and see how high your score is. Have someone think of their birthday and tell them you are going to guess it. Multiplication Worksheets Math Practice - Students will answer questions, recognize a row and a column, and solve multiplication equations. Trigonometry is the study of the relationship between the angles of triangles and their sides. People back then believe that the number of grains of sand is limitless. An icosagon is a shape with 20 sides. Well here's some pretty cool trivia stuff about the number nine you probably didn't know. But did you know that an easy way to remember pi to 7 places after the decimal. Here is Pi written to 50 decimal places: The term googol a 1 followed by zeroes was first used by a 9- year old boy,Milton Sirotta, in Enjoy trivia and information related to prime numbers, Fibonacci numbers, Pi and much more. It is equal to There is one 8x8 square, four 7x7 squares, nine 6x6 squares, 16 5x5 squares, 25 4x4 squares, 36 3x3 squares, 49 2x2 squares and 64 1x1 squares. Check for yourself at the Tessellations page. This can be written as: An easy way to remember this is by counting each word's letters in "May I have a large container of coffee?. Browse our extensive collection of math trivia and math fun stuff - math games, math tricks, math jokes, riddles, funny quotes, brain teasers, puzzles, mnemonics, humor and many more, to chase the math blues away! Math Facts for Kids. Check out our math facts for kids and enjoy exploring a wide range of fun trivia and interesting information. Learn about numbers, geometry, math history, famous mathematicians and other topics related to the world of mathematics. Looking for top math quizzes? Play math quizzes on ProProfs, the most popular quiz resource. Choose one of the thousands addictive. Mathematics facts on Sciensational - the coolest science facts website in the galaxy! A math student's companion consisting of the most useful rules and memoranda, collected from some of the best texts of the day, and practically tested by many. This work is licensed under a Creative Commons Attribution-NonCommercial License. This means you're free to copy and share these comics (but not to sell them). More details. Math trivia Rated 0/5 based on 43 review Mathematics Trivia

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# chasing 1. ### Proof using Element Chasing the associative law of symetric difference Hi there, I have to prove using Element Chasing that (A delta B) delta C = A delta ( B delta C) I have the Venn drawn, and was told to start with: let x be an element of (A delta B) delta C if x is an element of (A delta B) union(and) C but not in x element (A delta B)... 2. ### Cat chasing mouse problem Hi, Can anyone help me with this: We have a room H deep and W wide. In the far right corner is a mousehole. The cat starts in the bottom left corner, and the mouse starts in the top left corner i.e. cat starts at (0,0) and mouse at (0,H), and the mouse hole is at (W,H). The cat starts to...

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CATEGORIES: # Making the calculus rigorous Before you read: Should the calculus be rigorous? Why? Do you know who made it rigorous? I. Scan the article to say: - what Augustin-Louis Cauchy did during the 1820s - when the graph of a parabola is continuous and discontinuous judging by the picture - wben a function f(x) is differentiable - how Cauchy defined the integral of a function f(x) between the values a and b Monge's educational ideas were opposed by Lagrange, who favoured a more traditional and theoretical diet of advanced calculus and rational mechanics (the application of the calculus to the study of the motion of solids and liquids). Eventually Lagrange won, and the vision of mathematics that was presented to the world was that of an autonomous subject that was also applicable to a broad range of phenomena by virtue of its great generality, a view that has persisted to the present day. During the 1820s Augustin-Louis Cauchy lectured at the École Polytechnique on the foundations of the calculus. Since its invention it had been generally agreed that the calculus gave correct answers, but no one had been able to give a satisfactory explanation of why this was so. Cauchy rejected Lagrange's algebraic approach and proved that Lagrange's basic assumption that every function had a power series expansion was in fact false. Newton had suggested a geometric or dynamic basis for calculus, but this ran the risk of introducing a vicious circle when the calculus was applied to mechanical or geometric problems. Cauchy proposed basing the calculus on a sophisticated and difficult interpretation of the idea of two points or numbers being arbitrarily close together. Although his students disliked the new approach, and Cauchy was ordered to teach material that the students could actually understand and use, his methods gradually became established and refined to form the core of the modern rigorous calculus, a subject now called mathematical analysis. Traditionally, the calculus had been concerned with the two processes of differentiation and integration and the reciprocal relation that exists between them. Cauchy provided a novel underpinning by stressing the importance of the concept of continuity, which is more basic than either. He showed that, once the concepts of a continuous function and limit are defined, the concepts of a differentiable function and an integrable function can be defined in terms of them. Unfortunately, neither of these concepts is easy to grasp, and the much-needed degree of precision they bring to mathematics has proved difficult to appreciate. Roughly speaking, a function is continuous at a point in its domain if small changes in the input around the specified value only produce small changes in the output. Figure 4: Continuous and discontinuous functions. Date: 2015-01-29; view: 723 <== previous page | next page ==> Theory of equations | Encyclopædia Britannica, Inc. doclecture.net - lectures - 2014-2021 year. Copyright infringement or personal data (0.002 sec.)

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View more editions The Mathematical Palette # TEXTBOOK SOLUTIONS FOR The Mathematical Palette 3rd Edition • 1997 step-by-step solutions • Solved by publishers, professors & experts • iOS, Android, & web Over 90% of students who use Chegg Study report better grades. May 2015 Chegg Study Survey PROBLEM Chapter: Problem: SAMPLE SOLUTION Chapter: Problem: • Step 1 of 3 The digits 1, 9, 4 and 4 can be used as follows to create the numbers from 1 to 44 using the symbols addition, subtraction, multiplication, division, powers, square root. • Step 2 of 3 Other numbers are • Step 3 of 3 Remaining numbers are . . . . . Corresponding Textbook The Mathematical Palette | 3rd Edition 9781111793722ISBN-13: 1111793727ISBN: William H HoffmanAuthors:

