text:
Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem C. 1317. (November 2015)

C. 1317. The interior angles lying at vertices $\displaystyle A$, $\displaystyle B$, $\displaystyle C$ and $\displaystyle D$ of a pentagon $\displaystyle ABCDE$ are $\displaystyle 90^\circ$, $\displaystyle 60^\circ$, $\displaystyle 150^\circ$ and $\displaystyle 150^\circ$, respectively. Furthermore $\displaystyle AB=2BC=\frac 43 AD$. Prove that the line segment joining the intersection of lines $\displaystyle AE$ and $\displaystyle CD$ to the intersection of lines $\displaystyle AD$ and $\displaystyle BC$ is parallel to $\displaystyle AB$.

(5 pont)

Deadline expired on December 10, 2015.

### Statistics:

 157 students sent a solution. 5 points: 94 students. 4 points: 14 students. 3 points: 15 students. 2 points: 19 students. 1 point: 6 students. 0 point: 8 students. Unfair, not evaluated: 1 solutions.

Problems in Mathematics of KöMaL, November 2015


text:
Computer Science
LimitedEditionShawty:

Can someone help? I will post the question below:

LimitedEditionShawty:

Katrin369:

sooo um ya lets try

Katrin369:

what do you think was invented first?

LimitedEditionShawty:

A computer

Katrin369:

how many attempts do you have on this?

LimitedEditionShawty:

2

Katrin369:

Katrin369:

amm ok so try the computer first

Katrin369:

if that does not work

Katrin369:

try

LimitedEditionShawty:

no a microprocessor was made before a computer, I looked up when they were both made

Hoodmemes:

Ok I have done some research on each one The first IPhone was introduced on (June 29, 2007) The first computer was invented in (1943) The first cellular phone created on (April 3, 1973) The world wide web was created in (1989) The microprocessor was invented in (1971)

Katrin369:

same microprocessor: was invented 1971

Katrin369:

so i order its

LimitedEditionShawty:

ok so microprocessor, then computer, then the world wide web, and then first phone then iPhone

Katrin369:

computer microprocessor cellular phone world wide web IPhone

LimitedEditionShawty:

I think that is right, but a phone was made before the world wide web?

Katrin369:

ya I think

Katrin369:

ya

Katrin369:

the CELLULAR phone was

Hoodmemes:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @LimitedEditionShawty I think that is right, but a phone was made before the world wide web? $$\color{#0cbb34}{\text{End of Quote}}$$ The iphone was made (After) world wide web (2007)-Iphone World Wide Web-(1989)

Katrin369:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @Hoodmemes $$\color{#0cbb34}{\text{Originally Posted by}}$$ @LimitedEditionShawty I think that is right, but a phone was made before the world wide web? $$\color{#0cbb34}{\text{End of Quote}}$$ The iphone was made (After) world wide web (2007)-Iphone World Wide Web-(1989) $$\color{#0cbb34}{\text{End of Quote}}$$ and a cellular phone was invented (Before) the world wide web

Katrin369:

don't get those to mixed up ;)

LimitedEditionShawty:

Ok, so I just did it and the correct answer were fiirst computer, microprocessor , first phone, world wide web, then iPone

Katrin369:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @LimitedEditionShawty Ok, so I just did it and the correct answer were fiirst computer, microprocessor , first phone, world wide web, then iPone $$\color{#0cbb34}{\text{End of Quote}}$$ :)

LimitedEditionShawty:

thank you

Katrin369:

Np

Katrin369:

You can DM me or Hoodmemes if you have any questions:)

Hoodmemes:

np.

LimitedEditionShawty:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @Katrin369 You can DM me or Hoodmemes if you have any questions:) $$\color{#0cbb34}{\text{End of Quote}}$$ Ok :)

format: plain


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<meta http-equiv="refresh" content="1; url=/nojavascript/"> Identification of Angles by Vertex and Ray ( Read ) | Geometry | CK-12 Foundation
You are viewing an older version of this Concept. Go to the latest version.

# Identification of Angles by Vertex and Ray

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Remember the skateboard park from the Identify Intersecting and Parallel Lines Concept? Well, Cassie and James are talking about angles now. Take a look.

"Look at the angles of the walkway," James pointed out to Cassie as they looked at the design.

"What do you mean?"

"Well, there are many different angles that are all formed by the walkways. Each walkway has a line, then a turn. You see where the two lines meet, that is a vertex," James said.

"A what?"

"Boy, you need to pay attention in math class, then you would know the parts of an angle," James instructed.

Do you know the parts of an angle?

Pay attention and you will know them by the end of the Concept.

### Guidance

An angle is one of the key geometric figures that you will be working with in geometry. An angle is created when two rays connect at a common point.

You can see here that the two rays are connected at a common endpoint, called a vertex. This forms the angle. An angle is named by points on the rays.

This is angle $ABC$ . The vertex $B$ is always in the middle. The symbol for angle looks like a small angle. Here is how we can name the angle.

$\angle{ABC}$

Angle $ABC$ is named with this symbol.

Name these two angles on your own. Be sure that the vertex is in the middle.

#### Example A

Solution: $\angle{DEF}$

#### Example B

Solution: $\angle{LMN}$

#### Example C

What is the point called where two rays meet in an angle?

Solution: Vertex

Now back to the angles with James and Cassie. Here is the original problem once again.

"Look at the angles of the walkway," James pointed out to Cassie as they looked at the design.

"What do you mean?"

"Well, there are many different angles that are all formed by the walkways. Each walkway has a line, then a turn. You see where the two lines meet, that is a vertex," James said.

"A what?"

"Boy, you need to pay attention in math class, then you would know the parts of an angle," James instructed.

Do you know the parts of an angle?

By now, you should know the parts of an angle. Here is the answer.

An angle is formed when two rays meet at a common endpoint. This common endpoint is called the vertex.

Now James and Cassie can continue to look at the diagram of the school.

### Vocabulary

Point
a location in space that does not have size or shape.
Ray
a line that has one endpoint and continues indefinitely in one direction.
Line
a set of connected points without endpoints.
Line Segment
a set of connected points with two endpoints.
Point of Intersection
the point where two intersecting lines meet.
Intersecting Lines
lines that cross or meet at some point
Parallel Lines
Lines that do not cross or meet EVER and are equidistant.
Angle
a geometric figure formed by two rays that connect at a single point or vertex.
Vertex
The point of intersection of the lines or rays that form an angle

### Guided Practice

Here is one for you to try on your own.

Name the vertex and two rays of the following angle.

First, we can name the vertex of the angle. It is the point where the two rays meet.

The vertex is point E.

The two rays each start at the vertex and branch out.

The first one is ray ED. The second one is ray EF.

### Practice

Directions: Draw a picture to illustrate each of the named geometric figures.

1. $\overrightarrow{AB}$

2. $\overleftrightarrow{CD}$

3. $\overleftrightarrow{DE}$

4. $\angle{ABC}$

5. $\angle{LMN}$

6. $\overline{XY}$

7. $\overrightarrow{PQ}$

8. $\overleftrightarrow{GH}$

9. $\overleftrightarrow{AB} \parallel \overleftrightarrow{DE}$

10. $\overleftrightarrow{LM} \parallel \overleftrightarrow{DE}$

11. $\overleftrightarrow{RS} \parallel \overleftrightarrow{TU}$

12. $\overline{DF} \parallel \overline{XY}$

Directions: Define the following terms.

13. Ray

14. Line

15. Vertex

16. Line Segment


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# Nuclear Science and Techniques

《核技术》(英文版) ISSN 1001-8042 CN 31-1559/TL     2019 Impact factor 1.556

Nuclear Science and Techniques ›› 2018, Vol. 29 ›› Issue (9): 133

• LOW ENERGY ACCELERATOR, RAY AND APPLICATIONS •

### Design and field measurement of a dipole magnet for a newly developed superconducting proton cyclotron beamline

Jun-Sheng Zhang 1,2, Jin-Xing Zheng 1,2, Yun-Tao Song 1,2, Wu-Quan Zhang 1, Ming Li 1,2, Xian-Hu Zeng 1,2

1. 1 Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China
2 University of Science and Technology of China, Hefei 230031, China
• Contact: Jun-Sheng Zhang E-mail:zhangjunsheng90@126.com
PDF ShareIt Export Citation
Jun-Sheng Zhang, Jin-Xing Zheng, Yun-Tao Song, Wu-Quan Zhang, Ming Li, Xian-Hu Zeng. Design and field measurement of a dipole magnet for a newly developed superconducting proton cyclotron beamline.Nuclear Science and Techniques, 2018, 29(9): 133

Abstract:

The design, field quality optimization, multipole field analysis, and field measurement of a dipole for a newly developed superconducting proton cyclotron (SC200) beamline are presented in this paper. The maximum magnetic field of the dipole is 1.35 T; the bending radius is 1.6 m with a proton beam energy in the range of 70–200 MeV. The magnetic field was calculated with 2D and 3D simulations, and measured with a Hall mapping system. The pole shim and end chamfer were optimized to improve the field quality. Based on the simulated results, the multipole field components in the good-field region were studied to evaluate the field quality. The results showed that the field quality is better than ± 5 × 10-4 at 1.35 T with shimming and chamfering. For the transverse field homogeneity, the third-order (B3) and fifth-order (B5) components should be controlled with symmetrical shims. The second-order (B2) component was the main disturbance for the integral field homogeneity; it could be improved with an end chamfer. The magnet manufacturing and field measurement were performed in this project. The measurement results demonstrated that the magnetic design and field quality optimization of the 45° dipole magnet can achieve the desired high field quality and satisfy the physical requirements.


text:
WARNING THIS IS AN OLDER WEB PAGE FROM A COURSE GIVEN IN 2017 AND REMAINS POSTED HERE FOR REFERENCE ONLY The course webpage for the 2019 version of the course.Math 4160: Combinatorial Mathematics - Fall 2017

Contact information:

Mike Zabrocki
Course will take place CLH 110 - TR 2:30-3:45pm
Office: TEL 2026
email: zabrocki@mathstat.yorku.ca
office hours: Monday 12-1pm, Thursday 10-11am or by appointment

Course description:

Topics from algebra of sets, permutations, combinations, occupancy problems, partitions of integers, generating functions, combinatorial identities, recurrence relations, inclusion-exclusion principle, Polya's theory of counting, permanents, systems of distinct representatives, Latin rectangles, block designs, finite projective planes, Steiner triple systems. Prerequisites: SC/MATH 2022 3.00 or SC/MATH 2222 3.00; six credits from 3000-level mathematics courses without second digit 5; or permission of the course coordinator.

