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https://www.experts-exchange.com/questions/25092300/Service-Request-SR-mf-003-Change-Request5.html | 1,575,738,502,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540500637.40/warc/CC-MAIN-20191207160050-20191207184050-00190.warc.gz | 692,309,336 | 24,202 | # Service Request SR-mf-003 Change Request5
on
Write the program in Java (with a graphical user interface) and have it calculate and display the mortgage payment amount from user input of the amount of the mortgage, the term of the mortgage, and the interest rate of the mortgage. Allow the user to loop back and enter new data or quit. Please insert comments in the program to document the program.
I just can't figure out to use the array to calculate the Principal Paid, Interest Paid, and Balance that changes from payment 001 to XXX. (for example, 30 years loan is 360 times)
How can we loop the calculation to be from pay cycle 001 to 360 for example?
Use "for" statement, but this is too diffciult.
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Java Developer
Top Expert 2010
Commented:
for (payment=1; payment<=360; payment++)
{
System.out.println("Payment: "+payment);
.....
}
Commented:
Thank you super black belt!
Since there are 3 different loan options, how can I apply it to the for( ) statement?
If I do not know well, I may need to use the for() statement 3 times to output the uniquie calculation.
From you code, I can understand that calculation will repert 360 times. If the diffierent option is selected, then another for() statement should be used. For example, for(pay=1; pay=<180;pay++).
How can I apply the array to this?
I think I need to use like : int[] term={7,15,30}; double[] interest ={5.35;5.50;5.75};
Java Developer
Top Expert 2010
Commented:
use nested loops
for (int i=0; i<3; i++) {
int t = term[i];
double int = interest[i];
...
for (payment=1; payment<=360; payment++)
{
System.out.println("Payment: "+payment);
.....
}
}
Commented:
Hello!
When I look at your codes, I think that we can repeat the calculation for 3 options without writing the same kind of codes for 3 time. Am I right? The next step is to figure out the way to output the data as Month,-Principal paid,-Interest paid, and-Balance. Is there a simple way to format the data?
I would like to use the JTextArea using the NetBeans. In fact that I built a GUI part without any calculation part. Am I right that above calculation part of coding should be written under the
calculate action perfromed() section? It seems to me that calculation was made when I clicked the calculation button when I wrote some calculation codes under this statement.
Please help. I am sorry that I need more basics to deal with this, but I have to complete somehow. Allow me to excuse!
Java Developer
Top Expert 2010
Commented:
> I think that we can repeat the calculation for 3 options without writing the same kind of codes for 3 time. Am I right?
correct
> The next step is to figure out the way to output the data as Month,-Principal paid,-Interest paid, and-Balance. Is there a simple way to format the data?
first do it unformatted, then post a new question and I'll look at the formatting for you there
> Am I right that above calculation part of coding should be written under the
calculate action perfromed() section?
correct
Commented:
Great instructor!
I will write some code tonight, and post it. It will be hard, but I will try my best so that you will know where I am at.
Thanks again for the support.
Commented:
Hello,
I have to use a combobox, and I learned that I use the "getSelectedIntex() method to get the selected item. Can I use the switch statement to do the calculation?
Example:
// create the combo box
String[] options = new String[] {"Option 1", "Option 2", "Option 3"};
myComboBox = new JComboBox(options)
...
// get the selected option
int selectedOption = myComboBox.getSelectedIndex();
switch (selectedOption) {
case 0: // Option 1
// do your stuff with option 1
break;
case 1: // Option 2
// do your stuff with option 2
break;
case 2: // Option 3
// do your stuff with option 3
break;
}
Question: I do not understand where I can put this. When I made a GUI using the NetBeans, event lisenter stuff for the combobox is made already, and there is a method for this. Do I need to write those code there?
If so, I do not think the calculation(when I press the calculation butoon) button which is another method will never know this. Last week, I could write every calculation codes under the actionbuttonperformed method to make it work. This time, there are multiple choices due to combobox use. I need to know how to tell the calculationbuttonactionperform to know which option is selected.
Here is the codes:
/*
* To change this template, choose Tools | Templates
* and open the template in the editor.
*/
/*
* MortgageGUI2.java
*
* Created on Jan 26, 2010, 9:32:59 AM
*/
package mortgage2;
import javax.swing.JComboBox;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JScrollPane;
import java.text.DecimalFormat;
/**
*
*/
public class MortgageGUI2 extends javax.swing.JFrame {
DecimalFormat c = new DecimalFormat("\$,###,###,###.00");
/** Creates new form MortgageGUI2 */
public MortgageGUI2() {
initComponents();
loanamtfield.setText(null);
}
/** This method is called from within the constructor to
* initialize the form.
* WARNING: Do NOT modify this code. The content of this method is
* always regenerated by the Form Editor.
*/
@SuppressWarnings("unchecked")
// <editor-fold defaultstate="collapsed" desc="Generated Code">
private void initComponents() {
jLabel1 = new javax.swing.JLabel();
titlelabel = new javax.swing.JLabel();
loanamountlabel = new javax.swing.JLabel();
loanoptionslsabel = new javax.swing.JLabel();
calculate = new javax.swing.JButton();
clear = new javax.swing.JButton();
endprogram = new javax.swing.JButton();
monthpaylabel = new javax.swing.JLabel();
monthpay = new javax.swing.JLabel();
loanamtfield = new javax.swing.JTextField();
loanOption = new javax.swing.JComboBox();
jScrollPane1 = new javax.swing.JScrollPane();
jLabel1.setText("jLabel1");
setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE);
titlelabel.setFont(new java.awt.Font("Tahoma", 1, 14));
titlelabel.setText("Mortgage Calculator V2");
loanamountlabel.setFont(new java.awt.Font("Tahoma", 1, 12));
loanamountlabel.setText("Loan Total Amount: \$");
loanoptionslsabel.setFont(new java.awt.Font("Tahoma", 1, 12));
loanoptionslsabel.setText("Loan Option(select from available choice) :");
calculate.setText("Calculate");
public void actionPerformed(java.awt.event.ActionEvent evt) {
calculateActionPerformed(evt);
}
});
clear.setText("Clear");
clear.setActionCommand("clear");
public void actionPerformed(java.awt.event.ActionEvent evt) {
clearActionPerformed(evt);
}
});
endprogram.setText("End Program");
public void actionPerformed(java.awt.event.ActionEvent evt) {
endprogramActionPerformed(evt);
}
});
monthpaylabel.setText("Your Monthly Payment Under This Loan is: \$");
monthpay.setText("monthlypay");
loanamtfield.setText("loanamount");
loanOption.setModel(new javax.swing.DefaultComboBoxModel(new String[] { "7 years at 5.35%", "15 years at 5.5%", "30 years at 5.75%", " " }));
public void actionPerformed(java.awt.event.ActionEvent evt) {
loanOptionActionPerformed(evt);
}
});
javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
getContentPane().setLayout(layout);
layout.setHorizontalGroup(
);
layout.setVerticalGroup(
);
pack();
}// </editor-fold>
private void calculateActionPerformed(java.awt.event.ActionEvent evt) {
}
private void clearActionPerformed(java.awt.event.ActionEvent evt) {
loanamtfield.setText(null);
monthpay.setText(null);
}
private void endprogramActionPerformed(java.awt.event.ActionEvent evt) {
System.exit(0);
}
private void loanOptionActionPerformed(java.awt.event.ActionEvent evt) {
}
/**
* @param args the command line arguments
*/
public static void main(String args[]) {
java.awt.EventQueue.invokeLater(new Runnable() {
public void run() {
new MortgageGUI2().setVisible(true);
}
});
}
// Variables declaration - do not modify
private javax.swing.JButton calculate;
private javax.swing.JButton clear;
private javax.swing.JButton endprogram;
private javax.swing.JLabel jLabel1;
private javax.swing.JScrollPane jScrollPane1;
private javax.swing.JComboBox loanOption;
private javax.swing.JLabel loanamountlabel;
private javax.swing.JTextField loanamtfield;
private javax.swing.JLabel loanoptionslsabel;
private javax.swing.JLabel monthpay;
private javax.swing.JLabel monthpaylabel;
private javax.swing.JLabel titlelabel;
// End of variables declaration
}
Java Developer
Top Expert 2010
Commented:
one question at a time :)
please close this question, and open a new one with your new question
Chief Technology Officer
Most Valuable Expert 2011
Commented:
This question has been classified as abandoned and is closed as part of the Cleanup Program. See the recommendation for more details.
Do more with | 1,983 | 8,828 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2019-51 | latest | en | 0.861433 |
http://en.wikipedia.org/wiki/Language_of_mathematics | 1,417,006,403,000,000,000 | text/html | crawl-data/CC-MAIN-2014-49/segments/1416931006855.76/warc/CC-MAIN-20141125155646-00008-ip-10-235-23-156.ec2.internal.warc.gz | 91,486,595 | 15,259 | # Language of mathematics
The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language (for example English) using technical terms and grammatical conventions that are peculiar to mathematical discourse (see Mathematical jargon), supplemented by a highly specialized symbolic notation for mathematical formulas.
Like natural languages in general, discourse using the language of mathematics can employ a scala of registers. Research articles in academic journals use a more formal tone than oral exchanges over a scribbled-upon napkin in the university cafeteria.
## What is a language?
Here are some definitions of language:
• a systematic means of communicating by the use of sounds or conventional symbols WordNet
• a system of words used in a particular discipline WordNet
• the code we all use to express ourselves and communicate to others Speech & Language Therapy Glossary of Terms
• a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements Noam Chomsky.
These definitions describe language in terms of the following components:
• A vocabulary of symbols or words
• A grammar consisting of rules of how these symbols may be used
• A community of people who use and understand these symbols
• A range of meanings that can be communicated with these symbols
Each of these components is also found in the language of mathematics.
## The vocabulary of mathematics
Mathematical notation has assimilated symbols from many different alphabets and typefaces. It also includes symbols that are specific to mathematics, such as
$\forall \ \exists \ \nabla \ \wedge \ \infty.$
Mathematical notation is central to the power of modern mathematics. Though the algebra of Al-Khwārizmī did not use such symbols, it solved equations using many more rules than are used today with symbolic notation, and had great difficulty working with multiple variables (which using symbolic notation can simply be called $x, y, z$, etc.). Sometimes formulas cannot be understood without a written or spoken explanation, but often they are sufficient by themselves, and sometimes they are difficult to read aloud or information is lost in the translation to words, as when several parenthetical factors are involved or when a complex structure like a matrix is manipulated.
Like any other profession, mathematics also has its own brand of technical terminology. In some cases, a word in general usage has a different and specific meaning within mathematics—examples are group, ring, field, category, term, and factor. For more examples, see Category:Mathematical terminology.
In other cases, specialist terms have been created which do not exist outside of mathematics—examples are tensor, fractal, functor. Mathematical statements have their own moderately complex taxonomy, being divided into axioms, conjectures, theorems, lemmas and corollaries. And there are stock phrases in mathematics, used with specific meanings, such as "if and only if", "necessary and sufficient" and "without loss of generality". Such phrases are known as mathematical jargon.
The vocabulary of mathematics also has visual elements. Diagrams are used informally on blackboards, as well as more formally in published work. When used appropriately, diagrams display schematic information more easily. Diagrams also help visually and aid intuitive calculations. Sometimes, as in a visual proof, a diagram even serves as complete justification for a proposition. A system of diagram conventions may evolve into a mathematical notation – for example, the Penrose graphical notation for tensor products.
## The grammar of mathematics
The grammar used for mathematical discourse is essentially the grammar of the natural language used as substrate, but with several mathematics-specific peculiarities.
Most notably, the mathematical notation used for formulas has its own grammar, not dependent on a specific natural language, but shared internationally by mathematicians regardless of their mother tongues. This includes the conventions that the formulas are written predominantly left to right, also when the writing system of the substrate language is right-to-left, and that the Latin alphabet is commonly used for simple variables and parameters. A formula such as
$\sin x + a\cos 2 x \ge 0\,$
is understood by Chinese and Israeli mathematicians alike.
Such mathematical formulas can be a part of speech in a natural-language phrase, or even assume the role of a full-fledged sentence. For example, the formula above, an equation, can be considered a sentence or sentential phrase in which the greater than or equal to symbol has the role of a verb. In careful speech, this can be made clear by pronouncing "≥" as "is greater than or equal to", but in an informal context mathematicians may shorten this to "greater or equal" and yet handle this grammatically like a verb. A good example is the book title Why does E = mc2?;[1] here, the equals sign has the role of an infinitive.
Mathematical formulas can be vocalized (spoken aloud). The vocalization system for formulas has to be learned, and is dependent on the underlying natural language. For example, when using English, the expression "ƒ (x)" is conventionally pronounced "eff of eks", where the insertion of the preposition "of" is not suggested by the notation per se. The expression "$\tfrac{dy}{dx}$", on the other hand, is vocalized like "dee-why-dee-eks", with complete omission of the fraction bar, in other contexts often pronounced "over". The book title Why does E = mc2? is said aloud as Why does ee equal em see-squared?.
Characteristic for mathematical discourse – both formal and informal – is the use of the inclusive first person plural "we" to mean: "the audience (or reader) together with the speaker (or author)".
## The language community of mathematics
Mathematics is used by mathematicians, who form a global community composed of speakers of many languages. It is also used by students of mathematics. As mathematics is a part of primary education in almost all countries, almost all educated people have some exposure to pure mathematics. There are very few cultural dependencies or barriers in modern mathematics. There are international mathematics competitions, such as the International Mathematical Olympiad, and international co-operation between professional mathematicians is commonplace.
## The meanings of mathematics
Mathematics is used to communicate information about a wide range of different subjects. Here are three broad categories:
• Mathematics describes abstract structures: on the other hand, there are areas of pure mathematics which deal with abstract structures, which have no known physical counterparts at all. However, it is difficult to give any categorical examples here, as even the most abstract structures can be co-opted as models in some branch of physics (see Calabi-Yau spaces and string theory).
• Mathematics describes mathematics: mathematics can be used reflexively to describe itself—this is an area of mathematics called metamathematics.
Mathematics can communicate a range of meanings that is as wide as (although different from) that of a natural language. As English mathematician R.L.E. Schwarzenberger says:
My own attitude, which I share with many of my colleagues, is simply that mathematics is a language. Like English, or Latin, or Chinese, there are certain concepts for which mathematics is particularly well suited: it would be as foolish to attempt to write a love poem in the language of mathematics as to prove the Fundamental Theorem of Algebra using the English language.
## Alternative views
Some definitions of language, such as early versions of Charles Hockett's "design features" definition, emphasize the spoken nature of language. Mathematics would not qualify as a language under these definitions, as it is primarily a written form of communication (to see why, try reading Maxwell's equations out loud). However, these definitions would also disqualify sign languages, which are now recognized as languages in their own right, independent of spoken language.
Other linguists believe no valid comparison can be made between mathematics and language, because they are simply too different:
Mathematics would appear to be both more and less than a language for while being limited in its linguistic capabilities it also seems to involve a form of thinking that has something in common with art and music. - Ford & Peat (1988) | 1,682 | 8,635 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2014-49 | longest | en | 0.905504 |
http://www.adammil.net/math/topic_topNumbersDivisibility.html | 1,701,812,122,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100568.68/warc/CC-MAIN-20231205204654-20231205234654-00681.warc.gz | 62,722,460 | 5,033 | # Divisibility
Ambidextrous, adj.: Able to pick with equal skill a right-hand pocket or a left. -- Ambrose Bierce, "The Devil's Dictionary"
## Math
Note: If you cannot view some of the math on this page, you may need to add MathML support to your browser. If you have Mozilla/Firefox, go here and install the fonts. If you have Internet Explorer, go here and install the MathPlayer plugin.
Math > Number theory > Divisibility
### Divisibility
Divisibility among the integers and natural numbers
#### Contents:
Definition of divisor [tags: divisor]
Given `x,y in ZZ` with `x != 0`, `x` is a divisor of `y` if there exists an integer `t` such that `x*t=y`.
`(EE t in ZZ)(x*t=y)`
If `x` is a divisor of `y`, we can also say "`x` divides `y`", and we write "`x div y`". 0 is not a divisor of any integer, but all nonzero integers are divisors of zero, and of course 1 is a divisor of every integer. A proper divisor of `y` is a divisor `x` such that `x != y`.
Similarly, given `a,b in NN`, `a div b` if `(EE u in NN)(a*u=b)`.
If `y` is not zero, then there are only finitely many divisors, because by Divisors are not greater, `|x|<=|y|`.
Definition of multiple [tags: multiple]
For `n in ZZ`, the set of multiples of `n` is
`{n*t:t in ZZ}`
The set of multiples of `n` can be abbreviated `nZZ`. Each element of this set is called a multiple of `n`.
Definition of common divisor [tags: divisor]
For `x,y in ZZ`, `t` is a common divisor of `x` and `y` if `t div x and t div y`.
Every pair of integers has at least one common divisor, because 1 divides every integer. If `x` or `y` is nonzero, then there are only finitely many common divisors. (See the definition of divisor.)
Definition of GCD [tags: GCD divisor]
For `x,y in ZZ`, `t` is the greatest common divisor (GCD) of `x` and `y` if:
`t div x and t div y and (AA u in ZZ)(u div x and u div y => u <= t)`
This definition says that `t` is the GCD of `x` and `y` if it is a common divisor of `x` and `y`, and every other common divisor is less than or equal to `t`. The greatest common divisor of `x` and `y` is written `GCD(x,y)`.
If `x` or `y` is nonzero then a GCD exists because there are only finitely many common divisors (see the definition of common divisor), and one of them is the greatest. If `x` and `y` are both zero, then there is no GCD because there are infinitely many common divisors. The GCD is always positive because 1 is a common divisor of every pair of integers, and 1 is greater than all nonpositive integers.
Definition of common multiple [tags: multiple]
For `x,y in ZZ`, `t` is a common multiple of `x` and `y` if `t` is a multiple of `x` and `t` is a multiple of `y`.
Definition of LCM [tags: LCM multiple]
For `x,y in ZZ-{0}`, `t` is the least common multiple (LCM) of `x` and `y` if:
1. `t` is a positive common multiple of `x` and `y`, and
2. Every positive common multiple of `x` and `y` is greater than or equal to `t`.
Note that if `x=0` or `y=0`, the least common multiple is defined to be zero. The least common multiple of `x` and `y` is written `LCM(x,y)`.
Theorem: Nonzero integers have LCM [tags: multiple LCM]
Given `x,y in Z-{0}`, there exists a positive common multiple of `x` and `y`.
Proof: Let `z=xyc`, where `c in {-1,1}`. If `xy` is negative, let `c=-1`. Otherwise, let `c=1`. Then, `z>0`, and since `z=xyc`, `z` is a multiple of both `x` and `y`. Therefore, every pair of nonzero integers `x` and `y` has a positive common multiple. Furthermore, since the set of possible positive common multiples is bounded from below (by zero), there exists a common multiple that is less than or equal to all others. So every pair of nonzero integers has a least common multiple.
Theorem: Divisor divides multiples [tags: divisor multiple]
If `a div b`, then `a div nb` for all `n in ZZ`.
Proof: If `a div b`, then there exists an integer `m` such that `am=b`. Given any integer `n`, `n*b=n*am=a*nm`, and clearly `a div a*nm`. Therefore, `a div nb`.
Hypothesis: Divisors of a product [tags: divisor multiple]
If `a div b and c div d`, then `a div bd and c div bd and ac div bd`.
Theorem: Divisor of a sum [tags: divisor]
If `a div b and b div c`, then `a div b+c and a div b-c`.
Proof: If `a div b` and `a div c`, then there exist integers `m` and `n` such that `am=b` and `an=c`. Then `b+c=am+an=a(m+n)`. Clearly, `a div a(m+n)`, so `a div b+c`. Similarly, `a div b-c`.
Theorem: Divisors are transitive [tags: divisor]
If `a div b and b div c`, then `a div c`.
Proof: If `a div b` and `b div c`, then by definition there exist integers `m` and `n` such that `am=b` and `bn=c`. Substituting `am` for `b` in `bn=c`, we get `amn=c`. Because there exists an integer `mn` such that `a*mn=c`, `a div c`.
Theorem: Divisors are not greater [tags: divisor]
For `a,b in NN`, if `a div b`, then `a<=b`.
Proof: By the definition of divisor, there exists a natural number `m` such that `am=b`. By Product of natural number factors is not less, we know that `a<=am`, and since `am=b`, `a<=b`.
This can be extended to the integers because the absolute value of a nonzero integer is a natural number. For `x,y in ZZ` where `y != 0`, if `x div y` then `|x|<=|y|`
Corollary (of Divisors are not greater): Proper divisors are not greater than half [tags: divisor]
For `a,b in NN`, if `a div b and a!=b`, then `a<=b/2`.
Corollary (of Divisors are not greater): Symmetric divisors have the same magnitude [tags: divisor]
If `a div b and b div a`, then `|a|=|b|`.
Hypothesis: Product of divisors [tags: divisor]
For `a,b,c in NN`, if `a div b and b div c and a<=sqrt(c) and b<=sqrt(c)`, then `ab div c`.
Hypothesis: Odd numbers have odd divisors [tags: odd divisor]
If `b` is odd and `a div b`, then `a` is odd.
This basically says that all divisors of odd numbers are themselves odd.
Hypothesis: Common divisors divide GCD [tags: GCD divisor]
If `t` is a common divisor of `x` and `y`, then `t div GCD(x,y)`.
Hypothesis: Product of relative primes [tags: prime GCD]
If `GCD(a,b)=1` (ie, `a` and `b` are relatively prime) and `t!=0`, then `GCD(at,bt)=|t|`.
If `a` and `b` are relatively prime, then their sets of divisors have nothing in common except 1. So if we multiply both numbers by `t`, the sets of divisors of the resulting products will have nothing in common except 1 and `|t|`, so the GCD of the products will be `|t|`.
Hypothesis: Relationship between GCD and LCM [tags: GCD LCM]
`LCM(x,y)=(xy)/(GCD(x,y))`
If `d=GCD(x,y)` then `d div x and d div y`. By definition, there exist integers `m` and `n` such that `x=md` and `y=nd`. Then `xy=md*nd`. We can divide `xy` by `d`, producing `(xy)/d=mnd`. This quantity is still a common multiple of `x` and `y` (because it's equal to both `nx` and `my`). Because `d=GCD(x,y)`, `m` and `n` are the smallest possible numbers such that `x=md` and `y=nd`. That is to say, `mnd=(xy)/d` is the least common multiple. | 2,088 | 6,841 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2023-50 | longest | en | 0.845838 |
https://crypto.stackexchange.com/questions/10728/can-an-rsa-private-key-have-several-public-keys/10731 | 1,726,791,731,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652073.91/warc/CC-MAIN-20240919230146-20240920020146-00680.warc.gz | 163,784,290 | 42,503 | # Can an RSA private key have several public keys?
Ok, so my cryptography lecturer in University posed this question at the end of the RSA key generation lecture as a brain teaser.
I have been thinking about this and I think I have come up with a way ( I am aware it's not practical and very vulnerable - but I would love for you guys to punch holes through it ):
Use RSA to generate public and private key pair.
Make an additive hash function that takes in any input and adds the ASCII value of each character and gives that as an output. ( I am aware additive hash has horrible distribution, for example, ABC, BAC, ACB all have the same hash output -- but theoretically, this can be used as an advantage to solve our problem )
Now take your public key and generate several possible keys by jumbling up the on and off bits.
Give these jumbled up keys to potential customers.
Put our hash function on the server.
When a customer puts in his jumbled up public-key - Hash function calculates the hash - which should be similar to original public key generated by RSA. The customer gets access.
Once again I am aware that this is very vulnerable and terrible. It cant be used in the real world. But does it answer the question my lecturer posed?
EDIT:
I am sorry for the confusion. This question has nothing to do with collisions and exploiting the maths ( Those are definitely valid ways to do that - but they weren't what my lecturer was referring too - they were discussed in the lecture itself. ). The way my lecturer asked this question was - " come up with ways to make several public keys related to a single private key - nevermind how vulnerable your solution is ".
• Can't you just add integer multiples of $\phi(N)$ to a public key to generate an infinite number of valid public keys for any private key? Commented Oct 3, 2013 at 0:44
• I didn't know that was possible ... so adding ϕ(N) to (n,e) gives another public key which is paired with (n,d) private key. I wasn't even aware this was possible .. But thanks Commented Oct 3, 2013 at 0:47
• Well think about how public and private keys are generated. You just need $e$ and $d$ s.t. $e*d = 1 mod \phi(N)$. Adding multiples of $\phi(N)$ changes nothing, because they'll just drop out in the modular reduction. Commented Oct 3, 2013 at 0:50
• Plus, if you do that and someone gets hold of two public keys, he can take the difference and get hold of a multiple of $\varphi{(N)}$, and, well, game over. Commented Oct 3, 2013 at 2:47
• Commented Sep 9, 2019 at 2:19
@pg1989 has not only the right answer but the only answer if you assume the goal is to have multiple RSA encryption exponents that correspond to the same decryption exponent.
\begin{align} e_1 \cdot d & \equiv 1 \pmod{\phi(N)}\\ e_2 \cdot d & \equiv 1 \pmod{\phi(N)}\\ (e_1 - e_2) \cdot d & \equiv 0 \pmod{\phi(N)} \end{align}
But since $$d$$ is relatively prime to $$\phi(N)$$, by Euclid's lemma $$\phi(N)$$ must divide $$e_1 - e_2$$ :
$$e_1 \equiv e_2 \pmod{\phi(N)}$$
In other words, any two public RSA exponents that share a private exponent must differ by some multiple of $$\phi(N)$$.
I highly suspect this is what your professor was thinking. Although, as @Thomas points out if the multiple is small and someone gets hold of both public keys, they can factor $$N$$. Now, maybe if you use a big multiple...
[Update]
As @fgrieu notes in a comment, I have conflated $$\phi(N) = (p-1)(q-1)$$ with $$\operatorname{LCM}(p-1, q-1)$$. Replace the former with the latter in the above derivation for the right answer.
• The necessary and sufficient condition for a public expoment $e_j$ to work with private key $d$ is $e_j\cdot d\equiv1\pmod{\mathrm{LCM}(p-1,q-1)}$. This increases the number of $e_j$ we can choose for a given maximum for the $e_j$, compared to the sufficient but not necessary $e_j\cdot d\equiv1\pmod{\phi(p-1,q-1)}$. As stated by Thomas, two holders of $e_j$ could collude and factor the public modulus.
– fgrieu
Commented Oct 3, 2013 at 5:01
• In the second equation above, read $\phi(N)$ or $(p-1)\cdot(q-1)$ where there is $\phi(p-1,q-1)$, sorry.
– fgrieu
Commented Oct 3, 2013 at 5:42 | 1,107 | 4,150 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 10, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2024-38 | latest | en | 0.964302 |
https://socratic.org/questions/show-that-the-nuclear-density-of-1h1-mass-no-1-atomic-no-1-is-over-10-14-times-g#617082 | 1,643,336,271,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305341.76/warc/CC-MAIN-20220128013529-20220128043529-00320.warc.gz | 571,585,813 | 5,945 | Show that the nuclear density of 1H1(mass no-1&atomic no-1)is over 10^14 times greater than its atomic density (assume the atom to have the radius of the first Bohr orbit).In this question,what should I put for nuclear mass&atomic mass?
May 20, 2018
see below
Explanation:
You don't need a number for mass. You are comparing densities, and the related mass, $M$, is the same in each case, ie the proton.
• $\frac{\frac{M}{V} _ 1}{\frac{M}{V} _ 2} = {V}_{2} / {V}_{1}$
So you are really comparing the (spherical) volumes of the H nucleus and the H first orbital.
Common approximation:
• radius of any nucleus: $1 \text{ fm}$
• radius of any atom: $1 \text{ Å}$
Google for the actual dimensions if you want to be more precise :) | 213 | 736 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2022-05 | latest | en | 0.825493 |
www.tedkidd.com | 1,472,061,112,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982292607.17/warc/CC-MAIN-20160823195812-00193-ip-10-153-172-175.ec2.internal.warc.gz | 719,244,833 | 10,177 | # Home Energy Calculator
Like to know what MPG YOUR HOUSE GETS?
Wonder how much could you reasonably cut?
STEP ON THIS SCALE. FIND OUT HOW YOUR HOME MEASURES UP!
Enter your square footage, annual heating fuel use, then click CALCULATE:
(Email or call me if you want help figuring that out.)
This movie requires Flash Player 9
Enter your annual use, house size, Click CALCULATE
a pop up triangle estimates your ENERGY OPPORTUNITY.
(Get your annual consumption from RGE Here)
WHAT DOES IT MEAN? LOOK BELOW:
KEY to 4 Pop Up Categories:
\$\$\$ – GREAT opportunity – Probable 50-70% energy reduction opportunity. This indicates a very expensive energy bill. You may also have difficulty keeping the home evenly comfortable (because most of the heat created is quickly going outdoors). This home typically has snow melting off the roof before other homes in the neighborhood and ice damming may be a frustrating and costly problem. Often this homeowner has spent money trying to improve efficiency and been frustrated with modest to poor results. Please feel free to schedule a visit. You are my ideal client as your energy savings is likely to more than pay for your improvements.
\$\$ – Good opportunity – Probable 20-50% energy reduction opportunity. Usually these homeowners want to see me because they feel the money they are spending on energy does not balance with the comfort they are receiving. These people want to understand where the best opportunities for improvement lie before investing in improvements rather than using the old “throw money and hope” approach. If you heat with Oil or Propane, the dollar savings opportunity can be quite significant. Please feel free to schedule a visit
\$ – Some opportunity – Probable 10-20% energy reduction opportunity. If you fall in this category your dollar savings opportunity is probably not great unless your house is bigger than 2500 square feet and/or you heat with propane or oil (for example: \$1 per square foot per year energy cost at 2010 prices is high). If you heat with Natural Gas and fall into this category your motivation for seeing me would be comfort imbalance issues, problems with ice dams, or your equipment has passed its life expectancy and you want to thoroughly explore your options and avoid making a 15-20 year mistake. Please feel free to call and discuss.
Small Opportunity – Probable 5-10% savings without extreme measures. Basically anybody could get to Net Zero Energy Home, but at what cost? You spend more fueling your Prius than your home. While cost effective opportunities to stop wasting energy are plentiful, once those are addressed further improvements tend NOT to be about saving money. At some point the incremental cost of energy improvements becomes higher than the energy saved can justify on its own. Homeowners with energy use approaching net zero want energy independence and are willing to pay a premium for it. Please e-mail me if you are looking for help.
Remember, energy efficiency doesn’t mean turning back the thermostat…
…it means keeping the heat in the house!
If your energy reduction hopes align with my rough calculator, we should get together. Contact me to discuss a free energy visit today.
I save my customers 30 – 70% on their energy costs. CLICK HERE TO SEE DOCUMENTED RESULTS
This energy calculator will help you get a very general idea of your house’s energy efficiency and will provide an the opportunity for improvement. All you need to know is your heating fuel type, annual amount used, and your homes square footage. Our houses require a certain amount of heat which usually doesn’t vary much from year to year (unless weatherization occurs). There are a number of ways to determine annual gas usage:Call gas company and ask.
1. Call gas company and ask.
2. Login to your account and get usage history. (Click HERE for RGE)
3. Look at current meter read, then look at year ago meter read from a bill and subtract.
4. Go to the chart in a recent bill and look at each month. With a straight edge roughly determine the usage and write it down. Add 12 months usage together.
If you have problems calculating you annual usage feel free to send me your bills and I will try to help.
SCHEDULING VISITS Currently I am scheduling visits via e-mail and telephone. Eventually there will be a calendar that homeowners can use to more conveniently schedule visits right on-line. If you want to schedule via e-mail, please send the following information:
2. Size of home and approximate annual energy use or monthly budget for electric and gas or oil.
3. 2-3 times during the next two weeks that everyone involved in improvement decisions will be available. 7pm is a fine time to request.
4. Primary reason for requesting a free energy visit.
This will be a very informative meeting. Generally there is a bit of discussion that occurs after I leave, if all parties are not up to speed on what was discussed we have not effectively utilized our time. So there should be as few distractions as possible. Visits can last as much as two hours.
Only this first visit is at no cost to you, so make the best of it.
DON’T KNOW YOUR ANNUAL ENERGY USE? – Do you have a rough idea of your annual cost? Send that to me and I’ll calculate it for you.
Therms are currently a little over \$1 – so if you are on budget, multiply the gas bill by 12 for annual therms – you’ll be close enough.
Propane and Oil are a bit more variable, you’ll probably need to call your supplier for annual use.
NOTES: This chart is under beta testing and the marker’s are very general. If you are in the green well below “typical energy star home,” you may be in pretty good shape. Currently works best for houses between 1500-2500 sf. IF YOUR HOUSE IS LARGER THAN 3000 SF and you are below THE ENERGY STAR MARKER there may still be significant \$ saving opportunity for you.
If your home is larger than 1500 square feet and you fall above the energy star marker, please feel free to send me your square footage and energy use, and I’ll give you a rough estimate of what your energy saving opportunity is.
Energy cost is no longer a good gauge of consumption. Prices fluctuate so much and can vary significantly depending upon provider, I use actual energy consumption for the calculator. This will allow you to determine how much of an energy hog their home is without having the results skewed by discrepancies in energy price. This way we can more accurately see how big your opportunity is to save energy and improve comfort. A house heating with oil may cost50% more than the identical house using natural gas – yet the natural gas house is the energy hog because it uses more heat energy. You need to track energy units used (therms, gallons, etc…), not cost to determine your savings opportunity.
This scale is only a rough estimator, as adjustments for house size is not part of the calculations. Energy use per square foot should go down for larger the house everything else being equal. Bigger houses may tend to be more in the green scale when they actually represent better opportunities for saving than smaller houses that show further in the yellow. For example, a super insulated 1200 sf house will use more than 1/2 the energy of a super insulated 2400 sf house with just for heat. Therefore it will be inaccurately more to the right than a larger home. Another variable not addressed is number or occupants and other energy uses. Hot water in the 1200 sf house with 4 occupants may be significantly higher than in the 2400 sf house with 2 occupants – and that is not adjusted for here.
If you don’t know your annual consumption but you do know your annual cost, here’s a very basic rule of thumb for determining your energy savings opportunity and if we should schedule a free energy visit. Based upon past experience:
• I REALLY WANT TO SEE YOU if you heat with Natural Gas and spend more than \$1.00 per square foot per year. (Oil, Propane, or Electric the number is roughly double)
• I AM HAPPY TO SEE YOU if you spend \$.50 to \$1.00
• I WILL COME TO SEE YOU if you spend less than \$.50, but you are either freezing or your house is already fairly efficient. I hope there are comfort or durability issues you want to address. Please don’t expect miracles when it comes to saving money on energy.
By taking a comprehensive look at energy savings opportunities it is not uncommon for Home Performance customers to save 30% – 70% on their energy bills, whereas a new furnace may save 5-10% on energy cost (if sized properly, if installed properly, if your duct work is not undersized, if… if… if…).
Like to know how big your energy savings opportunity is? First we need to find out if your house is currently consuming like a Hummer or Toyota Corrolla. The challenge is to gauge where you are now, so you can see how much you would benefit by switching to Prius consumption. By tracking your miles per fill to the amount of fuel used we know how efficient our cars operate. We can compare our cars to similar cars to determine how well we are doing. To obtain major efficiency gains in auto travel means changing cars. If we trade our clunker in for a Prius we know we can expect to go from 15 mpg to 50.
Is your house a Hummer or a Prius? Turn your Hummer into a Prius without having to move!
It is not necessary to “trade in” your home for similar gains in efficiency, in fact most new homes only offer modest improvement in energy consumption over older homes. Many of the homes I’ve worked on are fairly new.
This energy calculator will help you get a very general idea of your house’s energy efficiency and will provide an the opportunity for improvement. All you need to know is your heating fuel type, annual amount used, and your homes square footage. Our houses require a certain amount of heat which usually doesn’t vary much from year to year (unless weatherization occurs). There are a number of ways to determine annual gas usage:Call gas company and ask.
1. Call gas company and ask.
2. Login to your account and get usage history. (Click HERE for RGE)
3. Look at current meter read, then look at year ago meter read from a bill and subtract.
4. Go to the chart in a recent bill and look at each month. With a straight edge roughly determine the usage and write it down. Add 12 months usage together.
If you have problems calculating you annual usage feel free to send me your bills and I will try to help.
If you don’t know your annual consumption but you do know your annual cost, here’s a very basic rule of thumb for determining your energy savings opportunity and if we should schedule a free energy visit. Based upon past experience:
• I REALLY WANT TO SEE YOU if you heat with Natural Gas and spend more than \$1.00 per square foot per year. (Oil, Propane, or Electric the number is roughly double)
• I AM HAPPY TO SEE YOU if you spend \$.50 to \$1.00
• I WILL COME TO SEE YOU if you spend less than \$.50, but you are either freezing or your house is already fairly efficient. I hope there are comfort or durability issues you want to address. Please don’t expect miracles when it comes to saving money on energy.
Most people’s single largest energy expense is heating their homes.
USE THE CALCULATOR ABOVE TO DETERMINE YOUR HEAT ENERGY SAVINGS OPPORTUNITY.
QUESTIONS? I would love to answer them, e-mail me at: homeenergyvisit@gmail.com or call (585) 466-4NRG, that’s (585) 466-4674. Call me any time – 24 hours a day. | 2,575 | 11,558 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2016-36 | longest | en | 0.908468 |
http://flyingsalmon.net/blog/ | 1,696,211,308,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510942.97/warc/CC-MAIN-20231002001302-20231002031302-00679.warc.gz | 13,272,296 | 11,923 | Sunday, October 01, 2023
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https://oeis.org/A024857 | 1,631,944,802,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056297.61/warc/CC-MAIN-20210918032926-20210918062926-00608.warc.gz | 504,426,362 | 3,706 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
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A024857 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = (Fibonacci numbers). 2
1, 2, 7, 11, 27, 44, 91, 147, 278, 450, 806, 1304, 2257, 3652, 6181, 10001, 16677, 26984, 44551, 72085, 118220, 191284, 312300, 505312, 822513, 1330854, 2161907, 3498039, 5674751, 9181940 (list; graph; refs; listen; history; text; internal format)
OFFSET 2,2 COMMENTS Essentially the same as A023864 with different indexing. LINKS Harvey P. Dale, Table of n, a(n) for n = 2..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-1,-1,-3,2,1,1,1). FORMULA G.f.:(-1-x^5-2*x^2-x)/((x^2+x-1)*(x^4+x^2-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009] MATHEMATICA CoefficientList[Series[( (-1-x^5-2x^2-x)/((x^2+x-1)(x^4+x^2-1)^2) ), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 3, -2, -1, -1, -3, 2, 1, 1, 1}, {1, 2, 7, 11, 27, 44, 91, 147, 278, 450}, 30] (* Harvey P. Dale, Dec 26 2016 *) CROSSREFS Sequence in context: A024479 A295138 A023864 * A024481 A024591 A309465 Adjacent sequences: A024854 A024855 A024856 * A024858 A024859 A024860 KEYWORD nonn AUTHOR STATUS approved
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Last modified September 18 01:54 EDT 2021. Contains 347504 sequences. (Running on oeis4.) | 642 | 1,668 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2021-39 | latest | en | 0.565474 |
https://bendwavy.org/klitzing/incmats/quadippady.htm | 1,643,316,415,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305288.57/warc/CC-MAIN-20220127193303-20220127223303-00717.warc.gz | 177,441,593 | 2,423 | Acronym quadippady Name quasidisprismatodishecatonicosachoron,Unholey Terror Cross sections ` ©` Circumradius sqrt(2) = 1.414214 General of army hi Colonel of regiment dattady Externallinks
The quasidisprismatodishecatonicosachoron is an edge-faceting of the ditetrahedronary dishecatonicosachoron (dattady). As such it is a fissary polychoron (Type A), as its vertices are coincident by 4 and edges coincident by pairs. Thus it looks like Type B. Its vertex figure is a (mostly empty) compound faceting of x3v3o.
As abstract polytope quadippady is automorph, thereby replacing pentagons by pentagrams, resp. replacing doe by gissid and pip by stip.
Incidence matrix according to Dynkin symbol
```x5o3o5/3x – Type A
. . . . | 2400 | 3 3 | 3 6 3 | 1 3 3 1
----------+------+-----------+----------------+----------------
x . . . | 2 | 3600 * | 2 2 0 | 1 2 1 0
. . . x | 2 | * 3600 | 0 2 2 | 0 1 2 1
----------+------+-----------+----------------+----------------
x5o . . | 5 | 5 0 | 1440 * * | 1 1 0 0
x . . x | 4 | 2 2 | * 3600 * | 0 1 1 0
. . o5/3x | 5 | 0 5 | * * 1440 | 0 0 1 1
----------+------+-----------+----------------+----------------
x5o3o . ♦ 20 | 30 0 | 12 0 0 | 120 * * *
x5o . x ♦ 10 | 10 5 | 2 5 0 | * 720 * *
x . o5/3x ♦ 10 | 5 10 | 0 5 2 | * * 720 *
. o3o5/3x ♦ 20 | 0 30 | 0 0 12 | * * * 120
```
```x5o3/2o5/2x – Type A
. . . . | 2400 | 3 3 | 3 6 3 | 1 3 3 1
------------+------+-----------+----------------+----------------
x . . . | 2 | 3600 * | 2 2 0 | 1 2 1 0
. . . x | 2 | * 3600 | 0 2 2 | 0 1 2 1
------------+------+-----------+----------------+----------------
x5o . . | 5 | 5 0 | 1440 * * | 1 1 0 0
x . . x | 4 | 2 2 | * 3600 * | 0 1 1 0
. . o5/2x | 5 | 0 5 | * * 1440 | 0 0 1 1
------------+------+-----------+----------------+----------------
x5o3/2o . ♦ 20 | 30 0 | 12 0 0 | 120 * * *
x5o . x ♦ 10 | 10 5 | 2 5 0 | * 720 * *
x . o5/2x ♦ 10 | 5 10 | 0 5 2 | * * 720 *
. o3/2o5/2x ♦ 20 | 0 30 | 0 0 12 | * * * 120
```
```x5/4o3o5/2x – Type A
. . . . | 2400 | 3 3 | 3 6 3 | 1 3 3 1
------------+------+-----------+----------------+----------------
x . . . | 2 | 3600 * | 2 2 0 | 1 2 1 0
. . . x | 2 | * 3600 | 0 2 2 | 0 1 2 1
------------+------+-----------+----------------+----------------
x5/4o . . | 5 | 5 0 | 1440 * * | 1 1 0 0
x . . x | 4 | 2 2 | * 3600 * | 0 1 1 0
. . o5/2x | 5 | 0 5 | * * 1440 | 0 0 1 1
------------+------+-----------+----------------+----------------
x5/4o3o . ♦ 20 | 30 0 | 12 0 0 | 120 * * *
x5/4o . x ♦ 10 | 10 5 | 2 5 0 | * 720 * *
x . o5/2x ♦ 10 | 5 10 | 0 5 2 | * * 720 *
. o3o5/2x ♦ 20 | 0 30 | 0 0 12 | * * * 120
```
```x5/4o3/2o5/3x – Type A
. . . . | 2400 | 3 3 | 3 6 3 | 1 3 3 1
--------------+------+-----------+----------------+----------------
x . . . | 2 | 3600 * | 2 2 0 | 1 2 1 0
. . . x | 2 | * 3600 | 0 2 2 | 0 1 2 1
--------------+------+-----------+----------------+----------------
x5/4o . . | 5 | 5 0 | 1440 * * | 1 1 0 0
x . . x | 4 | 2 2 | * 3600 * | 0 1 1 0
. . o5/3x | 5 | 0 5 | * * 1440 | 0 0 1 1
--------------+------+-----------+----------------+----------------
x5/4o3/2o . ♦ 20 | 30 0 | 12 0 0 | 120 * * *
x5/4o . x ♦ 10 | 10 5 | 2 5 0 | * 720 * *
x . o5/3x ♦ 10 | 5 10 | 0 5 2 | * * 720 *
. o3/2o5/3x ♦ 20 | 0 30 | 0 0 12 | * * * 120
```
```Type B
600 | 12 | 12 24 12 | 4 12 12 4
-----+------+----------------+----------------
2 | 3600 | 2 4 2 | 1 3 3 1
-----+------+----------------+----------------
5 | 5 | 1440 * * | 1 1 0 0
4 | 4 | * 3600 * | 0 1 1 0
5 | 5 | * * 1440 | 0 0 1 1
-----+------+----------------+----------------
♦ 20 | 30 | 12 0 0 | 120 * * *
♦ 10 | 15 | 2 5 0 | * 720 * *
♦ 10 | 15 | 0 5 2 | * * 720 *
♦ 20 | 30 | 0 0 12 | * * * 120
``` | 2,255 | 4,815 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2022-05 | latest | en | 0.61264 |
https://huchengbei.com/blog/ | 1,566,441,617,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027316718.64/warc/CC-MAIN-20190822022401-20190822044401-00315.warc.gz | 485,692,541 | 4,556 | ## PAT(A) 1135. Is It A Red-Black Tree (30)
### 1135. Is It A Red-Black Tree (30)
There is a kind of balanced binary search tree named red-black tree in the data structure. It has the following 5 properties:
## PAT(A) 1134. Vertex Cover (25)
### 1134. Vertex Cover (25)
A vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. Now given a
## PAT(A) 1133. Splitting A Linked List (25)
### 1133. Splitting A Linked List (25)
Given a singly linked list, you are supposed to rearrange its elements so that all the negative values appear before all of the non-negatives, and all the values in [0, K]
## PAT(A) 1132. Cut Integer (20)
### 1132. Cut Integer (20)
Cutting an integer means to cut a K digits long integer Z into two integers of (K/2) digits long integers A and B. For example, after cutting Z = 167334,
## PAT(A) 1127. ZigZagging on a Tree (30)
### 1127. ZigZagging on a Tree (30)
Suppose that all the keys in a binary tree are distinct positive integers. A unique binary tree can be determined by a given pair of postorder and inorder traversal sequences.
