url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
http://www.jiskha.com/display.cgi?id=1361885077 | 1,498,233,481,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320070.48/warc/CC-MAIN-20170623151757-20170623171757-00192.warc.gz | 535,476,704 | 3,695 | # math
posted by on .
6-1x0+2÷2
• math - ,
anyway if you meant 6-1x * 0 + 2/2 = 6-0 +1 = 7
or if you meant 6-1x + 2/2 we get 6-1x+1 = 7-1x | 80 | 143 | {"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} | 3.625 | 4 | CC-MAIN-2017-26 | latest | en | 0.862664 |
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-molecular-science-5th-edition/chapter-3-chemical-reactions-questions-for-review-and-thought-topical-questions-page-149e/63b | 1,686,285,392,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224655247.75/warc/CC-MAIN-20230609032325-20230609062325-00342.warc.gz | 863,055,442 | 14,985 | ## Chemistry: The Molecular Science (5th Edition)
7.98 g of $Fe_2O_3$
1. Calculate the number of moles of $Fe$: 55.85* 1 = 55.85g/mol $5.58g \times \frac{1 mol}{ 55.85g} = 0.100mol (Fe)$ - As we determined in the last exercise, the balanced reaction is: $4Fe + 3O_2 -- \gt 2Fe_2O_3$ The ratio of $Fe$ to $Fe_2O_3$ is 4 to 2: $0.100 mol (Fe) \times \frac{ 2 mol(Fe_2O_3)}{ 4 mol (Fe)} = 0.050mol (Fe_2O_3)$ 2. Calculate the mass of $Fe_2O_3$: 55.85* 2 + 16* 3 = 159.7g/mol $0.050 mol \times \frac{ 159.7 g}{ 1 mol} = 7.98g (Fe_2O_3)$ | 250 | 533 | {"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} | 3.484375 | 3 | CC-MAIN-2023-23 | latest | en | 0.44189 |
https://ko.coursera.org/learn/linear-algebra-machine-learning/reviews?authMode=signup&page=34 | 1,582,779,399,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146647.82/warc/CC-MAIN-20200227033058-20200227063058-00033.warc.gz | 404,562,887 | 140,843 | Mathematics for Machine Learning: Linear Algebra(으)로 돌아가기
# 임페리얼 칼리지 런던의 Mathematics for Machine Learning: Linear Algebra 학습자 리뷰 및 피드백
4.7
4,820개의 평가
879개의 리뷰
## 강좌 소개
In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Since we're aiming at data-driven applications, we'll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you'll write code blocks and encounter Jupyter notebooks in Python, but don't worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before. At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning....
## 최상위 리뷰
##### NS
Dec 23, 2018
Professors teaches in so much friendly manner. This is beginner level course. Don't expect you will dive deep inside the Linear Algebra. But the foundation will become solid if you attend this course.
##### CS
Apr 01, 2018
Amazing course, great instructors. The amount of working linear algebra knowledge you get from this single course is substantial. It has already helped solidify my learning in other ML and AI courses.
필터링 기준:
## Mathematics for Machine Learning: Linear Algebra의 876개 리뷰 중 826~850
교육 기관: Li J
May 20, 2018
nice
교육 기관: Reed R
Jul 14, 2018
The stated goal of the course is to provide a sufficient base of knowledge in linear algebra for applied data science i.e. (a) to teach linear algebra without gory proofs or endless grinding through algorithms by hand and (b) to foreground geometric interpretations of linear algebra that can be recalled for many data science techniques and visualized with common data science tools. While I appreciate this goal and enjoyed the early foray into projection, I never felt the "a ha" moments I did as an undergrad in a class that used Gil Strang's "Introduction to Linear Algebra" (which I reread alongside this course as a supplement). The course seems to ask for some faith that various concepts introduced earlier in the course will be united by the end, but never makes good; opting instead for a kind of sleight of hand: having students implement the Page Rank algorithm with the intention that this will draw together the core concepts of the course. It could be that I was just looking for a more complete treatment of the subject than the course ever intends to offer, but I strongly felt that with a bit of restructuring, that the subject could be presented primarily intuitively, but with a level of clarity and artfulness in its conclusion that will ensure that students remember the core concepts beyond when they remember its presentation.
교육 기관: Eitan A
Jan 13, 2020
As of this writing, I am almost done with week 4 of Mathematics for Machine Learning: Linear Algebra. The content of the course is excellent and professor David Dye's lectures are to be commended no doubt. The reason for my low rating is because the programming assignments are broken and that's really not acceptable for paid offering such as this. To clarify, at various points throughout this course, students are asked to complete a programming assignment. The student is presented with a button which says, "Open Notebook". The student is supposed to click this button and be redirected to a Jupyter Notebook (and interactive Python execution environment). Unfortunately, instead of being redirected, click on this button results in a "404 Not Found" error. There are various discussions in the class discussion forum regarding this issue (some months old), but no action has been taken to resolve this issue. Luckily, someone taking the course managed to find the programming assignments and posted them on google docs for others to use. I've been working these which is fine, but as I said, we're paying for these courses, someone should be resolving this.
교육 기관: Anweshita D
Jun 29, 2018
Your discussion forum really needs to be better. It seems to be the only place where any sort of doubt clearing can be done and very rarely have I seen TA's answering unless it's a grading issue. The problem with this sort of answering is that if any coding concepts are unclear, either they are solved by trial and error or after going through Google multiple times. And for a course that is paid for, I shouldn't have to make this much of an effort just to have my doubts cleared.
교육 기관: Chika
Jun 13, 2019
The videos were well structured, but the quiz sometimes were far more difficult than the practice questions in video. I had posted on forum but no comment nor reply. Quiz answers were not elaborate enough to understand after making mistakes. So I had to ask my father who's extremely good at maths many times, for explanations. Without hi help I might not have been able to understand as well. Need improvement.
교육 기관: Nathan C
Jan 26, 2019
Having no background in linear Algebra made it difficult to complete the quizzes, assignments and exams. Even with the instruction (which was good) I found the hands on portions to be different from what was being explained in the videos. I will instead have to take the key concepts and do more research on my own to fully understand them.
교육 기관: Fernando B d M
May 14, 2018
Like most of Coursera's courses there are no staff members available in the forums (which is extremely shameful for Coursera - repeating the same boring pattern over the years). Don't even try it if you have never seen linear algebra or python before. Otherwise, it's useful for practicing a few concepts or refreshing others.
교육 기관: Mattia P
Mar 30, 2018
Nice course, with many insights. Sometimes the topics are given too quickly, I would have rather preferred less arguments but discussed more thoroughly. Nevertheless, I think this is a good one, especially if you've already got some background and you're looking for some general content to build upon it using academic books.
교육 기관: Alois H
May 06, 2019
Teaching quality is good overall, except for a few jumps towards the end, where it's hard to follow. Quizzes and assignments well designed.
Unfortunately, and contrary to other courses I've taken, the forum seems completely un-monitored (as of May 2019), so don't expect much help from there.
교육 기관: Marie-Luise K
Jan 16, 2020
Overall, it was a good summary to understand linear algebra. To get into the topic, I had to read through additional material as the videos and tasks provided in this course were a little shallow to my liking. I, personally would have liked more applicable machine learning examples.
교육 기관: Ilaria G
Oct 24, 2019
I believe that the programming required in the assignments are not beginner level. I had never coded on Python before and I thought that there wasn't enough support on how to test my code before submitting, for example. On the other hand, the math topics were really interesting.
교육 기관: Chakravarthy R
Sep 16, 2019
It was too fast for me. I answered many questions just by chance. But i got an overview of the concepts like diagonalisation , inverse, transpose, basis, span , eigen and so on. I am hoping that i will build on this.
교육 기관: POR M H
Feb 01, 2020
I am feeling like something is missing during the last part of the course when it comes to Page Rank Algorithm. There should be more explanation to how the math works or comes to its formula.
교육 기관: 丁榕
Aug 30, 2018
I think the course is more suitable for those who have had comprehensive theoretical knowledge in linear algebra and intend to learn more about its practical use and its relevance to code.
교육 기관: Manuel M
Jan 26, 2019
The course feels very disorganized in general. Some quizzes are about 10 standard deviations from the average difficulty, which is befuddling to say the least.
교육 기관: chanhee
Feb 25, 2020
It is good course for machine learning. But I didn't fully understand the page rank system with damping.
More explanation of damping is needed for the newbie.
교육 기관: Vignesh N M
Sep 12, 2018
Transition from explanation of basic to advanced concepts could have been better. There was an assumption that few things was already know to the learner.
교육 기관: Alexander D
Aug 07, 2018
Not enough focus on how material connects to machine learning. A case study example would help, as would a very slow, detailed step-by-step illustration.
교육 기관: Cindy X
Dec 21, 2018
I think this course is a little bit hard for a beginner with python. And I hope that the teacher can talk more about the Machine learning part.
교육 기관: BT
Dec 29, 2019
The Eigen system could have been better explained. The last quiz was too hard and the concepts required were not covered
교육 기관: Aaron H
Oct 17, 2019
Lot of the concepts seemed glossed over and could have used more guided practice and/or linkages to real world problems.
교육 기관: Matt
Feb 24, 2019
This course would be perfect if more elaboration on the maths required to complete the quizzes, was provided.
교육 기관: shanmugha
Dec 11, 2019
i expected a practical mathematic approach rather than only mathematical approach.but page rank algo is good
교육 기관: Jared E
May 26, 2018
Overall good, but some nasty difficulty with the programming assignments... especially the last one.
교육 기관: Alberto M
Apr 04, 2019
Good material if you want to refresh your knowledge, poor programming assignment support/feedback | 2,230 | 9,847 | {"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} | 2.78125 | 3 | CC-MAIN-2020-10 | latest | en | 0.922933 |
http://www.antiessays.com/free-essays/Appendix-A-115287.html | 1,519,082,763,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812855.47/warc/CC-MAIN-20180219231024-20180220011024-00033.warc.gz | 431,656,137 | 7,995 | ### Welcome
Anti Essays offers essay examples to help students with their essay writing.
# Appendix A Essay
• Submitted by: weezy2
• on October 5, 2011
• Category: English
• Length: 4,639 words
Below is an essay on "Appendix A" from Anti Essays, your source for research papers, essays, and term paper examples.
A60
Appendix A
Review of Fundamental Concepts of Algebra
A.6
Linear Inequalities in One Variable
Introduction
Simple inequalities were discussed in Appendix A.1. There, you used the inequality symbols , and ≥ to compare two numbers and to denote subsets of real numbers. For instance, the simple inequality x ≥ 3 denotes all real numbers x that are greater than or equal to 3. Now, you will expand your work with inequalities to include more involved statements such as 5x and 3 ≤ 6x 1 < 3. 7 < 3x 9
What you should learn
• Represent solutions of linear inequalities in one variable. • Solve linear inequalities in one variable. • Solve inequalities involving absolute values. • Use inequalities to model and solve real-life problems.
Why you should learn it
Inequalities can be used to model and solve real-life problems. For instance, in Exercise 101 on page A68, you will use a linear inequality to analyze the average salary for elementary school teachers.
As with an equation, you solve an inequality in the variable x by finding all values of x for which the inequality is true. Such values are solutions and are said to satisfy the inequality. The set of all real numbers that are solutions of an inequality is the solution set of the inequality. For instance, the solution set of x 1 < 4
is all real numbers that are less than 3. The set of all points on the real number line that represent the solution set is the graph of the inequality. Graphs of many types of inequalities consist of intervals on the real number line. See Appendix A.1 to review the nine basic types of intervals on the real number line. Note that each type of interval can be classified as bounded or unbounded.
Example 1
Intervals and Inequalities
Write an inequality to represent each interval, and state whether the interval is bounded or unbounded. a. b. d. a. b. d. 3, 5 3, , 3, 5 corresponds to 3, , corresponds to corresponds to 3 < x ≤ 5. 3 < x.
< x <
c. 0, 2...
• Submitted by: weezy2
• on October 5, 2011
• Category: English
• Length: 4,639 words
• Views: 828
• Popularity Rank: 95632
• 1 rating(s)
### Citations
##### MLA Citation
"Appendix A". Anti Essays. 19 Feb. 2018
<http://www.antiessays.com/free-essays/Appendix-A-115287.html>
##### APA Citation
Appendix A. Anti Essays. Retrieved February 19, 2018, from the World Wide Web: http://www.antiessays.com/free-essays/Appendix-A-115287.html | 687 | 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} | 4.625 | 5 | CC-MAIN-2018-09 | latest | en | 0.93559 |
https://physics.stackexchange.com/questions/251021/question-about-the-dirac-equation/514972 | 1,601,555,810,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402131412.93/warc/CC-MAIN-20201001112433-20201001142433-00258.warc.gz | 540,040,037 | 34,485 | # Question about the Dirac equation
Energy and momentum of a particle can be expressed by equation $$E^2=p_1^2c^2+p_2^2c^2+p_3^2c^2+m^2c^4\hspace{40pt}(1)$$ Equation (1) can be divided into $E$ on both sides. We obtain $$E=\frac{v_1}{c}p_1\,c+\frac{v_2}{c}p_2\,c+\frac{v_3}{c}p_3\,c+\frac{v_4}{c}m\,c^2\hspace{40pt}(2)$$ where $v^2=v_1^2+v_2^2+v_3^2$, and $v_4=\sqrt{c^2-v^2}$; The Dirac equation has the form $$i\hbar\frac{\partial\psi}{\partial t}=(\alpha_1\hat p_1c+\alpha_2\hat p_2c+\alpha_3\hat p_3c+\alpha_4m\,c^2)\psi\hspace{30pt}(3)$$ where $\alpha_i$ is matrix $(i=1,2,3,4)$. From the principle of correspondence between (2) and (3) is $\alpha_i\rightarrow v_i/c$. In quantum mechanics, it is shown that the relativistic velocity operator $v_v=dx_v/dt$; $(v=1,2,3)$ is given by $\hat{v}_v=c\,\alpha_v$, ie is a matrix operator. Then relativistic velocity operator $v_4=\sqrt {c^2-v^2}$ is the matrix $\hat v_4=c\alpha_4$. Is it right? Does the equation (2) be the basis of the Dirac equation?
• Why don't you square your equation (2) and check if it returns your equation (1). Frankly, I don't understand how you divided (1) into (2). – Horus Apr 21 '16 at 6:31
• Let $v_4=\sqrt{c^2-v^2}$ then $$\frac{p_1c}{E}=\frac{mv_1c(c/v_4)}{mc^2(c/v_4)}=\frac{v_1}{c}$$ and so on. Let $E_0=mc^2$ then $$\frac{E_0}{E}=\frac{v_4}{c}$$; – Alexander Klimets Apr 21 '16 at 9:21
• Well your math seems to check out. However a quick search on the Dirac equation would already tell you that the $\alpha$ matrices have the Pauli matrices for elements, independent of velocity. Also simply squaring your equation (2), it is already evident that it does not return the original equation (1), not unless $v_i v_j = 0$ where i does not equal j. I have an idea on why this is so though I think I am wrong. – Horus Apr 21 '16 at 13:39
• From the textbook: $$\frac{dx_{\nu}}{dt}=\frac{\partial x_{\nu}}{\partial t}+[H, x_{\nu}]$$ where $$H=c\alpha_{\nu}p_{\nu}+mc^2\alpha_4$$ Since the operator $x_{\nu}$ does not depend on time, it will be $dx_{\nu}/dt=[H,x_{\nu}]$. We get $$\frac{dx_{\nu}}{dt}=[{c\alpha_{\mu}p_{\nu}+mc^2\alpha_4},x_{\nu}]$$ The matrix $\alpha_{\mu}$ commutes with $x_{\nu}$, so that the matrix $\alpha_{\mu}$ can be factored out. Finally we have $$v_{\nu}=dx_{\nu}/dt=c\alpha_{\mu}[p_{\mu},x_{\nu}]=c\alpha_{\mu}\delta_{\mu\nu}=c\alpha_{\nu}$$ – Alexander Klimets Apr 21 '16 at 18:42
The Dirac equation (according to my understanding), is an alternate form of the Klein-Gordon equation. The Dirac equation can be derived from the following equation. $$Z_{μ\ }Z^{μ}-m^{2}=0$$ Were,$$Z_{μ\ }= \left(E\ \ \ P\right)$$ and, $$Z^{μ}= \begin{pmatrix} E\\-P \end{pmatrix}$$
Where "E" is the operator of energy, and "P" is the operator of momentum. The equation:
$$Z_{μ\ }Z^{μ}-m^{2}=0$$
Is the 4-vector representation of the equation:
$$E^{2}-P^{2}-m^{2}=0$$
Which is just a rearranged form of the Mass-Energy equation, with natural-unit simplification namely,
$$E^{2}=\ P^{2}+m^{2\ }$$
Therefore, the Dirac equation is just the Schrodinger equation, with a relativistic Hamiltonian. I guess, if you start with a relativistic Hamiltonian, and rearrange it in 4-vector notation, and then substitute in Quantum operators for energy and momentum, you will eventually get some form of the Dirac equation!