The main goal of this course will be to develop four common tools of combinatorics that are used to enumerate finite sets: basic counting principles, bijective arguments, Pólya Theory and generating functions. We will apply these tools to examine specific examples of combinatorial objects. The emphasis of assignments will be on problem solving and development of combinatorial techniques.

The grade for this course will mostly be based on homework assignments (55%). You may work together on these assignments, but I want you to hand in your own work (YOU must work on these problems and they will be compositions so I expect your answers to be original even if you worked with someone). There will be a midterm (20%) and a final (25%) and, although these assignments are take home, you will be expected to work on those problems on your own. You will be able to consult with me on the midterm and final. On the take home assignments I expect original work.

Course references:

• There is no required textbook for this course, but the material that we will cover can be found in many references. If you feel that you want a textbook, a good one that covers this is How to Count: An Introduction to Combinatorics.
• I have taught this course three times before (2003, 2012 and 2014). The last two times I taught the course I took detailed notes: from 2012 and there were some updates from 2014. I will probably not have the time to write detailed notes this year, but I might try to improve what I have into a better form if we cover similar topics.
• Most assignments in this course are more about writing than being able to calculate. You will need to LaTeX your assignments.
• When I do examples in class or in the notes I will sometimes augment a calculation with a calculation in the computer algebra system Sage (e.g. to take a coefficient in a series). Sage is free to download or you can access Sage online through the sage cell server or by opening a Cocalc account. You are welcome to use programs you are more familiar with (e.g. Maple, Matlab or Mathematica) to do the same calculations or there are specific online tools that can do these calculations.
• Other material for this course, announcements and grades will be on the course moodle.
• I will add notes here and will continue to update them. They are based on what I talk about in class and previous versions (2012 and 2014).
• Homework assignments:

WARNING THIS IS AN OLDER WEB PAGE FROM A COURSE GIVEN IN 2017 AND IS HERE FOR REFERENCE ONLY

Announcements:

(Sept. 7, 2017) (I'm writing this at 10am for a 2:30pm class) So today we are going to look at how combinatorics can be used to compute sums of the form $1^r+2^r+...+n^r$. We will just do a bit of experimenting and conjecturing today, but then I want you to go home, watch some videos and do some homework and we will get to the punchline next time.
Please watch the following videos: Then I would like you to to prove the following results using telescoping sums:
• $1^3+2^3+...+n^3 = \frac{n^2(n+1)^2}{4}$
• $1^4+2^4+...+n^4 = \frac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$
• $(1)_k + (2)_k + ... + (n)_k = \frac{(n+1)_{k+1}}{k+1}$
Start typing up those in LaTeX. You don't have to hand it in next time, but you will hand it in when I give you your first homework assignment.

(Sept 7, 2017) In case you are interested in the sage commands that I used to compute $1^6+2^6+...+n^6$, I typed
[sum(i**6 for i in range(1,n+1)) for n in range(1, 11)]
and this gave me the first 10 terms of that sequence.

(Sept 21, 2017) I meant to post the homework yesterday, but there were (and still are) edits to do. The problems won't change, but I will add a few details so please check back. It will be due October 5, 2017. Homework #1. You will turn it in on the moodle in LaTeX/pdf format.

(Oct 5, 2017) I just posted the next homework assignment. It will be due in two weeks (Oct 25 ...corrected from Oct 19 and 23).

(Oct 6, 2017) Please copy the question that you are answering in your assignments. It is always so unclear when reading your assignments what an answer is referring to unless the complete question is there.

(Oct 12, 2017) Please figure out the answers to the matching worksheet for class today.

(Oct 12, 2017) The correct due date is October 25...corrected from Oct 23 and Oct 19 for the homework.

(Oct 12, 2017) I have a cleaner version of the proof of Euler's pentagonal number theorem that I presented roughly last time. A proof of this this result also appears in the recommended book "How to Count".

(Oct 19, 2017) I wrote up a full solution to the problem that we discussed in class today.

(Oct 20, 2017) I haven't had any time this week to finish the homework assignments. I'll start sending back your assignments. I pulled together some examples of what I was seeing to show that there was a range of "just great" (clear, complete, correct) to "really difficult to read." Here is a pdf where I pulled a few of these together.

(Oct 23, 2017) I uploaded feedback on your assignments. I won't be able to give quite so detailed remarks on future assignments, instead I will just give you a grade based on the types of remarks that I gave you here. I will give you until next Monday (Oct 30) to update your homework 1 (if you want). If you want to leave it as is, I will just grade the one that I have. Just as a reminder, I've extended the due date for the second assignment until Oct 25.

(Oct 31, 2017) I just posted the 3rd hw assignment (mostly on) exponential generating functions. It is due Nov 13 (but FYI, we also have the midterm this Thursday, Nov 2 - Monday, Nov 6)

(Nov 2, 2017) The midterm is available starting from 3pm today. It only has 3 problems. As you do this exam, I would like you to keep track of what references you consult (web pages, books, etc.). Please hand in the list with your midterm. Besides consultations with me, would like you to work alone on this assignment. I will have extra office hours for this class 11am-12pm on Friday November 3.

(Nov 17, 2017) Its late, but I want to post a version of the homework tonight, but it could potentially have some corrections.

(Nov 30, 2017) The final is posted. You have until December 8 to finish. If you have an early final schedule, I can extend the deadline, but I need to know in advance.

(Dec 2, 2017) I will hold office hours at the regularly scheduled times on Monday 12pm and Thursday 10am the week of December 4-8.

(Dec 4, 2017) Someone pointed out to me that question 3 did not mention that the expression we were looking was for colorings of the graph with k colors. I have corrected this.


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# How to create a .qs file

• Hello,

For my project that I waited for three days and didn't get any reply (!), here, I need some .qs file named installscript.qs.
I searched the Web and also some parts of Docs but could't find any clear solution for creating that file!
I think the problem of my program is likely that I don't have such a file.
If possible please tell me how to create that file.

Thanks.

• hi
Its mentioned here in this example

I think you just make it by hand. seems to be a script file.

• Thank you for the answer.

My config.xml is the same as the Docs:

<?xml version="1.0" encoding="UTF-8"?>
-<Installer>
<Name>Qt Calculator</Name>
<Version>1.4.0</Version>
<Title>Qt Framework Installer</Title>
<Publisher>Abbasi</Publisher>
<TargetDir>@HomeDir@/InstallationDirectory</TargetDir>
</Installer>

In the package.xml apparently I also need a .ui file. (pageform.ui):

<?xml version="1.0" encoding="UTF-8"?>
-<Package>
<DisplayName>Qt Calculator</DisplayName>
<Description>A Calculator Written in Qt by Purely C++ Code</Description>
<Version>1.4</Version>
<ReleaseDate>2017-07-17</ReleaseDate>
<Name>com.vendor.root</Name>
<Virtual>false</Virtual>
<Default>true</Default>
<Script>installscript.qs</Script>
-<UserInterfaces>
<UserInterface>pageform.ui</UserInterface>
</UserInterfaces>
</Package>

In the Docs, it says: In installscript.qs, we use the Component() function. But while I still don't have such a file how can write into it!!? My program still lacks it.

I then switched to the resource directory (the data folder) by CMD and ran this command (as in the Dos):

C:\Users\Abbasi\Desktop\package_directory\packages\com.vendor.product\data> C:\Qt\QtIFW2.0.1\bin\binarycreator.exe -c C:\Users\Abbasi\Desktop\package_directory\config\config.xml -p C:\Users\Abbasi\Desktop\package_directory\packages Qt_Calculator.exe

I got some errors.

seems to be a script file

Yes it is a script file, and my question is how to have such a file please?

• @tomy

I had used one of the example section as delivered with QTIFW. There is already a newer version QtIFW 2.0.5 available. There are a couple of different of installscript.qs there.

Btw, Funnily, your other post is listed as 2 days ago. Is this an issue with crossing the date line?

Also this is a user forum. You are hardly getting repsonses on issues with Qt IFW.

• @tomy said in How to create a .qs file:

Yes it is a script file, and my question is how to have such a file please?

Have you tried Just to create a new empty file and renamed it to installscript.qs ?

• @koahnig

I had used one of the example section as delivered with QTIFW. There is already a newer version QtIFW 2.0.5 available. There are a couple of different of installscript.qs there.