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[Agda] A different implementation of --without-K Pierre Boutillier pierre.boutillier at pps.univ-paris-diderot.fr Fri Nov 22 14:45:09 CET 2013 ```Hi, I'm working on this problem from the other side. I'm in Coq so I know that I don't have K but I try to push the pattern matching compiler further and further. (Sketch of that can been seen at http://gallium.inria.fr/blog/a-new-Coq-tactic-for-inversion/ ) If I knew a way to characterize the pattern matching problems my algorithm is able to tackle, my phd would have already been sent to its reviewers. Consequently, I'm really really interested by the condition you propose! :-) In fact, I give up on giving a characterisation and I claim that my algorithm works correctly if its type-checking in your (Agda) setting does not use variable - variable equality! That's correct (so I can only argue for your proposal) but not complete. I share with you my archenemy. The problem: {-# OPTIONS --without-K #-} module jouet where data nat : Set where O : nat S : (n : nat) -> nat data fin : nat -> Set where F1 : (n : nat) -> fin (S n) FS : {n : nat} (f : fin n) -> fin (S n) data finEq : {m : nat} -> fin m -> fin m -> Set where F1Eq : {m : nat} -> finEq (F1 m) (F1 m) FSEq : {m : nat} {f1 f2 : fin m} -> finEq f1 f2 -> finEq (FS f1) (FS f2) invertFSEq : {n : nat} {f1 f2 : fin n} -> finEq (FS f1) (FS f2) -> finEq f1 f2 invertFSEq x = {!x!} does NOT imply K. (crazy people could read above the CIC term for it found by my algorithm) But Agda is also right when it says: /tmp/jouet.agda:18,16-20 The variables n n f1 n f2 in the indices {_} FS f1 FS f2 are not distinct (note that parameters count as constructor arguments) when checking that the expression ? has type finEq .f1 .f2 So I'm stuck! I tried to shake my hands and say "unlinearity driven by the type of the inductive family are not K, others are" but I didn't succeed to find a convincing formulation. Definition diag_x1 (x1 : nat__) : Fin__ x1 -> Type := case x1 predicate fun (n2 : nat__) => Fin__ n2 -> Type of |O: fun (_ : Fin O) => True |S: fun (x0 : nat__) => fun (f1' : Fin__ (S_ x0)) => forall (f2 : Fin__ (S_ x0)), FinEq__ (S_ x0) f1' f2 -> Type end. Definition diag_x2 (x2 : nat__) : Fin__ x2 -> Type := case x2 predicate fun (n3 : nat__) => Fin__ n3 -> Type of |O: fun (_ : Fin__ O_) => True |S: fun (x0 : nat__) => fun (f2' : Fin__ (S_ x0)) => forall (f1'' : Fin__ x0), FinEq__ (S_ x0) (FS_ x0 f1'') f2' -> Type end. Definition diag_H (n0 : nat__) : forall (f1 f2 : Fin__ n), FinEq__ n f1 f2 -> Type := case n0 predicate fun (n1 : nat__) => forall (f4 f5 : Fin__ n1), FinEq__ n1 f4 f5 -> Type of |O: fun (f4 f5 : Fin__ O_) (_ : FinEq__ O f4 f5) => True__ |S: fun (x : nat) => fun (f4 : Fin (S x)) => case f4 predicate _diag_x1 of |F1: fun (n1 : nat__) => fun (f5 : Fin__ (S_ n1)) (_ : FinEq__ (S_ n1) (F1_ n1) f5) => True__ |FS: fun (n1 : nat__) (f5 : Fin__ (S n1)) => fun (f6 : Fin__ (S n1)) => (case f6 predicate _diag_x2 of |F1: fun (n2 : nat__) => fun (f7 : Fin n2) (_ : FinEq (S n2) (FS n2 f7) (F1 n2)) => True |FS: fun (n2 : nat__) (f7 : Fin__ n2) => fun (f8 : Fin__ n2) (_ : FinEq__ (S_ n2) (FS_ n2 f8) (FS_ n2 f7)) => FinEq__ n2 f8 f7 end f5) end end. Definition invert_H (n : nat__) (f1 f2 : Fin__ n) (H : FinEq__ (S_ n) (FS_ n f1) (FS_ n f2)) : FinEq__ n f1 f2 := case H predicate fun (n0 : nat__) (f f0 : Fin__ n0) (H' : FinEq__ n0 f f0) => _diag_n f f0 H' of |F1Eq: fun (_ : nat__) => I |FSEq: fun (m : nat__) (f' f'' : Fin__ m) (H0 : FinEq__ m f' f'') => H0 end. Le vendredi 22 novembre 2013 à 13:34 +0100, Jesper Cockx a écrit : > Dear all, > > Lately I have been working on a proof of correctness for the > --without-K flag in Agda (someone should do it, right?). The proof > itself is not quite ready for prime time, but during my investigations > I actually discovered a more general (and, in my eyes, simpler) > formulation of pattern matching without K. In order to play around > with this idea, I implemented a new flag to Agda. Since a good number > of people here seem interested in this subject, I thought I'd share > it. > > The idea is as follows: Suppose we want to split on a variable x of > type "D us" for some data type D with constructors "c_j : Delta_j -> D > vs_j". Instead of putting certain syntactic restrictions on the > indices "us" (as in the current implementation of --without-K), we > limit the algorithm for unification of "us" with "vs_j". We do this by > refusing to deleting reflexive equations of the form "x = x" where x > is a variable. All other unification steps (solution, injectivity, > disjointness, and acyclicity) keep working as usual. So for example, > we allow unifying "suc x" with "suc zero" or "suc x" with "suc > y" (where y != x), but not "suc x" with "suc x". This should rule out > any definitions that depend on K (if my proof is correct). It is also > more general than the current implementation, since the current > implementation guarantees that we will never encounter "x = x" during > unification. > > In the attachment, you can find a patch to darcs agda. At the moment, > it adds a new flag called --new-without-K that restricts the > unification algorithm as described above. Here is an example of the > error message: > K : (A : Set) (x : A) → (p : x ≡ x) → p ≡ refl > K A x refl = refl > > Cannot eliminate reflexive equation x = x of type A because K > has > been disabled. > when checking that the pattern refl has type x ≡ x > One advantage is that this solves the problem where you can split on a > variable of type "something ≡ x", but not "x ≡ something" (see > https://lists.chalmers.se/pipermail/agda/2013/005407.html and > https://lists.chalmers.se/pipermail/agda/2013/005428.html). For > example, the following examples typecheck with --new-without-K enabled > (but not with the old --without-K): > foo : (k l m : ℕ) → k ≡ l + m → {!!} > foo .(l + m) l m refl = {!!} > > bar : (n : ℕ) → n ≤ n → {!!} > bar .zero z≤n = {!!} > bar .(suc m) (s≤s {m} p) = {!!} > I also added two tests to /test/succeed and /test/fail. > > What I'd like you to do, is: > 1. Try out my modification on your favorite examples, > 2. Tell me what you think, > 3. If you think it's good, add it to the main Agda branch. > > Best regards, > Jesper Cockx > _______________________________________________ > Agda mailing list > Agda at lists.chalmers.se > https://lists.chalmers.se/mailman/listinfo/agda ```

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# How to reduce a number value by 1 in Google Sheets row • 2 replies • 1194 views So let’s say I’m counting inventory in a Google Spreadsheet and every time someone sends a payment I want the stock number to be reduced by 1. I currently use Zapier’s ‘Update Spreadsheet Row’ action, but the problem is that I can only replace the content of a cell, but I can’t just reduce the value by the amount of 1. So let’s say the value of that cell is 100 and I want to deduct 1 every time an action is triggered. How do I do that? ### 2 replies Userlevel 7 +14 Hi @K_B Try this… Action: GSheets - Lookup/Find Row Action: Formatter > Number > Perform Math Operation (Subtract 1) Action: GSheets - Update Row Userlevel 7 +11 Just wanted to follow up here to expand on Troy’s suggestion to show how to set up the Formatter step for cases where more than 1 of the same item is ordered. In the example below I’ve step up a Zap that uses the Shopify New Order trigger, but the process should work for any other app that’s sending the quantity ordered value to the Zap. • After the trigger step, a Lookup Spreadsheet Row action (step 2), would be used to search the spreadsheet for the relevant item that was ordered. More details on how to set up search actions like the Lookup Spreadsheet Row one can be found here: Search for existing data in Zaps • Then in a Formatter (Numbers > Perform Math Operation - Subtract) step, you’d select the column that contains the quantity for the relevant item in the Spreadsheet. And select the amount that was ordered from the trigger step: So when we test that action step, the amount ordered (1) is subtracted from the quantity (8), giving us the correct amount of 7: You would then select this output to use as the quantity value in the Update Spreadsheet Row step. This would mean that if 3 of the same item were ordered in a single order, the quantity in the spreadsheet would be reduced by 3. That being said, if it was only possible for one item to be purchased in an order then, instead of selecting the amount that was ordered you could just type in 1. This would mean that every time an order was placed the quantity found by step 2 would have 1 subtracted each time. For example: You can find out more about using Formatter (Numbers > Perform Math Operation) actions here:

