text:
Today I played a bit with JRI as part of rJava, a Java-R-interface. Here you can learn how to setup for Debian/Ubuntu/akins.

## Installation

Assuming you have a running version of Java and GNU’s R, you have to install r-cran-rjava :

## Shell environment

To talk to R through Java you have to specify three more environmental variables. First of all you need to publish you R installation path, my R is found in /usr/lib64/R :

If you didn’t or the path is wrong you’ll fall into trouble:

Second the $CLASSPATH needs to get an update. Precisely you have to add the archives JRIEngine.jar , JRI.jar and REngine.jar . In my case all of them can be found in /usr/lib/R/site-library/rJava/jri/ , so the $CLASSPATH should be set like that:

If the $CLASSPATH isn’t defined correctly you won’t be able to compile your Java code. Last but not least you have to add the native JRI-library to your $LD_LIBRARY_PATH , by default this lib is located in the same directory like the jar’s:

## Netbeans setup

Two of these three parts are also straight forward in Netbeans. First publish the location of the jar’s. Right-click on your project and choose Properties > Libraries. In the Compile-tab click Add JAR/Folder and search for the jar files. Next task is to adjust the library-path. Right-click on your project and choose Properties > Run. Add -Djava.library.path=.:/usr/lib/R/site-library/rJava/jri/ to the VM Options (modify the path to match your criteria). The third step is a little tricky. As far as I know there is no way to change the environment from within Netbeans, so you can’t create the variable R_HOME after Netbeans is started. In my opinion you have two options:

1. Export the variable before starting Netbeans:

you might want to write a wrapper script that does this step for you, or include the export in any of the resource files that are called before Netbeans starts (e.g. your .bashrc ).

1. Change the environment from within your project. At stackoverflow you can find a workaround, but I think this is a very lousy solution..

If you have further suggestions please let me know! Meanwhile George Bull published a setup guide for Netbeans on Windows hosts. Seems to be worthy to take a look at it ;-)

## Testcase

If you defined your environment properly, you should be able to utilize the REngine. I have a small script for you to test whether all things are fine:

You should be able to compile and run it, afterwards you’ll see a random number from an uniform distribution. Congratulations, well done :-P

You can actively support me!

greetings, I have a problem big problem, when I try to execute those steps, all work fine until the IDE configuration, I explain me better, I had installed Rjava, I had copied JAR requested, I had updated the environment variables in /etc/environment and until there all works configurate correctly, I work in Netbeans but I didn’t know if I had to do any configuration in the IDE. Finally when I run the program, it appear this “cannot find system Renviron”. Really I had tried all the possible things but I couldn’t fix it. Sorry for my english, and I will appreciate any help that you can give to me for understand why is the reason of my problem. Thanks

Hi Sebastian,

I added a Netbeans setup section to the article. I hope that solves some of your problems ;-)

Kind regards, Martin

Really, thank you so much for your help, it will be so useful, now I will follow with my project.

Greetings, Now my Java-R connection works, I can make some calculus. But I do not know how I can use R’s libraries like RODBC through Java, I tried with: re.eval("library(RODBC)") , that did not work. Can you help me to use this library? How can I test the library is actually loaded? Thanks

re.eval ("library(datasets)"); System.out.println (re.eval ("beaver1[1,1]").asDouble ());

Maybe your library can’t be found by R itself? Where is it located? Could you please tell me the thrown error!? Maybe changing the R library search path might help you:

re.parseAndEval(".libPaths(/DIR/OF/YOUR/LIB/)");

When I execute within R the command library(RODBC) it works. I just see I have /usr/local/lib/R/site-library/RODBC/libs/RODBC.so (I suppose that is the library is required). What is the JRI.jar version you are using? I have not got the parseAndEval method. Thanks again

Ok, sry, I just copied&pasted the code from another project. Unfortunately I’m not using org.rosuda.JRI.Rengine at this point. Sorry for that. Let’s continue this conversation via mail ;-)

OK, I will appreciate that. But I am interested in knowing about which jar library you are using, I may change it. Can you know my mail or I would publish it?

If you provided a correct mail address you should find my mail in your inbox. Otherwise choose one of these methods to contact me: {{ site.url }}/contact/ I’m sure we’ll fix this issue ;-)

Btw. I’m currently using 0.9-1-1 from Debian unstable. With this version the following should work:

re.eval(".libPaths(/DIR/OF/YOUR/LIB/)");

But let’s discuss via mail. I’ll afterwards post a summary here.

Greetings,

I am trying to use JRI to programming JAve with R. I am testing a simple program but i have a problem with the REngine constructor. The program exit with the value 10, without exception. I have followed the steps before but i cant fix the problem.

Thanks.

Hi Santiago,

Is it possible to invoke r functions or embedding r charts inside jasper’s ireport

It really help. Thank you so much.

hi, i hv the problem for runing this what mean Export the variable before starting Netbeans:

usr@srv $export R_HOME=/usr/lib64/R usr@srv$ netbeans

write at where?

actually my task is to write a java programing that will produce few value. Then i need to pass that value to R. then R will do some process eg sum the value with one. last pass it back to java. How can it work???

Hi sanky, unfortunately I don’t know jasper and so I don’t have answers to such specific questions, please try to ask for support at jasper.

Hi jesslim,

if you’re working on Linux/Unix just open a terminal and export the variable with

export R_HOME=/usr/lib64/R

Afterwards you can start Netbeans in the same session with the command

netbeans

If you’re using Windows I’m sorry, but I’m not able to help you. I’m sure there is some possibility to set this variable in your user-profile, but I recommend to ask someone who is more familiar with Windows ;-)

Kind regards, Martin

The reply is late. I am trying to investigate the best way to run simulations on my socket server with varying distributions of bytes. It looks like r-java can do it instead of expensive load runners.

Do you know of anyone who is doing it ?I asked the r-help list but they disregard generic questions like this.

Dear George, The post of Using JRI , R with NetBeans in Windows was an excellent guide. I am using Eclipse IDE and trying to call R via a Java program using JRI. I have gone through your post and tried to replicate the same thing in Eclipse IDE. I am yet to get a successful output out of the java program (TestR.java). Here is what I did:

1. Set R_Home variable => R_HOME = D:\Program Files\R\R-2.14.0
2. Set PATH variable => PATH = D:\Program Files\R\R-2.14.0\bin\x64;(contains R.dll) D:\Program Files\R\R-2.14.0\library\rJava\jri; (containsJRI.dll,JRI.jar,JRIEngine, REngine), D:\Program Files\R\R-2.14.0\library\rJava\jri\x64 (contains JRI.dll)
3. Added -Djava.library.path=D:\Program Files\R\R-2.14.0\library\rJava\jri\ to the VM arguments, and I executed the program and it gave the following error: “Could not find the main class: Files\R\R-2.14.0\library\rJava\jri. Program will exit. “

Hi, is there a way to get error messages from R back?

• CODE EXAMPLE: Rengine rEngine = new Rengine(new String [] {“–vanilla”}, false, null); rEngine.eval(“library(xts)”); rEngine.assign(“arrayValue”, DOUBLE DATA); rEngine.assign(“arrayDates”, DOUBLE DATA); rEngine.eval(“test = xts(arrayValue, order.by=arrayDates)”);

The last statement not only takes 1 minute to run, it also seems to fail (no test variable is created) -> Is there a way to get some log information?

Thank you and best regards!

Hi,

I’m trying to do this in DrJava but I believe I’m getting stuck with setting the R_HOME environmental variable in DrJava. Does anybody know how to do this?

Thanks

There’s an eclipse plugin that helps set up the R Java environment at http://www.studytrails.com/RJava-Eclipse-Plugin/.

This is not working in my windows machine. It throws exception

Cannot find JRI native library! Please make sure that the JRI native library is in a directory listed in java.library.path.

How can i solve it.My R global path is also right.

Unfortunately I’m at war with Windows. Thus, the only advise I have for you is switching to a proper operation system ;-) However, I hope you can fix this issue. If you found a solution please post it to help other Windows users.

@Swarga Bera For windows operating system, I would suggest to check on the environment variable of the windows operating system. I believe there is something called PATH and jri.dll should be searchable by the environment variable.

after changing the environment variable, do not forget to restart the machine.

hello

i m using this configuration but when i m launching R its stop immediatly with exit code 2

i have set up -Djava.library.path correctly because before setup this, i have the error that jri.dll coulnd’nt be found.

now have done this:

Rengine.DEBUG = 5;

System.out.println("Starting Rengine..");
System.out.println("R_HOME =" + System.getenv("R_HOME"));
System.out.println("java.library.path =" + System.getProperty("java.library.path"));
Rengine re = new Rengine(new String[] { "--vanilla" }, false, null);
if (!re.waitForR()) {
return;
}

and when i m running the programm, on line Rengine re = new Rengine(new String[] { "--vanilla" }, false, null); it stop with exit code 2, in the console outpu i have :

Starting Rengine.. R_HOME =D:\Users\pmancaux\Desktop\Dev\R\GNU_R\R-3.0.2\bin
java.library.path =D:\Users\pmancaux\Desktop\Dev\R\GNU_R\R-3.0.2\library\rJava\jri
Starting R...

Palex

same problem as Palex here…. everything used to work perfectly fine and now application crashes when i set up the Rengine (Rengine re=new Rengine(args, false, new TextConsole()); but i’ve used all syntax possible…)

no idea… its driving me nuts….

any help is dearly appreciated.


text:
# Lower bound on distance from k-coloring a grid without monochromatic rectangles

This question stems from this other question: Grid $k$-coloring without monochromatic rectangles

Given a grid coloring, I want to determine the least amount of rectangles you have to leave uncolored to remove all monochromatic rectangles from the coloring. This would give a lower bound on the number of changes you have to make to the coloring to reach a coloring that has no monochromatic rectangles. As a heuristic for A*, it would be admissible and monotonic.