I searched for that 2.0.5 for my Windows but didn't find, instead I downloaded qt-installer-framework-opensource-2.0.5-src and could find many installscript.qs files. I picked one plus an empty .ui file and named it to pageform. It's empty.
for the installscript.qs I put the code below into it after clearing its previous data.

function Component()
{
// Install to @RootDir@ instead of @HomeDir@ on Windows
if (installer.value("os") === "win") {
var homeDir = installer.value("HomeDir");
var targetDir = installer.value("TargetDir").replace(homeDir, "@RootDir@");
installer.setValue("TargetDir", targetDir);
}

// do not show component selection page
installer.setDefaultPageVisible(QInstaller.ComponentSelection, false);
// no startmenu entry so no need to ask where to create it
}

Now seemingly I have all needed stuffs. I re-ran the command in a CMD and again got errors! :(

Also this is a user forum. You are hardly getting repsonses on issues with Qt IFW.

Dont' millions of programmers create installers for their apps? Is there any simpler and easier means to create installers for our apps. If someone writes a code, they are more eager to create an installer for that, I suppose.

• @mrjj

Have you tried Just to create a new empty file and renamed it to installscript.qs?

Not honestly. But how to? What Project or Classes on Qt Creator IDE?

• @tomy
Just right click and create a text file then rename it. ( in your installer project folder)
Its just a text file type and you add the commands manually.
Seems to be nothing special you need to do.

• @mrjj
Very nifty mrjj. Thanks. :)

Some points in my mind:

• Is the command I use (in CMD) correct?
• Is it acceptable even if the pageform.ui file has nothing special?

• @tomy
Hi
Ï have never used the installer framework so I cant tell.
Did you try the simple example
http://doc.qt.io/qtinstallerframework/ifw-tutorial.html
to get to know it ?

• Hi,
Yeah, I used it. There should be some issue in paths in my stuff. :(

• @tomy
with spaces or what kind of issues?

• Please take a look at this:
https://postimg.org/image/kaf5gm31t/

• @tomy
Oh, there is something in the files it dont like. it seems.

When you tried the example , no errors were displayed?

• @mrjj
The code is of months ago but the Qt_Calculator.exe of Release mode now works fine in the data folder.
I think the problem is of either installscript.qs file or pageform.ui file. :(

• @tomy
But the errors seems to point to package.xml ?

• This is the contents of that file:
https://postimg.org/image/hsuszqcel/

I see nothing clearly wrong in it.

• @tomy
well the errors says it wont use name, but i fail to see the "meta" it talks about.
It also says the default and virtual should not be used together so maybe try to remove one?

• @mrjj
Well it worked, not completely although. :)

I removed that virtual line in the package.xml. And it is in the meta folder. Please look:
https://postimg.org/image/u84mw60p9/

Then re-done the command. It again returned some issues:
https://postimg.org/image/y1wdy7ihz/

It finally created an installer in the Result folder on desktop. But It doesn't put a shortcut of the program on desktop, and it's the contents of the installation folder:
https://postimg.org/image/kvdfu4zcb/

I think now I should somehow change the contents of installscript.qs file.

• @tomy
Yes the installscript.qs should contain the actual
code to execute while installing.

• Yes, it seems to be the last important issue on the app. How to change it to work fine, please?
This is its code:

function Component()
{
// Install to @RootDir@ instead of @HomeDir@ on Windows
if (installer.value("os") === "win") {
var homeDir = installer.value("HomeDir");
var targetDir = installer.value("TargetDir").replace(homeDir, "@RootDir@");
installer.setValue("TargetDir", targetDir);
}

// do not show component selection page
installer.setDefaultPageVisible(QInstaller.ComponentSelection, false);
// no startmenu entry so no need to ask where to create it
}

• @tomy
That i dont know
It seems to be commands from
http://doc.qt.io/qtinstallerframework/scripting.html

So you will also need some copy commands from ( i think)
http://doc.qt.io/qtinstallerframework/operations.html

• OK, mate. I will read both posts precisely and will post again to you here about the results.

• I read the pages and changed the installscript.qs to this:

function Component()
{
if (installer.value("os") === "win")
{
installer.setValue("ApplicationsDir", "ApplicationsDir");
}
}

My purposes were to first make the app be installed in C:\ProgramFiles folder and then to have a shortcut of the app on my Desktop.
The data folder contains a Qt_Calculator.icon file. These are all contents of that folder:
https://postimg.org/image/f3fddnww5/

Then I again used this command:
C:\Users\Abbasi\Desktop\package_directory\packages\com.vendor.product\data> C:\Qt\QtIFW2.0.1\bin\binarycreator.exe -c C:\Users\Abbasi\Desktop\package_directory\config\config.xml -p C:\Users\Abbasi\Desktop\package_directory\packages C:\Users\Abbasi\Desktop\Result\Qt_Calculator.exe

I got an error and a warning as below:
https://postimg.org/image/w6p5ajr25/

At the end, it created the installer but it works this way:
It creates an installer file in the Result folder and have the default path of C:\Users\Abbasi for installation and after installing it creates no shourcut on the Desktop.

• @tomy
I used this

Component.prototype.createOperations = function()
{
try {
// call the base create operations function
component.createOperations();
if (installer.value("os") == "win") {
try {
var userProfile = installer.environmentVariable("USERPROFILE");
installer.setValue("UserProfile", userProfile);
} catch (e) {
// Do nothing if key doesn't exist
}
}
} catch (e) {
print(e);
}
}

• Thank you for your reply, I used your code and only changed MyApp to Qt_Calculator but it even didn't create the installer! :( :(

Component.prototype.createOperations = function()
{
try {
// call the base create operations function
component.createOperations();
if (installer.value("os") == "win") {
try {
var userProfile = installer.environmentVariable("USERPROFILE");
installer.setValue("UserProfile", userProfile);
} catch (e) {
// Do nothing if key doesn't exist
}
}
} catch (e) {
print(e);
}
}

I used the command below and got errors:

And my data folder consists of:

• Hi @tomy the QInstallerFramework can be confusing, especiall if you don't have a workign example, like it seems to be the case for you.

I went and uploded the InstallerFramework example for an Installer with a -Windows- Start Menu entry.

Let's see if the fileupload system of the updated forum works:
seems like a admin/mod only thing.

It boils down to a few steps that we can walk through, if you want to.

if you unzip the file, you get a folder with 2 subfolders config and packages
in the config folder you'll find the config.xml,

In packages you'll find 2 folders data and meta. in Data you place all needed dlls files exe's you need to run your Application without Qt-Installed on your system.

In meta you place the installer script file additional ui-files licenzes etc.

Now open your cmd-line tool on windows.

Win-Key + R
cmd
Enter //ctrl +shift+ enter for elevated rights

//cd to your folder that contains config- and packages folders

//now enter:
c:\Path\to\QtInstallerFrameWork\bin\binarycreator.exe --offline-only -c config\config.xml -p packages TheNameYourInstallerShallHave.exe

let's see if you still get errors.

• Hmm, only some types are allowed it seems. ( even for mods)

• Thank you very much all.
The program/process works fine now.

I think I can use this process for any other new example too, with probably some modifications of course.

I have some questions that will be helpful for my information if they are answered.

1- What is that .ui file for? (while it contains almost nothing!)
2- You programmers do program, but don't you create installers for them? If not, so how could they be useful? And if yes, what tool (if not Qt Installer Framework) do you use for that?
3- Are the errors/warns I get while running the CMD command unimportant and should I ignore them?

Thanks.

Looks like your connection to Qt Forum was lost, please wait while we try to reconnect.


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# Uncertainty principle and the speed of light

If an EM wave only gives us a probability of where a photon may be at a given moment, and the HUP tells us that we can't know the exact location of the photon. Then would it be correct to say that a photon does not travel in a straight line?

If this is true, wouldn't the photon's crooked path mean that it must travel faster than $c$ for us to measure its straight line speed at $c$?

Here's a comparison to explain my question further: If two sprinters run a 100 yard dash in 10 seconds, but one sprinter is required to run in a zigzag manner wouldn't that runner need to run faster than the straight line sprinter for both runners to run the race in 10 seconds. Does the crooked traveling photon need to exceed $c$ for us to measure its straight line speed at $c$?

• the HUP tells us that we can't know the exact location of the photon. No, that is not true. Also, the photon does have not any definite path, crooked or straight. – user140606 Feb 8 '17 at 16:59
• When we measure c don't we assume it is traveling in a straight line? – Lambda Feb 8 '17 at 17:04
• We assume it, in order for it to correspond with what we expect classically, but in Q.M, the laws are different. The second answer on this question says it better than I can: physics.stackexchange.com/q/186170 – user140606 Feb 8 '17 at 17:11
• Great photo of the interferogram by the way. Lovely fringe visibility: I could look at interferograms all day, especially if they are taken with my favorite colors. – WetSavannaAnimal Feb 9 '17 at 0:01
• WetSavannaAnimal aka Rod Vance: Thank you. I have some shots where I put a paper cone under the image. It produces a cool 3d look. The interferometer is mounted onto steel tubing and is rock solid. I can carry it around and the fringes for the most part stay stationary. – Lambda Feb 9 '17 at 1:15

## 4 Answers

First of all, as Countto10 pointed out, in this other question you can find a nice discussion on the meaning of trajectories in quantum mechanics.