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Teaching Guide # Teaching Taxes Make friends with the IRS. Two things are certain in life: death and taxes. But there's another sure thing in the classroom: Shmoop. Don't call H&R Block when you're trying to teach taxes to your class. Check us out instead. In this guide you will find • personal and business tax activities. • a lesson exploring income tax reform. • discussion questions about income tax, sin tax, health care… we're surprised there isn't a tax tax to talk about. Our teaching guide makes it a little less taxing to talk about taxes. Just don't call us come April 15. ## What's Inside Shmoop's Economics Teaching Guides Shmoop is a labor of love from folks who love to teach. Our teaching guides will help you supplement in-classroom learning with fun, engaging, and relatable learning materials that bring economics to life. Inside each guide you'll find quizzes, activity ideas, discussion questions, and more—all written by experts and designed to save you time. Here are the deets on what you get with your teaching guide: • 3-5 activities to complete in class with your students, with detailed instructions for you and your students. • Discussion and essay questions for all levels of students. • Reading quizzes to be sure students are looking at the material through various lenses. • Resources to help make the topic feel more relevant to your 21st-century students. • A note from Shmoop's teachers to you, telling you what to expect from teaching the topic and how you can overcome the hurdles. With your purchase, you'll get unlimited access for 12 months. And if you like what you see, you can subscribe to all 200+ Teaching Guides for just \$19.84/month. ## Instructions for You 1. Sort your students into small groups and give them five minutes to decide what sort of business they would like to open. It must be a two-person operation; they must hire one—but only one—employee. 2. Provide your students with copies of the federal schedule C—the tax form for calculating profit or loss from a business. You can download copies here. Directions for the form are available here. 3. Tell them that their gross income for the year was \$150,000 and that they need to reduce their tax liability to \$75,000. 4. Tell them to fill out Part II, beginning with necessary costs (employee wages, office or shop mortgage or rental, vehicle expenses, etc.). 5. Once they have realistically itemized their necessary costs, they can add other expenses designed to reduce their tax liability and strengthen the business. For example, they may decide to spend more on advertising or build employee loyalty by starting a profit-sharing program. 6. Have the groups present their tax return to the rest of the class; the class should critique the group’s tax and growth strategy. Businesses are required to pay taxes, but the federal tax code provides all sorts of ways for a businessperson to strategically invest their resources. Tax planning is an important part of developing a business plan. Deciding whether to spend more on payroll or advertising, or insurance or machinery, can be a tough call. If you choose wisely though, the money you spend will grow your business and reduce your taxes. Be ready to make these tough decisions. ### OPTIONS FOR PURCHASE For teacher(s). Price: \$14.92 Good things come in affordable packages.

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# [R] shaded area between a curve and a circle Jinsong Zhao j@zh@o @end|ng |rom ye@h@net Sun Oct 23 17:05:29 CEST 2022 ```The figure is not ok. The coordinate of the normal curve is not the same as that of the circle. In fact, there are only four intersections other than eight that your figure show. Best, Jinsong On 2022/10/23 3:05, L... L... wrote: > Dear, I have a picture in which I draw a circle over the standard normal curve. See below the lines used to draw the figure. The figure is ok, but my problem is: How to shade the areas A, B, C, D, E and F? I know I have to find the points of intersection but I don't know how to find them. Suggestions will be welcome. > > library(plotrix) > > x <- seq(-3.0, 3.0, 0.01) > fy <- dnorm(x) > fy <- fy / max(fy) > > x11() > plot(x, fy, ylim = c(-1, 1), col = "white", lwd = 1.5, xlim = c(-3, 3), lty = 1) > draw.circle(0.0, 0.0, 2.00, border = 'blue', lty = 1, lwd = 0.8) > > lines(x, fy, type = 'l', ylim = c(-1,1), col = 'red', ) > lines(x,-fy, type = 'l', ylim = c(-1,1), col = 'red') > > text( 0.0, 0.90, "A"); text( 0.0,-0.90, "B") > text(-1.8, 0.25, "C"); text( 1.8, 0.25, "D") > text(-1.8,-0.25, "E"); text( 1.8,-0.25, "F") > > Best regards > > ML > > > > ________________________________ > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help

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CC-MAIN-2023-14

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http://reference.wolfram.com/language/ref/Ball.html

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# Ball Ball[p] represents the unit ball centered at the point p. Ball[p,r] represents the ball of radius r centered at the point p. Ball[{p1,p2,},r] represents a collection of balls of radius r. # Details • Ball is also known as center interval, disk, ball, and hyperball. • Ball can be used as a geometric region and a graphics primitive. • Ball[] is equivalent to Ball[{0,0,0}]. • Ball[n] for integer n is equivalent to Ball[{0,,0}], a unit ball in . • Ball represents a filled ball . The region is dimensional for point p of length . • Ball allows p to be any point in and r any positive real number. • Ball can be used in Graphics and Graphics3D. • In graphics, the points p, pi and radii r can be Scaled and Dynamic expressions. • Graphics rendering is affected by directives such as FaceForm, EdgeForm, Specularity, Opacity, and color. • Ball[{p1,p2,},{r1,r2,}] represents a collection of spheres with centers pi and radii ri. # Background & Context • Ball is a graphics and geometry primitive that represents a ball in -dimensional space. In particular, Ball[p,r] represents a (filled-in) ball in with center p and radius r, where r may be any non-negative real number and p can have any positive length . The shorthand form Ball[p] is equivalent to Ball[p,1] and Ball[n] is equivalent to Ball[ConstantArray[0, n],1], while Ball[] autoevaluates to Ball[{0,0,0}]. • Collections of ball objects (multi-balls) of common radius may be efficiently represented using Ball[{p1,,pk},r] and balls of varying radii represented using Ball[{p1,,pk},{r1,,rk}]. • Ball objects can be visually formatted in two and three dimensions using Graphics and Graphics3D, respectively. The appearance of Ball objects in graphics can be modified by specifying the edge directive EdgeForm (in 2D) or face directive FaceForm (in 3D), color directives such as Red, the transparency and specularity directives Opacity and Specularity, and the style option Antialiasing. • Ball may also serve as a region specification over which a computation should be performed. For example, Integrate[1,{x,y,z}Ball[{0,0,0},r]] and Volume[Ball[{0,0,0},r]] both return the volume of a 3D ball of radius . • Ball is related to a number of other symbols. Sphere represents the boundary of a ball, as can be computed using RegionBoundary[Ball[{x,y,z},r]]. Ball is a generalization of Interval and Disk to arbitrary dimension, and Ellipsoid is a generalization of Ball in the sense that Ball[{p1,,pk},1] is equivalent to Ellipsoid[{p1,,pk},ConstantArray[1,k]] for all . SphericalShell gives a filled shell obtained by removing a small ball from the interior of a larger concentric ball. Ball objects in 3D may be represented as ImplicitRegion[(x-u)2+(y-v)2+(z-w)2r2,{u,v,w}] or ParametricRegion[a{Cos[θ]Sin[ϕ],Sin[θ]Sin[ϕ],Cos[ϕ]}-{x,y,z},{{θ,0,2π},{ϕ,0,π},{a,0,r}]. Precomputed properties of the 3D ball and its variants in standard position are available using SolidData["entity", "property"] or EntityValue[Entity["Ball","entity"],"property"], where "entity" is one of "Ball" or "HalfBall". # Examples open allclose all ## Basic Examples(2) A unit ball in 3D: In[1]:= Out[1]= In 2D: In[3]:= Out[3]= Volume and centroid: In[1]:= Out[1]= In[2]:= Out[2]=

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https://acedessays.com/machine-learning-4/