## PAT(A) 1126. Eulerian Path (25)
### 1126. Eulerian Path (25)
In graph theory, an Eulerian path is a path in a graph which visits every edge exactly once. Similarly, an Eulerian circuit is an Eulerian path which starts and ends on the same vertex.
## PAT(A) 1125. Chain the Ropes (25)
### 1125. Chain the Ropes (25)
Given some segments of rope, you are supposed to chain them into one rope. Each time you may only fold two segments into loops and chain them into one | 439 | 1,621 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2019-35 | latest | en | 0.843772 |
https://www.cut-the-knot.org/exchange/badInfinity2.shtml | 1,713,033,772,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816832.57/warc/CC-MAIN-20240413180040-20240413210040-00514.warc.gz | 658,313,807 | 4,767 | Subject: Re: Division by Zero
Date: Thu, 07 Oct 2000 21:17:19 -0400
From: Alex Bogomolny
Dear Mickey:
It's not a question whether it's bad or not, but whether it's useful.
Strictly speaking, the limit of 1/x as x goes to 0 does not exist at all - it can't be declared infinity or anything else. The limit from the right, i.e., when x is strictly positive, may be considered as infinite. The limit from the left, i.e. when x is negative, may be declared a negative infinity.
Assume you go ahead and declare the two one-sided limits as infinite. What do you gain? Infinity thus defined is not a number. Infinity times 0 is undefined. So think before you do that.
Do not also put all infinities considered in mathematics into a single basket. There are many; each treated differently and is used for a different purpose.
There's a point at infinity and a line at infinity, there are cardinal and ordinal infinities, and more. They are all very different.
All the best,
Alexander Bogomolny | 244 | 992 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-18 | latest | en | 0.956165 |
http://www.linuxtopia.org/online_books/office_guides/openoffice_3_calc_user_guide/openoffice_calc_Address,_Indirect,_Offset,_Index_INDEX_returns_cells_inside_a_specified_range.html | 1,521,906,916,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257650730.61/warc/CC-MAIN-20180324151847-20180324171847-00511.warc.gz | 433,747,481 | 11,078 | On-line Guides
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OpenOffice Calc 3.x Guide
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## INDEX returns cells inside a specified range
INDEX returns the cells specified by a row and column number. The row and column number are relative to the upper left corner of the specified reference range. For example, using =INDEX(B2:D3; 1; 1) returns the cell B2. Table 14 lists shows the syntax for using the INDEX function.
Table 14. Syntax for INDEX.
Syntax Description
INDEX(reference) Return the entire range.
INDEX(reference; row) Returns the specified row in the range.
INDEX(reference; row; column) Returns the cell specified by row and column. A row and column of 1 returns the cell in the upper left corner of the range.
INDEX(reference; row; column; range) A reference range can contain multiple ranges. The range argument specifies which range to use.
The INDEX function can return an entire range, a row, or a single column (see Table 14). The ability to index based on the start of the reference range provides some interesting uses. Using the values shown in Table 1, Listing 12 finds and returns Bob’s quiz scores. Table 15 contains a listing of each function used in Listing 12.
Listing 12. Return Bob’s quiz scores.
```=SUM(OFFSET(INDEX(A2:G16; MATCH("Bob"; A2:A16; 0)); 0; 3; 1; 2))
```
Table 15. Breakdown of Listing 12.
Function Description
MATCH("Bob";A2:A16; 0) Returns 3 because Bob is the third entry in column A2:A16.
INDEX(A2:A16; 3) Returns the A4:G4—the row containing Bob’s quiz scores.
OFFSET(A4:G4; 0; 3; 1; 2) Returns the range D4:E4.
SUM(D4:E4) Returns the sum of Bob’s quiz scores.
A simple range contains one contiguous rectangular region of cells. It is possible to define a multi-range that contains multiple simple ranges. If the reference consists of multiple ranges, you must enclose the reference or range name in parentheses.
If reference argument to the INDEX function is a multi-range, then the range argument specifies which simple range to use (see Table 16).
Table 16. Using INDEX with a multi-range.
Function Returns
=INDEX(B2:G2; 1; 2) 93
=INDEX(B5:G5; 1; 2) 65
=INDEX((B2:G2;B5:G5); 1; 2) 93
=INDEX((B2:G2;B5:G5); 1; 2; 1) 93
=INDEX((B2:G2;B5:G5); 1; 2; 2) 65
OpenOffice Calc 3.x Guide
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Published under the terms of the Creative Commons License Design by Interspire | 752 | 2,803 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2018-13 | latest | en | 0.553079 |
https://www.studysmarter.us/textbooks/physics/college-physics-urone-1st-edition/electromagnetic-induction-ac-circuits-and-electrical-technologies/q103pe-an-rlc-series-circuit-has-a-250omega-resistor-a-100mu/ | 1,679,697,785,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945289.9/warc/CC-MAIN-20230324211121-20230325001121-00479.warc.gz | 1,127,280,779 | 23,062 | Suggested languages for you:
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Found in: Page 864
### College Physics (Urone)
Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000
# An RLC series circuit has a $$2.50\;\Omega$$ resistor, a $$100\;\mu H$$ inductor, and an $$80.0\;\mu F$$ capacitor. (a) Find the power factor at $$f = 120\;Hz$$. (b) What is the phase angle at $$120\;Hz$$? (c) What is the average power at $$120\;Hz$$? (d) Find the average power at the circuit's resonant frequency.
(a.)The power factor at $$f = 120\;Hz$$ is $$0.1498$$.
(b.) The phase angle at $$120\;Hz$$is $$81.4^\circ$$.
(c.) The average power at $$120\;Hz$$is $$0.1498{P_{\max }}$$.
(d.) The average power at the circuit's resonant frequency is $$0.1498{P_{\max }}$$.
See the step by step solution
## Step 1: Concept Introduction
A passive electrical component called an inductor stores energy in the form of a magnetic field. An inductor is a wire loop or coil in its most basic form. The coil's inductance is proportional to the number of turns it has.
A capacitor (also called a condenser) is a two-terminal passive electrical component that stores energy electrostatically in an electric field. Practical capacitors come in a variety of shapes and sizes, but they all have at least two electrical conductors (plates) separated by a dielectric (i.e., insulator).
## Step 2: Given Information
• The resistance value: $$2.50\;\Omega$$
• The inductance value: $$100\;\mu H$$
• The capacitance value: $$80.0\;\mu F$$
• The frequency value: $$f = 120\;Hz$$
## Step 3: Calculate the power factor
(a)
We are aware that the power factor is expressed as:
$$\cos \phi = \frac{R}{Z}$$
This means we'll have to figure out the circuit's reactance, $$Z$$. We already know that the reactance is expressed as,
$$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}}$$
This means we'll need to figure out the capacitor and inductor's active resistances, which are provided as
\begin{aligned} {X_C} &= \frac{1}{{2\pi fC}}\\{X_L} &= 2\pi fL\end{aligned}
The frequency in our case is $$120{\rm{ }}Hz$$ which means we will have,
\begin{aligned} {X_C} &= \frac{1}{{2\pi \times 120{\rm{ }}Hz \times 80.0\;\mu F\left( {\frac{{{{10}^{ - 6}}\;F}}{{1\;\mu F}}} \right)}}\\ &= \frac{1}{{2\pi \times 120{\rm{ }}Hz \times 8.00 \times {{10}^{ - 5}}\;F}}\\ &= 16.57\;\Omega \end{aligned}
\begin{aligned} {X_L} &= 2\pi \times 120\;Hz \times 100\;\mu H\left( {\frac{{{{10}^{ - 6}}\;H}}{{1\;\mu H}}} \right)\\ &= \;0.075\;\Omega \end{aligned}
As a result, the reactance will be
\begin{aligned} Z &= \sqrt {{{\left( {2.50\;\Omega } \right)}^2} + {{\left( {0.075\;\Omega - 16.57\;\Omega } \right)}^2}} \\ &= 16.68\;\Omega \end{aligned}
As a result, the power factor will be
\begin{aligned} \cos \phi &= \frac{R}{Z}\\ &= \frac{{2.5\;\Omega }}{{16.68\;\Omega }}\\ &= 0.1498\end{aligned}
Therefore, the power factor is $$0.1498$$.
## Step 4: Find the phase angle
(b) We know the value of the power factor, let's call it $$k$$, and that it is the cosine of the desired angle.
As a result, we can identify the latter as
\begin{aligned} k &= \cos \phi \\\phi &= \arccos \left( k \right)\end{aligned}
As a result, our angle will be in degrees.
\begin{aligned} \phi &= \arccos \left( {0.1498} \right)\\ &= 81.4^\circ \end{aligned}
Therefore, the phase angle is $$81.4^\circ$$.
## Step 5: Find the average power
c)
For this, we can expect the power to be
$$P = {U_{rms}}{I_{rms}}$$
However, we have no idea what the current or voltage values are. To conclude, one of these would be required. We can only predict that we will succeed.
\begin{aligned} {P_{rms{\rm{ }}}} &= {P_{\max }}\cos \phi \\ &= 0.1498{P_{\max }}\end{aligned}
Therefore, the average power is $$0.1498{P_{\max }}$$.
## Step 6: Find the average power at the circuit's resonant frequency.
d)
For this, we can expect the power to be
$$P = {U_{rms}}{I_{rms}}$$
However, we have no idea what the current or voltage values are. To conclude, one of these would be required. We can only predict that we will succeed.
\begin{aligned} {P_{rms{\rm{ }}}} &= {P_{\max }}\cos \phi \\ &= 0.1498{P_{\max }}\end{aligned}
Therefore, the average power is $$0.1498{P_{\max }}$$. | 1,401 | 4,250 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2023-14 | latest | en | 0.838783 |
https://www.tensorflow.org/api_docs/python/tf/raw_ops/SparseApplyRMSProp?hl=de | 1,632,731,737,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058373.45/warc/CC-MAIN-20210927060117-20210927090117-00250.warc.gz | 990,072,520 | 60,314 | # tf.raw_ops.SparseApplyRMSProp
Update '*var' according to the RMSProp algorithm.
Note that in dense implementation of this algorithm, ms and mom will update even if the grad is zero, but in this sparse implementation, ms and mom will not update in iterations during which the grad is zero.
mean_square = decay * mean_square + (1-decay) * gradient ** 2 Delta = learning_rate * gradient / sqrt(mean_square + epsilon)
$$ms <- rho * ms_{t-1} + (1-rho) * grad * grad$$
$$mom <- momentum * mom_{t-1} + lr * grad / sqrt(ms + epsilon)$$
$$var <- var - mom$$
var A mutable Tensor. Must be one of the following types: float32, float64, int32, uint8, int16, int8, complex64, int64, qint8, quint8, qint32, bfloat16, uint16, complex128, half, uint32, uint64. Should be from a Variable().
ms A mutable Tensor. Must have the same type as var. Should be from a Variable().
mom A mutable Tensor. Must have the same type as var. Should be from a Variable().
lr A Tensor. Must have the same type as var. Scaling factor. Must be a scalar.
rho A Tensor. Must have the same type as var. Decay rate. Must be a scalar.
momentum A Tensor. Must have the same type as var.
epsilon A Tensor. Must have the same type as var. Ridge term. Must be a scalar.
grad A Tensor. Must have the same type as var. The gradient.
indices A Tensor. Must be one of the following types: int32, int64. A vector of indices into the first dimension of var, ms and mom.
use_locking An optional bool. Defaults to False. If True, updating of the var, ms, and mom tensors is protected by a lock; otherwise the behavior is undefined, but may exhibit less contention.
name A name for the operation (optional).
A mutable Tensor. Has the same type as var.
[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"Missing the information I need" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"Too complicated / too many steps" },{ "type": "thumb-down", "id": "outOfDate", "label":"Out of date" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"Other" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }] | 636 | 2,342 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-39 | latest | en | 0.777037 |
http://encyclopedia2.thefreedictionary.com/Curschmann's+s's | 1,484,913,749,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280834.29/warc/CC-MAIN-20170116095120-00002-ip-10-171-10-70.ec2.internal.warc.gz | 87,332,614 | 13,348 | spiral
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Related to Curschmann's s's: asbestos bodies, Creola bodies, Reid index, Dittrich's plugs
spiral
1. Geometry one of several plane curves formed by a point winding about a fixed point at an ever-increasing distance from it. Polar equation of Archimedes spiral: r = aθ; of logarithmic spiral: log r = aθ; of hyperbolic spiral: rθ = a, (where a is a constant)
2. another name for helix
3. a flight manoeuvre in which an aircraft descends describing a helix of comparatively large radius with the angle of attack within the normal flight range
4. Economics a continuous upward or downward movement in economic activity or prices, caused by interaction between prices, wages, demand, and production
Spiral
Refers to forms that are generated by a continuous curve, traced by a point moving around a fixed point in a fixed plane, while steadily increasing the distance from that point.
Spiral
a plane curve going around a certain point an infinite number of times and approaching or receding from the point on each circuit. If this point is chosen as the pole of a polar coordinate system, then the spiral is given by a popular equation p = f (φ) such that f (φ + 2π) > f (φ) or f (φ + 2π) < f (φ) for all*. In particular, a spiral is obtained if f (φ) is a monotone increasing or decreasing positive function.
Figure 1. (a) Spiral of Archimedes, (b) logarithmic spiral, (c) Cornu spiral, (d) parabolic spiral, (e) hyperbolic spiral, (f) lituus, (g) si-ci spiral, (h) cochleold
The equation of the spiral of Archimedes (Figure 1 ,a) has the simplest form: ρ = α<t>. In the third century B.C., this spiral was studied by the ancient Greek mathematician Archimedes, in his treatise On Spirals, in connection with the problems of trisecting an angle and squaring the circle. Archimedes found the area bounded by an arc of the spiral extending from the pole to a certain point and by the line joining the pole and this point. This achievement was one of the first examples of the quadrature of a curvilinear region. The spiral of Archimedes is the pedal curve (seePEDAL CURVE) of the involute of a circle. This fact is made use of in certain drawbridge designs in balancing the variable tension of the chain. A cardioid eccentric cam—that is, an eccentric cam bounded by two arcs of Archimedean spirals—transforms uniform rotational motion into uniform translational motion. The distance between diametrically opposite points on the periphery of the cam is constant. The French mathematician P. de Fermat studied the generalized spiral of Archimedes (ρ/α)n = (Φ/2π)m and found the area bounded by an arc of the spiral extending from the pole to a certain point and by the line joining the pole and this point.
The equation ρ = ae defines the logarithmic, or equiangular, spiral (Figure l,b). The logarithmic spiral intersects all radius vectors drawn from the pole at the same angle α, where cot α = k. This property of the logarithmic spiral is made use of in designing rotary cutters in order to ensure a constant cutting angle. The logarithmic spiral is also encountered in the theory of spiral cases for hydraulic turbines. The theory of gear wheels makes use of the following property: two equal logarithmic spirals rotating about their poles can roll along each other without slipping. Gear trains with variable gear ratios can be obtained in this way.
In the stereographic projection of a sphere onto a plane, a logarithmic spiral is the projection of a loxodrome, which is a curve that cuts all meridians at the same angle. The Italian mathematician E. Torricelli determined the length of an arc of a logarithmic spiral: the arc length is proportional to the difference between the lengths of the radius vectors of the end points of the arc; more precisely, the arc length is (ρ2 ρ1))/cos α. The Swiss scientist J. Bernoulli showed that the evolute and caustic of a logarithmic spiral are logarithmic spirals. When a logarithmic spiral is rotated about the pole, the curve obtained is homothetic to the original curve. Under inversion with respect to a circle, a logarithmic spiral is transformed into a logarithmic spiral.
Another spiral of practical importance is the Cornu spiral, or clothoid, which is used in the graphic solution of certain problems in diffraction (Figure 1 ,c). The parametric equations of this spiral have the form
The Cornu spiral is an ideal transition curve for use in railroad tracks, since the spiral’s radius of curvature increases in proportion to the arc length.
There exist spirals that are involutes of closed curves. An example is the involute of a circle. The names of some spirals stem from the resemblance of the spirals’ polar equations to the equations of curves in Cartesian coordinates. For example, the parabolic spiral (Figure 1 ,d) has the equation (a – ρ)2 = , and the hyperbolic spiral (Figure l,e) has the equation ρ = α/φ. Other spirals include the lituus (Figure 1 ,f), whose equation is ρ2 = α/Φ, and the si-ci spiral (Figure 1 ,g), whose parametric equations have the form
where si(t) and ci(i) are known as the sine integral and cosine integral, respectively. The curvature of this spiral is an exponential function of the arc length. Such spirals are used in french curves.
Reminiscent of a spiral is the cochleoid (Figure l,h), whose equation is φ = (α sin φ)/φ. This curve passes through the pole an infinite number of times, and each succeeding loop lies within the preceding loop.
Spirals are encountered in the study of singularities of differential equations (seeSINGULAR POINT).
Space curves that make an infinite number of circuits about an axis, for example, the helix, are also sometimes referred to as spirals.
What does it mean when you dream about a spiral?
Spiraling, either upward or downward, is often used figuratively to refer to the rapid rise and fall of finances. It may also symbolize flux in weather, health, and employment cycles, to name just a few. It can also simply mean that the dreamer feels things are “spiraling out of control.”
spiral
[′spī·rəl]
(mathematics)
A simple curve in the plane which continuously winds about itself either into some point or out from some point.
spiral
A continuously wound reinforcement in the form of a cylindrical helix.
spiral
A maneuver in which an airplane descends rapidly in a steeply banked turning flight path. The angle of attack remains within the normal range in a spiral. The aircraft speed tends to increase unless other-wise controlled by actions such as throttling back and/or using airbrakes.
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Open / Close | 1,553 | 6,688 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2017-04 | longest | en | 0.891061 |
https://cs.stackexchange.com/questions/75120/how-to-determine-the-fewest-number-of-comparisons-for-heapsort | 1,604,117,246,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107912807.78/warc/CC-MAIN-20201031032847-20201031062847-00534.warc.gz | 254,797,711 | 33,402 | # How to determine the fewest number of comparisons for Heapsort?
I'm currently doing an exercise that asks to prove that Standard-Heapsort requires at fewest $\frac{1}{8} n \log(n) - O(n)$ comparisons, in its best case.
In its average case, Heapsort only requires $2n\log(n) - O(n)$ comparisons, although I don't know how to prove the best case scenario.
Can someone possibly hint me where to start with my calculation, I have no idea how to prove fewest number of comparisons, always been either worst case or most comparisons up until now.
• This paper might be of some interest, showing how to create a construction that results in $\sim \frac{1}{2} n \log n$ moves in the best-case. Where each move requires 2 comparisons, thus taking $\sim n \log n$ comparison. This doesn't follow your $\frac{1}{8} n \log n$, but maybe a similar construction can be found to fit this. – ryan May 8 '17 at 22:43
• Yeah I've scoured through that, I literally reaad about 10 papers on Heapsort analysis and Algorithms, it doesn't seem like there's anywhere that has a proof for this – roughosing May 9 '17 at 6:53
• If you prove that it takes $\ge n \log n$ comparisons, then you've proven it takes $\ge \frac{1}{8} n \log n$ comparisons. Yes, you'll have to deal with the asymptotics, but it sounds like that should be doable. Rather than searching for some other existing solution that pattern-matches the expression you already have, perhaps you could try to understand the techniques in that paper and see if they are useful. – D.W. May 9 '17 at 13:51
• I think the exercise is asking for a proof on the fewest number of comparisons, not to prove an inequality, so for some best-case heap to prove that it can be done in as few as 1/8 n log(n) comparisons. I've read through that whole paper and the re-edit from 1992, plus watched around 20 videos on Heapsort and Heapify Optimization and I'm still stumped – roughosing May 9 '17 at 14:11
• Even easier, how many comparisons are needed when you insert the values in asc order? and how many comparisons are required to repair then? This can only be the best case (min-heap). Heapify costs O(n), when you insert the value in order you dont need a repair (except for one comparison each without traversing parents). So you need to calculate the limit of "delete-min" for a continously shrinking tree when the currently biggest value is at the root and deleteD-min again. At least that is what comes first to mind. – Sam May 9 '17 at 21:11 | 624 | 2,482 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2020-45 | latest | en | 0.955454 |
https://wordwall.net/resource/3603665/acertando-os-produtos-not%C3%A1veis | 1,600,775,150,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400205950.35/warc/CC-MAIN-20200922094539-20200922124539-00621.warc.gz | 711,805,711 | 13,393 | Create better lessons quicker
Correto: (√5 – 2).(√5 + 2) = 1, (x+a)² = x² + 2ax+ a², (x-a)² = x² - 2ax+ a², (x+a)(x-a) = x² - a², (x+2)² = x² + 4x + 4, ( x- 3 )² = x² - 6x + 9, ( x+ 4 )( x- 4 ) = x² - 16, (3x – 4z)² = 9x² – 24xz + 16z², (2 + x)³ = x³ + 6x² + 12x + 8, (2 – x)³ = – x³ + 6x² – 12x + 8, Incorreto: (√5 – 2).(√5 + 2) = 2√5, (x+a)² = 2x+ 2a, (x+a)² = 2x - 2a, (x+a)(x-a) = 2x, (x+2)² = 2x + 4, ( x- 3 )² =2 x- 6, ( x+ 4 )( x- 4 ) = 2x, (3x – 4z)² = 6x – 8z , (2 + x)³ = 6 +3x , (2 – x)³ = 6 – 3x, | 350 | 509 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2020-40 | latest | en | 0.257129 |
https://code.activestate.com/recipes/576746-drain-of-pesticide-solution-calculation/history/1/ | 1,643,244,102,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305006.68/warc/CC-MAIN-20220126222652-20220127012652-00523.warc.gz | 230,309,053 | 5,386 | Welcome, guest | Sign In | My Account | Store | Cart
```# Donyo Ganchev, Agricultural University, Plovdiv, Bulgaria
# donyo@abv.bg
from statlib import anova
choice=None
def an():
num_ob=input('Enter the number of observations: ')
var=[0]*num_ob
control=[0]*num_ob
an=[0]*2
ks=[0]*2
kw=[0]*2
index=0
while index<num_ob:
print index+1
var[index]=input('Enter the values of the variant: ')
index+=1
print \
"""
"""
index1=0
while index1<num_ob:
print index1+1
control[index1]=input('Enter the values of the control: ')
index1+=1
an=anova.F_oneway(var, control)
ks=anova.ks_2samp(var, control)
kw=anova.kruskalwallish(var, control)
print \
"""
"""
print "ANOVA p-value is: ", an[1]
if an[1]<0.05:
print "There is statisticaly significant differences"
else:
print "There is no statisticaly significant differences"
print \
"""
"""
print "Kolmogorov - Smirnoff p-value is: ", ks[1]
if ks[1]<0.05:
print "There is statisticaly significant differences"
else:
print "There is no statisticaly significant differences"
print "Kruskal-Wallish p-value is: ", kw[1]
print \
"""
"""
if kw[1]<0.05:
print "There is statisticaly significant differences"
else:
print "There is statisticaly significant differences"
while choice!="0":
print \
"""
One-way ANOVA, Kolmogorov - Smirnoff and Kruskal-Wallish Test Calculation Program
Used module: Python - Statlib
Created by Donyo Ganchev, Agricultural University, Plovdiv, Bulgaria
1 - Begin calculation
0 - Exit
"""
choice= raw_input("Choice: ")
if choice == "0":
exit()
elif choice=="1":
an ()
choice=None
def dr():
pc=input('Enter percent concentration of working solution: ')
del_norm=input('Enter the delivery norm of the dispenser machine: ')
cor_con=(pc*100)/del_norm
print \
""""
"""
print "Rectification concentration according to delivery norm: ", cor_con
while choice!="0":
print \
"""
Rectification concentration according to delivery norm of the dispenser machine
1 - Begin calculation
0 - Exit
"""
choice= raw_input("Choice: ")
if choice == "0":
exit()
elif choice=="1":
dr()
``` | 563 | 2,103 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2022-05 | latest | en | 0.615808 |
http://www.chegg.com/homework-help/questions-and-answers/show-that-the-principal-curvatures-of-the-surface-y-cosz-a-x-sinz-a-where-a-is-a-non-zero--q3401402 | 1,369,431,807,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368705069221/warc/CC-MAIN-20130516115109-00085-ip-10-60-113-184.ec2.internal.warc.gz | 386,053,610 | 8,008 | ## Differential Geometry - Principal Curvatures
Show that the principal curvatures of the surface y cos(z/a) = x sin(z/a) where a is a non-zero constant, are +/- a/(x^2 + y^2 + a^2). In particular, the mean curvature of the surface is zero. | 67 | 241 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2013-20 | latest | en | 0.746345 |
https://examobjective.in/mcq-industrial-engg-production-management-mcq-6/ | 1,670,098,737,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710936.10/warc/CC-MAIN-20221203175958-20221203205958-00601.warc.gz | 275,605,205 | 31,440 | SECTION-1
#### INDUSTRIAL ENGG. & PRODUCTION MANAGEMENT MCQ
##### Q51. For beta distribution, the variance is given by
$\text { (a) } \frac{t_{P}-t_{O}}{2}$
$\text { (b) } \frac{t_{p}-t_{O}}{c}$
$\text { (c) }\left(\frac{t_{p}-t_{O}}{6}\right)^{2}$
$\text { (d) } \frac{t_{p}+t_{O}}{2} \text { . }$
Ans: $\text { (c) }\left(\frac{t_{p}-t_{O}}{6}\right)^{2}$
##### Q52. The deviation is the difference between
(a) mean time and the time under consideration
(b) the time under consideration and the mean time
(c) the time under consideration and optimistic time
(d) pessimistic time and optimistic time.
Ans: (b) the time under consideration and the mean time
##### Q53. Variance is defined as the
(a) square of the deviation
(b) mean of the squared deviation
(c) square root of the deviation
(d) none of the above.
Ans: (b) mean of the squared deviation
##### Q54. The probability factor is given by the relation
$\text { (a) } Z=\frac{T_{S}+T_{E}}{2}$
$\text { (b) } Z=\frac{T_{S}-T_{E}}{6}$
$\text { (c) } Z=\frac{T_{S}+T_{E}}{4}$
$\text { (d) } Z=\frac{4 T_{S}+T_{E}}{6} \text { . }$
where TS = Scheduled time of completion, and TE = Earliest expected time of completion.
Ans: $\text { (b) } Z=\frac{T_{S}-T_{E}}{6}$
##### Q55. The probability factor is
(a) always positive
(b) always zero
(c) always negative
(d) any one of the above
Ans: (d) any one of the above
##### Q56. If the probability factor is positive, the changes of completing the project in time are
(a) less than 50%
(b) more than 50%
(c) 50%
(d) none of the above.
Ans: (b) more than 50%
##### Q57. The time span by which the starting (or finishing) of an activity can be delayed without delaying the completion of the project, is known as
(a) independent float
(b) free float
(c) total float
(d) interfering float.
Ans: (c) total float
##### Q58. The time by which the activity completion time can be delayed without affecting the start of succeeding activities, is known as
(a) independent float
(b) free float
(c) total float
(d) interfering float.
Ans: (b) free float
##### Q59. The difference between total float and free float is known as
(a) independent float
(b) free float
(c) total float
(d) interfering float.
Ans: (d) interfering float.
##### Q60. Total float is always
(a) positive
(b) negative
(c) zero
(d) any one of the above
Ans: (d) any one of the above
.1 3 4 5 6 7
DEAR READERS IF YOU FIND ANY ERROR/TYPING MISTAKE PLEASE LET ME KNOW IN THE COMMENT SECTIONS OR E-MAIL: [email protected]
##### Read More Sections of Industrial Engg. and Production Management
Each section contains maximum 80 Questions. To practice more questions visit other sections.
Industrial Engg. and Production Management MCQ – Section-1
Industrial Engg. and Production Management MCQ – Section-2
Industrial Engg. and Production Management MCQ – Section-3
Industrial Engg. and Production Management MCQ – Section-4 | 877 | 2,957 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.28125 | 3 | CC-MAIN-2022-49 | latest | en | 0.704156 |
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Post subject: Least squares fitting for non-linear curve in C++Posted: Fri Sep 15, 2017 4:24 pm
Joined: Fri Sep 15, 2017 3:36 pm
Posts: 2
I want to perform a least square fitting on my data set using this code :
Code:
void function(const alglib::real_1d_array &coeff, const alglib::real_1d_array &x, double &func, void *ptr)
{
func = coeff[0] / pow( 1 + coeff[1] * coeff[2] * x[0] , 1 / coeff[3] );
}
void main()
{
int N = 10;
int C = 4;
double epsx = 0.000001;
double diffstep = 0.0001;
alglib::lsfitstate state;
alglib::lsfitreport report;
alglib::ae_int_t maxits = 0;
alglib::ae_int_t info;
alglib::real_2d_array xAxis;
xAxis.setlength(N, 1);
alglib::real_1d_array yAxis;
yAxis.setlength(N);
alglib::real_1d_array cArray;
cArray.setlength(C);
/* Filling arrays .... */
std::cout << " x " << xAxis.tostring(2) << std::endl; //printing xarray
std::cout << " y " << yAxis.tostring(2) << std::endl; // printing yarray
std::cout << " c " << cArray.tostring(10) << std::endl; //printing yarray
alglib::lsfitcreatef(xAxis,yAxis, cArray, diffstep, state);
alglib::lsfitsetcond(state, epsx, maxits);
alglib::lsfitfit(state, function);
lsfitresults(state, info, cArray, report);
std::cout << " Best fit coefficients " << cArray.tostring(12) << std::endl;
std::cout << " Informations " << int(info) << std::endl;
}
Here is what i get in my console :
x [[0.00],[1.00],[2.00],[3.00],[4.00],[5.00],[6.00],[7.00],[8.00],[9.00]]
y [0.00,184.00,184.00,184.00,184.00,184.00,554.00,356.00,340.00,340.00]
c [554.0000000000,1.0000000000,0.0060000000,554.0000000000]
Best fit coefficients []
Informations about algorithm -8
I dont know what is the signification of the error code -8.
I dont get any coeffcients as a result. But i think my mistake comes from the data x, y i am using because when i use the dataset(only x and y array, i still keep my function that i want to fit my data and the coeff array) provided in alglib documentation, i get this results :
x [[-1.00],[-0.80],[-0.60],[-0.40],[-0.20],[0.00],[0.20],[0.40],[0.60],[0.80],[1.00]]
y [0.22,0.38,0.58,0.79,0.94,1.00,0.94,0.79,0.58,0.38,0.22]
c [554.0000000000,1.0000000000,0.0060000000,554.0000000000]
Best fit coefficients [0.621302545335,0.999951946642,0.000084880705,553.999951049188]
Informations 2
I obtain coefficients . So, my first guess is that my mistake comes from the x and y data i am using but i dont know how to explain it or maybe i am missing smth. I would appreciate some help. I apoligize for my poor english and if you need further informations about my code, just let me know.
Julien.
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Post subject: Re: Least squares fitting for non-linear curve in C++Posted: Mon Sep 18, 2017 11:44 am
Joined: Fri May 07, 2010 7:06 am
Posts: 921
Hi!
1. -8 error code means that NAN/INF values were detected in the target function. Say, you tried to divide by zero - and returned INF to optimizer. Or tried to calculate sqrt(-1) - and returned NAN.
Your target function, coeff[0] / pow( 1 + coeff[1] * coeff[2] * x[0] , 1 / coeff[3] ), can fail in such way if 1 + coeff[1] * coeff[2] * x[0] become negative or zero. You have to put constraints on coefficients in order to prevent it. Constrain coeff[1] and coeff[2] to be non-negative, it will work. It can be done with lsfitsetbc() function call.
It may also help to constrain coeff[3] in a similar way.
2. The whole composition of your target function is very unstable. You can easily get very small or very large values by playing with coeff[3]. And there exists a redundancy between coeff[1] and coeff[2] - they enter expression only as product, which makes solution non-unique (you can multiply one of them by 2, divide another one by 2, and get same function value).
So, I recommend you to find good initial values for the algorithm. In such cases you can not rely on convergence from any initial point, you have to provide good one in order to converge to good solution.
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Post subject: Re: Least squares fitting for non-linear curve in C++Posted: Wed Sep 20, 2017 1:27 pm
Joined: Fri Sep 15, 2017 3:36 pm
Posts: 2
Hi Sergey,
I want to thank you for your detailled response. I will try what you just told me and am pretty sure it will works !
Again, thank you very much, you made my day!
Julien
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Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group | 1,597 | 5,230 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2024-30 | latest | en | 0.5626 |
https://www.riddlesandanswers.com/v/234764/a-certain-mathematician-his-wife-and-their-teenage-son-all-play-a-fair-game-of-chess-one-day-when/ | 1,701,941,920,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100651.34/warc/CC-MAIN-20231207090036-20231207120036-00293.warc.gz | 1,059,351,733 | 22,563 | # TWO IN A ROW RIDDLE
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## Two In A Row Riddle
A certain mathematician, his wife, and their teenage son all play a fair game of chess. One day when the son asked his father for 10 dollars for a Saturday night date, his father puffed his pipe for a moment and replied, "Let's do it this way. Today is Wednesday. You will play a game of chess tonight, tomorrow, and a third on Friday. If you win two games in a row, you get the money."
"Whom do I play first, you or mom?"
"You may have your choice," said the mathematician, his eyes twinkling.
The son knew that his father played a stronger game than his mother. To maximize his chance of winning two games in succession, should he play father-mother-father or mother-father-mother?
Hint: Who does he need to beat to win?
Father-mother-father
To beat two games in a row, it is necessary to win the second game. This means that it would be to his advantage to play the second game against the weaker player. Though he plays his father twice, he has a higher chance of winning by playing his mother second.
Did you answer this riddle correctly?
YES NO | 274 | 1,149 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2023-50 | latest | en | 0.988539 |
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FOR MORE CLASSES VISIT www.fin571tutor.com
FIN 571 Week 1 Financial Ratio Analysis (Walmart) FIN 571 Week 1 Financial Ratio Analysis (General Motors) FIN 571 Week 2 Stock Valuation and Analysis (Apple) FIN 571 Week 2 Stock Valuation and Analysis (Amazon) FIN 571 Week 2 Stock Valuation and Analysis (Target) FIN 571 Week 2 Stock Valuation and Analysis (Walmart) FIN 571 Week 2 Stock Valuation and Analysis (Ford) FIN 571 Week 3 Using the Payback Method, IRR, and NPV FIN 571 Week 4 Assignment Rate of Return for Stocks and Bonds (2 Papers) FIN 571 Week 3 Researching Industry Financial Statistics FIN 571 Week 6 Signature Assignment Short Term Funding (2 PPT) FIN 571 Week 5 Assignment Capital Market Efficiency Paper (2 Papers) FIN 571 Week 5 Assignment Effect of Debt Issuance on Stock Valuation FIN 571 Final Exam Guide (New, 2017)
FIN 571 Final Exam Guide (New, 2018)
FOR MORE CLASSES VISIT www.fin571tutor.com
Question 1 The underlying assumption of the dividend growth model is that a stock is worth: A. An amount computed as the next annual dividend divided by the required rate of return. B. An amount computed as the next annual dividend divided by the market rate of return. C. The same amount computed as any other stock that pays the same current dividend and has the same required rate of return. D. The present value of the future income that the stock is expected to generate. E. The same amount to every investor regardless of their desired rate of return. • Question 2 You plan to invest \$6,500 for three years at 4 percent simple interest. What will your investment be worth at the end of the three years? A. \$6,941.11 B. \$7,280.00 C. \$7,311.62 D. \$6,760.00 E. \$7,250.00 • Question 3 A firm has a debt-equity ratio of.64, a pre tax cost of debt of 8.5 percent, and a required return on assets of 12.6 percent, What is the cost of equity if you ignore taxes ? A. 16.38% B. 8.55% C. 15.22% D. 11.22% E. 8.06% • Question 4 What is the present value of \$6,811 to be received in one year if the discount rate is 6.5 percent ? A. \$6,395.31 B. \$7,253.72 C. \$6,023.58 D. \$6,643.29 E. \$6,671.13 • Question 5 Under the____________ method, the underwriter buys the securities for less than the offering price and accepts the risk of not selling the issue, while under the _________ method, the underwriter does not purchase the shares but merely acts as an agent. A. Best efforts; firm commitment B. Seasoned; unseasoned
C. Firm commitment; best efforts D. Negotiated offer; competitive offer E. Competitive offer; negotiated offer Question 6 All else held constant, interest rate risk will increase when the time to maturity: A. Increase or the coupon rate increases. B. Increase or the coupon rate decreases. C. Decrease and the coupon rate equals zero. D. Decrease or the coupon rate increases. E. Decrease or the coupon rate decreases. Question 7
The process of planning and managing a firm’s long-term assets is called:
A. Agency cost analysis. B. Working capital management. C. Financial depreciation. D. Capital structure. E. Capital budgeting. Question 8
An efficient capital market is one in which:
A. Securities always offer a positive NPV. B. Taxes are irrelevant. C. All investments earn the market rate of return. D. Brokerage commissions are zero. E. Security prices reflect all available information. Question 9 Which one of these statements is correct concerning the cash cycle? A. Increasing the accounts payable period increases all cash cycle. B. A positive cash cycle is preferable to a negative cash cycle. C. The cash cycle can exceed the operating cycle if the payables period is equal to zero. D. The longer the cash cycle, the more likely a firm will need external financing. E. A dopting a more liberal accounts receivable policy will tend to decrease the cash cycle. Question 10 The costs of avoiding a bankruptcy filing by a financially distressed firm are classified as _______ costs. A. Direct bankruptcy B. Financial solvency C. Flotation
D. Indirect bankruptcy E. Capital structure Question 11 Which one of the following is an example of a nondiversifiable risk? A. A well-respected president of a firm suddenly resigns B. A well-respected chairman of the Federal Reserve Bank suddenly resigns C. A poorly managed firm suddenly goes out of business due to lack of sales D. A key employee suddenly resigns and accepts employment with a key competitor E. A well-managed firm reduces its work force and automates several jobs Question 12 One disadvantage of the corporate form of business ownership is the: A. Limited liability protection provided for all owners. B. Unlimited life of the firm. C. Difficulties encountered when changing ownership. D. Double taxation of profits. E. Firms ability to raise cash. Question 13 Which one of the following statements about preferred stock is true? A. There is no significant difference in the voting rights granted to preferred and common shareholders. B. If preferred dividends are non-cumulative, then preferred dividends not paid in a particular year will be carried forward to the next year. C. Preferred stock usually has a stated liquidating value of \$100 per share. D. Unlike dividends paid on common stock. Dividends paid on preferred stock are a taxdeductible expenses. E. Dividends on preferred stock payable during the next twelve months are considered to be a corporate liability. Question 14 Book value : A. Is adjusted to market value whenever the market value exceeds the stated book value. B. Is based on historical cost. C. Is equivalent to market value for firms with fixed assets. D. Generally tends to exceed market value when fixed assets are included. E. Is more of a financial than an accounting valuation. Question 15 The primary goal of financial management is to: A. Avoid financial distress. B. Maintain steady growth sales and net earnings. C. Maximize the current value per share of the existing stock. D. Minimize operational costs and maximize firm efficiency. E. Maximize current dividends per share of the existing stock.
Question 16 Which term defines the tax rate that applies to the next dollar of taxable income earned ? A. Deductible B. Total C. Marginal D. Residual E. Average Question 17 Lois is purchasing an annuity that will pay \$5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent ? A. \$56,191.91 B. \$52,970.07 C. 54,282.98 D. \$66,916.21 E. 56,677.98 Question 18 The cash flow resulting from a firm’s ongoing, normal business activities is referred to as the: A. Net capital spending. B. Cash flow to investors. C. Additions to net working capital. D. Operating cash flow. E. Cash flow to retained earnings. Question 19 The market price of a bond increases when the: A. Par value decreases. B. Coupon rate decreases. C. Discount rate decreases. D. Face value decreases. E. Coupon is paid annually rather than semiannually Question 20 The excess return you earn by moving from a relatively risk-free investment to a risky investment is called : A. Arithmetic average return. B. Geometric average return. C. Time premium. D. Risk premium. E. Inflation premium. Question 21 A firn has a total debt ratio of . 47. This means the firn has 47 cents in debt for every: A. \$ 1 in fixed assets.
B. \$ 53 in total equity. C. \$ 1 in total equity. D. \$ 1 in current assets. E. \$ 53 in total assets. Question 22 A ll else equal, the contribution must increase as: A. Both the sales price and variable cost per unit increase. B. The variable cost per unit declines. C. The fixed cost per unit declines. D. Sales price per unit declines. E. The sales price minus the fixed per unit increases. Question 23 A project has an initial cost of \$2,250.The cash inflows are \$0,\$500,\$900,and \$700 for years 1 to 4, respectively. What is the payback period ? A. 3.92 years B. 2.84 years C. Never D. 2.97 years E. 3.98 years Question 24 Ratios that measure a firm’s ability to pay its bills over the short run without undue stress are known as: A. Liquidity measures. B. Asset management ratios. C. Long-term solvency measures. D. Profitability ratios. E. Market value ratios. Question 25 The discount rate that makes the net present value of an investment exactly equal to zero is called the: A. Profitability index. B. External rate of return. C. Averages accounting return. D. Equalizer. E. Internal rate of return. Question 26 An interest rate that is compounded monthly, but is expressed as if the rate were compounded annually, is called the________ rate. A. Compound interest B. Stated interest C. Effective annual D. Periodic interest
E. Daily interest Question 27 Which one of the following statements is false? A. If sales are seasonal, the percentages shown on an aging schedule will vary during the year. B. Aging schedules are used to monitor accounts receivable. C. An aging schedule includes only overdue accounts D. Investments in accounts equal average daily sales times average collection period. E. Collection efforts may involve legal action. Question 28 Which one of these is a correct definition ? A. Long-term debt is defined as a residual claim on a firm’s assets. B. Current assets are assets with short lives, such as inventory, C. Tangible assets are fixed assets such as patents. D. Current liabilities are debts that must be repaid in 18 months or less. E. Net working capital equals current assets plus current liabilities. Question 29 Futures contracts contrast with forward contracts by: A. Allowing the seller to deliver any day during the delivery month. B. Requiring contract fulfilment by the two originating parties. C. Providing an option for the buyer rather than an obligation. D. Marking to the market on a weekly basis. E. Allowing the parties to negotiate the contract size. Question 30 The higher the inventory turnover, the: A. Lesser the amount of inventory held by a firm. B. Higher the inventory as a percentage of total assets. C. Less time inventory items remain on the shelf. D. Greater the inventory of inventory help by a firm. E. Longer it takes firm to sell its inventory.
FIN 571 Week 1 DQ 1
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What is ethics? If you follow all applicable rules and regulations, are you an ethical person?
FIN 571 Week 1 DQ 2
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Assume that interest rates have increased substantially. Would this tend to increase or decrease the market value (meaning the price an investor in the firm's paper is willing to pay) of a firm’s liabilities (relative to the book value of liabilities)?
This question is referring to a firm's liability such as a bond or debenture that has been issued in the markets. What happens to the price an investor who is looking to purchase that bond or debenture is willing to pay if the market interest rate increases above the rate that the bond or debenture pays.
FIN 571 Week 1 Financial Ratio Analysis (Apple)
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Purpose of Assignment The purpose of this assignment is to help students gain a better understanding of the financial statements used for corporate financial reporting and the key ratios used to make business decisions. Assignment Steps Select a Fortune 500 Company from one of the following industries: • Pharmaceutical • Energy • Retail • Automotive • Computer Hardware Review the balance sheet and income statement in the company's 2015 Annual Report. Calculate the following ratios using Microsoft® Excel®: • Current Ratio • Quick Ratio • Debt Equity Ratio • Inventory Turnover Ratio • Receivables Turnover Ratio • Total Assets Turnover Ratio •Profit Margin (Net Margin) Ratio • Return on Assets Ratio Analyze in 1,050 words why each ratio is important for financial decision making. Submit your analysis as well as your calculations. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 1 Financial Ratio Analysis (General Motors)
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Purpose of Assignment The purpose of this assignment is to help students gain a better understanding of the financial statements used for corporate financial reporting and the key ratios used to make business decisions. Assignment Steps Select a Fortune 500 Company from one of the following industries: • Pharmaceutical • Energy • Retail • Automotive • Computer Hardware Review the balance sheet and income statement in the company's 2015 Annual Report. Calculate the following ratios using Microsoft® Excel®: • Current Ratio • Quick Ratio • Debt Equity Ratio • Inventory Turnover Ratio • Receivables Turnover Ratio • Total Assets Turnover Ratio •Profit Margin (Net Margin) Ratio • Return on Assets Ratio Analyze in 1,050 words why each ratio is important for financial decision making. Submit your analysis as well as your calculations. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 1 Financial Ratio Analysis (Pfizer)
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Purpose of Assignment The purpose of this assignment is to help students gain a better understanding of the financial statements used for corporate financial reporting and the key ratios used to make business decisions. Assignment Steps Select a Fortune 500 Company from one of the following industries: • Pharmaceutical • Energy • Retail • Automotive • Computer Hardware Review the balance sheet and income statement in the company's 2015 Annual Report. Calculate the following ratios using Microsoft® Excel®: • Current Ratio • Quick Ratio • Debt Equity Ratio • Inventory Turnover Ratio • Receivables Turnover Ratio • Total Assets Turnover Ratio •Profit Margin (Net Margin) Ratio • Return on Assets Ratio Analyze in 1,050 words why each ratio is important for financial decision making. Submit your analysis as well as your calculations. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 1 Financial Ratio Analysis (Walmart)
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Purpose of Assignment The purpose of this assignment is to help students gain a better understanding of the financial statements used for corporate financial reporting and the key ratios used to make business decisions. Assignment Steps Select a Fortune 500 Company from one of the following industries: Pharmaceutical Energy
Retail Automotive Computer Hardware Review the balance sheet and income statement in the company's 2015 Annual Report. Calculate the following ratios using MicrosoftÂŽ ExcelÂŽ: Current Ratio Quick Ratio Debt Equity Ratio Inventory Turnover Ratio Receivables Turnover Ratio Total Assets Turnover Ratio Profit Margin (Net Margin) Ratio Return on Assets Ratio Analyze in 1,050 words why each ratio is important for financial decision making. Submit your analysis as well as your calculations. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 1 Individual Assignment Business Structures
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Watch the "Your Business Structure" and "Corporate Business Structures" videos on the Electronics Reserve Readings page. Identify the different business structures. Write a 350 to 700 word explanation of how each business structure might and might not be advantageous. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 DQ 1
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In order to receive proper credit, please reply to this message when posting your answers to WK2 DQ1.