The connection between the equation, $$Z_{μ\ }Z^{μ}-m^{2}=0$$ and the Dirac equation, can be found in this video: https://www.youtube.com/watch?v=jjG2Y_dMsbI
I hope this helps! | 1,257 | 3,486 | {"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": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2020-40 | latest | en | 0.785523 |
https://www.coursehero.com/file/6863398/BUS306-MOD1-SLP-CV/ | 1,516,712,195,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891926.62/warc/CC-MAIN-20180123111826-20180123131826-00269.warc.gz | 873,246,896 | 68,071 | BUS306 MOD1 SLP CV
# BUS306 MOD1 SLP CV - 20 40 60 70 80=270 Total cost of the...
This preview shows pages 1–3. Sign up to view the full content.
TRIDENT UNIVERSITY INTERNATIONAL Module 1 Session Long Project BUS306 Quantitative Reasoning February 22, 2012
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
A={Fuel, Clothes, Electricity, Food, Mortgage} B={Smartphone, iPad, BluRay Player, Movies, Vacation Trip} A={20, 40, 60, 70, 80} B={90, 120, 30, 60, 40} Items in the union of Set A and Set B: A B={ Fuel, Clothes, Electricity, Food, Mortgage, Smartphone, iPad, BluRay Player, Movies, Vacation Trip} Items in the intersection of Set A and Set B: Α∩Β = Ø Total cost of Set A if it contains one unit of each item:
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: 20+40+60+70+80=270 Total cost of the union set if it contains one unit of each item: 20+2(40)+2(60)+70+80+90+120+30=610 A ∪ B={610} Total cost of the intersection: Α∩Β = Ø (no identical items between both sets, yet identical pricing exists) What will the total cost of the union and of the intersection be if you consider two set A's and three set B's: Α∩Β = Ø A=20+40+60+70+80=270 2 x 270=540 B=90+120+ 30+60+40=340 3 x 340=1020 540+1020=1560 A ∪ B={1560}...
View Full Document
{[ snackBarMessage ]}
### Page1 / 3
BUS306 MOD1 SLP CV - 20 40 60 70 80=270 Total cost of the...
This preview shows document pages 1 - 3. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online | 492 | 1,596 | {"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} | 4.03125 | 4 | CC-MAIN-2018-05 | latest | en | 0.748028 |
https://www.thestudentroom.co.uk/showthread.php?t=4212069 | 1,529,813,309,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267866191.78/warc/CC-MAIN-20180624024705-20180624044705-00182.warc.gz | 941,794,246 | 38,421 | You are Here: Home >< GCSEs
# Triangle watch
1. I want to find the perimeter of a right-angeled triangle which AB=7cm and AC=10cm so i want to find AB which is on the base the answer should the to 2 decimal places is it even possible to get such a answer for this? If you cant draw the triangle then here is the link https://drive.google.com/file/d/0B4X...ew?usp=sharing
2. (Original post by Awesome Brother)
I want to find the perimeter of a right-angeled triangle which AB=7cm and AC=10cm so i want to find AB which is on the base the answer should the to 2 decimal places is it even possible to get such a answer for this? If you cant draw the triangle then here is the link https://drive.google.com/file/d/0B4X...ew?usp=sharing
Use Pythagoras to find the length of the base and then you can work out the perimeter.
3. (Original post by usycool1)
Use Pythagoras to find the length of the base and then you can work out the perimeter.
Thanks
TSR Support Team
We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.
This forum is supported by:
Updated: July 13, 2016
Today on TSR
### Edexcel C4 Maths Unofficial Markscheme
Find out how you've done here
### 932
students online now
Exam discussions
Poll
Useful resources
## Study tools
### Essay expert
Learn to write like a pro with our ultimate essay guide.
See where you can apply with our uni match tool
### Make study resources
Create all the resources you need to get the grades.
### Create your own Study Plan
Organise all your homework and exams so you never miss another deadline.
### Resources by subject
From flashcards to mind maps; there's everything you need for all of your GCSE subjects.
### Find past papers
100s of GCSE past papers for all your subjects at your fingertips. | 459 | 1,878 | {"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} | 2.96875 | 3 | CC-MAIN-2018-26 | latest | en | 0.888531 |
https://physicsoverflow.org/33719/intuition-nekreasovs-instanton-partition-partitions-represent | 1,618,186,109,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038065903.7/warc/CC-MAIN-20210411233715-20210412023715-00296.warc.gz | 551,179,416 | 27,508 | # Intuition behind Nekreasov's instanton partition function. What do the partitions represent exactly?
+ 4 like - 0 dislike
633 views
I am struggling to understand many things behind Nekrasov's solution. Firstly I want to understand the following
1. In this theory, $a$ represents VEVs the Higgs scalar. So, is the gauge field of the hyper broken? The theory is broken from $SU(N)$ to what?
and then
1. How are the Young diagrams related to the point like $k$-instantons? And why do we sum over these Young diagrams? Is there an intuitive way to understand it?
A readable reference is the Master thesis A Pedagogical Introduction to the AGT Conjecture by Robert J. Rodger, chapter 3. (PDF)
This post imported from StackExchange Physics at 2015-10-15 11:24 (UTC), posted by SE-user Marion
edited Oct 15, 2015
Tip: Consider adding references and context in order to get useful and focused answers.
This post imported from StackExchange Physics at 2015-10-15 11:24 (UTC), posted by SE-user Qmechanic
I did, but I don't think it will be of any help. Only someone working on this field can actually help (I think). Let's see.
This post imported from StackExchange Physics at 2015-10-15 11:24 (UTC), posted by SE-user Marion
+ 5 like - 0 dislike
When the complex scalar in the vector multiplet has a non-trivial VEV $a$, then indeed the gauge group is spontaneously broken and we have the Higgs mechanism. As any field of the vector multiplet, the complex scalar is adjoint valued and so, classically, the gauge group is broken to the stabilizer of $a$ in the adjoint representation. For generic $a$, it is simply the maximal torus of the gauge group but for special $a$ the unbroken subgroup can be larger. For $G=U(N)$, by gauge transformation one can assume $a$ diagonal, $a=diag(a_1,...,a_N)$. If all the $a_i$ are distinct then $U(N)$ is broken to its maximal subgroup $U(1)^{N}$.
The Young diagrams come from the localization at the fixed points of the instantons moduli space. The Nekrasov partition function is a priori defined as a path integral. Using supersymmetry and after computation of the perturbative part, this path intergral can be reduced to a sum over the instanton number of finite dimensional integrals over the moduli spaces of instantons. These integrals are then computed by localization with respect to the action of the group $T \times U(1)^2$ where $T=U(1)^N$ is the maximal torus of the gauge group $U(N)$ and where $U(1)^2$ is the maximal torus of the group $SO(4)$ of rotations of the Euclidean four dimensional space. $(a_1,...,a_N)$ will appear as the equivariant parameters with respect to $T$ and $(\epsilon_1,\epsilon_2)$ as equivariant parameter with respect to $U(1)^2$. The key point is that that the fixed points of $T \times U(1)^2$ acting on the moduli space of $U(N)$ instantons of instanton charge $k$ are naturally parametrized by the data of $N$ Young diagrams whose sum of sizes is equal to $k$. To understand that, one has to realize a subtle point: the instanton moduli space is in general singular, due to point-like instantons, and to have well-defined integrals, one has to consider a smooth moduli space. A way to resolve the singularity is to turn on a noncommutative deformation of the spacetime and the Young diagrams parametrize fixed points on the moduli space of instantons on this non-commutative spacetime. As we consider fixed points for the action of $U(1)^2$, each fixed point corresponds to a non-commutative instanton localized at the origin of spacetime. As we consider fixed points for the action of $T$, each fixed point corresponds to a non-commutative $U(N)$ instanton which is in fact a direct sum of $N$ non-commutative $U(1)$ instantons. The notion of $U(1)$ instanton may sound stange: in the commutative world, such things do not exist but they exist in the non-commutative world.
So it remains to realize the following: to give a $U(1)^2$-invariant non-commutative $U(1)$ instanton of charge $k$ at the origin of $\mathbb{R}^4$ is the same thing that to give a Young diagram with $k$ boxes. To do that, one has to understand what is a non-commutative $U(1)$ instanton of charge $k$ sitting at the origin. Let me just say that it is a $U(1)$ gauge field configuration with a singular behavior at the origin and that if the instanton is $U(1)^2$ invariant, this singular behavior is completely determined by the shape of a Young diagram. (A mathematically precise formulation of a non-commutative $U(1)$ instanton is as the ideal sheaf of a non-reduced point in $\mathbb{C}^2$. A Young diagram is exactly a way to describe a possibly non-reduced $U(1)^2$-invariant point sitting at the origin of $\mathbb{C}^2=\mathbb{R}^4$).
answered Oct 15, 2015 by (5,140 points)
edited Oct 15, 2015 by 40227
@40227
(1) In what sense do you mean "special value of $a$"? Can you give an example? I was under the impression that $\phi$ (the complex scalar) always belongs to the Cartan subalgebra of $G$. What is different in the case of $SU(N)$?
(2) In what sense the instanton moduli space is singular? I.e. having two point-like instantons sitting at the same place? Would you be able to tell us how this is resolved by considering the Uhlenbeck compactification (which is mentioned in the article above but not clearly to my opinion). Of course this is related to the Hilber scheme of points. Is there a nice way to understand it?
(3) Also, if it is not too much, how does the $U(1)^2 \subset SO(4)$ you talk about related to the $\Omega$ background? Can you give us some nice intuition on how the $\Omega$ background it comes into the whole thing? I seem to understand the idea that we can consider a 5 or 6 dimensional theory and reduce it down to 4, but strictly from a 4 dimensional point of view, how do we understand it?
I apologize for all those questions, but I was about to ask a very very similar question. Basically I might actually ask a new question at PO very related to this one.
(1)The complex scalar $\phi$ is valued in the (complexification) of the Lie algebra of the gauge group $G$ and so its expectation value $a$ too. But up to gauge transformation, one can indeed assume that $a$ belong to the Cartan Lie algebra. In the case of $G=U(N)$, it is what I have written: $a$ is diagonal, $a=diag(a_1,...,a_n)$. For $G=U(N)$, non-special means all the $a_i$s distinct ans special means some $a_i$s equal. For a general semisimple Lie algebra, what I call "special" means in the union of the root hyperplanes.
(2) If by instanton one means a smooth configuration of the gauge field then the moduli space of instantons on $\mathbb{R}^4$ is smooth but it is non-compact. Of the reason for that is the possibility for the instanton size to shrink. The natural way to cure that is the Uhlenbeck compactification, which includes point-like instantons (It is what I call instanton moduli space is my answer). But this space is singular and indeed it happens when point like instantons come together. For example, consider the space of the Uhlenbeck compactification describing two point-like instantons, it is $Sym^2(\mathbb{R}^4)=(\mathbb{R}^4 \times \mathbb{R}^4)/(\mathbb{Z}/2)$ which is singular along the fixed point of the $\mathbb{Z}/2$-action, i.e. the diagonal in $\mathbb{R}^4 \times \mathbb{R}^4$. One obtains a smooth moduli space only by going to noncommutative instantons, i.e. by replacing symmetric products of copies of $\mathbb{C}^2$ by Hilbert schemes of points in $\mathbb{C}^2$.
3)Indeed working equivariantly with respect to $U(1)^2$ is the $\Omega$-background: $\epsilon_1$ and $\epsilon_2$ are the corresponding equivariant parameters. It is a natural way to localize the physics near the origin and so to cure the problems related to the non-compactness of $\mathbb{C}^2$.
@40227
Hi,
Why is the moduli space of two instants isomorphic to $Sym^2(\mathbb{R}^4)$? Can you please provide with some physical interpretation of the Uhlenbeck compactification? Am I correct to say that the moduli space of two point-like instantons is a copy of $\mathbb{R}^4$ for each except that we have to mod out the points that the two instantons might be sitting at the same position.
This of course brings me to the following question. The moduli space of a $k$-instanton configuration can be described by taking $k$ point-like instantons, right? Then this space is singular due to the fact that you can two instantons living at the same point. But, why is this considered a singularity? And also, what is the problem of the space being non-compact (being copies of $\mathbb{R}^4$? Why does the moduli space of the instantons need to be compact?
Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor) Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOve$\varnothing$flowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register. | 2,491 | 9,725 | {"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} | 2.9375 | 3 | CC-MAIN-2021-17 | latest | en | 0.892589 |
https://www.geeksforgeeks.org/amazon-interview-experience-194-for-software-support-engineer/?ref=rp | 1,685,952,050,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224651325.38/warc/CC-MAIN-20230605053432-20230605083432-00237.warc.gz | 835,705,694 | 32,782 | GeeksforGeeks App
Open App
Browser
Continue
# Amazon Interview Experience | 194 (For Software Support Engineer)
It was a usual Job Application at Amazon’s Job Site, I got their call few days later.
Process:- 1 Written Aptitude(Coding) + 3 Technical Round + 1 HR Round
1) One Written Test – 8 Problem statement – 1 Hour Time – from Basic to Mid-level difficulty, for which we have to write the Logic/Algorithms
Some which I remember were good enough are –
i) Given a Folder path in a Directory Structure. E.g. “temp/reg”; you need to find all the files with extensions “.c” in this folder as well as in the sub-folders.
ii) Finding the Longest Palindrome Sub-String in the given string.
iii) From the given string, print the Alphabets which occur more than once in the string.
iv) Given two Integers A & B, Print the number of bits to be flipped in order to convert ‘A’ to ‘B’.
v) Implement EnQueue() and DeQueue() of Queue DS using Push() and Pop() of Stack DS. Write Steps and Sequence.
Possible Solutions:- (Logic)
i) Use Linked-List DS to store the Folder Path in a Node. Open the Folder with First Node, filter all the “.c” extension files, and add the sub-folders in the linked-list, until all the nodes in the linked-list are explored.
ii) Use ‘frame’ variable with value starting from 2, increasing till size ‘n’, and check by shifting this frame by one position, if the sub-string is a Palindrome or not.
iii) Basic Char to ASCII conversion and back to Characters. Create an Array of 26 slots for alphabets. Convert the input string to UpperCase before proceeding.
iv) Convert to Binary Representation and Compare as String Characters. If not same, then increment the counter. Remember, we have to only display the Number of bits flipped.
v) Use Operational Logic for Priority Queue, and for –
a) EnQueue – Push everything in Stack1.
b) DeQueue – (Check if Stack1 is Not empty)Pop everything from Stack1 and Push them one by one to Stack2. Then Pop top element from Stack2 as Result. For Next DeQueue do reverse, i.e. from Stack2 to Stack1.
2) 1st Technical Round
i) Write Program to Reverse a Linked List.
ii) Discussion on a Scenario and Debugging/Troubleshooting the error.
3) 2nd Technical Round
i) The similar Debugging/Troubleshooting scenario.
ii) Add the Numbers present in the String and display.
E.g. “abc123def-567ghi89jk”
Here take ‘-‘ as negative number symbol.
iii) Find the Pair of Array elements summing up to value ‘k’, in a Sorted Array. Optimize it from Complexity ‘N^2’ to ‘NlogN’ using Binary Search.
4) 3rd Technical + Managerial Round
i) Some OS Related Questions.
ii) UNIX Commands – Which I couldn’t recall!
iii) Project Experience and Why want to Join Amazon and similar ones.
Though I couldn’t clear the 3rd Round, the overall experience was good.
## Remember:-
—————————
>> Please check their Technical Requirement, and revise your concepts of OS(How Process works, Process Life Cycle, RAM, Virtual Memory, DeadLocks etc.), UNIX(Revise Basic Commands like ‘grep’ etc.).