How would you calculate this number? My first attempt, a greedy algorithm that uncolors one of the cells which is involved in the most rectangles until there are no rectangles left, sometimes overestimates.

• "This would give a lower bound on the number of changes you have to make to the coloring to reach a coloring that has no monochromatic rectangles." I'm not sure this is correct, as it could be the case that by the legally-colored cells elsewhere in the grid, you've forced a situation where no colors will work for the conflicting cells. – Daniel Apon May 26 '11 at 23:00
• See, for example, Rohan Puttgunta's almost-17x17 4-coloring here: cs.umd.edu/~gasarch/BLOGPAPERS/17x17almost.txt (There are no monochromatic rectangles in the coloring, but the cell marked + cannot be colored legally.) -- assuming you mean a tight lower bound. – Daniel Apon May 26 '11 at 23:03
• @Daniel I know it won't usually be a tight lower bound. I'm just looking for a good heuristic to apply an A* or best-first search. – Null Set May 27 '11 at 0:11
• @Daniel It was in fact that example that inspired me to frame it this way. A fully colored version of that example would evaluate to at least 1 move away from the solution, and I'm ok with that. – Null Set May 27 '11 at 0:15
• @Null: how are you going to limit the exponential growth of the A* algorithm? – Marzio De Biasi May 27 '11 at 16:22

format: plain


text:
# $\tau_1$ coarser topology than $\tau_2$

I know the following definition of coarser topologies:

If $\tau_1$ and $\tau_2$ are two topologies on $X$, we say $\tau_1$ is coarser than $\tau_2$ if $\tau_1\subseteq\tau_2$.

In my book about topology there is an alternative way to describe coarser topologies:

$\tau_1$ coarser than $\tau_2 \iff \forall x\in X \, \forall B^1\in\mathcal{B}^1(x): \exists B^2\in \mathcal{B}^2(x):B^2\subseteq B^1$

where $\forall x\in X$, $\mathcal{B}^1(x),\mathcal{B}^2(x)$ are neighborhood bases for $\tau_1$ and $\tau_2$

I do not see the relation between coarser topologies and different neighborhood bases, may you could help me with that.

-

The below proof for the $\Leftarrow$ direction follows this ProofWiki proof.

The idea is that, given any basis element $B^1$, we can find a neighbourhood $B^2 \in \mathcal B^2(b)$ for each $b \in B^1$ since in this case $B^1 \in \mathcal B^1(b)$. $B^1$ will be the union of these neighborhoods. Then the neighborhood bases for $\tau_1$ are contained in $\tau_2$, hence so is $\tau_1$ itself.

So for each $b \in B^1$, $U_b = \bigcup \{B^2 \in \mathcal B^2(b): B^2 \subseteq B^1\}$ is non-empty, contained in $B^1$, and open in $\tau_2$.

It is clear that $B^1 \subseteq \bigcup\limits_{b \in B^1} U_b$; it is equally clear that the converse inclusion holds. Thus $B^1 \in \tau_2$.

We see that the trick is to apply the condition to every element of a (neighborhood basis) element $B^1$ of $\tau_1$. The approach taken above avoids using the Axiom of Choice by simply taking all valid $B^2$.

For the converse, $\Rightarrow$ direction, let $\mathcal B^1(x)$ be a neighbourhood basis around $x$ for $\tau_1$, and let $\mathcal B^2(x)$ be one for $\tau_2$.

Now every $B^1$ is an open $\tau_2$-neighbourhood around $x$ as well. By the definition of neighbourhood basis, there must be a $B^2 \in \mathcal B^2(x)$ such that $B^2 \subseteq B^1$.

Thus indeed the two are equivalent.

-
Thank you, do you also have an idea for the other direction $=>$ ? – Voyage Apr 16 '13 at 9:01


text:
# A number theory problem by Akshat Sharda

Given a positive integer $$n$$, let $$P(n)$$ be the product of the nonzero digits of $$n$$.

If $$n$$ has only one digit, then $$P(n)$$ is equal to that digit.

$S = P(1)+ P(2)+\ldots+P(999)$

Find the largest prime factor of $$S$$ ?

×


text:
# Complex Natural Logarithm

These sketches illustrate the complex natural logarithm and the images of simple lines and the circle. Each file has a Complex Natural Log tool that takes z, the origin, and the unit point as inputs.

The construction is based on the polar form of a complex number $z=r \cdot e^{i \theta}$, as well as other unstated assumptions about complex powers of e and the complex logarithm (one being that they work the same way for complex numbers as they do for real numbers).

We start with $f(z)=ln(z) =ln \left(re^{i\theta}\right) =ln(r)+ln\left(e^{i\theta}\right) =ln(r)+i\theta$

What we see is that the natural log of a complex number $z=r \cdot e^{i \theta}$ is another complex number with rectangular coordinates $\left(ln(r),\theta\right)$.

#### Image of a Horizontal Line

This file shows the Image of a Horizonal Line under the complex natural log map.

#### Image of a Vertical Line

This file shows the Image of a Vertical Line under the complex natural log map.

#### Image of an Arbitrary Line

This file shows the Image of an Arbitrary Line under the complex natural log map.

#### Image of a Circle

Nothing would be complete without the Image of a Circle under the complex natural log map.


text:
# Splitting Logical Expression in list of expressions

I have long results of a Reduce statement in the form of {(expr1) || (expr2) || (expr3) || ...}

I am looking for a way to split them into a list {expr1, expr2, expr3, ...}

Even better, I would be happy to split the internal expressions to lists at the '&& operators as well.

• So how do you want a mixture of Ands and Ors to be treated? – J. M.'s discontentment Jul 16 '16 at 15:31
• Luckily the || are outside the expressions, and internally the expressions only have &&. I would probably prefer to have it converted into some canonical form first. – Ron Jul 16 '16 at 15:35
• Now that you bring it up: look at BooleanConvert[]. – J. M.'s discontentment Jul 16 '16 at 15:41
• In certain cases results of Reduce can be transformed into rules by using ToRules, then this post might be helpful Assign the results from a Solve to variable(s). Nevertheless you should remember that Reduce and Solve are not equivalent in general What is the difference between Reduce and Solve?. – Artes Jul 16 '16 at 15:42
• That was helpful - thanks! (though ToRules didn't apply in this case). – Ron Jul 16 '16 at 16:17

When the expression is inside a List use Apply at level 1

list1 = {(expr1) || (expr2) || (expr3)};

List @@@ list1

(*  {{expr1, expr2, expr3}}  *)

list2 = {(expr1) && (expr2) && (expr3)};

List @@@ list2

(*  {{expr1, expr2, expr3}}  *)

If there is no external List then just use Apply

list3 = (expr1) || (expr2) || (expr3);

List @@ list3

(*  {expr1, expr2, expr3}  *)

list4 = (expr1) && (expr2) && (expr3);

List @@ list4

(*  {expr1, expr2, expr3}  *)
`
• I found out Level does the same thing. Converting to normal form using BooleanConvert prior to applying it helped. Many thanks! – Ron Jul 16 '16 at 16:18


text:
location:  Publications → journals → CMB
Abstract view

# Classification of Quantum Tori with Involution

Published:2002-12-01
Printed: Dec 2002
• Yoji Yoshii
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

Quantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type $\rmA_1$, $\rmC$ and $\BC$. We classify them in the category of algebras with involution. From this, we obtain precise information on the root systems of extended affine Lie algebras of type $\rmC$.
 MSC Classifications: 16W50 - Graded rings and modules


text:
5

# 3B3ADraw the most stable isomer of 1,3-dimethylcyclohexaneDraw the most stable conformation of cis- -1-chloro-2-isopropylcyclohexane3C3DDraw the ring-flipped confor...

## Question

###### 3B3ADraw the most stable isomer of 1,3-dimethylcyclohexaneDraw the most stable conformation of cis- -1-chloro-2-isopropylcyclohexane3C3DDraw the ring-flipped conformation:Draw the stereoisomer of 2-bromo-1,3- dimethylcyclohexane which is LEAST susceptible to E2 reactionsCH3Br

3B 3A Draw the most stable isomer of 1,3-dimethylcyclohexane Draw the most stable conformation of cis- -1-chloro-2-isopropylcyclohexane 3C 3D Draw the ring-flipped conformation: Draw the stereoisomer of 2-bromo-1,3- dimethylcyclohexane which is LEAST susceptible to E2 reactions CH3 Br

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text:
# Override max graphics dimensions in latex?

So, I'm writing a report on powerautomate flow code. I'm attaching screenshots in the appendix of code (because it's visual code blocks), but these are VERY large images. (3500x21094) with a really tight ratio.

I'm using code inspired by this post to split the images into pages :

\documentclass[11pt,a4paper]{article}
\usepackage{fp}
\usepackage{graphicx}
\graphicspath{ {./Assets/} }
\newcommand{\cropImg}[3]{
\FPeval{\top}{#2 / #3}
\FPeval{\bot}{(#3-#2-1) / #3}

width=\textwidth,
trim={0 {\bot\height} 0 {\top\height}},
clip, % needed for trim to work
]{#1}
}

\begin{document}
\cropImg{LargePowerFlowImage}{1}{10}

\end{document}

I'm running into "dimensions too large" when running this on some of my tallest screenshots when building though.

This link suggests this is because I'm going beyond the capacity of latex, and the images wouldn't fit.HOWEVER it's only too big as an actual image, and the result of \cropimage is well within reason.