Suppose you own \$1 million worth of 30-year Treasury bonds. Is this asset riskless? You own \$1 million worth of 90-day Treasury bills. You “roll over” this investment every 90 days by reinvesting the proceeds in another issue of 90-day Treasury bills. Is this investment riskless? Can you think of an asset that is truly riskless?
FIN 571 Week 2 DQ 2
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Suppose rf is 5% and rM is 10%. According to the SML and the CAPM, an asset with a beta of −2.0 has a required return of negative 5% [= 5 − 2(10 − 5)]. Can this be possible? Does this mean that the asset has negative risk? Why would anyone ever invest in an asset that has an expected and required return that is negative? Explain
FIN 571 Week 2 Individual Assignment Business Structure Advice
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Write a 350 to 700 word response to the following e-mail: Dear Consultant, I am currently starting a business and developing my business plan. I'm in need of some advice on how to start forming my business. I am not sure exactly how it will be financed and whether or not I want to take on partners. I am interested and willing to learn the intricacies of my options to determine how to best proceed with my plan. Please advise on what my options are, the advantages and disadvantages of each, and possible tax consequences for each scenario? Respectfully, John Owner
Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 Individual Assignment Ethics and Finance
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The Sarbanes-Oxley Act of 2002 (SOX) was passed as the result of the Enron scandal and other instances of accounting fraud. This act was passed to strengthen the role of the Securities and Exchange Commission (SEC). Research a case of corporate financial abuse related to the Sarbanes-Oxley Act of 2002 and apply this to your current work or desired place of employment. Create a 1,400-word analysis of the application of SOX in which you include the following: Discuss the mistakes made by the company and their leadership. Discuss the steps leadership could have taken to prevent or mitigate the repercussions. Explain the role of market pressures on unethical behavior. Examine the influence of the basics of finance and how the Sarbanes-Oxley Act of 2002 changed things. Evaluate the influence of Sarbanes-Oxley Act on ethical behavior. Are businesses more ethical since the enactment? Explain the changes companies needed to make in how they use and present financial statements. Discuss how SOX has affected your current place of employment if at all, and if not, how it has affected others in the same industry. Cite a minimum of 2 scholarly sources. Format your paper consistent with APA guidelines. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 Individual Assignment Ratio Analysis Problems
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Ratio Analysis Problems Ratio Analysis (Individual Assignment) You may use excel or word.doc format for this assignment. Please post your homework as a word.doc or excel file in the class discussion section below by the due date. 1. Analysis of cost of goods sold problem. 1992 1993 1994 Gross Profit Margin 60% 55% 51% What is happening to cost of goods sold? As was done in the week 2 online lecture on ratio analysis, please assume sales of 1 dollar each year as you do your analysis. This problem follows the process shown in the Week 2 Ratio Analysis online lecture section titled: "Another Income Statement Analytical Approach: Percent of Sales" (5 points) 2. Overhead (or Sales, General and Administrative Expense) problem. 1992 1993 1994 Gross Profit Margin 40% 39% 41% Operating Margin (NOI/Sales) 15% 10% 5% What is happening to S,G and A (or overhead expenses)? Please set up an illustration assuming sales of 1.00 dollar each year just as you did in problem number one. (5 points) 3. Balance Sheet Problem 1992 1993 1994 Annual Sales Growth (over prior yr) + 1% 0% +1% Current Ratio 3.5X 2X 1.2X Average Collection Period 25 days 30 days 55 days What is happening to liquidity? Why? What are some follow-up questions your would ask? (5 points) 4. Using the data provided below, which is the better managed company? Why? Please support your answers by calculating appropriate ratios. (5 points) Company A Company B Sales 10 million dollars 20 million dollars Net Income 1 million dollars 2 million dollars Total Assets 10 million dollars 15 million dollars Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 Stock Valuation and Analysis (Amazon)
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Purpose of Assignment The purpose of this assignment is to allow students the opportunity to research a Fortune 500 company stock using the popular online research tool Yahoo Finance. The tool allows the student to review analyst reports and other key financial information necessary to evaluate the stock value and make an educated decision on whether to invest. Assignment Steps Resources: Yahoo Finance Select a Fortune 500 Company from one of the following industries: • Pharmaceutical • Energy • Retail • Automotive • Computer Hardware • Manufacturing • Mining Access Yahoo Finance and enter the company name. Review the financial information and statistics provided for the stock you selected and answer the following: • What is the ticker symbol of the company you chose? • What is the Current Stock Price? • What is the Market Cap for the stock you chose? • What is the Price to Earnings Ratio? • What is the Dividend and Yield? • What is the Enterprise Value? • What is the Beta? • Was there a Stock Split, and if so, when? • What was the closing stock price for the last 5 days? • What was the 52 Week High for this stock? • What is the Book Value per Share? • What type of rating are analysts recommending (i.e. buy, hold, etc.)? • What is the target price analysts are predicting for this stock? • What is the analyst's average revenue estimate for next year? •What are some of the significant news items and press releases made by the company over the last year? Explain in 700 words why you would or would not recommend investing in this stock. • Describe the relationship between the value of the stock and the price to earnings ratio. •What information does the Market Capitalization (Market Cap) and Beta provide to the investor? Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 Stock Valuation and Analysis (Apple)
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Purpose of Assignment
The purpose of this assignment is to allow students the opportunity to research a Fortune 500 company stock using the popular online research tool Yahoo Finance. The tool allows the student to review analyst reports and other key financial information necessary to evaluate the stock value and make an educated decision on whether to invest. Assignment Steps Resources: Yahoo Finance Select a Fortune 500 Company from one of the following industries: Pharmaceutical Energy Retail Automotive Computer Hardware Manufacturing Mining Access Yahoo Finance and enter the company name. Review the financial information and statistics provided for the stock you selected and answer the following: What is the ticker symbol of the company you chose? What is the Current Stock Price? What is the Market Cap for the stock you chose? What is the Price to Earnings Ratio? What is the Dividend and Yield? What is the Enterprise Value? What is the Beta?
Was there a Stock Split, and if so, when? What was the closing stock price for the last 5 days? What was the 52 Week High for this stock? What is the Book Value per Share? What type of rating are analysts recommending (i.e. buy, hold, etc.)? What is the target price analysts are predicting for this stock? What is the analyst's average revenue estimate for next year? What are some of the significant news items and press releases made by the company over the last year? Explain in 700 words why you would or would not recommend investing in this stock. Describe the relationship between the value of the stock and the price to earnings ratio. What information does the Market Capitalization (Market Cap) and Beta provide to the investor? Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 Stock Valuation and Analysis (Ford)
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Purpose of Assignment The purpose of this assignment is to allow students the opportunity to research a Fortune 500 company stock using the popular online research tool Yahoo Finance. The tool allows the student to review analyst reports and other key financial information necessary to evaluate the stock value and make an educated
decision on whether to invest. Assignment Steps Resources: Yahoo Finance Select a Fortune 500 Company from one of the following industries: • Pharmaceutical • Energy • Retail • Automotive • Computer Hardware • Manufacturing • Mining Access Yahoo Finance and enter the company name. Review the financial information and statistics provided for the stock you selected and answer the following: • What is the ticker symbol of the company you chose? • What is the Current Stock Price? • What is the Market Cap for the stock you chose? • What is the Price to Earnings Ratio? • What is the Dividend and Yield? • What is the Enterprise Value? • What is the Beta? • Was there a Stock Split, and if so, when? • What was the closing stock price for the last 5 days? • What was the 52 Week High for this stock? • What is the Book Value per Share? • What type of rating are analysts recommending (i.e. buy, hold, etc.)? • What is the target price analysts are predicting for this stock? • What is the analyst's average revenue estimate for next year? •What are some of the significant news items and press releases made by the company over the last year? Explain in 700 words why you would or would not recommend investing in this stock. • Describe the relationship between the value of the stock and the price to earnings ratio. •What information does the Market Capitalization (Market Cap) and Beta provide to the investor? Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 Stock Valuation and Analysis (Target)
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Purpose of Assignment The purpose of this assignment is to allow students the opportunity to research a Fortune 500 company stock using the popular online research tool Yahoo Finance. The tool allows the student to review analyst reports and other key financial information necessary to evaluate the stock value and make an educated decision on whether to invest. Assignment Steps Resources: Yahoo Finance Select a Fortune 500 Company from one of the following industries: • Pharmaceutical • Energy • Retail • Automotive • Computer Hardware • Manufacturing • Mining Access Yahoo Finance and enter the company name. Review the financial information and statistics provided for the stock you selected and answer the following: • What is the ticker symbol of the company you chose? • What is the Current Stock Price? • What is the Market Cap for the stock you chose? •
What is the Price to Earnings Ratio? • What is the Dividend and Yield? • What is the Enterprise Value? • What is the Beta? • Was there a Stock Split, and if so, when? • What was the closing stock price for the last 5 days? • What was the 52 Week High for this stock? • What is the Book Value per Share? • What type of rating are analysts recommending (i.e. buy, hold, etc.)? • What is the target price analysts are predicting for this stock? • What is the analyst's average revenue estimate for next year? •What are some of the significant news items and press releases made by the company over the last year? Explain in 700 words why you would or would not recommend investing in this stock. • Describe the relationship between the value of the stock and the price to earnings ratio. •What information does the Market Capitalization (Market Cap) and Beta provide to the investor? Click the Assignment Files tab to submit your assignment.
FIN 571 Week 2 Stock Valuation and Analysis (Walmart)
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Purpose of Assignment The purpose of this assignment is to allow students the opportunity to research a Fortune 500 company stock using the popular online research tool Yahoo Finance. The tool allows the student to review analyst reports and other key financial information necessary to evaluate the stock value and make an educated decision on whether to invest. Assignment Steps Resources: Yahoo Finance Select a Fortune 500 Company from one of the following industries: • Pharmaceutical • Energy • Retail • Automotive • Computer Hardware • Manufacturing • Mining Access Yahoo Finance and enter the company name. Review the financial information and statistics provided for the stock you selected and answer the following: • What is the ticker symbol of the company you chose? • What is the Current Stock Price? • What is the Market Cap for the stock you chose? • What is the Price to Earnings Ratio? • What is the Dividend and Yield? • What is the Enterprise Value? • What is the Beta? • Was there a Stock Split, and if so, when? • What was the closing stock price for the last 5 days? • What was the 52 Week High for this stock? • What is the Book Value per Share? • What type of rating are analysts recommending (i.e. buy, hold, etc.)? • What is the target price analysts are predicting for this stock? • What is the analyst's average revenue estimate for next year? •What are some of the significant news items and press releases made by the
company over the last year? Explain in 700 words why you would or would not recommend investing in this stock. • Describe the relationship between the value of the stock and the price to earnings ratio. •What information does the Market Capitalization (Market Cap) and Beta provide to the investor? Click the Assignment Files tab to submit your assignment.
FIN 571 Week 3 DQ 1
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Why are interest rates on short-term loans not necessarily comparable to each other? Give three possible reasons.
FIN 571 Week 3 DQ 2
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Optical Supply Company offers credit terms of 2/10, net 60. If Optical Supply is considering a change in its credit terms to one of those indicated, explain whether the change should increase or decrease sales. (a) 2/10, net 30, (b) net 60, (c) 3/15, net 60, (d) 2/10, net 30, 30 extra
FIN 571 Week 3 Individual Assignment Interpreting Financial Results
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Resource: Financial Statements for the company assigned by your instructor in Week 2. Review the assigned company's financial statements from the past three years. Calculate the financial ratios for the assigned company's financial statements, and then interpret those results against company historical data as well as industry benchmarks: Compare the financial ratios with each of the preceding three (3) years (e.g. 2014 with 2013; 2013 with 2012; and 2012 with 2011). Compare the calculated financial ratios against the industry benchmarks for the industry of your assigned company.
Write a 500 to 750 word summary of your analysis. Show financial calculations where appropriate. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 3 Researching Industry Financial Statistics
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Purpose of Assignment The purpose of this assignment is to allow the students an opportunity to complete their financial evaluation of a company using the financial research database Plunkett Research Online. Plunkett Research Online provides in-depth analysis of a company's financials, comparisons to industry averages, a list of top executives, how the company compares to other competitors in terms of revenue, number of employees, market capitalization and other key financial metrics. Assignment Steps Resources: Plunket Research Online located in the Week 3 Electronic Reserve Readings; MicrosoftÂŽ ExcelÂŽ Access the the Plunkett Research database in the University Library by following these steps: Click on the University Library link. Click "Company Directories and Financials" under Library Resources. Click "Plunkett Research Online" under Company Directory and Financials. Review the following "HOW TO USE" videos: Plunkett Research Online Overview How to Export Company and Exec. Lists How to Build-a-Report How to Use Industry Analytics How to Research an Industry How to Use Company Profiles Click "Research A Company."
Select a company (i.e. Walmart) and input into the Search Box. Scroll through the search results to choose the correct company. Click the link to the company profile (in blue). Review the Company Profile and answer the following questions in Microsoft® Word: What is the Ticker Symbol for the company you have selected? When was the company established? How many employees does it have? What is the NAICS Code? Who is the CEO? Where does the company rank in terms of Total Revenue when compared to its competitors? Where does the company rank in terms of Net Income when compared to its competitors? Where does the company rank in terms of Return on Assets when compared to its competitors? What is the Revenue in 2014 and 2015? What was the Gross Margin in 2014 and 2015? What was the Earnings per Share in 2014 and 2015? Save the Company Profile as a PDF document. Compare the 2015 Company Financials to the Industry Averages and export the results into a Microsoft® Excel® document. Add a new column in your Microsoft® Excel® document titled "Change" and calculate the difference between the company's 2015 financial results and the industry averages. Explain in 1,050 words how the company you selected compares to the industry averages in terms of financial profitability, liquidity and solvency, and why the difference is important. Also review the financial statements over the last three years, and discuss any positive and negative trends would you report to the company's management.
Submit the calculations as well as the explanation. Click the Assignment Files tab to submit your assignment. Note: Grades are awarded based upon individual contributions to the Learning Team assignment. Each Learning Team member receives a grade based upon his/her contributions to the team assignment. Not all students may receive the same grade for the team assignment.
FIN 571 Week 3 Team Assignment Financial Statement Interpretation
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Select three publicly traded companies. Choose one each from the following sectors: manufacturing, service, and retail. At least one of the three companies should be foreign. If possible, choose from among the team members' places of business or similar industries. Calculate the following: Current ratio Quick ratio Net profit margin Asset utilization Financial leverage Analyze the Return on Equity (ROE) for the last 2 years using the DuPont method. Develop a 2,100-word comparison of your three companies in which you include the following: Discuss the differences in the industries Discuss the different measurement conventions and how this affects presentations. Contrast IASB basis for accounting (IFRS) and FASB/GAAP accounting. Compare the three companies and their strategies for managing their working capital. Discuss the financial ratios and analyses and what they indicate about the companies and their financial forecast.
Incorporate the calculated ratios and analysis into the paper. Include the financial statements for the 3 companies as an appendix to the paper. Cite at least 3 scholarly sources. Format the paper consistent with APA guidelines. Click the Assignment Files tab to submit your assignment.
FIN 571 Week 3 Using the Payback Method, IRR, and NPV
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The purpose of this assignment is to allow the student to calculate the project cash flow using net present value (NPV), internal rate of return (IRR), and the payback methods. Assignment Steps Resources: Corporate Finance Create a 350-word memo to management including the following: • Describe the use of internal rate of return (IRR), net present value (NPV), and the payback method in evaluating project cash flows. • Describe the advantages and disadvantages of each method. Calculate the following time value of money problems: 1. If you want to accumulate \$500,000 in 20 years, how much do you need to deposit today that pays an interest rate of 15%? 2. What is the future value if you plan to invest \$200,000 for 5 years and the interest rate is 5%?
3. What is the interest rate for an initial investment of \$100,000 to grow to \$300,000 in 10 years? 4. If your company purchases an annuity that will pay \$50,000/year for 10 years at a 11% discount rate, what is the value of the annuity on the purchase date if the first annuity payment is made on the date of purchase? 5. What is the rate of return required to accumulate \$400,000 if you invest \$10,000 per year for 20 years. Assume all payments are made at the end of the period. Calculate the project cash flow generated for Project A and Project B using the NPV method. • Which project would you select, and why? • Which project would you select under the payback method? The discount rate is 10% for both projects. • Use Microsoft®Excel®to prepare your answer. • Note that a similar problem is in the textbook in Section 5.1. Sample Template for Project A and Project B:
Show all work. Submit the memo and all calcluations
FIN 571 Week 4 Assignment Rate of Return for Stocks and Bonds (2 Papers)
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The purpose of this assignment is to allow the student an opportunity to calculate the rate of return of equity and debt instruments. It allows the student to understand the effects of dividends; capital gains; inflation rates; and how the nominal rate of return affects valuation and pricing. The assignment also allows the student to apply concepts related to CAPM, WACC, and Flotation Costs to understand the influence of debt and equity on the company's capital structure. Assignment Steps Resources: Corporate Finance Calculate the following problems and provide an overall summary of how companies make financial decisions in no more than 700 words, based on your answers:
1. 1) Stock Valuation: A stock has an initial price of \$100 per share, paid a dividend of \$2.00 per share during the year, and had an ending share price of \$125. Compute the percentage total return, capital gains yield, and dividend yield. 2. 3. 2) Total Return: You bought a share of 4% preferred stock for \$100 last year. The market price for your stock is now \$120. What was your total return for last year? 4. 5. 3) CAPM: A stock has a beta of 1.20, the expected market rate of return is 12%, and a risk-free rate of 5 percent. What is the expected rate of return of the stock? 6. 7. 4) WACC: The Corporation has a targeted capital structure of 80% common stock and 20% debt. The cost of equity is 12% and the cost of debt is 7%. The tax rate is 30%. What is the company's weighted average cost of capital (WACC)? 8. 9. 5) Flotation Costs: Medina Corp. has a debt-equity ratio of .75. The company is considering a new plant that will cost \$125 million to build. When the company issues new equity, it incurs a flotation cost of 10%. The flotation cost on new debt is 4%. What is the initial cost of the plant if the company raises all equity externally? 10.
Secondly: he purpose of this assignment is to allow the student an opportunity to explain what it means to have an efficient capital market. Students will gain an understanding of the different levels of market efficiency and how behavioral finance can inhibit reaching market transparency. Assignment Steps Resources: Microsoft® Word Explain in 525 words what it means to have efficient capital market, including: • Describe the behavioral challenges in achieving efficiency. • Discuss the three forms of market efficiency. • What are the implications to corporate finance? • Would you consider the real estate market an efficient capital market? Please explain why or why not.
FIN 571 Week 4 DQ 1
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A firm uses a single discount rate to compute the NPV of all its potential capital budgeting projects, even though the projects have a wide range of nondiversifiable risk. The firm then undertakes all those projects that appear to have positive NPVs. Briefly explain why such a firm would tend to become riskier over time.
FIN 571 Week 4 DQ 2
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Phyllis believes that the firm should use straight-line depreciation for a capital project because it results in higher net income during the early years of the project’s life. Joanna believes that the firm should use the modified accelerated cost recovery system depreciation because it reduces the tax liability during the early years of the project’s life. Assuming you have a choice between depreciation methods, whose advice should you follow? Why?
FIN 571 Week 4 Individual Assignment Analyzing Pro Forma Statements
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Decide upon an initiative you want to implement that would increase sales over the next five years, (for example, market another product, corporate expansion, and so on). Using the sample financial statements, create pro forma statements of five year projections that are clear, concise, and easy to read. Be sure to double check the calculations in your pro forma statements. Make assumptions that support each line item increase or decrease for your forecasted statements.
Discuss and interpret the financials in relation to the initiative. Make recommendations on potential discretionary financing needs. Write a 350 - 700 word analysis of the company's short term and long term financing needs and determine strategies for the company to manage working capital.
Click the Assignment Files tab to submit your assignment.
FIN 571 Week 4 Team Assignment Operating Leverage and Forecasting
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Operating Leverage and Forecasting Problems Team Assignment Please complete the following problems. When calculating earnings per share and PE ratios, please show your work. This problem is similar to the examples shown in the lecture. You manufacture hunting pack systems in China for 80 dollars each, including shipping. The manufacturing costs only include variable costs. Variable costs are not calculated as a percentage of sales in this case. Sales are a function of the number of packs sold and the price per pack. Likewise, variable costs are a function of the number of packs sold and the cost to produce each pack. You sell these packs to retailers for 200 dollars each. In the current year you will sell 100,000 packs. Your fixed costs including such items as insurance, marketing, travel, shows, office supplies, warehouse rentals etc. totals 5 million dollars this year and are not part of the 80 dollars per pack manufacturing cost. The federal income tax rate for your company is 40 percent. Your company is publicly traded on the NASDAQ with 1,000,000 shares outstanding. Please create a current income statement using the same format as found in the lecture. (5 points) Please calculate earnings per share. (2 points)
Please calculate the price/earnings multiple assuming that the current stock price is 10 dollars per share. (2 points) Create a two-year forecast of the income statement from the information provided in problem number one. Please create three columns of data: current year, year 2, and year 3. Assume that sales increase ten percent per year for year's two and three. Please show the earnings per share for each of the three years. (10 points) 3. Please estimate the stock price for year's two and three, assuming that the current PE multiple remains constant for each of the two forecasted years. (6 points).
FIN 571 Week 5 Assignment Capital Market Efficiency Paper (2 Papers)
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Purpose of Assignment The purpose of this assignment is to allow the student an opportunity to explain what it means to have an efficient capital market. Students will gain an understanding of the different levels of market efficiency and how behavioral finance can inhibit reaching market transparency. Assignment Steps Resources: MicrosoftÂŽ Word Explain in 525 words what it means to have efficient capital market, including: Describe the behavioral challenges in achieving efficiency. Discuss the three forms of market efficiency. What are the implications to corporate finance? Would you consider the real estate market an efficient capital market? Please explain why or why not.
FIN 571 Week 5 Assignment Effect of Debt Issuance on Stock Valuation
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Purpose of Assignment The purpose of this assignment is to demonstrate to students how the issuance of debt to purchase outstanding common stock could affect the value of the company's equity and redefine the capital structure. The problem will also allow students to explore the effect of corporate taxes through debt financing. Assignment Steps Resources:Corporate Finance Scenario: Hightower, Inc. plans to announce it will issue \$2.0 million of perpetual debt and use the proceeds to repurchase common stock. The bonds will sell at par with a coupon rate of 5%. Hightower, Inc. is currently an all-equity company worth \$7.5 million with 400,000 shares of common stock outstanding. After the sale of the bonds, the company will maintain the new capital structure indefinitely. The company currently generates annual pretax earnings of \$1.5 million. This level of earnings is expected to remain constant in perpetuity. The tax rate is 35%. Prepare a 1,050-word memo advising the management of Hightower, Inc. on the financial impact, including the following: • What is the expected return on the company's equity before the announcement of the debt issue? • Construct the company's market value balance sheet before the announcement of the debt issue. What is the price per share of the firm's equity? • Construct the company's market value balance sheet immediately after the announcement of the debt issue.
• What is the company's stock price per share immediately after the repurchase announcement? • How many shares will the company repurchase as a result of the debt issue? How many shares of common stock will remain after the repurchase? • What is the required return on the company's equity after the restructuring? • Discuss the advantages and disadvantages of debt financing over equity financing.
FIN 571 Week 5 DQ 1
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Because the weighted average is always a correct measure of a required return, why do firms not create securities to finance each project and offer them in the capital market in order to accurately determine the required return for the project?
FIN 571 Week 5 DQ 2
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The development of the new issue junk bond market had important implications for capital structure choice. The existence of a viable junk bond market means that firms can
comfortably maintain higher degrees of leverage than they could prior to the development of this market. Do you agree or disagree? Justify your answer.
FIN 571 Week 5 Individual Assignment DCF and WACC Problems
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Discounted Cash Flows and WACC Homework Problems Please post the answers (and show your work) in the assignments section by midnight the last day of the week assigned.
Calculate the future value of 1,535 invested today for 8 years at 6 percent. (5 points) What is the total present value of the following cash stream, discounted at 8 percent? (5 points) Year 1 2 3 4 5
Amount 400 750 945 145 78
3. If you invested \$2,000 per year into an IRA for 30 years and received 6 percent return each year, what would the account balance be in 30 years? (5 points) 4. A friend gives you a proposition. If you give him 1,500 dollars today, he will guarantee your receive 12 percent a year for the next 5 years. How much money will you receive from him at the end of 5 years? (5 points)
5. You want to buy a new Computer Aided Design (CAD) system for your business. The cost of the system is \$150,000 and you expect to save over \$40,000 per year in reduced labor costs. Please calculate the net present value of the CAD if your required return is 10 percent and the life of the system is expected to be 5 years. (10 points) 6. Your company is considering converting its heating system in the main office from coal to heating oil. The initial cost of removing the coal fired furnace and installing an new oil fired unit is \$60,000. The life of the analysis is 7 years. In the past you spent \$25,000 per year on coal. The new company says you will spend no more than \$15,000 per year on heating oil. If your required return is 12 percent, should you make this investment? Please calculate the net present value of this project. (10 points) 7. You have collected the following information: a. b. c. d. e. f.
the yield on your company’s preferred stock 8% the yield on your company’s debt 10% the required return on your company’s common stock and internal equity 12% debt total \$5,000,000 preferred stock current market value \$10,000,000 common stock and retained earnings total value \$20,000,000
Please calculate the pre-tax weighted average cost of capital (WACC) for your company. (10 points) 8. Your company’s marginal income tax rate is 40%. Please calculate the post tax WACC from the information provided in problem 7. (10 points)
FIN 571 Week 5 Team Assignment Capital Budgeting Assignment, Part 1 (New Heritage Doll)
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Acting as the executive team for a small company, your team will apply the principles of capital budgeting to invest in growth and cash flow improvement opportunities in three phases over 10 simulated years. Each opportunity has a unique financial profile and you must analyze the effects on working capital. Examples of opportunities include taking on new customers, capitalizing on supplier discounts, and reducing inventory. The team must understand how the income statement, balance sheet, and statement of cash flows are interconnected and be able to analyze forecasted financial information to consider possible effects of each opportunity on the firm's financial position. The company operates on thin margins with a constrained cash position and limited available credit. You must optimize use of internal and external credit as you balance the desire for growth with the need for maintaining liquidity. Create a 1,050-word analysis of the team members' decisions during each phase (1-3) and how they influenced each member's final results. Analyze the influence of member's decisions on sales outcomes or metrics of SNC. Analyze the influence of member's decisions on EBIT outcomes or metrics of SNC. Assess the influence of member's decisions on Net Income outcomes or metrics of SNC. Analyze the influence of member's decisions on Free Cash Flow outcomes or metrics of SNC. Assess the influence of member's decisions on Total Firm Value outcomes or metrics of SNC. Cite a minimum of two scholarly references. Format your assignment consistent with APA guidelines.
FIN 571 Week 5 Working Capital Simulation Managing Growth, Part 1 (SNC)
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Acting as the executive team for a small company, your team will apply the principles of capital budgeting to invest in growth and cash flow improvement opportunities in three phases over 10 simulated years. Each opportunity has a unique financial profile and you must analyze the effects on working capital. Examples of opportunities include taking on new customers, capitalizing on supplier discounts, and reducing inventory. The team must understand how the income statement, balance sheet, and statement of cash flows are interconnected and be able to analyze forecasted financial information to consider possible effects of each opportunity on the firm's financial position. The company operates on thin margins with a constrained cash position and limited available
credit. You must optimize use of internal and external credit as you balance the desire for growth with the need for maintaining liquidity. Sign-in to the Harvard Business Simulation and review each of the following: Welcome Statement How to Play Terminology Primer More Details (this includes information to help you understand how to play the simulation) Complete the Harvard Business Simulation individually and track and save your results. Create a 1,050-word analysis of the team members' decisions during each phase (1-3) and how they influenced each member's final results. Analyze the influence of member's decisions on sales outcomes or metrics of SNC. Analyze the influence of member's decisions on EBIT outcomes or metrics of SNC. Assess the influence of member's decisions on Net Income outcomes or metrics of SNC. Analyze the influence of member's decisions on Free Cash Flow outcomes or metrics of SNC. Assess the influence of member's decisions on Total Firm Value outcomes or metrics of SNC. Cite a minimum of two scholarly references. Format your assignment consistent with APA guidelines.
FIN 571 TUTOR Principal Education / fin571tutor.com
FIN 571 TUTOR Principal Education / fin571tutor.com
Advertisement | 11,560 | 53,467 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2018-43 | latest | en | 0.849106 |
https://www.gauthmath.com/solution/i1117475060 | 1,670,500,297,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711336.41/warc/CC-MAIN-20221208114402-20221208144402-00013.warc.gz | 814,419,180 | 64,947 | Gauthmath
# Given that fx=dfrac x1-x1-2x2 , show that fx can be expressed as dfrac 11-x-dfrac 21-2x+dfrac 11-2x2.Hence, or otherwise, find the first three terms in the expansion of fx in ascending powers of x. State the range of values of x for which the expansion is valid.1-2x-1 may be written down directly if x is replaced by 2x in the expansion of 1-x-1.
Question
### Gauthmathier5060
YES! We solved the question!
Check the full answer on App Gauthmath
Given that , show that can be expressed as .
Hence, or otherwise, find the first three terms in the expansion of in ascending powers of . State the range of values of for which the expansion is valid.
may be written down directly if is replaced by in the expansion of .
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Gauth Tutor Solution
4.7
### Lydia
Mechanical engineer
Tutor for 4 years
Let .
Hence .
So .
By the binomial expansion,
.
This is valid when AND .
that is, when .
Explanation
valid for , that is .
Hence .
This is valid when AND .
that is, when .
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Clear explanation (75) | 296 | 1,096 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2022-49 | latest | en | 0.86563 |
https://www.enotes.com/homework-help/my-math-homework-says-sally-traveled-12-miles-10-477217 | 1,519,049,943,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812665.41/warc/CC-MAIN-20180219131951-20180219151951-00659.warc.gz | 863,535,321 | 11,020 | # so my math homework says, "sally traveled 12 miles in 10 minutes, what is her average speed (unit rate)?" i need help :))
electreto05 | Certified Educator
The velocity is a quantity that characterizes the kinematic state of a body. In general, the speed is defined as the ratio between space and time. Although the speed of a body may be different at different times of a movement, you can define an average speed as the total distance traveled divided by the time elapsed.
v = Δd/Δt
Δd → Distance traveled in the interval Δt
In this case:
Δd = 12 miles, and Δt = 10 minutes
v = 12 miles/10 minutes = 1.2 miles/minutes
In this case the unit of measurement is miles/minutes. To express this unity in the international system(S.I), the miles should be expressed in meters and the minutes, in seconds:
1 mile = 1609.3 meters
1 minute = 60 seconds.
then:
12 miles = 19311.6 meters
10 minutes = 600 seconds
v = (19311.6/600) = 32.19 meters/second
So the average speed of sally, is 1.2 miles/minutes or 32.19 meters/second
rsarvar1a | Student
I'm surprised that nobody responded with the most typical unit rate for speed: miles per hour.
Let's come back to the question. Sally travelled 12 miles in 10 minutes. To make things easier, let's first make this a unit rate for minutes. If Sally travels 12 miles in 10 minutes, we can find how long she travels in 1 minute:
12 (miles) / 10 (minutes) = 1.2 (miles per minute)
Therefore, Sally travels 1.2 miles per minute.
Now, let's take this unit rate and convert to a new unit rate: miles per hour.
As we know, there are 60 minutes in an hour. If Sally travels 1.2 miles in 1 minute, she travels 1.2 miles times 60 minutes in 60 minutes.
So:
1.2 (miles per minute) * 60 (minutes in an hour) = 72 (miles per hour)
Therefore, Sally is travelling at 72 miles per hour.
brokenarsenal | Student
To calculate the average speed you use:
Distance
---------
Time
In the equation Sally travels 12 miles ----> 12 Miles
----------
In the equation Sally travels for 10 min ---> 10 Min
12 divided by 10 = 1.2 miles per minute
Hope this helps! :)
jesterswag | Student
average speed (unit rates) = how fast she ran ÷ the time she ran in
average speed = 12 ÷ 10
average speed = 1.2 miles per min
you can check this by doing 1.2 x 10 = 12 which how much she ran | 642 | 2,326 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.375 | 4 | CC-MAIN-2018-09 | latest | en | 0.82896 |
http://www.enotes.com/homework-help/expand-squareroot-c-1-6-452386 | 1,469,863,514,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257832942.23/warc/CC-MAIN-20160723071032-00318-ip-10-185-27-174.ec2.internal.warc.gz | 415,506,906 | 10,056 | # Expand ( (Squareroot of c ) -1) ^6
Posted on
Expand `(sqrt(c)-1)^6`
`(sqrt(c) - 1)^2*(sqrt(c) - 1)^2 *(sqrt(c) - 1)^2`
`(sqrt(c) - 1)^2 = c - 2csqrt(c) + 1`
From 2nd step replace to have:
`(c - 2csqrt(c) + 1) (c - 2csqrt(c) + 1) (c - 2csqrt(c) + 1)`
Use distributive property to get:
`c^3 - 6c^2sqrt(c) + 15c^2 - 20csqrt(c) + 14c - 6sqrt(c) + c + 1`
Posted on
`(sqrt(c)-1)^6=sum_(r=0)^6(^6C_r(sqrt(c))^(6-r)(-1)^r)`
`=^6C_0(sqrt(c))^6(-1)^0+^6C_1(sqrt(c))^5(-1)^1+^6C_2(sqrt(c))^4(-1)^2+`
`^6C_3(sqrt(c))^3(-1)^3+^6C_4(sqrt(c))^2(-1)^4+^6C_5(sqrt(c))^1(-1)^5+`
`^6C_6(sqrt(c))^0(-1)^6`
`=c^(6/2)-6c^(5/2)+15c^(4/2)-20c^(3/2)+15c^(2/2)-6c^(1/2)+1`
`=c^3-6c^2sqrt(c)+15c^2-20csqrt(c)+15c-6sqrt(c)+1`
Here we have used binomial theorem for expansion and
`^6C_r=(6!)/(r!(6-r)!)`
`sqrt(c)=c^(1/2)` | 429 | 813 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2016-30 | longest | en | 0.430067 |
http://nedrilad.com/Tutorial/topic-58/GPU-Pro-Advanced-Rendering-Techniques-297.html | 1,506,261,993,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818690029.51/warc/CC-MAIN-20170924134120-20170924154120-00229.warc.gz | 240,043,269 | 5,298 | Game Development Reference
In-Depth Information
triangles are the same, we can use similar triangles to determine where the point
P will project to:
y
f
Y
Z ,
=
yY
Z
y =
.
Here we denote world coordinates in 3D space as capital letters, while the image
space coordinates are denoted with lowercase letters. The same relationship can
be used to show the mapping of P in the x -direction as well:
fX
Z
x =
.
With these two simple relationships, it is possible to project a point in the scene
to a point in the image. However, to go the other direction and take an image
point and unproject it back into the world, we can only determine a ray along
which the point must lay. This is because a traditional camera only produces
an intensity value at each pixel—you no longer have any information about how
deep into the scene the point was when the image was taken. Fortunately for
us, the Kinect has two different camera systems—one of which produces a depth
value at each pixel. The next section discusses how to take advantage of this fact
and find a mapping between the 2D depth and color images we are given and the
3D objects that appear in them.
2.3.2 Kinect Coordinate Systems
When we are given a depth image from the Kinect, we are essentially given three
pieces of data for each pixel. The first two are the x and y image coordinates
where that particular pixel is located. In addition, the value stored at that pixel
provides the world-space distance from the depth camera. This is precisely the
Z distance that we used from Figure 2.6 when projecting a point onto the image.
Given this additional piece of data, we can easily determine the world-space point
that every pixel in the depth image represents by changing around our previous
equations:
xZ
f
X =
,
yZ
f
Y =
.
This allows us to utilize the Kinect to produce 3D representations of the scene
that it is viewing. That is already an interesting capability, but we also want
to be able to map the color-image stream to this 3D representation so that we | 468 | 2,018 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2017-39 | latest | en | 0.922464 |
http://zh.wikipedia.org/wiki/%E7%B4%A0%E6%95%B8%E5%AE%9A%E7%90%86 | 1,432,520,166,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207928114.23/warc/CC-MAIN-20150521113208-00212-ip-10-180-206-219.ec2.internal.warc.gz | 857,428,954 | 15,719 | # 素數定理
（重定向自素數定理
$\pi(x)\approx\frac{x}{\ln\,x}$
$\pi(x)={\rm Li} (x) + O \left(x e^{-\frac{1}{15}\sqrt{\ln\,x}}\right)$，當x 趨近∞。
$x$ $\boldsymbol{\pi}(x)$[1] $\boldsymbol{\pi}(x)-\frac{x}{\ln x}$[2] $\frac{\boldsymbol{\pi}(x)}{\frac{x}{\ln x}}$ ${\rm Li} (x) - \boldsymbol{\pi} (x)$[3] $\frac{x}{\boldsymbol{\pi}(x)}$
10 4 −0.3 0.921 2.2 2.500
102 25 3.3 1.151 5.1 4.000
103 168 23 1.161 10 5.952
104 1,229 143 1.132 17 8.137
105 9,592 906 1.104 38 10.425
106 78,498 6,116 1.084 130 12.740
107 664,579 44,158 1.071 339 15.047
108 5,761,455 332,774 1.061 754 17.357
109 50,847,534 2,592,592 1.054 1,701 19.667
1010 455,052,511 20,758,029 1.048 3,104 21.975
1011 4,118,054,813 169,923,159 1.043 11,588 24.283
1012 37,607,912,018 1,416,705,193 1.039 38,263 26.590
1013 346,065,536,839 11,992,858,452 1.034 108,971 28.896
1014 3,204,941,750,802 102,838,308,636 1.033 314,890 31.202
1015 29,844,570,422,669 891,604,962,452 1.031 1,052,619 33.507
1016 279,238,341,033,925 7,804,289,844,393 1.029 3,214,632 35.812
1017 2,623,557,157,654,233 68,883,734,693,281 1.027 7,956,589 38.116
1018 24,739,954,287,740,860 612,483,070,893,536 1.025 21,949,555 40.420
1019 234,057,667,276,344,607 5,481,624,169,369,960 1.024 99,877,775 42.725
1020 2,220,819,602,560,918,840 49,347,193,044,659,701 1.023 222,744,644 45.028
1021 21,127,269,486,018,731,928 446,579,871,578,168,707 1.022 597,394,254 47.332
1022 201,467,286,689,315,906,290 4,060,704,006,019,620,994 1.021 1,932,355,208 49.636
1023 1,925,320,391,606,803,968,923 37,083,513,766,578,631,309 1.020 7,250,186,216 51.939
$p(n)\sim n\ln\,n.$
$\pi(x) = {\rm Li} (x) + O\left(\sqrt x \ln\,x\right)$ | 907 | 1,638 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2015-22 | latest | en | 0.38866 |
http://www.slideserve.com/imelda-matthews/common-core-mathematics-standards-grade-k | 1,508,635,104,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824931.84/warc/CC-MAIN-20171022003552-20171022023552-00720.warc.gz | 545,700,300 | 15,471 | Common Core Mathematics Standards: Grade K
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# Common Core Mathematics Standards: Grade K - PowerPoint PPT Presentation
Common Core Mathematics Standards: Grade K. Watch the box!. Keep your eyes on the box…. Watch the box!. How many dots did you see?. Ten and “some more”. Ten and “some more”. Number Sense…. What do those two words mean to you ? What concepts do your students struggle with?
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### Common Core Mathematics Standards: Grade K
Watch the box!
the box…
Watch the box!
How many dots did you see?
Number Sense…
• What do those two words mean to you ?
• What concepts do your students struggle with?
• How has the Common Core influenced what “number sense” means compared to before?
Math Games
• Make 10 … use two cards and build it with cubes
• Add and Compare…. “War with 2 cards”
• Snap It – take 5 cubes and connect them. Wait for directions.
• Close to 2
Close to 2
• Most kids will break away 2 then count what is left
• E.g., 5-3… using a “jig”
• Star t with 5, put the 2 in the final box
• Draw just one card at first, build it and then snap it off
Ten Plus
• Draw Two Number Cards and build them with cubes on your Ten Frame
• If your sum is greater than 10 rewrite the equation as 10 + __. For example if your number cards are 7+5 you would write 7+5 = 10+2
• Keep your sums organized… like…
• Sums to 11
• Sums to 12
• Sums to 13, etc.
5+ 8 = 13 = 10+3
• 5 + 8 = 10 + 3
• For each task solve it
• Use an equation and one other representation when you solve it
• Complete the table
• What makes a task difficult/easy?
• Algebra??? Really… where ?
Standards for Mathematical Practice
• What are these?
• Why do these matter?
• How could we help students to…
• Make sense and persevere while doing these?
• Model with an equation or representation?
• Attend to precision through communicating about strategies and mathematical ideas?
• Construct a viable argument or critique the reasoning of others?
• Does the type of numbers that we choose matter?
• Subtract 40
• Subtract 12
• Subtract 19
• Does the type of numbers that we choose matter?
• Let’s do some mental math
Number sense/algebra
• Talking about the math during game
• Breaking numbers apart, putting them back together
• Wild card…holding number in their head
• Benchmark numbers
• Fluency with combinations, facts
• Place value
Mathematical Practices
• How do we incorporate these more frequently into our classrooms?
• Incorporating these into assessment
• Choose a CCSSM from your grade level- try to focus on OA or NBT Domains
• Write a few tasks that have some rigor and create the possibility of incorporating the Standards for Mathematical Practices.
• Doing Mathematics- tasks that require students to pick a strategy to solve a real-world problem and then explain what they did
Examples
• A carpet is split into smaller sections that has 5 columns and 4 rows. If 2 of the sections have crates in them and the rest are empty, how many sections are empty?
• There are 125 children in the cafeteria. 176 more children arrive. Five minutes later, 89 of the children are in line and the rest are sitting down. How many children are sitting down?
Resources….
• DPI Math wiki
• Unpacking document
• Standards for Math Practice explanation
• 1 unit on number sense per grade level
• Lessons for Learning (being revised this summer)
Show Me Demo
• http://www.showme.com/sh/?h=0hl4iem
Drew Polly- [email protected]
Watch the box!
the box…
Watch the box!
How many dots did you see?
Fishing Situations
• You go fishing every day for a week.
• Each day you catch 2 more fish than the day before.
• Scenario 1:
• If you catch 1 fish on Day 1, how many fish will you catch each day? After 7 days how many fish will you have caught?
Fishing Situations
• You go fishing every day for a week.
• Each day you catch 2 more fish than the day before.
• Scenario 2:
• After 7 days you have caught 63 fish.
• How many fish did you catch each day?
Fishing Situations | 1,150 | 4,632 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2017-43 | latest | en | 0.874755 |
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Posted by PITHOCRATES - July 10th, 2013
Technology 101
(Originally published November 30th, 2011)
Despite Precise Celestial Navigation a lot of Ships and Valuable Cargoes still got Lost at Sea
Open sea navigation was once very perilous. It took a long time before ships ventured from sight of the shoreline. And a lot of technology. Boats used to go the long way across the Mediterranean Sea. Because being in open water at night without any visible landmarks was very dangerous. So they hugged the coastline. Adding days to every voyage. And more danger. Because the longer at sea the greater the risk there was of sinking. Especially when you were skirting the rock-infested shallows of the shoreline.
The Sumerians charted the stars. The Greeks continued this work, producing charts that could tell you what latitude (north/south position) you were at by looking at the stars and planets. By measuring the angle of the stars and planets above the horizon. The Arabs created one of the first tools to measure these angles. The kamal. Knowing this angle you could do a little math and look at a pre-calculated table of values. And get your latitude. Better instruments followed. The cross-staff. The astrolabe. And then the sextant. The gold standard of angle measuring until the advent of Global Positioning Satellites (GPS). Calculating longitude (east/west position) was a bit more complicated. Because the earth rotated. Which required some more skillful measuring and more calculations. And/or a reliable and accurate clock. To adjust your results by the time of day. As the time as well as the stars moved from east to west as the planet rotated.