>> Practice basic Problems like, Searching, Sorting, Fibonacci, Factorial, Recursion, Stack, Queue, Linked List and their Application.
Hope it helps for the new Applicants!
If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
My Personal Notes arrow_drop_up | 837 | 3,443 | {"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} | 2.859375 | 3 | CC-MAIN-2023-23 | latest | en | 0.858162 |
https://www.jobilize.com/physics3/course/10-7-medical-applications-and-biological-effects-of-nuclear-by-opensta?qcr=www.quizover.com&page=4 | 1,563,912,263,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195529664.96/warc/CC-MAIN-20190723193455-20190723215455-00357.warc.gz | 711,936,018 | 21,945 | # 10.7 Medical applications and biological effects of nuclear radiation (Page 5/18)
Page 5 / 18
Typical doses received during diagnostic x-ray exams
Procedure Effective Dose (mSv)
Chest 0.02
Dental 0.01
Skull 0.07
Leg 0.02
Mammogram 0.40
Barium enema 7.0
Upper GI 3.0
CT abdomen 10.0
## What mass of ${}^{137}\text{Cs}$ Escaped chernobyl?
The Chernobyl accident in Ukraine (formerly in the Soviet Union) exposed the surrounding population to a large amount of radiation through the decay of ${}^{137}\text{Cs}$ . The initial radioactivity level was approximately $A=6.0\phantom{\rule{0.2em}{0ex}}\text{MCi}.$ Calculate the total mass of ${}^{137}\text{Cs}$ involved in this accident.
## Strategy
The total number of nuclei, N , can be determined from the known half-life and activity of ${}^{137}\text{Cs}$ (30.2 y). The mass can be calculated from N using the concept of a mole.
## Solution
Solving the equation $A=\frac{0.693\phantom{\rule{0.2em}{0ex}}N}{{t}_{1\text{/}2}}$ for N gives
$N=\frac{A\phantom{\rule{0.2em}{0ex}}{t}_{1\text{/}2}}{0.693}.$
Entering the given values yields
$N=\frac{\left(6.0\phantom{\rule{0.2em}{0ex}}\text{MCi}\right)\left(30.2\phantom{\rule{0.2em}{0ex}}\text{y}\right)}{0.693}.$
To convert from curies to becquerels and years to seconds, we write
$N=\frac{\left(6.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{Ci}\right)\left(3.7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{10}\phantom{\rule{0.2em}{0ex}}\text{Bq/Ci}\right)\left(30.2\phantom{\rule{0.2em}{0ex}}\text{y}\right)\left(3.16\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{7}\phantom{\rule{0.2em}{0ex}}\text{s/y}\right)}{0.693}=3.1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{26}.$
One mole of a nuclide ${}^{A}\text{X}$ has a mass of A grams, so that one mole of ${}^{137}\text{Cs}$ has a mass of 137 g. A mole has $6.02\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{23}$ nuclei. Thus the mass of ${}^{137}\text{Cs}$ released was
$m=\left(\frac{137\phantom{\rule{0.2em}{0ex}}\text{g}}{6.02\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{23}}\right)\left(3.1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{26}\right)=70\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\text{g}=70\phantom{\rule{0.2em}{0ex}}\text{kg}.$
## Significance
The mass of ${}^{137}\text{Cs}$ involved in the Chernobyl accident is a small material compared to the typical amount of fuel used in a nuclear reactor. However, approximately 250 people were admitted to local hospitals immediately after the accident, and diagnosed as suffering acute radiation syndrome. They received external radiation dosages between 1 and 16 Sv. Referring to biological effects in [link] , these dosages are extremely hazardous. The eventual death toll is estimated to be around 4000 people, primarily due to radiation-induced cancer.
Check Your Understanding Radiation propagates in all directions from its source, much as electromagnetic radiation from a light bulb. Is activity concept more analogous to power, intensity, or brightness?
power
## Summary
• Nuclear technology is used in medicine to locate and study diseased tissue using special drugs called radiopharmaceuticals. Radioactive tags are used to identify cancer cells in the bones, brain tumors, and Alzheimer’s disease, and to monitor the function of body organs, such as blood flow, heart muscle activity, and iodine uptake in the thyroid gland.
• The biological effects of ionizing radiation are due to two effects it has on cells: interference with cell reproduction and destruction of cell function.
• Common sources of radiation include that emitted by Earth due to the isotopes of uranium, thorium, and potassium; natural radiation from cosmic rays, soils, and building materials, and artificial sources from medical and dental diagnostic tests.
• Biological effects of nuclear radiation are expressed by many different physical quantities and in many different units, including the rad or radiation dose unit.
## Key equations
Atomic mass number $A=Z+N$ Standard format for expressing an isotope ${}_{Z}^{A}\text{X}$ Nuclear radius, where r 0 is the radius of a single proton $r={r}_{0}{A}^{1\text{/}3}$ Mass defect $\text{Δ}m=Z{m}_{p}+\left(A-Z\right){m}_{n}-{m}_{\text{nuc}}$ Binding energy $E=\left(\text{Δ}m\right){c}^{2}$ Binding energy per nucleon $BEN=\frac{{E}_{b}}{A}$ Radioactive decay rate $-\frac{dN}{dt}=\lambda N$ Radioactive decay law $N={N}_{0}{e}^{\text{−}\lambda t}$ Decay constant $\lambda =\frac{0.693}{{T}_{1\text{/}2}}$ Lifetime of a substance $\stackrel{–}{T}=\frac{1}{\text{λ}}$ Activity of a radioactive substance $A={A}_{0}{e}^{\text{−}\lambda t}$ Activity of a radioactive substance (linear form) $\text{ln}\phantom{\rule{0.2em}{0ex}}A=\text{−}\lambda t+\text{ln}\phantom{\rule{0.2em}{0ex}}{A}_{0}$ Alpha decay ${}_{Z}^{A}\text{X}\to {}_{Z-2}^{A-4}\text{X}+{}_{2}^{4}\text{H}\text{e}$ Beta decay ${}_{Z}^{A}\text{X}\to {}_{Z+1}^{\phantom{\rule{1.5em}{0ex}}A}\text{X}+{}_{-1}^{\phantom{\rule{0.7em}{0ex}}0}\text{e}\phantom{\rule{0.2em}{0ex}}\text{+}\phantom{\rule{0.2em}{0ex}}\stackrel{–}{v}$ Positron emission ${}_{Z}^{A}\text{X}\to {}_{Z-1}^{\phantom{\rule{1.5em}{0ex}}A}\text{X}+{}_{\text{+}1}^{\phantom{\rule{0.7em}{0ex}}0}\text{e}\phantom{\rule{0.2em}{0ex}}\text{+}\phantom{\rule{0.2em}{0ex}}v$ Gamma decay ${}_{Z}^{A}\text{X}*\to {}_{Z}^{A}\text{X}+\gamma$
#### Questions & Answers
A round diaphragm S with diameter of d = 0.05 is used as light source in Michelson interferometer shown on the picture. The diaphragm is illuminated by parallel beam of monochromatic light with wavelength of λ = 0.6 μm. The distances are A B = 30, A C = 10 . The interference picture is in the form of concentric circles and is observed on the screen placed in the focal plane of the lens. Estimate the number of interference rings m observed near the main diffractive maximum.
A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a 50-Ωresistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?
how does colour appear in thin films
in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
derivation of lateral shieft
hi
Imran
total binding energy of ionic crystal at equilibrium is
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Refraction does not occur in concave mirror. If refraction occurs then I don't know about this.
Sushant
What is motion
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
DHEERAJ
These substance create harmful radiation like alpha particle radiation, beta particle radiation, gamma particle radiation
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
Cavendish Experiment to Measure Gravitational Constant. ... This experiment used a torsion balance device to attract lead balls together, measuring the torque on a wire and equating it to the gravitational force between the balls. Then by a complex derivation, the value of G was determined.
Triio
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
as a free falling object increases speed what is happening to the acceleration
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
acceleration also increases
Jay
there are two correct answers depending on whether air resistance is considered. none of those answers have acceleration increasing.
Michael
Acceleration is the change in velocity over time, hence it's the derivative of the velocity with respect to time. So this case would depend on the velocity. More specifically the change in velocity in the system.
Big
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
give any fix value to wave length
Rafi
40 cm into change mm
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends.
Prema
what is physics? | 2,763 | 8,997 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 31, "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} | 4.1875 | 4 | CC-MAIN-2019-30 | longest | en | 0.716343 |
danielzeiss.me | 1,721,410,432,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514917.3/warc/CC-MAIN-20240719170235-20240719200235-00776.warc.gz | 172,361,671 | 28,769 | # Feedback to my post “The past is not the future”
Thank you for the feedback to my latest blog post about how the past is not the future.
There was one interesting question if there is a way to explain the topic in a more formal mathematical way. And yes, all our minds do not work in the same way, and since it is my fundamental belief that there is no right or wrong way of seeing our world, I looked into it and want to share the results with you:
The mind’s way of thinking in this situation is that a person A makes an experience. Since person A has no knowledge what so ever in this example, we will call this person A0 at the beginning of the experience. The experience we will call Ex and because it is the first experience of this kind, we will call it Ex1. Let’s say for the better understanding of the fact that Ex is a horseback riding lesson. And this horseback riding lesson ends with person A being thrown off the horse, which for person A is a negative outcome.Now the mind stores that A0 and Ex1 have a negative and not desired outcome.
For this example we assume that two years later the same person will have another chance to experience Ex (horseback riding) and the above dialog might have taken place, preventing the person to actually do it. The mind remembers Ex and remembers the negative outcome and basically warns person A to not get into that danger.
The problem with this is, that the mind is calculating on a wrong basis. While A0 and Ex1 had a negative outcome, they actually produced a person A1 with the experience from Ex1. So the person after having Ex1 is different from the person before. So the equation two years later would read that person A1 will have a second time the experience Ex, therefore we call it Ex2. The mind has no data what so ever for A1 and Ex2 and interpolates that it is similar to A0 and Ex1 having the negative outcome.
This association can only be wrong, because person A1 now knows what caused the negative outcome in Ex1. This might have been that the horse got scared because the radio played something suddenly loud, or any other conscious or unconscious reason, so person A1 can be prepared.
The problem is just that the mind did a flawed interpolation, just for the sake of avoiding danger. This avoidance with danger has a price. The price is freedom. If the mind avoids danger, it also limits itself in expressing freedom, by limiting the experiences it allows us to have.So the answer is:
A0 + Ex1 != A1 + Ex2
Please keep that in mind and help your friend, or the person you are with to not limit themselves by avoiding danger, but to be open to new experiences. | 569 | 2,643 | {"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} | 3.109375 | 3 | CC-MAIN-2024-30 | latest | en | 0.956544 |
https://physicshelpforum.com/threads/elastic-collision.223/ | 1,586,495,069,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371886991.92/warc/CC-MAIN-20200410043735-20200410074235-00489.warc.gz | 631,258,990 | 15,007 | # Elastic collision
#### SengNee
$$\displaystyle m_1=3kg$$
$$\displaystyle u_1=10ms^{-1}$$
$$\displaystyle m_2=2kg$$
$$\displaystyle u_2=0$$
The collision is elastic.
Find:
$$\displaystyle v_1$$ and $$\displaystyle v_2$$
By using total kinetic energy is conserved, I get 2 sets of answer.
$$\displaystyle v_1=10$$ , $$\displaystyle v_2=0$$
$$\displaystyle v_1=2$$ , $$\displaystyle v_2=12$$
Which is the correct answer?Or both are acceptable?
#### DivideBy0
There are two equations you can use:
Conservation of momentum:
$$\displaystyle m_1u_1+m_2u_2 = m_1v_1+m_2v_2$$
Difference in departing speeds = -(Difference in starting speeds)
$$\displaystyle u_1-u_2 = v_2-v_1$$
(Derived from conservation of kinetic energy)
Solving simultaneously, the only solution is $$\displaystyle v_1 = 2$$, $$\displaystyle v_2 = 12$$
If you think about it practically, how could it be possible that the speeds are the same afterwards?
SengNee
#### topsquark
Forum Staff
$$\displaystyle m_1=3kg$$
$$\displaystyle u_1=10ms^{-1}$$
$$\displaystyle m_2=2kg$$
$$\displaystyle u_2=0$$
By using total kinetic energy is conserved, I get 2 sets of answer.
$$\displaystyle v_1=10$$ , $$\displaystyle v_2=0$$
Which is the correct answer?Or both are acceptable?
DivideBy0 is absolutely correct, but I would like to mention the more general circumstance to the set of answers to any such problem. Typically you will get two "possible" answers, one of which will be unphysical. The problem isn't so much that the initial and final velocities of the particles are the same, the problem is that in order for this to be true particle 1 would have to pass through particle 2! This is typically the kind of thing that happens: one of the solutions has one particle passing through the other which is, of course, impossible.
-Dan
SengNee | 535 | 1,815 | {"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} | 4.03125 | 4 | CC-MAIN-2020-16 | latest | en | 0.875189 |
http://www.gurufocus.com/term/interest_coverage/MSFT%5EM/Interest%2BCoverage/ | 1,419,271,951,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1418802775656.66/warc/CC-MAIN-20141217075255-00119-ip-10-231-17-201.ec2.internal.warc.gz | 555,792,478 | 24,155 | Switch to:
(:)
Interest Coverage
0.00 (As of . 20)
Interest Coverage is a ratio that determines how easily a company can pay interest expenses on outstanding debt. It is calculated by dividing a companys Operating Income (EBIT) by its Interest Expense. 's Operating Income for the six months ended in . 20 was \$0.00 Mil. 's Interest Expense for the six months ended in . 20 was \$0.00 Mil. 's interest coverage for the quarter that ended in . 20 was 0.00. The higher the ratio, the stronger the companys financial strength is.
MSFT^M' s 10-Year Interest Coverage Range
Min: 0 Max: 0
Current: 0
During the past 0 years, the highest interest coverage of was . The lowest was . And the median was .
MSFT^M's Interest Coverageis ranked lower than
100% of the Companies
in the Global industry.
( Industry Median: vs. MSFT^M: )
Definition
Interest Coverage is a ratio that determines how easily a company can pay interest expenses on outstanding debt. It is calculated by dividing a companys Operating Income (EBIT) by its Interest Expense:
If Interest Expense is negative and Operating Income is positive, then
Interest Coverage = -1 * Operating Income / Interest Expense
Else if Interest Expense is negative and Operating Income is negative, then
did not have earnings to cover the interest expense.
Else if Interest Expense is 0 and Long-Term Debt is 0, or Interest Expense is positive, then
's Interest Coverage for the fiscal year that ended in . 20 is calculated as
Here, for the fiscal year that ended in . 20, 's Interest Expense was \$0.00 Mil. Its Operating Income was \$0.00 Mil. And its Long-Term Debt was \$0.00 Mil.
's Interest Coverage for the quarter that ended in . 20 is calculated as
Here, for the six months ended in . 20, 's Interest Expense was \$0.00 Mil. Its Operating Income was \$0.00 Mil. And its Long-Term Debt was \$0.00 Mil.
* All numbers are in millions except for per share data and ratio. All numbers are in their own currency.
The higher the ratio, the stronger the companys financial strength is.
Explanation
Ben Graham requires that a company has a minimum interest coverage of 5 with the companies he invested. If the interest coverage is less than 2, the company is burdened by debt. Any business slow or recession may drag the company into a situation where it cannot pay the interest on its debt.
Interest Coverage is an important factor when GuruFocus ranks a companys overage financial strength.
Related Terms
Historical Data
* All numbers are in millions except for per share data and ratio. All numbers are in their own currency.