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Final Goal: Optimize the portfolio of (experimental) varieties to be grown at the target farm. Information about the target farm is available in the evaluation dataset. The optimal portfolio can have at most 5 varieties of soybean. It is not necessary but you are welcome to use the methods you learn in prescriptive analytics class to construct the optimal portfolio. If you are not familiar with optimization, come up with a meaningful heuristics to construct the portfolio. You are encouraged to divide the project work into three components: Descriptive Analytics, Predictive Analytics, and Prescriptive Analytics. I. Descriptive Analytics Perform an exploratory data analytics to unearth patterns in the given data to educate yourself about the given data. For example, 1. Plot the latitudes and longitudes on a map to visualize the locations of farms. Identify where the target/evaluation farm is located. It should be noted that most of the farms are located in the Midwest of the US. 2. Generate frequency distribution for varieties. Decide if you have enough data for each variety to build dedicated prediction models for every variety. 3. Check to see if there is any relationship between the locations and varieties. Explore if certain varieties are grown more often in some regions than in other regions. 4. Look for patterns in weather variables. Explore relationships between locations and weather related variables. 5. Plot the distribution of the yield variables. Based on the plot, what do you think a realistic goal for the optimal portfolio at the target farm? II. Predictive Analytics Decide a target variable to help you with the project goal. Variety_Yield and Yield_Difference are good candidates for the target variable. Based on the frequency distribution generated in the descriptive analytics, decide which varieties will have its own prediction model. Also, decide which varieties are going to be combined in the same model. Have an identifier for varieties in the combined model so that predictions can be made for individual varieties. Generate models using the following algorithms (if your target variable is continuous): 1. Linear Regression 2. LASSO 3. Regression Tree 4. Bagging 5. Random Forest 6. Boosted Trees 7. Neural Network Generate models using the following algorithms (if your target variable is categorical): 8. Logistic Regression 9. Classification Tree 10. Bagging 11. Random Forest 12. Boosted Trees 13. Neural Network 14. Support Vector Machine Using these models, predict the yield or yield difference for every potential variety at the target/evaluation farm. Depending upon the choice of your target variable, these predictions need not be yield or yield difference. Make predictions for multiple weather related uncertainties. Ensure that chosen weather related scenarios are suitable for the location of the target / evaluation farm. III. Prescriptive Analytics Optimize the portfolio of (experimental) varieties to be grown at the target farm. Experimental varieties are in the column identified as ‘Varieties’. The optimal portfolio can have at most 5 varieties of soybean. It is not necessary but you are welcome to use the methods from the prescriptive analytics class or other optimization classes to construct the optimal portfolio. If you are not familiar with optimization, you can invent your own heuristic to make the recommendation. There will not be any grade penalty for not using optimization. Using a good heuristic will be sufficient to get a good score for this part of the project. Your recommendation should explicitly identify the varieties to be grown and percentage of the farm land allocated for growing those varieties. The percentage of the farm land should add up to 100 percent. Here are two sample heuristics, 15. Naïve Heuristics Based on the predictions, rank the varieties according to their yield potential and recommend the top 5 varieties to be grown at the farm. You could potentially allocate 20 percent of the land for each variety. 16. Mean-Risk Heuristics Based on the predictions, rank varieties based on the mean yield and risk in yield. Recommend the top 5 varieties in these rankings. Allocate land based on the mean yield and risk in yield. Key things to remember while writing the report Perform a literature search using library resources to identify journal publications relevant to your topic. In the literature, do you find interesting methods to make similar recommendations? What do you think about those methods? How is your approach different from those methods? Did your project add incremental value to these existing publications? Note: Utilize at least six peer-reviewed journal (Management Science, Interfaces, Operations Research, Journal of Operations Management, Production of Operations Management, Journal of Portfolio Management, Journal of Finance, etc) or conference articles to synthesize your arguments about the existing methods in the literature. The final report should include Title of the project, Abstract, Keywords, Introduction, Literature Review, Methodology and Analysis, Conclusion, and References. Remember to include the following components in your report: 1) Title. Convey a message using 12 words. Readers should understand the content of the entire report by just reading the title. 2) Abstract. Summarize your report using 300 words. Some readers would read just the abstract to figure out if they would like to read the entire report. You should write a captivating summary of the entire report here. Note: You should just read the title and abstract of many publications as part of your literature review before deciding on the articles that you would like to utilize in your project. 3) Keywords. Include three to five keywords relevant to your project. 4) Introduction. This section should introduce your project. You should include discussions about: What is the motivation behind this project? What is the goal of this project? Which organization benefits from this study? What are the Research Question(s) answered by this project? What methods were utilized? What are the important results and conclusions? 5) Literature Review. Utilize library databases like JSTOR, INFORMS, PUBMED, etc. to find relevant studies (peer-reviewed articles) to your topic. Do you find publications addressing this same problem? Did you add more value to the existing literature by completing this project? Note: Do not base your opinion/findings based on articles that are not peer-reviewed i.e. utilizing newspapers and magazines articles alone are not adequate. 6) Methodology and Analysis. Concisely describe the methods and analysis used in the project. 7) Conclusion – Summarize your methods, analysis, results, and recommendations. What is unique about your work? What are the findings? Are there any surprises? Are the findings beneficial to any organization? 8) References – Include references from your Literature Review. Sample Solution

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http://physics.stackexchange.com/questions/33710/momentum-in-quantum-mechanics

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# Momentum in quantum mechanics In quantum mechanics, we can have some superposition of matter waves that have different wavelengths. If then, can't momentum of a particle change every time measurement takes place? Or should I regard the momentum of a particle as the momentum of the wave packet which has single wavelength and frequence? If then, isn't the momentum of a particle always fixed? Then why do we need uncertainty principle? I think I am somehow messed up with uncertainty principle, but I am unsure what it is... - In the words of Dirac: "A measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured." The state of a quantum system is described by some superpostion (linear combination) of states in whatever basis you choose. For discussions about momentum it is convenient to use the basis of states that are eigenstates of the momentum operator. Now, a wave packet will be a superposition of momentum eigenstates, and the uncertainty in the momentum is given by the width of the wavepacket. However (and this is the crucial point), when you make a measurement of the momentum, the system will jump into one of the eigenstates of the system and the measurement of momentum will be the eigenvalue that corresponds to the given eigenstate. So making the measurement on the system actually changes the state of the system! After the measurement is made the system is no longer in the superposition of states (which had uncertainty in the momentum) but instead is in an eigenstate of definite momentum with no uncertainty. Any further momentum measurement will give this same value. In addition to this you should know that on performing a measurement the probability of obtaining a particular eigenvalue is $|c_n|^2$, where $c_n$ is the coefficient of the particular eigenstate in the linear superposition. The above forms the very core of quantum mechanics and is known as the superpostion principle and holds for any physical observable. It is covered in detail in all good quantum mechanics texts, I particularly recommend section 1.4 of Sakurai's "Modern Quantum Mechanics" where I found the Dirac quote. I think the difficulty you are having in your understanding comes from the contrast in the idealised formalism given above where momentum eigenstates are delta functions, and the reality of real world measurements that can never measure exact values of such continuous observables. In the real world a particle will always be represented by some form of wave packet with some spread in position and momentum. It is sensible to define the position and momentum as the central values of these distributions and be aware that there is some uncertainty in these values. The more accurately we measure one, the more the uncertainty in the other will increase. Whenever a more accurate measurement is made, the state of the system changes and the wave packet becomes more and more localised (in position or momentum space). Future measurements will then be more likely to produce values in this localised region. - How can momentum be conserved, then? – Mark Lucas Aug 8 '12 at 10:27 and then, when we measure the location of a particle, it does not move at all? But this is not true.. – Mark Lucas Aug 8 '12 at 10:29 I have added the final paragraph to my answer to hopefully answer these questions: 1. If there is uncertainty in momentum it can only be conserved up to this uncertainty. 2. The position of the wavepacket will move. However if you were able to measure the momentum exactly and force the system into an idealised momentum eigenstate the position would of course be completely uncertain (the wave function would be infinitely spread out). – Mistake Ink Aug 8 '12 at 12:01

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CC-MAIN-2016-30

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https://tutorbin.com/questions-and-answers/question-2-the-angular-velocity-w-of-a-body-is-given-by-w-51-3j-6k-the-velocity-v-at-a-point-p-with-displacement-vector

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Search for question Question # Question 2: The angular velocity, w, of a body is given by w=-51+3j-6k. The velocity, V. at a point P with displacement vector r=41-7j-3k, can be calculated from the formula V=wxr. Calculate the velocity V, and write your answer in the form [x,y,z], where x, y and z are the x, y and z components of V. Note that you must use square brackets [and], and separate entries by a comma. Fig: 1

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CC-MAIN-2024-38

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http://beaconlearningcenter.com/Lessons/Lesson.asp?ID=2711

