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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 | 3.15625 | CC-MAIN-2024-22 |
## 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 | 2.6875 | CC-MAIN-2024-18 |
# 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. | 4.3125 | CC-MAIN-2018-34 |
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 | 2.984375 | CC-MAIN-2024-38 |
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> | 2.859375 | CC-MAIN-2020-45 |
# 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
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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 | 3 | CC-MAIN-2019-51 |
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 | 2.59375 | CC-MAIN-2017-09 |
# 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; }
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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
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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]
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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.
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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 :)
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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.
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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.
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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!
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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 | 3.03125 | CC-MAIN-2021-31 |
# 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. | 3.78125 | CC-MAIN-2020-24 |
# 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:
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• Two bricks
One brick weighs 1kg and half a brick, how many weigh two bricks?
• Bricks
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• 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?
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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? | 3.90625 | CC-MAIN-2021-25 |
# 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 | 2.71875 | CC-MAIN-2024-10 |
# 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`````` | 3.34375 | CC-MAIN-2021-31 |
# 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. | 2.71875 | CC-MAIN-2024-10 |
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 | 2.734375 | CC-MAIN-2019-13 |
# 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. | 3.515625 | CC-MAIN-2017-34 |
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] | 2.671875 | CC-MAIN-2021-39 |
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# 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
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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. | 4.96875 | CC-MAIN-2024-30 |
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. | 3.703125 | CC-MAIN-2020-05 |
⚠️ 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)
``` | 2.78125 | CC-MAIN-2024-22 |
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Ch07 - Chapter 7 Utility and Demand I The Households Budget...
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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.
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# Deflection Of Cantilever Beam Due To Shear Forces
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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]
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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.
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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 | 3.796875 | CC-MAIN-2019-35 |
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# CS135 Exam Review Session
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## Eric Folland
on 14 March 2011
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#### 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 | 2.65625 | CC-MAIN-2018-47 |
## 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 … | 2.71875 | CC-MAIN-2019-26 |
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 | 2.671875 | CC-MAIN-2024-30 |
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. | 2.828125 | CC-MAIN-2020-10 |
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• 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.
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# 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
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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 | 2.921875 | CC-MAIN-2023-50 |
# 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
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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 | 3.6875 | CC-MAIN-2013-20 |
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.
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• 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.
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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?
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• 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 ?.
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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.
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• 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.
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• 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.
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• 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.
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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.
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• 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.
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• As for WATER AND AIR, they can be PROVEN to exist. Do the same for GRAVITY and i will GLADLY AGREE :))
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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.
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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.
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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?
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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!!!
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9. Yes, classical Newtonian gravity is due to mono magnetic repulsion by gravitons .
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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.
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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
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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 ...
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# 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 | 3.421875 | CC-MAIN-2021-39 |
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. | 2.640625 | CC-MAIN-2024-22 |
# 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. | 3.515625 | CC-MAIN-2022-49 |
# 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)
``````
- | 2.953125 | CC-MAIN-2014-41 |
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