Annual Data
interest_coverage At Loss At Loss At Loss At Loss At Loss At Loss At Loss At Loss At Loss At Loss
Semi-Annual Data
interest_coverage At Loss At Loss At Loss At Loss At Loss At Loss At Loss At Loss At Loss At Loss
Get WordPress Plugins for easy affiliate links on Stock Tickers and Guru Names | Earn affiliate commissions by embedding GuruFocus Charts
GuruFocus Affiliate Program: Earn up to \$400 per referral. ( Learn More) | 703 | 3,044 | {"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} | 2.546875 | 3 | CC-MAIN-2014-52 | longest | en | 0.961079 |
https://www.askiitians.com/forums/7-grade-maths/find-the-cost-of-polishing-a-circular-table-top-of_271118.htm | 1,726,434,879,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651647.78/warc/CC-MAIN-20240915184230-20240915214230-00056.warc.gz | 602,275,064 | 42,653 | # Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹15/m2 . (Take π = 3.14)
Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student
From the question it is given that, Diameter of the circular table-top = 1.6 m
We know that, radius (r) = d/2
= 1.6/2
= 0.8 m
Then,
Area of the circular table-top =πr^2
= 3.14 × 0.8^2
= 3.14 × 0.8 ×0.8
= 2.0096 m^2
Cost for polishing 1 m^2area =₹15 From the question it is given that, Diameter of the circular table-top = 1.6 m We know that, radius (r) = d/2
= 1.6/2 = 0.8 m
Then,
Area of the circular table-top =πr^2
= 3.14 × 0.82
= 3.14 × 0.8 ×0.8 = 2.0096 m^2
Cost for polishing 1 m^2area =₹15 [given]
Cost for polishing 2.0096 m^2area =₹15 × 2.0096
=₹30.144
Hence, the Cost for polishing 2.0096 m2area is₹30.144.
Thanks | 340 | 819 | {"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 | 4 | CC-MAIN-2024-38 | latest | en | 0.81677 |
https://myhomeworkhelp.com/know-the-right-technique-to-preparation-of-cash-flow-homework-answers/ | 1,719,172,967,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198864850.31/warc/CC-MAIN-20240623194302-20240623224302-00851.warc.gz | 361,242,150 | 55,134 | WhatsApp us
# Know the Right Technique to Preparation of Cash Flow Homework Answers
by Jul 9, 2017Accounting
The cash flow accounting is a statement in financial accounting that deals with the movement of cash and its counterparts in and out of business. It is due to the changes in balance sheet and income accounts. Hence, the primary use of cash flow statement is to determine whether the company can pay the fixed and variable expenditure in addition to earning profits.
It is also known as the statement of cash flows in accounting. The cash flow statement is used by the people to determine whether the firm will be able to cover the expenses or not. It is used by potential lenders, accountants, investors, contractors, etc. These people need to know whether the organization is financially sound so that they’ll become sure that the company will be able to repay their money back to them. You can use these basics for the preparation of cash flow homework answers.
Calculating Cash Flow
The first step for the preparation of cash flow homework answers is to determine the cash flow. For this, you can consider the following points.
• First, you have to determine the operating cash flow ratio. To do this, divide the total current liabilities with the company’s cash flow derived from the operations.
• Next, find the accounting cash flow. You can add the net income and expenses to the depreciation and amortization value.
• Sum all the above to determine the cash flow available for repaying.
• After that, subtract the current liabilities from the current assets of the company.
• The next thing is to determine whether the company can grow more money by making investments. Calculate this by subtracting the expenses of capital investments from the total cash flow of operations.
• Finally, add all the cash inflows from the beginning period of the company and subtract all the expenses. The result is the cash flow you need.
Once you get enough information about the topic, you can start the preparation of cash flow homework answers. For completing your homework, you can manage a schedule to give importance to this particular issue. Here are some tips you can follow.
• Know the concept well
The first thing you need to think about is to learn the topic before trying to solve any of its questions. It will be difficult to answer if you don’t understand it or you understand it less. It will take more time for getting the solutions. Therefore, first read the topic. Take some time to research. After you know the subject well, you can move to the next tip.
• Understand the questions
Understanding the problems is also important. It is the next step after you know the concept. You need to read the question and find out whether you can solve it or not. If you understand the question, the next step is to find the answers. However, if you don’t get it, you need to reread the concept that is related to the question. It will help you to figure out the solution.
Again, if you’re still not able to solve it, you can take some help. You can find a lot of people or resources to help you out from trouble.
• Try to find the answers
If you successfully solve the answers on your own, then it’s good. However, if you’re facing any difficulty, then you have to follow some tactics. Finding answers on your own is the best way for the preparation of cash flow homework answers.
We know that the subjects are not so easy and it can’t be possible on everyone’s part to handle it. In that case, you can take help to complete the home assignments.
Seeking help from different sources
There are many ways in which you can take assistance for your homework. The sources help you in solving the problems. The simple method is to take the help of books. Read the book and also check out the solved examples. It can give you new ideas and ways to solve the answer. However, you can also take help from the following sources.
• Online
The online method of preparation of cash flow homework answers is quite popular now. Both teachers and students can use it to find the answers. There are websites you can find online which provides homework help services. You can use these services to complete your homework. It comes with a price which you’ve to pay. Nonetheless, the prices are pretty low. One can easily afford it.
• Tuition
You can also take help of tuitions. If the subject seems difficult to you or you’re facing problems finding the answer, then you can receive assistance from the tutors. It is somewhat similar to that of studying in the class. However, you have to give more time to review and clarify all your doubts. You can ask your tutor to make you understand.
• Teachers
Your class teacher or the subject teacher can also assist you with your home task. The teachers are trustworthy. The best method is you understand in the class and ask your doubts whenever you feel it. They’ll help you to understand the topic.
• Parents
Parents are the best teachers. If they know something regarding cash flow, then they’ll help you. You can also be comfortable discussing your doubts with them. Hence, they can also be of great help to you. Sometimes, parents also use the online help services to know things better.
Students use these services to save time. The most important aspect is you can learn a lot using someone’s help. It is because the way one handles a problem is different from the other person. Hence, if you find that your way of solving is distinct from the one you are receiving help, you learn two different ways of solving the problem. Now, you can find the convenient option for yourself. If for some reason you didn’t find help in the class, you can always use these above options to get over your homework.
With practice, you can be perfect. Hence, for the preparation of cash flow homework answers, you need some time, practice and a little guidance. Taking help from other sources will save your time. However, you shouldn’t use it as a mean to get rid of the task. If you’ve enough time to submit the work, try to find out whether you’re able to solve it on your own or not. It’ll help you in the exam. You can also use different books regarding cash flow to study and gather information for reference. | 1,324 | 6,303 | {"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-2024-26 | latest | en | 0.944258 |
https://forum.mrmoneymustache.com/post-fire/how-do-you-factor-social-security-into-your-withdrawal-stategy/ | 1,548,233,718,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547584328678.85/warc/CC-MAIN-20190123085337-20190123111337-00157.warc.gz | 518,885,058 | 27,116 | ### Author Topic: How do you factor social security into your withdrawal stategy (Read 7620 times)
#### NaturallyHappier
• Stubble
• Posts: 129
• Age: 53
• FIRED 3/10/2017
##### How do you factor social security into your withdrawal stategy
« on: December 23, 2017, 03:08:29 PM »
I am wondering how others factor future SS into their withdrawal strategy. I am 50 years old and FIRE. I will collects SS at 70. I want to factor the SS into my earlier withdrawals since I will need to withdraw less from the stash once I start collecting SS. So, lets say I want to live off a fixed 4% of the actual stash amount with annual inflation adjustments. The actual % I can withdraw in the pre-SS years is something more than 4% since I am going to be withdrawing something significantly less than 4% once I am collecting SS.
My approach so far has been to take the annual SS amount (adjusted for early retirement) and simply multiply it by a conservative 15 years ( collect at 70 and conservatively say I pass away at 85). I am not discounting the SS annual amount because the dollars from the SS administration are already in today's dollars. This gets the SS in a lump sum value in today's dollars. Then I divide it by the more optimistic 100 year lifetime less my current 50 years. For example.
SS Annual Income = 50K
SS Annuity in today's dollars = 50K * 15 Yrs = 750K
Remaining optimistic life = 100 Yrs - 50 Yrs Age = 50 Yrs
Amount above 4% I can spend because of SS = 750K / 50 Yrs = 15K
So if my stash is \$1M and my expenses are \$55K I can withdraw 4% of the stash plus \$15K to get to my \$55K withdraw.
I considered just adding the SS Annuity above to the stash and then just taking 4% of that amount, but that assumes the SS Annuity grows with the stash. That is not correct since SS grows with inflation (CPI-U) only.
I am wondering how others are doing this? My approach is super conservative, but I am wondering if others that are smarter than I have a better approach.
As a side note, I am actually 51, I just wanted to make the numbers easy. Also, I am planning to use the EM withdrawal strategy from from the book "Living Off Your Money" by M. McClung, instead of the 4% with annual inflation adjustments presented above. Again I am simplifying in the example above.
#### ysette9
• Magnum Stache
• Posts: 3641
• Location: Bay Area, CA
##### Re: How do you factor social security into your withdrawal stategy
« Reply #1 on: December 23, 2017, 06:05:14 PM »
I am a long way out from SS but I run an estimate on their website, and then input that as an additional income line item into cFIREsim.
#### NaturallyHappier
• Stubble
• Posts: 129
• Age: 53
• FIRED 3/10/2017
##### Re: How do you factor social security into your withdrawal stategy
« Reply #2 on: December 23, 2017, 06:23:10 PM »
ysette9,
Thanks for the reply. Good suggestion. I have done that in the past, but I am trying now to figure out how to handle it when figuring out how much I can withdraw during the draw down phase now that I am already FIRE. I also have a spreadsheet that projects SS out into the future and while that helped me figure out whether I could FIRE and gives me a good feel as to how much more I can withdraw, but it does not help me much in actually putting together a withdrawal strategy spreadsheet.
I need to project future SS back to today to figure out how much I can safely withdraw now knowing that SS will be available later.
• Magnum Stache
• Posts: 4656
##### Re: How do you factor social security into your withdrawal stategy
« Reply #3 on: December 23, 2017, 06:39:55 PM »
I would be cautious with imputing Social Security payments at your age. You will not be eligible to collect until 2029, and that's only if the minimum age to collect is not raised. The trust fund will be exhausted around 2034, and if nothing is done, your annuity will be cut by around 25 percent. I would project five years at your estimated payment at 62 and 75 percent of the inflation adjusted amount beginning in 2034.
#### Monkey Uncle
• Handlebar Stache
• Posts: 1406
• Location: West-by-god-Virginia
##### Re: How do you factor social security into your withdrawal stategy
« Reply #4 on: December 24, 2017, 05:18:15 AM »
This is a bit tangential to the question you asked, but I suggest comparing various SS start ages in cFiresim. You may find that it is better to start collecting earlier as opposed to waiting until you're 70. When I ran my numbers, I actually got the best maximum safe spend by starting both my and DW's SS payments at 62. This is because starting early reduces the amount we have to pull from the stash early on, which reduces sequence of return risk.
Also, if Congress changes benefit amounts to address the funding shortfall, I believe they will be less likely to cut my benefits if I am already drawing them. Sort of a "get it while you can" situation.
#### NaturallyHappier
• Stubble
• Posts: 129
• Age: 53
• FIRED 3/10/2017
##### Re: How do you factor social security into your withdrawal stategy
« Reply #5 on: December 24, 2017, 05:49:16 AM »
This is a bit tangential to the question you asked, but I suggest comparing various SS start ages in cFiresim. You may find that it is better to start collecting earlier as opposed to waiting until you're 70. When I ran my numbers, I actually got the best maximum safe spend by starting both my and DW's SS payments at 62. This is because starting early reduces the amount we have to pull from the stash early on, which reduces sequence of return risk.
Also, if Congress changes benefit amounts to address the funding shortfall, I believe they will be less likely to cut my benefits if I am already drawing them. Sort of a "get it while you can" situation.
Interesting, so back testing proved that it may actually be better to start early. I have modeled this in spreadsheets using a relatively low return rate and found it was slightly better to wait. So you are saying that using real historic returns then proves the opposite.
#### rab-bit
• Stubble
• Posts: 114
##### Re: How do you factor social security into your withdrawal stategy
« Reply #6 on: December 24, 2017, 05:51:48 AM »
+1 for @Monkey Uncle comment, I have found the same thing. If you have plenty of income in the later years, it can be helpful to pull as much of that as possible to the earlier years.
Regarding your original question, I have done it a little differently. I have a spreadsheet that figures out the WR each year based on the income that I need minus any other income sources. So for example, in the first few years, we have only rental property income so I find that my required WR is around 7%. When my SS benefits start at 62, it drops to around 5%, and eventually to 3% after my wife's SS and some pensions begin. Since this final WR is below the 4% SWR, I know we should be okay.
« Last Edit: December 24, 2017, 06:48:21 AM by rab »
#### freya
• Stubble
• Posts: 202
##### Re: How do you factor social security into your withdrawal stategy
« Reply #7 on: December 24, 2017, 06:35:13 AM »
I'm a little older than the OP (54), and have been wrestling with the same issue. I did it in a maybe hokey way but it works for me:
I calculated annual expenses as same as current (in today's dollars) plus extra to cover costs of medical insurance and copays/deductible, in two phases: prior to age 70, and after age 70. At age 70, expenses are reduced by the Social Security benefit. I used my actual benefit minus 20% to cover potential cuts, and further assumed that the entire benefit is subject to tax. All numbers in today's dollars, with assumption that current expenses, savings and SS will track inflation.
I then calculated the savings required for age 70 expenses at a 4% SWR. This is less than my current savings, so I then assume I can spend down the excess. The amount of this spend-down (divide by #years until age 70) gets added to the 4% SWR from the post-age 70 savings pot.
Reaching FI happens when the income from the age-70 savings pot plus annual spend-down exceeds annual expenses. This is a much lower number than a straight calculation of savings = expenses * 25 yields, and accordingly speeds up the FI timetable.
Definitely interested to see how other people handle this. I prefer my own spreadsheets to depending entirely on FIREcalc, although this tool is much appreciated.
#### Blackeagle
• Stubble
• Posts: 121
• Location: Wichita, KS
##### Re: How do you factor social security into your withdrawal stategy
« Reply #8 on: December 24, 2017, 07:34:18 AM »
I have not been factoring social security into my FIRE calculations at all. There will probably be a 20 year gap between when I retire and when I claim social security. With that big a gap the difference between a stache I can live on indefinitely, and a stache that I can live on until I start supplementing it with social security is pretty small. Easier to just aim for the slightly larger starting stache and think of social security as gravy.
#### NaturallyHappier
• Stubble
• Posts: 129
• Age: 53
• FIRED 3/10/2017
##### Re: How do you factor social security into your withdrawal stategy
« Reply #9 on: December 24, 2017, 07:57:16 AM »
I'm a little older than the OP (54), and have been wrestling with the same issue. I did it in a maybe hokey way but it works for me:
I calculated annual expenses as same as current (in today's dollars) plus extra to cover costs of medical insurance and copays/deductible, in two phases: prior to age 70, and after age 70. At age 70, expenses are reduced by the Social Security benefit. I used my actual benefit minus 20% to cover potential cuts, and further assumed that the entire benefit is subject to tax. All numbers in today's dollars, with assumption that current expenses, savings and SS will track inflation.
I then calculated the savings required for age 70 expenses at a 4% SWR. This is less than my current savings, so I then assume I can spend down the excess. The amount of this spend-down (divide by #years until age 70) gets added to the 4% SWR from the post-age 70 savings pot.
Reaching FI happens when the income from the age-70 savings pot plus annual spend-down exceeds annual expenses. This is a much lower number than a straight calculation of savings = expenses * 25 yields, and accordingly speeds up the FI timetable.
Definitely interested to see how other people handle this. I prefer my own spreadsheets to depending entirely on FIREcalc, although this tool is much appreciated.
I am not understanding how you are doing it. Let me try to summarize to see if I even have it half right.
You divide your remaining years into pre SS and post SS.
For post SS, you figure what you will need to live on each year and subtract out 80% of SS and Taxes on 80% of SS. Then you take what is left and figure you need 25 times that amount in your stash for that period of your life. That amount covers post retirement.
After that I am lost.
#### Monkey Uncle
• Handlebar Stache
• Posts: 1406
• Location: West-by-god-Virginia
##### Re: How do you factor social security into your withdrawal stategy
« Reply #10 on: December 24, 2017, 09:08:27 AM »
This is a bit tangential to the question you asked, but I suggest comparing various SS start ages in cFiresim. You may find that it is better to start collecting earlier as opposed to waiting until you're 70. When I ran my numbers, I actually got the best maximum safe spend by starting both my and DW's SS payments at 62. This is because starting early reduces the amount we have to pull from the stash early on, which reduces sequence of return risk.
Also, if Congress changes benefit amounts to address the funding shortfall, I believe they will be less likely to cut my benefits if I am already drawing them. Sort of a "get it while you can" situation.