ABD: EveryShipout initializing macros ( FP-EVAL ( FP-UPN ( FP-DIV ) ) )
( FP-EVAL ( FP-UPN ( FP-SUB ) ( FP-SUB ) ( FP-DIV ) ) )
! Dimension too large.
<argument> \ht \@tempboxa

l.19   \cropImg{FlowCompute}{1}{10}

Is there a way to override Latex's limits on graphics size so I can import those screenshots into the code, where they are broken down ? (also posted on Reddit

• as the links says there is a maximum size TeX can handle. It doesn't matter that you crop, it has to get the natural size first. Reduce the size in some external graphic program. Aug 6 at 9:27
• you are not hitting any limit related to graphics some intermdiate length has size bigger than \maxdimen so you overflow tex arithmetic this is a hard limit but you can probably re-arrange the calculations to require different arithmetic, or better generate the images using external tools so they are correct size without scaling or trimming. Aug 6 at 9:36
• @DavidCarlisle is it possible to renewcommand or something similar to change that limit within a document ? Breaking down those screenshots in subcomponents would be a bit of a pain. Aug 6 at 12:29
• No it is built in to the syntax of TeX, you can not change this even if you compile the TeX program from source. It is almost certainly better anyway to do this externally. You are scaling and cropping a bitmap but that is just a pdf masking, the full large bitmap data is included if you trim. It may or may re-use the bitmap data or may include it all again for each tile depending on ... things Aug 6 at 12:38
• Oh okay. thanks :) Aug 7 at 8:26


text:
• Design and Analysis of Algorithms
• Home

# Design and Analysis Fractional Knapsack

The Greedy algorithm could be understood very well with a well-known problem referred to as Knapsack problem. Although the same problem could be solved by employing other algorithmic approaches, Greedy approach solves Fractional Knapsack problem reasonably in a good time. Let us discuss the Knapsack problem in detail.

## Knapsack Problem

Given a set of items, each with a weight and a value, determine a subset of items to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.

The knapsack problem is in combinatorial optimization problem. It appears as a subproblem in many, more complex mathematical models of real-world problems. One general approach to difficult problems is to identify the most restrictive constraint, ignore the others, solve a knapsack problem, and somehow adjust the solution to satisfy the ignored constraints.

### Applications

In many cases of resource allocation along with some constraint, the problem can be derived in a similar way of Knapsack problem. Following is a set of example.

• Finding the least wasteful way to cut raw materials
• portfolio optimization
• Cutting stock problems

### Problem Scenario

A thief is robbing a store and can carry a maximal weight of W into his knapsack. There are n items available in the store and weight of ith item is wi and its profit is pi. What items should the thief take?

In this context, the items should be selected in such a way that the thief will carry those items for which he will gain maximum profit. Hence, the objective of the thief is to maximize the profit.

Based on the nature of the items, Knapsack problems are categorized as

• Fractional Knapsack
• Knapsack

## Fractional Knapsack

In this case, items can be broken into smaller pieces, hence the thief can select fractions of items.

According to the problem statement,

• There are n items in the store

• Weight of ith item $w_{i} > 0$

• Profit for ith item $p_{i} > 0$ and

• Capacity of the Knapsack is W

In this version of Knapsack problem, items can be broken into smaller pieces. So, the thief may take only a fraction xi of ith item.

$$0 \leqslant x_{i} \leqslant 1$$

The ith item contributes the weight $x_{i}.w_{i}$ to the total weight in the knapsack and profit $x_{i}.p_{i}$ to the total profit.

Hence, the objective of this algorithm is to

$$maximize\:\displaystyle\sum\limits_{n=1}^n (x_{i}.p_{}i)$$

subject to constraint,

$$\displaystyle\sum\limits_{n=1}^n (x_{i}.w_{}i) \leqslant W$$

It is clear that an optimal solution must fill the knapsack exactly, otherwise we could add a fraction of one of the remaining items and increase the overall profit.

Thus, an optimal solution can be obtained by

$$\displaystyle\sum\limits_{n=1}^n (x_{i}.w_{}i) = W$$

In this context, first we need to sort those items according to the value of $\frac{p_{i}}{w_{i}}$, so that $\frac{p_{i}+1}{w_{i}+1}$ ≤ $\frac{p_{i}}{w_{i}}$ . Here, x is an array to store the fraction of items.

Algorithm: Greedy-Fractional-Knapsack (w[1..n], p[1..n], W)
for i = 1 to n
do x[i] = 0
weight = 0
for i = 1 to n
if weight + w[i] ≤ W then
x[i] = 1
weight = weight + w[i]
else
x[i] = (W - weight) / w[i]
weight = W
break
return x

### Analysis

If the provided items are already sorted into a decreasing order of $\mathbf{\frac{p_{i}}{w_{i}}}$, then the whileloop takes a time in O(n); Therefore, the total time including the sort is in O(n logn).

### Example

Let us consider that the capacity of the knapsack W = 60 and the list of provided items are shown in the following table −

Item A B C D
Profit 280 100 120 120
Weight 40 10 20 24
Ratio $(\frac{p_{i}}{w_{i}})$ 7 10 6 5

As the provided items are not sorted based on $\mathbf{\frac{p_{i}}{w_{i}}}$. After sorting, the items are as shown in the following table.

Item B A C D
Profit 100 280 120 120
Weight 10 40 20 24
Ratio $(\frac{p_{i}}{w_{i}})$ 10 7 6 5

### Solution

After sorting all the items according to $\frac{p_{i}}{w_{i}}$. First all of B is chosen as weight of B is less than the capacity of the knapsack. Next, item A is chosen, as the available capacity of the knapsack is greater than the weight of A. Now, C is chosen as the next item. However, the whole item cannot be chosen as the remaining capacity of the knapsack is less than the weight of C.

Hence, fraction of C (i.e. (60 − 50)/20) is chosen.

Now, the capacity of the Knapsack is equal to the selected items. Hence, no more item can be selected.

The total weight of the selected items is 10 + 40 + 20 * (10/20) = 60

And the total profit is 100 + 280 + 120 * (10/20) = 380 + 60 = 440

This is the optimal solution. We cannot gain more profit selecting any different combination of items.

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text:
2013
11-10

# References

Editors of an electronic magazine make draft versions of the documents in the form of text files. However, publications should meet some requirements, in particular, concerning the rules of reference use. Unfortunately, lots of the draft articles violate some rules. It is desirable to develop a computer program that will make a publication satisfy all the rules from a draft version.

Let’s call a “paragraph” a set of lines in the article going one after another, so that paragraphs are separated by at least one empty line (an “empty line” is a line that containing no characters different from spaces). Any paragraph can contain an arbitrary number of references. A reference is a positive integer not greater than 999 enclosed in square brackets (for example: [23]). There will be no spaces between the brackets and the number. The square brackets are not used in any other context but reference.

There can be two types of paragraph – “regular” and “reference description”. Reference description differs from the regular paragraph because it begins with the reference it describes, for example:

[23] It is the description …

The opening square bracket will be at the first position of the first line of the “reference description” paragraph (i.e. there will be no spaces before it). No reference description paragraph will contain references inside itself.

Each reference will have exactly one corresponding description and each description will have at least one reference to it.

To convert a draft version to a publication you have to use the following rules.

• References should be renumbered by the successive integer numbers starting from one in the order of their first appearance in the regular paragraphs of the source draft version of the document.
• Reference descriptions should be placed at the end of the article ordered by their number.
• The order of “regular” paragraphs in the document should be preserved.
• Your program should not make any other changes to the paragraphs.

The input file will be a text file containing a draft article your program should process. All lines will be no more than 80 characters long. Any reference description will contain no more than 3 lines. The input file will contain up to 40000 lines.

The output file contains the result of processing. All paragraphs should be separated by one “true” empty line (i.e. a line that contains no characters at all). There should be no empty lines before the first paragraph.

[5] Brownell, D, "Dynamic Reverse Address Resolution Protocol
(DRARP)", Work in Progress.

The Reverse Address Resolution Protocol (RARP) [10] (through the
extensions defined in the Dynamic RARP (DRARP) [5]) explicitly
addresses the problem of network address discovery, and includes an
automatic IP address assignment mechanism.

[10] Finlayson, R., Mann, T., Mogul, J., and M. Theimer, "A Reverse
Address Resolution Protocol", RFC 903, Stanford, June 1984.

[16] Postel, J., "Internet Control Message Protocol", STD 5, RFC 792,
USC/Information Sciences Institute, September 1981.

The Trivial File Transfer Protocol (TFTP) [20] provides for transport
of a boot image from a boot server.  The Internet Control Message
Protocol (ICMP) [16] provides for informing hosts of additional routers
via "ICMP redirect" messages.

[20] Sollins, K., "The TFTP Protocol (Revision 2)",  RFC 783, NIC,
June 1981.

Works [10], [16] and [20] can be obtained via Internet.

The Reverse Address Resolution Protocol (RARP) [1] (through the
extensions defined in the Dynamic RARP (DRARP) [2]) explicitly
addresses the problem of network address discovery, and includes an
automatic IP address assignment mechanism.

The Trivial File Transfer Protocol (TFTP) [3] provides for transport
of a boot image from a boot server.  The Internet Control Message
Protocol (ICMP) [4] provides for informing hosts of additional routers
via "ICMP redirect" messages.

Works [1], [4] and [3] can be obtained via Internet.

[1] Finlayson, R., Mann, T., Mogul, J., and M. Theimer, "A Reverse
Address Resolution Protocol", RFC 903, Stanford, June 1984.

[2] Brownell, D, "Dynamic Reverse Address Resolution Protocol
(DRARP)", Work in Progress.

[3] Sollins, K., "The TFTP Protocol (Revision 2)",  RFC 783, NIC,
June 1981.

[4] Postel, J., "Internet Control Message Protocol", STD 5, RFC 792,
USC/Information Sciences Institute, September 1981.