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## Fishing for Fun ### Juanita LooperHernando County Schools #### Description Students categorize fish crackers into groups by color then compare the 2 groups using the symbols <, =, and >. #### Objectives The student uses concrete objects to solve number sentences with equalities and inequalities (using the symbols greater than, =, less than). #### Materials -Work mats (suitable ones might be found in a math kit) -Blue construction paper -1 12” x 18” sheet of construction paper per student (any color but blue) -Glue -Laminator -Cheese and pretzel flavored fish crackers (or any other objects that can be divided into 2 groups by some characteristic--colored or shaped candies, cereals, chips or math manipulatives) -Pretzel sticks -Baggies or containers for easy distribution #### Preparations 1. Secure or prepare work mats. Cut out two blue lakes big enough on which to put piles of fish crackers. Glue them to any color 12” x 18” construction paper with enough space between lakes to make the symbols with pretzel sticks. 2. Laminate mats. 3. Purchase two kinds of fish crackers (or other objects) and pretzel sticks. 4. Organize crackers and pretzels in baggies for easy distribution. Each baggie should have 7 to 10 of each type of cracker and 2 pretzel sticks. #### Procedures DAY 1 1. Ask the children, “Did you ever get really tired of writing and wish you had a shortcut for some words? Well, mathematicians must get really tired because they’ve made shortcuts for lots of words. We call those shortcuts symbols. I’m going to teach you about three symbols today.” 2. Discuss with students the symbols <, >. (Think of an arrow always pointing to the baby or smallest thing or group.) 3. Pass out baggies of supplies. 4. Practice making < and > with pretzel sticks. 5. Pass out work mats and fish crackers. 6. Tell the students to separate crackers into 2 groups by color. Put the brown fish in one pile. Place them in one lake. Put the orange fish in the other lake. Count the fish in each lake. 7. Have the students make the correct symbol using pretzel sticks between the two lakes. 8. Continue this practice, telling the students to put various numbers of fish in each lake, always making sure one lake has more than the other. DAY 2 1. Review yesterday’s symbols, and introduce =. Use the same two pretzel sticks as yesterday’s symbols. Explain that this doesn’t make an arrow because it is used when there is no baby object or group. It is important to stress at this time that the = symbol is used when the object or groups are [exactly] the same size. 2. Pass out work mats and fish and have the students practice making equal groups in each lake. 3. Have the students do a mixed practice of equalities and inequalities. (Example: Place 3 fish on the left side. Place 6 fish on the right side. Put the correct symbol in the middle using pretzel sticks.) #### Assessments 1. Observe students making all three symbols (<, =, >) with pretzel sticks on work mats. 2. Observe students placing proper symbol between two piles of fish crackers. Assist any student showing difficulty with the task. #### Extensions ESOL/ESL or ESE students can be paired with a helper.

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https://sandbox.momath.org/home/varsity-math/varsity-math-week-30/

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# Varsity Math, Week 30 This week, it’s gold fever for the Varsity Math team… ### Split Vote A team of 58 prospectors has just recovered a number of identical gold nuggets equal to the answer to last week’s Talking Midpoints problem. They decide upon the following scheme to divide up their treasure. The oldest prospector will propose a plan for how many nuggets each gets; nuggets cannot be divided or discarded. Then all 58 of the prospectors will vote on the plan. If the plan gets at least two more yes votes than no votes, the treasure will be divided according to plan, and the prospectors will all go their separate ways. If it does not, the oldest prospector is ejected from the team and from the International Prospector’s Union, and the process repeats with the 57 remaining prospectors, with the now-oldest prospector proposing a new plan, to be ratified with at least two more yes votes than no, or rejected otherwise, and so on. The prospectors will always act in their own self-interest according to the following priorities: (1) No prospector wants to be ejected from the Union; (2) Every prospector wants to maximize his share of the treasure; (3) Every prospector considers the certainty of a given number of nuggets now to be superior to any chance, less than certainty, of the same number of nuggets later; and (4) all else being equal, every prospector prefers to have less competition by trying to ensure that as many prospectors as possible are ejected from the Union. The priority order of these goals means, for example, that a prospector will never forego a larger share of the treasure for the sake of having an additional team member ejected from the Union. Is there a plan that the oldest prospector can propose that will prevent his ejection from the International Prospector’s Union? If so, what is the largest number of nuggets the oldest prospector can keep in such a plan? ### Treasure Trek Prospector Pete has buried three gold nuggets within a one mile by one mile plot of land. In an effort to slow down and foil thieves, Pete selected locations for the three nuggets to maximize the total distance one has to walk to dig up all three nuggets, starting from the first nugget chosen and ending when the last nugget is reached. How far would you be forced to walk to dig up all three of Prospector Pete’s nuggets? ## Solution to Week 29 Patriotic Packing. Since the glass height and the box height match and the glasses must be upright, this is really a two-dimensional problem of packing circles into a rectangle. Also, to simplify the numbers slightly, notice that we can divide everything by two: the problem is the same as packing unit-diameter circles into a six-by-eight rectangle. It is tempting therefore to think of placing the circles in a square grid pattern, for a total of 48 circles fitting in the rectangle. On the other hand, it is well known that the overall most efficient packing of circles in the plane is in a hexagonal grid, so we need to check how many circles can fit in the rectangle in a hexagonal grid pattern. Imagine an infinite hexagonal grid of unit-diameter circles; how can a six-by-eight rectangle be placed thereon to maximize the number of circles in the rectangle? First, note that we can assume that at least one circle must be tangent to a side of the rectangle — if not, consider the circle that comes closest to a side without being tangent to it, and slide the rectangle toward the center of that circle until it becomes tangent. No formerly whole circles are cut off, because if so, they would have been closer to a side. So all that might possibly happen is that a previously partial circle may have become whole. In any case, the number of circles does not decrease. Similarly, we can assume that at least one side is tangent to more than one circle, because we can rotate the rectangle by the smallest increment that makes one side tangent to two circles. Again, this can’t cut off any formerly whole circles, so the number of circles in the rectangle is no fewer after the rotation. Now it is a matter of trying different configurations in which some side is tangent to at least two circles in a hexagonal packing. A little playing around will make it clear that there are only two orientations that are contenders for packing the most circles — one in which the long side of the rectangle lines up along a row of circles, and one in which the short side of the rectangle lines up along a row of circles. In the former case, we get three rows of 8 circles plus three rows of 7 circles, or 45 circles, into the rectangle — not as good as the square grid. But in the latter case, we get five rows of 6 circles plus four rows of 5 circles for a total of 50 circles, i.e., glasses that the team can pack in a box. (To verify that all 9 rows can fit in the box this way, note that the centers of the rows are the height of a unit equilateral triangle apart, i.e., √3/2, and there is one extra unit of space between the centers of the circles and the walls, and that 1 + 4√3 < 8.) Coach Newton pontificates: Sometimes problem writers like to put in a sneaky backdoor hint. In this case, the best packing for the glasses is the same arrangement as the stars on the American flag! Incidentally, since the flag used a square grid arrangement of the stars back when there were 48 states, this problem shows that you can use equally large stars for 50 states as you could for 48 states. There may be one other thing bothering you. How do we really know that 50 is the greatest number of glasses that can fit? After all, there seems to be wasted space at the two ends of the rows that have only five circles. If we could just consolidate some of that space… Because of the overwhelming optimality of the hexagonal close packing for the plane as a whole, and how well a six-by-eight rectangle meshes with that packing, it’s considered extremely unlikely that any irregular packing could squeeze in a 51st glass (or in other words, we’ll have to make the stars slightly smaller if the United States ever gets a 51st state). But on the other hand, to the best of my knowledge, nobody has ever rigorously proved that it’s impossible to fit in a 51st circle. It’s amazing how easily mathematics can take us to the realm of unsolved mysteries! ## Recent Weeks Links to all of the puzzles and solutions are on the Complete Varsity Math page. Come back next week for answers and more puzzles.