Interesting, so back testing proved that it may actually be better to start early. I have modeled this in spreadsheets using a relatively low return rate and found it was slightly better to wait. So you are saying that using real historic returns then proves the opposite.
I think it probably depends on your personal circumstances, so I would encourage you to run the numbers for yourself. The older you are when you FIRE, the closer you are to drawing SS during the early years of retirement. I think this has a bigger impact on sequence of return risk than for someone who FIREs in their 30s and then has 30 years of retirement to get through before they can start drawing.
Also I should emphasize that my metric of interest is maximum safe annual spending amount, not total return or average ending stash size. IIRC, my runs that began SS at 62 showed a higher max spend, but a lower average ending stash size.
« Last Edit: December 24, 2017, 09:15:09 AM by Monkey Uncle »
#### NaturallyHappier
• Stubble
• Posts: 129
• Age: 53
• FIRED 3/10/2017
##### Re: How do you factor social security into your withdrawal stategy
« Reply #11 on: December 24, 2017, 09:56:58 AM »
This is a bit tangential to the question you asked, but I suggest comparing various SS start ages in cFiresim. You may find that it is better to start collecting earlier as opposed to waiting until you're 70. When I ran my numbers, I actually got the best maximum safe spend by starting both my and DW's SS payments at 62. This is because starting early reduces the amount we have to pull from the stash early on, which reduces sequence of return risk.
Also, if Congress changes benefit amounts to address the funding shortfall, I believe they will be less likely to cut my benefits if I am already drawing them. Sort of a "get it while you can" situation.
Interesting, so back testing proved that it may actually be better to start early. I have modeled this in spreadsheets using a relatively low return rate and found it was slightly better to wait. So you are saying that using real historic returns then proves the opposite.
I think it probably depends on your personal circumstances, so I would encourage you to run the numbers for yourself. The older you are when you FIRE, the closer you are to drawing SS during the early years of retirement. I think this has a bigger impact on sequence of return risk than for someone who FIREs in their 30s and then has 30 years of retirement to get through before they can start drawing.
Also I should emphasize that my metric of interest is maximum safe annual spending amount, not total return or average ending stash size. IIRC, my runs that began SS at 62 showed a higher max spend, but a lower average ending stash size.
If you are interested in maximizing withdrawal rates, then I would recommend reading "Living Off Your Money" by M. McClung if you have not already. It is an expensive book @\$35.00, but worth every penny in my opinion. He goes through many different withdrawal methods and back tests them thoroughly against historical data to see how they hold up and he recommends the EM or ECM methods. He gives the reader the results of his back testing to show why he recommends them. He even comes up with a new method himself that looks very promising, but he eventually throws it out because of the possibility of outliving your stash in a couple bad years. He also has a free spreadsheet that implements his withdrawal method and his harvesting method @ https://gumroad.com/l/OfsGt/free.
#### freya
• Stubble
• Posts: 202
##### Re: How do you factor social security into your withdrawal stategy
« Reply #12 on: December 24, 2017, 01:34:10 PM »
I'm a little older than the OP (54), and have been wrestling with the same issue. I did it in a maybe hokey way but it works for me:
I calculated annual expenses as same as current (in today's dollars) plus extra to cover costs of medical insurance and copays/deductible, in two phases: prior to age 70, and after age 70. At age 70, expenses are reduced by the Social Security benefit. I used my actual benefit minus 20% to cover potential cuts, and further assumed that the entire benefit is subject to tax. All numbers in today's dollars, with assumption that current expenses, savings and SS will track inflation.
I then calculated the savings required for age 70 expenses at a 4% SWR. This is less than my current savings, so I then assume I can spend down the excess. The amount of this spend-down (divide by #years until age 70) gets added to the 4% SWR from the post-age 70 savings pot.
Reaching FI happens when the income from the age-70 savings pot plus annual spend-down exceeds annual expenses. This is a much lower number than a straight calculation of savings = expenses * 25 yields, and accordingly speeds up the FI timetable.
Definitely interested to see how other people handle this. I prefer my own spreadsheets to depending entirely on FIREcalc, although this tool is much appreciated.
I am not understanding how you are doing it. Let me try to summarize to see if I even have it half right.
You divide your remaining years into pre SS and post SS.
For post SS, you figure what you will need to live on each year and subtract out 80% of SS and Taxes on 80% of SS. Then you take what is left and figure you need 25 times that amount in your stash for that period of your life. That amount covers post retirement.
After that I am lost.
OK let me see if I can explain it better.
Prior to age 70, my expenses are assumed to be what they are today plus some extra for things like medical insurance that are covered by employment benefits now. I assume no other sources of income, so the stash has to provide all living expenses.
After age 70, my expenses are the same, but I now have a new source of income (SS). My stash now needs to supply only the portion of expenses not covered by SS.
The minimum stash amount thus has two components: one for after 70 which has to survive indefinitely, and one for before age 70 which can be spent down. It's sort of what the OP did, I just took a different approach and don't need to make any longevity assumptions.
BTW totally agree that I would not consider SS if retiring before, say, age 45. It's too long a time horizon for this to make any difference.
Also, as far as sequence of returns risk, I'm not terribly concerned about that as my long term savings is in the Permanent Portfolio. A 4% SWR in that portfolio is far safer than it is for a typical stock/bond portfolio. The bit of CAGR you give up for that protection is worth it to me.
#### Monkey Uncle
• Handlebar Stache
• Posts: 1406
• Location: West-by-god-Virginia
##### Re: How do you factor social security into your withdrawal stategy
« Reply #13 on: December 24, 2017, 02:17:03 PM »
This is a bit tangential to the question you asked, but I suggest comparing various SS start ages in cFiresim. You may find that it is better to start collecting earlier as opposed to waiting until you're 70. When I ran my numbers, I actually got the best maximum safe spend by starting both my and DW's SS payments at 62. This is because starting early reduces the amount we have to pull from the stash early on, which reduces sequence of return risk.
Also, if Congress changes benefit amounts to address the funding shortfall, I believe they will be less likely to cut my benefits if I am already drawing them. Sort of a "get it while you can" situation.
Interesting, so back testing proved that it may actually be better to start early. I have modeled this in spreadsheets using a relatively low return rate and found it was slightly better to wait. So you are saying that using real historic returns then proves the opposite.
I think it probably depends on your personal circumstances, so I would encourage you to run the numbers for yourself. The older you are when you FIRE, the closer you are to drawing SS during the early years of retirement. I think this has a bigger impact on sequence of return risk than for someone who FIREs in their 30s and then has 30 years of retirement to get through before they can start drawing.
Also I should emphasize that my metric of interest is maximum safe annual spending amount, not total return or average ending stash size. IIRC, my runs that began SS at 62 showed a higher max spend, but a lower average ending stash size.
If you are interested in maximizing withdrawal rates, then I would recommend reading "Living Off Your Money" by M. McClung if you have not already. It is an expensive book @\$35.00, but worth every penny in my opinion. He goes through many different withdrawal methods and back tests them thoroughly against historical data to see how they hold up and he recommends the EM or ECM methods. He gives the reader the results of his back testing to show why he recommends them. He even comes up with a new method himself that looks very promising, but he eventually throws it out because of the possibility of outliving your stash in a couple bad years. He also has a free spreadsheet that implements his withdrawal method and his harvesting method @ https://gumroad.com/l/OfsGt/free.
Thanks for the tip. I'll have to check it out.
#### Mr. Green
• Handlebar Stache
• Posts: 1790
• Age: 35
• Location: Wilmington, NC
##### Re: How do you factor social security into your withdrawal stategy
« Reply #14 on: December 25, 2017, 07:15:59 AM »
SS will be the gravy on top of our other income. We intend to use it to boost our spending in our 60s and 70s while we're still healthy enough for long distance travel, then cover any potential increase in medical expenses as our health declines.
#### secondcor521
• Handlebar Stache
• Posts: 1808
• Age: 49
• Location: Boise, Idaho
• Big cattle, no hat.
##### Re: How do you factor social security into your withdrawal stategy
« Reply #15 on: December 25, 2017, 11:45:30 AM »
Just to throw another method out there, here's how I do it at age 48 and FIREd for about 2 years:
I take my age 67 (FRA for me) benefit from the SS website. I then project this forward monthly at my chosen inflation rate (3%) out to age 83. I then take 40% of that number as a conservative amount I choose to plan on given the funding issues everyone knows about. I then only consider the amounts from age 67 to age 83. (Why 83? I don't remember exactly, but I think that is a reasonable estimate of my 50th percentile life expectancy.)
I then take the NPV of the sum of those payments, using that same 3% as the discount rate and add that sum into my FIRE stash. I then take 4% of that FIRE stash as the upper limit on what I can spend.
Currently I am spending only about 2.38% of my FIRE stash, so I feel pretty comfortable about things.
When I run cFIREsim, I use my FIRE stash without Social Security and add in my Social Security payments as an additional income stream coming on line when I hit FRA. I feel that approach is the closest to the way cFIREsim is intended to be used and it also keeps things as simple as possible. And simplicity helps avoid mistakes in math that could occur and make the results a less reliable projection.
For some perspective, doing it this way is about 25% more conservative than the OP's method with my numbers, and considerably more complicated. The NPV that I add in for Social Security is only about 12% of my total FIRE stash.
Bottom line in my case, Social Security is a nice addition but isn't that much of a factor in my personal situation.
#### SwordGuy
• Magnum Stache
• Posts: 4613
• Location: Fayetteville, NC
##### Re: How do you factor social security into your withdrawal stategy
« Reply #16 on: December 25, 2017, 12:02:11 PM »
+1 for @Monkey Uncle comment, I have found the same thing. If you have plenty of income in the later years, it can be helpful to pull as much of that as possible to the earlier years.
Regarding your original question, I have done it a little differently. I have a spreadsheet that figures out the WR each year based on the income that I need minus any other income sources. So for example, in the first few years, we have only rental property income so I find that my required WR is around 7%. When my SS benefits start at 62, it drops to around 5%, and eventually to 3% after my wife's SS and some pensions begin. Since this final WR is below the 4% SWR, I know we should be okay.
Sorry to be morbid, but I rarely see this point discussed and it's relevant.
If one of you dies, do the expenses drop enough to keep the final WR below the 4% SWR? Because if they won't, then the surviving partner will have higher odds of a failure.
#### rab-bit
• Stubble
• Posts: 114
##### Re: How do you factor social security into your withdrawal stategy
« Reply #17 on: December 25, 2017, 12:50:37 PM »
@SwordGuy I agree that this is important and I have thought about it. In our case, when one of us dies we would lose the lower of the two SS benefits. All other income sources would remain unchanged. Increasing the WR from 3% to 4% would offset about half of that, and I'm confident that the rest could be absorbed through lower expenses (one less person so lower food, medical and possibly housing costs).
Of course everyone's situation is different, so YMMV.
« Last Edit: December 25, 2017, 01:04:56 PM by rab »
#### Monkey Uncle
• Handlebar Stache
• Posts: 1406
• Location: West-by-god-Virginia
##### Re: How do you factor social security into your withdrawal stategy
« Reply #18 on: December 25, 2017, 01:13:54 PM »
@SwordGuy I agree that this is important and I have thought about it. In our case, when one of us dies we would lose the lower of the two SS benefits. All other income sources would remain unchanged. Increasing the WR from 3% to 4% would offset about half of that, and I'm confident that the rest could be absorbed through lower expenses (one less person so lower food, medical and possibly housing costs).
Of course everyone's situation is different, so YMMV.
In our case, it is highly likely that the surviving spouse will downsize to a smaller, less expensive house.
#### soccerluvof4
• Magnum Stache
• Posts: 3994
• Location: Artic Midwest
• Retired at 50
##### Re: How do you factor social security into your withdrawal stategy
« Reply #19 on: December 26, 2017, 03:28:29 AM »
SS will be the gravy on top of our other income. We intend to use it to boost our spending in our 60s and 70s while we're still healthy enough for long distance travel, then cover any potential increase in medical expenses as our health declines.
This is how we look at it as well , just in case against all my reasoning it would not be there for us.
#### rab-bit
• Stubble
• Posts: 114
##### Re: How do you factor social security into your withdrawal stategy
« Reply #20 on: December 26, 2017, 04:22:24 AM »
@SwordGuy I agree that this is important and I have thought about it. In our case, when one of us dies we would lose the lower of the two SS benefits. All other income sources would remain unchanged. Increasing the WR from 3% to 4% would offset about half of that, and I'm confident that the rest could be absorbed through lower expenses (one less person so lower food, medical and possibly housing costs).
Of course everyone's situation is different, so YMMV.
In our case, it is highly likely that the surviving spouse will downsize to a smaller, less expensive house.
Another thing to consider is that once SS age is reached, the time that your money needs to last is starting to get shorter than the 30 years built into the 4% rule. Even at age 62, life expectancy is probably 25 years or less, so this should reduce the risk of one spouse running out of money after the other spouse passes and the lower SS benefit is lost.
#### dude
• Handlebar Stache
• Posts: 2289
##### Re: How do you factor social security into your withdrawal stategy
« Reply #21 on: December 26, 2017, 09:39:34 AM »
I plan to wait until 70 (spouse is 7 years younger than me and I'm the higher earner). I've basically calculated that I need a 1.9% draw until 62, then a 4%-5% draw from 62-70*, at which point, I start taking SS (projected to be @\$35k). RMD's come at 70.5, and I'm likely to have way more income than I'll be able to spend, unless (and I fully expect this is coming down the pike) the assholes in charge start means-testing SS. I will confess that I'm contemplating taking SS earlier depending on what the political climate is like in 2027 when I turn 62, because as someone mentioned, the Trust Fund "surplus" runs out in 2034, just 7 years later, right as I'll be approaching 70 years old. So I may claim it earlier in hopes of being grandfathered into whatever 11th hour "solution" Congress comes up with then, or if the numbers suggest that collecting the Age 62 amount outweighs waiting for 75% of the full amount at age 70.
*If my account has survived/avoided a bad sequence of returns hit in the first 10 years, I should have no problem bumping to 5, 6 or even 7%.
#### jim555
• Handlebar Stache
• Posts: 1908
##### Re: How do you factor social security into your withdrawal stategy
« Reply #22 on: December 26, 2017, 10:31:08 AM »
Having a pension (starting from 55-65) and SS (starting from 62-70) means a floor of income that covers the basics. So I could spend down faster in the front years and less in the back years. I could even spend to zero to age 70 and just rely on pension/SS from then on. Solves the problem of leaving money on the table.
• Handlebar Stache
• Posts: 1830
##### How do you factor social security into your withdrawal stategy
« Reply #23 on: January 06, 2018, 07:44:15 AM »
My Hub and I started Social Security (SS) at age 63 and 62 1/2. We both had to go on Obamacare and to receive the subsidy we had to keep income below \$63,000. With our 2 SS checks, one small pension our income level is around \$49,500. We then withdraw from IRA but only take about \$10K. So we have a total income of close to \$60K. If we need more money we withdraw from savings. My point is that our SS checks tally around \$43K a year that we are drawing for 3 and 3 1/2 years before Full Retirement Age (FRA). We will have drawn approx. \$150K from SS and not taken that out of our IRA's. Our break even point is around 78-80 years old. I know financial people advise to not withdraw from SS till your FRA or age 70 but for those who have children and want to be able to give them an inheritance, seems to me using SS money instead of savings is the better way to go. You can will your savings, you cannot will Social Security.
#### BTDretire
• Handlebar Stache
• Posts: 2307
##### Re: How do you factor social security into your withdrawal stategy
« Reply #24 on: January 07, 2018, 07:48:36 AM »
I'm still trying to get a handle on when to start collecting. I have always thought I'd wait until 70 to get the max, I'm 62 now, wife is 58.
However, I'm also looking at RMDs and even with a modest 6% growth rate I'm looking about \$50k of RMDs when we are both doing required RMDs. If we both wait until 70 to retire out SS
income will be about \$48k, plus dividends from non-tax deferred accounts, we will have a sizeable taxable yearly income that we can't get out of. Nice problem to have, but my job is to minimize taxes and maximize the NW while living a comfortable life.
The end result desired is to live well and leave as much to the kids as we can.