//* @author: Yeming Hu"cslittleye@gmail.com"
import java.util.*;
import java.io.*;

public class Main
{
public static Map< Integer,Integer> mapOldToNew;
public static Map< Integer,Integer> mapNewToOld;
public static int counter = 1;
public static void main(String[] args) throws Exception
{
Map< Integer, StringBuilder> references = new HashMap< Integer,StringBuilder>(1000);
mapOldToNew = new HashMap< Integer,Integer>(1000);
mapNewToOld = new HashMap< Integer,Integer>(1000);
boolean isInsidePara = false;
boolean isRegPara = true;
boolean isBegin = true;
String num = "";
String line = null;
StringBuilder para = null;
String id = "";
while(true)
{
if(line == null)
{
break;
}
if(line.trim().length() == 0)
{
if(isInsidePara)
{
isInsidePara = false;
if(isRegPara)
{
//regulars[numReg++] = para;
}else
{
int in = Integer.parseInt(id);
references.put(in,para);
}
}
}else
{
if(!isInsidePara)
{
isInsidePara = true;
if(line.startsWith("["))
{

para = new StringBuilder(240);
isRegPara = false;
id = "";
for(int i = 1; i < line.length(); i++)
{
char ch = line.charAt(i);
if(ch == ']')
{
break;
}
id += ch;
}
para.append(line);
para.append("\n");
}else
{
isRegPara= true;
if(isBegin)
{
isBegin = false;
}else
{
System.out.write('\n');
}
printRegLine(line);
}
}else
{
if(isRegPara)
{
printRegLine(line);
}else
{
para.append(line);
para.append("\n");
}
}
}
}

if(isInsidePara)
{
if(isRegPara)
{
//regulars[numReg++] = para;
}else
{
int in = Integer.parseInt(id);
references.put(in,para);
}
}

boolean insideRef = false;
for(int j = 1; j < counter; j++)
{
StringBuilder sb = references.get(mapNewToOld.get(j));
System.out.write('\n');

num = "";
insideRef = false;
for(int i = 0; i < sb.length(); i++)
{
char ch = sb.charAt(i);
if(ch == '[')
{
insideRef = true;
System.out.write(ch);
}else if(ch == ']')
{
insideRef = false;
int in = Integer.parseInt(num);
num = "";
System.out.print(mapOldToNew.get(in));
System.out.write(ch);
}else if(insideRef)
{
num += ch;
}else
{
System.out.write(ch);
}
}
}
}

public static void printRegLine(String sb)
{
String num = "";
boolean insideRef = false;
for(int i = 0; i < sb.length(); i++)
{
char ch = sb.charAt(i);
if(ch == '[')
{
insideRef = true;
System.out.write(ch);
}else if(ch == ']')
{
insideRef = false;
int in = Integer.parseInt(num);
Integer value = mapOldToNew.get(in);
if(value == null)
{
mapOldToNew.put(in,counter);
mapNewToOld.put(counter,in);
counter++;
}
num = "";
System.out.print(mapOldToNew.get(in));
System.out.write(ch);
}else if(insideRef)
{
num += ch;
}else
{
System.out.write(ch);
}
}
System.out.write('\n');
}
}


text:
# Tag

Sort by:

### Catalan's Constant

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted (this work), (e.g., Borwein et al. 2004, p. 49), or (Wolfram Language).Catalan's constant may be defined by(1)(Glaisher 1877, who however did not explicitly identify the constant in this paper). It is not known if is irrational.Catalan's constant is implemented in the WolframLanguage as Catalan.The constant is named in honor of E. C. Catalan (1814-1894), who first gave an equivalent series and expressions in terms of integrals. Numerically,(2)(OEIS A006752). can be given analytically by the following expressions(3)(4)(5)where is the Dirichlet beta function, is Legendre's chi-function, is the Glaisher-Kinkelin constant, and is the partial derivative of the Hurwitz zeta function with respect to the first argument.Glaisher (1913) gave(6)(Vardi..

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# CONCEPT QUESTIONS Predict the Product. Provide the stable organic product(s) for the reactions below. 1. Mgº,...

###### Question:

CONCEPT QUESTIONS Predict the Product. Provide the stable organic product(s) for the reactions below. 1. Mgº, CH3CH2OCH2CH3 2. CO2 (g) 3. H2O, HCI 1. ~ MgBr (1 eq.) Olo o 2. H2O, HCI Mechanism. Using ChemDraw, provide the complete mechanism for the following transformation. You must include appropriate arrows, intermediates, and formal charges. 1. Mgci OY - HS 2. H2O, HCI HS

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-- 0.077283--


text:
# Electrolysis and law of electrolysis

Electrolysis Process

In simple words, the electrolysis process is the decomposition of the given element under the impact of the electric current.

Or,

Electrolysis refers to a method which uses a DC (direct current or direct electric current) to operate in other respects, the chemical non-spontaneous reactions.

As per the financial perspective, electrolysis plays an important role in elements’ separation from the naturally occurring sources like ores with the use of an electrolyte. In this, the voltage which is required for the electrolysis process to take place is known as the decomposition potential.

The relationship between the amount of electric charge passing through the electrolyte and the quantity of substance accumulated at electrodes was introduced in 1834 by Faraday, in the “law of electrolysis” form.

As per the law, substance’s mass liberated or deposited at any electrode is proportional directly to the quantity of electric charge passed through. That is, w a q

Where,

w = substance’s mass liberated or deposited

q = quantity of electric charge passed

This proportion can be assembled into equality by:

w = zq

Where,

z = proportionality constant known as the electrochemical equivalent

It’s called the substance’s mass in gms liberated or deposited by letting pass one-coulomb charge.

Faraday’s second law describes that substance’s mass liberated or deposited at any electrode by passing a specific amount of electric charge is proportional in a direct manner to its chemically equivalent weight.

That is w a E

Where,

w = substance’s mass in gms

E = chemical equivalent weight, calculated in grams as per equivalent =

w = E moles of electrons

1 mole of electrons is having charge:

= 1.6 10–19 6.023 x 1023 ≈ 96500 C

This charge is known as the 1 Faraday.

So, if one Faraday charge is passed, it means that we are letting to pass electron of one mole and by the passage of one Faraday charge of 1 gram, substance’s equivalent weight will be liberated or deposited.

On combining, the first law and the second one, we get

The summarization of Faraday’s laws can be done as:

M = QM / Fz

where:

• m = substance’s mass liberated at the electrode in gms
• Q = total electric charge which passes through a substance in coulombs (C)
• F = Faraday constant whose value is 96485.33289(59) C mol−1
• M = substance’s molar mass in gms/mol
• z = ions’ valence number of a substance where the electrons are transferred per ion

Points to Remember,

M/z is identical to substance’s equivalent weight, which is changed.


text:
Next: , Previous: , Up: Markup for Rich Contents   [Contents][Index]

### 12.4 Special Symbols

You can use LaTeX-like syntax to insert special symbols—named entities—like ‘\alpha’ to indicate the Greek letter, or ‘\to’ to indicate an arrow. Completion for these symbols is available, just type ‘\’ and maybe a few letters, and press M-TAB to see possible completions. If you need such a symbol inside a word, terminate it with a pair of curly brackets. For example

Pro tip: Given a circle \Gamma of diameter d, the length of its
circumference is \pi{}d.

A large number of entities is provided, with names taken from both HTML and LaTeX; you can comfortably browse the complete list from a dedicated buffer using the command org-entities-help. It is also possible to provide your own special symbols in the variable org-entities-user.

During export, these symbols are transformed into the native format of the exporter back-end. Strings like ‘\alpha’ are exported as ‘α’ in the HTML output, and as ‘$$\alpha$$’ in the LaTeX output. Similarly, ‘\nbsp’ becomes ‘ ’ in HTML and ‘~’ in LaTeX.

If you would like to see entities displayed as UTF-8 characters, use the following command108:

C-c C-x \ (org-toggle-pretty-entities)

Toggle display of entities as UTF-8 characters. This does not change the buffer content which remains plain ASCII, but it overlays the UTF-8 character for display purposes only.

In addition to regular entities defined above, Org exports in a special way109 the following commonly used character combinations: ‘\-’ is treated as a shy hyphen, ‘--’ and ‘---’ are converted into dashes, and ‘...’ becomes a compact set of dots.

#### Footnotes

##### (108)

You can turn this on by default by setting the variable org-pretty-entities, or on a per-file base with the ‘STARTUP’ option ‘entitiespretty’.

##### (109)

This behavior can be disabled with ‘-’ export setting (see Export Settings).