The Chinese developed the magnetic compass. A helmsman steered his ship by the compass. The navigator checked the angles of celestial bodies (sun, moon, stars and planets), checked time and the ship’s speed to fix the ship’s position. By determining latitude and longitude. The navigator fed course headings and course corrections to the helmsman. Armed with these skills, tools, celestial charts and tables, the navigator could do a little math and navigate a ship across a vast ocean day or night to any port in the world. Transporting valuable cargoes safely and timely across the globe. Pretty impressive for the time. But despite this precise celestial navigation, a lot of ships still got lost at sea. As well as their valuable cargoes.
The Joint-Stock Company and Insurance Reduced the High Risks of Transoceanic Shipping
No matter how well a navigator could fix a ship’s position there were some things he just couldn’t do. Such as avoid an uncharted reef. Prevent a mutiny. Fend off pirates. Fend off enemy warships. Make storms go away. Or even see through dense fog. Simply put being on a small wooden ship in the middle of an ocean was very dangerous. Which poised quite the problem for early global trade.
It was a huge investment to put a ship to sea. It took another huge investment to fill a ship with valuable cargo. And if that ship didn’t make it back to sell that cargo it was very bad news for the investor. A lost ship could financially ruin them. So not only could you get rich in this new global trade you could become impoverished. Which made rich people reluctant to finance this early trade. Because it was so risky. Two things helped to reduce this risk to manageable levels. Insurance. And the joint-stock company.
A group of investors could buy stock into a company that was going to make numerous voyages on various ships. In exchange for a share of the profits from this trade each investor paid a share of its cost. Thus the joint-stock company spread the risk to multiple investors, reducing the risk to any one person. So one lost ship would not cause financial ruin to any one investor. Thus encouraging investment into this lucrative new trade of transoceanic shipping. And with the advent of insurance, shippers could insure each voyage for a small affordable fee. By collecting this small fee on every voyage the insurer could pay for the few ships and cargoes lost at sea. Not the investors. Thus further encouraging investment into this very risky endeavor.
The smartphone you can’t live without today most likely came to you via a large container ship from a port across some ocean. It made a long and perilous voyage to get to you. Which wouldn’t have been possible without celestial navigation, insurance and the joint-stock company. The things that made transoceanic shipping possible. Most of which are still in use today. As they were when brave mariners took to the open seas in those small wooden ships of yesteryear.
www.PITHOCRATES.com
The Line of Diocletian, the Byzantine Empire, Italian City-States, Banking, Usury and the Protestant Reformation
Posted by PITHOCRATES - January 3rd, 2012
History 101
Europe began to Awake from its Slumber of the Dark Ages in about 1300 Italy
Once upon a time the only lending was to help someone in need. Such as someone with a poor harvest to survive the winter. We did it out of the goodness of our hearts to help others in need. So to charge interest for a loan like this would have been cruel. Taking advantage of someone’s misfortune wasn’t the Christian thing to do. Or the Jewish. Or the Muslim. That’s why no one then charged interest for loaning money. You just didn’t kick a person when he or she was down. And if you did you could expect some swift justice from the religious authorities. As well as the state.
Rome was once the center of the civilized world. All roads led to Rome, after all. Then Diocletian split the Empire into two in 285. Along the Line of Diocletian. Into East (Greek) and West (Latin). The West included Rome and fell around 486, ushering in the European Dark Ages. Meanwhile the Eastern half, the Byzantine Empire, carried on. And skipped the Dark Ages. Its capital was Constantinople (named in 330) . Formerly Byzantium. Modern day Istanbul. Where all Asian overland trade routes led to. This city of Emperor Constantine. His city. Who reunited East and West. And adopted Christianity as the Empire’s new religion (381). Located at the crossroads between Europe and Asia, trade flourished and made the Byzantine Empire rich. And long lasting. Until weakened by the Venetian-financed Fourth Crusade (1202–1204). (The Latin Christians’ attack on the Greek Christians was fallout from the Great Schism of 1054 where Christianity split between Latin Catholic and Greek Orthodox). And then falling to the Ottomans in 1453.
Europe began to awake from its slumber in about 1300 Italy. Great city-states arose. Genoa. Pisa. And Venice. Like those early Greek city-states. Great ports of international trade. Rising into trade empires with the decline of the Byzantine Empire. Where these Italian merchants bought and sold all of those Asian goods. Putting great commercial fleets to sea to bring those Asian goods into Genoa, Pisa and Venice. Getting rich. But to make money they had to have money. Because in the international trade game you had to first buy what you sold. Which included the cost of those great merchant fleets. And how did they pay for all of this? They borrowed money from a new institution called banking.
That Europe that Slumbered during the Dark Ages Arose to Rule International Trade
Modern finance was born in Italy. Everything that makes the commercial economy work today goes back to these Italian city-states. From international banking and foreign exchange markets to insurance to the very bookkeeping that kept track of profits and losses. It is here we see the first joint-stock company to finance and diversify the risk of commercial shipping. London would use the joint-stock company to later finance the British East India Company. And Amsterdam the Dutch East India company. Where the Dutch and the English sent ships across oceans in search of trade. Thanks to their mastery of celestial navigation. And brought back a fortune in trade. Putting the great Italian city-states out of business. For their direct sea routes were far more profitable than the overland routes. Because the holds of their ships could hold far more than any overland caravan could.
The Catholic opposition to usury (charging interest to borrow money) opened the new banking industry to the oppressed Jews in the European/Christian cities. For it was one of the few things the Christian rulers let the Jews do. Which they did. Even though it was technically against their religion. And they did it well. For they had an early monopoly. Thanks to that same Catholic Church. Then came another schism in the Christian church. The Protestant Reformation. Where, among other things, Protestants said the Old Testament did not bind them to all rules that the Jews had to follow. Then John Calvin took it a step further and said commercial loans could charge interest. And, well, the rest is banking history.
Europe was then the dominant region of the world. That region that slumbered during the Dark Ages arose to rule international trade. Thanks to their navigational abilities. And their banking centers. Which financed their trade. And the great things to come.
The Enlightenment led to the Modern World, Limited Government, the Industrial Revolution and Beyond
With the fall of the Byzantine Empire and the rise of the Italian city-states, Greek thinkers left the Byzantine Empire and went West. To those rich Italian city-states. Bringing with them great books of Greek knowledge. The intellectual remnants of the Roman Empire. Translated them. And massed produced them on the new printing press. And kicked off the Enlightenment. Which then spread throughout Europe.
The Enlightenment led to the modern world. From limited government. To the Industrial Revolution. And beyond. All thanks to those Italian city-states. International trade. And banking.
www.PITHOCRATES.com
Celestial Navigation, Insurance and the Joint Stock Company
Posted by PITHOCRATES - November 30th, 2011
Technology 101
Despite Precise Celestial Navigation a lot of Ships and Valuable Cargoes still got Lost at Sea
Open sea navigation was once very perilous. It took a long time before ships ventured from sight of the shoreline. And a lot of technology. Boats used to go the long way across the Mediterranean Sea. Because being in open water at night without any visible landmarks was very dangerous. So they hugged the coastline. Adding days to every voyage. And more danger. Because the longer at sea the greater the risk there was of sinking. Especially when you were skirting the rock-infested shallows of the shoreline.
The Sumerians charted the stars. The Greeks continued this work, producing charts that could tell you what latitude (north/south position) you were at by looking at the stars and planets. By measuring the angle of the stars and planets above the horizon. The Arabs created one of the first tools to measure these angles. The kamal. Knowing this angle you could do a little math and look at a pre-calculated table of values. And get your latitude. Better instruments followed. The cross-staff. The astrolabe. And then the sextant. The gold standard of angle measuring until the advent of Global Positioning Satellites (GPS). Calculating longitude (east/west position) was a bit more complicated. Because the earth rotated. Which required some more skillful measuring and more calculations. And/or a reliable and accurate clock. To adjust your results by the time of day. As the time as well as the stars moved from east to west as the planet rotated.
The Chinese developed the magnetic compass. A helmsman steered his ship by the compass. The navigator checked the angles of celestial bodies (sun, moon, stars and planets), checked time and the ship’s speed to fix the ship’s position. By determining latitude and longitude. The navigator fed course headings and course corrections to the helmsman. Armed with these skills, tools, celestial charts and tables, the navigator could do a little math and navigate a ship across a vast ocean day or night to any port in the world. Transporting valuable cargoes safely and timely across the globe. Pretty impressive for the time. But despite this precise celestial navigation, a lot of ships still got lost at sea. As well as their valuable cargoes.
The Joint-Stock Company and Insurance Reduced the High Risks of Transoceanic Shipping
No matter how well a navigator could fix a ship’s position there were some things he just couldn’t do. Such as avoid an uncharted reef. Prevent a mutiny. Fend off pirates. Fend off enemy warships. Make storms go away. Or even see through dense fog. Simply put being on a small wooden ship in the middle of an ocean was very dangerous. Which poised quite the problem for early global trade.
It was a huge investment to put a ship to sea. It took another huge investment to fill a ship with valuable cargo. And if that ship didn’t make it back to sell that cargo it was very bad news for the investor. A lost ship could financially ruin them. So not only could you get rich in this new global trade you could become impoverished. Which made rich people reluctant to finance this early trade. Because it was so risky. Two things helped to reduce this risk to manageable levels. Insurance. And the joint-stock company.
A group of investors could buy stock into a company that was going to make numerous voyages on various ships. In exchange for a share of the profits from this trade each investor paid a share of its cost. Thus the joint-stock company spread the risk to multiple investors, reducing the risk to any one person. So one lost ship would not cause financial ruin to any one investor. Thus encouraging investment into this lucrative new trade of transoceanic shipping. And with the advent of insurance, shippers could insure each voyage for a small affordable fee. By collecting this small fee on every voyage the insurer could pay for the few ships and cargoes lost at sea. Not the investors. Thus further encouraging investment into this very risky endeavor.
The smartphone you can’t live without today most likely came to you via a large container ship from a port across some ocean. It made a long and perilous voyage to get to you. Which wouldn’t have been possible without celestial navigation, insurance and the joint-stock company. The things that made transoceanic shipping possible. Most of which are still in use today. As they were when brave mariners took to the open seas in those small wooden ships of yesteryear.
www.PITHOCRATES.com | 3,266 | 14,834 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2020-24 | latest | en | 0.881805 |
https://nlinux.org/if-which-of-the-following-represents-approximate-values-of-and-for/ | 1,657,166,866,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104683683.99/warc/CC-MAIN-20220707033101-20220707063101-00785.warc.gz | 464,056,030 | 5,477 | Please usage the word "theta" or an actual Greek letter to signify angle. Even tho" I capture your drift, your "cos 0 = 0.3090" was at initially confmaking use of.
You are watching: If , which of the following represents approximate values of and , for ?
Keep in mind the adhering to facts:
(sin theta)^2 + (cos theta)^2 = 1
tan theta = sin theta / cos theta
Hence, if we begin through cos theta = 0.3090, and desire sin theta, we use the Pythagorean Theorem: (sin theta)^2 = 1 - (cos theta)^2.
Here, (sin theta)^2 = 1 - (0.3090)^2
= 1 - 0.0955, or 0.9045.
Hence, sin theta +√0.9045 = +0.9511.
We currently know both sin theta and also cos theta, and have the right to easily uncover tan theta from the formula above:
sin theta 0.9511
tan theta = ---------------- = ---------------- = 3/-880
cos theta 0.3090
The second nlinux.org is the correct one.
Send
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The price would be diminished by 18 bozats
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The complying with information is offered in the question
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p = 300 - 18x
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3 i think
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The original fraction is equal to
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----> equation A
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×
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×
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# Lecture 2 so 211 games
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### Lecture 2 so 211 games
1. 1. GAMESan introductionJohn Bradford, Ph.D.
2. 2. What are ‘Games?’• In “game theory,” a ‘GAME’ is aninteraction of decision-makers.– The Key idea is that players makedecisions that affect one another.• Ingredients of a game:1. The players2. Their options (i.e. possible ‘moves’)3. Possible outcomes4. ‘Payoffs’- (i.e. players preferencesamong those outcomes)
3. 3. What are ‘Games?’• A ‘Game’ in this sense includesgames like chess, tic-tac-toe,football, basketball, etc.• A ‘game’ as defined alsoincludes any real-life situationin which our decisionsinfluence one another.– (Remember the definition ofsociology?)
4. 4. Describing Games• Remember, a game is simply asituation of interactivedecisions. We can describethese interactive situations:1. Verbally2. Using a matrix (= table)3. Using a Tree diagram
5. 5. Matrix DescriptionsRock, Paper, ScissorsSTEP 1: Write down the optionsfor both players in a table.– Player 1 = row chooser– Player 2 = column chooserROCK PAPER SCISSORSROCKPAPERSCISSORS
6. 6. Matrix DescriptionsRock, Paper, ScissorsSTEP 2: Write down the ‘payoffs’ (i.e. preferences) foreach possible joint outcome.– Below I use numbers, +1 to indicate a win, -1, toindicate a loss, and 0 to indicate a draw.– Note that there are two different payoffs!ROCK PAPER SCISSORSROCK 0,0 -1, +1 +1, -1PAPER +1, -1 0, 0 -1, +1SCISSORS -1, +1 +1, -1 0,0PLAYER 1PLAYER 2
7. 7. Matrix DescriptionsRock, Paper, Scissors• By convention, the first number is the payoff toPlayer 1 (the row chooser). The second number isthe payoff to Player 2 (the column chooser).– If you only see one number, it is always from the pointof view of Player 1.ROCK PAPER SCISSORSROCK 0,0 -1, +1 +1, -1PAPER +1, -1 0, 0 -1, +1SCISSORS -1, +1 +1, -1 0,0PLAYER 1PLAYER 2
8. 8. Matrix Descriptions• Notice that:1. Players make their moves simultaneously ( theydo not take turns), and also that,2. R…P…S… is depicted as a ZERO-SUM GAME.– “Zero-sum” refers to a situation in which thegains of one player are exactly offset by thelosses of another player. If the total gains of theparticipants are added up, and the total lossesare subtracted, they will sum to zero.• TOTAL GAINS = TOTAL LOSSES
9. 9. Zero-sum• In a zero-sum game, one person’sgain comes at the expense ofanother person’s loss.• Example: Imagine a pizza of fixedquantity. If you eat one more slicethan I do, I necessarily eat one sliceless! More for you = Less for me.• Example: A thief becomes richerby stealing from others, but thetotal amount of wealth remains thesame.
10. 10. Zero-sum• Rule: a game is zero-sum if payoffs sum toZERO under all circumstances.– For example, Player 1 chooses Rock and Player 2chooses Scissors. The aggregate payoff is:1 – 1 = 0.ROCK PAPER SCISSORSROCK 0,0 -1, +1+1, -1PAPER +1, -1 0, 0 -1, +1SCISSORS -1, +1 +1, -1 0,0
11. 11. Zero-sum• Example: ‘Matching Pennies’– Rules: In this two-person game, each player takes a pennyand places it either heads-up or tails-up and covers it sothe other player cannot see it. Both players’ pennies arethen uncovered simultaneously. Player 1 is calledMatchmaker and gets both pennies if they show the sameface (heads or tails). Player 2 is called Variety-seeker andgets both pennies if they show opposite faces (one heads,the other tails).HEADS TAILSHEADS +1, -1 -1, +1TAILS -1, +1 +1, -1MatchmakerVariety-Seeker
12. 12. Constant-sum and Variable-sum• Not all games are zero-sum games!1. A situation in which the total payoffs are fixedand never change, but do not necessarily equalzero, is called a constant-sum game.– Note: Zero-sum games are a kind of constant-sumgame in which the constant-sum is zero.2. Variable-sum games are those in which the sumof all payoffs changes depending on the choicesof the players! The game prisoner’s dilemma isa classic example of this! (You will have to showthis yourself)
13. 13. Tree Diagrams• Tree diagrams (aka ‘decision-trees’) are usefuldepictions of situations involving sequentialturn-taking rather than simultaneous moves.• Asking Boss for a Raise?Employee0,0Boss2, -2-1, 0
14. 14. Tree Diagrams(tic-tac-toe)
15. 15. Dominant Strategy• In Game Theory, a player’s dominant strategyis the choice that always leads to a higherpayoff, regardless of what the other player(s)choose.– Not all games have a dominant strategy, andgames may exist in which one player has adominant strategy but not the other.– In the game prisoner’s dilemma, both playershave a dominant strategy. Can you determinewhich choice dominates the others? | 1,389 | 4,879 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2016-26 | latest | en | 0.777114 |
https://www.arithmix.com/content/how-to-calculate-gross-logo-retention-rate-in-sage-100 | 1,708,520,175,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473472.21/warc/CC-MAIN-20240221102433-20240221132433-00446.warc.gz | 702,886,644 | 17,210 | # How To Calculate Gross Logo Retention Rate in Sage 100 | Arithmix
Learn how to calculate the gross logo retention rate in Sage 100 with our step-by-step guide. Increase your understanding of this important metric and improve your business's retention strategy.
Calculating gross logo retention rate is an essential task for businesses that want to track their customer retention. This metric measures the percentage of customers who continue to do business with your company over a specific period. In this article, we will discuss what gross logo retention rate is, when it is valuable to calculate it, and how to calculate it using Sage 100.
## What Is Gross Logo Retention Rate?
Gross logo retention rate is a metric that measures the percentage of customers who continue to do business with your company over a specific period. It is calculated by dividing the number of customers who continue to do business with your company by the total number of customers you had at the beginning of the period. The result is then multiplied by 100 to get the percentage.
Gross logo retention rate is an essential metric because it helps businesses understand how well they are retaining their customers. It is a good indicator of customer loyalty and satisfaction. A high gross logo retention rate means that customers are happy with your products or services and are likely to continue doing business with you in the future.
## When Is It Valuable To Calculate Gross Logo Retention Rate?
Gross logo retention rate is valuable to calculate for any business that wants to track its customer retention. It is particularly useful for businesses that rely on repeat customers, such as subscription-based services or businesses that sell products with a long lifespan.
Calculating gross logo retention rate can help businesses identify areas where they need to improve their customer service or product offerings. It can also help businesses identify which customers are most loyal and valuable to their business.
## How to Calculate Gross Logo Retention Rate Using Sage 100
To calculate gross logo retention rate using Sage 100, you will need to follow these steps:
1. Identify the period you want to measure. This could be a month, quarter, or year.
2. Count the number of customers you had at the beginning of the period.
3. Count the number of customers who continued to do business with you during the period.
4. Divide the number of customers who continued to do business with you by the total number of customers you had at the beginning of the period.
5. Multiply the result by 100 to get the percentage.
For example, let's say you had 100 customers at the beginning of the year, and 80 of them continued to do business with you throughout the year. To calculate your gross logo retention rate, you would divide 80 by 100 and then multiply the result by 100 to get a retention rate of 80%.
In conclusion, calculating gross logo retention rate is an essential task for businesses that want to track their customer retention. It is a good indicator of customer loyalty and satisfaction and can help businesses identify areas where they need to improve their customer service or product offerings. By following the steps outlined in this article, you can easily calculate your gross logo retention rate using Sage 100.
## How Do You Calculate Gross Logo Retention Rate in Sage 100
Sage 100 itself isn’t naturally geared towards letting you calculate complex metrics like Gross Logo Retention Rate. As an alternative, teams typically use products like Arithmix to import data from Sage 100 and build out dashboards.
## What is Arithmix?
Arithmix is the next generation spreadsheet - a collaborative, web-based platform for working with numbers that’s powerful yet easy to use. With Arithmix you can import data from systems like Sage 100, combine it with data from other systems, and create calculations like Gross Logo Retention Rate.
In Arithmix, data is organized into Tables and referenced by name, not by cell location like a spreadsheet, simplifying calculation creation. Data and calculations can be shared with others and re-used like building blocks, vastly streamlining analysis, model building, and reporting in a highly scalable and easy to maintain platform. Data can be edited, categorized (by dimensions) and freely pivoted. Calculations are automatically copied across a dimension - eliminating copy and paste of formulas. | 862 | 4,450 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2024-10 | latest | en | 0.952779 |
https://www.studypool.com/discuss/1008987/main-algebraic-solution-15?free | 1,481,366,889,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698543035.87/warc/CC-MAIN-20161202170903-00359-ip-10-31-129-80.ec2.internal.warc.gz | 1,023,282,701 | 15,415 | ##### main algebraic solution
Mathematics Tutor: None Selected Time limit: 1 Day
May 30th, 2015
Let x represent the width of the rectangle. Then x + 2 represents the length of the rectangle.
That means that the perimeter of the rectangle is , and the perimeter of the square is then , so the side of the square must measure
The area of the rectangle is then and the area of the square is and the sum of these two areas gives the total area function with respect to the width of the rectangle:
for which you want to find a minimum value.
Algebra Solution:
This function represents a parabola opening upwards because of the positive lead coefficient. Since the parabola opens upward the value of the function at the vertex will represent a minimum values. The x-coordinate of the vertex for any parabola of the form is given by . For this situation:
But before we do anything with that, we need to make sure that 3 makes sense as a value for the width. The domain of the total area function, in that it is a polynomial function with integer coefficients, is all real numbers. But for this situation, the actual domain is somewhat restricted. Certainly the width of the rectangle cannot be less than zero, so that gives us a practical bottom end to the area domain. On the other end, if the width were greater than 7, then the length would be greater than 9 and the perimeter would then be larger than the 32 inches we started with. Hence, the practical domain of the total area function is:
In that 3 is contained in that interval, 3 is an acceptable solution. The value of the function at 3 is:
Which makes sense because if the width of the rectangle is 3, then the length is 5 making the area of the rectangle 15. It also makes the perimeter of the rectangle 16, so the perimeter of the square must also be 16, the side 4, and the area 16. So the total area is 31. This also gives us the answer to the question posed, namely you cut the wire exactly in half -- 2 pieces each 16 inches long.
Calculus Solution:
The function is continuous and twice differentiable over its entire domain, so a local extrema can be found wherever the first derivative is equal to zero and that extreme point will be a minimum if the second derivative is positive at that point.
Hence the function has an extreme point at
, hence positive for all x.
Hence is a local minimum.
Therefore width = 3, length = 5, perimeter of rectangle = 16, i.e., cut the wire in half.
John
May 30th, 2015
...
May 30th, 2015
...
May 30th, 2015
Dec 10th, 2016
check_circle | 609 | 2,554 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2016-50 | longest | en | 0.88976 |
https://blog.starrmatica.com/2016/08/ | 1,620,634,660,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989115.2/warc/CC-MAIN-20210510064318-20210510094318-00204.warc.gz | 164,778,553 | 10,583 | One of the most common questions we are asked is how our library of digital content supports the Common Core. The easy answer is that our entire library has been aligned to the Common Core standards, so teachers can find resources related to each standard. The more complex answer is that there are many pieces of content that can be used in flexible ways to support each individual standard, and it is up to teachers to choose the content that best supports their lesson and their students.
Here are four pieces of digital content a teacher might choose from StarrMatica’s library to support and enhance the teaching of: CCSS.MATH.CONTENT.K.CC.C.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.
Students learn how to compare numbers and objects to learn to identify which is more than, greater than, less than, and equal to.
Students learn to pair two groups of objects to comparison count.
Students help feed pets by choosing the group of food that is more than less than, smaller than, larger than, or greater than.
Students help feed pets by choosing the correct symbol (<, >, =) to compare two groups of food.
Before we look ahead to a new school year, we wanted to take a moment to look back at the new content that was added during last school year. Here’s a list of the new content we shared in our monthly newsletters throughout the year last year. Be sure to read to the end for a sneak peek at what we have planned this year!
K-2 Summarizing Book Features: Students learn how to summarize, sequence, find main ideas, and identify features of fiction and nonfiction books.
Featured Resource: Circus Trains
Sequence how-to instructions and fiction paragraphs by putting train cars into the correct order. (You must be a StarrMatica member to access this content.)
Science Topic: Light and Sound
Learn how shadows are formed and learn what happens to the shape and size of shadows at different times of the day and in different seasons.
Science Topic: Oceans
Featured Resource: Ocean Zones
Learn about four different ocean zones. Then try to place six fish in the correct zones based on their descriptions.
Science Topic: Science Careers and the Scientific Process
Featured Resource: Career Town
Explore career town to learn about different job possibilities.
K-2 Data and Graphs: Students learn how to create and read tally charts, picture graphs, bar graphs, and line plots.
Featured Resource: Bar Graph Pets
Help Mindy collect data about the pets in her shop and create a bar graph with two or three categories. (You must be a StarrMatica member to access this content.)
Science Topic: Classification and Heredity
Featured Resource: Dog Breeding
Breed a certain type of border collie puppy by selecting parents with the right traits.
Science Topic: Soil
Featured Resource: Soil Safari
Journey through the soil in this Earth Ship to learn about the creatures that help create soil. Find an organism that can eat a toxic chemical that is threatening to destroy the meadow!
K-2 2D and 3D Shapes: Students learn about 2D shapes, 3D shapes, symmetry, patterns, and spatial thinking.
Featured Resource: Wrapping Paper Symmetry
Liam is creating drawings on the wrapping paper for Olivia’s present. Help Liam finish each drawing so it is symmetrical. (You must be a StarrMatica member to access this content.)
Math Topic: Line Plots
Featured Resource: The Data Bank Research Company
Gather data by surveying customers. Then create a line plot of the data, create a bar graph to display the data, and answer questions about the data.
And this year, look for new content to help you teach K-2 Measurement, Chemistry, Microorganisms, Compass Skills, and Grammar topics! | 826 | 3,850 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2021-21 | longest | en | 0.94836 |
http://spamdestructor.com/error-propagation/propagation-of-error-equation-example.php | 1,539,965,974,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583512411.13/warc/CC-MAIN-20181019145850-20181019171350-00092.warc.gz | 352,604,467 | 5,940 | Home > Error Propagation > Propagation Of Error Equation Example
# Propagation Of Error Equation Example
## Contents
Generated Mon, 24 Oct 2016 19:44:35 GMT by s_wx1087 (squid/3.5.20) Ratliff Chemistry 2.208 προβολές 13:16 Error Calculation Example - Διάρκεια: 7:24. ISSN0022-4316. A. (1973). More about the author
In this example, the 1.72 cm/s is rounded to 1.7 cm/s. The error propagation methods presented in this guide are a set of general rules that will be consistently used for all levels of physics classes in this department. If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe the region within which the true value of The uncertainty u can be expressed in a number of ways.
## Error Propagation Physics
This ratio is very important because it relates the uncertainty to the measured value itself. Since both distance and time measurements have uncertainties associated with them, those uncertainties follow the numbers throughout the calculations and eventually affect your final answer for the velocity of that object. We know the value of uncertainty for∆r/r to be 5%, or 0.05. Journal of Sound and Vibrations. 332 (11).
In both cases, the variance is a simple function of the mean.[9] Therefore, the variance has to be considered in a principal value sense if p − μ {\displaystyle p-\mu } And again please note that for the purpose of error calculation there is no difference between multiplication and division. Measurement Process Characterization 2.5. Error Propagation Average Lorne Nix 304 προβολές 4:55 Calculating the Propagation of Uncertainty - Διάρκεια: 12:32.
Sometimes, these terms are omitted from the formula. Error Propagation Chemistry soerp package, a python program/library for transparently performing *second-order* calculations with uncertainties (and error correlations). doi:10.1016/j.jsv.2012.12.009. ^ Lecomte, Christophe (May 2013). "Exact statistics of systems with uncertainties: an analytical theory of rank-one stochastic dynamic systems". https://en.wikipedia.org/wiki/Propagation_of_uncertainty In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them.
Example: F = mg = (20.4 kg)(-9.80 m/s2) = -199.92 kgm/s2 δF/F = δm/m δF/(-199.92 kgm/s2) = (0.2 kg)/(20.4 kg) δF = ±1.96 kgm/s2 δF = ±2 kgm/s2 F = -199.92 Error Propagation Inverse See Ku (1966) for guidance on what constitutes sufficient data. Since we are given the radius has a 5% uncertainty, we know that (∆r/r) = 0.05. doi:10.2307/2281592.
## Error Propagation Chemistry
We will state the general answer for R as a general function of one or more variables below, but will first cover the specail case that R is a polynomial function go to this web-site Lisa Gallegos 5.064 προβολές 8:44 Propagation of Error - Ideal Gas Law Example - Διάρκεια: 11:19. Error Propagation Physics How can you state your answer for the combined result of these measurements and their uncertainties scientifically? Error Propagation Square Root Pchem Lab 3.658 προβολές 11:19 CH403 3 Experimental Error - Διάρκεια: 13:16.
If q is the sum of x, y, and z, then the uncertainty associated with q can be found mathematically as follows: Multiplication and Division Finding the uncertainty in a my review here Chemistry Biology Geology Mathematics Statistics Physics Social Sciences Engineering Medicine Agriculture Photosciences Humanities Periodic Table of the Elements Reference Tables Physical Constants Units and Conversions Organic Chemistry Glossary Search site Search Correlation can arise from two different sources. Given two random variables, $$x$$ and $$y$$ (correspond to width and length in the above approximate formula), the exact formula for the variance is: V(\bar{x} \bar{y}) = \frac{1}{n} \left[ X^2 Error Propagation Definition
Retrieved 2016-04-04. ^ "Propagation of Uncertainty through Mathematical Operations" (PDF). Practically speaking, covariance terms should be included in the computation only if they have been estimated from sufficient data. doi:10.6028/jres.070c.025. click site Journal of the American Statistical Association. 55 (292): 708–713.
The system returned: (22) Invalid argument The remote host or network may be down. Error Propagation Excel This is desired, because it creates a statistical relationship between the variable $$x$$, and the other variables $$a$$, $$b$$, $$c$$, etc... In the first step - squaring - two unique terms appear on the right hand side of the equation: square terms and cross terms.
## Also, notice that the units of the uncertainty calculation match the units of the answer.
1. Berkeley Seismology Laboratory.
2. Journal of Sound and Vibrations. 332 (11).
3. In the following examples: q is the result of a mathematical operation δ is the uncertainty associated with a measurement.
4. Reciprocal In the special case of the inverse or reciprocal 1 / B {\displaystyle 1/B} , where B = N ( 0 , 1 ) {\displaystyle B=N(0,1)} , the distribution is
5. If you're measuring the height of a skyscraper, the ratio will be very low.
6. Then σ f 2 ≈ b 2 σ a 2 + a 2 σ b 2 + 2 a b σ a b {\displaystyle \sigma _{f}^{2}\approx b^{2}\sigma _{a}^{2}+a^{2}\sigma _{b}^{2}+2ab\,\sigma _{ab}} or
7. Derivation of Arithmetic Example The Exact Formula for Propagation of Error in Equation 9 can be used to derive the arithmetic examples noted in Table 1.
8. The extent of this bias depends on the nature of the function.
Example: An angle is measured to be 30°: ±0.5°. Please see the following rule on how to use constants. These instruments each have different variability in their measurements. Error Propagation Calculus Simplification Neglecting correlations or assuming independent variables yields a common formula among engineers and experimental scientists to calculate error propagation, the variance formula:[4] s f = ( ∂ f ∂ x
Caveats and Warnings Error propagation assumes that the relative uncertainty in each quantity is small.3 Error propagation is not advised if the uncertainty can be measured directly (as variation among repeated General functions And finally, we can express the uncertainty in R for general functions of one or mor eobservables. Knowing the uncertainty in the final value is the correct way to officially determine the correct number of decimal places and significant figures in the final calculated result. navigate to this website Eq.(39)-(40).
Keith (2002), Data Reduction and Error Analysis for the Physical Sciences (3rd ed.), McGraw-Hill, ISBN0-07-119926-8 Meyer, Stuart L. (1975), Data Analysis for Scientists and Engineers, Wiley, ISBN0-471-59995-6 Taylor, J. Advantages of top-down approach This approach has the following advantages: proper treatment of covariances between measurements of length and width proper treatment of unsuspected sources of error that would emerge if The end result desired is $$x$$, so that $$x$$ is dependent on a, b, and c. Robbie Berg 8.782 προβολές 18:16 Error and Percent Error - Διάρκεια: 7:15.
Now a repeated run of the cart would be expected to give a result between 36.1 and 39.7 cm/s. Function Variance Standard Deviation f = a A {\displaystyle f=aA\,} σ f 2 = a 2 σ A 2 {\displaystyle \sigma _{f}^{2}=a^{2}\sigma _{A}^{2}} σ f = | a | σ A So, rounding this uncertainty up to 1.8 cm/s, the final answer should be 37.9 + 1.8 cm/s.As expected, adding the uncertainty to the length of the track gave a larger uncertainty Generated Mon, 24 Oct 2016 19:44:33 GMT by s_wx1087 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection
Since f0 is a constant it does not contribute to the error on f. You will sometimes encounter calculations with trig functions, logarithms, square roots, and other operations, for which these rules are not sufficient. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Define f ( x ) = arctan ( x ) , {\displaystyle f(x)=\arctan(x),} where σx is the absolute uncertainty on our measurement of x.
JCGM 102: Evaluation of Measurement Data - Supplement 2 to the "Guide to the Expression of Uncertainty in Measurement" - Extension to Any Number of Output Quantities (PDF) (Technical report). Matt Becker 11.257 προβολές 7:01 Basic Rules of Multiplication,Division and Exponent of Errors(Part-2), IIT-JEE physics classes - Διάρκεια: 8:52. Generally, reported values of test items from calibration designs have non-zero covariances that must be taken into account if $$Y$$ is a summation such as the mass of two weights, or Pearson: Boston, 2011,2004,2000. | 2,154 | 8,808 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2018-43 | latest | en | 0.798799 |
http://www.parttimescholar.com/search?updated-max=2013-01-02T05:28:00-08:00&max-results=10&reverse-paginate=true | 1,657,189,620,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104690785.95/warc/CC-MAIN-20220707093848-20220707123848-00677.warc.gz | 96,238,268 | 25,389 | ## Posts
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### Thor and the Einstein-Rosen Bridge
Relocation always takes a toll on one's life. I am speaking from experience as this is my second move in 2 years. Worst of all, the 9 to 5 in Hong Kong is sometimes like the 9 to 10, especially when you work in a foreign company and expected to do early morning or evening meetings with North America. As a result, I have lost a lot of blogging time. Luckily, I recently managed to squeeze in time to watch the movie Thor , in 3D! I went to the movies not expecting any physics lessons, but Natalie Portman mentioned a number of astrophysics concepts, including the Einstein-Rosen Bridge that connected Asgard to Earth. In a layman's world, this bridge is more commonly known as a wormhole . A wormhole is essentially a warp in space-time, thus creating a shortcut for traversing between two physical points in space and time. Think of the analogy of drawing two points on a piece of paper placed on a table. When the paper is lying flat, the distance between the two points is X cm. If | 1,206 | 5,548 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2022-27 | latest | en | 0.928808 |
http://mathoverflow.net/feeds/question/44630 | 1,368,903,220,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368696382705/warc/CC-MAIN-20130516092622-00061-ip-10-60-113-184.ec2.internal.warc.gz | 165,499,016 | 2,132 | Clifford Algebra and Gamma matrices: is this relation generally true for any dimension? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T18:53:39Z http://mathoverflow.net/feeds/question/44630 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/44630/clifford-algebra-and-gamma-matrices-is-this-relation-generally-true-for-any-dime Clifford Algebra and Gamma matrices: is this relation generally true for any dimension? Osiris 2010-11-02T23:57:57Z 2010-11-03T22:49:36Z <p>I expect the following relation to be vanishing. But it seems not that obvious.</p> <p><code>$\Gamma_{ab}^{\lambda}t^at^b \Gamma_{\lambda c(d)}t^c=0$</code></p> <p>where $t^a$ are even ghosts, "$ab$" are indices for matrix element, and $\lambda$ denote different Gamma matrices. The Einstein summation convention is used above, i.e. we will sum over all indices except $d$.</p> <p>I checked for both 3D and 4D Clifford algebra. The relation above seems to be right. But not sure whether it is generally true.</p> <p>Does the following equation also vanishes? </p> <p><code>$\Gamma_{\lambda a b}t^a t^b C^{\lambda} C^{\alpha}C^{\beta}=0$</code></p> <p>where $C^{\lambda}$ are odd ghosts, i.e. $C^{\alpha}C^{\beta}=-C^{\beta}C^{\alpha}$. </p> <p>The left hand side of the equation above is supposed to be something in $\wedge^2 V$, where <code>$V=\{ C^{\lambda}|\lambda=1,2,\cdots,D \}$</code>. $D$ is the dimension of the space.</p> http://mathoverflow.net/questions/44630/clifford-algebra-and-gamma-matrices-is-this-relation-generally-true-for-any-dime/44633#44633 Answer by José Figueroa-O'Farrill for Clifford Algebra and Gamma matrices: is this relation generally true for any dimension? José Figueroa-O'Farrill 2010-11-03T01:35:31Z 2010-11-03T01:35:31Z <p>It's not clear to me what you mean by "even ghosts". Do you mean perhaps that $t^a t^b = t^b t^a$?</p> <p>If so, then you will find that the identity is only valid in 3, 4, 6 and 10 dimensions and with lorentzian signature. Indeed, this identity is essentially the condition for the vanishing of a fermionic trilinear which appears in the supersymmetric variation of Yang-Mills coupled minimally to an adjoint fermion, which in turn is the obstruction to the existence of "pure" supersymmetric Yang-Mills.</p> <p>It is no accident that those dimensions are 2 plus the dimensions of the real division algebras: $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$. In fact, the identities are well-known identities for these algebras. In particular, when the dust clears, the ten-dimensional identities are the celebrated Moufang identities.</p> <p>Of course, if I got the definition of the even ghosts wrong, then what I say above is probably wrong.</p> | 822 | 2,748 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2013-20 | latest | en | 0.751043 |
https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_10B_Problems/Problem_11&oldid=141643 | 1,653,352,234,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662562106.58/warc/CC-MAIN-20220523224456-20220524014456-00378.warc.gz | 153,452,257 | 10,213 | # 2017 AMC 10B Problems/Problem 11
## Problem
At Typico High School, $60\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\%$ say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it? SID M LIKES RIMLI LMFAOOOOOOO
$\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%$
## Video Solution
~savannahsolver
2017 AMC 10B (Problems • Answer Key • Resources) Preceded byProblem 10 Followed byProblem 12 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions | 312 | 838 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2022-21 | latest | en | 0.721878 |
https://www.centralgalaxy.com/altitude-measurement/ | 1,723,117,261,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640726723.42/warc/CC-MAIN-20240808093647-20240808123647-00584.warc.gz | 545,517,333 | 33,515 | # How to Measure the Altitude of Aircraft And Spacecraft?
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50, 40, 30, 20, 10…… You may have heard this on a flight simulation when the simulated aircraft is landing. Or you might have seen the Mars landing footage of the Perseverance rover (click the link if you haven’t watched this). Well, we have to precisely measure the altitude to conduct these actions successfully. Here’s an introduction to the method and tools used for these measurements.
#### Altimeters
For an aircraft, we use altimeters. It’s an instrument to measure how high it is. With an introduction that’s as brief as this, you’ll probably ask, “How does an altimeter work?” Therefore, let’s answer this question in the following paragraphs. (National Geographic, 2014).
To understand how altimeters work, we must first learn about gravity. As you all know, gravity is the force pulling things downward. This force holds the atmosphere from escaping into space and keeps Earth near the Sun so that the right temperature can be continuously maintained. Therefore, the air is denser near the ground since most air is pushed downward while very little air is floating up in the thermosphere. (National Physical Laboratory, n.d.). In fact, about 75% of the atmosphere’s mass is in the troposphere, which is the innermost layer of the atmosphere. (NASA Space Place, 2019).
As a result, it is possible to measure your altitude using air pressure as it is calculable when considering gravity and the atmospheric pressure at sea level. An altimeter that uses this method contains a barometer used to sense the air pressure to obtain altitude data.
This type of altimeters are generally useful on Earth. But what about other scenarios where there’s no atmosphere or the sensor isn’t exposed to air? In that case, we need to use other methods to know how high the object is.
#### Using Light
If you want to measure altitude when there’s no air around you, you may need to get a bit more creative. We have to use light waves, and we call the instruments laser altimeters or radar altimeters.
The instrument consists of an emitter that emits some electromagnetic radiation, a receiver that looks for the signal, and a very precise timer to get the exact round-trip time. Then, the onboard computer will multiply the time by the speed of light to obtain the distance the light wave has traveled between the emitter and the receiver, and just divide the result by two to get the distance of the aircraft/spacecraft to the ground. (P. Falkner, R. Schulz, 2015).
For instance, if it takes 0.00267 seconds for light to go from the spacecraft to the ground and back, its altitude is 0.00267 * 299792458 / 2. That’s about 400 kilometers (400000 meters), which is the approximate altitude of the International Space Station! (Elizabeth Howell, 2018).
Other than altitude measurements, these altimeters provide essential data to know the effect of climate change. For instance, ICESat-2 uses a laser altimeter to measure the elevation of ice structures. (“Our Mission”, n.d.; “Space Lasers”, n.d.). Besides, the Sentinel-6 spacecraft uses a radar altimeter to obtain the rising sea level. (NASA Jet Propulsion Laboratory, n.d.).
#### Stereo Vision
Let’s say you put an object close to your eyes. Then, stare at it with your left eye. Now, stare at it with your right eye but don’t move your head. Can you see the difference? Well, that’s the thing that enables stereo vision to measure distance.
If there is a distance between the two cameras, they have a different view of the object. For altitude measurements, the object is the ground. If the two cameras are looking at the same object, they can use the difference in the object’s viewing angle to measure the distance to the target.
#### Why Should We Measure Altitude Precisely?
Well, if the aircraft or spacecraft is going to rendezvous with something or dodge dangerous obstacles, they need to measure their altitude correctly. For instance, the plane needs to maintain the correct altitude across its descent to touch down in the desired spot on the runway. Moreover, they need to follow the ATC’s instructions with precise altitude and speed measurements. If not, they could crash into something.
For space probes, it must be even more accurate. Consider deorbit burns. The crew needs to land at the right spot to ensure safety. Therefore, the burn need to take place at the right altitude and with the right deceleration to send it in an orbit to intercept Earth’s atmosphere at the right spot.
#### Conclusion
So, we’ve talked about using atmospheric pressure and light waves to measure the altitude of an aircraft or spacecraft. We’ve also discussed the importance of precise altitude measurements in the last section. To find out more, please visit the webpages in the references below.