#### Lake161
• Stubble
• Posts: 113
• Location: NorCal
##### Re: How do you factor social security into your withdrawal stategy
« Reply #25 on: January 07, 2018, 11:00:39 AM »
For a really deep dive into the math around SS and withdrawal rates: https://earlyretirementnow.com/2017/01/04/the-ultimate-guide-to-safe-withdrawal-rates-part-4-social-security-pensions/
Also on that site, recommendations for how much to discount SS to account for the risk that Congress will shrink your benefits before you get there, based on your current age:
Age 55+: no discount. Political suicide to mess with this cohort
46-54: -10%
40-45: -15%
<40: -20%
#### BTDretire
• Handlebar Stache
• Posts: 2307
##### Re: How do you factor social security into your withdrawal stategy
« Reply #26 on: January 07, 2018, 12:40:19 PM »
For a really deep dive into the math around SS and withdrawal rates: https://earlyretirementnow.com/2017/01/04/the-ultimate-guide-to-safe-withdrawal-rates-part-4-social-security-pensions/
I found this of interest: https://tinyurl.com/y8ymz23
It says (in graph form) retiring at FRA may be better than 70 if you live past 92. I would like to do the calculations, with all the key assumptions listed at the end but I don't find the calculator.
The article was found here in the list of SS articles, near the bottom.
http://www.analyzenow.com/Articles/Social%20Security/Social%20Security.htm
Others can try this, it is basically, what if I stop paying SS taxes now but don't collect for years down the road.
I followed the directions in the last paragraph and I get a number slightly higher than what SS projects with me working until 66 and collecting at 66 vs working until 62 and collecting at 66.
I know that's not correct. Don't see how I could have made a mistake. If other can make it work, then I'll post my data for others to peruse.
#### weirdlair
• Stubble
• Posts: 186
• Location: Midwest
• Impeach the orange idiot
##### Re: How do you factor social security into your withdrawal stategy
« Reply #27 on: January 07, 2018, 12:55:01 PM »
I'm still trying to get a handle on when to start collecting. I have always thought I'd wait until 70 to get the max, I'm 62 now, wife is 58.
However, I'm also looking at RMDs and even with a modest 6% growth rate I'm looking about \$50k of RMDs when we are both doing required RMDs. If we both wait until 70 to retire out SS
income will be about \$48k, plus dividends from non-tax deferred accounts, we will have a sizeable taxable yearly income that we can't get out of. Nice problem to have, but my job is to minimize taxes and maximize the NW while living a comfortable life.
The end result desired is to live well and leave as much to the kids as we can.
We struggle with this as well, but have several years before we are 62. RMDs + SS + pension will result in a very large tax bill. We might just have the higher wage earner wait until FRA (or maybe 70) to collect SS, and the other start at 62.
#### hdatontodo
• Bristles
• Posts: 272
• Location: Balto Co, MD
##### Re: How do you factor social security into your withdrawal stategy
« Reply #28 on: January 07, 2018, 03:46:56 PM »
Others can try this, it is basically, what if I stop paying SS taxes now but don't collect for years down the road.
I downloaded the social security Windows benefit calculator in which you manually enter each year of 30-some years of earnings and specify the retirement year.
I'm 57. I put in that I worked through 2017 and would retire at 62. The amount was \$1,825/mo. If I cleared 2017 to \$0 income, it said my monthly benefit would be \$1804.
#### MDM
• Walrus Stache
• Posts: 8857
##### Re: How do you factor social security into your withdrawal stategy
« Reply #29 on: January 07, 2018, 04:27:39 PM »
I followed the directions in the last paragraph and I get a number slightly higher than what SS projects with me working until 66 and collecting at 66 vs working until 62 and collecting at 66.
I know that's not correct. Don't see how I could have made a mistake. If other can make it work, then I'll post my data for others to peruse.
There is also the SocialSecurity tab in the case study spreadsheet, for those who prefer spreadsheets to canned programs.
#### NaturallyHappier
• Stubble
• Posts: 129
• Age: 53
• FIRED 3/10/2017
##### Re: How do you factor social security into your withdrawal stategy
« Reply #30 on: January 08, 2018, 04:49:47 AM »
You can also use my google spreadsheet (make a copy for yourself) to calculate the effect of ER on your SS income.
This will tell you how much you can expect to receive at 62, 65 and 70, but wont tell you whether it is better to take it early. To do that I think you need to first come up with the age you expect to expire and then add up the amount you would receive by that time at each age to see which is highest.
#### Monkey Uncle
• Handlebar Stache
• Posts: 1406
• Location: West-by-god-Virginia
##### Re: How do you factor social security into your withdrawal stategy
« Reply #31 on: January 08, 2018, 05:03:48 AM »
You can also use my google spreadsheet (make a copy for yourself) to calculate the effect of ER on your SS income.
This will tell you how much you can expect to receive at 62, 65 and 70, but wont tell you whether it is better to take it early. To do that I think you need to first come up with the age you expect to expire and then add up the amount you would receive by that time at each age to see which is highest.
SS is actuarially designed to pay out the same amount of lifetime benefits regardless of the age at which you start. So if you live to the average life expectancy for your age/sex, you get the same amount over your lifetime whether you start at 62 or 70 or any age in between. The only way to optimize from this perspective is if you have some special knowledge of when you expect to die.
#### NaturallyHappier
• Stubble
• Posts: 129
• Age: 53
• FIRED 3/10/2017
##### Re: How do you factor social security into your withdrawal stategy
« Reply #32 on: January 08, 2018, 05:59:09 AM »
SS is actuarially designed to pay out the same amount of lifetime benefits regardless of the age at which you start. So if you live to the average life expectancy for your age/sex, you get the same amount over your lifetime whether you start at 62 or 70 or any age in between. The only way to optimize from this perspective is if you have some special knowledge of when you expect to die.
Good point. It does not take into consideration gender, or family history, so most will have some special knowledge....or at least an informed guess as to whether they expect to live shorter or longer.
#### SwordGuy
• Magnum Stache
• Posts: 4613
• Location: Fayetteville, NC
##### Re: How do you factor social security into your withdrawal stategy
« Reply #33 on: January 11, 2018, 08:57:35 PM »
If you are a high earner, most of what you're paying into social security is being given to someone else. So if you quit working a few years early (just make sure it's no so many you don't qualify for SS!!!!), it really doesn't make much difference at all.
#### Classical_Liberal
• Handlebar Stache
• Posts: 1023
• Age: 42
##### Re: How do you factor social security into your withdrawal stategy
« Reply #34 on: January 11, 2018, 10:28:34 PM »
You can will your savings, you cannot will Social Security.
I think I've thought of everything and then this... Smart!
One other thing to consider is market conditions once one becomes eligible for SS, particularly for the equity heavy investor (most of us). For example, if at 63 you see a rather large, longer term correction point and assets take a hit, it may be advantageous to start drawing SS early. This will help avoid drawdowns and allow you to be more price sensitive in assets sales. If there's a bull in your early-mid 60's, then it might make more sense to keep SS as longevity insurance, allowing for more aggressive investing later in life.
before you get there, based on your current age:
Age 55+: no discount. Political suicide to mess with this cohort
46-54: -10%
40-45: -15%
<40: -20%
This is probably very realistic, but I'm a pessimist.
Personally, I'm only 41. I do, however, think it's foolish to not account for some income from SS. At my low spending levels it's just too much money to ignore and would cost me years of extra working. I'm very conservative and assume 50% of my current earned benefit (ie if I never contributed again). Obviously this amount goes up each year I do work. This method basically provides me with a minimum inflation adjusted stash amount I need to maintain to age 62(early SS if I opt for it) for a 4%WR. Once I near that age, future benefit levels will likely be less opaque and I can adjust accordingly.
Stash/25 >= Post Fire Annual Spend - (earned SS benefit @ 67 *.5)
If I'm FIRE'd, under age 62, and this equation becomes unbalanced; I need to fix it while I still have decent earning power.
In assuming a 50% of current earned benefit, I feel it's still extremely likely I will see more money from the system than I'm planning(both through new contributions and potential future fixes to the system). A good enough safety margin for my tastes.
« Last Edit: January 11, 2018, 11:05:42 PM by Classical_Liberal »
#### rab-bit
• Stubble
• Posts: 114
##### Re: How do you factor social security into your withdrawal stategy
« Reply #35 on: January 12, 2018, 06:09:10 AM »
It's been stated many times and in many places, including here:
https://www.ssa.gov/policy/docs/ssb/v70n3/v70n3p111.html
that SS will remain solvent until around 2037 after which it will be able to pay out around 75% of scheduled benefits. So I think that even for younger people, a 25% reduction in expected SS benefits is a reasonable lower bound. As @Classical_Liberal mentioned, ignoring SS completely could result in working years longer than you would need to otherwise, and none of us wants that!
#### des999
• Stubble
• Posts: 168
##### Re: How do you factor social security into your withdrawal stategy
« Reply #36 on: January 12, 2018, 10:48:13 AM »
my expected SS with wife is about 40k plus a small pension. That would easily cover my expenses. I am starting to think about a draw down scenario that is more for 20-25 years, until the SS kicks in. Even if it went to 0 I would be technically be ok as I could live off of SS.
This would assume SS is still in place as is today, so I have to take that into consideration, but I am more of a believer that it will be fine as too many people rely on it for them to let it crash and burn (some minor tweaks).
I also do not think I'll run my stash to 0 or close to it, but it makes me feel better knowing I have SS waiting.
I am 38, for a frame of reference.
#### mamagoose
• Bristles
• Posts: 355
• Location: FL
##### Re: How do you factor social security into your withdrawal stategy
« Reply #37 on: January 12, 2018, 10:56:34 AM »
We do not include it as expected income in retirement. If we do receive it (30 years from now), we will be the most generous grandparents ever.
#### TheWifeHalf
• Bristles
• Posts: 496
##### Re: How do you factor social security into your withdrawal stategy
« Reply #38 on: January 12, 2018, 02:37:50 PM »
Our plan (might change of course)
TheHusbandHalf worked for the railroad a little over 10 years in our first years of marriage. He paid what they call Tier 1 and Tier 2. I think Tier 1 is like social security.
That Tier 2 payment gives him (last checked 4 months ago) \$500/mo, and is paid with his Social Security check. So, he will get 36,000 at FRA, I will get half of that 2 years later, total 54,000.
He plans to stop working Jan 4 2019 At the time, he will have had that employer 28 years and will be 62 1/2. Between then and his FRA, we will use the money I got from a car accident to live, and to convert as much tIRA to Roth. The accident money is capitial gains and this is where I won't say anymore because I don't fully understand it. We will get health, dental insurance through his employer and (something I made him check) I will still be covered if something happens to him, say at 63 or 64. His medical insurance as a retiree: the company pays half and he is one of the highest seniority employees so the company pays another 30%. So, he will pay 20% of whatever the insurance is at the time..
When he stops working he will get his pension in a lump sum and it will go in his tIRA
I have DNA on my mother's and father's side that lead me to believe I will go on into my mid 90's. He, mid 80's. This is why we are waiting until his FRA, because it might be 35 years that we get SS. If not, oh well. He has over 35 years of paying into SS or equivalent, so those 4 years of not working will not bring his monthly SS check down.
Something interesting, at least to me:
His brother worked for the railroad all his working days. In that case, a rr retiree gets Railroad Retirement, not SS. He is allowed, and did, retire at 60. He gets 7000 per month, his wife gets half. I'm not sure that all is worth the wear and tear on his body, but I say, Good for them!
#### Brahmaniac
• Posts: 3
##### Re: How do you factor social security into your withdrawal stategy
« Reply #39 on: January 16, 2018, 09:25:23 PM »
People who don't include Social Security are being mindless Sheeple, repeating media talking points instead of engaging their brain.
Medicare is more likely to run out of money than Social Security but I don't see any of them saying "I just assume I'll have to pay \$50,000 a year for health insurance when I'm 85 and if Medicare is actually still around I'll consider it a bonus."
(I mean, seriously, have you priced private health care for a pair of 80 year olds with pre-existing conditions?)
Since their retirement won't work at all without Medicare paying for their health care at an advanced age, they just assume it will be around to make all their numbers work. Even though it is more underfunded than Social Security and in much bigger trouble.
There is no world in which Medicare still exists but Social Security doesn't.
#### dude
• Handlebar Stache
• Posts: 2289
##### Re: How do you factor social security into your withdrawal stategy
« Reply #40 on: January 17, 2018, 01:16:53 PM »
People who don't include Social Security are being mindless Sheeple, repeating media talking points instead of engaging their brain.
Medicare is more likely to run out of money than Social Security but I don't see any of them saying "I just assume I'll have to pay \$50,000 a year for health insurance when I'm 85 and if Medicare is actually still around I'll consider it a bonus."
(I mean, seriously, have you priced private health care for a pair of 80 year olds with pre-existing conditions?)
Since their retirement won't work at all without Medicare paying for their health care at an advanced age, they just assume it will be around to make all their numbers work. Even though it is more underfunded than Social Security and in much bigger trouble.
There is no world in which Medicare still exists but Social Security doesn't.
Yep, and old people vote. There is no way they (and the AARP) are going to let them take Medicare away. Down the road, we're all looking at hefty income tax increases to pay for this shit, especially after the GOP tax bill does its damage. Hopefully, people will WTFU and make the billionaires pony up.
• Handlebar Stache
• Posts: 1830
##### Re: How do you factor social security into your withdrawal stategy
« Reply #41 on: January 18, 2018, 05:13:38 AM »
Let's say you take Social Security (SS) at age 62 and are making \$20,000 a year. You collect for 8 years then die at age 70. You would have collected \$160,000 during that 8 years time. That is money you have not had to pull from your IRA's savings, bank accounts, etc. So had you waited till age 70 to get the big reward from Social Security, you would have gotten nothing because you died and the gubment doesn't pay dead people. However, your spouse would get the bigger check. I like the idea of using my SS money at an earlier age for a longer period of time and letting my little green soldiers (IRA's, etc.) grow big and strong. I have no children to will my money to but if I did, I would prefer to use my SS check to live on and leave my stache as untouched as possible. Hub and I collect \$43,600 with two SS checks plus a small pension which brings our income up to almost \$50K a year. Not bad income for not actually working for it! LOL! Love my 'welfare' checks! Laughing all the way to the bank! Hahahahaha!
#### MasterStache
• Handlebar Stache
• Posts: 1829
##### Re: How do you factor social security into your withdrawal stategy
« Reply #42 on: January 18, 2018, 06:34:23 AM »
SS will be the gravy on top of our other income. We intend to use it to boost our spending in our 60s and 70s while we're still healthy enough for long distance travel, then cover any potential increase in medical expenses as our health declines.
This is how we look at it as well , just in case against all my reasoning it would not be there for us.
Us as well. I don't factor SS at all. If we get some, awesome, it will help likely with medical and pay for some travel. My wife's pension is likely more relevant and we do factor that in somewhat.
#### fattest_foot
• Pencil Stache
• Posts: 593
##### Re: How do you factor social security into your withdrawal stategy
« Reply #43 on: January 18, 2018, 10:35:57 AM »
It's been stated many times and in many places, including here:
https://www.ssa.gov/policy/docs/ssb/v70n3/v70n3p111.html
that SS will remain solvent until around 2037 after which it will be able to pay out around 75% of scheduled benefits. So I think that even for younger people, a 25% reduction in expected SS benefits is a reasonable lower bound. As @Classical_Liberal mentioned, ignoring SS completely could result in working years longer than you would need to otherwise, and none of us wants that!
Just a correction, but the Social Security Trust Fund will remain solvent until 2037. Social Security remains solvent as long as there's still a payroll deduction for it and a pool of workers to draw from. The reason it drops 75% when the Trust Fund runs out of money is that they're essentially using it as an additional payment to current retirees because there's just too much money.
If you look at it as Social Security will always pay 100%, but current retiree's are getting about 133%, it'd be more accurate.
#### Bateaux
• Handlebar Stache
• Posts: 1266
• Location: Port Vincent
##### Re: How do you factor social security into your withdrawal stategy
« Reply #44 on: January 18, 2018, 12:05:23 PM »
My hope is that Social Security will be enough to over health care. I'm skeptical that it will be there in the two decades before I'll draw. Offsetting the cost of increased medical costs with SS I'd consider a win.
#### Classical_Liberal
• Handlebar Stache
• Posts: 1023
• Age: 42
##### Re: How do you factor social security into your withdrawal stategy
« Reply #45 on: January 18, 2018, 08:12:38 PM »
People who don't include Social Security are being mindless Sheeple, repeating media talking points instead of engaging their brain.