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https://www.geeksforgeeks.org/microsoft-interview-experience-off-campus-internship-2020-summer/?ref=leftbar-rightbar

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# Microsoft Interview Experience | Off Campus Internship 2020 Summer 1. ONLINE ROUND [ONE TEST 2019] [90 mins] • This round was open to students from all the Institutes across India. • This round had 3 coding questions. • Coding questions were very straightforward and were mostly implemented based on little logic required. • One of the questions was • Given a JSON string find the max depth of the string. • Example “a:{b:{a:‘z’, b:‘y’}, c:{z:[2,3]}}”. • Here the max depth is 3. • I was able to solve and submit all 3 questions within 15 or 20 mins. • After a month or, so I got a call for Online Interview. 2. ONLINE INTERVIEW [45 mins] • This round focused on Data Structures, Algorithms, and Implementation. • Only one question was asked in this round. • Problem: Implement a DS that supports 3 operations. • Insert • Delete • Get Random Element (Return a uniformly random element from the set of elements) • It is guaranteed that the elements are unique. • I was asked to implement DS that supports all these operations in O(1) time. • After 15 mins or so I was able to come up with an optimal solution and was able to implement the same within 20 mins. • After a week I received a mail for Onsite Interview. • My Solution. ONSITE INTERVIEW • The interview was at Hyderabad. • Onsite Interview consisted of 2 Rounds. • In my batch, there were 25 students out of which 9 got selected for the Internship. 3. ONSITE ROUND 1 [TECHNICAL] [75 mins] • This round was majorly focused on System Design but 2 DSA questions were also asked. • Question 1 Given a matrix find a submatrix with the maximum sum. • The naive solution takes O(n ^ 4) time. • This is a standard DP question and can be solved in O(n ^ 3) time using  2D Kadane Algorithm. • I gave both solutions. • Question 2 Given a row-wise and column-wise sorted matrix find a given element. • The naive solution takes O(n ^ 2) time. • Can be solved in O(n * log n) time by applying binary search in every row or column. • Can also be solved in O(n) time by starting the search from the top right element. • I gave all 3 solutions. • Both questions were asked in the first 15 minutes of the interview and the rest of the Interview was focused on System Design. • Question 3 Design a Restaurant Management System. 4. ROUND 2 [TECHNICAL + HR] [40 mins] • During this round, Interviewer asked related to resume and my projects. • Question 1 Tell me about yourself. • Question 2 Given two very big numbers (each more than 500 digits), multiply them. • Question 3 In one of my Internships I had created a website (along with one friend), So he asked me to explain my entire process of website development from requirement gathering till deployment. • Similar questions were asked regarding my other projects. • I have done an Internship in my summer vacation of the second year at Samsung R&D Bangalore, So Interviewer asked me whether Samsung offered me an Internship this year and also asked me about my experience there. • The Last Question Three Qualities why we should hire you? • It is a standard question and I gave the answer that I read online. I was selected for the Summer 2020 Internship, also received a PPO at the end of my Internship. All the best for your interviews. Write your Interview Experience or mail it to contribute@geeksforgeeks.org My Personal Notes arrow_drop_up Check out this Author's contributed articles. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. Article Tags : Practice Tags : 6 Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.

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Cody # Problem 615. Nilpotent matrix Solution 90355 Submitted on 20 May 2012 This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass %% x = 1; y_correct = false; assert(isequal(isnilpotent(x),y_correct)) ``` ``` 2   Fail %% x = gallery('chebspec',5,0); y_correct = true; assert(isequal(isnilpotent(x),y_correct)) ```Error: Assertion failed. ``` 3   Fail %% x = gallery('chebspec',3,0); y_correct = true; assert(isequal(isnilpotent(x),y_correct)) ```Error: Assertion failed. ``` 4   Pass %% x = [1 0 0;0 2 0; 0 0 -3]; y_correct = false; assert(isequal(isnilpotent(x),y_correct)) ``` ``` 5   Pass %% x = [6 -9; 4 -6]; y_correct = true; assert(isequal(isnilpotent(x),y_correct)) ``` ``` 6   Pass %% x = rand(50); y_correct = false; assert(isequal(isnilpotent(x),y_correct)) ``` ```

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https://whatsupwhimsy.com/how-to-find-endpoint-with-midpoint-and-other-endpoint-57

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Finding Endpoint Given Midpoint The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the Deal with mathematic equation Math can be difficult, but with a little practice, it can be easy! Get help from expert tutors If you need help with your homework, our expert writers are here to assist you. Solve mathematic equation Solving math problems can be a fun and rewarding experience. Find the missing endpoint, Given the other endpoint and the If you know one endpoint (x1,y1) and the midpoint (a,b), but you do not know the other endpoint (x2,y2), then by rewriting the midpoint formula: {a = x1+x2 2 ⇒ 2a = x1 + x2 ⇒ x What is the Endpoint Formula? How to find the midpoint of a line segment. In order to find the midpoint of the line segment joining the endpoints A and B: Find the average of the \textbf{x} coordinates of the two • 1 Always on Time If you're looking for a punctual person, you can always count on me. • 2 Top Professionals Whether you're looking for a new career or simply want to learn from the best, these are the professionals you should be following. • 3 If you want to enhance your educational performance, focus on your study habits and make sure you're getting enough sleep. • 4 Answers in 5 seconds In just 5 seconds, you can get the answer to your question. Given one endpoint and midpoint in (x,y) of a line segment Given this is your equation for the midpoint: v.x = (xa + xb) / 2; value of x, transform it into something like this: m = (a + b) / 2; and just figure out the b out of that equation, it's just Clear up mathematic problem Having trouble with math? Don't worry, our experts can help clear up any confusion and get you on the right track. Reach support from expert teachers If you're looking for support from expert teachers, you've come to the right place. Get the Most useful Homework solution