#### References and Credits
1. Amy Shira Teitel. (2011, November 18). Do-It-Yourself Guide to Measuring the Moon’s Distance. Retrieved April 18, 2021, from https://www.universetoday.com/91120/do-it-yourself-guide-to-measuring-the-moons-distance/
2. Elizabeth Howell. (2018, February 8). International Space Station: Facts, History & Tracking. Retrieved April 18, 2021, from https://www.space.com/16748-international-space-station.html
3. “Our Mission”. (n.d.). Retrieved April 18, 2021, from https://icesat-2.gsfc.nasa.gov/mission
4. P. Falkner, R. Schulz. (2015). Laser Altimeter. Retrieved April 18, 2021, from https://www.sciencedirect.com/topics/earth-and-planetary-sciences/laser-altimeter
5. NASA Jet Propulsion Laboratory. (n.d.). Sentinel-6 Launch Press Kit | Spacecraft and Instruments. Retrieved April 18, 2021, from https://www.jpl.nasa.gov/news/press_kits/sentinel-6/mission/spacecraft/
6. NASA Space Place. (2019, June 28). Troposphere. Retrieved April 18, 2021, from https://spaceplace.nasa.gov/troposphere/
7. National Geographic. (2014, June 23). Altimeter. Retrieved April 18, 2021, from https://www.nationalgeographic.org/encyclopedia/altimeter/
8. National Physical Laboratory. (n.d.). Why does atmospheric pressure change with altitude? Retrieved April 18, 2021, from https://www.npl.co.uk/resources/q-a/atmospheric-altitude-pressure-changes
9. “Space Lasers”. (n.d.). Retrieved April 18, 2021, from https://icesat-2.gsfc.nasa.gov/space-lasers | 1,457 | 6,293 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2024-33 | latest | en | 0.919586 |
https://turconconstructors.com/2g8h3/article.php?c54e56=python-code-to-find-inverse-of-a-matrix | 1,656,309,681,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103328647.18/warc/CC-MAIN-20220627043200-20220627073200-00254.warc.gz | 645,803,203 | 10,927 | # python code to find inverse of a matrix
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## python code to find inverse of a matrix
a) (0+0)=0, b) (1+0)=1, c) (1+1)=0 and C Programming Codes Multiply to Matrix print(np.allclose(np.dot(ainv, a), np.eye(3))) Notes Inverse of a matrix can find out in many ways. It can be shown that the number of linearly independent rows of a matrix is always equal to the number of linearly independent columns. Steps involved in the Example. Features Matlab version is available to use it for analysis User-friendly Android app is available Finding the inverse of a large matrix often isn’t easy, so quantum physics calculations are sometimes limited to working with unitary operators, U, where the operator’s inverse is equal to its adjoint, (To find the adjoint of an operator, A, you find the transpose by interchanging the rows and columns, AT. To find the inverse of a 2x2 matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc). The space doesn’t change when we apply the identity matrix to it . In mathematics, and in particular linear algebra, the Moore–Penrose inverse + of a matrix is the most widely known generalization of the inverse matrix. Transpose is a new matrix result from when all the elements of rows are now in column and vice -versa. This is a C++ program to Find Inverse of a Graph Matrix. I need to have my function to flag unsuitable matrices (i.e., not 2 * 2 or 3 * 3) with a message box and then stop. I find the modular multiplicative inverse (of the matrix determinant, which is $1×4-3×5=-11$) with the extended Euclid algorithm (it is $-7 \equiv 19 \pmod{26}$). Like, in this case, I want to transpose the matrix2. Using determinant and adjoint, we can easily find the inverse of a square matrix using below formula, If det(A) != 0 A-1 = adj(A)/det(A) Else "Inverse doesn't exist" Inverse is used to find the solution to a system of linear equation. which is its inverse. Examples: Input : 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Output : 1 2 3 4 5 8 1 4 5 6 7 8 Recommended: Please solve it on “PR Since the resulting inverse matrix is a $3 \times 3$ matrix, we use the numpy.eye() function to create an identity matrix. Inverse of a matrix exists only if the matrix is non-singular i.e., determinant should not be 0. We saw that $\bs{x}$ was not altered after being multiplied by $\bs{I}$. How to find the inverse of 3×3 matrix? Kite is a free autocomplete for Python developers. A tool that I have developed in both Matlab and Java in the context of Linear Algebra and Numerical Analysis courses to make it easy to calculate the inverse of a matrix. What is the difficulty level of this exercise? You can verify the result using the numpy.allclose() function. In this tutorial, we will learn how to find modular multiplicative inverse using Python. Inverse of a Matrix Definition. In Python, we can implement a matrix as nested list (list inside a list). Next: Write a NumPy program to compute the inverse of a given matrix. Let’s try to understand what this term means. The shortest code is RARELY the best code. Then take the complex […] In the previous section we have discussed about the benefit of Python Matrix that it just makes the task simple for us. I am using the formula involving the adjoint of the matrix. for all matrix det==0 and show inverse doesn't exist ! I don't recommend using it. The matrix inverse of $\bs{A}$ is denoted $\bs{A}^{-1}$. Add each bits from the two binary numbers separately starting from LSB. Assuming that there is non-singular ( i.e. The code can be found here.It can do a variety of functions, such as addition, subtraction, multiplication, division (multiplying by inverse of another matrix), and solving a system of equations. Modular Multiplicative Inverse: Consider two integers n and m.MMI(Modular Multiplicative Inverse) is an integer(x), which satisfies the condition (n*x)%m=1. Python Program to Inverse Matrix Using Gauss Jordan. You can check the proof. Here we find out inverse of a graph matrix using adjoint matrix and its determinant. Examine why solving a linear system by inverting the matrix using inv(A)*b is inferior to solving it directly using the backslash operator, x = A\b.. Matrix Inverse Using Gauss Jordan Method Pseudocode Earlier in Matrix Inverse Using Gauss Jordan Method Algorithm , we discussed about an algorithm for finding inverse of matrix of order n. In this tutorial we are going to develop pseudocode for this method so that it will be easy while implementing using programming language. You can find the transpose of a matrix using the matrix_variable .T. Submitted by Anuj Singh, on July 17, 2020 . Now the question arises, how to find that inverse of matrix A is A-1. Then calculate adjoint of given matrix. Free source code and tutorials for Software developers and Architects. Password ... anyway this way has problem too! Code Finds the Sum of 2 Binary Numbers Take two Binary Numbers as input. Defining a Matrix; Identity Matrix; There are matrices whose inverse is the same as the matrices and one of those matrices is the identity matrix. Like that, we can simply Multiply two matrix, get the inverse and transposition of a matrix. Contribute your code (and comments) through Disqus. x lies in the domain {0,1,2,3,4,5,…..,m-1}. In python, by using the NumPy library we can find out the determinant, inverse, and rank of a matrix. Matrix Rank with Python. The number of linearly independent columns is always equal to the number of linearly independent rows. We can treat each element as a row of the matrix. In Python, the arrays are represented using the list data type. Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. | 1,387 | 5,874 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2022-27 | latest | en | 0.860583 |
http://math.ubooks.pub/Books/ON/M1/1703/C06S5M003.html | 1,519,346,502,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891814300.52/warc/CC-MAIN-20180222235935-20180223015935-00792.warc.gz | 226,849,010 | 5,966 | ### 6-5. Fictitious Forces and Non-inertial Frames: The Coriolis Force
Learning Objectives
• Discuss the inertial frame of reference.
• Discuss the non-inertial frame of reference.
• Describe the effects of the Coriolis force.
What do taking off in a jet airplane, turning a corner in a car, riding a merry-go-round, and the circular motion of a tropical cyclone have in common? Each exhibits fictitious forces—unreal forces that arise from motion and may seem real, because the observer’s frame of reference is accelerating or rotating.
When taking off in a jet, most people would agree it feels as if you are being pushed back into the seat as the airplane accelerates down the runway. Yet a physicist would say that you tend to remain stationary while the seat pushes forward on you, and there is no real force backward on you. An even more common experience occurs when you make a tight curve in your car—say, to the right. You feel as if you are thrown (that is, forced) toward the left relative to the car. Again, a physicist would say that you are going in a straight line but the car moves to the right, and there is no real force on you to the left. Recall Newton’s first law.
Figure 1: (a) The car driver feels herself forced to the left relative to the car when she makes a right turn. This is a fictitious force arising from the use of the car as a frame of reference. (b) In the Earth’s frame of reference, the driver moves in a straight line, obeying Newton’s first law, and the car moves to the right. There is no real force to the left on the driver relative to Earth. There is a real force to the right on the car to make it turn.
We can reconcile these points of view by examining the frames of reference used. Let us concentrate on people in a car. Passengers instinctively use the car as a frame of reference, while a physicist uses Earth. The physicist chooses Earth because it is very nearly an inertial frame of reference—one in which all forces are real (that is, in which all forces have an identifiable physical origin). In such a frame of reference, Newton’s laws of motion take the form given in Dynamics: Newton's Laws of Motion The car is a non-inertial frame of reference because it is accelerated to the side. The force to the left sensed by car passengers is a fictitious force having no physical origin. There is nothing real pushing them left—the car, as well as the driver, is actually accelerating to the right.
Let us now take a mental ride on a merry-go-round—specifically, a rapidly rotating playground merry-go-round. You take the merry-go-round to be your frame of reference because you rotate together. In that non-inertial frame, you feel a fictitious force, named centrifugal force(not to be confused with centripetal force), trying to throw you off. You must hang on tightly to counteract the centrifugal force. In Earth’s frame of reference, there is no force trying to throw you off. Rather you must hang on to make yourself go in a circle because otherwise you would go in a straight line, right off the merry-go-round.
Figure 2: (a) A rider on a merry-go-round feels as if he is being thrown off. This fictitious force is called the centrifugal force—it explains the rider’s motion in the rotating frame of reference. (b) In an inertial frame of reference and according to Newton’s laws, it is his inertia that carries him off and not a real force (the unshaded rider has ${F}_{\text{net}}=0$ and heads in a straight line). A real force, ${F}_{\text{centripetal}}$, is needed to cause a circular path.
This inertial effect, carrying you away from the center of rotation if there is no centripetal force to cause circular motion, is put to good use in centrifuges (see Figure 3). A centrifuge spins a sample very rapidly, as mentioned earlier in this chapter. Viewed from the rotating frame of reference, the fictitious centrifugal force throws particles outward, hastening their sedimentation. The greater the angular velocity, the greater the centrifugal force. But what really happens is that the inertia of the particles carries them along a line tangent to the circle while the test tube is forced in a circular path by a centripetal force.
Figure 3: Centrifuges use inertia to perform their task. Particles in the fluid sediment come out because their inertia carries them away from the center of rotation. The large angular velocity of the centrifuge quickens the sedimentation. Ultimately, the particles will come into contact with the test tube walls, which will then supply the centripetal force needed to make them move in a circle of constant radius.
Let us now consider what happens if something moves in a frame of reference that rotates. For example, what if you slide a ball directly away from the center of the merry-go-round, as shown in Figure 4? The ball follows a straight path relative to Earth (assuming negligible friction) and a path curved to the right on the merry-go-round’s surface. A person standing next to the merry-go-round sees the ball moving straight and the merry-go-round rotating underneath it. In the merry-go-round’s frame of reference, we explain the apparent curve to the right by using a fictitious force, called the Coriolis force, that causes the ball to curve to the right. The fictitious Coriolis force can be used by anyone in that frame of reference to explain why objects follow curved paths and allows us to apply Newton’s Laws in non-inertial frames of reference.
Figure 4: Looking down on the counterclockwise rotation of a merry-go-round, we see that a ball slid straight toward the edge follows a path curved to the right. The person slides the ball toward point B, starting at point A. Both points rotate to the shaded positions (A’ and B’) shown in the time that the ball follows the curved path in the rotating frame and a straight path in Earth’s frame.
Up until now, we have considered Earth to be an inertial frame of reference with little or no worry about effects due to its rotation. Yet such effects do exist—in the rotation of weather systems, for example. Most consequences of Earth’s rotation can be qualitatively understood by analogy with the merry-go-round. Viewed from above the North Pole, Earth rotates counterclockwise, as does the merry-go-round in Figure 4. As on the merry-go-round, any motion in Earth’s northern hemisphere experiences a Coriolis force to the right. Just the opposite occurs in the southern hemisphere; there, the force is to the left. Because Earth’s angular velocity is small, the Coriolis force is usually negligible, but for large-scale motions, such as wind patterns, it has substantial effects.
The Coriolis force causes hurricanes in the northern hemisphere to rotate in the counterclockwise direction, while the tropical cyclones (what hurricanes are called below the equator) in the southern hemisphere rotate in the clockwise direction. The terms hurricane, typhoon, and tropical storm are regionally-specific names for tropical cyclones, storm systems characterized by low pressure centers, strong winds, and heavy rains. Figure 5 helps show how these rotations take place. Air flows toward any region of low pressure, and tropical cyclones contain particularly low pressures. Thus winds flow toward the center of a tropical cyclone or a low-pressure weather system at the surface. In the northern hemisphere, these inward winds are deflected to the right, as shown in the figure, producing a counterclockwise circulation at the surface for low-pressure zones of any type. Low pressure at the surface is associated with rising air, which also produces cooling and cloud formation, making low-pressure patterns quite visible from space. Conversely, wind circulation around high-pressure zones is clockwise in the northern hemisphere but is less visible because high pressure is associated with sinking air, producing clear skies.
The rotation of tropical cyclones and the path of a ball on a merry-go-round can just as well be explained by inertia and the rotation of the system underneath. When non-inertial frames are used, fictitious forces, such as the Coriolis force, must be invented to explain the curved path. There is no identifiable physical source for these fictitious forces. In an inertial frame, inertia explains the path, and no force is found to be without an identifiable source. Either view allows us to describe nature, but a view in an inertial frame is the simplest and truest, in the sense that all forces have real origins and explanations.
Figure 5: (a) The counterclockwise rotation of this northern hemisphere hurricane is a major consequence of the Coriolis force. (credit: NASA) (b) Without the Coriolis force, air would flow straight into a low-pressure zone, such as that found in tropical cyclones. (c) The Coriolis force deflects the winds to the right, producing a counterclockwise rotation. (d) Wind flowing away from a high-pressure zone is also deflected to the right, producing a clockwise rotation. (e) The opposite direction of rotation is produced by the Coriolis force in the southern hemisphere, leading to tropical cyclones. (credit: NASA)
#### Section Summary
• Rotating and accelerated frames of reference are non-inertial.
• Fictitious forces, such as the Coriolis force, are needed to explain motion in such frames.
#### Conceptual Questions
###### Exercise 1
When a toilet is flushed or a sink is drained, the water (and other material) begins to rotate about the drain on the way down. Assuming no initial rotation and a flow initially directly straight toward the drain, explain what causes the rotation and which direction it has in the northern hemisphere. (Note that this is a small effect and in most toilets the rotation is caused by directional water jets.) Would the direction of rotation reverse if water were forced up the drain?
###### Exercise 2
Is there a real force that throws water from clothes during the spin cycle of a washing machine? Explain how the water is removed.
###### Exercise 3
In one amusement park ride, riders enter a large vertical barrel and stand against the wall on its horizontal floor. The barrel is spun up and the floor drops away. Riders feel as if they are pinned to the wall by a force something like the gravitational force. This is a fictitious force sensed and used by the riders to explain events in the rotating frame of reference of the barrel. Explain in an inertial frame of reference (Earth is nearly one) what pins the riders to the wall, and identify all of the real forces acting on them.
###### Exercise 4
Action at a distance, such as is the case for gravity, was once thought to be illogical and therefore untrue. What is the ultimate determinant of the truth in physics, and why was this action ultimately accepted?
###### Exercise 5
Two friends are having a conversation. Anna says a satellite in orbit is in freefall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not 9.80 ${\text{m/s}}^{2}$. Who do you agree with and why?
###### Exercise 6
A non-rotating frame of reference placed at the center of the Sun is very nearly an inertial one. Why is it not exactly an inertial frame? | 2,400 | 11,272 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2018-09 | latest | en | 0.95724 |
https://us.metamath.org/mpeuni/mbfmco.html | 1,718,820,993,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861828.24/warc/CC-MAIN-20240619154358-20240619184358-00688.warc.gz | 541,531,526 | 6,473 | Mathbox for Thierry Arnoux < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > Mathboxes > mbfmco Structured version Visualization version GIF version
Theorem mbfmco 31607
Description: The composition of two measurable functions is measurable. See cnmpt11 22277. (Contributed by Thierry Arnoux, 4-Jun-2017.)
Hypotheses
Ref Expression
mbfmco.1 (𝜑𝑅 ran sigAlgebra)
mbfmco.2 (𝜑𝑆 ran sigAlgebra)
mbfmco.3 (𝜑𝑇 ran sigAlgebra)
mbfmco.4 (𝜑𝐹 ∈ (𝑅MblFnM𝑆))
mbfmco.5 (𝜑𝐺 ∈ (𝑆MblFnM𝑇))
Assertion
Ref Expression
mbfmco (𝜑 → (𝐺𝐹) ∈ (𝑅MblFnM𝑇))
Proof of Theorem mbfmco
Dummy variable 𝑎 is distinct from all other variables.
StepHypRef Expression
1 mbfmco.2 . . . . 5 (𝜑𝑆 ran sigAlgebra)
2 mbfmco.3 . . . . 5 (𝜑𝑇 ran sigAlgebra)
3 mbfmco.5 . . . . 5 (𝜑𝐺 ∈ (𝑆MblFnM𝑇))
41, 2, 3mbfmf 31598 . . . 4 (𝜑𝐺: 𝑆 𝑇)
5 mbfmco.1 . . . . 5 (𝜑𝑅 ran sigAlgebra)
6 mbfmco.4 . . . . 5 (𝜑𝐹 ∈ (𝑅MblFnM𝑆))
75, 1, 6mbfmf 31598 . . . 4 (𝜑𝐹: 𝑅 𝑆)
8 fco 6523 . . . 4 ((𝐺: 𝑆 𝑇𝐹: 𝑅 𝑆) → (𝐺𝐹): 𝑅 𝑇)
94, 7, 8syl2anc 587 . . 3 (𝜑 → (𝐺𝐹): 𝑅 𝑇)
10 unielsiga 31472 . . . . 5 (𝑇 ran sigAlgebra → 𝑇𝑇)
112, 10syl 17 . . . 4 (𝜑 𝑇𝑇)
12 unielsiga 31472 . . . . 5 (𝑅 ran sigAlgebra → 𝑅𝑅)
135, 12syl 17 . . . 4 (𝜑 𝑅𝑅)
1411, 13elmapd 8418 . . 3 (𝜑 → ((𝐺𝐹) ∈ ( 𝑇m 𝑅) ↔ (𝐺𝐹): 𝑅 𝑇))
159, 14mpbird 260 . 2 (𝜑 → (𝐺𝐹) ∈ ( 𝑇m 𝑅))
16 cnvco 5744 . . . . . 6 (𝐺𝐹) = (𝐹𝐺)
1716imaeq1i 5915 . . . . 5 ((𝐺𝐹) “ 𝑎) = ((𝐹𝐺) “ 𝑎)
18 imaco 6093 . . . . 5 ((𝐹𝐺) “ 𝑎) = (𝐹 “ (𝐺𝑎))
1917, 18eqtri 2847 . . . 4 ((𝐺𝐹) “ 𝑎) = (𝐹 “ (𝐺𝑎))
205adantr 484 . . . . 5 ((𝜑𝑎𝑇) → 𝑅 ran sigAlgebra)
211adantr 484 . . . . 5 ((𝜑𝑎𝑇) → 𝑆 ran sigAlgebra)
226adantr 484 . . . . 5 ((𝜑𝑎𝑇) → 𝐹 ∈ (𝑅MblFnM𝑆))
232adantr 484 . . . . . 6 ((𝜑𝑎𝑇) → 𝑇 ran sigAlgebra)
243adantr 484 . . . . . 6 ((𝜑𝑎𝑇) → 𝐺 ∈ (𝑆MblFnM𝑇))
25 simpr 488 . . . . . 6 ((𝜑𝑎𝑇) → 𝑎𝑇)
2621, 23, 24, 25mbfmcnvima 31600 . . . . 5 ((𝜑𝑎𝑇) → (𝐺𝑎) ∈ 𝑆)
2720, 21, 22, 26mbfmcnvima 31600 . . . 4 ((𝜑𝑎𝑇) → (𝐹 “ (𝐺𝑎)) ∈ 𝑅)
2819, 27eqeltrid 2920 . . 3 ((𝜑𝑎𝑇) → ((𝐺𝐹) “ 𝑎) ∈ 𝑅)
2928ralrimiva 3177 . 2 (𝜑 → ∀𝑎𝑇 ((𝐺𝐹) “ 𝑎) ∈ 𝑅)
305, 2ismbfm 31595 . 2 (𝜑 → ((𝐺𝐹) ∈ (𝑅MblFnM𝑇) ↔ ((𝐺𝐹) ∈ ( 𝑇m 𝑅) ∧ ∀𝑎𝑇 ((𝐺𝐹) “ 𝑎) ∈ 𝑅)))
3115, 29, 30mpbir2and 712 1 (𝜑 → (𝐺𝐹) ∈ (𝑅MblFnM𝑇))
Colors of variables: wff setvar class Syntax hints: → wi 4 ∧ wa 399 ∈ wcel 2115 ∀wral 3133 ∪ cuni 4824 ◡ccnv 5542 ran crn 5544 “ cima 5546 ∘ ccom 5547 ⟶wf 6341 (class class class)co 7151 ↑m cmap 8404 sigAlgebracsiga 31452 MblFnMcmbfm 31593 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1912 ax-6 1971 ax-7 2016 ax-8 2117 ax-9 2125 ax-10 2146 ax-11 2162 ax-12 2179 ax-ext 2796 ax-sep 5190 ax-nul 5197 ax-pow 5254 ax-pr 5318 ax-un 7457 This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-fal 1551 df-ex 1782 df-nf 1786 df-sb 2071 df-mo 2624 df-eu 2655 df-clab 2803 df-cleq 2817 df-clel 2896 df-nfc 2964 df-ne 3015 df-ral 3138 df-rex 3139 df-rab 3142 df-v 3482 df-sbc 3759 df-csb 3867 df-dif 3922 df-un 3924 df-in 3926 df-ss 3936 df-nul 4277 df-if 4451 df-pw 4524 df-sn 4551 df-pr 4553 df-op 4557 df-uni 4825 df-iun 4907 df-br 5054 df-opab 5116 df-mpt 5134 df-id 5448 df-xp 5549 df-rel 5550 df-cnv 5551 df-co 5552 df-dm 5553 df-rn 5554 df-res 5555 df-ima 5556 df-iota 6304 df-fun 6347 df-fn 6348 df-f 6349 df-fv 6353 df-ov 7154 df-oprab 7155 df-mpo 7156 df-1st 7686 df-2nd 7687 df-map 8406 df-siga 31453 df-mbfm 31594 This theorem is referenced by: rrvadd 31795 rrvmulc 31796
Copyright terms: Public domain W3C validator | 2,225 | 3,570 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-26 | latest | en | 0.19097 |
https://www.unitconverters.net/pressure/megapascal-to-exapascal.htm | 1,713,678,149,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817729.0/warc/CC-MAIN-20240421040323-20240421070323-00406.warc.gz | 977,308,216 | 3,335 | Home / Pressure Conversion / Convert Megapascal to Exapascal
# Convert Megapascal to Exapascal
Please provide values below to convert megapascal [MPa] to exapascal [EPa], or vice versa.
From: megapascal To: exapascal
### Megapascal to Exapascal Conversion Table
Megapascal [MPa]Exapascal [EPa]
0.01 MPa1.0E-14 EPa
0.1 MPa1.0E-13 EPa
1 MPa1.0E-12 EPa
2 MPa2.0E-12 EPa
3 MPa3.0E-12 EPa
5 MPa5.0E-12 EPa
10 MPa1.0E-11 EPa
20 MPa2.0E-11 EPa
50 MPa5.0E-11 EPa
100 MPa1.0E-10 EPa
1000 MPa1.0E-9 EPa
### How to Convert Megapascal to Exapascal
1 MPa = 1.0E-12 EPa
1 EPa = 1000000000000 MPa
Example: convert 15 MPa to EPa:
15 MPa = 15 × 1.0E-12 EPa = 1.5E-11 EPa | 299 | 662 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-18 | latest | en | 0.356234 |
https://stonespounds.com/157-7-pounds-in-stones-and-pounds | 1,709,326,780,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475701.61/warc/CC-MAIN-20240301193300-20240301223300-00547.warc.gz | 533,413,168 | 4,843 | # 157.7 pounds in stones and pounds
## Result
157.7 pounds equals 11 stones and 3.7 pounds
You can also convert 157.7 pounds to stones.
## Converter
One hundred fifty-seven point seven pounds is equal to eleven stones and three point seven pounds (157.7lbs = 11st 3.7lb). | 77 | 276 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2024-10 | latest | en | 0.830683 |
https://www.physics.uoguelph.ca/problem-8-75-inelastic-collision-part-8-c | 1,653,383,641,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00704.warc.gz | 1,080,114,239 | 12,506 | # Problem 8-75 Inelastic collision - Part 8 - C
Two trucks have a completely inelastic collision. After the collision, they have a common velocity of $11 \;m/s$ at $35^\circ$ south of west. Before the collision, one truck $(\text{mass} \; 2.3\times10^4\; kg)$ has a velocity of $15\; m/s$ at $51^\circ$ south of west. Determine the initial velocity (magnitude and direction) of the other truck $(\text{mass} \; 1.2\times10^4\; kg).$
Accumulated Solution
$v_{1x} = (-15) \cos 51 \\ v_{2x} = v_2 \cos \theta \\ v_x{'} = (-11) \cos 35 \\ m_1v_{1x} + m_2v_{2x} = (m_1 + m_2)v_x{'} \\ v_{2x} = -8.2\; m/s \\ v_{1y} = (-15) \sin 51 \\ v_{2y} = v_2 \cos \theta \\ v_y{'} = (-11) \sin 35 \\ v_{2y} = 3.9 \;m/s\\ v_2 = 9.1\; m/s$
Correct. The original choice of direction for $v_2$ in the figure (up and to the right) was incorrect but it doesn't matter for we now know it is up $(v_y +)$ to the left $(v_x -)$ as in this figure:
The value of $\theta$ is given by:
(A) $\theta = \tan^{-1}3.9/8.2$
(B) $\theta = \sin^{-1}3.9/9.1$
(C) $\theta = \cos^{-1}8.2/9.1$ | 419 | 1,065 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2022-21 | latest | en | 0.775566 |
https://dyscalculiaservices.com/?p=45 | 1,544,958,928,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376827639.67/warc/CC-MAIN-20181216095437-20181216121437-00417.warc.gz | 579,045,046 | 15,059 | Understanding Fractions
Introducing fractions in the traditional abstract way (a/b) has the risk that the concept is not connected with your child’s previous daily life experiences. The new concept is ‘hanging loose’ and it will be almost impossible to access and apply it later on.
If this sounds like what is happening with your child: read on, there is a simple cure:
Like with many other mathematical concepts, we overlook that most children already have a basic idea about fractions. Storybooks tell about dividing treasures and kids see things being dived at the kitchen table and in school all the time, so they have formed an understanding in their mind about what dividing something into fractions is.
This is a valuable developmental step and a child feels really proud when we acknowledge that her understanding of how you can share and divide things into smaller parts is important.
The boxed conversation starters do not put the child on the spot and do not add to the usual math anxiety. Your child’s answer shows us the key to the preferred type of examples, that will help your child link the new knowledge to what she has already anchored in her long term memory. It tells you how to guide your child to the proverbial door knob that will open the door to deeper understanding and successful application of the fractions concept in different types of questions.
How to use the Fractions Booklet
What does it mean to share? How do we use fractions in our daily lives? Asking questions makes learning interactive and fun. Time and again it is proven that engaging in a conversation or an activity is the most effective way to learn!
Title: My Fractions Book
1. Do you know family and friends to share with?
2. What are things you can share? What is the name for a part or fraction?
3. How can you divide something to share it?
4. How do you know you divide evenly so you have equal parts? What is a fraction?
5. How do you know how big your part is?
6. How do you tell somebody else what her part is?
7. What are ways to divide a round item, like a pizza?
8. What are ways to divide a rectangular item, like a chocolate bar
The boxed suggestions are communication starters. Be sure to ask questions on the go like: what is the best example and how would you say that? Use these examples and wording wherever you can.
The answers to these questions give you insight in your child’s thinking and progress so you can give as many specific compliments as possible and you can help exactly where needed. The written answers or drawings will show your child’s understanding. If you see a glitch, do not rush through the book thinking that it will magically ‘click’ later on, but take the time to ask more guiding questions and redo difficult pages before going on. When completed, staple the book together with a nice cover as a keep sake. Give ample praise. | 588 | 2,878 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2018-51 | longest | en | 0.946042 |
https://math.stackexchange.com/questions/2459897/moving-from-one-coupling-to-another | 1,718,222,266,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861183.54/warc/CC-MAIN-20240612171727-20240612201727-00382.warc.gz | 337,215,263 | 35,851 | # Moving from one Coupling to another
Let $X,Y$ be two discrete random variables. Two joint mass distributions (couplings) with marginals $X$ and $Y$ and with entries $p_{i,j}=\mathbb{P}_1(X=i,Y=j)$ and $p_{i,j}'=\mathbb{P}_2({X=i,Y=j})$ correspond to two matrices $(p_{i,j}), (p_{i,j}').$
Is there a linear transformation that maps $(p_{i,j})\mapsto(p_{i,j}')$?
If not, is there a way to move from a given coupling of $X,Y$ to any other coupling of $X,Y$?
The reason I ask is because I have a coupling of $X,Y$ and I wonder if a specific coupling exists. If there are any results that allow us to go from a given coupling to any other coupling, perhaps this can be used to provide the desired coupling or show that it doesn't exist.
There is no linear transformation in general. Let $p_{i,j}=1/4$ for each $1\le i,j\le 2$ and $p'_{i,j}=1/2$ if $i=j$, 0 otherwise. Then we would need a matrix $A$ with $$\frac14 A \begin{bmatrix}1&1\\1&1\end{bmatrix}=\frac12\begin{bmatrix}1&0\\0&1\end{bmatrix}$$ But the rank of the product of two matrices is $\le$ the minimum of the ranks, so this is impossible.
• @TheSubstitute Actually assuming the distributions are not degenerate, i.e., the matrices have full rank, then you can do it with a linear transformation. Just multiply both sides by the inverse of a matrix to find $A$. Commented Oct 10, 2017 at 22:16 | 407 | 1,357 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2024-26 | latest | en | 0.824625 |
https://www.civilconcept.com/how-to-calculate-cutting-length-in-bar-bending-schedule/?print=print | 1,618,156,183,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00350.warc.gz | 827,608,091 | 5,531 | # How to calculate cutting length in bar bending schedule? -Numerical
In this article, I am going to explain how to calculate cutting length in bar bending schedule for steel of different types of structure.
Bar Bending of steel is an estimation of the cutting of steel. I have summarised in the previous article. If you have not read, then read here.
## Steps involved in finding the cutting length
1. First of writing the dimension of the structure.
2. Note down the diameter of steel bars for which cutting length is to be calculated.
3. Now, deduct the concrete cover or clear cover to get the actual length of perimeter bars.
4. Calculate the length of the hook of the bars.
5. Calculate the bend length of steel bars.
6. Add step 3 and 4 and subtract step 5 from it.
7. It will gives you total cutting length of steel bars.
## General Formula to calculate cutting length of any steel bars:
Cutting Length of bars = Perimeter of Shape + Total hook length – Total Bend Length
## Standards value of Bends & Hooks used in construction
• 1 Hook length = 9d or 75mm
• 45° Bend length = 1d
• 90° Bend length = 2d
• 135° Bend length = 3d
Remember, d = Diameter of Bar
## 1) Cutting length of the main bar with hook
Circled part is known as Hook whose length is 9d.
Length of hook = 9d, where d is the diameter
Cutting length = A + 2 x (9d – 2 x 2d) = 7d
2d is subtracted to for bending of a steel rod at 90°. There are two bends in one hook length so, multiply it by two.
On-Site
## 2) Cutting length of the main bar with bend:
Length of hooks varies from = 10d to 16d, where d = diameter
Length of main bar = L + 12d + 12d – length of bends
(Taking hook length = 12d)
On-Site
## 3) Cutting length of a crank or bent up bar:
Calculating for cutting length of the bar
Clear span + crank length + Development L – (1d x No. of bends) – (2d x No. of bends)
Clear span + (2 x 0.42 x h) + (2 x Ld) – (1d x No. of bends) – (2d x No. of bends)
Depth of bar crank
h= Slab thickness – (2 x clear cover) – d
45 Bend = 1d
90 Bend = 2d
On-Site
## 4) Cutting length for Rectangular Stirrups or Ties:-
On-Site
Rectangular column or rectangular beams are generally used in construction. So, we need to calculate mostly the cutting length of rectangular stirrups.
Numerical Example,
Find the cutting length of the rectangular tie having diameter 8 mm and column having size 230mm x 450mm and clear cover 40 mm.
Given,
Diameter of ties/stirrups = 8 mm
Clear Cover = 40 mm
Dimension of column = 450 mm x 230 mm
Formula,
(L) = Total Cutting length of Rectangular Stirrup = Perimeter of Rectangular Stirrup + Total Hook length – Total Bend Length
Step:-1
Perimeter of Rectangular stirrups (P) = 2a +2b
Where, a = A – Clear Cover – Clear Cover = 230 – 20 – 20 = 190 mm
b = B – Clear Cover – Clear Cover = 450 – 20 – 20 = 410 mm
Therefore,
(P) = 2a +2b
(P) = 2 x 190 +2 x 410 = 1200 mm
Step:- 2
Total Hook length = 9d+9d = 18 d = 18 x 8 = 144 mm (Because there is two hooks and length of one hook is 9d, where d is diameter of stirrups.)
Step:-3
Total Bend Length = (3 x 900 Bend length + 2 x 1350 Bend length)
= 3 x 2d + 2 x 3d
= 12d
= 12 x 8
= 96mm
(Because there are three bends of 900 and two bends of 1350)
Step:-4
Hence Put all the value in above formula we get,
(L) = Total Cutting length of Rectangular Stirrup = Perimeter of Rectangular Stirrup + Total Hook length – Total Bend Length
(L) = 1200 mm + 144 mm – 96mm
(L) = 1448 mm
Hence the total cutting length of rectangular stirrups or ties is 14.48 cm or 0.1448 meter.
## 5) Cutting length of triangular stirrups:
Formula,
Total Cutting length of Triangular Stirrup = Perimeter of Triangle + Total Hook length – Total Bend Length
Q) Find the cutting length of triangular stirrups having diameter 8 mm and dimension of column (400 x 450) mm with clear cover 25 mm.
Given,
Dimension of Column = 450mm x 400mm
Diameter of stirrups = 8 mm
Clear Cover = 25 mm
Now,
X = 450-20-20 = 410mm
Y = 400-20-20 = 360mm
From Pythagorean theorem,
Formula,
Total Cutting length of Triangular Stirrup = Perimeter of Triangle + Total Hook length – Total Bend Length
Step:- 1
Perimeter of Triangular stirrups = H + H + X = 414.27 mm + 414.27 mm + 410mm
P = 1238.54 mm
Step: – 2
Total Length of the hooks: 9d +9d = 18d = 18 x 8 = 144 mm
Since, there are two hooks of 9d.
Step:-3
Total length of Bends = 4 x 3d = 12d= 12 x 8 = 96mm
Since, there are 4 bends which are bent at an angle of 1350
Step: – 4
Use formula,
Total Cutting length of Triangular Stirrup (L) = Perimeter of Triangle + Total Hook length – Total Bend Length
(L) = 1238.54 mm + 144 mm96mm
(L) = 1286.54 mm
Hence the total cutting length of rectangular stirrups = 1286.54 mm = 128.65 cm or 1.286 meter.
On-Site
## 6) Cutting Length for Circular Stirrup:
Find the cutting length of circular stirrups having diameter 8 mm and dimension of column is 1000 mm with clear cover 25 mm.
Given,
Diameter of Column = 1000 mm
Diameter of stirrups (d) = 8 mm
Clear Cover (C/C) = 25 mm
Formula,
Total Cutting length of Circular Stirrup or Ring (L) = Circumference of Circular Stirrup + Total Hook length – Total Bend Length
Step:-1
Circumference of Circular Stirrup = πD
But,
D is the diameter of the stirrups ring not the column.
To calculate the diameter of circular stirrups we have to subtract he clear cover from the diameter of the column.
So, D = Diameter of column – clear cover of left side – clear cover of right side.
i.e D = 1000 – 25 – 25 = 950 mm
Now,
Circumference of Circular Stirrup = πD
= 3.14 x 950
= 2983 mm
Step:-2
Total Length of the hook = 9d+9d= 18d = 18 x 8 = 144 mm
Where d is diameter of stirrups.
Since, There are two hooks and length of one hooks is 9d.
Step:- 3
Total Length of Bends: = = 2 x 3d = 6d= 6 x 8 = 48mm
Since, There are 2 bends which are bent at an angle of 1350
Length of one bends at 1350 is 3d.
Step:- 4
Use the formula,
Total Cutting length of Circular Stirrup or Ring (L) = Circumference of Circular Stirrup + Total Hook length – Total Bend Length
(L) = 2983 mm + 144 mm – 48mm
= 3079 mm 0r, 307.9 cm or 3.079 meter
## 7) Cutting length of diamond stirrups:
Q) Find the cutting length of diamond stirrups having diameter 8 mm and dimension of column 400mm x 400mm with clear cover 20 mm.
Given,
The dimension of Column = 400m x 400m
The diameter of diamond stirrups = 8 mm
Clear cover = 20 mm
Now,
X = 400 – Clear Cover – Clear cover = 400-20-20 = 360mm
Y = 400 – Clear Cover – Clear cover = 400-20-20 =360mm
Now,
Formula,
Total Cutting length of Diamond Stirrup = Perimeter of Diamond shape + Total Hook length – Total Bend Length
Step:- 1
Perimeter of Diamond shape = 4 x H = 4 x 254.5 = 1016 mm
Step:- 2
Total Hook length = 9d +9d = 18d = 18 x 8 =144 mm
Since, There are two hooks of length 9d.
Step :-3
Total Bend Length = 3 x 900 Bend length + 2 x 1350 Bend length= 3 x 2d + 2 x 3d = 12d = 12 x 8 = 96mm
Since, There are 3 bends which are bent at an angle of 90 and 2 bends which are bent at an angle of 1350
Step:-4
Use Formula,
Total Cutting length of Diamond Stirrup(L) = Perimeter of Diamond shape + Total Hook length – Total Bend Length
(L) = 1016 mm + 144 mm + 96mm
(L) = 1256 mm
Hence, Total cutting length of diamond stirrups is 1256 mm = 125.6 cm or 1.256 meter.
On-Site
## 8) Cutting length of spiral or helix stirrups:
Q) Calculate the total length of spirals having diameter of spiral bars 8mm and length of the pile 20 m, Pitch or spacing for the spiral bar is 200mm and diameter of the pile is 1m; assume clear cover is 50mm for pile?
Given,
Diameter of pile = 1 meter = 1000mm
Pitch or spacing of spiral bar = 200mm
Length of pile = 20m
Diameter of spiral bar = 8 mm
Clear cover = 50mm
We have,
Diameter of Spiral ring = Diameter of pile – Clear cover – Clear cover = 1000 – 50 – 50 = 900 mm
Formula,
Total Cutting length of spiral bar = Length of the spiral bar + Total length of laps
Step:- 1
Calculate Total length of the spiral bar = no of Spirals x Length of one spiral ring
But,
Length of one spiral ring = = 3.41 x 900 mm = 3069 mm (Where D is Diameter of Spiral.)
Now, Using formula,
Total length of the spiral bar (L) = N.o of Spirals x Length of one spiral ring
= 101 x 3069
= 309969 mm
Step:-2
Total length of laps = Numbers of laps required x Length of one Lap
Here,
Numbers of laps required = Total length of spirals x
= 309969 mm x = 25.8
25.8 say 26 nos.
Also,
Length of one Lap = 50 D = 50 x 8 = 400 mm (Assume)
Now,
Total length of laps = Numbers of laps required x Length of one Lap
Total length of laps = 26 x 400 = 10400 mm
Hence,
Using Formula,
Total Cutting length of spiral bar (Lc) = Length of the spiral bar + Total length of laps
(Lc) = 309969 mm + 10400 mm
(Lc) = 320369 mm
Hence, the total cutting length of Spiral stirrups is 320369 mm = 32036.9 cm or 320.369 meter.
On-Site
## 9) Cutting length of chair bar
Cutting length of chair bar = 2A + 2D +B – (4 x 90 Bend Length)
Where, A = (2 x spacing) + 50 , and B = 50d
D = Footing height – [(Upper + Lower CC) + ( Upper side main & dist bar dia + Lower side main bar dia)]
On-Site
Hence in this way we can calculate cutting length of steel in bar bending schedule.
I hope this article on “how to calculate cutting length in bar bending schedule” remains helpful for you.
Happy Learning – Civil Concept
Contributed by,
Civil Engineer – Ranjeet Sahani | 2,902 | 9,467 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2021-17 | latest | en | 0.881834 |
http://mathhelpforum.com/geometry/151345-solidmensuration-print.html | 1,526,825,344,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863570.21/warc/CC-MAIN-20180520131723-20180520151723-00555.warc.gz | 178,650,817 | 3,270 | # SolidMensuration
• Jul 19th 2010, 05:11 AM
cutiemike1
SolidMensuration
Questions from Kern and Bland pp8 #'s 17,19,21
http://i104.photobucket.com/albums/m...ike1/num17.jpg
19. The base of an isosceles triangle is 16 in. and the altitude is 15 in. Find the radius of the inscribed circle.
http://i104.photobucket.com/albums/m...ike1/num21.jpg
in #17 about the race track i can't read clearly the value of SC = ..... maybe perhaps it is too old copy.. ^^
• Jul 19th 2010, 06:50 AM
Wilmer
What are you asking for? Full solutions? How far did you get?
On the 1/4 mile track: did you calculate that the semi-circles each have length of 345,
calculated this way : (5280/4 - 630) / 2 ?
Did you do some "searching", like Googling "inscribed circle of isosceles triangle" ?
• Jul 19th 2010, 03:31 PM
cutiemike1
Quote:
Originally Posted by Wilmer
What are you asking for? Full solutions? How far did you get?
On the 1/4 mile track: did you calculate that the semi-circles each have length of 345,
calculated this way : (5280/4 - 630) / 2 ?
Did you do some "searching", like Googling "inscribed circle of isosceles triangle" ?
#17..Where did you get this formula?? And how? I can't still figure it out.But I know that the race track which is equal to 1mile should be divide in order to get a quarter mile..
#19..I did some research and this is what i found out..
r = 2*(area of triangle) / (a+b+c)
= 2 * [0.5 * 4 * √(3^2 - (4/2)^2)] / (3+3+4)
= 2 * 2√5 / 10
= 2 / √5
Now my questions is..how did it come up with that kind of formula in "r".??
#21..It's hard.. I tried to use trigonometric functions.. T_T
• Jul 19th 2010, 04:21 PM
Wilmer
Quote:
Originally Posted by cutiemike1
....But I know that the race track which is equal to 1mile...
WHERE did you get 1 mile? Problem clearly states 1/4 mile.
• Jul 19th 2010, 04:26 PM
cutiemike1
oh yeah! i'm sorry... | 612 | 1,864 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2018-22 | latest | en | 0.915635 |
https://math.stackexchange.com/questions/3198375/matrix-and-vectors-find-3-vectors | 1,558,927,821,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232260658.98/warc/CC-MAIN-20190527025527-20190527051527-00093.warc.gz | 538,387,797 | 32,718 | # Matrix and vectors (Find 3 Vectors)
I am having a bad time with this matrix and vector situation, and I think the solution is kind a trick in some part of the computation, but I don't know how to find this:
Find 3 vectors (different than Zero), $$\vec{x},\vec{y},\vec{b} \in \mathbb{R}^3$$, where $$A\vec{x}=\vec{b}$$ and $$B\vec{y}=\vec{b}$$ $$A =\begin{bmatrix} 0 && 1 && 2\\ 1 && 1 && 1\\ 2 && 1 && 0 \end{bmatrix}$$ $$B =\begin{bmatrix} 1 && -1 && 0\\ 0 && 0 && 1\\ 1 && 1 && 0 \end{bmatrix}$$
Basically, what I have done, is multiplying the matrices by a vector $$\vec{X} = (X_1, X_2, X_3)$$ and the other matrix by a vector $$\vec{Y} = (Y_1, Y_2, Y_3)$$.
Then, as I am multiplying a matrix $$(3 \times 3)$$ with a vector $$(3 \times 1)$$, my result is a new vector $$(3 \times 1)$$.
But then, I don't know what to do next, can someone help me with a kind advice on this?
• This is easy. You can take $x=y=b=(0,0,0)$. – Dietrich Burde Apr 23 at 15:13
• Thank you @DietrichBurde, I forgot to mention that should be different than Zero. – jguzmaje Apr 23 at 15:38
• The only thing that I can think of is to let $$\vec{x} = \begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$$ Do the same for $\vec{y}$. Since $A\vec{x} = \vec{b}$ and $B\vec{y} = \vec{b}$, we have that $A\vec{x} = B\vec{y}$. Doing the expansion will yield three equations with six unknowns. Not solvable. The only other thing I could think of would be to find $A^{-1}$ and $B^{-1}$ because you have equations $\vec{x} = A^{-1}B\vec{y}$ and $\vec{y} = B^{-1}A\vec{x}$. This may just give you the same three equations... – JacobCheverie Apr 23 at 15:41
• No “tricks” necessary, but a solid understanding of the properties of systems of linear equations helps make this much easier. – amd Apr 23 at 19:19
I would start by looking for candidates for $$\vec b$$. For the equation $$A\vec x=\vec b$$ to have any solution at all, $$\vec b$$ must lie in $$A$$’s column space, and likewise it must also lie in $$B$$’s column space. $$B$$’s column space is clearly all of $$\mathbb R^3$$, but the columns of $$A$$ are linearly dependent (the sum of the outer columns is twice the central column). So, pick any convenient-looking multiple of any column of $$A$$ (or a convenient-looking linear combination of them) as $$\vec b$$ and then solve the two equations for $$\vec x$$ and $$\vec y$$. For any particular choice of $$\vec b$$, there’s a degree of freedom in the choice of a corresponding $$\vec x$$, but if you construct $$\vec b$$ as I suggest you should be able to write down a value for $$\vec x$$ without doing any more work. (Hint: interpret the product $$A\vec x$$ as a linear combination of the columns of $$A$$.) | 882 | 2,690 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2019-22 | latest | en | 0.821537 |
http://fuelzilla.com/sun-heat/Re-Quick-built-shelter-3994-.htm | 1,623,658,085,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487611641.26/warc/CC-MAIN-20210614074543-20210614104543-00411.warc.gz | 20,068,242 | 9,839 | # Re: Quick built shelter?
Posted by nicksanspam on October 26, 2005, 8:06 am
Omaha, where 540 Btu/ft^2 of sun falls on the ground and 990 falls on
a south wall on an average 24.4 F December day with a 32.9 daily max?
How about a plastic film greenhouse?
Three people can put up a \$00 14'x96' greenhouse kit in a field in a day.
A 20'x24' ID greenhouse might have 7 \$0 20'-diameter semi-circular bows
on 4' centers, each using 8 8' 1x3s. Screw 1x3 spacer blocks every 2' to 4,
bend them to a 10' radius, bend 4 more and screw them onto the blocks to
make a curved sandwich, add 3 24' 1x3 purlins between the bows, cover them
with a \$8 24'x32' piece of 4-year UV greenhouse polyethylene film, and add
endwall framing on 4' centers with another 314 ft^2 (\$6) of poly film.
Then add another greenhouse around it, 1' larger, and fill the space between
them with R36 bags of mulch, dry leaves, etc, with a few voids for windows.
If 0.9x24x(540x5.5+990x9.5) = 268K Btu of sun enters the lower third of the
south wall over 6 hours on an average December day and 6h(T-24)276ft^2/R1
leaves it during the day and 18h(65-24)276/36 leaves it at night and
24(T-24)276/36 leaves the ceiling and 24(65-24)276/36 leaves the north wall
and 24(65-24)314/36 leaves the endwalls, T = 159 F inside the south wall
and near the ceiling during the day :-) Well, maybe 130, given windows and
radiation loss from the south wall.
If C Btu/F of ceiling mass is 130 F on an average day and cools to 75 over
5 24 F cloudy days while providing 5x24(65-24)1082/36 = 148K Btu of heat,
C = 148K/(130-75) = 2689, eg 2689/62 = 43 ft^3 of water in 2 \$2 20'x30"
poly film ducts laid flat 4' wide with 3" of water inside, over foil (to
avoid overheating the space below) over wire fence under the ceiling.
Solar heat, and poly film "windows," and a few PV panels and CFs...