Next: Embedded LaTeX, Previous: Subscripts and Superscripts, Up: Markup for Rich Contents   [Contents][Index]


text:
### Praxis Raw Score Calculator

praxis raw score calculator. Praxis Raw Score Calculator! View the latest news and breaking news today. The same formula was used by LoadRunner version 6. Unlike your other Praxis scores, the raw score measures the number of questions you got right, not the number of correct answers. Praxis raw score conversion table 2020 Praxis raw score conversion table 2020 • July 28-29, 2020 and September 9-10, 2020. This raw score calculator will find a raw score given a z-score, mean, and standard deviation. The two scorers and are added to get your final score. mk-materace. Slp praxis raw score conversion table 2018 I'm eager to know what to expect before the results come out and would be grateful if someone could give a rough estimate to convert raw scores to percentile/ IQ. A variety of self-assessment tools including the AP world history test score calculator, Praxis practice test score conversions or the SAT subject test world history raw. Details: HOW TO CONVERT A PRAXIS II RAW SCORE INTO A PRAXIS II UNOFFICIAL SCORE: Step 1: Turn the ratio of your Praxis II raw score into a percentage. For the Praxis English Language Arts: Content Knowledge test, the recommended passing score1 is 79 out of a possible 110 raw-score points. She scored the same or higher than 16 percent of kids her age in the general population. Table for Praxis Tests PDF 1 2 3 Related searches for praxis 1 raw score conversion table LSAT PrepTest Raw Score Conversion Charts LSAT Blog praxis 1 raw score conversion table Bing Praxis II scores TeacherN June 6th, 2019 - We could say that a raw score of zero questions correct would translate into a scaled score of 100 and that a raw score. praxis raw score calculator Scaled score, the familiar 120-180 number, is a conversion of the raw score. eastern time on the score report date for your test date. › Get more: Praxis raw score tableDetail Science. The praxis core test score is calculated using a combination of human and computer scoring. Details: Praxis 5169(revised) raw to scaled score correlation table. Step 2: Add 100 to your Praxis raw score calculator - doeh. praxis: [noun] action, practice: such as. Your Praxis raw score has one unique trait that separates it from both the unofficial and official score. The official score, along with a pass/not pass designation, will come later because the raw score on each test is actually weighted according to its difficulty, which makes sense. Receiving your scores. Unlike raw scores, you can interpret scale scores across different sets of test questions. But what do all of these calculations mean for you? Using conversion tables as a PSAT score calculator allows you to form a rough idea as to how many questions you'll need to answer. That means you got 35/56 because there are 56 total questions on the Praxis Core Math. calculate the Total Raw Score for Story 1, transfer the values for Items 1---32 Subtotals that you have calculated on page 4 to Slp praxis raw score conversion table 2018 The Obama Soros Plan To Destroy America Real Jew News. How are Praxis scores calculated raw score? The raw score is calculated on a scale of zero to the total number of questions on the test. exercise or practice of an art, science, or skill. Individual Intelligence and Adaptive Testing Raw Score Conversion Table Praxis Test 3 / 32 Between Praxis 5061 And 5161 count of the actual number of correct answers you gave. About calculator score Praxis raw. 19/21 = 90. It will also show the highest scores for any other praxis test you have taken in the last 10 years. If a Praxis question asks you to select two answers, and you only choose one of the two answers correctly, this would count as one wrong question in your raw. Step 2: Add 100 to your percentage number to get your scaled unofficial score. Raw Score Conversion Table 3: Cross-Test Scores Conversion Equation 3: Calculate Your Cross-Test Scores. Make statistics easier with the use of these calculators: scaled score, raw. Raw Score Calculator with a Step by Step Solution. The tests are not identical. Connection Between z-scores and raw scores. April 19th, 2019 - The basic score on any test is the raw score which is simply the number of questions a student answered correctly You can interpret a raw score only in terms of a particular set of test questions A scale score is a conversion of the raw score onto a scale that is common to all test forms for that assessment Scal. Praxis Ii Raw Score Conversion Table 2016 Joomlaxe com April 6th, 2019 - On this page you can read or download praxis ii raw score conversion table 2016 in PDF format If you don t see any interesting for you use our search form on. Jan 01, 2011 · As a. score for licensure certification for the praxis speech language pathology test the recommended passing score is 74 out of a possible 108 raw score points the scaled score associated with a raw score of 74 is 162 on a 100200 scale, recommend a new passing score for audiology certification purposes standard setting technical report made. ) The weighted score is confusing…. How do you convert raw score to scaled praxis? Science. I was averaging 80% on the prep exams and failed the test the first time with a raw score of 26 which is less than 50% correct. Constructed response questions-essay questions and written short answer questions-are not included in your raw score. Score reports for CR tests that are given continuously are available 21 calendar days after the day of the test. That translated to a weighted score 153. scores as reported by the NYC DOE. This comprehensive practice book with 6 full length and realistic ISEE Lower Level Math practice tests help you measure your exam readiness, find your weak areas, and succeed on the ISEE Lower Level Math test. MS Excel uses below formula to calculate 90 th percentile: 90 th Percentile = 0. In most states, you needed a 140 to pass. Calculate Raw Score from Z Score: Make use of this online z score to raw score calculator to conveniently find the raw score based on the z Health. customary practice or conduct. Score reports are available for 2 years in your account. We will probably never get a definite conversion function to go from raw scores to scaled scores but I bet that if enough people posted their raw scores and resulting scaled scores we could get a pretty good correlation. Also, make use of the example given below to understand the manual calculation steps. If you want to calculate the z score based on the raw score, mean, and standard deviation, see Z Score Calculator. How to Calculate your Praxis Score - NavaED. Maximum raw score can be 100 which is converted to a highest scale score of 450 using the below conversion chart of raw score to TOEIC score. Raw Score Calculator Travel! Ready booking hotels, flight, restaurant for trip tourist now. Your score report will be emailed to you, if you requested this option when you registered, and will be available in your account beginning at 10:00 p. Praxis raw score calculator - ebiq. This means Jane’s score was below the average score of 100. 4 day ago Make the necessary calculations to get statistical results. Depending on what your distribution represents, start by either writing the formula for the raw score of a population:  x = \mu. 098 111 93 106. The raw score calculator will use these values to generate the range your raw score is most likely to fall between. Licensure Pass Rates: Undergraduate & Graduate Programs Undergraduate Programs: Elementary Education. From 2016-2020, most candidates from MC have been awarded state licensure based on Praxis II Elementary Education (K-6): Content Area and Principles of Learning & Teaching (K-6) exams, exceeding the state and national accreditation requirement of 80%. Details: Calculate Raw Score from Z Score: Make use of this online z score to raw score calculator to conveniently find the raw score based on the z score. , we know that the transformation formula is scaled score ‘= (raw score + 15)/2. The method to find out 90 th percentile has been changed in LoadRunner version 7 and above. Slp praxis raw score conversion table 2018 The University of Utah on Instagram: “Since Arts Bash can translate. Those raw scores I included (26, 27,22) equaled a 182 scaled score! I encourage everyone to please keep trying, keep studying, and don't let a first (or second!) failure discourage I took praxis at home on May 29 and received an unofficial score of 182. Raw scores give the actual score, while z scores are used to show. In respect to this, how do you convert raw scores to Praxis? HOW TO CONVERT A PRAXIS II RAW SCORE INTO A PRAXIS II UNOFFICIAL SCORE: Step 1: Turn the ratio of your Praxis II raw score into a percentage. How to Calculate your Praxis Score - KathleenJasper. Each edition of a test has its own table to convert from a raw score to the official score so there is a standard across all forms of the. If you are look for Praxis raw score calculator, simply found out our text below. book related act raw score conversion table april 20th 2019 raw score conversion table staar raw score conversion table praxis test raven raw score percentile conversion table 17 explore test 03a raw score conversion explore test raw score conversion, american mensa email or write to the address Praxis Raw Score …Wij willen hier een. Your maximum score. scores across different sets of test questions, 24 raw score on praxis 2 5161 pdf free pdf download now source 2 24 raw score on praxis 2 5161 pdf free pdf download there could be some typos or mistakes below html to pdf converter made. Example: The Praxis 5081 raw score I described above is 92/130. 3 all right calculate the Z scores for each of the following June 19th, 2018 - Stanford 10 Test Interpretation group who got the same raw score or a lower raw score on the test The OLSAT 8 is a measure of school ability''LSAT Score Conversion Chart Alpha Score June 21st, 2018. (Read more about Praxis score scaling here. Praxis Score Calculator Market! markets indexes, bonds, forex, ETFs, analysis, stock quotes. The result will automatically be calculated and shown. Praxis raw score calculator" Keyword Found Websites Step 1: Turn the ratio of your Praxis II raw score into a percentage. Calculate Raw Score from Z Score: Make use of this online z score to raw score calculator to conveniently find the raw score based on the z score. How do you evaluate Praxis scores? For example, let’s say on the Praxis Core Math your raw score is 35. Your score report will include your overall score, pass/fail status, and the range of possible scores overall and in each category. googleusercontent. Now that we know about this association, we also know that a z-score is obtained from normalizing the raw score. Instead, the test makers add up all of your correct answers to get what they call a “raw” score. › Get more: Praxis raw score conversion tableView Markets. This is an important distinction because on the Praxis, certain questions have more than one answer. If we apply the formula, we get that for a raw score of 10; it corresponds to a scaled score of 12. ( Read … praxis raw score conversion table. Calculating the raw score can be used for all types of data sets. Each test is scored separately, and every state that requires passing scores for. The Cattell Scale, like other IQ scales, places its average score at 100. There are two scoring models used for scoring Praxis tests: The first model requires that two scorers rate your response to each question independently. Score Report Dates. Praxis raw score calculator" Keyword Found Websites. praxis blog, praxis raw score question slp reddit, praxis i conversion chart gapsc , new praxis looking for last minute study tips speech, praxis raw score conversion table 5354 booklection com, whats the difference between raw and scaled scores , praxis ii raw score conversion table 2016 joomlaxe com, how to calculate your praxis score test. presents the equipercentile conversion of raw scores on the advanced raven to raw score on the standard raven and also to the iq scale raw scores below 9 on the, raven s educational case study cpm cvs on the cpm he obtained a total raw score of 29 this score converted to a standard. Your overall score will represent your raw score or the number of correctly answered questions. The percentile ranking is your score in comparison to the scores of the other candidates who finished. The z score is the numerical value which represents how many standard deviations a score is above the mean. The scaled score range for the previous version of the The STAR Math. Details: For example, let's say on the Praxis Core Math your raw score is 35. For example: Jane obtained a standard score of 85 (-1 SD) on the WISC, which is ranked at the 16th percentile and is classified as low average. The raw score computed is the actual score, or value, obtained. Scale scores allow direct comparisons of student performance between specific sets of test questions from different test administrations. This calculator calculates the raw score value from the z score, the mean, and the standard deviation. The raw score is calculated on a scale of zero to the total number of questions on the test. Enter the three values, then you will get an answer and step-by-step explanation on how you … praxis raw score calculator. com: Praxis Middle School Math 5169 Study Guide (Added 3 minutes ago) Test Prep Book's Praxis Middle School Math 5169 Study Guide: Praxis II Middle School Mathematics 5169 Test Prep & Practice Test Questions Developed by Test Prep Books for test takers trying to achieve a passing score on the Middle School Math Praxis exam, this comprehensive study guide includes: •Quick Overview. Understanding Your Praxis Raw Score - Magoosh Blog The Praxis Core Academic Skills for … Praxis raw score calculator Page 2/6. Praxis Scores: Raw vs Unofficial So if you take the Praxis Core English exam and get 50 out of the 56 questions right, your raw score would be 50. The number of correct responses is called the 'raw score,' with one point for each correct response. My friend took it the day before and received 175. Then drop the percent sign. Cattell Culture Fair Test | IQ Test Prep Nov 14, 2018 · The. Details: · The raw score is calculated on a scale of zero to the total number of questions on the test. Instructions: Use this Raw Score Calculator to transform a z-score into a raw score. Learn exactly how your final score is computed. 5% or a 63%. (165 is the minimum score to pass in my state. Keeping this in view, how is the Praxis test score? On most Praxis ® tests, each selected-response question answered correctly is worth one raw point; your total raw score is the number of questions answered correctly on the full test. A total raw score on such a test represents the number of correct multiple-choice answers added to the ratings on the essay questions. How to Calculate your Praxis Score. A scale score is a conversion of the raw score onto a scale that is common to all test forms for that assessment. On some constructed-response tests, the ratings assigned by the scorers are simply added together to determine your total raw score. You need to follow the chart. Please provide the information required below. To calculate your raw Math score, tally your correct answers on the No Calculator and Calculator subsections. The scaled score associated with a raw score of 79 is 167 on a 100–200 scale. ) Ultimately, your raw score provides a simple, easy-to-understand look at how you’ve done on an exam you just took. Praxis raw score calculator A recent study found that combining raw scores on the. 9 * (Number of Values – 1) + 1. " I would post the source, but since I am new, I cannot post links, yet. Your true praxis score—both in official and unofficial form—are calculated on a scale that starts at 100 and goes to 200. 3 goldman fristoe test of articulation 3 score report. Details: This raw score calculator will find a raw score given a z-score, mean, and standard deviation. "96% of my students showed growth in literacy on our end-of-the-year standardized assessment, and I know that ReadWorks was a factor. For example, let's say on the Praxis Core Math your raw score is 35. In contrast, the unofficial score is more complex. The raw score formula is simply the z-score formula solved for x, the raw score. Raw Score Calculator with a Step by Step Solution. Your score report for the test will contain raw points scored along with the total available raw points for that category of the test. The raw score is converted to a ‘scaled score’ using the statistical method of ‘equating. Praxis Raw Scores Conversion Table Praxis II scores TeacherN June 6th, 2019 - We could say that a raw score of zero questions correct would translate into a scaled score of 100 and that a raw score of 120 correct would translate into a scaled score of 200 there are probably some details here about which Praxis is being coy. Praxis Raw Score Converter! free convert online with more formats like file, document, video, audio Details: HOW TO CONVERT A PRAXIS II RAW SCORE INTO A PRAXIS II UNOFFICIAL SCORE › Get more: Slp praxis raw score conversionView Convert. Listen to credible commentators. Example: The Praxis 5081 raw score I described above is 92/130. 2013 praxis raw score conversion table 2017 Golden Education World Book Document ID 7389880f Golden Education World Book Praxis Raw Score Conversion Table 2017 Description Of. Apply the formula to every raw score to get your scaled score. Next, divide 35 by 56, and you get 62. How to Calculate Your Praxis Score. How to Calculate Scores on a Practice Praxis Test Bizfluent. The number of correct answers you give is your raw score. Praxis raw scores are calculated only from selected response questions-questions that are multiple choice or numeric entry. The actual exam is harder that the exams in this book or any other test prep exams that I used.