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Skip to main content ABC News Can You Plug The White House Leak? Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-sized and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,1 and you may get a shoutout in next week’s column. If you need a hint, or if you have a favorite puzzle collecting dust in your attic, find me on Twitter. ## Riddler Express From Ted Vician, an Oval Office stumper: Let’s say you’re the president of the United States. You have a problem: Someone on your staff keeps leaking stories to the press. So you and your new chief of staff devise a plan. You will give different pieces of information to different staffers so that you’ll learn who the leakers are by what information ends up in the newspaper or on TV. (You know you have only one leaker, and you know he or she leaks any story he or she is given.) If there are 100 people on your staff, how many different stories do you need to identify your leaker for sure? ## Riddler Classic From Dan Waterbury, a tricky table-top geometry problem: Fans of Dungeons & Dragons will have fond feelings for four-sided dice, which are shaped like regular tetrahedrons. Some might have noticed, in those long hours of fantasy battle, that if you touch five of these pyramids face-to-face-to-face, they come agonizingly close to forming a closed pentagon. Alas, there remains a tiny angle of empty space left between two of the pyramids. What is the measure of that angle? ## Solution to last week’s Riddler Express Congratulations to рџ‘Џ Jillian Waid рџ‘Џ of Orwell, Ohio, winner of last week’s Express puzzle! A class of 30 children is playing a game where they all stand in a circle along with their teacher. The teacher is holding two things: a coin and a potato. The game progresses like this: The teacher tosses the coin. Whoever holds the potato passes it to the left if the coin comes up heads and to the right if the coin comes up tails. The game ends when every child except one has held the potato, and the one who hasn’t is declared the winner. How do a child’s chances of winning change depending on where they are in the circle? In other words, what is each child’s win probability? Surprisingly (to me, anyway) each child, no matter where they are in the circle, has the same win probability: 1/30! The puzzle’s submitter, Chris Thornett, walks us through how to get there: Let’s choose a random child and call her Carol. Call the people to her left and right Angela and Bob, respectively. (Angela or Bob could be the teacher.) Either Angela or Bob (or both) must touch the potato before Carol. If Angela touches the potato before Bob, then Carol will win if — and only if — Bob touches it before she does, because this will involve the potato being passed via every other child. The probability of this happening is the same as the probability of a simple random walk moving 29 places to the left before it moves one place to the right. That probability can be calculated as one in 30 (using techniques such as the optional stopping theorem from martingale analysis). Of course, if Bob touches the potato before Angela, then Carol’s win probability is exactly the same, by symmetry. We are now looking instead at a random walk moving 29 places to the right before it moves one place to the left, but the probability does not change. So the probability given either scenario (which are mutually exclusive, and one must happen) is one in 30, so the overall probability is one in 30. Solver Jason Ash confirmed this mathematical result with 2 million computer simulations of this game of hot potato: ## Solution to last week’s Riddler Classic Congratulations to рџ‘Џ Alexander Kobulnicky рџ‘Џ of Portland, Maine, winner of last week’s Classic puzzle! There is a bathroom in your office building that has only one toilet. There is a small sign stuck to the outside of the door that you can slide from “Vacant” to “Occupied” so that no one else will try the door handle (theoretically) when you are inside. Unfortunately, people often forget to slide the sign to “Occupied” when entering, and they often forget to slide it to “Vacant” when exiting. Assume that 1/3 of bathroom users don’t notice the sign upon entering or exiting. Whatever the sign reads before their visit, it still reads the same thing during and after their visit. Another 1/3 of the users notice the sign upon entering and make sure that it says “Occupied” as they enter. However, they forget to slide it to “Vacant” when they exit. The remaining 1/3 of the users are very conscientious: They make sure the sign reads “Occupied” when they enter and “Vacant” when they exit. Finally, assume that the bathroom is occupied exactly half of the time. There is a 62.5 percent chance that the bathroom is occupied if the sign says “Occupied.” There is a 75 percent chance that the bathroom is vacant if the sign says “Vacant.” The puzzle’s submitter, Dave Moran, explains the math: Call the three types of users conscientious (C), semi-conscientious (S) and unconscientious (U). C makes sure the sign is “Occupied” upon entering and “Vacant” upon exiting. S makes sure the sign is “Occupied” upon entering but leaves it at “Occupied” upon exiting. U doesn’t notice the sign at all. If the sign reads “Occupied,” there are four possibilities: 1. Bathroom is occupied by a C. 2. Bathroom is occupied by an S. 3. Bathroom is occupied by a U, and the most recent previous user who was not a U was an S. 4. Bathroom is vacant, and the most recent previous user who was not a U was an S. Possibilities 3 and 4 require a bit of explanation. If the bathroom is currently occupied by a U, it doesn’t matter how many of the preceding users were also U. All that matters is whether the most recent non-U was an S or a C. If it was a C, the sign would read “Vacant” — that conscientious user would’ve slid the sign to “Vacant” upon exiting, and the unconscientious users wouldn’t have changed it. If it was an S, it would read “Occupied.” The same reasoning applies to 4 if the bathroom is currently vacant. So, the probability that the bathroom really is occupied is simply: [(1) + (2) + (3)]/[(1) + (2) + (3) + (4)] The probability of (1) = 1/2 x 1/3 = 1/6 (1/2 chance the bathroom is really occupied and 1/3 chance it’s a C) The probability of (2) = 1/2 x 1/3 = 1/6 (1/2 chance the bathroom is occupied and 1/3 chance it’s an S) The probability of (3) = 1/2 x 1/3 x 1/2 = 1/12 (1/2 chance the bathroom is occupied, 1/3 chance it’s a U and 1/2 chance most recent user who was not a U was an S) The probability of (4) = 1/2 x 1/2 = 1/4 (1/2 chance the bathroom is vacant, 1/2 chance most recent user who was not a U was an S) So the probability is [5/12]/[2/3] = 5/8 = 62.5 percent chance the bathroom is occupied if the sign says “Occupied.” If the sign reads “Vacant,” there are only two possibilities: 1. Bathroom is vacant, and the most recent previous user who was not a U was a C (because an S would have left the sign at “Occupied”). 2. Bathroom is occupied by a U, and the most recent previous user who was not a U was a C. The probability of (5) = 1/2 x 1/2 = 1/4 The probability of (6) = 1/2 x 1/3 x 1/2 = 1/12 (5)/[(5) + (6)] = [1/4]/[1/3] = 3/4 = 75 percent chance the bathroom is vacant if the sign says “Vacant.” Knock knock! For the more visual among you, solver Billy Hines illustrated the possibilities of trips into and out of the bathroom and what that means for the state of the sign: Solver Laurent Lessard took a different approach altogether and showed how the problem could be solved using Markov chains. For extra credit, solver Matt Fay illustrated how these probabilities change as the types of bathroom users in your office change. Intuitively, the more conscientious the employees are, the more accurate the bathroom sign becomes: ## Want to submit a riddle? Email me at oliver.roeder@fivethirtyeight.com. ## Footnotes 1. Important small print: For you to be eligible, I need to receive your correct answer before 11:59 p.m. EDT on Sunday. Have a great weekend! Oliver Roeder was a senior writer for FiveThirtyEight. He holds a Ph.D. in economics from the University of Texas at Austin, where he studied game theory and political competition. Filed under

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# Let A = [[-4,-7,6],[5,10,-10],[-1,-1,0]] , vector v =[[4],[-1],[5]] , vector w = [[-2],[2],[1]] , vector x = [[4],[-4],[3]] Type yes or no:  Is vector x in NulA? sciencesolve | Teacher | (Level 3) Educator Emeritus Posted on You need to test if X is the null space of matrix A, hence, you need to solve the following equation, such that: `A*X = 0` `((-4,-7,6),(5,10,-10),(-1,-1,0))*((x_1),(x_2),(x_3)) = ((0),(0),(0))` Performing the multiplication of matrices yields: `((-4x_1 - 7x_2 + 6x_3),(5x_1 + 10x_2 - 10x_3),(-x_1 - x_2)) =` `((0),(0),(0))` You need to solve for `x_1,x_2,x_3` the following system of equations, such that: `{(-4x_1 - 7x_2 + 6x_3 = 0),(5x_1 + 10x_2 - 10x_3 = 0),(-x_1 - x_2 = 0):}` Replacing -`x_2` for `x_1` yields: `{(4x_2 - 7x_2 + 6x_3 = 0),(-5x_2 + 10x_2 - 10x_3 = 0):}` `{(-3x_2 + 6x_3 = 0),(5x_2 - 10x_3 = 0):} => {(-3x_2 =- 6x_3),(5x_2 - 10x_3 = 0):} => {(x_2 = 2x_3),(5x_2 - 10x_3 = 0):} ` Replacing 2`x_3` for `x_2` yields: `10x_3 - 10x_3 = 0 => x_3 = 0, x_2 = 0, x_1 = 0` You may notice that `X = ((0),(0),(0))` does not coincide with the given `X = ((4),(-4),(3))` , hence, X is not the kernel of matrix A.

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BBA Finance Degree Courses MBA Cost Accounting Certification Exam Tests MBA Cost Accounting Practice Test 105 Books: Apps: The Estimating Cost Function using Quantitative Analysis Quiz Questions and Answers PDF (Estimating Cost Function using Quantitative Analysis Quiz with Answers PDF e-Book) download Ch. 11-105 to prepare MBA Cost Accounting Practice Tests. Solve Cost Function and Behavior MCQ with answers PDF, Estimating Cost Function using Quantitative Analysis Multiple Choice Questions (MCQ Quiz) for online business management classes. The Estimating Cost Function using Quantitative Analysis Quiz App Download: Free learning app for estimating cost function using quantitative analysis, inventory types, inventoriable cost and period cost, value engineering, insurance and lock in costs, internal controls accounting, inventory costing methods test prep for online BBA business administration. The Quiz MCQ: An estimation of relationship between one independent variable and the dependent variable is known as; "Estimating Cost Function using Quantitative Analysis" App Download (Free) with answers: Two way regression; Simple regression; One variable series; Multiple regression; for online business management classes. Learn Cost Function and Behavior Questions and Answers, Apple eBook to download free sample for online accounting certificate programs. ## Estimating Cost Function using Quantitative Analysis Questions and Answers : MCQ 105 MCQ 521: An estimation of relationship between one independent variable and the dependent variable is known as 1. simple regression 2. Two way regression 3. One variable series 4. multiple regression MCQ 522: The wages and other benefits, provided to assembly line workers and operators of machine are classified under the 1. work in process costs 2. finished costs 3. direct manufacturing labor costs 4. indirect manufacturing labor costs MCQ 523: The kind of cost which on elimination, would not reduce the perceived usefulness that customers can obtain by using the market offering is known as 1. designed-in costs 2. locked-in costs MCQ 524: The compelling strategic plan, promoting coordination and providing framework of performance are MCQ 525: In an actual quantity of cost allocation used, base is multiplied to an actual fixed overhead rates, to calculate ### Estimating Cost Function using Quantitative Analysis Learning App: Free Download (Android & iOS) The App: Estimating Cost Function using Quantitative Analysis Quiz App to learn Estimating Cost Function using Quantitative Analysis Textbook, Cost Accounting Quiz App, and Business Mathematics Quiz App. The "Estimating Cost Function using Quantitative Analysis Quiz" App to free download iOS & Android Apps includes complete analytics with interactive assessments. Download App Store & Play Store learning Apps & enjoy 100% functionality with subscriptions! Estimating Cost Function using Quantitative Analysis App (Android & iOS) Cost Accounting App (iOS & Android) Business Mathematics App (Android & iOS) BBA Economics App (iOS & Android)