The propane stove, and gravity fed hot water? The 130 F ceiling water might
help distill wastewater in a duct with holes near the top surrounding the
inner duct, with another duct around that to condense it and no loss of heat
to the outdoors.
And solid walls and doorlocks, vs mad dogs and a chain link/razor-wire fence.
Nick
Posted by Larry Caldwell on October 26, 2005, 3:39 pm
nicksans...@ece.villanova.edu wrote:
Gee, a whole other chapter to Three Little Pigs.
Posted by nicksanspam on October 26, 2005, 9:07 pm
Karl, Dick and Scooter?
Nick
Posted by Larry Caldwell on October 27, 2005, 3:41 pm
nicksans...@ece.villanova.edu
Dumb, Dumber, and Total Idiot.
But then, if you want to bet on no wind storms in the winter in the
Midwest, put your money down, bub.
Posted by The Smolenski's on October 26, 2005, 11:25 pm
How about a large 12foot high x 20 feet x60 feet plastic sheeted space with
with a series of smaller plastic sheeted spaces within. I live by lake
michigan and saw a family at a beachfront campground with a huge
tarp(30'x30') set up for shade and 4 small tents set up under. the tents
were the sleeping spaces and the area left over was this large covered
living space. It was quite spacious and looked more inviting than the big
buck motorhomes parked nearby.
the whole idea is to have this large encompassing envelope sheltering a
series of smaller envelopes
when the sun is out the outer areas are liveable space
or something that can be temporarily heated when entertaining. for private
times you can head into one of the smaller structures some might be covered
with green tarp material for sleeping others might be black tarp togive
ultimate privacy like fior a bathroom
the secret would to have a nice cheap plywood lfloor for the whole space you
might want to lay an insulating layer of straw under the ply floor
smo
smo
<
•
• Subject
• Author
• Date
Re: Quick built shelter? Larry Caldwell 10-26-2005
Re: Quick built shelter? nicksanspam 10-26-2005
Re: Quick built shelter? Larry Caldwell 10-27-2005
Re: Quick built shelter? The Smolenski's 10-26-2005
Re: Quick built shelter? Katherine 10-27-2005
Re: Quick built shelter? Larry Caldwell 10-27-2005
Re: Quick built shelter? Bob Morrison 10-27-2005
Re: Quick built shelter? Larry Caldwell 10-28-2005
Re: Quick built shelter? ms_peacock 10-28-2005
Re: Quick built shelter? Larry Caldwell 10-29-2005
Re: Quick built shelter? ms_peacock 10-30-2005
Re: Quick built shelter? Susan \(Cobbers... 10-29-2005 | 1,325 | 4,364 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2021-25 | latest | en | 0.932427 |
http://www.physicsforums.com/showthread.php?t=197250 | 1,394,452,271,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394010776091/warc/CC-MAIN-20140305091256-00026-ip-10-183-142-35.ec2.internal.warc.gz | 475,296,988 | 7,738 | # How to Find E°cell Values
by salman213
Tags: e°cell, values
P: 303 I needed to find the E°cell (always positive for a galvanic cell), based on the following (unbalanced) reaction: IO3-(aq) + Fe2+(aq) --> Fe3+(aq) + I2(s) So E°cell = Ecathode - Eanode I made the half reactions Fe3+ (aq) ---> Fe2+(aq) EĜ = +0.77 V (i found this reaction in my table) IO3-(aq) ---> I2(s) balanced the 2nd one to 12 H + 2IO3 + 5e- ---> I2 + 6H2O EĜ = I cannot find this value in that table I FOUND IT ONLINE ON A WEBSITE TO BE EĜ = +1.19V, HOW DID THEY GET THIS VALUE! Anyone know?
P: 1,504
Quote by salman213 I needed to find the E°cell (always positive for a galvanic cell), based on the following (unbalanced) reaction: IO3-(aq) + Fe2+(aq) --> Fe3+(aq) + I2(s) So E°cell = Ecathode - Eanode I made the half reactions Fe3+ (aq) ---> Fe2+(aq) EØ = +0.77 V (i found this reaction in my table) IO3-(aq) ---> I2(s) balanced the 2nd one to 12 H + 2IO3 + 5e- ---> I2 + 6H2O EØ = I cannot find this value in that table I FOUND IT ONLINE ON A WEBSITE TO BE EØ = +1.19V, HOW DID THEY GET THIS VALUE! Anyone know?
2IO3-(aq) + 10Fe2+(aq) + 12H+ --> 10Fe3+(aq) + I2(s) + 6H2O;
E° = +1.19 - 0.77 = +0.42V.
(1) 2IO3-(aq) + 12 H+ + 10e- ---> I2(s) + 6H2O
You can find its E° if you know the E° of other similar reactions from which you can get that one, for example:
(2) IO3-(aq) + 6H+ +6e- --> I- + 3H2O;_______>E°(2) = +1.08V
(3) I2(s) + 2e- --> 2I- ;____________________>E°(3) = +0.53V
Reaction (1) is given by: 2*Reaction(2) - Reaction(3) and so:
Delta G°(1) = 2*Delta G°(2) - Delta G°(3)
Now you use the equation: Delta G° = -nF*Delta E° where n is the number of electrons of the reaction, so you have:
-10F*Delta E°(1) = 2*[-6F*Delta E°(2)] - [-2F*Delta E°(3)]
10*Delta E°(1) = 12*Delta E°(2) - 2*Delta E°(3)
Delta E°(1) = (1/10)[12*Delta E°(2) - 2*Delta E°(3)] =
= (1/5)[6*Delta E°(2) - Delta E°(3)] =
= (1/5)[6*1.08 - 0.53] = +1.19V.
P: 303 wowi would never have that of that...:S how is the delta G of the first equation equal to the delta G if the second and third with those operations. Like how do we know to relate delta G?
P: 1,504
## How to Find E°cell Values
Quote by salman213 wowi would never have that of that...:S how is the delta G of the first equation equal to the delta G if the second and third with those operations. Like how do we know to relate delta G?
Do you agree on the fact that Reaction (1) is given by 2*Reaction(2) - Reaction(3) ?
2*Reaction(2) = 2IO3-(aq) + 12H+ +12e- --> 2I- + 6H2O
- Reaction(3) = 2I- --> I2(s) + 2e-
Now you sum them:
2IO3-(aq) + 12H+ +12e- + 2I- --> 2I- + 6H2O + I2(s) + 2e-
you simplify canceling 2I- and 2e- on both members:
2IO3-(aq) + 12H+ +10e- --> 6H2O + I2(s).
About summing ΔG: if you have
(1) A --> B you know that ΔG(1) = G(B) - G(A)
(2) C --> D you know that ΔG(2) = G(D) - G(C)
(3) A + C --> B + D you know that ΔG(3) = G(B + D) - G(A + C)
But G(B + D) - G(A + C) = G(B) + G(D) - G(A) - G(C) =
= G(B) - G(A) + G(D) - G(C) = ΔG(1) + ΔG(2)
Related Discussions Precalculus Mathematics Homework 3 Biology, Chemistry & Other Homework 4 Precalculus Mathematics Homework 6 Introductory Physics Homework 11 Introductory Physics Homework 8 | 1,263 | 3,202 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2014-10 | longest | en | 0.733413 |
https://square-root.net/6-squared | 1,695,663,021,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233509023.57/warc/CC-MAIN-20230925151539-20230925181539-00226.warc.gz | 584,677,670 | 27,964 | Home » Squared Numbers » 6 Squared
# 6 Squared
6 squared, (6)2, is the number you get when multiplying 6 times 6.
It can also be looked at as exponentiation involving the base 6 and the exponent 2.
The term is usually pronounced six times six or six squared.
The square of 6 is a perfect square because the number is the product of the two equal integers 6.
It can be written as 6 × 6 or in exponential form.
Read on to learn everything about the number six squared, including useful identities.
## Calculator
±
Reset
(6)2 = 36
6 × 6 = 36
The inverse operation of squaring six is extracting the square root of 6, explained here.
In the next section we elaborate on what is 6 squared and there you can also find our calculator.
## What is 6 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 6 has an area of 36.
6 squared equals the sum of the first 6 odd numbers:
In addition, the number can be calculated from 5 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(6)2 = 52 + 5 + 6 = 52 + 11 = 36
It can be also be computed from 5 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(6)2 = 2 x 52 – 42 + 2 = 2 x 25 – 16 + 2 = 36
The difference between the perfect square of 6 and its predecessor, 5, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 6 – 1 = 11 = (6)2 – 52 = 36 – 25 = 11
6 is even, and the square numbers of even numbers are also even: (2n)2 = 4n2.
Squares of even numbers like 6 are divisible by 4 for
= n2.
If you want to calculate the square of any number, not only integers like 6, you can use our calculator above.
Enter your number; nothing else to be done.
A square similar to 6 is, for example: square of 8.
Click on the question which is of interest to you to see the collapsible content answer.
### What is the Square of 6?
The square of 6 is 36.
### How do you Write 6 Squared?
6 squared can be written as (6)2 (a small 2 is placed to the top right of 6) or 6^2.
### Is There a Square Root of 6?
Yes, the square roots of 6 are ±2.4494897428.
### What is the Perfect Square of 6?
The perfect square of 6 is 6 × 6 = 36.
### How Do You Square 6?
You square 6 by multiplying 6 by itself.
### Is 6 a Square Number?
No, 6 is the square of the irrational number 2.4494897428.
### What is the Square of Negative 6?
The square of negative 6 is 36.
If something remains unclear do not hesitate getting in touch with us.
We are constantly trying to improve our site, and truly appreciate your feedback.
The following table contains the squares of numbers close to 6.
NumberSquare
11
24
39
416
525
636
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## Six Squared
By reading so far you know all about squaring the number 6 and calculating it using recursive methods, or as sum, product or by exponentiation.
6 squared is equivalent to 36.
If you were searching for what is 6 squared in math or if you typed whats 6 squared in the search engine you now have all the answers, too.
The same goes for searches like square6, and 6 to the 2nd power, just to name a few more examples people are often looking for.
Note that you can also find many perfect squares including 6 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
## Conclusion
To sum up,
6 squared = 6 × 6 = (6)2 = 36.
The exponentiation form is mostly used to denote six squared.
If this article about the square of 6 has been of help to you then please share it by means of the social buttons. | 1,020 | 3,572 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2023-40 | longest | en | 0.935712 |
https://web2.0calc.com/questions/help-please_12671 | 1,591,405,393,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348509264.96/warc/CC-MAIN-20200606000537-20200606030537-00229.warc.gz | 596,076,134 | 6,297 | +0
0
130
5
Given an obtuse triangle $ABC$ with $\angle ABC$ obtuse, extend $\overline{AB}$ past $B$ to a point $D$ such that $\overline{CD}$ is perpendicular to $\overline{AB}$. Let $F$ be the point on line segment $\overline{AC}$ such that $\overline{BF}$ is perpendicular to $\overline{AB}$, and extend $\overline{BF}$ past $F$ to a point $E$ such that $\overline{BE}$ is perpendicular to $\overline{CE}$. Given that $\angle ECF = \angle BCD$, show that $\triangle ABC \sim \triangle BFC$.
Apr 26, 2020
#1
+633
+1
Hello! Does https://www.duolingo.com/ offer courses in taking the effort to read the "Unwrapped LaTeX" language? I am willing to pay a fortune!
Apr 27, 2020
#2
+109527
0
AELN is being sarcastic.
I Just thought I would point that out since it will go over the top of guests head,
Apr 27, 2020 | 263 | 816 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2020-24 | longest | en | 0.763687 |
http://fitness.stackexchange.com/questions/2764/how-are-calories-calculated-in-food?answertab=votes | 1,462,410,892,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860125750.3/warc/CC-MAIN-20160428161525-00032-ip-10-239-7-51.ec2.internal.warc.gz | 105,948,686 | 15,907 | # How are calories calculated in food [closed]
How are calories calculated in food?
Do they sum all the energy in every molecule? By for example, by burning the stuff up and calculating the energy output.
Or is this value supposed to represent the energy that a human body will extract from that food?
Or do they only sum up the elements that we are supposed to digest (Protein, Carbs, Fat) ?
For example, wood contains a lot of energy. We can see that by burning it. But the human body is not able to break done the fibers to extract the enery from wood. We do not eat wood but I suppose there are multiple elements contained in food that we do not digest but that contain energy.
Also, Fat contains a lot of energy compared to carbs or proteins but the human body has a much more difficult time to process fat and extract energy from it (catabolism).
Is it the energy outputed from the catabolism of fat that is calculated or again the theoretical quantity energy in fat (burning it).
-
## closed as off topic by Baarn, Matt Chan♦Dec 10 '12 at 4:45
Questions on Physical Fitness Stack Exchange are expected to relate to physical fitness within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.
wikipedia has your answer here: en.wikipedia.org/wiki/Food_energy – michael Jul 6 '11 at 18:48
This question is no longer on topic here, since the FAQ changed. – Baarn Dec 9 '12 at 20:22
What exactly:
The number of calories in a food is a measure of how much potential energy that food has.
How to find out:
A particular food item will be ignited, the [...] calorimeter will trap the heat of the burning food, and the water above will absorb the heat, and cause the temperature (T) of the water to increase. By measuring the change in temperature (ΔT) of a known volume of water, students will be able to calculate the amount of energy in the food tested because the heat gained by the water will equal the heat lost by the food item.
• Do they sum all the energy in every molecule? By for example, by burning the stuff up and calculating the energy output.
Yes, they BURN it when finding laboratory measurements.
-
[en.wikipedia.org/wiki/Food_energy] disagrees."The amount of food energy associated with a particular food could be measured by completely burning the dried food in a bomb calorimeter, a method known as direct calorimetry.[5] However, the values given on food labels are not determined in this way." – michael Aug 10 '11 at 18:18
Well, you are right, I got one line wrong - that was not from the source but my own. I removed that. – Steeven Aug 10 '11 at 19:34 | 645 | 2,848 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2016-18 | latest | en | 0.948131 |
https://stackoverflow.com/questions/27436748/python-reduce-list-of-strings-string | 1,701,960,148,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00827.warc.gz | 606,560,579 | 43,082 | # Python: reduce (list of strings) -> string
>>> import functools as ft
>>> bk = ft.reduce(lambda x, y: x[0] + "." + y[0], ['alfa', 'bravo', 'charlie', 'delta'])
>>> bk
'a.d'
>>> km = ft.reduce(lambda x, y: x + y, [1, 2, 3, 4])
>>> km
10
>>> bk = ft.reduce(lambda x, y: x[0] + y[0], ['alfa', 'bravo', 'charlie', 'delta'])
>>> bk
>>>
I expected something like 'a.b.c.d' or 'abcd'. Somehow, can't explain the results. There are similar questions here, but not quite like this one.
The result of executing the function passed as the first parameter, will be the first parameter to that function in the next iteration. So, your code works like this
lambda x, y: x[0] + "." + y[0]
1. When x, y are 'alfa' and 'bravo' respectively, a.b.
2. Now, x will be a.b and y will be 'charlie', so result will be a.c
3. Now, x will be a.c and y will be 'delta', so result will be a.d
That is why the result is a.d
To get what you wanted, take all the first characters from all the strings to form a list and join all the elements together with ., like this
print(".".join([item[0] for item in data]))
# a.b.c.d
Note: I won't prefer this way, but for the sake of completeness, you can do it with reduce, like this
data = ['alfa', 'bravo', 'charlie', 'delta']
print(ft.reduce(lambda x, y: x + ("." if x else "") + y[0], data, ""))
# a.b.c.d
Now, the last empty string will be the first value for x in the first iteration. And we use . only if x is not an empty string otherwise we use an empty string, so that the concatenation would give the result you wanted.
• '.'.join([item[0] for item in data]) - no need for building list in memory, better '.'.join(item[0] for item in data) Dec 12, 2014 at 9:32
• @KlassIvan Yes, but building a list makes str.join run faster. Dec 12, 2014 at 10:39
• I thought it's vice versa. Need to check Dec 12, 2014 at 10:59
If you want to use the reduce the most elegant way would be to do:
from functools import reduce | 584 | 1,946 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2023-50 | latest | en | 0.742555 |
https://www.hitpages.com/doc/4508526491729920/26/ | 1,485,037,693,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281226.52/warc/CC-MAIN-20170116095121-00426-ip-10-171-10-70.ec2.internal.warc.gz | 929,934,399 | 6,502 | X hits on this document
# Chapter 1 Describing Data with Graphs - page 26 / 36
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26 / 36
Example 1.11
Twenty-five households are polled in a marketing survey, and Table 1.12 lists the numbers of quarts of milk purchased during a particular week. Construct a relative frequency histogram to describe the data.
Table 1.12
0 3 5 4 3
2 1 3 1 2
1 1 2 0 1
4 3 2 2 2
2 2 2 3 4
Solution
The variable being measured is “ number of quarts of milk,” which is a discrete variable that takes on only integer values. In this case, it is simplest to choose the classes or intervals as the integer values over the range of observed values: 0, 1, 2, 3, 4, and 5.
©1998 Brooks/Cole Publishing/ITP
Document views 138 Page views 138 Page last viewed Sat Jan 21 21:43:27 UTC 2017 Pages 36 Paragraphs 312 Words 2599
Comments | 283 | 962 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2017-04 | latest | en | 0.756666 |
http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-talk/12462 | 1,603,492,342,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107865665.7/warc/CC-MAIN-20201023204939-20201023234939-00457.warc.gz | 15,902,618 | 2,958 | ```On Mon, 12 Mar 2001, Benjamin J. Tilly wrote:
> >===== Original Message From Mathieu Bouchard <matju / sympatico.ca> =====
> >On Mon, 12 Mar 2001, Benjamin J. Tilly wrote:
> >> >(oh, btw. Ben's version takes over 3 times longer. i'm now testing with
> >> >n=10**30 and using >/dev/null)
> >> We have a winner. If you want all of the Hamming numbers less
> >> than a fixed bound, this appears fastest.
> >
> >I believe there are faster ways than that, but I don't want to go that
> >far...
>
> Well fastest of the submitted solutions. :-)
>
> >> Theoretically the sort is k*log(k) where k is the number of
> >> elements. Practically if you raise n large enough for that to
> >> matter, you will run out of memory on the machine. :-)
> >
> >the hamming function, where h(1)=1, is very close to
> >
> >proc{|k| 0.185*6.9893**(k**(1/3.0)) }
> >
> >which can be used as a reliable approximation for large values of k
>
> Ah, I didn't know that. Well with that fact you should be
> able to indeed do well.
>
I was about to post that Ben was the winner since matju's solution didn't
adhere to my initial posting (the n first hamming numbers and not the
hamming numbers less than a fixed bound) but the above formula should turn
things around.
Thanks for all nice solutions, this was fun.
My solution is slower than yours but shorter when you've got
LazyArray's (It's simple to define them if you build on
MetaRuby; they're basically as the ProcAsArray example but allowing a
length of Infinity):
def hamming_sequence(gens)
hs = LazyArray.new([1]) {|i, me|
# Having an explicit state is ugly; there's probably a nicer
solution
unless me.state["inner"]
me.state["inner"] = merge(gens.map{|gen| hs.map {|v| gen*v}})
end
me.state["inner"][i-1]
}
end
# The n first
hamming_sequence([2,3,5])[0...1000]
This solution is basically the same as the perl one pointed to by
Ben. Expressing it in Ruby makes things a fair amount cleaner though...
Regards,
Robert
``` | 553 | 1,961 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2020-45 | latest | en | 0.93088 |
http://mediawar.info/holt-geometry-8-2-problem-solving-trigonometric-ratios-42/ | 1,586,477,796,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371880945.85/warc/CC-MAIN-20200409220932-20200410011432-00169.warc.gz | 114,153,957 | 8,662 | # HOLT GEOMETRY 8-2 PROBLEM SOLVING TRIGONOMETRIC RATIOS
AC Use your answers from Items 5 and 6 to write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. Round to the nearest hundredth. Use a calculator and trigonometric ratios to find each length. The tangent tan of an angle is the ratio of the length of the leg adjacent the angle to the length of the leg to the angle. Published by Cody Norton Modified over 3 years ago. Holt Geometry Solving Right Triangles Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems. Feedback Privacy Policy Feedback.
How wide is the river? Registration Forgot your password? Auth with social network: Then use side lengths from the figure to complete the indicated trigonometric ratios. Round to the nearest tenth.
The sine sin of an angle is the ratio of the length of the leg hypotenuse.
## 8-2 Trigonometric Ratios Holt McDougal Geometry Holt Geometry.
What about this hol The tangent tan of an angle is the ratio of the length of the leg adjacent the angle to the length of the leg to the angle. Round to the nearest hundredth. Auth with social network: If you wish to download it, please recommend it to your friends in any social system.
UIUC ECONOMICS SUPPORTING COURSEWORK
The cosine cos of an angle is the ratio of the length of the leg hypotenuse to the angle to the length of the. A plane is on the prlblem slope and is 1 mile feet from touchdown. Trigonometric functions wikipedialookup. Then use side lengths from the figure to complete the indicated trigonometric ratios.
Write each trigonometric ratio as a simplified fraction and as a decimal rounded to the nearest hundredth.
AC Use your answers from Items 5 and 6 to write each trigonometric ratio as a fraction and as a trigonomeyric rounded to the nearest hundredth. Define the sine, cosine, and tangent of acute angles in a right triangle. Use the formula you developed in Exercise 5 to find the missing side length in each triangle. My presentations Profile Feedback Log out.
Develop a formula for finding the area. Given the lengths of two sides of a triangle and the measure of the included angle, the area of the triangle can be found. Registration Forgot your password?
Feedback Privacy Policy Feedback. Part II Find each length. About project SlidePlayer Terms of Service. Thank you for your participation! We think you have liked this presentation. Trigonometric Ratios Example 1: Label Opposite, adjacent, or hypotenuse. Part I Use a special right triangle to write each trigonometric ratio as a triglnometric.
HOMEWORK PORTAL BRRSD
Round to the nearest hundredth. To use this website, you must agree to our Privacy Policyincluding cookie policy.
Share buttons are a geometryy bit lower. She places stakes feet apart on the far side of the river and she is standing at point A. Sine and Cosine Expectation: Sine and Cosine Ratios If the wires make an angle of 25 degrees to the ground, how high is the flagpole? Published by Cody Norton Modified over 3 years ago.
Round to the nearest tenth. | 690 | 3,107 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2020-16 | latest | en | 0.886567 |
https://community.fabric.microsoft.com/t5/Desktop/Re-ordering-the-x-axis-values-quot-Sort-By-quot-not-working/m-p/542384/highlight/true | 1,708,497,715,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473370.18/warc/CC-MAIN-20240221034447-20240221064447-00266.warc.gz | 194,517,004 | 116,860 | cancel
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Frequent Visitor
## Re-ordering the x-axis values - "Sort By" not working
I have a chart where the x-axis values are showing as:
0-3 months, 10-12 months, 4-6 months, 7-9 months (see picture below)
and i want them to be in ascending order. i am sorting by "months open" and have it selected by "Sort Ascending"
This is the grouping i have for the months and this is what is being sorted:
Not sure why the "10-12" months group shows between 0-3 and 4-6, and I've searched other forum posts to try their solutions but nothing is working for me.
Any help will be greatly appreciated!
Thank you.
1 ACCEPTED SOLUTION
Community Champion
Make a calculated column that specifies the group, then put that group on the X-axis. You should be able to put the extra space that will help with sorting.
Group =
SWITCH( TRUE(), Age <= 3, " 0-3 Months", Age > 3 && Age <= 6, " 4-6 Months", ...
Alternatively to the extra space, you calculate the group in a column and also create a dimension table with the same groups. Put a field on the new table that indicates the sort order, and you can use the "Sort by Column" functionality (on the Modeling tab) to indicate the order of the groups. Something like
Group Sort Order
0-3 Months 1
4-6 Months 2
etc
6 REPLIES 6
Frequent Visitor
Community Champion
Make a calculated column that specifies the group, then put that group on the X-axis. You should be able to put the extra space that will help with sorting.
Group =
SWITCH( TRUE(), Age <= 3, " 0-3 Months", Age > 3 && Age <= 6, " 4-6 Months", ...
Alternatively to the extra space, you calculate the group in a column and also create a dimension table with the same groups. Put a field on the new table that indicates the sort order, and you can use the "Sort by Column" functionality (on the Modeling tab) to indicate the order of the groups. Something like
Group Sort Order
0-3 Months 1
4-6 Months 2
etc
Frequent Visitor
your post helped me figure out the solution, which i found in this post.
https://community.powerbi.com/t5/Desktop/Custom-Sorting-in-PowerBI/td-p/126534
the solution was posted by @v-haibl-msft so thank you both for helping me figure this out!
see correct order below:
thanks again!
Community Champion
All of your group names are text strings - they are no longer treated as numbers.
You can put a space character at the beginning of your group names that contain numbers less than 10, and then they should sort correctly (space comes alphabetically before 0).
Hope this helps
David
Frequent Visitor
Just tried adding a space @ the beginning of the group names (0-3, 4-6, 7-9) and the space character wasn't saved in the grouping name.
so instead of (space)0-3 it was just 0-3.
Community Champion
Apologies - I didn't test it, I just assumed you would be able to do it (you can do it in the source data, but not in the groups). You may need to look at calculating groups in a way different from the built-in group functionality in PowerBI (calculated column, etc).
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Engage with the Fabric engineering team, hear of product updates, business opportunities, and resources in the Fabric Partner Community. | 912 | 3,726 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-10 | latest | en | 0.869267 |
https://testbook.com/question-answer/what-value-should-come-in-the-place-of-question-ma--63a18e2fea81a71a6c493dc3 | 1,726,513,908,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651710.86/warc/CC-MAIN-20240916180320-20240916210320-00702.warc.gz | 524,141,348 | 46,764 | # What value should come in the place of question mark (?) in the following question?336 ÷ 12 + 875 ÷ 25 = ?
This question was previously asked in
OSSC BSSO Official Paper 2022 (Held On: 07th Nov 2022 Shift 3)
View all OSSC BSSO Papers >
1. 57
2. 61
3. 59
4. 63
Option 4 : 63
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## Detailed Solution
Given:
336 ÷ 12 + 875 ÷ 25 = ?
Concept used:
BODMAS
Calculation:
Let the missing value be 'x'
336 ÷ 12 + 875 ÷ 25 = x
28 + 35 = x
63 = x
∴ 336 ÷ 12 + 875 ÷ 25 = 63 | 213 | 545 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2024-38 | latest | en | 0.772249 |
https://brainmass.com/business/business-math/calculating-stock-and-portfolio-beta-240367 | 1,495,606,610,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607802.75/warc/CC-MAIN-20170524055048-20170524075048-00579.warc.gz | 750,961,016 | 19,300 | Share
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# Calculating stock and portfolio beta
There are two stocks, stock A and stock B. The price of stock A today is \$70. The price of stock A next year will be \$50 if the economy is in recession, \$80 if the economy is normal and \$95 if the economy is expanding. The attendant probabilities of recession, normal times, and expansion are 0.2, 0.6, 0.2, respectively. Stock A pays no dividend. Assume the CAPM is true. Other information about the market includes:
SD(Rm)= Standard deviation of the market portfolio = 0.10
SD(Rb)= Standard deviation of stock B's return = 0.12
Rb= Expected return on stock B = 0.10
Corr(Ra,Rm)= The correlation of stock A and the market = 0.7
Corr(Rb,Rm)= The correlation of stock B and the market = 0.34
Corr(Ra,Rb)= The correlation of stock A and stock B = 0.6
What is the beta of the portfolio consisting of 30% of stock A and 70% of stock B?
#### Solution Preview
Please refer attached file for better clarity of tables and formulas.
Solution:
Stock A
State of economy Probability Price Return*
P R P*R P*(R-Mean)^2
Recession 0.2 50 -0.28571 -0.05714285 0.029755102
Normal 0.6 80 0.14286 ...
#### Solution Summary
Solution describes the steps to calculate beta of stock A and B with the help of statistics given. It also calculates beta of portfolio consisting of stock A and stock B.
\$2.19 | 372 | 1,359 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2017-22 | longest | en | 0.869898 |
https://www.turito.com/ask-a-doubt/Mathematics-evaluate-given-expression-using-distributive-property-6-5-9-90-84-39-20-q608dd4 | 1,716,628,257,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058789.0/warc/CC-MAIN-20240525065824-20240525095824-00016.warc.gz | 910,333,821 | 16,483 | Mathematics
Easy
Question
# Evaluate given expression using distributive property 6 × (5 + 9).
Hint:
## The correct answer is: 84
### We have to find the value of 6 × (5+9). Using distributive property of multiplication, we get6 × (5 + 9) = (6 × 5) + (6 × 9) = 30 + 54 = 84.Hence, the correct option is C.
We can also find the result by using BODMAS rule. | 116 | 361 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2024-22 | latest | en | 0.784136 |
https://homeworkexperts.us/when-different-masses-are-suspended-from-a-spring-the-spring-stretches-by-different-amounts-as/ | 1,632,883,412,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780061350.42/warc/CC-MAIN-20210929004757-20210929034757-00291.warc.gz | 334,884,851 | 8,560 | # When different masses are suspended from a spring, the spring stretches by different amounts as…
When different masses are suspended from a
spring, the spring stretches by different amounts as shown in the Table below.
Masses are 1.0 gram.
(a) Graph the applied force (in Newtons)
versus the stretch (in meters) of the spring, and determine the best fit
straight line. (b) Determine the spring constant (N/m) of the spring from the
slope of the best fit line, (c) If the spring is stretched by 20.0 cm, estimate
the force acting on the spring using the best fit line. | 136 | 571 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2021-39 | latest | en | 0.891947 |
https://electronics.stackexchange.com/questions/105147/emf-in-an-open-circuit | 1,660,533,340,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572127.33/warc/CC-MAIN-20220815024523-20220815054523-00132.warc.gz | 238,652,886 | 64,721 | # EMF in an Open Circuit?
Lets assume we have a wire passing a magnetic field, it is know that EMF is induced due to the magnetic field, what if the wire is not connected to a circuit what happens?
Is there ay voltage in the wire? I doubt there, is.. and current can not flow in an open circuit so what will happen?
A loop of wire, with the ends not touching nor connected to anything else, is this:
simulate this circuit – Schematic created using CircuitLab
If you look at the schematic, it even makes intuitive sense, graphically. As you can see at the gap between the capacitor "plates", the "wires" are not touching. That the plates (which are really just the wires that make up your loop) are really small and far apart doesn't make it not a capacitor: it just makes the capacitance very low, some picofarads at most.
Normally it's so low we can ignore it, but in this case, there's nothing else, so it's pretty key. When the magnetic flux through the loop changes, an EMF is induced just as you'd expect. Some current does flow, according to the governing laws of a capacitor:
$$I(t) = C\frac{\mathrm{d}V(t)}{\mathrm{d}t}$$
Of course, with C = 1pF, the current will be very low indeed, and if the EMF isn't changing ($\mathrm{d}V(t)/\mathrm{d}t = 0$), then there is no current.
• EMF would be the same value regardless of the circuit being open or closed correct? Apr 3, 2014 at 5:33 | 358 | 1,398 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2022-33 | latest | en | 0.952745 |
https://mathoverflow.net/questions/59281/quantitative-measurement-of-infinite-dimensionality | 1,606,315,651,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141182794.28/warc/CC-MAIN-20201125125427-20201125155427-00039.warc.gz | 406,677,621 | 30,852 | # Quantitative measurement of infinite dimensionality
I recently encountered the metric mean dimension, which is a numerical metric invariant of (discrete time, compact space) dynamical systems that refines topological entropy for infinite-entropy systems. I am wondering if anything similar can be found in the literature for any metric notion of dimension (Let say that by metric'' means bi-Lipschitz invariant).
Put another way, I have a compact metric space $X$ that has infinite dimension for any sensible notion of dimension, and I would like to make this statement quantitative. I see two ways to do this.
The first one is to mimic the box-dimension, and consider the (extra-polynomial) growth rate of the smallest number of $\varepsilon$-balls needed to cover $X$ when $\varepsilon^{-1}$ goes to infinity. This is the simplest way to go, but I am concerned by the fact that box dimension have not as nice a behavior than Hausdorff dimension (for example countable spaces can have positive box dimension).
The second one, suggested by Greg Kuperberg, is to mimic Hausdorff dimension but replacing the family of "size functions" $(x\mapsto x^s)_s$ by another family with similar properties, like $(x\mapsto\exp(-\lambda/x)_\lambda)$.
My question is the following: do you know any example of such an invariant in the literature? Where is it used, in what purpose?
Gideon Schechtman and I speculated on a notion of dimension (we call it complexity) of a general metric space that comes from the theory of Lipschitz $p$-summing operators that Farmer and I introduced. A metric space has finite complexity provided the Lipschitz $1$-summing norm of the identity function on the space is finite. For an infinite set with all distances one, which we consider a simple metric space, the Lipschitz $1$-summing norm of the identity is two. For $\mathbb{R}^n$, this parameter is about $n^{1/2}$. When the Lipschitz $1$-summing norm of the identity is infinite, the asymptotics of the Lipschitz $(p,1)$-summing norm of the identity as $p$ decreases to one describes the complexity of the space (the point being that for $p>1$, this parameter is always finite and tends to the Lipschitz $1$-summing norm when $p$ decreases to one).
For our speculation, see the last paragraph of section 5 in our paper
Diamond graphs and super-reflexivity, J. Topology and Analysis 1 (2009), no. 2, 177–189.
We have not followed up on this notion and have no idea whether it is good for anything.
• Thanks ; this construction seems however more difficult to interpret than the more or less straightforward examples I gave. I don't feel how difficult it is to estimate these summing norms. – Benoît Kloeckner Mar 25 '11 at 12:35
• It is certainly more difficult to understand than the examples you mentioned, and it is difficult to compute for many examples. It is however quite natural when you come into metric geometry from geometric functional analysis. – Bill Johnson Mar 26 '11 at 12:05
After failing to find any evidence that the notions I asked for have been previously defined, I chose to write things down. The resulting paper is available: A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces. Wasserstein spaces were my initial target, while (generalized) Hilbert cubes are handy reference spaces.
By the way, I should stress that using the family of functions $(x\mapsto \exp(-\lambda/x))_\lambda$ suggested in the question is a bad idea: the resulting analogue to Hausdorff dimension is not bi-Lipschitz invariant. One has to use cruder families like $(x\mapsto \exp(-x^{-s}))_s$.
Is it good policy to accept my own answer so that the question is not left open? | 868 | 3,699 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2020-50 | latest | en | 0.899324 |
https://download.racket-lang.org/releases/6.12/doc/racklog/racket-w-logic.html | 1,519,147,597,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891813059.39/warc/CC-MAIN-20180220165417-20180220185417-00082.warc.gz | 636,856,891 | 6,749 | ### 3Using Conventional Racket Expressions in Racklog
The arguments of Racklog predicates can be any Racket objects. In particular, composite structures such as lists, vectors, strings, hash tables, etc can be used, as also Racket expressions using the full array of Racket’s construction and decomposition operators. For instance, consider the following goal:
(%member x '(1 2 3))
Here, %member is a predicate, x is a logic variable, and '(1 2 3) is a structure. Given a suitably intuitive definition for %member, the above goal succeeds for x = 1, 2, and 3.
Now to defining predicates like %member:
(define %member (%rel (x y xs) [(x (cons x xs))] [(x (cons y xs)) (%member x xs)]))
Ie, %member is defined with three local variables: x, y, xs. It has two clauses, identifying the two ways of determining membership.
The first clause of %member states a fact: For any x, x is a member of a list whose head is also x.
The second clause of %member is a rule: x is a member of a list if we can show that it is a member of the tail of that list. In other words, the original %member goal is translated into a subgoal, which is also a %member goal.
Note that the variable y in the definition of %member occurs only once in the second clause. As such, it doesn’t need you to make the effort of naming it. (Names help only in matching a second occurrence to a first.) Racklog lets you use the expression (_) to denote an anonymous variable. (Ie, _ is a thunk that generates a fresh anonymous variable at each call.) The predicate %member can be rewritten as
(define %member (%rel (x xs) [(x (cons x (_)))] [(x (cons (_) xs)) (%member x xs)]))
#### 3.1Constructors
We can use constructors — Racket procedures for creating structures — to simulate data types in Racklog. For instance, let’s define a natural-number data-type where 0 denotes zero, and (succ x) denotes the natural number whose immediate predecessor is x. The constructor succ can be defined in Racket as:
(define succ (lambda (x) (vector 'succ x)))
Addition and multiplication can be defined as:
(define %add (%rel (x y z) [(0 y y)] [((succ x) y (succ z)) (%add x y z)])) (define %times (%rel (x y z z1) [(0 y 0)] [((succ x) y z) (%times x y z1) (%add y z1 z)]))
We can do a lot of arithmetic with this in place. For instance, the factorial predicate looks like:
(define %factorial (%rel (x y y1) [(0 (succ 0))] [((succ x) y) (%factorial x y1) (%times (succ x) y1 y)]))
#### 3.2%is
The above is a very inefficient way to do arithmetic, especially when the underlying language Racket offers excellent arithmetic facilities (including a comprehensive number “tower” and exact rational arithmetic). One problem with using Racket calculations directly in Racklog clauses is that the expressions used may contain logic variables that need to be dereferenced. Racklog provides the predicate %is that takes care of this. The goal
(%is X E)
unifies X with the value of E considered as a Racket expression. E can have logic variables, but usually they should at least be bound, as unbound variables may not be palatable values to the Racket operators used in E.
We can now directly use the numbers of Racket to write a more efficient %factorial predicate:
(define %factorial (%rel (x y x1 y1) [(0 1)] [(x y) (%is x1 (- x 1)) (%factorial x1 y1) (%is y (* y1 x))]))
A price that this efficiency comes with is that we can use %factorial only with its first argument already instantiated. In many cases, this is not an unreasonable constraint. In fact, given this limitation, there is nothing to prevent us from using Racket’s factorial directly:
(define %factorial (%rel (x y) [(x y) (%is y (racket-factorial x))]))
or better yet, “in-line” any calls to %factorial with %is-expressions calling racket-factorial, where the latter is defined in the usual manner:
(define racket-factorial (lambda (n) (if (= n 0) 1 (* n (racket-factorial (- n 1))))))
#### 3.3Lexical Scoping
One can use Racket’s lexical scoping to enhance predicate definition. Here is a list-reversal predicate defined using a hidden auxiliary predicate:
(define %reverse (letrec ([revaux (%rel (x y z w) [('() y y)] [((cons x y) z w) (revaux y (cons x z) w)])]) (%rel (x y) [(x y) (revaux x '() y)])))
(revaux X Y Z) uses Y as an accumulator for reversing X into Z. (Y starts out as (). Each head of X is consed on to Y. Finally, when X has wound down to (), Y contains the reversed list and can be returned as Z.)
revaux is used purely as a helper predicate for %reverse, and so it can be concealed within a lexical contour. We use letrec instead of let because revaux is a recursive procedure.
#### 3.4Type Predicates
Racklog provides a couple of predicates that let the user probe the type of objects.
The goal
succeeds if X is an atomic object.
The predicate %compound, the negation of %constant, checks if its argument is not an atomic object.
The above are merely the logic-programming equivalents of corresponding Racket predicates. Users can use the predicate %is and Racket predicates to write more type checks in Racklog. Thus, to test if X is a string, the following goal could be used:
(%is #t (string? X))
User-defined Racket predicates, in addition to primitive Racket predicates, can be thus imported. | 1,445 | 5,277 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2018-09 | latest | en | 0.823886 |
http://smallbusiness.chron.com/definition-total-intangible-amortization-expense-36399.html | 1,477,345,740,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719784.62/warc/CC-MAIN-20161020183839-00398-ip-10-171-6-4.ec2.internal.warc.gz | 237,619,072 | 20,693 | # Definition of Total Intangible Amortization Expense
by Bryan Keythman, studioD
An asset is a resource that generates an economic benefit for a business. An intangible asset is a non-physical asset, such as a copyright, patent or trademark. You recognize intangible assets in your records only when you acquire them from another party. Amortization spreads the cost of an intangible asset over its useful life. You cannot amortize an intangible asset with an indefinite life, such as goodwill. The total intangible amortization expense is the sum of each of your individual intangible assets’ amortization expenses during an accounting period. You must calculate this total each period and report it on your income statement.
Determine the amount your small business paid to purchase an intangible asset. For example, assume you paid \$20,000 to acquire a patent from another business.
Estimate the intangible asset’s useful life, which is the number of years you expect to receive an economic benefit from it. Also, estimate its residual value, which is the value you expect it will have at the end of its useful life. For example, assume your patent has a useful life of 10 years and no residual value.
Subtract the intangible asset’s residual value from its cost. Divide the result by its useful life to determine its annual amortization expense. Do this for each intangible asset you own. In this example, since the intangible asset has no residual value, divide \$20,000 by 10 years to get a \$2,000 annual amortization expense.
Calculate the sum of each individual intangible asset’s amortization expense to determine your total intangible amortization expense. Continuing with the example, assume you have another patent with a \$5,000 amortization expense. Add the \$5,000 amortization expense of that patent to the \$2,000 amortization expense of the other patent to get \$7,000 in total intangible amortization expense.
Write “amortization expense” and the amount of your total intangible amortization expense as a line item on your annual income statement to report the expense to financial statement users. In this example, write “amortization expense \$7,000” on your income statement. | 460 | 2,206 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2016-44 | longest | en | 0.927156 |
http://www.velocityreviews.com/forums/t24843-help-with-sorting.html | 1,394,705,721,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1394678664178/warc/CC-MAIN-20140313024424-00053-ip-10-183-142-35.ec2.internal.warc.gz | 612,232,409 | 7,258 | Velocity Reviews > Perl > Help with sorting...
# Help with sorting...
Joe Trubisz
Guest
Posts: n/a
02-16-2004
Hi...
I have something like this:
\$rec = {};
\$rec->{a} = 1;
\$rec->{b} = 4;
\$D{\$rec->{a}}=\$rec;
\$rec = {};
\$rec->{a} = 2;
\$rec->{b} = 1;
\$D{\$rec->{a}}=\$rec;
\$rec = {};
\$rec->{a} = 3;
\$rec->{b} = 3;
\$D{\$rec->{a}}=\$rec;
What I want to do is sort D based on the value of b.
Can someone explain to me what the sort command should look like?
I'm stumped!