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# When to use Roman and Italic Font in Math

I am wondering when to use roman or italic font in math mode. I found that variables should be italicized and functions like max should be put in roman.

I found some sites on the topic, e.g. this or this, but I still have some uncertainties. Somewhere else I found that concrete entities should be put in roman font.

• I am not sure what a concrete entity is.
• In the following example: should letter or startmarker etc. appear in roman font?
• The subscript free is not a variable, but descriptional text. Thus, it should be romanized?

Edit 1: The formulas startmarker, letter, only etc. are abbreviations for formulas in some logic such as First Order Logic.

• Using words as variables is SOP in programming, but not math. Using words in subscripts is okay. Jun 9, 2015 at 13:51
• Put every text in \text{}, every variable is italicized by default, and each constant (concrete entity) like e or pi can be set \mathrm{e}. No rule for that but personally I strongly recommend that. Just try to distinguish between text and math. Right now, your are writing "f times r times e times e" in your subscript. Most people set functions and operators upright as well: \sin\max\mathrm{d}x... (Off topic: you forgot the spaces after your \equiv) Jun 9, 2015 at 13:51
• Please tell us what the meaning of "only", "letter", "startmarker", and "endmarker" is: are they names of variables, operators (like "sin" and "log"), constants (like the base of the natural logarithms), or something else?
– Mico
Jun 9, 2015 at 13:53
• never use the default math italic for multi-letter words so never $only$ if you need italic words in math use $\mathit{only}$ Jun 9, 2015 at 14:27
• @JohnKormylo: I prefer to have speaking names, as I use many more such formulas. @David Carlisle: I put all words in formulas in \mathit. @LaRiFaRi: Thanks for the remark Jun 9, 2015 at 14:55

This is going to be opinion-based, so I'll first suggest a strategy for typing your document.

\usepackage{amsmath}

\newcommand{\func}[1]{\operatorname{\mathit{#1}}}  % or \mathrm
\newcommand{\const}[1]{\mathit{#1}}                % or \mathrm
\newcommand{\wsub}[1]{\mathrm{#1}}                 % 'word' subscript

Then you can type

$\func{letter}(\sigma,c)\equiv\func{startmarker}(c)$
$\func{only}_{\wsub{free}}(\{c_{0}\})$

Of course you can add shorthands for the functions you use most often

\newcommand{\letter}{\func{letter}}
\newcommand{\startmarker}{\func{startmarker}}
\newcommand{\only}[1][]{%
\func{only}%
\if\relax\detokenize{#1}\relax _{\wsub{#1}}\fi
}

and the above formulas would be

$\letter(\sigma,c)\equiv\startmarker(c)$
$\only[free](\{c_{0}\})$

The definition of \only with an optional textual subscript can be simpler if xparse is used:

\usepackage{xparse}
\NewDocumentCommand{\only}{o}{%
\func{only}%
\IfValueT{#1}{_{\wsub{#1}}}%
}

Or you can opt for an even simpler \newcommand{\only}{\func{only}} and type

$\only_{\wsub{free}}(\{c_{0}\})$

Now my opinions. A function such as startmarker is not a “standard” function like max, log or sin. Those function names should always be typeset upright in order to emphasize their “fixed” meaning. The function you define in your document are not of universal use, so you can choose between upright or italic. Just be consistent and that's the purpose of the definitions I propose.

If you later decide that functions such as startmarker should be typeset upright, just remove \mathit from the definition of \func (or replace it by \mathrm, but since we are already under \operatorname this is not needed).

For constants it's a similar problem. I never typeset constants upright (that's something I leave to physicists), but I understand others can have different ideas.

Surely you won't place two multiletter constants next to each other without an explicit multiplication sign: so

\const{foo}\cdot\const{bar}

and not \const{foo}\const{bar}.

• Thanks for the example with xparse Jun 10, 2015 at 10:11


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# Earth:SPEARpesticides

Typical stream in an agricultural landscape

SPEARpesticides (Species At Risk) is a trait based biological indicator system for streams which quantitatively links pesticide contamination to the composition of invertebrate communities.[1] The approach uses species traits that characterize the ecological requirements posed by pesticide contamination in running waters. Therefore, it is highly specific and only slightly influenced by other environmental factors.[2] SPEARpesticides is linked to the quality classes of the EU Water Framework Directive (WFD)[3]

## History

SPEARpesticides has been first developed for Central Germany[1] and updated.[4] SPEARpesticides was adapted and validated for streams and mesocosms worldwide and provides the first ecotoxicological approach to specifically determine the ecological effects of pesticides on aquatic invertebrate communities. Denmark,[5][6] Finland,[6] France,[6] Germany,[1][6] Switzerland Australia[7][8] Russia[9] Mesocosms[10]

## Calculation

Concept of SPEARpesticides

SPEARpesticides estimates pesticide effects and contamination. The calculation is based on monitoring data of invertebrate communities as ascertained for the EU Water Framework Directive (WFD). A simplified version of SPEARpesticides is included in the ASTERICS software for assessing the ecological quality of rivers. A detailed analysis is enabled by the free SPEAR Calculator. The SPEAR Calculator provides most recent information on species traits and allows specific user settings. The SPEARpesticides index is computed as relative abundance of vulnerable 'SPecies At Risk' (SPEAR) to be affected by pesticides. Relevant species traits comprises the physiological sensitivity towards pesticides, generation time, migration ability and exposure probability. The indicator value of SPEARpesticides at a sampling site is calculated as follows:

$\displaystyle{ SPEAR_{pesticides} = \frac{\sum_{i=1}^n \log(x_i+1)y}{\sum_{i=1}^n \log (x_i+1)} }$

with n = number of taxa; xi = abundance of taxon i; y = 1 if taxon i is classified as SPEAR-sensitive; y = 0 if taxon i is classified as SPEAR-insensitive.


text:
# what is the best estimate of the company's net operating income? Assume that the fixed monthly... 1 answer below »

Gayne Corporation's contribution margin ratio is 12% and its fixed monthly expenses are $84,000. If the company's sales for a month are$738,000, what is the best estimate of the company's net operating income? Assume that the fixed monthly expenses do not change.