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https://www.bbcgoodfood.com/user/4526516/recipe/easy-white-sandwhich-loaf

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Ingredients • 500g Strong white flour • 7ml instant yeast • 8g salt • 350ml water Method • STEP 1 For sandwich loaf tin: 807g strong white flour 11g instant yeast 16g salt 565ml water • STEP 2 You will need: 2 x large mixing bowls, Digital weighing scales, Cling film, Spatula or wooden spoon, Sunflower oil for greasing tin, Olive oil for greasing mixing bowls, Rolling pin, Jug to measure water, Dough scraper, Dough lame, Loaf tin, Tin for putting water into to create steam, And plastic spray bottle (optional) • STEP 3 A very important point regarding loaf tins, a lot of tins say they are 2lb, but actually aren't and this can lead to the dough collapsing because it isn't properly supported or the dough's oven spring going over the sides because the tin is too low. The best way to work out the size of your tin is to put it empty on weighing scales, fill it with water to the top and work out how many ml there are for example 1300ml is 1300g. You want a dough that is 60% volume of the tin for white flour or 70% for wholegrain of the tins volume for a loaf that will fill the tin well. So based on the 1300ml we would need a white dough that is 780 (to work this out I divided 1300 by 100 x 60 to work out 60 percent which gave me 780, this is weight of the dough before baking). The best tin in my opinion is an 800g sandwich loaf tin (23cm long, 12cm wide and 12cm tall) which needs more than 800g of dough, so don't be confused by tin size labels. To adjust recipes to suit tin volumes, here is a website with a dough converter: http://bakerybits.co.uk/dough-calculator-bakerybits • STEP 4 Measure out the flour, and put yeast and salt on opposite sides of the bowl. A good way to measure water is on the weighing scales using a jug as 1ml of water weights the same as 1g so 350ml is 350g. Make a well in the middle add the water a bit at a time, using a spatula or a spoon continuing mixing until all water has been added. You will notice that it becomes difficult to mix the dough with just the spatula, so use your hands instead to fold the dough over on itself inside the bowl until it feels firm and comes together. • STEP 5 Lightly flour the work surface and knead the dough for 10 minutes, use a bit more flour if you need to, a dough scraper is very useful at this stage. Divide the dough into two and oil 2 mixing bowls with olive oil, put each ball into 2 separate glass bowls, the bowls should be big enough to allow the dough to at least double in size. Move the balls around so they are covered in the oil. Cover with Clingfilm and leave for a 1 hour and 30 minutes. • STEP 6 Just before 1 hour and 30 minutes is up, turn on the oven to 220 conventional, 200 fan and Gas mark 7, make sure the shelves are arranged so a tin can fit in and the dough has enough room to rise 2-3 inches above the top of the tin, also you need to be able to have a empty tin (I use a 20cm or 8 inch sandwich cake tin) which will be later filled with boiling water to create steam. I have two shelves, one right at the bottom for the empty tin and one on the next level where the loaf tin will go. To test if your dough has risen, use to wet fingers to gently press about 1 inch into and poke two holes into the dough, if the holes stay then the dough has risen enough as it doesn't have any more energy to fill the holes, if it fills in then it needs more time, so keep checking and testing every 5 minutes. If the holes collapse then it has over risen, no need to panic as we just take time off the proofing time. For example if it has over risen by 10 minutes, we reduce time that the dough proofs in tin by 10 minutes and put it into the oven. • STEP 7 Next, lightly flour the work surface, make sure you have lightly oiled the tin with sunflower oil (not olive or vegetable as they vaporize) and you have a rolling pin. Punch both dough's down removing the air, join both together and knead for 30-60 seconds. Then fold the edges of the dough into the centre, moving the dough round as you do, you should end up with a tight ball; this creates tension on the surface of the loaf and helps give the loaf structure. Place the ball on the work surface and using both hands slightly underneath, continue until all the dough is rolled up and sealed. Using a rolling pin, roll the dough out to a large rectangle, the width should be no wider than the tin. When you have done this, start with one end and fold over the dough about a good inch or two from the bottom, using the heel of your hand press firmly on the seal, roll the roll of dough forward and seal again, remember to press firmly as you do. Keep going until all the dough has been rolled and sealed, put the dough into the tin with the seal at the bottom and gently flatten the dough roll in the tin. This video will help: https://www.youtube.com/watch?v=wx5I5O_RoeI • STEP 8 Cover the tin with a tea towel and leave to rise for 30-35 minutes, less if it has over risen. Fill the empty tin that is in the oven with hot/warm water. You can also use the spray bottle to create more steam. To check if the dough has proven enough using your small finger gently poke the dough in the corner, if it fills back then it needs another 5 minutes and then check again in another corner, if it doesn't fill back in then it is ready for the oven. Use a dough lame to score the bread before going into the oven. This controls the oven spring and stood the crust from tearing open. You can cut straight down the middle or a few diagonal cuts across the width of the dough. • STEP 9 The oven should be at the right temperature, steamy and ready for the tin. You can sprinkle water on top and dust with flour and gently rub to give a stone baked affect, you can also spray (using a plastic spray bottle) the top of the dough as this will keep the crust softer for longer and allow for more oven spring. You can also spray the oven before and after the loaf goes into the oven but once the oven door is closed do not open the door for the first 5-10 minutes as this is when the oven spring happens and the crust forms. I would also recommend that you slash the top of the dough with a very sharp serrated knife or dough lame, you can do a long vertical slash all the way down the middle of the loaf, but my personal favorite is 3-4 equally spaced diagonal cuts, make sure that they are quite deep. • STEP 10 Bake at 220 conventional, 200 fan and Gas mark 7 for 20 minutes, remembering to turn the loaf every 10 minutes for an even bake. Turn down to 200 conventional, 180 fan and gas mark 5-6, for 35 minutes, then remove from the loaf from the tin and put back on the shelf for 5 minutes, the loaf if ready when removed from the tin it sounds hollow like a drum. For extra crispiness, you can remove the loaf from the tin and place back in the oven for a further 5 minutes. Let the loaf cool down on a wire rack. Rate this recipe What is your star rating out of 5? Choose the type of message you'd like to post Choose the type of message you'd like to post Overall rating A star rating of 4.5 out of 5.2 ratings

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### Theory 1 Relating chance and probability 2 Terminologies in probability 3 What is the probability of an event ### Exercises 1 Find the number of outcomes Difficulty: easy 2 2 Find out! Difficulty: easy 1 3 Write the outcomes Difficulty: medium 2.5 4 Find the probability Difficulty: medium 3 5 Choose the correct answer Difficulty: medium 4 6 Say true or false Difficulty: hard 4 7 Let's play! Difficulty: hard 6 ### Tests 1 Training test Difficulty: medium 6 ### Teacher manual 1 Methodical recommendation

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Search by Topic Resources tagged with Factorials similar to Binomial Coefficients: Filter by: Content type: Stage: Challenge level: There are 6 results Broad Topics > Numbers and the Number System > Factorials N000ughty Thoughts Stage: 4 Challenge Level: Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . . Fac-finding Stage: 4 Challenge Level: Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful. Factoring Factorials Stage: 3 Challenge Level: Find the highest power of 11 that will divide into 1000! exactly. Factorial Stage: 4 Challenge Level: How many zeros are there at the end of the number which is the product of first hundred positive integers? Powerful Factorial Stage: 3 Challenge Level: 6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!? Forgotten Number Stage: 3 Challenge Level: I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

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