Heisenberg's uncertainty principle tells you that when you measure the photon's position or momentum (or any other pair of complementary variables), you will find the results to always affect each other. In other words, a photon cannot have a definite value of position and momentum at the same time.

This does not really come into play if you are trying to measure the speed of light using single photons. Let us imagine for the purpose an experiment in which a single photon is emitted at point $A$ at a known time $t$, and travels towards the point $B$. After the photon is emitted, its wavefunction will expand and evolve according to a variety of factors. For example, the smaller the error in the transverse position when it is emitted, the faster its wavefunction will disperse and so the harder it will be to detect it at $B$. This kind of things can however be taken care of relatively easily, so to make the probability of detecting the photon in $B$ high enough. When this detection event happens, we can measure the time it took and derive the speed of light accordingly.

The photon did not follow a zig zag path going from $A$ to $B$. It didn't simply because that is not how a photon usually travels, and nothing in Heisenberg's uncertainty principle says it should. Its wavefunction did evolve in the process, but it is wrong to think of this in terms of a point particle jiggling around. It means instead that the probabilities of detecting the photon in the various transverse points vary with the longitudinal position.

As a final note, it is worth noting that there should be a lot of buts and ifs in the above argument. For example, I assumed that the emitted photon can be more or less be thought of as a particle-like thing, in the sense of it being relatively well localized. A photon can however also be highly delocalized, or have a complex inner structure. This kind of things can matter: an interesting example is a recent experiment by Bareza and Hermosa in which it was shown that photons carrying an orbital angular momentum can have (in the vacuum) a group velocity smaller than $c$. This is an interesting reminder that the speed of light being $c$ only strictly holds for plane waves in the vacuum, not really for light with finite extent and complex inner structure.

Your crooked path argument holds for a classical electromagnetic wave going through a medium. That is why the speed of light in a medium can be less than c, the speed of light in vacuum. At the photon level it is that photons effectively go a larger distance at velocity c, as they interact individually with the lattice of the material, and a lower group velocity is measured.

In vacuum there are no interactions for the photon, which is a point particle, and its velocity is c and the same is true for the light beam. The Heisenberg uncertainty does not enter.

The validation of this is the validation of the special theory of relativity which has been tested by the myriads of experiments in physics.

From the point of view of worry that the HUP might contradict the existence of the speed limit $c$, one can assuage your worries by pointing out that:

1. $c$ does not primarily mean the speed of light, rather it is a geometric constant that defines our spacetime and experimentally light is observed to move at that speed. See more about this in my answer here and
2. The ban on speeds amounts to a limit to the speed at which information, or a cause-effect relationship can propagate. So an inferred speed exceeding $c$ is not needfully a problem: it only violates known physics if the speed can be interpreted as a propagation speed for a cause-effect relationship. Thus, for example, phase speeds of waves can happily exceed $c$, e.g. at anomalous dispersion wavelengths for light propagation in dielectric materials. Moreover, gainsaying many texts, even group velocities can exceed $c$ in some wavelength bands and for slightly weird materials: that's not even a problem because, although the group velocity approximates the signal speed propagation, it's not exact and the step response of the medium still propagates at less than $c$.

Any speed inferred from the kind of reasoning you are making falls into the category in my point (2) above. There are two reasons for this:

1. Lone photons without quantum measurement cannot be used to transmit information. In particle physics, the propagation of the electromagnetic field is calculated from a superposition of paths of photons - and so called "off-shell" photons (those with speeds other than $c$ - above or below)- enter this calculation. This is not a problem, because information-bearing aspects of the field are still calculated to propagate at $c$;
2. I don't think you have a sound conception of a photon. Please don't take that as an attack as there are a great many education resources out there that give people these kinds of ideas (I was 35 before I shifted on from these ideas). The modern idea is subtler, but much simpler and much sounder logically than the 1920s Bohrian ideas that are still taught. I recommend you begin with Daniel Sank's glorious answer here. Inspired by his answer, I followed up with this one (which may also be useful to you). Indeed, for massless particles like the photon, one cannot even define a sound notion of "position" as one can for nonrelativistic electrons following the nonrelativistic Schrödinger equation.

Light does travel in a straight line, or else there wouldn't be shades!! lol

The EM Wave

The EM wave is used to describe the possibilities of finding a particle at a certain location. But we can't say that the particle is at some particular point in the wave because then we lose the wave analogy. We can only say that the particle exists somewhere in the wave, and by that, we mean the particle is simultaneously everywhere on the wave.

So if the wave continues throughout the universe, that means at the next point in time, the particle could appear from anywhere throughout the universe.

So does that mean an electron near you could end up being at the edge of the universe at the very next moment? YES!!

But basically, the consequences of particles ending up at a very far distance is extremely low that it's considered never to happen.

The Action

In the Uncertainty Principle, there is this thing called action.

The action calculates the crest and troughs in a wave using the mass, time, and distance between the starting and final position of a particle or an object.

If say the final position of a particle is 10 units away(large distance for the particle say), the action of this would correspond to the crest of the wave(skipping the math); simultaneously, the same particle would also appear somewhere on that original wave, say, its 10.1 units away from the final position, the action would correspond to the trough of the wave. Lastly, we only have to add these waves together in order to get the final wave function for the final position of the wave.

The crest and the troughs cancel each other out, and so we get a final wave function of nearly zero possibility of finding the particle at such a large distance.

On the other hand, the possibilities of a particle ending up at a close location are huge. Because instead of canceling each other out, the waves stacks themselves up into a larger wave with much more amplitude, which means a higher chance of finding the particle at that location.

That's why the particles can't get far from their original position, and therefore you shouldn't be worried about its speed exceeding the speed of light.

## protected by Qmechanic♦Feb 8 '17 at 23:59

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

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# How Interesting Is A Basketball Tournament?

Yes, I can hear people snarking, “not even the tiniest bit”. These are people who think calling all athletic contests “sportsball” is still a fresh and witty insult. No matter; what I mean to talk about applies to anything where there are multiple possible outcomes. If you would rather talk about how interesting the results of some elections are, or whether the stock market rises or falls, whether your preferred web browser gains or loses market share, whatever, read it as that instead. The work is all the same.

To talk about quantifying how interesting the outcome of a game (election, trading day, whatever) means we have to think about what “interesting” qualitatively means. A sure thing, a result that’s bound to happen, is not at all interesting, since we know going in that it’s the result. A result that’s nearly sure but not guaranteed is at least a bit interesting, since after all, it might not happen. An extremely unlikely result would be extremely interesting, if it could happen.

In the language of probability, we might describe an result, like, Georgetown winning a game, by some shorthand such as G. We write the probability of an outcome happening as something like pG, or if that seems like too much bother to typeset, p(G). The probability of a particular result is, by definition, some number from 0 (it’s impossible for it to happen) up to 1 (it’s mandatory that it happens), with the increasing number corresponding to the result being more likely. We seem to be looking at an idea of “interesting” that starts out at some large number for a probability pG that’s at or near 0 and which decreases until it gets to a minimum when pG is at 1, since a sure thing is a boring result, while an unlikely result is interesting.

That hasn’t pinned down very much, but then we haven’t finished thinking about what a measure for “interesting” ought to be. For example, suppose we have two different results: say, result C, University of Connecticut winning a game, and result B, Baylor losing a game. A long as these results are independent — one happening doesn’t change the probability of the other happening, which is probably the case unless Connecticut is playing Baylor — then our measure for how interesting it is that Connecticut wins and Baylor loses should be at least as big as how interesting it is the Connecticut wins, or how interesting it is that Baylor loses.

What this is pointing to is a measure of “interesting” that’s based on a logarithm of the probability of the particular result. The logarithm of 1 — the probability of our sure event — is 0. If the probability of result C is pC and the probability of result B is pB, and C and B are independent results so that one happening doesn’t affect the chance the other happens, then the probability that both happen is pC times pB, and the logarithm of the product pC times pB is the logarithm of pC plus the logarithm of pB.

There is one little flaw: the logarithm of a number between 0 and 1 is a negative number, and that’s just the opposite of what we want. That’s easy to fix, though. Just use minus one times the logarithm of the probability, and we have something that perfectly matches what we wanted. The minus logarithm of a probability starts out extremely high — infinitely high, in fact — if the probability is 0; as te probability of the result increases, the minus logarithm decreases, dropping to its smallest value of zero when the probability gets to 1; the minus logarithm of the product of two probabilities is the minus logarithm of the first probability plus the minus logarithm of the second probability. It’s almost perfectly matched to our needs.

So a logarithm seems the way to go, although that raises a follow-up question: which logarithm? The logarithm of a number depends on the base of the logarithm, which can easily be any positive number. If you choose a logarithm base of 10, for example, then 100 has a logarithm of 2, because 102 is equal to 100. If you choose a logarithm base of 5, though, then 100 has a logarithm of about 2.8614, since 52.8614 is approximately 100. If you choose a logarithm base of e — about 2.71828, and this is known as the “natural” logarithm — then 100 has a logarithm of about 4.6052, since 2.718284.6052 is just about 100.

So which one to use? In a sense, it doesn’t make a difference: the qualitative results are going to be the same, with the difference just being how big the numbers are. It’s like the difference between measuring a length in inches, meters, miles, or light-years; the results are all going to be compatible, and the only good reason to choose one over the other is what gives convenient numbers.