A) $565,440 B)$654,000

C) $88,560 D)$4,560

Sachin K
Solution: D) $4,560 Gayne Corporation Details Figures Sales$738,000 contribution margin ratio 12% Contribution (12% *...

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text:
## 31.2-1

Prove that equations $\text{(31.11)}$ and $\text{(31.12)}$ imply equation $\text{(31.13)}$.

(Omit!)

## 31.2-2

Compute the values $(d, x, y)$ that the call $\text{EXTENDED-EUCLID}(899, 493)$ returns.

$(29, -6, 11)$.

## 31.2-3

Prove that for all integers $a$, $k$, and $n$,

$\gcd(a, n) = \gcd(a + kn, n)$.

• $\gcd(a, n) \mid \gcd(a + kn, n)$.

Let $d = \gcd(a, n)$, then $d \mid a$ and $d \mid n$.

Since

$$(a + kn) \mod d = a \mod d + k \cdot (n \mod d) = 0$$

and $d \mid n$, we have

$$d \mid \gcd(a + kn, n)$$

and

$$\gcd(a, n) \mid \gcd(a + kn, n).$$

• $\gcd(a + kn, n) \mid \gcd(a, n)$.

Suppose $d = \gcd(a + kn, n)$, we have $d \mid n$ and $d \mid (a + kn)$.

Since

$$(a + kn) \mod d = a \mod d + k \cdot (n \mod d) = a \mod d = 0,$$

we have $d \mid a$.

Since $d \mid a$ and $d \mid n$, we have

$$d \mid \gcd(a, n)$$

and

$$\gcd(a + kn, n) \mid \gcd(a, n).$$

Since

$$\gcd(a, n) \mid \gcd(a + kn, n)$$

and

$$\gcd(a + kn, n) \mid \gcd(a, n),$$

we have

$$\gcd(a, n) = \gcd(a + kn, n).$$

## 31.2-4

Rewrite $\text{EUCLID}$ in an iterative form that uses only a constant amount of memory (that is, stores only a constant number of integer values).

EUCLID(a, b)
while b != 0
t = a
a = b
b = t % b
return a

## 31.2-5

If $a > b \ge 0$, show that the call EUCLID$(a, b)$ makes at most $1 + \log_\phi b$ recursive calls. Improve this bound to $1 + \log_\phi(b / \gcd(a, b))$.

$$b \ge F_{k + 1} \approx \phi^{k + 1} / \sqrt{5}$$

$$k + 1 < \log_\phi \sqrt{5} + \log_\phi b \approx 1.67 + \log_\phi b$$

$$k < 0.67 + \log_\phi b < 1 + \log_\phi b.$$

Since $d \cdot a \mod d \cdot b = d \cdot (a \mod b)$, $\gcd(d \cdot a, d \cdot b)$ has the same number of recursive calls with $\gcd(a, b)$, therefore we could let $b' = b / \gcd(a, b)$, the inequality $k < 1 + \log_\phi(b') = 1 + \log_\phi(b / \gcd(a, b))$. will holds.

# 31.2-6

What does $\text{EXTENDED-EUCLID}(F_{k + 1}, F_k)$ return? Prove your answer correct.

• If $k$ is odd, then $(1, -F_{k-2}, F_{k - 1})$.
• If $k$ is even, then $(1, F_{k-2}, -F_{k - 1})$.

## 31.2-7

Define the $\gcd$ function for more than two arguments by the recursive equation $\gcd(a_0, a_1, \cdots, a_n) = \gcd(a_0, \gcd(a_1, a_2, \cdots, a_n))$. Show that the $\gcd$ function returns the same answer independent of the order in which its arguments are specified. Also show how to find integers $x_0, x_1, \cdots, x_n$ such that $\gcd(a_0, a_1, \ldots, a_n) = a_0 x_0 + a_1 x_1 + \cdots + a_n x_n$. Show that the number of divisions performed by your algorithm is $O(n + \lg (max \{a_0, a_1, \cdots, a_n \}))$.

Suppose

$$\gcd(a_0, \gcd(a_1, a_2, \cdots, a_n)) = a_0 \cdot x + \gcd(a_1, a_2, \cdots, a_n) \cdot y$$

and

$$\gcd(a_1, \gcd(a_2, a_3, \cdots, a_n)) = a_1 \cdot x' + \gcd(a_2, a_3, \cdots, a_n) \cdot y',$$

then the coefficient of $a_1$ is $y \cdot x'$.

EXTENDED-EUCLID(a, b)
if b == 0
return (a, 1, 0)
(d, x, y) = EXTENDED-EUCLID(b, a % b)
return (d, y, x - (a / b) * y)

EXTENDED-EUCLID-MULTIPLE(a)
if a.length == 1
return (a[0], 1)
g = a[a.length - 1]
xs = [1] * a.length
ys = [0] * a.length
for i = a.length - 2 downto 0
(g, xs[i], ys[i + 1]) = EXTENDED-EUCLID(a[i], g)
m = 1
for i = 1 to a.length
m *= ys[i]
xs[i] *= m
return (g, xs)

## 31.2-8

Define $\text{lcm}(a_1, a_2, \ldots, a_n)$ to be the least common multiple of the $n$ integers $a_1, a_2, \ldots, a_n$, that is, the smallest nonnegative integer that is a multiple of each $a_i$. Show how to compute $\text{lcm}(a_1, a_2, \ldots, a_n)$ efficiently using the (two-argument) $\gcd$ operation as a subroutine.

GCD(a, b)
if b == 0
return a
return GCD(b, a % b)

LCM(a, b)
return a / GCD(a, b) * b

LCM-MULTIPLE(a)
l = a[0]
for i = 1 to a.length
l = LCM(l, a[i])
return l

## 31.2-9

Prove that $n_1$, $n_2$, $n_3$, and $n_4$ are pairwise relatively prime if and only if

$\gcd(n_1n_2,n_3n_4) = \gcd(n_1n_3, n_2n_4) = 1.$

More generally, show that $n_1, n_2, \ldots, n_k$ are pairwise relatively prime if and only if a set of $\lceil \lg k \rceil$ pairs of numbers derived from the $n_i$ are relatively prime.

Suppose $n_1n_2 x + n_3n_4 y = 1$, then $n_1(n_2 x) + n_3(n_4 y) = 1$, thus $n_1$ and $n_3$ are relatively prime, $n_1$ and $n_4$, $n_2$ and $n_3$, $n_2$ and $n_4$ are the all relatively prime. And since $\gcd(n_1n_3, n_2n_4) = 1$, all the pairs are relatively prime.

General: in the first round, divide the elements into two sets with equal number of elements, calculate the products of the two set separately, if the two products are relatively prime, then the element in one set is pairwise relatively prime with the element in the other set. In the next iterations, for each set, we divide the elements into two subsets, suppose we have subsets $\{ (s_1, s_2), (s_3, s_4), \ldots \}$, then we calculate the products of $\{ s_1, s_3, \ldots \}$ and $\{ s_2, s_4, \ldots \}$, if the two products are relatively prime, then all the pairs of subset are pairwise relatively prime similar to the first round. In each iteration, the number of elements in a subset is half of the original set, thus there are $\lceil \lg k \rceil$ pairs of products.

To choose the subsets efficiently, in the $k$th iteration, we could divide the numbers based on the value of the index's $k$th bit.


text:
×

# Roots

can a number 100 zeros 100 ones 100 twos is a perfect square? Prove it.

Note by Royston Dsouza
2 years, 5 months ago

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No. Hint:- Look at divisibility by 3 and 9.

- 2 years, 5 months ago

How does it help?

- 2 years, 5 months ago

Digit sum of the number is $$300$$. Therefore, it is divisible by 3, since 3 divides 300. But it is not divisible by 9, since 9 does not divide 300. Since the number is divisible by 3 but not 9, it can't be a perfect square/

- 2 years, 5 months ago


text:
# Thread: verifying a trigonometric identity

1. ## verifying a trigonometric identity

how would you verify (cosx-cosy)/(sinx+siny) + (sinx-siny)/(cosx+cosy) =0

2. Originally Posted by wolfxpax
how would you verify (cosx-cosy)/(sinx-siny) + (sinx-siny)/(cosx+cosy) =0
Don't forget to use parentheses (as in red above) to make the meaning unambiguous. Also, it looks to me as though one of those – signs should be a +.

Anyway, to prove the identity, put the left side over a common denominator, and see what happens to the numerator.


text:
시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 (추가 시간 없음) 512 MB43375.000%

## 문제

Consider the number $x$ stored in uint32 data type. We can multiply or divide it by $2$ any number of times in any order. Can we obtain the number $y$ after some sequence of operations?

When $a$ is stored in an uint32, and we multiply it by $2$, it transforms into $(a \cdot 2) \bmod 2^{32}$. For example, $(3 \cdot 2) \bmod 2^{32} = 6$, and $(2\,147\,483\,649 \cdot 2) \bmod 2^{32} = 2$.

When $a$ is stored in an uint32, and we divide it by $2$, it transforms into $\left\lfloor\frac{a}{2}\right\rfloor$. For example, $\left\lfloor\frac{6}{2}\right\rfloor = 3$, and $\left\lfloor\frac{3}{2}\right\rfloor = 1$.