Medicare is more likely to run out of money than Social Security but I don't see any of them saying "I just assume I'll have to pay \$50,000 a year for health insurance when I'm 85 and if Medicare is actually still around I'll consider it a bonus."
(I mean, seriously, have you priced private health care for a pair of 80 year olds with pre-existing conditions?)
Since their retirement won't work at all without Medicare paying for their health care at an advanced age, they just assume it will be around to make all their numbers work. Even though it is more underfunded than Social Security and in much bigger trouble.
There is no world in which Medicare still exists but Social Security doesn't.
Great comment! Forced me to look through my own bias and cognitive dissonance. We need more thought provoking posters now-a-days; too many facebook of FI comments and too little well though out posts.
My hope is that Social Security will be enough to over health care. I'm skeptical that it will be there in the two decades before I'll draw. Offsetting the cost of increased medical costs with SS I'd consider a win.
Speaking of facebook of FI comments... I'm always seriously amazed how people will see a trend for a few years and then extrapolate that into the future indefinitely. It's not as if medical costs have no upper limit.
If SS disappears about 50% of grandma&pa's are literally starving in the streets. As long as Western civilization is intact, so to will SS remain intact; or at least a very orderly transition to another program.
#### BTDretire
• Handlebar Stache
• Posts: 2307
##### Re: How do you factor social security into your withdrawal stategy
« Reply #46 on: January 21, 2018, 08:49:40 AM »
Let's say you take Social Security (SS) at age 62 and are making \$20,000 a year. You collect for 8 years then die at age 70. You would have collected \$160,000 during that 8 years time. That is money you have not had to pull from your IRA's savings, bank accounts, etc. So had you waited till age 70 to get the big reward from Social Security, you would have gotten nothing because you died and the gubment doesn't pay dead people. However, your spouse would get the bigger check. I like the idea of using my SS money at an earlier age for a longer period of time and letting my little green soldiers (IRA's, etc.) grow big and strong. I have no children to will my money to but if I did, I would prefer to use my SS check to live on and leave my stache as untouched as possible. Hub and I collect \$43,600 with two SS checks plus a small pension which brings our income up to almost \$50K a year. Not bad income for not actually working for it! LOL! Love my 'welfare' checks! Laughing all the way to the bank! Hahahahaha!
Collecting early is certainly one way to go, but what if you live to 85 yrs old and the stock market has a 10 year plateau when you are 62 to 72. Your nest egg will have no growth, but your SS check would grow by 8% a year from 62 to 70, if you waited.
We have had a 311% growth in the S&P during the last 9 years, this has a lot of people thinking that is just the way it is.
On the other hand The S&P was 1527 in Mar, 2000 and got back up to 1527 again in Mar, 2013. That's 13 years of just earning the dividends.
#### Mr. Green
• Handlebar Stache
• Posts: 1790
• Age: 35
• Location: Wilmington, NC
##### Re: How do you factor social security into your withdrawal stategy
« Reply #47 on: January 21, 2018, 01:44:39 PM »
It's been stated many times and in many places, including here:
https://www.ssa.gov/policy/docs/ssb/v70n3/v70n3p111.html
that SS will remain solvent until around 2037 after which it will be able to pay out around 75% of scheduled benefits. So I think that even for younger people, a 25% reduction in expected SS benefits is a reasonable lower bound. As @Classical_Liberal mentioned, ignoring SS completely could result in working years longer than you would need to otherwise, and none of us wants that!
Just a correction, but the Social Security Trust Fund will remain solvent until 2037. Social Security remains solvent as long as there's still a payroll deduction for it and a pool of workers to draw from. The reason it drops 75% when the Trust Fund runs out of money is that they're essentially using it as an additional payment to current retirees because there's just too much money.
If you look at it as Social Security will always pay 100%, but current retiree's are getting about 133%, it'd be more accurate.
This is inaccurate. The system is designed so that what retirees get currently is 100%. If the Trust Fund is exhausted that simply means the money paid in can no longer support the amount paid out, and the formula needs to change.
#### Monkey Uncle
• Handlebar Stache
• Posts: 1406
• Location: West-by-god-Virginia
##### Re: How do you factor social security into your withdrawal stategy
« Reply #48 on: January 22, 2018, 04:29:03 AM »
Let's say you take Social Security (SS) at age 62 and are making \$20,000 a year. You collect for 8 years then die at age 70. You would have collected \$160,000 during that 8 years time. That is money you have not had to pull from your IRA's savings, bank accounts, etc. So had you waited till age 70 to get the big reward from Social Security, you would have gotten nothing because you died and the gubment doesn't pay dead people. However, your spouse would get the bigger check. I like the idea of using my SS money at an earlier age for a longer period of time and letting my little green soldiers (IRA's, etc.) grow big and strong. I have no children to will my money to but if I did, I would prefer to use my SS check to live on and leave my stache as untouched as possible. Hub and I collect \$43,600 with two SS checks plus a small pension which brings our income up to almost \$50K a year. Not bad income for not actually working for it! LOL! Love my 'welfare' checks! Laughing all the way to the bank! Hahahahaha!
Collecting early is certainly one way to go, but what if you live to 85 yrs old and the stock market has a 10 year plateau when you are 62 to 72. Your nest egg will have no growth, but your SS check would grow by 8% a year from 62 to 70, if you waited.
We have had a 311% growth in the S&P during the last 9 years, this has a lot of people thinking that is just the way it is.
On the other hand The S&P was 1527 in Mar, 2000 and got back up to 1527 again in Mar, 2013. That's 13 years of just earning the dividends.
That situation is precisely when you need to be collecting a SS benefit. It helps ease sequence of return risk because you are pulling less out of your portfolio.
It's been said before, but it bears repeating: if you live to the normal life expectancy for someone your age, your total inflation-adjusted payout over your lifetime is the same regardless of the age at which you start collecting. That 8%/yr growth in your SS payment is offset by the fact that you aren't getting a benefit check from age 62 to 70. It is NOT the same thing as an 8% return on an investment.
What really matters is what is happening with your portfolio during those years, and the age at which you actually die. Unfortunately neither of those things can be predicted with any accuracy. The best you can do is model your personal situation using a tool like cFiresim to see which strategy would have optimized your metric of interest in the worst-case market return scenarios of the past.
« Last Edit: January 22, 2018, 07:39:05 AM by Monkey Uncle »
#### Classical_Liberal
• Handlebar Stache
• Posts: 1023
• Age: 42
##### Re: How do you factor social security into your withdrawal stategy
« Reply #49 on: January 22, 2018, 08:55:01 AM »
The best you can do is model your personal situation using a tool like cFiresim to see which strategy would have optimized your metric of interest in the worst-case market return scenarios of the past.
Actually, the best thing you can do is wait until you're eligible. Then, take one of the unknowns out of the equation. IOW, am I at high risk for a sequence issues based on real world market conditions from 62-70? Then decide when to take SS. If sequence issues are not a problem you have free longevity insurance, taking the other unknown out of the equation.
It's like having a lifeline against one or the other (sequence of returns nightmare or super-long life). You get to choose when to take the lifeline based on risk factors at the time. | 14,609 | 59,067 | {"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} | 2.703125 | 3 | CC-MAIN-2019-04 | latest | en | 0.929879 |
https://marcycookmath.com/index.php?option=com_virtuemart&category_id=10&page=shop.browse&Itemid=20&limit=20&limitstart=20&redirected=1&Itemid=20 | 1,685,871,703,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649741.26/warc/CC-MAIN-20230604093242-20230604123242-00057.warc.gz | 411,746,103 | 8,208 | Tiling Task Card Packets include 20 unique task cards on card stock, 3 backdrop cards, tracking sheets, suggestions and answer sheets. These are contained in a printed manila envelope for convenient storing. A set of number tiles 0 - 9 is needed for each task card.
4 - 7
### FRACTION & NUMBER LINE TILES DIGITAL
comparing common fractions ( )using a visual model of a number line between zero and one
Challenge Level:
DIGITAL FORMAT
(view & accomplish tasks on computer, ipad, or other hand held device with google)
\$10.00
4 - 7
### FRACTION & NUMBER LINE TILES
comparing common fractions ( )using a visual model of a number line between zero and one
Challenge Level:
PDF FORMAT
(You will receive both color and black and white files for printing.)
\$10.00
4 - 7
### FRACTION COMPARISON TILES DIGITAL
comparing two fractions with different numerators and different denominators using visual models to record comparisons with symbols
Challenge Level:
DIGITAL FORMAT
(view & accomplish tasks on computer, ipad, or other hand held device with google)
\$10.00
4 - 7
### FRACTION COMPARISON TILES
comparing two fractions with different numerators and different denominators using visual models to record comparisons with symbols
Challenge Level:
PDF FORMAT
(You will receive both color and black and white files for printing.)
\$10.00
4 - 8
### FRACTION TILES DIGITAL
experimenting with number tiles to form common fractions; example: fractions equivalent to 3/4
Challenge Level:
DIGITAL FORMAT
(view & accomplish tasks on computer, ipad, or other hand held device with google)
\$10.00
4 - 8
### FRACTION TILES
experimenting with number tiles to form common fractions; example: fractions equivalent to 3/4
Challenge Level:
PDF FORMAT
(You will receive both color and black and white files for printing.)
\$10.00
4 - 8
### FRACTIONAL PART TILES DIGITAL
finding fractional parts of whole numbers; examples: 1/3 of 39; less than 1/4 of 100
Challenge Level:
DIGITAL FORMAT
(view & accomplish tasks on computer, ipad, or other hand held device with google)
\$10.00
4 - 8
### FRACTIONAL PART TILES
finding fractional parts of whole numbers; examples: 1/3 of 39; less than 1/4 of 100
Challenge Level:
PDF FORMAT
(You will receive both color and black and white files for printing.)
\$10.00
5 - 8
### MULTI-DECI TILES
multiplying decimal fractions
Challenge Level:
\$15.00
5 - 8
### MULTI-DECI TILES DIGITAL
multiplying decimal fractions
Challenge Level:
DIGITAL FORMAT
(view & accomplish tasks on computer, ipad, or other hand held device with google)
\$10.00
5 - 8
### MULTI-DECI TILES
multiplying decimal fractions
Challenge Level:
PDF FORMAT
(You will receive both color and black and white files for printing.)
\$10.00
5 - 8
### PERCENTAGE TILES I
changing common fractions to decimals and decimals to percents and vice versa
Challenge Level:
\$15.00
5 - 8
### PERCENTAGE TILES II
computing the three basic types of percent problems
Challenge Level:
\$15.00
3 - 6
### PICTURE FRACTION TILES DIGITAL
forming common fractions from pictures, including equivalent fractions and geometry vocabulary for part of a total group
Challenge Level:
DIGITAL FORMAT
(view & accomplish tasks on computer, ipad, or other hand held device with google)
\$10.00
3 - 6
### PICTURE FRACTION TILES
forming common fractions from pictures, including equivalent fractions and geometry vocabulary for part of a total group
Challenge Level:
PDF FORMAT
(You will receive both color and black and white files for printing.)
\$10.00
5 - 8
### +/- DECI TILES
addition and subtraction of decimal fractions
Challenge Level:
\$15.00
3 - 6
### VIEW A FRACTION TILES DIGITAL
forming common fractions from pictures, including equivalent fractions and comparisons of fractions
Challenge Level:
DIGITAL FORMAT
(view & accomplish tasks on computer, ipad, or other hand held device with google)
\$10.00
3 - 6
### VIEW A FRACTION TILES
forming common fractions from pictures, including equivalent fractions and comparisons of fractions
Challenge Level:
PDF FORMAT
(You will receive both color and black and white files for printing.)
\$10.00
5 - 8
### VISUALIZING TILES
dealing with representational models for common fractions, percent, ratio, and square numbers
Challenge Level:
\$15.00 | 1,045 | 4,352 | {"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} | 2.78125 | 3 | CC-MAIN-2023-23 | latest | en | 0.812005 |
https://www.jiskha.com/questions/1819058/decide-whether-the-equation-is-an-identity-a-conditional-equation-or-a-contradiction | 1,627,665,784,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153971.20/warc/CC-MAIN-20210730154005-20210730184005-00657.warc.gz | 880,251,900 | 5,266 | # algebra
Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
2[3-(5-5x)] - x = -10 + 3(2 + 3x)
1. 👍
2. 👎
3. 👁
2[3-(5-5x)] - x = -10 + 3(2 + 3x)
2[3-5+5x] - x = -10 + 6 + 9x
2[-2+5x] - x = -4 + 9x
-4 + 10x - x = -4 + 9x
0 = 0
If that happens, your original equation is an identity, and is true for all values of x
If the variable drops away and you end up with a true statement, it is true for all values of x (like yours)
If the variable drops away and you end up with a false statement, the equation has no solution.
e.g. 3x + 5 = 3x = 6
5 = 6, false!! Thus no value of x is that ever going to make a true statement
1. 👍
2. 👎
👤
Reiny
2. Classify the equation as a conditional equation, an identity, or a contradiction.
3(6q−9)+7(q+4)=5(6q+8)−5(q+1)
1. 👍
2. 👎
## Similar Questions
Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. NOTE: when I write + it has a minus on the bottom too x^2+7=0 a. x= +7 b. x = +3.5 c. x= 0 d. no solution ***
2. ### Algebra
Solve the equation. Identify any extraneous solutions. √a=-2 A.4 is a solution of the original equation. B.4 is a solution of the original equation. -4 is an extraneous solution***** C.-4 is a solution of the original equation.
3. ### ALGEBRA
The table below shows two equations: Equation 1 |3x - 1| + 7 = 2 Equation 2 |2x + 1| + 4 = 3 Which statement is true about the solution to the two equations? Equation 1 and equation 2 have no solutions. Equation 1 has no solution
4. ### Calculus AB
Analyze the function ln x=cx^2 to find the unique value of c such that there is exactly one solution to the equation. To do this find the value of c such that both sides of the equation have equivalent slopes at some point; this
1. ### Math
In the following example, tell whether the answer is the solution to the equation. If the answer is no, identify the solution to the equation 1. 45x=180;x=4 A. Yes B. no, x=6 C. no, x=2 In the following example, tell whether the
2. ### Algebra
Determine whether the equation is an identity conditional equation or inconsistent equation 7(×-4)=×+2
3. ### Algebra Linear Inequalities Help
8. The system below has the solution of (1,3) where A, B, C, D, E, and F are all nonzero real numbers. Ax+By=C, Dx+Ey=F Which of the following systems would not have (1,3) as the solution? A- Ax+By=C & (2A-D)x+(2B+E)y=C-2F B-
4. ### algebra
(1) Is the equation true false or open? 9p + 8 = 10p + 7 A. open;there is a variable ***** B. true;the expressions are all the same for all values of the variiables C. false;the expressions are never the same (12) Which equation
1. ### Math
I'm suppose to 'determine whether the equation is an identity or a conditional equation. A) -6(x-3)+5 = -2x+10 I solved this and got x = 13/4. How am I suppose to figure out whether its identity or conditional equation? Same goes
2. ### math
(1)Is the Equation true, false, or open? 4y + 8 = 6y + 3 A. True; the expressionas are the same for all values of variables B. False; the expressions are never the same ****** C. Open; there is a varible (12)Which equation is an
3. ### Math
Here are two stories: The initial freshman class at a college is 10% smaller than last year’s class. But then during the first week of classes, 20 more students enroll. There are then 830 students in the freshman class. A store
4. ### Math
Identify the equation as an identity, inconsistent equation or conditional equation. 1-3/2x=7/4 my answer is it is an inconsistent equation | 1,096 | 3,579 | {"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} | 4.34375 | 4 | CC-MAIN-2021-31 | latest | en | 0.839173 |
https://ubco-biology.github.io/BIOL202/vis_cat_barchart.html | 1,708,697,212,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474412.46/warc/CC-MAIN-20240223121413-20240223151413-00708.warc.gz | 598,125,949 | 12,637 | ## 6.4 Create a bar graph
We use a bar graph to visualize the frequency distribution for a single categorical variable.
We’ll use the ggplot approach with its geom_bar function to create a bar graph. The ggplot function comes with the ggplot2 package, which itself is loaded as part of the tidyverse.