Making for a convenient number, then, is to use the logarithm with a base of 2. We’re looking at results that are well-defined to either happen or not happen, and with a logarithm base 2, a result that has probability of 1/2 of happening has a minus logarithm of 1. This seems neat and clean. I’ll throw in some other reasons to make this sound like it makes sense shortly. And, really, if you don’t want to use the logarithm base 2, use some other one. It’ll change the numbers, but not important things like whether one event is more interesting than another.

But simply taking a minus logarithm of the probability of a result doesn’t quite satisfy our sense of how interesting the outcome of a game would be. We can all agree that result S, in which the players for Siena are just about to win when they are struck by rays from a strange magnetic meteorite and transform into superheroes, would be an extraordinarily interesting outcome, but it is so unlikely to happen that the possibility doesn’t make the game more interesting. We need to compensate for this, make our measure of how interesting a result is smaller for results that just don’t happen.

The way we finally patch this up is to multiply the probability of the result by this minus logarithm of the probability, which is a result we could derive rigorously, but I suspect that’s not going to be more convincing. To find how interesting the outcome of the game is, we work out all the different results that we’re interested in — call them A, B, C, and so on, up through some highest imaginable letter such as D — and then add up:

$\left(-p_A \cdot \log\left(p_A\right)\right) + \left(-p_B \cdot \log\left(p_B\right)\right) + \left(-p_C \cdot \log\left(p_C\right)\right) + \left(-p_D \cdot \log\left(p_D\right)\right)$

Here log means the logarithm base 2, but like I said, if you prefer some other base pick that. And yeah, you can remove some of those parentheses, but I didn’t want to write that you were adding together things on a line that didn’t have any plus signs in it.

If all you’re interested in is, for a single game, whether let’s say Siena wins or loses, then there’s two results, W and L. But the probability that Siena loses has to be exactly one minus the probability that Siena wins — the rules of the contest rule out ties, and I suppose they have some way of handling interrupted games — so how interesting the result of Siena’s game is ought to be:

$- p_W \cdot \log\left(p_W\right)- \left(1 - p_W\right)\cdot \log\left(1 - p_W\right)$

(We could also have worked this out from the perspective of the probability of L happening, Siena losing, but why not take the sunny interpretation? Also they’re not in the 2015 contest anyway.)

Now, if the probability of Siena winning pW is 1 — a sure thing — then the outcome of the game is utterly uninteresting; we know what it is without it being done, and our formula there gives an interest level of 0 (although if you want to show that’s so you will have to do a little bit of work). If the probability of Siena winning is 0 — a sure loss — then again, it’s not an interesting game, and again, it has an interest level of 0. If Siena has a slight chance of losing, say pW is 0.9, then the game is a bit interesting, coming in at about 0.469. If Siena has only a slight chance of winning, say pW is 0.1, then the game is just as interesting since it’s just as not-quite-foregone a conclusion: this measure comes in at 0.469. If Siena has a modest but not really good chance of winning, say pW is 0.35, then the game is still more interesting, about 0.93407. And if its chance of winning were 0.65 instead — a modest but not good chance of losing — the game has an interest of 0.93407 again. If the game is a perfect toss-up, Siena having a chance of 0.5 of winning, then the interest level is exactly 1. (If we’d picked logarithms with another base, the interest level would be some other number here.) I like to think this makes intuitive sense; ultimately, we were curious about one thing in the game, the answer to the question, “did Siena win?” 1 seems to me like a reasonable measurement then.

So, by this metric, if a team has a fifty percent chance of winning a game, then the game itself has an interest level of 1, which is probably as reasonable as you could hope. And if the outcome of every game is independent — the result of one game doesn’t change the probability of a win or a loss in other games —- then we should expect the result of 63 separate games to be 1 plus 1 plus 1 et cetera, 63 times over. So if the outcome of a single game, where each team has a 50-50 chance of winning, is 1, then the outcome of the whole tournament with every team evenly matched so is 63.

So that’s at least one answer to the question of how interesting a March Madness-style best-of-64-teams single-elimination tournament is: it’s 63.

## Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

## 14 thoughts on “How Interesting Is A Basketball Tournament?”

1. I’ll hop in at the sweet 16. I’m be in charge of cheering and you can be in charge of the stats :D Super cool post, Joseph!

Like

1. Thanks. I hope to be interesting with this sort of thing. I actually do have a follow-up in the works.

Liked by 1 person

1. Great! I caught the Notre Dame vs Butler game…WOW! Excellence right to the end :D

Like

1. Oh, good, good. Uhm … I called the outcome of that right, if I’m reading my brackets correctly. That seems to have turned out all right.

Liked by 1 person

2. Math as in stats, calculus or algebra has been my weakest link. Still I managed to do Bs for math subjects in university. I am enjoying the way you use math to define things and just want to say thanks for making math not so complicated. This is your passion in spreading math in your topics of your blog 😊 Thanks for the teaching and I am learning☺

Like

3. Excellent post!! Are you perhaps planning to write about entropy?

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# [Tex/LaTex] Code highlighting in ConTeXt

contexthighlighting

What is the best way to highlight code when using ConTeXt? I am aware of support for specific languages, as described on the ConTeXt wiki, but it seems rather limited at present. I know that we could also rely on vim, through the t-vim module.

Now, I wonder if there exists more automated ways to deal with other languages like R, Python, Lisp, Asymptote? Also, I would like to be able to combine verbatim and mathematical notations, as it is currently available in Minted, for example.

A working example would be very appreciated.

If you are willing to use an external tool, then t-vim provides highlighting for many languages. You can use it as follows: define a typing

\usemodule[vim]
\definevimtyping [RUBY]  [syntax=ruby]

and then use it either as an evnironment

    \startRUBY
...
\stopRUBY

or inline

    \inlineRUBY{...}

This module does not support math escape, but with luatex, it is easy to support. Here is a complete example.

\newcatcodetable\minimalmathtable

\startcatcodetable \minimalmathtable
\catcode\backslashasciicode  = \escapecatcode
\catcode\leftbraceasciicode  = \begingroupcatcode
\catcode\rightbraceasciicode = \endgroupcatcode
\catcode\endoflineasciicode  = \activecatcode
\catcode\formfeedasciicode   = \activecatcode
\catcode\spaceasciicode      = \activecatcode
\catcode\dollarasciicode     = \mathshiftcatcode
\stopcatcodetable

\unprotect
\starttexdefinition mathescaped #1
\pushcatcodetable
\setcatcodetable \minimalmathtable
\ctxcommand{parsemath(\!!bs #1 \!!es)}
\popcatcodetable
\stoptexdefinition
\protect

\startluacode
local function unescape(content)
local s = string.gsub(content, '\\\\', '\\')
s = string.gsub(s, '\\{', '{')
s = string.gsub(s, '\\}', '}')
return s
end

local dollar = lpeg.P("$") local nodollar = (1 - dollar) local math = lpeg.Cs(dollar * nodollar^0 * dollar) / unescape local any = lpeg.P(1) local match = lpeg.Cs( (math + any)^0 ) function commands.parsemath(content) local s = lpeg.match(match, content) tex.sprint(s) end \stopluacode \usemodule[vim] \startcolorscheme[pscolor] \definesyntaxgroup [Comment] [command=\mathescaped] \stopcolorscheme \definevimtyping[python][syntax=python] \starttext \startpython # Returns$\sum_{i=1}^{n}i\$
def sum_upto(n)
r = range(1, n+1)
return sum(r)
\stoppython

\stoptext

The same restrictions as the listings package apply, i.e., spaces are active, so you should avoid spaces in math mode.

EDIT: The new (2012.12.17) version of t-vim module supports math escape in the Comment region. To active it you need to pass escape=on to \definevimtyping and use \m{...} or \math{...} for math mode. Thus, instead of the above kludge, you can use

\definevimtyping[python][syntax=python, escape=on]

\startpython
# Returns \m{\sum_{i=1}^{n}i}
def sum_upto(n)
r = range(1, n+1)
return sum(r)
\stoppython


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# Convert Pdf To Png Mac Command Line

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### conversion TeX to image over command line - TeX - LaTeX

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### Mac convert pdf to png command line

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### conversion TeX to image over command line - TeX - LaTeX

MacOS How to convert BMP files to JPEG or PNG format. How to Convert PDF to PNG for Mac/ PC. There are various of worthwhile reasons to convert Portable Document Format - PDF and save as PNG image file on Mac machine or PC. Mac PCL to Any Converter Shell for Mac PDF Stitcher Command Line for Mac.iSkysoft PDF Converter Pro for Mac is a. works from the command prompt. convert multi page pdf to png mac I have a lot.jpeg.png and.pdf Files and I want to convert all of them to.tiff all at once. Application wrapper to the SIPS command line utility. convert pdf to png mac.

• conversion TeX to image over command line - TeX - LaTeX
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• 12.01.2017В В· In computing, Batch processing is the execution of a series of tasks in a program non-interactively. In this guide will offer you 4 simple ways to batch convert several .PNG images to .JPG and vice-versa using Linux command-line tools. Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related.

Mac PCL to Any Converter Shell for Mac PDF Stitcher Command Line for Mac.iSkysoft PDF Converter Pro for Mac is a. works from the command prompt. convert multi page pdf to png mac I have a lot.jpeg.png and.pdf Files and I want to convert all of them to.tiff all at once. Application wrapper to the SIPS command line utility. convert pdf to png mac 16.01.2013В В· The ability to convert a single image file has been around for quite some time and that shouldnвЂ™t be a mystery to those who have used Preview before, but the group conversion ability is limited to newer versions of the app in Mac OS X.