## 입력

The first line contains an integer $t$, the number of test cases ($1 \le t \le 1000$). The next $t$ lines describe test cases, one per line. Each test case is given by two integers $x$ and $y$ ($0 \le x, y < 2^{32}$).

## 출력

For each test case, print a single word on a separate line: "Yes" if we can turn $x$ into $y$ using the allowed operations, or "No" otherwise.

## 예제 입력 1

2
2147483649 1
9 13

## 예제 출력 1

Yes
No

## 노트

In the first test case, we can multiply $x$ by $2$, and then divide the result by $2$ to get $y$.

In the second test case, there is no way to turn $x$ into $y$.


text:
# Sh:438

• Goldstern, M., Judah, H. I., & Shelah, S. (1993). Strong measure zero sets without Cohen reals. J. Symbolic Logic, 58(4), 1323–1341.
• Abstract:
If ZFC is consistent, then each of the following are consistent with ZFC + 2^{{\aleph_0}}=\aleph_2:

1.) X subseteq R is of strong measure zero iff |X| \leq \aleph_1 + there is a generalized Sierpinski set.

2.) The union of \aleph_1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size \aleph_2.

• Version 1993-08-29_10 (27p) published version (20p)
Bib entry
@article{Sh:438,
author = {Goldstern, Martin and Judah, Haim I. and Shelah, Saharon},
title = {{Strong measure zero sets without Cohen reals}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {58},
number = {4},
year = {1993},
pages = {1323--1341},
issn = {0022-4812},
mrnumber = {1253925},
mrclass = {03E35 (04A15 04A20)},
doi = {10.2307/2275146},
note = {\href{https://arxiv.org/abs/math/9306214}{arXiv: math/9306214}},
arxiv_number = {math/9306214}
}


text:
# Guidelines for USGS Researchers and Grad Student Applicants

The steps in the process are outlined below.

Steps for INTERN Collaborations at USGS

• A student is identified in one of several ways.
• USGS researcher who would like to attract a graduate student intern submits a profile through this form, and a prospective student finds you through the public GRO Opportunities page
• USGS researchers reach out to their academic colleagues to share their interest in hosting an intern
• A student approaches a USGS researcher with a project idea
• Student and USGS researcher talk and agree on project goals, budget, etc.
• The student writes and submits an application to NSF.
• This program is a supplemental grant program, so the proposal must be linked to an existing NSF grant.
• That existing grant might the the student's Graduate Research Fellowship, or it might be a grant to a faculty member at the university, commonly the student's advisor.
• It is recommended that the student and advisor have a conversation with the NSF Program Officer who oversees the grant before submitting the INTERN proposal.
• Start with the IP agreement early (below) since that may take some time to get through the University approval
• NSF conducts eligibility review, merit review, and makes awards.

NSF INTERN Program Specifics (DCL 21-013)

• This program is open to any M.S. or Ph.D. student who is supported by an NSF grant to their advisor or another researcher
• The maximum amount is $55,000 for travel, tuition, stipend, and relocation costs; up to$2500 can be used for materials and supplies, and \$2500 for the Faculty Advisor to travel to USGS during the internship.
• The internship is up to 6-months, and students can apply for second grant for an additional 6-months.
• There are two required elements that USGS must provide:
• A letter from the host mentor describing the opportunity and mentorship
• A signed agreement on Intellectual Property Rights (here)
• NOTE: This form has been approved by USGS. The first step for applicants is to get their University signature, which may take some time. If the University requests changes to the form, bring that to Eleanour Snow (esnow at usgs.gov) who will get USGS approval for the changes.
• This is submitted as a supplement to the original NSF Grant. The faculty advisor should contact their NSF program officer before submitting.
• Review is usually quick
• The Faculty member will be notified
• USGS researcher informs YES office of arrangements
• At the end of the internship, the student submits a report to NSF with a copy to YES office
• Deadline: These are accepted anytime, but there is a target date of April 15th for current fiscal year funding. That means that if a great proposal is submitted in May or June, it might be funded, but it might be pushed to the next fiscal year instead.

Notes for USGS Researchers

The YES office is responsible for managing, facilitating, and reporting on this program. Please visit our on internal SharePoint site for additional information and a very short reporting form for recording application, award, and outcomes. Don't hesitate to contact us with questions.

NSF’s core value for these programs is the professional growth of the student. The proposed collaboration should offer the student professional experiences they cannot get at their home institution, such as access to USGS facilities, field sites, or data they would not otherwise have, new skill development, or collaboration in a new scientific direction. Exposure to a different work culture was also important, so the students are expected to come to the USGS, rather than collaborate from their home institution.

Assisting with the NSF Application

Students applying to these programs will submit a short supplemental funding request to NSF. It is expected that the student and the USGS researcher will have conversations prior to preparing the application and that, although the student will take the lead in writing and submitting the application, you will collaborate on the description of the project, term, and budget.

How to Find Students

NSF links interested students to this USGS website where they can view posted research profiles. USGS YES Office is also working on ways to widely publicize the website. However, reaching out through your own networks to identify students who might be interested in your opportunity will improve your success. To be eligible, students must be pursuing an M.S. or Ph.D., supported by an NSF grant, and a U. S. citizen. Here are some strategies:

• Reach out to researchers who are working in your field, friends, and colleagues, or through professional societies that you are involved in, and ask them if they have an NSF-supported student who would be interested.
• Directly approach students you know, or students who presented interesting papers at the last meeting you attended.
• Use the NSF website to search for active grants in your field, and approach the PIs. NSF Grant Search – all awards
• You can narrow your search by NSF Directorate by using the formatting at NSF-GEO awards.
• Search the list of NSF Graduate Research Fellows. The list is sortable by field of study. Focus on awards in the last 5 years.

What About the Cost?

The cost to the USGS should be minimal for this opportunity. Students are supported by NSF and are engaged by USGS on Volunteer Agreements managed by the sponsoring Science Center, so there is no salary requirement. There is some cost associated with background checks and IDs. NSF provides funds that go directly to the student’s home institution to help support the research. They can be used in a variety of ways per NSF guidelines such as travel, field expenses, meeting costs, etc. You should talk this over with your prospective student during budget preparation.


text: The classical half line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this talk, we study the problem in which the static Robin condition $bq(0,t)+q_x(0,t)=0$ is replaced with a dynamic Robin condition; $b=b(t)$ is allowed to vary in time. We present a solution representation, and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential equation for the Dirichlet boundary value. We implement the fractional Frobenius method to solve this equation, and justify that the error in the approximate solution of the original problem converges appropriately. We also demonstrate an argument for existence and unicity of solutions to the original dynamic Robin problem for the heat equation. Finally, we extend these results to linear evolution equations of arbitrary spatial order on the half line, with arbitrary linear dynamic boundary conditions.


text:
# Solve for 0 ≤ θ ≤ 2π (pi)

1. Apr 12, 2009

### rought

1. The problem statement, all variables and given/known data

Solve for 0 ≤ θ ≤ 2π (pi). Give the exact values.

tan^2θ=2tanθsinθ

2. Apr 12, 2009

### Dunkle

First off, observe that this equation holds when $$tan(\theta) = 0$$, so you should be able to find three solutions immediately.

Now, try and find more solutions. Hint: you can safely divide by $$tan(\theta)$$ now because you know it's not equal to 0. Then, remember that
$$tan(\theta) = \frac{sin(\theta)}{cos(\theta)}$$.

Let's see what you can do from there!

3. Apr 12, 2009

### rought

ok I worked it out and i got: cosθ=0 and cosθ=1/2 which gave me π/2 and π/3 ... does that seem right?

4. Apr 12, 2009

### Dunkle

The $$cos(\theta) = 1/2$$ is correct, but I don't know how you arrived at $$cos(\theta) = 0$$. If $$cos(\theta) = 0$$, then $$tan(\theta)$$ is undefined. Although both sides are undefined, it does not mean they are equal. That would be similar to saying 1/0 = 0/0, which is not true! Also, remember there are two solutions for $$cos(\theta) = 1/2$$ on $$[0,2\pi]$$, one of them is $$\pi/3$$ as you mentioned. What do you think the other one is? Drawing a graph out might help.

5. Apr 12, 2009

### rought

the other one would be 5π/3

here's what I did

tan^2θ=2tanθsinθ
sin^2 θ/cos^2 θ=2(sinθ/cosθ).sinθ
sin^2 θ/cos^2 θ=2(sin^2 θ/cosθ)
1/cos^2 θ=2/cosθ
2cos^2 θ-cosθ=0
cosθ(2cosθ -1)=0

cosθ=0 and 2cosθ -1=0

6. Apr 12, 2009

### Dunkle

Ok, I see what you did now. The reason that doesn't work is because, as I mentioned in my previous post, $$tan(\theta)$$ is undefined when $$cos(\theta) = 0$$. So, this is not a valid answer.

Here's what I was attempting to get you to do:

$$tan^{2}(\theta) = 2tan(\theta)sin(\theta) => tan(\theta) = 2sin(\theta) => \frac{sin(\theta)}{cos(\theta)} = 2sin(\theta) => \frac{1}{cos(\theta)} = 2 => cos(\theta) = \frac{1}{2}$$

You can divide by $$tan(\theta)$$ and $$sin(\theta)$$ because we assume that $$tan(\theta) \ne 0$$ because we already found the solutions when $$tan(\theta) = 0$$.

Is this clear?

7. Apr 12, 2009

### qntty

Generally if you are stuck, put everything in terms of cosines and sines so that you can combine and cancel things.

$$\cos{\theta}$$ doesn't work because tangent is undefines when cosθ=0. You also divided by sinθ, which assumes that $$\sin{\theta}\not= 0$$. This caused you to lose that solution which works.

8. Apr 12, 2009

### rought

ah ok thanks a ton guys =]