TIA,
Joe
Joe Smith
Guest
Posts: n/a
02-16-2004
Joe Trubisz wrote:
> \$rec = {};
> \$rec->{a} = 1;
> \$rec->{b} = 4;
> \$D{\$rec->{a}}=\$rec;
> \$rec = {};
> \$rec->{a} = 2;
> \$rec->{b} = 1;
> \$D{\$rec->{a}}=\$rec;
> \$rec = {};
> \$rec->{a} = 3;
> \$rec->{b} = 3;
> \$D{\$rec->{a}}=\$rec;
>
> What I want to do is sort D based on the value of b.
print "\$D{\$_}{a} \$D{\$_}{b}\n" for sort {\$D{\$a}{b} cmp \$D{\$b}{b}} keys %D;
-Joe | 382 | 926 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2014-10 | latest | en | 0.577742 |
http://isabelle.in.tum.de/repos/isabelle/raw-diff/d74182c93f04/src/HOL/Library/Product_Vector.thy | 1,611,450,462,000,000,000 | text/plain | crawl-data/CC-MAIN-2021-04/segments/1610703538741.56/warc/CC-MAIN-20210123222657-20210124012657-00455.warc.gz | 47,535,184 | 1,165 | diff -r eb64ffccfc75 -r d74182c93f04 src/HOL/Library/Product_Vector.thy --- a/src/HOL/Library/Product_Vector.thy Mon Aug 08 10:26:26 2011 -0700 +++ b/src/HOL/Library/Product_Vector.thy Mon Aug 08 10:32:55 2011 -0700 @@ -28,13 +28,13 @@ instance proof fix a b :: real and x y :: "'a \ 'b" show "scaleR a (x + y) = scaleR a x + scaleR a y" - by (simp add: expand_prod_eq scaleR_right_distrib) + by (simp add: prod_eq_iff scaleR_right_distrib) show "scaleR (a + b) x = scaleR a x + scaleR b x" - by (simp add: expand_prod_eq scaleR_left_distrib) + by (simp add: prod_eq_iff scaleR_left_distrib) show "scaleR a (scaleR b x) = scaleR (a * b) x" - by (simp add: expand_prod_eq) + by (simp add: prod_eq_iff) show "scaleR 1 x = x" - by (simp add: expand_prod_eq) + by (simp add: prod_eq_iff) qed end @@ -174,7 +174,7 @@ instance proof fix x y :: "'a \ 'b" show "dist x y = 0 \ x = y" - unfolding dist_prod_def expand_prod_eq by simp + unfolding dist_prod_def prod_eq_iff by simp next fix x y z :: "'a \ 'b" show "dist x y \ dist x z + dist y z" @@ -373,7 +373,7 @@ unfolding norm_prod_def by simp show "norm x = 0 \ x = 0" unfolding norm_prod_def - by (simp add: expand_prod_eq) + by (simp add: prod_eq_iff) show "norm (x + y) \ norm x + norm y" unfolding norm_prod_def apply (rule order_trans [OF _ real_sqrt_sum_squares_triangle_ineq]) @@ -423,7 +423,7 @@ unfolding inner_prod_def by (intro add_nonneg_nonneg inner_ge_zero) show "inner x x = 0 \ x = 0" - unfolding inner_prod_def expand_prod_eq + unfolding inner_prod_def prod_eq_iff by (simp add: add_nonneg_eq_0_iff) show "norm x = sqrt (inner x x)" unfolding norm_prod_def inner_prod_def | 539 | 1,634 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2021-04 | latest | en | 0.557652 |
https://web2.0calc.com/questions/help-please_29552 | 1,579,693,602,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250606975.49/warc/CC-MAIN-20200122101729-20200122130729-00185.warc.gz | 739,272,605 | 6,216 | +0
0
165
2
can you solve the initial value problem for:
dy/dx= xy-2x+y-2 , y(2)= -1
Aug 19, 2019
#1
+23861
+2
can you solve the initial value problem for:
$$\dfrac{dy}{dx}= xy-2x+y-2,\ y(2)= -1$$
$$\begin{array}{|rclcl|} \hline \mathbf{\dfrac{dy}{dx}} &=&\mathbf{ xy-2x+y-2 } \\\\ \dfrac{dy}{dx} &=& x(y-2)+ (y-2) \\\\ \dfrac{dy}{dx} &=& (y-2)(x+1) \\\\ \dfrac{dy}{(y-2)} &=& (x+1)dx \\\\ \large{ \int } \dfrac{1}{(y-2)}\ dy &=&\large{ \int } (x+1)\ dx \\\\ \mathbf{\ln(y-2) + c_1} &=& \mathbf{\dfrac{x^2}{2} +x + c_2 } \\ \hline && \ln(y-2) + c_1 &=& \dfrac{x^2}{2} +x + c_2 \quad | \quad y(2) = -1 \\ && \ln(-1-2) + c_1 &=& \dfrac{2^2}{2} +2 + c_2 \\ && \ln(-3) + c_1 &=& 4 + c_2 \quad | \quad \boxed{\mathbf{c_1 = -\ln(-3)}} \\ && \ln(-3) -\ln(-3) &=& 4 + c_2 \\ && 0 &=& 4 + c_2 \\ && \mathbf{c_2} &=& \mathbf{-4} \\ \hline \mathbf{\ln(y-2) -\ln(-3)} &=& \mathbf{\dfrac{x^2}{2} +x -4 } \\ \ln\left(\dfrac{y-2}{-3}\right) &=& \dfrac{x^2}{2} +x -4 \\ \dfrac{y-2}{-3} &=& e^\left(\dfrac{x^2}{2} +x -4 \right) \\ y-2 &=& -3e^\left(\dfrac{x^2}{2} +x -4 \right) \\ \mathbf{ y(x)} &=& \mathbf{2-3e^\left(\dfrac{x^2}{2} +x -4 \right)} \\ \hline \end{array}$$
Aug 19, 2019
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https://writingsgate.com/2022/04/28/the-institutional-research-office-has-recently-conducted-a-survey-group-of-consumers-according-to-demographic-data-the-research-office-has-given-you/ | 1,669,562,288,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00309.warc.gz | 667,562,993 | 19,330 | Home » The institutional research office has recently conducted a survey group of consumers.According to demographic data, the research office has given you…
# The institutional research office has recently conducted a survey group of consumers.According to demographic data, the research office has given you…
The institutional research office has recently conducted a survey group of consumers.According to demographic data, the research office has given you the following:
Typical weekly consumer income \$800
Price of Frosty Cola \$10.00 per case
Price of Coca-Cola \$20.00 per case
You want to break this data down for the chief financial officer in two forms: a slope- intercept equation for the typical consumer’s budget constraint and a graphical analysis showing him the typical consumer’s budget set. The CFO has specifically asked for the price of Frosty Cola to be the good on the vertical axis. (Round any quantity to the nearest whole unit in each part, if necessary.)
a) Derive the equation for the budget constraint in slope-intercept form.
b) Illustrate and explain the typical consumer’s budget set (again, place quantity of Frosty Cola on the vertical axis).
c) The CFO asks you if the price of Frosty Cola were to decrease to \$5.00 per case, what would happen to the budget constraint? Illustrate and explain.
d) Lastly, the CFO asks you that if the typical consumer wished to purchase seven cases of Coca-Cola, how much Frosty Cola could that individual purchase? Calculate and show. Assume the original data.
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JUMP TO: Module A Module B | Module C | Module D | Final Exam
### Module A Resources
#### Chapter 1
Section 1.1
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Video: Section 1.1
Section 1.2
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Section 1.3
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Video: Section 1.3
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Section 1.5
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Section 1.7
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#### Chapter 2
Section 2.1
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Video: Section 2.1
Section 2.2
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Section 2.3a
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Handout: Linear Equations with Fractions
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#### Chapter 5
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#### Chapter 4
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### Module D Resources
#### Chapter 9
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#### Chapter 10
Section 10.1
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Section 10.2
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Section 10.4
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# 1 plus -4 equals
Updated: 8/17/2019
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Related questions
### What is 1 plus 1 plus 1 plus 1-4 plus g equals?
1 plus 1 plus 1 plus 1 equals 1 times 4. 1 times 4 equals 4. 4 minus 4 equals 0. 0
### What is 4 plus 1 plus 4 plus 77685769844446473 plus 3 plus 8 plus 1 plus 23122312 plus 6 plus 1 equals 2 plus 9870998342523322424 plus 4?
4+1=5. Plus 4 equals 9. Plus 77685769844446473 equals 77685769844446482. Plus 3 equals 77685769844446485. Plus 8 equals 77685769844446493. Plus 1 equals 77685769844446494. Plus 9870998342523322424 equals 1064785604097768918. Plus 4 equals 1064785604097768922.
### 3 plus 1 plus 4 equals?
3 plus 1 plus 4 equals 8
### Does 1 plus 1 plus 1 plus 1 equals 3.8?
No...it equals 4...
20
### If 1 plus 1 equals 2 2 plus 2 equals 22?
no if 1 plus 1 equals 2 then 2 plus 2 equals 4.
### What is 6 plus 1 plus 3 plus 4?
6+1 equals 7. Plus 3 equals 10. Plus 4 equals 14.
### 4 plus 3 equals?
4 plus 3 equals 7
-4
42
2048
4 + 4 + 1 = 9 | 449 | 1,117 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2024-33 | latest | en | 0.330494 |
https://www.ijert.org/gauss-legendre-quadrature-over-a-unit-circle | 1,719,284,296,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865545.19/warc/CC-MAIN-20240625005529-20240625035529-00798.warc.gz | 707,275,527 | 17,579 | # Gauss Legendre quadrature over a unit circle
DOI : 10.17577/IJERTV2IS90441
Text Only Version
#### Gauss Legendre quadrature over a unit circle
Abstract
K. T. Shivaram Department of Mathematics,
Dayananda sagar college of Engineering, Bangalore
This paper presents a Gauss Legendre quadrature over a unit circle region
, 0 1, 0 1 2 , are derived using transformation of variables new Gaussian points and corresponding weights are calculated. The numerical evaluation of the unit circle domain integrals of any arbitrary functions is illustrated with some numerical examples.
Keywords: Finite element method, Gauss Legendre quadrature , unit circle region, extended numerical integration
1. The finite element method is essentially a numerical method for the approximate solution of practical problems arising in engineering and scientific analysis. The advantages of the finite element technique over other alternatives are more fully appreciated in two dimensional situations. Surface integrals are used in multiple areas of physics and engineering. In particular, they are used for Problems involving calculations of mass of a shell, center of mass and moments of inertia of a shell, fluid flow and mass flow across a surface, electric charge distributed over a surface, plate bending, plane strain, heat conduction over a plate, and similar problems in other areas of engineering which are very difficult to analyse using analytical techniques, These problems can be solved using the finite element method.
From the literature review we may realize that several works in numerical integration using Gaussian quadrature over triangle region and linear convex quadrilateral region have been carried out [1-6,12]. The both Gaussian and Szego quadrature formulae depend on the location of the singularities of the integrand f(z) with respect to the unit circle given in [8-9]
The paper is organized as follows. In Section 2 we will introduce the Gauss Legendre quadrature formula over unit circle region and In Section 3 we compare the numerical results with some illustrative examples.
2. The Numerical integration of an arbitrary function f over the unit circle is given by
I = f x, y dx dy = 1 1 2 , = 1 1 2 ,
(1)
A 0 0 0 0
Where A is the unit circle { 0, 0 , 1, 0 , (0, 1) } in the xy – plane
The integral of the eqn.(1) can be transformed to r plane. Transformation is
= + + (2)
2 2
= + + (3)
2 2
a = 0, b = 1 and = 0, = /2 eqn.(2) and eqn.(3) becomes
= +1
2
, = + 1 /4
Transform the rectangle in to the standard square 1 , 1. by change of variables it follows that
= cos = +1 cos( + 1 /4 ) (4)
2
= sin = +1 sin( + 1 /4 ) (5)
2
we have
I = 1 12 , = 1 1 ( , , , ) (6)
0 0 1 1
Where J , is the Jacobians of the transformation
, =
= (+1)
16
From eqn. (6) , we can write as
I = 1 1
( +1 cos +1 , +1 sin +1 ) (+1)
1 1 2 4 2 4 16
=
=
=1
=1
(+1) ( , , , )
(7)
16
16
Where , are Gaussian points and , are corresponding weights. We can rewrite eqn.
(7) as
I = =× ( , )
(8)
16
16
Where = (+1) , (8a)
2
2
= +1 cos( + 1 /4 ) , (8b)
2
2
= +1 sin( + 1 /4 ) , (8c)
if = 1,2,3, , , = 1,2,3,
we find out new Gaussian points , and weights coefficients of various order N =5,10,15,20 by using eqn.(8a),(8b) and(8c) and tabulated in Table 1
Table 1. Gaussian Points and weighting coefficient over the region A for N = 5
0.04678278193197457 0.00345349702889218 0.001034081387155891 0.23013914053182605 0.01698883232754596 0.010276459848115595 0.49864320092023384 0.03680975653306203 0.026464987076637744 0.76714726130864160 0.05663068073857810 0.034255616016519705 0.95050361990849350 0.07016601603723191 0.021009825862875650 0.04386178550298574 0.01663427484182355 0.002089003109145616 0.21576984525046589 0.08182920205630174 0.020760026087276687 0.46750920355886550 0.17729958992551350 0.053463335645804765 0.71924856186726520 0.27276997779472530 0.069201601782065640 0.89115662161474560 0.33796490500920360 0.042443072755489704 0.03317043357436901 0.03317043357436901 0.002482949164761447 0.16317574027498855 0.16317574027498850 0.024674970184659700 0.35355339060000000 0.35355339060000000 0.063545498810389080 0.54393104091155890 0.54393104091155890 0.082251701106949830 0.67393634761217880 0.67393634761217880 0.050447024988514070 0.01663427484182356 0.04386178550298574 0.002089003109145616 0.08182920205630176 0.21576984525046589 0.020760026087276687 0.17729958992551353 0.46750920355886550 0.053463335645804765 0.27276997779472534 0.71924856186726520 0.069201601782065640 0.33796490500920370 0.89115662161474560 0.042443072755489704 0.00345349702889215 0.04678278193197457 0.001034081387155891 0.01698883232754580 0.23013914053182605 0.010276459848115595 0.03680975653306168 0.49864320092023384 0.026464987076637744 0.05663068073857757 0.76714726130864160 0.034255616016519705 0.07016601603723124 0.95050361990849350 0.021009825862875650
3. Exact value Order Computed value 1 1 x2 xy 1) dydx = 0.1666666667 0 0 1 y 2 N=5 0.1657006169130470 N=10 0.1665461244505496 N=15 0.1665743377735694 N=20 0.1666497582248984 1 1 x2 1 2) 1 x 2 y 2 dydx = 0.5443965226 0 0 N=5 0.5443959985924995 N=10 0.5447587157947142 N=15 0.5445440217870158 N=20 /td> 0.5443965510242446 1 1 y2 2 3) e x sin(x y)dydx = 0.4339584397 0 0 N=5 0.4339594454705387 N=10 0.4355817866124337 N=15 0.4336350226254936 N=20 0.4339585168822540 1 1 x2 4) x 2 y 2 dydx = 0.5235987756 0 0 N=5 N=10 N=15 N=20 0.523598773172042 0.526152432804568 0.523273240355146 0.523598898977512 1 1 x2 x 4 y 4 5) 1 x 2 y dydx = 0.1761129344 0 0 N=5 0.176121028788965 N=10 N=15 N=20 0.177904823327757 0.176094429817746 0.176112985432682 1 1 y2 6) x2 y 2 sin(10x)dydx = 0.08799717224 0 0 N=5 N=10 N=15 N=20 0.093765742603105 0.082329251719011 0.088395981414517 0.087997185681533
In this paper we have derived Gauss Legendre quadrature method for calculating integral over a unit circle region x, y 0 x 1, 0 y 1 x2 , new Gaussian points and its weights are calculated of various order N = 5, 10,15,20. We have then evaluate the typical integrals governed by the proposed method. The results obtained are in excellent agreement with the exact value
1. P. C. Hammer, O. J. Marlowe and A. H. Stroud, Numerical integration over simplexes and cones, Math. Tables Other Aids Computation, 10, 130136 (1956).
2. P.C.Hammer and A.H.Stroud, Numerical integration over simplexes, Math. Tables and other Aids to computation, 10(1956) 137-139.
3. P.C.Hammer and A.H.Stroud, Numerical evaluation of multiple integrals, math.Tables Other Aids computation. 12(1958) 272-280.
4. M.Abramowicz and I.A.Stegun(eds), Handbook of mathematical functions, Dover Publications, Inc. New York(1965).
5. J.N.Reddy, an introduction to the Finite Element Method, ,Tata McGraw- Hill edition third edition(2005).
6. H.T.Rathod and K.V.Nagaraja, Gauss Legendre quadrature over a triangle, J.Indian Inst.Sci.,Oct.2004,84,183-188
7. W. Gautschi, On the zeros of polynomials orthogonal on the semicircle, SIAM J. Math. Anal. 20 (1989), pp. 738743.
8. L.Daruis, P. Gonz_alez-Vera, Szeg polynomials and quadrature formulas on the unit circle, Appl. Numer. Math. 36 (2000) 79112.
9. Leyla Daruis, Pablo Gonz alez-Vera and Francisco Marcell Gaussian quadrature formulae on the unit circle Journal of Computational and Applied Mathematics, 2002, vol. 140, no. 1-2, p. 159-183
10. M. Alfaro, F. Marcell-an, Carath-eodory functions and orthogonal polynomials on the unit circle, Complex Methods in Approximation Theory, Universidad de Almer-Ia, 1997, pp. 1 22.
11. W.B. Jones, H. Waadeland, Bounds for remainder terms in Szego quadrature on the unit circle, Approximation and Computation, in: R.V.M. Zahar (Ed.), International Series of Numerical Mathematics, Vol. 119, Birkh;auser, Basel, 1994, pp. 325346.
12. H.T.Rathod, and K.T. Shivaram, Some composite numerical integration schemes for an arbitrary linear convex quadrilateral region, International e-Journal of Numerical Analysis and Related Topics Vol.4, March 2010, pp.19-58, | 2,727 | 8,002 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2024-26 | latest | en | 0.8381 |
https://mathematica.stackexchange.com/questions/215126/prepending-different-numbers-to-sublists | 1,708,783,362,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474533.12/warc/CC-MAIN-20240224112548-20240224142548-00642.warc.gz | 390,326,687 | 38,830 | # Prepending different numbers to sublists
This problem relates to Prepend 0 to sublists I have the list
t1 = Table[m = n + IntegerReverse[n]; n = m, {n, 3}, {i, 1, 4}]
giving
{{2, 4, 8, 16}, {4, 8, 16, 77}, {6, 12, 33, 66}}
But I want to start with the first value n so I should get
{{1, 2, 4, 8, 16}, {2, 4, 8, 16, 77}, {3, 6, 12, 33, 66}}
It can be done by
Prepend[#, #[[1]]/2] & /@ t1
But this is cheatingly awkward. How can I do it properly or within the Table command? I tried Hold and Prepend inside Table but did not get anywhere.
• Flatten /@ Thread[{Range[3], t1}] seems natural enough. Feb 22, 2020 at 5:53
MapIndexed[Join[#2, #] &, Table[n = n + IntegerReverse[n], {n, 3}, {i, 4}]]
To get the same result using only Table:
Table[n = If[i == 0, n, n + IntegerReverse[n]], {n, 3}, {i, 0, 4}] | 318 | 817 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2024-10 | latest | en | 0.847822 |
https://wikimili.com/en/Thompson%27s_construction | 1,582,132,478,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875144165.4/warc/CC-MAIN-20200219153707-20200219183707-00096.warc.gz | 635,172,238 | 19,458 | # Thompson's construction
Last updated
In computer science, Thompson's construction algorithm, also called the McNaughton-Yamada-Thompson algorithm [1] , is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). [2] This NFA can be used to match strings against the regular expression. This algorithm is credited to Ken Thompson.
## Contents
Regular expressions and nondeterministic finite automata are two representations of formal languages. For instance, text processing utilities use regular expressions to describe advanced search patterns, but NFAs are better suited for execution on a computer. Hence, this algorithm is of practical interest, since it can compile regular expressions into NFAs. From a theoretical point of view, this algorithm is a part of the proof that they both accept exactly the same languages, that is, the regular languages.
An NFA can be made deterministic by the powerset construction and then be minimized to get an optimal automaton corresponding to the given regular expression. However, an NFA may also be interpreted directly.
To decide whether two given regular expressions describe the same language, each can be converted into an equivalent minimal deterministic finite automaton via Thompson's construction, powerset construction, and DFA minimization. If, and only if, the resulting automata agree up to renaming of states, the regular expressions' languages agree.
## The algorithm
The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. [3] More precisely, from a regular expression E, the obtained automaton A with the transition function δ respects the following properties:
• A has exactly one initial state q0, which is not accessible from any other state. That is, for any state q and any letter a, ${\displaystyle \delta (q,a)}$ does not contain q0.
• A has exactly one final state qf, which is not co-accessible from any other state. That is, for any letter a, ${\displaystyle \delta (q_{f},a)=\emptyset }$.
• Let c be the number of concatenation of the regular expression E and let s be the number of symbols apart from parentheses — that is, |, *, a and ε. Then, the number of states of A is 2sc (linear in the size of E).
• The number of transitions leaving any state is at most two.
• Since an NFA of m states and at most e transitions from each state can match a string of length n in time O(emn), a Thompson NFA can do pattern matching in linear time, assuming a fixed-size alphabet. [4] [ better source needed ]
### Rules
The following rules are depicted according to Aho et al. (2007), [1] p. 122. In what follows, N(s) and N(t) are the NFA of the subexpressions s and t, respectively.
The empty-expression ε is converted to
A symbola of the input alphabet is converted to
The union expressions|t is converted to
State q goes via ε either to the initial state of N(s) or N(t). Their final states become intermediate states of the whole NFA and merge via two ε-transitions into the final state of the NFA.
The concatenation expressionst is converted to
The initial state of N(s) is the initial state of the whole NFA. The final state of N(s) becomes the initial state of N(t). The final state of N(t) is the final state of the whole NFA.
The Kleene star expressions* is converted to
An ε-transition connects initial and final state of the NFA with the sub-NFA N(s) in between. Another ε-transition from the inner final to the inner initial state of N(s) allows for repetition of expression s according to the star operator.
• The parenthesized expression (s) is converted to N(s) itself.
With these rules, using the empty expression and symbol rules as base cases, it is possible to prove with mathematical induction that any regular expression may be converted into an equivalent NFA. [1]
## Example
Two examples are now given, a small informal one with the result, and a bigger with a step by step application of the algorithm.
### Small Example
The picture below shows the result of Thompson's construction on (ε|a*b). The pink oval corresponds to a, the teal oval corresponds to a*, the green oval corresponds to b, the orange oval corresponds to a*b, and the blue oval corresponds to ε.
### Application of the algorithm
As an example, the picture shows the result of Thompson's construction algorithm on the regular expression (0|(1(01*(00)*0)*1)*)* that denotes the set of binary numbers that are multiples of 3:
{ ε, "0", "00", "11", "000", "011", "110", "0000", "0011", "0110", "1001", "1100", "1111", "00000", ... }.
The upper right part shows the logical structure (syntax tree) of the expression, with "." denoting concatenation (assumed to have variable arity); subexpressions are named a-q for reference purposes. The left part shows the nondeterministic finite automaton resulting from Thompson's algorithm, with the entry and exit state of each subexpression colored in magenta and cyan, respectively. An ε as transition label is omitted for clarity unlabelled transitions are in fact ε transitions. The entry and exit state corresponding to the root expression q is the start and accept state of the automaton, respectively.
The algorithm's steps are as follows:
q: start converting Kleene star expression (0|(1(01*(00)*0)*1)*)* b: start converting union expression 0|(1(01*(00)*0)*1)* a: convert symbol 0 p: start converting Kleene star expression (1(01*(00)*0)*1)* d: start converting concatenation expression 1(01*(00)*0)*1 c: convert symbol 1 n: start converting Kleene star expression (01*(00)*0)* f: start converting concatenation expression 01*(00)*0 e: convert symbol 0 h: start converting Kleene star expression 1* g: convert symbol 1 h: finished converting Kleene star expression 1* l: start converting Kleene star expression (00)* j: start converting concatenation expression 00 i: convert symbol 0 k: convert symbol 0 j: finished converting concatenation expression 00 l: finished converting Kleene star expression (00)* m: convert symbol 0 f: finished converting concatenation expression 01*(00)*0 n: finished converting Kleene star expression (01*(00)*0)* o: convert symbol 1 d: finished converting concatenation expression 1(01*(00)*0)*1 p: finished converting Kleene star expression (1(01*(00)*0)*1)* b: finished converting union expression 0|(1(01*(00)*0)*1)* q: finished converting Kleene star expression (0|(1(01*(00)*0)*1)*)*
An equivalent minimal deterministic automaton is shown below.
## Relation to other algorithms
Thompson's is one of several algorithms for constructing NFAs from regular expressions; [5] an earlier algorithm was given by McNaughton and Yamada. [6] Converse to Thompson's construction, Kleene's algorithm transforms a finite automaton into a regular expression.
Glushkov's construction algorithm is similar to Thompson's construction, once the ε-transitions are removed.
## Related Research Articles
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack.
In theoretical computer science and formal language theory, a regular language is a formal language that can be expressed using a regular expression, in the strict sense of the latter notion used in theoretical computer science.
In computer science and automata theory, a Büchi automaton is a type of ω-automaton, which extends a finite automaton to infinite inputs. It accepts an infinite input sequence if there exists a run of the automaton that visits one of the final states infinitely often. Büchi automata recognize the omega-regular languages, the infinite word version of regular languages. It is named after the Swiss mathematician Julius Richard Büchi who invented this kind of automaton in 1962.
In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. Deterministic refers to the uniqueness of the computation run. In search of the simplest models to capture finite-state machines, Warren McCulloch and Walter Pitts were among the first researchers to introduce a concept similar to finite automata in 1943.
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if
In the theory of computation, a generalized nondeterministic finite automaton (GNFA), also known as an expression automaton or a generalized nondeterministic finite state machine, is a variation of a nondeterministic finite automaton (NFA) where each transition is labeled with any regular expression. The GNFA reads blocks of symbols from the input which constitute a string as defined by the regular expression on the transition. There are several differences between a standard finite state machine and a generalized nondeterministic finite state machine. A GNFA must have only one start state and one accept state, and these cannot be the same state, whereas a NFA or DFA both may have several accept states, and the start state can be an accept state. A GNFA must have only one transition between any two states, whereas a NFA or DFA both allow for numerous transitions between states. In a GNFA, a state has a single transition to every state in the machine, although often it is a convention to ignore the transitions that are labelled with the empty set when drawing generalized nondeterministic finite state machines.
In theoretical computer science, more precisely in the theory of formal languages, the star height is a measure for the structural complexity of regular expressions and regular languages. The star height of a regular expression equals the maximum nesting depth of stars appearing in that expression. The star height of a regular language is the least star height of any regular expression for that language. The concept of star height was first defined and studied by Eggan (1963).
In automata theory, an alternating finite automaton (AFA) is a nondeterministic finite automaton whose transitions are divided into existential and universal transitions. For example, let A be an alternating automaton.
A finite-state transducer (FST) is a finite-state machine with two memory tapes, following the terminology for Turing machines: an input tape and an output tape. This contrasts with an ordinary finite-state automaton, which has a single tape. An FST is a type of finite-state automaton that maps between two sets of symbols. An FST is more general than a finite-state automaton (FSA). An FSA defines a formal language by defining a set of accepted strings, while an FST defines relations between sets of strings.
In the theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) which recognizes the same formal language. It is important in theory because it establishes that NFAs, despite their additional flexibility, are unable to recognize any language that cannot be recognized by some DFA. It is also important in practice for converting easier-to-construct NFAs into more efficiently executable DFAs. However, if the NFA has n states, the resulting DFA may have up to 2n states, an exponentially larger number, which sometimes makes the construction impractical for large NFAs.
In computer science, in particular in automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input.
In quantum computing, quantum finite automata (QFA) or quantum state machines are a quantum analog of probabilistic automata or a Markov decision process. They provide a mathematical abstraction of real-world quantum computers. Several types of automata may be defined, including measure-once and measure-many automata. Quantum finite automata can also be understood as the quantization of subshifts of finite type, or as a quantization of Markov chains. QFAs are, in turn, special cases of geometric finite automata or topological finite automata.
In automata theory, DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this task are known and described in standard textbooks on automata theory.
In computer science, more specifically in automata and formal language theory, nested words are a concept proposed by Alur and Madhusudan as a joint generalization of words, as traditionally used for modelling linearly ordered structures, and of ordered unranked trees, as traditionally used for modelling hierarchical structures. Finite-state acceptors for nested words, so-called nested word automata, then give a more expressive generalization of finite automata on words. The linear encodings of languages accepted by finite nested word automata gives the class of visibly pushdown languages. The latter language class lies properly between the regular languages and the deterministic context-free languages. Since their introduction in 2004, these concepts have triggered much research in that area.
In graph theory, the cycle rank of a directed graph is a digraph connectivity measure proposed first by Eggan and Büchi. Intuitively, this concept measures how close a digraph is to a directed acyclic graph (DAG), in the sense that a DAG has cycle rank zero, while a complete digraph of order n with a self-loop at each vertex has cycle rank n. The cycle rank of a directed graph is closely related to the tree-depth of an undirected graph and to the star height of a regular language. It has also found use in sparse matrix computations and logic (Rossman 2008).
In automata theory, a branch of theoretical computer science, an ω-automaton is a variation of finite automatons that runs on infinite, rather than finite, strings as input. Since ω-automata do not stop, they have a variety of acceptance conditions rather than simply a set of accepting states.
The regular expression denial of service (ReDoS) is an algorithmic complexity attack that produces a denial-of-service by providing a regular expression that takes a very long time to evaluate. The attack exploits the fact that most regular expression implementations have exponential time worst case complexity: the time taken can grow exponentially in relation to input size. An attacker can thus cause a program to spend an unbounded amount of time processing by providing such a regular expression, either slowing down or becoming unresponsive.
In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma.
In computer science theory – particularly formal language theory – the Glushkov Construction Algorithm, invented by Victor Mikhailovich Glushkov, transforms a given regular expression into an equivalent nondeterministic finite automaton (NFA). Thus, it forms a bridge between regular expressions and nondeterministic finite automata: two abstract representations of the same class of formal languages.
In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton (DFA) is an UFA, but not vice versa. DFA, UFA, and NFA recognize exactly the same class of formal languages. On the one hand, an NFA can be exponentially smaller than an equivalent DFA. On the other hand, some problems are easily solved on DFAs and not on UFAs. For example, given an automaton A, an automaton A which accepts the complement of A can be computed in linear time when A is a DFA, it is not known whether it can be done in polynomial time for UFA. Hence UFAs are a mix of the worlds of DFA and of NFA; in some cases, they lead to smaller automata than DFA and quicker algorithms than NFA.
## References
1. Alfred Vaino Aho; Monica S. Lam; Ravi Sethi; Jeffrey D. Ullman (2007). "3.7.4 Construction of an NFA from a Regular Expression" (print). (2nd ed.). Boston, MA, USA: Pearson Addison-Wesley. p. 159–163. ISBN 9780321486813.
2. Louden, Kenneth C. (1997). "2.4.1 From a Regular Expression to an NFA" (print). Compiler construction : Principles and Practice (3rd ed.). 20 Park Plaza Boston, MA 02116-4324, US: PWS Publishing Company. pp. 64–69. ISBN 978-0-534-93972-4.CS1 maint: location (link)
3. Ken Thompson (Jun 1968). "Programming Techniques: Regular expression search algorithm". Communications of the ACM. 11 (6): 419–422. doi:10.1145/363347.363387.
4. Xing, Guangming. "Minimized Thompson NFA" (PDF).
5. Watson, Bruce W. (1995). A taxonomy of finite automata construction algorithms (PDF) (Technical report). Eindhoven University of Technology. Computing Science Report 93/43.
6. R. McNaughton, H. Yamada (Mar 1960). "Regular Expressions and State Graphs for Automata". IEEE Transactions on Electronic Computers. 9 (1): 39–47. doi:10.1109/TEC.1960.5221603. | 3,884 | 17,747 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2020-10 | latest | en | 0.898051 |
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If S and T are non-zero numbers and
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If S and T are non-zero numbers and [#permalink]
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04 Nov 2012, 08:20
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If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?
A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. None of the above
M18-19
[Reveal] Spoiler:
Explanation provided:
1/S + 1/T = S+T;
T+S/ST = S+T→;
Cross-multiply: S+T=(S+T)∗ST;
(S+T)(ST−1)=0. Either S+T=0 or ST=1. Now, notice that if S+T=0 is true then none of the options must be true.
Question:
I understand the way of the equation, however, what I would have done is interfere at the following step:
S+T = (S+T)*ST
-> (S+T)/(S+T)=ST
-> ST = 1
Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ??
best regards
P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere.
[Reveal] Spoiler: OA
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Last edited by Bunuel on 04 Nov 2012, 15:06, edited 1 time in total.
Renamed the topic and edited the question.
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Re: GMATClub M18-19 | Arithmetic: Equations [#permalink]
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04 Nov 2012, 08:46
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SirGMAT wrote:
If S and T are non-zero numbers and 1S+1T=S+T, which of the following must be true?
A. ST=1
B. S+T=1
C. 1/S=T
D. S/T=1
E. none of the above
Explanation provided:
1/S + 1/T = S+T;
T+S/ST = S+T→;
Cross-multiply: S+T=(S+T)∗ST;
(S+T)(ST−1)=0. Either S+T=0 or ST=1. Now, notice that if S+T=0 is true then none of the options must be true.
Question:
I understand the way of the equation, however, what I would have done is interfere at the following step:
S+T = (S+T)*ST
-> (S+T)/(S+T)=ST
-> ST = 1
Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ??
best regards
P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere.
Yes, this is not correct way of cancelling. I'll show you one example.
5* 0 = 3*0
if we cancel 0 on both side, we get 5=3. is it correct? No.
The crux (and the rule) is, we can cancel out a term only when we know its not 0. So the way it is done in explanation is absolutely correct and the right method.
Hope it helps
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Re: GMATClub M18-19 | Arithmetic: Equations [#permalink]
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04 Nov 2012, 09:43
SirGMAT wrote:
If S and T are non-zero numbers and 1S+1T=S+T, which of the following must be true?
A. ST=1
B. S+T=1
C. 1/S=T
D. S/T=1
E. none of the above
Explanation provided:
1/S + 1/T = S+T;
T+S/ST = S+T→;
Cross-multiply: S+T=(S+T)∗ST;
(S+T)(ST−1)=0. Either S+T=0 or ST=1. Now, notice that if S+T=0 is true then none of the options must be true.
Question:
I understand the way of the equation, however, what I would have done is interfere at the following step:
S+T = (S+T)*ST
-> (S+T)/(S+T)=ST
-> ST = 1
Is there some rule which forbids me to take this step? Or is the only option to realize so, that you perform the above given equation as well and realise that "S+T = 0" negates all other options than E.... ??
best regards
P.S. Sry if the format is terrible, this is the first question I am copying out of somewhere.
There was this fun derivation that my math teacher showed us in school. Just to demonstrate how cancelling of 0 could yield wrong results. He claimed that he could prove that 1=2 and hence all numbers are equal.
It goes as below:
Let,
$$a=b$$
Multiplying both sides by a, We get
$$a^2 = ab$$
Subtracting $$b^2$$ from both sides
$$a^2 - b^2 = ab - b^2$$
$$(a+b)(a-b) = b(a-b)$$
Cancelling $$(a-b)$$ on both sides,
$$a+b = b$$
Since $$a=b$$
$$a+a = a$$
$$2a = a$$
$$2=1$$
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Re: GMATClub M18-19 | Arithmetic: Equations [#permalink]
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04 Nov 2012, 15:06
Vips0000 wrote:
Yes, this is not correct way of cancelling. I'll show you one example.
5* 0 = 3*0
if we cancel 0 on both side, we get 5=3. is it correct? No.
The crux (and the rule) is, we can cancel out a term only when we know its not 0. So the way it is done in explanation is absolutely correct and the right method.
Hope it helps
Thanks - lol I am an idiot - ...! I even thought of the zero number things, but mistakenly memorized the prompt as telling me that the respective equation could not be "0", though it only said that each number alone is non-zero....
Thanks guys!
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Re: If S and T are non-zero numbers and [#permalink]
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04 Nov 2012, 15:08
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If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?
A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. None of the above
OE:
$$\frac{1}{S} + \frac{1}{T} = S + T$$ --> $$\frac{T+S}{ST}=S+T$$ --> cross-multiply: $$S+T=(S+T)*ST$$ --> $$(S+T)(ST-1)=0$$ --> either $$S+T=0$$ or $$ST=1$$. So, if $$S+T=0$$ is true then none of the options must be true.
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Re: If S and T are non-zero numbers and [#permalink]
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05 Nov 2012, 15:18
Bunuel wrote:
Oh sorry, only thought of the tags. Next time then!
Best regards
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Re: If S and T are non-zero numbers and [#permalink]
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07 Nov 2012, 01:12
Hi bunuel,
In this step:
s+t = (s+t)st can't we just cancel (s+t) and get ---> st =1?
thanks,
-K
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Re: If S and T are non-zero numbers and [#permalink]
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07 Nov 2012, 01:19
Bunuel wrote:
If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?
A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. None of the above
OE:
$$\frac{1}{S} + \frac{1}{T} = S + T$$ --> $$\frac{T+S}{ST}=S+T$$ --> cross-multiply: $$S+T=(S+T)*ST$$ --> $$(S+T)(ST-1)=0$$ --> either $$S+T=0$$ or $$ST=1$$. So, if $$S+T=0$$ is true then none of the options must be true.
Bunuel,
Inequalities, there is a rule that if you dont know the sign of denominator, then dont cross multiply. In your solution, how can you be so sure of the sign of ST. Please let me know if i am missing something
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Re: If S and T are non-zero numbers and [#permalink]
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07 Nov 2012, 02:30
kartik222 wrote:
Hi bunuel,
In this step:
s+t = (s+t)st can't we just cancel (s+t) and get ---> st =1?
thanks,
-K
Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.
So, if you divide (reduce) s+t = (s+t)st by (s+t), you assume, with no ground for it, that (s+t) does not equal to zero thus exclude a possible solution (notice that both st=1 AND (s+t)=0 satisfy the equation).
Hope it's clear.
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Re: If S and T are non-zero numbers and [#permalink]
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07 Nov 2012, 02:43
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Marcab wrote:
Bunuel wrote:
If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?
A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. None of the above
OE:
$$\frac{1}{S} + \frac{1}{T} = S + T$$ --> $$\frac{T+S}{ST}=S+T$$ --> cross-multiply: $$S+T=(S+T)*ST$$ --> $$(S+T)(ST-1)=0$$ --> either $$S+T=0$$ or $$ST=1$$. So, if $$S+T=0$$ is true then none of the options must be true.
Bunuel,
Inequalities, there is a rule that if you dont know the sign of denominator, then dont cross multiply. In your solution, how can you be so sure of the sign of ST. Please let me know if i am missing something
We are concerned with the sign when we cross-multiply an inequality because this operation might affect (flip) its sign (> to <, for example) but it's always safe to cross-multiply an equation.
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Re: If S and T are non-zero numbers and [#permalink]
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07 Nov 2012, 03:05
Thanks.
That cleared my doubt.
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Re: If S and T are non-zero numbers and [#permalink]
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10 Feb 2013, 06:03
Bunuel wrote:
If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?
A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. None of the above
OE:
$$\frac{1}{S} + \frac{1}{T} = S + T$$ --> $$\frac{T+S}{ST}=S+T$$ --> cross-multiply: $$S+T=(S+T)*ST$$ --> $$(S+T)(ST-1)=0$$ --> either $$S+T=0$$ or $$ST=1$$. So, if $$S+T=0$$ is true then none of the options must be true.
Bunuel,
Since S+T=0 OR ST=1 and the question asks what must be true, the answer is E ? Another way to answer the question. . Is my reasoning right?
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Re: If S and T are non-zero numbers and [#permalink]
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10 Feb 2013, 06:09
Sachin9 wrote:
Bunuel wrote:
If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?
A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. None of the above
OE:
$$\frac{1}{S} + \frac{1}{T} = S + T$$ --> $$\frac{T+S}{ST}=S+T$$ --> cross-multiply: $$S+T=(S+T)*ST$$ --> $$(S+T)(ST-1)=0$$ --> either $$S+T=0$$ or $$ST=1$$. So, if $$S+T=0$$ is true then none of the options must be true.
Bunuel,
Since S+T=0 OR ST=1 and the question asks what must be true, the answer is E ? Another way to answer the question. . Is my reasoning right?
Yes, if for example s=1 and t=-1 (s+t=1-1=0), then none of the options is true (none of the options MUST be true).
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Re: If S and T are non-zero numbers and [#permalink]
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10 Feb 2013, 07:04
I understand what you are trying to say bunuel..
my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..
So based on this reasoning, can we say the answer is E..?
For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..
Hope you are getting what I am trying to ask..
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Re: If S and T are non-zero numbers and [#permalink]
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10 Feb 2013, 14:55
Sachin9 wrote:
I understand what you are trying to say bunuel..
my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..
So based on this reasoning, can we say the answer is E..?
For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..
Hope you are getting what I am trying to ask..
I would say that don't generalize this point. You know that because there are two solutions, any of the given options need not be a MUST. But if u really have an option that says (s+t)(st-1)=0 then that MUST be true.
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Re: If S and T are non-zero numbers and [#permalink]
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10 Feb 2013, 19:17
Vips0000 wrote:
Sachin9 wrote:
I understand what you are trying to say bunuel..
my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..
So based on this reasoning, can we say the answer is E..?
For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..
Hope you are getting what I am trying to ask..
I would say that don't generalize this point. You know that because there are two solutions, any of the given options need not be a MUST. But if u really have an option that says (s+t)(st-1)=0 then that MUST be true.
But if u really have an option that says (s+t)(st-1)=0 then that MUST be true.
Ididn;t understand this.. if (s+t)(st-1)=0 then either s+t=0 or st-1=0.. we still have a OR here
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Re: If S and T are non-zero numbers and [#permalink]
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11 Feb 2013, 01:59
Sachin9 wrote:
Vips0000 wrote:
Sachin9 wrote:
I understand what you are trying to say bunuel..
my question is that since the equation results in 2 soln and we have a OR .. . that is soln 1 OR soln 2 and the question asks for MUST be true..
So based on this reasoning, can we say the answer is E..?
For something must be true , we cannot have soln 1 OR soln 2.. we need to have 1 soln / soln1 AND soln2..
Hope you are getting what I am trying to ask..
I would say that don't generalize this point. You know that because there are two solutions, any of the given options need not be a MUST. But if u really have an option that says (s+t)(st-1)=0 then that MUST be true.
But if u really have an option that says (s+t)(st-1)=0 then that MUST be true.
Ididn;t understand this.. if (s+t)(st-1)=0 then either s+t=0 or st-1=0.. we still have a OR here
If the question were to be this:
If S and T are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?
A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. None of the above
F. (s+t)(st-1)=0
Then your generalization will go wrong as you have an ans choice F that must hold true.
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Re: If S and T are non-zero numbers and [#permalink]
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11 Feb 2013, 02:55
I get it Vippss. But in all other cases, the generalization will hold good right?
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Re: If S and T are non-zero numbers and [#permalink]
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11 Feb 2013, 08:44
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Sachin9 wrote:
I get it Vippss. But in all other cases, the generalization will hold good right?
Rules are good, generalizations are not
Enjoy and practice kudos :-p
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Re: If S and T are non-zero numbers and [#permalink]
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11 Feb 2013, 08:51
Vips0000 wrote:
Sachin9 wrote:
I get it Vippss. But in all other cases, the generalization will hold good right?
Rules are good, generalizations are not
Enjoy and practice kudos :-p
why on earth do u need kudos u already done with ur gmat. .
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Re: If S and T are non-zero numbers and [#permalink] 11 Feb 2013, 08:51
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The question is simple: Suppose $f : \mathbb{R}^ 2 \to \mathbb{R}^ 2$ is continuous. Show that there exist $\lambda > 0$ and $x \in \mathbb{R}^2$ such that $f(x) = \lambda x$.
So basically, we have to show that there is at least one point that gets scaled by $f$. If $f$ has a fixed point $x^*$, then we are done, since we can then take $x = x^ *$ and $\lambda = 1$ and we are done. What we could do is arrive at a contradiction when assuming that the following is not true: for all $\lambda > 0$, we have that $(1/\lambda) f(x)$ has no fixed point $x^*$. Because then, by contradiction, there is a $\lambda$ such that the function $(1/\lambda) f(x)$ has a fixed point $x^*$, so that $f$ had to scale $x^*$ by exactly $\lambda$, which is what we wanted.
However, why should we arrive at contradiction? Since $f$ has no fixed point, why is it a problem if $(1/\lambda) f$ doesn't have one either?
• Do you know any fixed-point theorems? Have you tried adapting your situation to fit the conditions of such theorems? – Mees de Vries May 10 '16 at 14:19
• Yes, I know about the fixed-point theorems by Banach and Brouwer. Is there another useful one? – limitIntegral314 May 10 '16 at 14:20
• The one by Brouwer ought to do it. (Of course, you have to fit your situation into the conditions of the theorem.) Hint: you can even prove that $x$ lies in the unit disc. – Mees de Vries May 10 '16 at 14:24
• I think I got it. If $g$ is the restriction of $f$ to the unit disk, look at the image of $g$ and then divide all elements in said image by $\lambda$, the length of the vector that is the furthest away from the origin. Then $g$ divided by $\lambda$ is a function from the unit disk to the unit disk, and hence has a fixed point, which means $g$ (and hence $f$) had to scale that fixed point by $\lambda$. – limitIntegral314 May 10 '16 at 14:30 | 562 | 1,915 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2019-35 | latest | en | 0.948174 |
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# How do I calculate 10% of a total?
## How do I calculate 10% of a total?
To calculate 10 percent of a number, simply divide it by 10 or move the decimal point one place to the left. For example, 10 percent of 230 is 230 divided by 10, or 23. 5 percent is one half of 10 percent. To calculate 5 percent of a number, simply divide 10 percent of the number by 2.
What will be the 10% of 300?
Percentage Calculator: What is 10. percent of 300? = 30.
### How do you calculate 10% of a percent?
1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y
1. Convert the problem to an equation using the percentage formula: P% * X = Y.
2. P is 10%, X is 150, so the equation is 10% * 150 = Y.
3. Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
What will be the 10% of 350?
Percentage Calculator: What is 10 percent of 350? = 35.
#### How do I calculate 10 percent of my check?
If you are paid hourly, your gross pay might vary from paycheck to paycheck. Either way, take your gross earnings—the amount before taxes or other deductions are withheld—and multiply that number by 0.10. (This is the same as dividing by 10.)
How do you deduct 10 percent from an amount?
How do I calculate a 10% discount?
1. Take the original price.
2. Divide the original price by 100 and times it by 10.
3. Alternatively, move the decimal one place to the left.
4. Minus this new number from the original one.
5. This will give you the discounted value.
6. Spend the money you’ve saved!
## How can calculate percentage?
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.
What number is 10 percent of 50?
5
Answer: 10% of 50 is 5.
### What number is 10 percent of 700?
10 percent of 700 is 70.
What number is 10 percent of 400?
Percentage Calculator: What is 10. percent of 400? = 40.
#### How do you calculate 10 percent of basic salary?
The amount of tax deduction that can be claimed will be the least of the following:
1. (Actual rent paid) – (10% of the basic salary) = Rs. 12,000 – (10% of Rs. 23,000) = Rs. 9,700; or.
2. Actual HRA offered by the employer = Rs. 15,000; or.
3. 50% of the basic salary = 50% of Rs. 23,000 = Rs. 11,500.
How do I calculate the percentage of taxes taken out of my paycheck?
If you’d like to calculate the overall percentage of tax deducted from your paycheck, first add up the dollar amounts of each tax withheld. Divide the total of your tax deductions by your total, or gross, pay. Multiply the result by 100 to convert it to a percentage. | 737 | 2,719 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2023-23 | longest | en | 0.886465 |
blog.52challenges.com | 1,527,080,849,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865651.2/warc/CC-MAIN-20180523121803-20180523141803-00628.warc.gz | 37,135,688 | 10,835 | Some would probably say: a�?what kind of a question is that?! You just find a calorie calculator in the Internet, fill in some basic data and therea��s the answera�?. So maybe the question should be rephrased as: How do THEY know how many calories there is in food? And by a�?thema�? I mean nutritionists and the people who have developed the calorie calculators. Many of us count calories, but do we really know what the calories are?