09.08.2019В В· Quite easy. Also, you can utilize Mac Preview to convert PNG to PDF on Mac, even convert PDF to PNG on Mac for your purposes. As mentioned above, one can only convert one PNG to JPG with Preview per time. If you have multiple PNGs to convert, batch conversion will be better. How to convert PNG to JPG on Mac using command line I'm trying to convert, from the command line, .png files of screenshots created by scrot to pdf files. I can successfully do this within shotwell, but I'd like to do it from the command line.

You used to be able to convert BMP images to JPEG, PNG, or GIF format using the Mac Automator program, but as we've noted on my Mac batch image conversion tutorial, this functionality is currently broken, and unless you want to use the Mac command line, using Preview is the only current, free way I know to convert BMP images on a Mac. Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get

How to Convert PDF to PNG for Mac/ PC. There are various of worthwhile reasons to convert Portable Document Format - PDF and save as PNG image file on Mac machine or PC. Convert PDF to PNG Command Line (only $950.00) Windows XP/2003/Vista/7/8/10. Total PDF ConverterX is similar to Total PDF Converter, except it has no GUI. It can be operated in console mode only, and all operations are carried out via command line. Now, nearly all users of this tool refer to it as the most versatile server PDF converter and the handiest one to convert PDF via command line with Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get CoolUtils offers a highly efficient solution for exporting PDF files to image format вЂ“ convert PDF to JPEG command line utility that is capable of both single and batch conversions with fully adjustable parameters. It is Total PDF Converter X, working on Windows server and available for in-building into any client-server application. It is an ideal solution for local networks or online command line option to. A cross-platform GUI- and command-line converter for eps and pdf. mac convert eps to pdf command line For TeX and its derivatives, eps and pdf are the preferred graphics. 2009-РїРѕРІС–РґРѕРјР»РµРЅСЊ: 10-Р°РІС‚РѕСЂС–РІ: 6To run this command, say you have a file named file.pdf in your home directory that you want converted Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get convert pdf image Downloads at Download That. Aiseesoft PDF to Image Converter is the professional PDF to Image Converter program to convert PDF file to lots of image file for you to choose with high quality, such as convert PDF to JPG, PDF to GIF, PDF to TIFF, PNG, BMP, PCX, TGA and so on. Aiseesoft PDF to Image Converter, PDF to Image 05.06.2013В В· Apart from all the software available to convert image files, every Mac comes with the Preview app that can quickly convert most image file types. First, open the вЂ¦ Mac PCL to Any Converter Shell for Mac PDF Stitcher Command Line for Mac.iSkysoft PDF Converter Pro for Mac is a. works from the command prompt. convert multi page pdf to png mac I have a lot.jpeg.png and.pdf Files and I want to convert all of them to.tiff all at once. Application wrapper to the SIPS command line utility. convert pdf to png mac First command splits all pages second command converts page by page to png. You can keep them png or just convert them to jpeg. ls ./p*.png xargs -L1 -I {} convert {} -quality 100 -density 300 {}.jpg Compared to pdfimages, gs, and ImageMagick's convert I find inkscape's export the best in quality. Mac PCL to Any Converter Shell for Mac PDF Stitcher Command Line for Mac.iSkysoft PDF Converter Pro for Mac is a. works from the command prompt. convert multi page pdf to png mac I have a lot.jpeg.png and.pdf Files and I want to convert all of them to.tiff all at once. Application wrapper to the SIPS command line utility. convert pdf to png mac Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get First command splits all pages second command converts page by page to png. You can keep them png or just convert them to jpeg. ls ./p*.png xargs -L1 -I {} convert {} -quality 100 -density 300 {}.jpg Compared to pdfimages, gs, and ImageMagick's convert I find inkscape's export the best in quality. 20.10.2014В В· Use ImageMagick which is installed on most Linux systems by default. Simply using the convert command should work. convert file.png file.pdf as an example. If you want to do multiple png files to pdf in the same directory you can just modify the command to suit your needs and whether you want the .png files created to one .pdf or multiple. You ## Pdf to png mac command line WordPress.com Convert to PNG Mac Informer Command line application to. 15.01.2019В В· Also, it is the defaulted format to save screenshots. Unlike PNG, PDF works as a perfect carrier to present text, media and interactive elements on different platforms, which makes it necessary to convert PNG to PDF on Mac. There are 5 workarounds to convert PNG to PDF on Mac. Follow the tutorial and you will find how easy the PNG to PDF, Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related.. ### Pdf to png mac command line WordPress.com 10.4 Convert document formats on the command line Mac OS. The specialty of ImageMagick is that it uses "Command-line" to execute its functionality. ImageMagick runs well on Linux, UNIX, iOS and Window platforms. ImageMagick is a command line tool that can alter or change the form over bitmap pictures. Thus to convert the PDF to transparent PNG, the following steps will assist you: Step 1. Launch the, 20.10.2014В В· Use ImageMagick which is installed on most Linux systems by default. Simply using the convert command should work. convert file.png file.pdf as an example. If you want to do multiple png files to pdf in the same directory you can just modify the command to suit your needs and whether you want the .png files created to one .pdf or multiple. You. Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get 20.10.2014В В· Use ImageMagick which is installed on most Linux systems by default. Simply using the convert command should work. convert file.png file.pdf as an example. If you want to do multiple png files to pdf in the same directory you can just modify the command to suit your needs and whether you want the .png files created to one .pdf or multiple. You There's a new command line (unix) utility in OS X 10.4 called textutil which will convert document formats known to the Cocoa layer. According to the man page (man textutil), the formats supported are: txt, html, rtf, rtfd, doc, wordml, or webarchive. 18.01.2017В В· PNG to PDF - Convert PNG Images to PDF File on Mac/Windows/Online. Want to convert PNG to PDF? After all, in your daily work and life, you may need to convert PNG images to PDF file for sending people using email. How to Convert PDF to PNG for Mac/ PC. There are various of worthwhile reasons to convert Portable Document Format - PDF and save as PNG image file on Mac machine or PC. There's a new command line (unix) utility in OS X 10.4 called textutil which will convert document formats known to the Cocoa layer. According to the man page (man textutil), the formats supported are: txt, html, rtf, rtfd, doc, wordml, or webarchive. Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related. There's a new command line (unix) utility in OS X 10.4 called textutil which will convert document formats known to the Cocoa layer. According to the man page (man textutil), the formats supported are: txt, html, rtf, rtfd, doc, wordml, or webarchive. 16.01.2013В В· The ability to convert a single image file has been around for quite some time and that shouldnвЂ™t be a mystery to those who have used Preview before, but the group conversion ability is limited to newer versions of the app in Mac OS X. However, if you have a lot of BMP images, and want to convert them all to JPEG or PNG format, you'll probably want to look at a Mac command-line tool like ImageMagick. (Unfortunately my Mac batch image conversion tutorial using the Mac Automator doesn't work вЂ¦ There's a new command line (unix) utility in OS X 10.4 called textutil which will convert document formats known to the Cocoa layer. According to the man page (man textutil), the formats supported are: txt, html, rtf, rtfd, doc, wordml, or webarchive. You used to be able to convert BMP images to JPEG, PNG, or GIF format using the Mac Automator program, but as we've noted on my Mac batch image conversion tutorial, this functionality is currently broken, and unless you want to use the Mac command line, using Preview is the only current, free way I know to convert BMP images on a Mac. The specialty of ImageMagick is that it uses "Command-line" to execute its functionality. ImageMagick runs well on Linux, UNIX, iOS and Window platforms. ImageMagick is a command line tool that can alter or change the form over bitmap pictures. Thus to convert the PDF to transparent PNG, the following steps will assist you: Step 1. Launch the 18.01.2017В В· PNG to PDF - Convert PNG Images to PDF File on Mac/Windows/Online. Want to convert PNG to PDF? After all, in your daily work and life, you may need to convert PNG images to PDF file for sending people using email. 12.01.2017В В· In computing, Batch processing is the execution of a series of tasks in a program non-interactively. In this guide will offer you 4 simple ways to batch convert several .PNG images to .JPG and vice-versa using Linux command-line tools. Convert Files By Command Line. What is the command line? The command line is one of the most widely known, accepted and implemented methods for allowing one software app to initiate another app. That's why we've made it our goal to make all of our software command line able. Automate document conversions with the 'Convert Doc' command line using: I'm trying to convert, from the command line, .png files of screenshots created by scrot to pdf files. I can successfully do this within shotwell, but I'd like to do it from the command line. However, if you have a lot of BMP images, and want to convert them all to JPEG or PNG format, you'll probably want to look at a Mac command-line tool like ImageMagick. (Unfortunately my Mac batch image conversion tutorial using the Mac Automator doesn't work вЂ¦ 05.06.2013В В· Apart from all the software available to convert image files, every Mac comes with the Preview app that can quickly convert most image file types. First, open the вЂ¦ Mac PCL to Any Converter Shell for Mac PDF Stitcher Command Line for Mac.iSkysoft PDF Converter Pro for Mac is a. works from the command prompt. convert multi page pdf to png mac I have a lot.jpeg.png and.pdf Files and I want to convert all of them to.tiff all at once. Application wrapper to the SIPS command line utility. convert pdf to png mac Convert PNG Files Mac Informer. Featured Convert PNG Files free downloads and reviews. Latest updates on everything Convert PNG Files Software related. 16.01.2013В В· The ability to convert a single image file has been around for quite some time and that shouldnвЂ™t be a mystery to those who have used Preview before, but the group conversion ability is limited to newer versions of the app in Mac OS X. 12.12.2006В В· Hi Leute, die Suche findet nicht mal was bei "pdf"... wie klГ¤glich. Gibt es ein Freeware-Program um pdf in png umzuwandeln? Ich finde irgentwie keins...:noplan: Jemand ne Idee? 20.10.2014В В· Use ImageMagick which is installed on most Linux systems by default. Simply using the convert command should work. convert file.png file.pdf as an example. If you want to do multiple png files to pdf in the same directory you can just modify the command to suit your needs and whether you want the .png files created to one .pdf or multiple. You 15.01.2019В В· Also, it is the defaulted format to save screenshots. Unlike PNG, PDF works as a perfect carrier to present text, media and interactive elements on different platforms, which makes it necessary to convert PNG to PDF on Mac. There are 5 workarounds to convert PNG to PDF on Mac. Follow the tutorial and you will find how easy the PNG to PDF You used to be able to convert BMP images to JPEG, PNG, or GIF format using the Mac Automator program, but as we've noted on my Mac batch image conversion tutorial, this functionality is currently broken, and unless you want to use the Mac command line, using Preview is the only current, free way I know to convert BMP images on a Mac. Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get 15.01.2019В В· Also, it is the defaulted format to save screenshots. Unlike PNG, PDF works as a perfect carrier to present text, media and interactive elements on different platforms, which makes it necessary to convert PNG to PDF on Mac. There are 5 workarounds to convert PNG to PDF on Mac. Follow the tutorial and you will find how easy the PNG to PDF Convert Files By Command Line. What is the command line? The command line is one of the most widely known, accepted and implemented methods for allowing one software app to initiate another app. That's why we've made it our goal to make all of our software command line able. Automate document conversions with the 'Convert Doc' command line using: There's a new command line (unix) utility in OS X 10.4 called textutil which will convert document formats known to the Cocoa layer. According to the man page (man textutil), the formats supported are: txt, html, rtf, rtfd, doc, wordml, or webarchive. 05.06.2013В В· Apart from all the software available to convert image files, every Mac comes with the Preview app that can quickly convert most image file types. First, open the вЂ¦ 20.10.2014В В· Use ImageMagick which is installed on most Linux systems by default. Simply using the convert command should work. convert file.png file.pdf as an example. If you want to do multiple png files to pdf in the same directory you can just modify the command to suit your needs and whether you want the .png files created to one .pdf or multiple. You Convert PNG Files Mac Informer. Featured Convert PNG Files free downloads and reviews. Latest updates on everything Convert PNG Files Software related. 15.01.2019В В· Also, it is the defaulted format to save screenshots. Unlike PNG, PDF works as a perfect carrier to present text, media and interactive elements on different platforms, which makes it necessary to convert PNG to PDF on Mac. There are 5 workarounds to convert PNG to PDF on Mac. Follow the tutorial and you will find how easy the PNG to PDF The specialty of ImageMagick is that it uses "Command-line" to execute its functionality. ImageMagick runs well on Linux, UNIX, iOS and Window platforms. ImageMagick is a command line tool that can alter or change the form over bitmap pictures. Thus to convert the PDF to transparent PNG, the following steps will assist you: Step 1. Launch the 12.12.2006В В· Hi Leute, die Suche findet nicht mal was bei "pdf"... wie klГ¤glich. Gibt es ein Freeware-Program um pdf in png umzuwandeln? Ich finde irgentwie keins...:noplan: Jemand ne Idee? Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related. Convert PNG Files Mac Informer. Featured Convert PNG Files free downloads and reviews. Latest updates on everything Convert PNG Files Software related. 05.06.2013В В· Apart from all the software available to convert image files, every Mac comes with the Preview app that can quickly convert most image file types. First, open the вЂ¦ command line option to. A cross-platform GUI- and command-line converter for eps and pdf. mac convert eps to pdf command line For TeX and its derivatives, eps and pdf are the preferred graphics. 2009-РїРѕРІС–РґРѕРјР»РµРЅСЊ: 10-Р°РІС‚РѕСЂС–РІ: 6To run this command, say you have a file named file.pdf in your home directory that you want converted ### 10.4 Convert document formats on the command line Mac OS Pdf to png mac command line WordPress.com. 12.12.2006В В· Hi Leute, die Suche findet nicht mal was bei "pdf"... wie klГ¤glich. Gibt es ein Freeware-Program um pdf in png umzuwandeln? Ich finde irgentwie keins...:noplan: Jemand ne Idee?, I'd like to generate an image with math formulas with TeX from command line. Something like:$ tex-executable "E=\frac{m_1v^2}{2}" e2.png I have MacTex 2009 installed and I'm pretty sure that something like that already exists in this distribution..

MacOS How to convert BMP files to JPEG or PNG format. 12.12.2006В В· Hi Leute, die Suche findet nicht mal was bei "pdf"... wie klГ¤glich. Gibt es ein Freeware-Program um pdf in png umzuwandeln? Ich finde irgentwie keins...:noplan: Jemand ne Idee?, 09.08.2019В В· Quite easy. Also, you can utilize Mac Preview to convert PNG to PDF on Mac, even convert PDF to PNG on Mac for your purposes. As mentioned above, one can only convert one PNG to JPG with Preview per time. If you have multiple PNGs to convert, batch conversion will be better. How to convert PNG to JPG on Mac using command line.

### MacOS How to convert BMP files to JPEG or PNG format

womit pdf in png umwandeln? MacUser.de. CoolUtils offers a highly efficient solution for exporting PDF files to image format вЂ“ convert PDF to JPEG command line utility that is capable of both single and batch conversions with fully adjustable parameters. It is Total PDF Converter X, working on Windows server and available for in-building into any client-server application. It is an ideal solution for local networks or online Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related..

Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get 16.01.2013В В· The ability to convert a single image file has been around for quite some time and that shouldnвЂ™t be a mystery to those who have used Preview before, but the group conversion ability is limited to newer versions of the app in Mac OS X.

First command splits all pages second command converts page by page to png. You can keep them png or just convert them to jpeg. ls ./p*.png xargs -L1 -I {} convert {} -quality 100 -density 300 {}.jpg Compared to pdfimages, gs, and ImageMagick's convert I find inkscape's export the best in quality. Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related.

16.01.2013В В· The ability to convert a single image file has been around for quite some time and that shouldnвЂ™t be a mystery to those who have used Preview before, but the group conversion ability is limited to newer versions of the app in Mac OS X. I'd like to generate an image with math formulas with TeX from command line. Something like: $tex-executable "E=\frac{m_1v^2}{2}" e2.png I have MacTex 2009 installed and I'm pretty sure that something like that already exists in this distribution. 18.01.2017В В· PNG to PDF - Convert PNG Images to PDF File on Mac/Windows/Online. Want to convert PNG to PDF? After all, in your daily work and life, you may need to convert PNG images to PDF file for sending people using email. 18.01.2017В В· PNG to PDF - Convert PNG Images to PDF File on Mac/Windows/Online. Want to convert PNG to PDF? After all, in your daily work and life, you may need to convert PNG images to PDF file for sending people using email. Convert PDF to PNG Command Line (only$950.00) Windows XP/2003/Vista/7/8/10. Total PDF ConverterX is similar to Total PDF Converter, except it has no GUI. It can be operated in console mode only, and all operations are carried out via command line. Now, nearly all users of this tool refer to it as the most versatile server PDF converter and the handiest one to convert PDF via command line with Convert PDF to PNG Command Line (only $950.00) Windows XP/2003/Vista/7/8/10. Total PDF ConverterX is similar to Total PDF Converter, except it has no GUI. It can be operated in console mode only, and all operations are carried out via command line. Now, nearly all users of this tool refer to it as the most versatile server PDF converter and the handiest one to convert PDF via command line with Convert PDF to PNG Command Line (only$950.00) Windows XP/2003/Vista/7/8/10. Total PDF ConverterX is similar to Total PDF Converter, except it has no GUI. It can be operated in console mode only, and all operations are carried out via command line. Now, nearly all users of this tool refer to it as the most versatile server PDF converter and the handiest one to convert PDF via command line with Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related.

Mac PCL to Any Converter Shell for Mac PDF Stitcher Command Line for Mac.iSkysoft PDF Converter Pro for Mac is a. works from the command prompt. convert multi page pdf to png mac I have a lot.jpeg.png and.pdf Files and I want to convert all of them to.tiff all at once. Application wrapper to the SIPS command line utility. convert pdf to png mac 09.08.2019В В· Quite easy. Also, you can utilize Mac Preview to convert PNG to PDF on Mac, even convert PDF to PNG on Mac for your purposes. As mentioned above, one can only convert one PNG to JPG with Preview per time. If you have multiple PNGs to convert, batch conversion will be better. How to convert PNG to JPG on Mac using command line

09.08.2019В В· Quite easy. Also, you can utilize Mac Preview to convert PNG to PDF on Mac, even convert PDF to PNG on Mac for your purposes. As mentioned above, one can only convert one PNG to JPG with Preview per time. If you have multiple PNGs to convert, batch conversion will be better. How to convert PNG to JPG on Mac using command line 18.01.2017В В· PNG to PDF - Convert PNG Images to PDF File on Mac/Windows/Online. Want to convert PNG to PDF? After all, in your daily work and life, you may need to convert PNG images to PDF file for sending people using email.

Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related. Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get

Convert PDF to PNG Command Line (only $950.00) Windows XP/2003/Vista/7/8/10. Total PDF ConverterX is similar to Total PDF Converter, except it has no GUI. It can be operated in console mode only, and all operations are carried out via command line. Now, nearly all users of this tool refer to it as the most versatile server PDF converter and the handiest one to convert PDF via command line with 12.01.2017В В· In computing, Batch processing is the execution of a series of tasks in a program non-interactively. In this guide will offer you 4 simple ways to batch convert several .PNG images to .JPG and vice-versa using Linux command-line tools. 18.01.2017В В· PNG to PDF - Convert PNG Images to PDF File on Mac/Windows/Online. Want to convert PNG to PDF? After all, in your daily work and life, you may need to convert PNG images to PDF file for sending people using email. I'd like to generate an image with math formulas with TeX from command line. Something like:$ tex-executable "E=\frac{m_1v^2}{2}" e2.png I have MacTex 2009 installed and I'm pretty sure that something like that already exists in this distribution.

CoolUtils offers a highly efficient solution for exporting PDF files to image format вЂ“ convert PDF to JPEG command line utility that is capable of both single and batch conversions with fully adjustable parameters. It is Total PDF Converter X, working on Windows server and available for in-building into any client-server application. It is an ideal solution for local networks or online How to Convert PDF to PNG for Mac/ PC. There are various of worthwhile reasons to convert Portable Document Format - PDF and save as PNG image file on Mac machine or PC.

There's a new command line (unix) utility in OS X 10.4 called textutil which will convert document formats known to the Cocoa layer. According to the man page (man textutil), the formats supported are: txt, html, rtf, rtfd, doc, wordml, or webarchive. There's a new command line (unix) utility in OS X 10.4 called textutil which will convert document formats known to the Cocoa layer. According to the man page (man textutil), the formats supported are: txt, html, rtf, rtfd, doc, wordml, or webarchive.

Pdf to png mac command line Instead of opening your PDF file with the Preview app or other PDF reader and export it to PNG, you can easily use the command line.Id like to make a script on Mac OS 10. convert pdf to png mac os x 3 that converts a pdf to a png. batch convert pdf to png mac So I got sips to work on the command line but I cant get Convert to PNG Mac Informer. Featured Convert to PNG free downloads and reviews. Latest updates on everything Convert to PNG Software related.

12.01.2017В В· In computing, Batch processing is the execution of a series of tasks in a program non-interactively. In this guide will offer you 4 simple ways to batch convert several .PNG images to .JPG and vice-versa using Linux command-line tools. You used to be able to convert BMP images to JPEG, PNG, or GIF format using the Mac Automator program, but as we've noted on my Mac batch image conversion tutorial, this functionality is currently broken, and unless you want to use the Mac command line, using Preview is the only current, free way I know to convert BMP images on a Mac.

command line option to. A cross-platform GUI- and command-line converter for eps and pdf. mac convert eps to pdf command line For TeX and its derivatives, eps and pdf are the preferred graphics. 2009-РїРѕРІС–РґРѕРјР»РµРЅСЊ: 10-Р°РІС‚РѕСЂС–РІ: 6To run this command, say you have a file named file.pdf in your home directory that you want converted 05.06.2013В В· Apart from all the software available to convert image files, every Mac comes with the Preview app that can quickly convert most image file types. First, open the вЂ¦

Convert PDF to PNG Command Line (only \$950.00) Windows XP/2003/Vista/7/8/10. Total PDF ConverterX is similar to Total PDF Converter, except it has no GUI. It can be operated in console mode only, and all operations are carried out via command line. Now, nearly all users of this tool refer to it as the most versatile server PDF converter and the handiest one to convert PDF via command line with convert pdf image Downloads at Download That. Aiseesoft PDF to Image Converter is the professional PDF to Image Converter program to convert PDF file to lots of image file for you to choose with high quality, such as convert PDF to JPG, PDF to GIF, PDF to TIFF, PNG, BMP, PCX, TGA and so on. Aiseesoft PDF to Image Converter, PDF to Image

convert pdf image Downloads at Download That. Aiseesoft PDF to Image Converter is the professional PDF to Image Converter program to convert PDF file to lots of image file for you to choose with high quality, such as convert PDF to JPG, PDF to GIF, PDF to TIFF, PNG, BMP, PCX, TGA and so on. Aiseesoft PDF to Image Converter, PDF to Image Convert PNG Files Mac Informer. Featured Convert PNG Files free downloads and reviews. Latest updates on everything Convert PNG Files Software related.

Convert Files By Command Line. What is the command line? The command line is one of the most widely known, accepted and implemented methods for allowing one software app to initiate another app. That's why we've made it our goal to make all of our software command line able. Automate document conversions with the 'Convert Doc' command line using: How to Convert PDF to PNG for Mac/ PC. There are various of worthwhile reasons to convert Portable Document Format - PDF and save as PNG image file on Mac machine or PC.

command line option to. A cross-platform GUI- and command-line converter for eps and pdf. mac convert eps to pdf command line For TeX and its derivatives, eps and pdf are the preferred graphics. 2009-РїРѕРІС–РґРѕРјР»РµРЅСЊ: 10-Р°РІС‚РѕСЂС–РІ: 6To run this command, say you have a file named file.pdf in your home directory that you want converted 16.01.2013В В· The ability to convert a single image file has been around for quite some time and that shouldnвЂ™t be a mystery to those who have used Preview before, but the group conversion ability is limited to newer versions of the app in Mac OS X.

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# which algebraic expression represents the phrase four times a number

Question 1

Which algebraic expression represents the following: the sum of four times a number and six? a. [{MathJax fullWidth=’false’ \;4\left(x + 6\right) }] b. [{MathJax fullWidth=’false’ \;4\left(x \cdot 6\right) }] c. [{MathJax fullWidth=’false’ \;4x + 6 }] d. [{MathJax fullWidth=’false’ \;x + 4 \cdot 6 }] Sentence to expression : We can translate a sentence into an expression by using algebraic operations. Here, we use + for “more than”, – for “less than, multiplication for “times” etc.

Question 2

Question 3

Simplify the expression. Write with positive exponents only. [{MathJax fullWidth=’false’ \displaystyle \frac{10x^5y^4}{15x^3y^9} }] Simplifying Rational Expressions:


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How many distinct matrices are there of a given size, up to row equivalence?

If we define the equivalence relation ~ for matrices $A$ and $B$ such that $A$~$B$ iff $A$ is row equivalent to $B$, then how many equivalence classes does this impose on the set of all matrices? More specifically, what is the cardinality of the set of all equivalence classes? Does the cardinality change if we only look at matrices of a certain size? Has this problem already been solved?

• You don't mention if your matrices are square or not. Nevertheless, there is an infinity of classes because the class of $A$ is characterized by its set of solutions to $AX=0$, i.e., the kernel of $A$, and there are an infinity of possible kernels. See (en.wikipedia.org/wiki/Row_equivalence). – Jean Marie Sep 11 '16 at 22:12
• I didn't think it mattered, since matrices of different sizes cannot be row equivalent. – Zachary F Sep 11 '16 at 22:14
• Of course, but why I meant was different : We fix $m,n$, and consider only $m \times n$ matrices. Do you take $m=n$ ? – Jean Marie Sep 11 '16 at 22:19


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1. ## Perpendicular Vectors

Hi again

I am looking for a unit vector that is perpendicular to the following vectors

$a= 3i-j+4k$
$b=-3i-2j+2k$

So I know that find a perpendicular vector that $a.b=0$

So I get $(3,-1,4).(-3,-2,2)= (-9,2,8)$ but this isn't one of the options. I know that multiples of it can be also perpendicular, can someone point out where I'm going wrong?

Thanks

2. OK... I have seen an error in what I'm doing here. I want a vector perpendicular to both of them - they aren't perpendicular to each other so I can't find the dot product of a and b.

So what would I do instead? I'm very confused

3. Hello,
Originally Posted by Ian1779
OK... I have seen an error in what I'm doing here. I want a vector perpendicular to both of them - they aren't perpendicular to each other so I can't find the dot product of a and b.

So what would I do instead? I'm very confused
Do you know about the cross product ? (Cross product - Wikipedia, the free encyclopedia)

There's the formula in this section The explanation of what the cross product is is above.

And if you want a unit vector, once you get the result of the cross product, divide each ordinate by the length of the vector, that is $\sqrt{x^2+y^2+z^2}$ for a vector (x,y,z)

4. I did know about the cross product, but didn't realise I had to use it in this context.

I've now got the cross product which is $6i+18j-9k$

So I am dividing this now by $\sqrt{6^2+18^2+(-9)^2}$ Is that right? If so I think I'm there giving me

${\frac{2}{7}}i+{\frac{6}{7}}j-{\frac{3}{7}}k$

I hope I've got it?!

5. You missed a sign in the cross product: $6i-18j-9k$

6. Originally Posted by Ian1779
I did know about the cross product, but didn't realise I had to use it in this context.

I've now got the cross product which is $6i-18j-9k$

So I am dividing this now by $\sqrt{6^2+18^2+(-9)^2}$ Is that right? If so I think I'm there giving me

${\frac{2}{7}}i-{\frac{6}{7}}j-{\frac{3}{7}}k$

I hope I've got it?!
You can check by doing the scalar product with each of the other vectors =)
You can also check whether or not it is a unit vector, by calculating the norm of the latter vector.


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, 30.10.2019 03:15, Firdaus17f

# Regular pentagon area, sides 38cm,76cm find

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