Calories vs. calories
It all comes down to physics, actually. We used to talk, write and read about calories, which in terms of physics, are very small units of energy. In fact, talking about calories in food, we usually mean kilocalories (a.k.a. kcal or Calories). Herea��s the difference between the two:
• 1 calorie is the amount of energy needed to heat 1 gram of water to 1 Celsius degree
• 1 Calorie (kilocalorie, or kcal) is the amount of energy needed to heat 1 kilogram of water to 1 Celsius degree
Thus, 1 calorie is 1/1000 of a Calorie
The estimates given in calorie calculator are given in Calories (kcal), even if they say a�?caloriesa�?.
How does the process of measuring calories in food looks like?
To measure the amount of calories included in piece of food, the scientist use a piece of lab equipment called theA�bomb calorimeter. The bomb calorimeter is constructed of two chambers, one put inside of the other. They put a piece of food (of a certain mass) in the inner chamber.
Next, the chamber is filled up with oxygen and tightly locked. The outer chamber is filled with the measured amount of water. An electric spark ignites the food in oxygen a�� the food is literally burned.A�What is actually measured is the change of water temperature.
Basically, if the water gets warmer of 1 Celsius degree per kilogram, it means the food has 1 kcal. And if the temperature rises of 70 degrees per kilogram of water, the food has 70 kcal.
Does it mean the food producers burn food in the lab?
Probably, hardly any of them does. They estimate the calories on the basis of how much carbohydrates, protein and fat their product includes.
• 1 gram of carbohydrates is estimated as 4 kcal
• 1 gram of protein is estimated as 4 kcal
• 1 gram of fat is estimated as 9 kcal
Whata��s important, the estimation of calories used on food labels considers the fact that human body cannot a�?burna�? all of the food wea��re eating, as it takes place in the bomb calorimeter. For more details, see the movie below broadcasted by GUStrength.
Do we really need to count the calories?
As you can see, the numbers are just estimation rather than complete data. They do give us a sense of control over what we eat. But healthy eating isn’t just about the amount of calories. For instance, a wheatmeal biscuit and an apple are both 70 kcal. Both include carbohydrates and sugar. An apple, however, contains natural fructose, vitamins, amino acids, and fiber. The biscuit, on the other hand, is made of white flour, refined sugar, oil, and salt.
So it’s not only about how much energy we provide your body with, but in what ingredients the energy is actually contained. Also, we can estimate, on the basis of a table from the internet or a smartphone app, that a piece of meat wea��re going to eat for dinner is X kcal. But actually, wea��re not sure what percentage of the piece of meat is fat, and what percentage is protein. We estimate all the time.
All in all, the scrupulous counting of every calorie is not what we need to lose weight. The counting itself does not make us burn fat. We really do not have to count calories to know that it’s more beneficial for us to eat a piece of fruit instead of a cookie. But if you really need counting calories, and that’s what makes you happy, you should at least be aware of what youa��re actually counting.
Counting or not, be reasonable and dona��t let the numbers take control over your mind. | 912 | 3,890 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2018-22 | latest | en | 0.944729 |
https://www.slideserve.com/chemistrytutoring/physics-homework-help | 1,618,739,962,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038469494.59/warc/CC-MAIN-20210418073623-20210418103623-00450.warc.gz | 1,101,872,859 | 22,095 | # Physics Homework help - PowerPoint PPT Presentation
Physics Homework help
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Physics Homework help
## Physics Homework help
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##### Presentation Transcript
1. Arun Rao Kinematic equations
2. General Uses • These are used to describe the relationships between the following kinematic quantities: • Distance/displacement • Speed/velocity • Time • Acceleration • When there is an unknown, it can be solved for when the values of the other quantities are given
3. The Four Basic Kinematic Equations are: • V = V0 + a Δt • V2 = V02 + 2aΔs • S = V0Δt + 0.5 a Δt2 • S = (V0 + V)/2 × t
4. V = V0 + a Δt E.g. A car starts at rest and accelerates uniformly at 2 m/s2 for 5 seconds and stops accelerating from here on. Calculate its velocity after t = 5 seconds. Using V = V0 + a Δt, we sub in values 0 for V0, 2 for a and 5 for t. Solving for V, we get: V = 10 m/s
5. V2 = V02 + 2aΔs E.g. A train accelerates from 10 m/s to 40 m/s at an acceleration of 1m/s 2. what distance does it cover during this time. Using V2 = V02 + 2aΔs, we sub in values 40 for V, 10 for V0 and 1 for a. Re-arranging to solve for s, we get: S = 750 m
6. S = V0Δt + 0.5 a Δt2 E.g. A body starts from rest at a uniform acceleration of 3 m/s2. how long does it take to cover a distance of 100m. Using S = V0Δt + 0.5 a Δt2, we sub in values 3 for a, 0 for V0 and 100 for s. Re-arranging the equation and solving for t (using the quadratic formula), we get: t = 8.51 or -8.51 seconds. As time cannot be negative, t = 8.51 seconds.
7. S = (V0 + V)/2 × t A car decelerates from 20 m/s to 10 m/s over a period of 10 seconds. How far does it travel during this time period. Using S = (V0 + V)/2 × t, we sub in values 20 for V0, 10 for V and 10 for t. Solving for s, we get: S = 150m
8. Note: • All units must be converted such that they are uniform for different variable throughout the calculations. • Kinematic quantities that are scalar CANNOT be negative, hence any such alternate solutions obtained must be disregarded.
9. Standard units for the various quantities are as follows: • Speed – metres/second • Acceleration – metres/second squared • Distance – metres • Time - seconds
10. Thank you for listening/watching | 723 | 2,311 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.40625 | 4 | CC-MAIN-2021-17 | latest | en | 0.805246 |
https://admin.clutchprep.com/physics/practice-problems/86694/review-a-7-80-g-bullet-moving-at-575-m-s-strikes-the-hand-of-a-superhero-causing | 1,601,280,055,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401598891.71/warc/CC-MAIN-20200928073028-20200928103028-00364.warc.gz | 250,719,304 | 22,961 | # Problem: Review. A 7.80-g bullet moving at 575 m/s strikes the hand of a superhero, causing the hand to move 5.50 cm in the direction of the bullet’s velocity before stopping. (a) Use work and energy considerations to find the average force that stops the bullet. (b) Assuming the force is constant, determine how much time elapses between the moment the bullet strikes the hand and the moment it stops moving.
⚠️Our tutors found the solution shown to be helpful for the problem you're searching for. We don't have the exact solution yet.
###### Problem Details
Review. A 7.80-g bullet moving at 575 m/s strikes the hand of a superhero, causing the hand to move 5.50 cm in the direction of the bullet’s velocity before stopping. (a) Use work and energy considerations to find the average force that stops the bullet. (b) Assuming the force is constant, determine how much time elapses between the moment the bullet strikes the hand and the moment it stops moving.
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Net Work & Kinetic Energy concept. You can view video lessons to learn Net Work & Kinetic Energy. Or if you need more Net Work & Kinetic Energy practice, you can also practice Net Work & Kinetic Energy practice problems.
What textbook is this problem found in?
Our data indicates that this problem or a close variation was asked in Physics for Scientists and Engineers - Serway Calc 9th Edition. You can also practice Physics for Scientists and Engineers - Serway Calc 9th Edition practice problems. | 358 | 1,656 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2020-40 | latest | en | 0.898364 |
https://3jlearneng.blogspot.com/2016/04/castle-overrun-and-storm-boat-creating.html | 1,600,513,775,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400191780.21/warc/CC-MAIN-20200919110805-20200919140805-00622.warc.gz | 255,039,548 | 16,114 | ## Monday, April 18, 2016
### Castle overrun and storm the boat (creating games)
Playing Santorini with a make-shift set inspired the older two Js to create their own games. We test played J1's game, but haven't yet had a chance to test play J2's game.
# Castle Overrun
Equipment:
TRIO set. In particular, we used the 7x14 top, 5 short and 1 long magenta and 5 short and 1 long green straight connectors, 50+ 1x1x1 cubes. The long connectors are kings, the short connectors are soldiers. Key feature is that the cubes can stack on top of each other and on top of the soldier/king pieces.
Set-up:
Kings start in diagonally opposite corners with their soldiers one square away. Pre-placed cubes also start on positions (6, 3), (6, 5), (9, 3) and (9, 5).
You can see these details in the picture below (the extra chains of cubes were just on the board to give a tidy "resting" set-up when we weren't playing):
Turns
Turns alternate. On a player's turn, they move one of their pieces (the king or a soldier) one grid space (pieces can move diagonally). Then, they have an option of one of 3 possible actions:
• build a cube on an adjacent space (including diagonally adjacent). There is no limit to how high they can build. Think of this as building part of a wall or tower. A king can build two bricks on one turn.
• destroy the top cube on an adjacent space. This is tearing down a part of a wall.
• Attack an opponent's piece on an adjacent square. This involves putting a cube on top of that piece. The J's called this "pig-heading" and a piece with a cube on top is "pig-headed." If a soldier has 2 cubes on top, they get removed from the board. If a king gets 3 cubes on top, then it gets removed from the board.
Winning
First player to remove the opponent's king from the board is the winner.
Playability
There are some elements that suggest this game has possibilities, but the current rules quickly become a stalemate. First, we noticed that any attempt to pig-head an opponent is a half-suicide mission, since they can pig-head right back on their turn. There is one exception, but it involves the opponent accidentally walking into an obvious trap (and there's no reason why they would do that).
Also, the king can quickly build a fortress around himself before the enemy soldiers get close. Because the king can build two bricks on a turn, it would be impossible for the enemy soldiers to break through. In fact, this strategy is what gave us the idea for the name of the game.
Possible modifications
The main problem is that wall building is too fast. Perhaps we should allow the soldiers to break down two bricks each turn, but restrict all building to one brick at a time. This means that any fortress can, eventually, be broken down, if the siege army is unmolested.
# Storm the Boat
Equipment
Again, this is based on the TRIO set, but also requires 2 dice (choose your favorite sizes/shapes/markings).
Set-up
The straight connectors start in the same corner configuration as Castle Overrun:
Again, place one cube on each space (6, 3), (6, 5), (9, 3), (9, 5). Further, add bricks in a line from (1,2) to (4, 2) and (11, 6) to (14, 6).
There is another special piece in the center of the board, the boat:
Turns
Player rolls two dice and then moves a piece according to the values shown on the dice. They can move one piece for both values, or move two different pieces. Restrictions: movement is orthogonal (not diagonal) and pieces can not pass through a space occupied by another piece.
Pieces can move up one level on the boat. For example, if they are next to an open bottom magenta space, they can move onto the boat. If they are on the magenta level, they can move onto the blue seats.
After moving, the player pushes the boat one space toward their starting corner. This means that only one of the boat entry points is available at a time. This is like a moored boat rocking back and forth with the waves.
Winning
The first player to get three pieces onto the boat seats is the winner. They get a double win if their "king" is one of the pieces to get onto the boat.
Playability
This seems to be a solid racing game, similar to many other games for children. The boat mechanic adds a small twist. It seems playable and fun for kids, but lacks any deep strategy.
Possible modifications suggested have been:
(a) some way for the two teams to attack each other
(b) a way to release the boat from its anchor so that the movement is more extreme and/or erratic
(c) possibility for a team to attack the boat and sink it (perhaps to prevent an opponent from reaching the winning condition).
# Summary thoughts
Putting aside how good their games were, I was delighted with the ideas and enthusiasm both J1 and J2 had for creating their own games. While I had been hoping they would have been more pro-active about designing a DIY Santorini set the day before, it seems that exposing them to this gave them a boost of inspiration to try their own. | 1,166 | 4,980 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2020-40 | latest | en | 0.954773 |
https://convertoctopus.com/4105-miles-to-millimeters | 1,685,268,415,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224643663.27/warc/CC-MAIN-20230528083025-20230528113025-00383.warc.gz | 223,202,095 | 7,422 | ## Conversion formula
The conversion factor from miles to millimeters is 1609344, which means that 1 mile is equal to 1609344 millimeters:
1 mi = 1609344 mm
To convert 4105 miles into millimeters we have to multiply 4105 by the conversion factor in order to get the length amount from miles to millimeters. We can also form a simple proportion to calculate the result:
1 mi → 1609344 mm
4105 mi → L(mm)
Solve the above proportion to obtain the length L in millimeters:
L(mm) = 4105 mi × 1609344 mm
L(mm) = 6606357120 mm
The final result is:
4105 mi → 6606357120 mm
We conclude that 4105 miles is equivalent to 6606357120 millimeters:
4105 miles = 6606357120 millimeters
## Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 millimeter is equal to 1.5136935255477E-10 × 4105 miles.
Another way is saying that 4105 miles is equal to 1 ÷ 1.5136935255477E-10 millimeters.
## Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that four thousand one hundred five miles is approximately six billion six hundred six million three hundred fifty-seven thousand one hundred twenty millimeters:
4105 mi ≅ 6606357120 mm
An alternative is also that one millimeter is approximately zero times four thousand one hundred five miles.
## Conversion table
### miles to millimeters chart
For quick reference purposes, below is the conversion table you can use to convert from miles to millimeters
miles (mi) millimeters (mm)
4106 miles 6607966464 millimeters
4107 miles 6609575808 millimeters
4108 miles 6611185152 millimeters
4109 miles 6612794496 millimeters
4110 miles 6614403840 millimeters
4111 miles 6616013184 millimeters
4112 miles 6617622528 millimeters
4113 miles 6619231872 millimeters
4114 miles 6620841216 millimeters
4115 miles 6622450560 millimeters | 497 | 1,898 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2023-23 | latest | en | 0.712866 |
https://switzerite.blogspot.com/2010/02/bio-cube-famous-mathematicians.html | 1,590,988,857,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347414057.54/warc/CC-MAIN-20200601040052-20200601070052-00153.warc.gz | 560,208,578 | 23,181 | ## Tuesday, February 23, 2010
### Bio-Cube & Famous Mathematicians
Here's a great activity that has taken my classroom by storm. It's called the "Bio-Cube" and my students are sooo thrilled to be researching famous mathematicians from throughout history, reading their biographies, and preparing reports on them. They are acting like I've just been passing out tickets to Kings Dominion or free pony rides! Why? Because the Bio-Cube is a cool, fun, and unique kind of report.
Here's the deal. First, you need a biography. We are using stories from Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians by Luetta and Wilbert Reimer. These are chatty anecdotes that include some of the world's famous mathematical discoveries. I introduced the project by reading the chapter about Thales of Miletus. I demonstrated how pyramids cast a shadow using a 3-D Geometric Solid. I also demonstrated how salt dissolves in water using a plain dish of table salt and pouring water into it from a pitcher, waiting a minute, and then pouring the water from the dish back into the pitcher and showing how much of the salt has dissolved.
Today, I showed my students the Bio-Cube Planning Page (which you can download as a pdf here) and we reviewed the story, filling in the 6 key facts about Thales. I then showed them how you transfer your notes from the planning sheet to each of the six squares on the cube template (download a cube template). This planning sheet helps make notetaking more manageable, by telling students six key facts to research, and keeps the report from becoming overwhelming. After writing the information on my cube, I cut it out and glued the flaps to assemble my report.
My students were FASCINATED and can't wait for their mathematicians to be assigned to them! The authors of this book also wrote a second one. The top Amazon review for volume 1lists every chapter for both volumes and what mathematician is covered -- it's very helpful! | 427 | 1,981 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2020-24 | latest | en | 0.963091 |
https://www.greenyneko.com/2018/01/guild-wars-2-pvp-pips-vs-wvw-pips.html | 1,725,755,762,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650926.21/warc/CC-MAIN-20240907225010-20240908015010-00691.warc.gz | 762,438,842 | 21,868 | ## 10 January 2018
### Guild Wars 2: PvP Pips vs WvW Pips
So you may remember me checking out how many matches the PvP season in Guild Wars 2 takes and you may remember me doing some calculation on how much the WvW pips have taken. Today I'm gonna combine both calculations and research to compare them with each other!
#### Calculating How Long PvP Takes
We only know the amount of matches PvP takes but not the amount of time. Especially since this value changes according to every single match you may have, we can only assume an average which we can work with, but that should be no problem.
If you remember back in the PvP post we have found out that an average player or a player under platinum needs 61 to 224 matches to complete PvP. Next, we need to know how long a match takes on average. Unfortunately, you can only see your last ten PvP matches so I have to work with this.
These matches took me:
match length 10m 22s 14m 12m 15s 6m 8s 10m 8s 11m 33s 8m 36s 9m 30s 5m 54s 10m 10s conversion calculation 10 * 60 + 22 14 * 60 12 * 60 + 15 6 * 60 + 8 10 * 60 + 8 11 * 60 + 33 8 * 60 + 36 9 * 60 + 30 5 * 60 + 54 10 * 60 + 10 time in seconds 622 840 735 368 608 693 516 570 354 610
Now we can add up all the seconds and divide it through the amount of matches we've listed - ten matches. Doing so we'll get:
(622 + 840 + 735 + 368 + 608 + 693 + 516 + 570 + 354 + 610) / 10 = 591.6
Converting this back to minutes we have 591.6 / 60 = ~9.86 minutes per match. Next, we apply the queue time. Queues are on average around 2 minutes. The time, until everyone has readied up, is probably around 5 to 30 seconds on average more like 12 seconds. The map selection takes most likely around 8 seconds and the time until a match actually starts is on average about 55 seconds including the loading screens. Summing all this up we get 12 + 8 + 55 = 75 seconds, which is 75 / 60 = 1.25 minutes plus the 2 minutes from before. So I'd say it's safe to assume 3.25 minutes to wait for each match. Adding this to our previous number we now get 9.86 + 3.25 = 13.11 minutes for each match.
Now multiplying this with our amount of matches we need, we get between 13.11 * 61 = 799.71 minutes and 13.11 * 224 = 2936.64 minutes to complete the season track. Those numbers seem big, let's convert them to hours by dividing through 60 again. Now it's 799.71 / 60 = ~13.33 to 2936.64 / 60 = ~48.94 hours to complete it. That sounds fairly reasonable for how long a season goes.
Though we haven't gotten the real minimum here. A player who gets the most pips, that's what we have to calculate with to get a total minimum. At least we have our total maximum dependent on average time. We could calculate the maximum time with 15 minutes since that's how long a match can take at most, usually. However, it's extremely unlikely for every match to take that long.
Our next step is to assume the minimum amount of matches which is 45 matches. 45 matches taking ~13.11 minutes per match or 45 * 13.11 = 589.95 minutes, that's 589.95 / 60 = 9.833 hours.
Combining the total minimum and the maximum we get a range from 9.83 hours to ~48.94 hours.
#### Taking the WvW Time Consumption Into Consideration
We don't need to calculate much here since the prior post has taken care of this already. In the post, we've calculated that it takes between 6.36 hours and 40.28 hours.
#### Start the Comparison
Now that we have our numbers we can start to compare. The easiest way to compare is to calculate the reward we get in the same time unit. To get the same time unit we need to divide the reward through the time it takes to get it. Luckily I've already listed the rewards in the prior posts so here we go:
#### PvP Rewards
• 560 Shards of Glory
• 34 Unidentified Dyes
• 83 gold 85 silver
• 44 Transmutation Charges
• 100 PvP League Tickets
• 400 Ascended Shards of Glory
• Boxes of Grandmaster Marks
• 1 Llama Mini Choice Box
• 560 / 48.94 = 11.44 to 560 / 9.833 = 56.95 Shards of Glory every hour
• 34 / 48.94 = 0.69 to 34 / 9.833 = 3.46 Unidentified Dyes per hour
• 838500 / 48.94 = 17133 to 838500 / 9.833 = 85274 copper each hour
• 44 / 48.94 = 0.9 to 44 / 9.833 = 4.47 Transmutation Charges every hour
• 100 / 48.94 = 2.04 to 100 / 9.833 = 10.17 PvP League Tickets per hour
• 400 / 48.94 = 8.17 to 400 / 9.833 = 40.68 Ascended Shards of Glory an hour
• 3 / 48.94 = 0.06 to 3 / 9.833 = 0.31 Boxes of Grandmaster Marks each hour
• 1 / 48.94 = 0.02 to 1 / 9.833 = 0.1 Llama Mini Choice Box every hour
#### WvW Rewards
• 365 WvW Skirmish Claim Tickets
• 35 Skirmish Chests
• 76 Memories of Battle
• 142 Reward Track Progresses
• 11 Mist-Warped Packet
• Mist-Warped Bundles
• Mystic Coins
Next, we do the same with the WvW rewards but using the WvW times:
• 365 / 40.28 = 9.06 to 365 / 6.36 = 57.39 WvW Skirmish Claim Tickets every hour
• 35 / 40.28 = 0.87 to 35 / 6.36 = 5.5 Skirmish Chests an hour
• 76 / 40.28 = 1.89 to 76 / 6.36 = 11.95 Memories of Battle per hour
• 142 / 40.28 = 3.53 to 142 / 6.36 = 22.33 Reward Track Progresses each hour
• 11 / 40.28 = 0.27 to 11 / 6.36 = 1.73 Mist-Warped Packet every hour
• 3 / 40.28 = 0.07 to 3 / 6.36 = 0.47 Mist-Warped Bundles an hour
• 4 / 40.28 = 0.1 to 4 / 6.36 = 0.63 Mystic Coins per hour
#### Last Step
Now we either compare each piece with each other like WvW Skirmish Claim Tickets and their item prices with PvP League Tickets or we calculate the total worth of all items and compare that with each other. Another option would be to do both of these options.
So let's start comparing the tickets. In PvP, you need 20 of these for the Record of League Participation and another 30 for the Record of League Victories to upgrade your armor to legendary. In WvW you need 1095 to upgrade armor to legendary. This means you need 50 for PvP and 1095 for WvW, which is 1095 / 50 = 21.9 times more. So, in this case, WvW tickets need to be 21.9 times worth more. Looking at our calculation we see that WvW tickets are 9.06 / 2.04 = 4.44 or 57.39 / 10.17 = 5.64 times worth more. Off to a bad start for WvW.
Compared to PvP, WvW gives instant reward track progress boosts. Each one gives 25 points according to the Guild Wars 2 wiki. We get between 3.53 and 22.33 reward track progress each hour. That's between 3.53 * 25 = 88.25 and 22.33 * 25 = 558.25 per hour. This is something special the PvP reward track doesn't have, and it's hard to compare it. At least we can say you get up to a whole reward more in the reward tracks each hour.
Therefore PvP rewards up to 3 Grandmaster Marks and a Llama Mini Choice box, as well as Transmutation Charges. This is also hard to compare.
I haven't researched the Mist-Warped Packet and Mist-Warped Bundles as they drop differently from the Magic-Warped Packet and the Magic-Warped Bundles. At the same time, it heavily depends on the market. Same with mystic coins and unidentified dyes. So in this regard, WvW might be better than PvP if the market stands good. Unfortunately PvP rewards between 2 gold 27 silver 79 copper and 11 gold 33 silver and 87 copper every hour on the hand with no relation to the market.
Last but not least don't forget that WvW has drops, karma and event rewards, which PvP doesn't have.
#### Conclusion
PvP and WvW consume nearly the same time for getting the total amount of pips. A huge difference here is however that PvP's seasons tend to be 8 weeks long and WvW is only one week. So you need to do 8 weeks in one week in WvW, at the same time unique currencies like the tickets are rewarded only once the track is finished, so WvW gives you a lot more tickets if you think about it, but you need to work for those tickets, quite a lot. Another huge thing is that WvW rewards are dependent on market values. If certain market values like tier 6 materials or mystic coins are high in value the WvW weekly reward track is also high in value. Same counts towards blueprints of siege weapons. The last point that should be mentioned here is that WvW boosts your normal reward tracks, so if you go for those rewards WvW is gonna be your best bet. Or doing both if you have the time to do so.
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>> Join Discord | 2,531 | 8,334 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2024-38 | latest | en | 0.902139 |
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# What Is the Best Method for Dividing Polynomials by Binomials?
A:
### Quick Answer
The best method for dividing polynomials by binomials is through long division. The first step is to divide the highest degree polynomial term by the highest degree binomial term, writing the result above the division line. This result is then multiplied by the divisor with the resulting binomial subtracted from the polynomial. The remaining polynomial is then divided by the highest degree term of the binomial.
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### Full Answer
These steps are repeated until the remaining polynomial terms have lower degrees than the binomial. Divisions that result in a remainder can be written in two ways, one of which involves writing the remainder by denoting it with the letter "R." A better way, however is to express the remainder as a fractional number. The remainder is typically the numerator, while the divisor is the numerator of the fraction, which is usually added to the quotient. It is advisable to check the result by multiplying the quotient by the divisor and adding the remainder term. Some polynomials have missing terms, which must be included in the long division in order to obtain a viable answer. Missing terms are typically associated with the value zero, but they are a crucial component of the subtraction step.
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1. What is the probability that the two beverages will be of the same kind? 2. What is the probability that the two beverages will be different? 3. What is the probability | 679 | 2,724 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2020-50 | longest | en | 0.919421 |
https://ww2.mathworks.cn/matlabcentral/answers/589657-extracting-numeric-values-from-symbolic-variables | 1,723,698,628,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641151918.94/warc/CC-MAIN-20240815044119-20240815074119-00194.warc.gz | 486,298,282 | 28,854 | # Extracting numeric values from symbolic variables
16 次查看（过去 30 天）
ali akbar 2020-9-6
I have two matrices say
x=[2 4 9 10];
syms c [1 4];
x==c
it returns
2=c1
4=c2
9=c3
10=c4
However when I write c1 in command window, it returns symbolic 'c1'.
I wanted to extract these numeric values or assign these values to c vector. How one would go around this.
### 采纳的回答
x==c
The "==" operator is normally used as a logic comparison operation, not an assignment. In the case of using symbolic variables, "==" defines an equation, which could be solved, for example, with the matlab function solve. If you want to give values to your variables, use only one "=" sign, for example:
x=[2 4 9 10];
syms c [1 4];
>> c(1) = 2
c =
[ 2, c2, c3, c4]
>> c=x
c =
2 4 9 10
##### 2 个评论显示 无隐藏 无
“ is a logic operation”. Not in this case when it contains a symbolic variables it forms an equation.
You're right, it becomes an equation when it contain symbolic variables. Since I believe he was knew to matlab I thought the more general definition of the operator would be easier to understand/apply to future cases. I will edit the answer accordingly
### 更多回答（3 个）
== forms an equation , it DOESN’T assign any values.
##### 1 个评论显示 -1更早的评论隐藏 -1更早的评论
Alphonce Owayo 2021-2-23
For example;
syms x y
eqn1=x+y==20;
eqn2=2.3x-9y==13;
soln=vpasolve(eqn1,eqn2);
xsoln=soln.x;
ysoln=soln.y;
or
xsoln=double(soln.x);
ysoln=double(son.y);
disp(xsoln);
disp(ysoln);
##### 0 个评论显示 -2更早的评论隐藏 -2更早的评论
Alphonce Owayo 2021-2-23
shown above is how to extract numeric values from symbolic variables and display them in the command window.
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https://infinitylearn.com/questions/chemistry/grams-hydrogen-reacts-with-grams-oxygen-form-water | 1,726,180,810,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651498.46/warc/CC-MAIN-20240912210501-20240913000501-00009.warc.gz | 299,481,789 | 25,013 | # Stoichiometry and Stoichiometric Calculations
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# 4 grams of Hydrogen reacts with 40 grams of Oxygen to form water. Excess reagent in the reaction is
Moderate
Solution
## Alternatively: 4 gm ${\mathrm{H}}_{2}$ = 4 equivalents which reacts with 4 equivalents of ${\mathrm{O}}_{2}$, 32 gms. Mass of excess ${\mathrm{O}}_{2}$ = 40 - 32 = 8gm.
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## Problem 78GP Chapter 6
Physics: Principles with Applications | 6th Edition
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Problem 78GP
A 65-kg hiker climbs to the top of a 3700-m-high mountain. The climb is made in 5.0 h starting at an elevation of 2300 m. Calculate (a) the work done by the hiker against gravity, (b) the average power output in watts and in horsepower, and (c) assuming the body is 15% efficient, what rate of energy input was required.
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Feb 4, 2018
See below....
Explanation:
You asked about the question, right but the answer will not be appropriate for all.
• We know that the dental formula of an adult is color(red)("I"-2;" C"-1" PM"-2;" M"-3
• For a child, it is color(red)("I"-2;" C"-1" PM"-0;" M"-2
• I will say that a $16$-year-old boy will have a dental formula like the one of an adult. | 126 | 421 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2018-51 | latest | en | 0.891102 |
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# A bomb at rest explodes into three fragments. Two of these fragments with mass m1 =...
A bomb at rest explodes into three fragments. Two of these fragments with mass m1 = 2 kg, and m2 = 1 kg respectively, travel in left direction; the other fragment with mass m3 = 3 kg travels in opposite direction. If the velocities of fragments 1 and 2 are v1 = 5 m/s and v2 = 2 m/s respectively, find the velocity of fragment 3.
According to conservation of linear momentum,
The momentum of an isolated system remains constant. Momentum is said to be conserved over time; that is, momentum is neither created nor destroyed, only transformed from one form to another.
Momentum before explosion = Momentum after collision
Let M be the total mass of bomb and u initial velocity.
According to sign convention,velocity towards right is taken positive and towards left, negative
Initially at rest, implies
Velocity of fragment 3 is 4 m/s towards right
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https://cloud.tencent.com/developer/article/1348604 | 1,604,048,422,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107909746.93/warc/CC-MAIN-20201030063319-20201030093319-00326.warc.gz | 269,190,892 | 72,297 | # leetcode: 15. 3Sum
## Problem
```# Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0?
# Find all unique triplets in the array which gives the sum of zero.
#
# Note: The solution set must not contain duplicate triplets.
#
# For example, given array S = [-1, 0, 1, 2, -1, -4],
#
# A solution set is:
# [
# [-1, 0, 1],
# [-1, -1, 2]
# ]```
## AC
```class Solution():
def threeSum(self, x):
x.sort()
res = []
for left in range(len(x) - 2):
mid, right = left + 1, len(x) - 1
while mid < right:
s = x[left] + x[mid] + x[right]
if s == 0:
if [x[left], x[mid], x[right]] not in res:
res.append([x[left], x[mid], x[right]])
mid, right = mid + 1, right - 1
elif s < 0:
mid += 1
else:
right -= 1
return res
if __name__ == '__main__':
assert Solution().threeSum([-1, 0, 1, 2, -1, -4]) == [[-1, -1, 2], [-1, 0, 1]]
assert Solution().threeSum([1 ,1, 1, -2]) == [[-2, 1, 1]]```
```class Solution():
def threeSum(self, x):
x.sort()
res = []
for left in range(len(x) - 2):
if left == 0 or x[left] != x[left-1] and x[left] <= 0:
mid, right = left + 1, len(x) - 1
while mid < right:
s = x[left] + x[mid] + x[right]
if s == 0:
res.append([x[left], x[mid], x[right]])
mid, right = mid + 1, right - 1
while mid < right and x[mid] == x[mid - 1]:
mid += 1
while mid < right and x[right] == x[right + 1]:
right -= 1
elif s < 0:
mid += 1
else:
right -= 1
return res
if __name__ == '__main__':
assert Solution().threeSum([-1, 0, 1, 2, -1, -4]) == [[-1, -1, 2], [-1, 0, 1]]
assert Solution().threeSum([1 ,1, 1, -2]) == [[-2, 1, 1]]```
0 条评论
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• ### [剑指offer] 数值的整数次方 [剑指offer] 数值的整数次方
给定一个double类型的浮点数base和int类型的整数exponent。求base的exponent次方。 | 922 | 2,121 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2020-45 | latest | en | 0.232474 |
https://www.physicsforums.com/threads/calculate-the-minimum-force-required.1046949/ | 1,701,479,227,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100309.57/warc/CC-MAIN-20231202010506-20231202040506-00405.warc.gz | 1,040,591,113 | 22,130 | # Calculate the minimum force required
misconception... to think that the block will always move when there is a force that is greater than the friction.
Homework Statement
A block of mass 10kg is placed on a rough horizontal surface with a coefficient of friction of 0.5. the minimum force required to move the block is.(g=10 m/s*s)
Relevant Equations
coefficint of friction * normal reaction = friction force
I tried taking the components but got stuck there on what value of theta I should take
What's ##\theta##?
PeroK said:
What's ##\theta##?
that's the angle
like sin30 here 30 is theta
that's the angle
What angle?
PeroK said:
What angle?
the angle on which the force is acting on the block with respect to horizontal
the angle on which the force is acting on the block with respect to horizontal
Ah, okay. How far did you get in analysing the forces? Can you post where you got stuck?
well I drew this diagram first
then for friction to be minimum I took b as my direction force acting on block
then wrote the equations
Fcosθ+N=mg------(1)
Fsinθ-friction of coefficient *N=ma-------(2)
now I don't know what to do after this
well I drew this diagram first View attachment 316634
then for friction to be minimum I took b as my direction force acting on block
then wrote the equations
Fcosθ+N=mg------(1)
Fsinθ-friction of coefficient *N=ma-------(2)
now I don't know what to do after this
You need to put an arrow on forces in your diagram.
Do you think you should pull the block above the horizontal or below the horizontal?
I don't understand the point of A and B.
PeroK said:
You need to put an arrow on forces in your diagram.
Do you think you should pull the block above the horizontal or below the horizontal?
I don't understand the point of A and B.
actually, ignore them
just think that te force applied on the block Is in the direction of B
actually, ignore them
just think that te force applied on the block Is in the direction of B
Are you sure about that? You want to pull the block into the ground? Isn't that going to increase friction and make it harder to move?
its going to pull the block off the ground.
can you just solve it on a piece of paper and post it
it would be very kind of you.
its going to pull the block off the ground.
am i wrong?
You do not know ##\theta##. However, for every value of ##\theta## there will be a corresponding necessary force. The minimum force required will be the smallest of those forces.
Orodruin said:
You do not know ##\theta##. However, for every value of ##\theta## there will be a corresponding necessary force. The minimum force required will be the smallest of those forces.
yeah i understand it
sir PeroK
help!
nailed it man
sir PeroK
help!
Your making a fundamental mistake by pulling the block into the ground. That said, if you set up your equations to allow ##\theta## to be positive or negative, then the solution would show that minumim force involves pulling the block at an angle above the horizontal.
My advice is to redraw your diagram with ##\theta## above the horizontal.
The other point is that the minimum force to move the block involves zero accleration. I.e. when the horizontal force on the block equals the frictional force.
PeroK said:
Your making a fundamental mistake by pulling the block into the ground. That said, if you set up your equations to allow ##\theta## to be positive or negative, then the solution would show that minumim force involves pulling the block at an angle above the horizontal.
My advice is to redraw your diagram with ##\theta## above the horizontal.
The other point is that the minimum force to move the block involves zero accleration. I.e. when the horizontal force on the block equals the frictional force.
if i take acceleration to be zero I would give me the force that would not move the block
to make a block move it need to have some acceleration
PeroK said:
Your making a fundamental mistake by pulling the block into the ground. That said, if you set up your equations to allow ##\theta## to be positive or negative, then the solution would show that minumim force involves pulling the block at an angle above the horizontal.
My advice is to redraw your diagram with ##\theta## above the horizontal.
The other point is that the minimum force to move the block involves zero accleration. I.e. when the horizontal force on the block equals the frictional force.
yeah got your point the θ must be above the horizontal.
thank you
if i take acceleration to be zero I would give me the force that would not move the block
to make a block move it need to have some acceleration
With the minimum force the acceleration is negligible. Above that minimum the block will move and below it the block won't move. It's a common idea.
PeroK said:
With the minimum force the acceleration is negligible. Above that minimum the block will move and below it the block won't move. It's a common idea.
considering small acceleration to be negligible we can say that
nailed it man
View attachment 316635
I don't see how you got that answer, but it doesn't look right.
Generally, you need calculus to minimise something in a problem with a continuous variable.
PeroK said:
Generally, you need calculus to minimise something in a problem with a continuous variable.
it is a basic level question of my coaching institute's daily practice paper intended for the preparation of JEE
so I think it is ought to be a little easy(not including problems with continuous variable)
it is a basic level question of my coaching institute's daily practice paper intended for the preparation of JEE
so I think it is ought to be a little easy(not including problems with continuous variable)
you are guiding me the question with understanding of high level physics
and I don't think it applies to these questions
still I am open to learn new things
it is a basic level question of my coaching institute's daily practice paper intended for the preparation of JEE
so I think it is ought to be a little easy(not including problems with continuous variable)
Then, perhaps the answer is just ##50 N##? Which is the minumum horizontal force to overcome friction. Considering a force applied at an angle is definitely a more advanced problem.
Last edited:
this
PeroK said:
Then, perhaps the answer is just ##25 N##? Which is the minumum horizontal force to overcome friction. Considering a force applied at an angle is definitely a more advanced problem.
this question has option sgiven as follows
a-20√3N
b-50√3N
c-50N
d-20√5 N
this
this question has option sgiven as follows
a-20√3N
b-50√3N
c-50N
d-20√5 N
Okay, the answer is one of those, but not a).
THE ANSWER GIVEN IS 20√5 maybe by considering that it is close to 25 as it was asked to be minimum | 1,559 | 6,780 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2023-50 | latest | en | 0.945742 |
https://mathoverflow.net/questions/288150/what-are-the-patterns-of-the-sequence-of-polynomials | 1,568,674,965,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514572964.47/warc/CC-MAIN-20190916220318-20190917002318-00044.warc.gz | 583,578,773 | 23,144 | # What are the patterns of the sequence of polynomials? [closed]
In my research, I obtained a sequence of polynomials (I am only able to compute the first 4 of them): \begin{align} & f(2) = 1+t, \\ & f(3) = 1+4t+3t^2, \\ & f(4) = 1+6t+12t^2+7t^3, \\ & f(5) = 1+8t+20t^2+28t^3+15t^4. \end{align} Is it possible to find the general formula of $f(n)$ using these 4 polynomials? Some patterns are:
1. The constant term is 1.
2. The highest degree term is $(2^{n-1}-1)t^{n-1}$.
3. $(1+t)$ is a factor of each polynomial.
Thank you very much.
## closed as unclear what you're asking by Max Alekseyev, darij grinberg, Denis Serre, Alexey Ustinov, Chris GodsilDec 18 '17 at 11:08
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
• Without definition, your question is meaningless. The next term, $f(6)$, is obviously $42$. – FindStat Dec 10 '17 at 12:14
• I don't know - I was joking. The serious point is that asking for the next term without definition of the sequence is meaningless. – FindStat Dec 10 '17 at 12:21
• You need to explain how you got the first four polynomials in order for anyone to comment on finding the next one. – Stanley Yao Xiao Dec 10 '17 at 12:37
• I don't think that the question is meaningless. I often try to understand data whose origin is irrelevant. – Richard Stanley Dec 10 '17 at 14:47
• @RichardStanley: I would guess that the OP is trying to compute homology of some complexes (with Euler characteristic 0). If he said what exactly it is, the suggestions would not be that wild. – Mark Sapir Dec 10 '17 at 19:47
## 1 Answer
Your data can be fitted with
$f(n)=(1+t) \left( \sum_{k=0}^{n-2} (2(2^k-1)(n-k-1)+1)t^k \right)$
• This is consistent with fedja's guess. Your guess may be as good as anyone's. – Todd Trimble Dec 11 '17 at 3:04 | 626 | 2,051 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2019-39 | latest | en | 0.94052 |
https://mrfixitca.com/symbol-for-ac-voltage-on-a-multimeter/ | 1,709,243,491,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474853.43/warc/CC-MAIN-20240229202522-20240229232522-00097.warc.gz | 403,256,818 | 30,155 | # What is the Symbol for AC Voltage on a Multimeter
When using a multimeter, you will see two voltage symbols. And for testing AC voltage, you must know the symbols to use it properly. In this article, you will get information about “what is the symbol for ac voltage on a multimeter.”
The symbol for the AC voltage on the multimeter is V, with the wavy line on it. The wavy line indicates the AC current, and V means voltage.
However, the DC voltage symbol is V with one dotted and a solid line. But the straight line or any dash is the symbol for the dc. The AC voltage is only measured in vols.
## What is the symbol for AC voltage on a multimeter?
AC voltage symbol on the multimeter is V〜. In the symbol V〜, V denotes voltage, and the 〜 sign means alternating current (that changes its direction). The voltage of alternating(changing) current is known as AC voltage.
Remember that the home power supply is AC voltage, and the batteries supply DC voltage
On some previous multimeter models, VAC is written on the dial (knob) to represent AC voltage instead of V〜. Signs are written on the multimeter’s surface around the dial(knob). You have to rotate the dial to the V〜 sign to check the AC voltage of a circuit.
We can measure from 200 to 600 AC volts with a multimeter. As an AC supply is available to homes at a higher level (120 or 240V), the multimeter has only a high range(200 and 600 V) to test AC voltage.
However, DC(direct current) voltage comes through the battery, ranging from small to large. That’s why multimeters have millivolts to 600V range for DC current.
## How to test AC voltage with a multimeter
To test AC voltage:
Wear protective gloves and turn on the power of the testing circuit.
• Set your multimeter to V〜(or VAC), and select a range(200 or 600V) above the circuit’s voltage you are testing.
• Connect the red probe to the live wire and the black probe to the ground wire.
• The multimeter will display the voltage of the circuit.
• To know if the circuit is fine and has maximum voltage compare the multimeter’s voltage reading of the live and ground wire with your home voltage supply(120 or 240V).
• The tested circuit should have voltage reding near your power supply if the tested circuit is fine.
• If the tested circuit is faulty, the voltage will decrease too much than your power supply, such as 100 or fewer volts in a 120V circuit.
### Major symbols on the multimeter
The standard multimeter contains the following symbols:
1. Hold button (hold button hold a test reading until you reset the multimeter)
2. Min\max button(to set minimum and maximum range)
3. Range button(capture reading in a specific range)
4. AC voltage(V〜)
5. Dc voltage(V⎓)
6. Resistance(Ω)
7. Continuity())))
8. Diode test(⇥)
9. AC(A〜) and DC(A⎓) current
### Units on a multimeter
While measuring an electrical quantity, you can select different ranges of units, such as:
1. DC voltage can be measured in millivolts and volts.
2. You can measure DC Amperage in amps(A), milliamps(mA), and microamps(µA)
3. Resistance is measured in ohms, mega ohms(Ω), kilohms(kΩ), and megaohms(MΩ).
#### Conclusion
The voltage function on the multimeter is used to measure the voltage of the AC source and DC battery. AC voltage is represented as Vand DC as V.
But If you have clear information about the symbol used on the multimeter, you will get an accurate output and be able to use the device properly.
When you know the multimeter’s symbol, you can perform all of the functionality efficiently in a short time. You get familiar with the buttons and the multimeter symbol, so you can use it like a pro.
The symbol varies from model to model, but many models have this standard symbol in this article. You should also check the manual to understand the symbols.
Related Guides:
Our team comprises dedicated professional Engineers, researchers, and experienced DIY enthusiasts who completed hundreds of projects in Home improvement, Electricle and Electronics. Read more | 929 | 4,002 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2024-10 | longest | en | 0.88668 |
https://www.stata.com/statalist/archive/2003-05/msg00292.html | 1,722,870,755,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640451031.21/warc/CC-MAIN-20240805144950-20240805174950-00374.warc.gz | 786,155,152 | 4,464 | # st: A STATA code for verification of a check digit
From Chantal Mascarenhas <[email protected]> To [email protected] Subject st: A STATA code for verification of a check digit Date Wed, 14 May 2003 17:33:19 +0200
Title: Message
Hi! I would like to know if there is a STATA code to use for verification of a check digit like the one used in SAS. This applies to the Swedish Personnummer that everyone has in Sweden. It is comprised of 10 digits (12) if the century is included. The first 6 are the birth date in YYMMDD followed by a 3 digit birth number and a last digit which is a check digit comprised of the previous 9 digits calculated by algorithm.
For example, 780924 0505
Here is a description of how it works in SAS:
### SAS code for verifying the check digit
```/*******************************************
PNR_CHK.SAS
This code reads 10-digit person numbers and
checks that the check digit (the 10th digit
in the PNR) is correct.
It is assumed that PNR is a character
variable of length 10.
*******************************************/
/*******************
********************/
data temp;
input pnr \$ 1-10;
cards;
3103170993
3103170999
6812241450
6812241457
6511280693
6511280692
;
run;
data pnr_chk;
set temp;
length product \$ 18 result \$ 3;
array two_one {9} (2 1 2 1 2 1 2 1 2);
/*********************************************
multiply each of the first 9 digits in PNR by
the corresponding digit in the array two_one
and concatenate the result.
The COMPRESS function removes blanks.
*********************************************/
do i = 1 to 9;
product=compress(product||(substr(pnr,i,1)
*two_one{i}));
end;
/** Now we sum the digits **/
do i = 1 to length(product);
sum=sum(sum,substr(product,i,1));
end;
/** extract the check digit from PNR **/
chk=substr(pnr,10,1);
/** calculate the correct check digit **/
corr_chk=mod(10-mod(sum,10),10);
if chk=corr_chk then result='ok';
label
chk='Actual check number'
corr_chk='Correct check number'
pnr='Personnummer (10 digits)'
;
run;
proc print data="pnr_chk;"
var pnr chk product sum corr_chk result;
run;
```
Thanks and very curious,
Chantal.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Chantal Mascarenhas - Doktorand/Ph.D Student
Dept. of Medical Epidemiology & Biostatistics
Karolinska Institutet
Nobels V�g 12A
P.O. Box 281
SE - 171 77 Stockholm
SWEDEN.
Tel: +46 (0)8 524 82307
Mob: +46 (0)73 785 6378
Fax: +46 (0)8 31 49 75
Email: [email protected]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | 677 | 2,492 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2024-33 | latest | en | 0.586588 |
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