To produce the bar graph, we use a frequency table as the input. Thus, let’s repeat the creation of the “tiger.table” from the preceding section, but this time we exclude the adorn_totals line of code, because we don’t want the “total” row to be plotted in the bar graph.
tiger.table <- tigerdeaths %>%
count(activity, sort = TRUE) %>%
mutate(relative_frequency = n / sum(n))
Recall that the “tiger.table” is a sort of summary presentation of the “activity” variable:
tiger.table
## # A tibble: 9 × 3
## activity n relative_frequency
## <chr> <int> <dbl>
## 1 Grass/fodder 44 0.5
## 2 Forest products 11 0.125
## 3 Fishing 8 0.09091
## 4 Herding 7 0.07955
## 5 Disturbing tiger kill 5 0.05682
## 6 Fuelwood/timber 5 0.05682
## 7 Sleeping in house 3 0.03409
## 8 Walking 3 0.03409
## 9 Toilet 2 0.02273
It shows the total counts (frequencies) of individuals in each of the nine “activity” categories.
And although in the code chunk below you’ll see that we provide an “x” and a “y” variable for creating the graph, remember that we’re really only visualizing a single categorical variable.
Let’s provide the code first, and explain after.
ggplot(data = tiger.table, aes(x = reorder(activity, n), y = n)) +
geom_bar(stat = "identity") +
ylab("Frequency") +
xlab("Activity") +
coord_flip() +
theme_bw()
All figures produced using the ggplot2 package start with the ggplot function. Then the following arguments:
• The tibble (or dataframe) that holds the data (“data = tiger.table”)
• An “aes” argument (which stands for “aesthetics”), within which one specifies the variables to be plotted; here we’re plotting the frequencies from the “n” variable in the frequency table as the “y” variable, and the “activity” categorical variable as the “x” variable. To ensure the proper sorting of the bars, we use the reorder function, telling R to reorder the activity categories according to the frequencies in the n variable
• Then there’s a plus sign (“+”) to tell the ggplot function we’re not done yet with our graph - there are more lines of code coming (think of it as ggplot’s version of the “pipe”)
• Then the type of graph, which uses a function starting with “geom”; here we want a bar graph, hence geom_bar
• The geom_bar function has its own argument: “stat = ‘identity’” tells it just to make the height of the bars equal to the values provided in the “y” variable, here n.
• The ylab function sets the y-axis label
• The xlab function sets the x-axis label
• The coord_flip function tells it to rotate the graph horizontally; this makes it easier to fit the activity labels on the graph
• Then the theme_bw function indicates we want a simple black-and-white theme
There you have it: a nicely formatted bar graph!
REMINDER Don’t forget to include a good figure caption! Here’s a snapshot of the full code chunk that produced the bar graph above:
1. Bar graph: Try creating a bar graph using the birds dataset, which includes data about four types of birds observed at a wetland. | 859 | 3,562 | {"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} | 2.53125 | 3 | CC-MAIN-2024-10 | latest | en | 0.702827 |
https://resources.quizalize.com/view/quiz/short-quiz-in-math-6-gives-the-value-of-numbers-expressed-in-exponential-notation-923abd9f-d735-41ea-b0d6-3b5e2a22795f | 1,721,504,047,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517515.18/warc/CC-MAIN-20240720174732-20240720204732-00492.warc.gz | 422,889,944 | 15,344 | # Short Quiz in Math 6 gives the value of numbers expressed in exponential notation
## Quiz by Quizalize Premium (Philippines)
Mathematics
### Our brand new solo games combine with your quiz, on the same screen
Correct quiz answers unlock more play!
5 questions
• Q1
What is the value of 43?
64
12
7
16
30s
M6NS-IIf-147
• Q2
What is the value of 25?
10
32
16
8
30s
M6NS-IIf-147
• Q3
What is the value of (5/6)2?
7/8
125/216
10/12
25/36
30s
M6NS-IIf-147
• Q4
What is the value of (0.2)3?
0.08
0.6
0.8
0.008
30s
M6NS-IIf-147
• Q5
What is the missing exponent in 10? = 1000?
2
3
100
10
30s
M6NS-IIf-147
Teachers give this quiz to your class | 251 | 643 | {"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} | 2.609375 | 3 | CC-MAIN-2024-30 | latest | en | 0.758713 |
https://questions.examside.com/past-years/jee/question/pthe-electric-current-through-a-wire-varies-with-time-as--jee-main-physics-units-and-measurements-eeycnoem0wfugx8l | 1,721,688,784,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517927.60/warc/CC-MAIN-20240722220957-20240723010957-00418.warc.gz | 401,293,625 | 55,186 | 1
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1
The electric current through a wire varies with time as $$I=I_0+\beta t$$, where $$I_0=20 \mathrm{~A}$$ and $$\beta=3 \mathrm{~A} / \mathrm{s}$$. The amount of electric charge crossed through a section of the wire in $$20 \mathrm{~s}$$ is :
A
80 C
B
800 C
C
1000 C
D
1600 C
2
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1
Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across $$A$$ and $$B$$, their readings are $$V_1, V_2$$ and $$V_3$$. Choose the correct option.
A
$$V_1=V_2$$
B
$$V_1 \neq V_3-V_2$$
C
$$V_1+V_2=V_3$$
D
$$V_1+V_2>V_3$$
3
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1
A current of $$200 \mu \mathrm{A}$$ deflects the coil of a moving coil galvanometer through $$60^{\circ}$$. The current to cause deflection through $$\frac{\pi}{10}$$ radian is :
A
120 $$\mu$$A
B
180 $$\mu$$A
C
30 $$\mu$$A
D
60 $$\mu$$A
4
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1
Wheatstone bridge principle is used to measure the specific resistance $$\left(S_1\right)$$ of given wire, having length $$L$$, radius $$r$$. If $$X$$ is the resistance of wire, then specific resistance is ; $$S_1=X\left(\frac{\pi r^2}{L}\right)$$. If the length of the wire gets doubled then the value of specific resistance will be :
A
$$\frac{S_1}{4}$$
B
$$2 \mathrm{~S}_1$$
C
$$\frac{\mathrm{S}_1}{2}$$
D
$$S_1$$
EXAM MAP
Medical
NEET | 549 | 1,491 | {"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} | 2.90625 | 3 | CC-MAIN-2024-30 | latest | en | 0.762071 |
https://slides.com/andreicacio/javascript-the-basics-types-values-variables-1 | 1,713,114,258,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816893.19/warc/CC-MAIN-20240414161724-20240414191724-00249.warc.gz | 498,073,329 | 21,186 | I
# Types
Numbers
Strings
Booleans
null & undefined
Objects
## Types
are
kinds of values
that can be
represented manipulated
in a programming language
JavaScript types
can be categorized as follows
primitives / objects
&
mutable immutable
## primitives / objects
primitives
numberstringbooleannullundefined / symbols
objects
any value that does not belong to the primitive type
# NumberS
JavaScript has a single number type
there is no distinction between integer values and floating-point values
all numbers are represented in 64-bit floating-point format
the largest and smallest numbers that can be represented are
1.7976931348623157e+308
&
5e-324
when a number appears directly in a JavaScript program
it is called a numeric literal
Integer literals
base 10
a sequence of digits
base 16
0X or 0x followed by hexadecimal digits 0-9 A-F
base 8
(octal)
0 followed by digits 0-7
base 2
(binary)
0b followed by 0s or 1s
``````15 //=> 15 in base 10
0xF //=> 15 in base 16
017 //=> 15 in base 8
0b1100 //=> 12 in base 2
``````
## Floating-point literals
use traditional syntax for real numbers
or
the exponential notation which
represents the real number multiplied by 10
to the power of the exponent
``````0.15 //=> 0.15
.15 //=> 0.15
0.15e+2 //=> 15 (0.15 * (10 * 10))
0.15e-2 //=> 0.0015 (0.15 / (10 * 10))``````
## Arithmetic operations
work with numbers is done using basic arithmetic operators
- subtraction
* multiplication
/ division
% modulo (remainder)
&
a set of functions and constants
for more complex operations
``Math.pow(2, 53) Math.round(.6) Math.ceil(.6) Math.floor(.6)Math.abs(-5) Math.max(x,y,z) Math.min(x,y,z) Math.random()Math.PI Math.E Math.sqrt(3) Math.pow(3, 1/3)Math.sin(0) Math.log(10) Math.exp(3) Math.log(100)/Math.LN10 Math.log(512)/Math.LN2``
in JavaScript there are no errors
in cases of
overflow
underflow
or
division by zero
overflow
when the result of a numeric operation is larger
than the largest representable number the result is
Infinity
when a negative value becomes larger than the largest
representable negative number the result is
-Infinity
adding / subtracting / multiplying / dividing
infinite values
by anything else
results in an infinite value
underflow
when the result of a numeric operation is closer to zero
than the smallest representable number
thresult is 0
if it occurs from a negative number
negative zero is returned
``````15 / 1.8e+308 //=> 0
-15 / 1.8e+308 //=> -0``````
negative zero value (-0)
is almost indistinguishable to positive zero
except when used as a divisor
``15/-0 === 15/0 //=> false``
division by zero
is not an error
it simply returns Infinity or -Infinity
BUT
there is one exception
zero divided by zero evaluates to NaN
## Predefined global variables
Infinity
holds the positive infinity
anything larger than the largest representable number
isFinite()
returns true if its argument is a number other than
NaNInfinity-Infinity
``````isFinite(10); //=> true
isFinite(0.1); //=> true
isFinite(10.1e+7); //=> true
isFinite(Infinity); //=> false
isFinite(10/0); //=> false
isFinite(NaN); //=> false``````
NaN
holds the not-a-number value
isNaN()
returns true if its argument is NaN
or a non-numeric value such as a string or an object
``````isNaN(NaN); //=> true
isNaN('ten'); //=> true
isNaN({}); //=> true
isNaN(10); //=> false
isNaN('10'); //=> false
isNaN(0xF); //=> false
``````
## Strings
are JavaScript’s type for representing text
a string is an immutable ordered sequence of 16-bit values
which typically represents a Unicode character
the length of a string is the number of 16-bit values it contains
empty string
is the string with the
length equal to 0
there is no special type that represents a single element of a string
## String Literals
to represent a string literally simply enclose the characters of the string
within a matched pair of single or double quotes (' or ")
## Escape sequences
the backslash character (\) combined with the character that follows
represents a character that is otherwise not represented in the string
\0 — the NUL character (\u0000) \b — backspace (\u0008)
\t — horizontal tab (\u0009) \n — newline (\u000A)
\v — vertical tab (\u000B) \f — form feed (\u000C)
\r — carriage return (\u000D) \" — double quote (\u0022)
\' — apostrophe or single quote (\u0027) \\ — backslash (\u005C)
\xXX — character code specified by two hexadecimal digits XX
\uXXXX — character code specified by four hexadecimal digits XXXX
if the \ character precedes any character
other than the ones mentioned above
the backslash is simply ignored
## Working with strings
concatenation
using the + operator
joins two strings
appending the second to the first
length property
used to determine the length of a string
``````var str = 'JavaScript';
str.length //=> 10``````
invoking methods methods on strings
``````var str = 'JavaScript';
str.charAt(0); //=> "J"
str.substring(5,10); //=> "cript"
str.split(''); //=> ["J", "a", "v", "a", "S", "c", "r", "i", "p", "t"]
str.toLowerCase(); //=> "javascript"
str.replace('J', 'j'); //=> "javaScript"``````
## strings
are immutable
always remember that
some methods will return a new string
and they do not modify the string on which they are invoked
``````var str = 'JavaScript';
var newStr = str.toUpperCase();
console.log(str); //=> "JavaScript"
console.log(newStr); //=> "JAVASCRIPT"
``````
## TEMPLATE LITERALS (ES2015)
Template literals (template strings) are string literals allowing embedded expressions. You can use multi-line strings and string interpolation features with them
Unlike string literals, template literal uses
`
``var str = `JavaScript`;``
You can include expression statements with template literals
syntax: \${ expression }
very useful when concatenating strings
``````var language = 'JavaScript';
```
# Booleans
## Booleans
there are only two values possible for this type
true / false
they are usually the result of comparisons
``````'JavaScript' === 15 //=> false
15 === 15 //=> true
'15' != 15 //=> false``````
any value can be converted to a boolean value
undefined / null / 0 / -0 / NaN / "" (empty string)
convert to false & are called
falsy values
all other values convert to true & are called
truthy values
toString() method
can be invoked on booleans to convert them
to "true" or "false" strings
## Boolean operators
&& (AND)
evaluates to a truthy value if and only if both of its operands are truthy
otherwise it evaluates to a falsy value
``10 < 15 && 15 > 10 //=> true``
| | (OR)
evaluates to a truthy value if either one (or both) of its operands is truthy
and evaluates to a falsy value if both operands are falsy
``15 < 10 || 15 > 10 //=> true ``
! (NOT)
evaluates to true if its operand is falsy and evaluates to false if its operand is truthy
``15 < 10 === !true //=> true``
## Null
is a keyword that evaluates to a special value
used to indicate the absence of a value
it is typically regarded as the
sole member of its own type
&
it can be used to indicate no value for
numbers, strings or objects
## UNDEFINED
is a predefined global variable
which also indicates the absence of value
BUT
a deeper kind of absence
it is the value
of variable that have not been initialized
of object property or array element that does not exist
returned by functions that have no return value
of function parameters for which no argument is supplied
undefined is system-level unexpected
error-like absence of value
null is program-level expected
normal absence of value
despite the differences null & undefined both
indicate the absence of value
can be used interchangeably
are falsy values
behave like false when a boolean value is required
none of them have got any properties or methods
using . or [] notation
to access a property or method
of these values causes a TypeError
``````var person = {
name: 'John Doe',
children: null
};
person.children.length; //=> TypeError: Cannot read property 'length' of null
obj.children[0] //=> TypeError: Cannot read property '0' of null``````
## Symbols
is a unique data type and may be used as an identifier for object properties
creating a symbol:
``````var symbol = Symbol('description');
console.log(symbol) // Symbol(description) ``````
no two symbols are ever alike:
``Symbol() === Symbol(); // false``
# Objects
## Object types
are
any values that does not belong to the primitive types
an ordinary object
is a collection of properties
where each property has a name or key
&
a value
``````var obj = {
keyOne: 'valueOne',
keyTwo: 'valuerTwo',
keyN: 'valueN'
};``````
## Object Literals
objects are useful for collecting & organizing data
the most common things to do with objects are
create
&
set / query / delete / test / enumerate
their properties
special kind of objects
arrays
functions
global object
wrapper objects
## ARRAYS
are
ordered collection of numbered values
JavaScript includes a special syntax for working with arrays
and arrays have some special behavior that distinguishes them from ordinary objects
``````var arr = [1000, 'string', function () {}, { name: 'JavaScript'}, [1, 2]];
``````
## a function is
an object that has executable code associated with it
it may be invoked to run that executable code and return a computed value
JavaScript defines a special language syntax for working with them
## The Global Object
is a regular object that serves a very important purpose
its properties are the globally defined symbols
that are available to a JavaScript program
when the JavaScript interpreter starts it creates a new
global object and gives it an initial set of properties that define
global properties like undefined, Infinity, NaN
global functions like isNaN(), parseInt(), eval()
constructor functions like Date(), RegExp(), String(), Object(), Array()
global objects like Math and JSON
besides all predefined global values
global object also holds program-defined globals
## WRAPPER objects
strings / numbers / booleans
are not objects
so why do they have properties?
because whenever you try to refer to a property
JavaScript
converts the string value to an object
as if by calling
new String() / new Number() / new Boolean()
this object inherits all methods available on
strings, numbers or booleans
and is used to resolve the property reference
once the property has been resolved
the newly created object is discarded
in conclusion
wrapper objects
are
temporary objects
created when you access
a property of a
string / number / boolean
it is possible to explicitly create wrapper objects
by invoking the String(), Number(), or Boolean() constructors
````new String('JavaScript'); ```` //=> String {0: "J", 1: "a", 2: "v", 3: "a", 4: "S", 5: "c", 6: "r",
// 7: "i", 8: "p", 9: "t", length: 10}``````
JavaScript converts wrapper objects into the wrapped
primitive value as necessary
``````var s = "test", n = 1, b = true; //=> a string, number, and boolean value
var S = new String(s); //=> a string object
var N = new Number(n); //=> a number object
var B = new Boolean(b); //=> a boolean object ``````
the objects usually
but not always, behave just like the values
== equality operator treats a value and its wrapper object as equal
=== strict equality operator distinguishes them
the typeof operator will also show the difference
between a primitive value and its wrapper objects
By Andrei Cacio
• 1,087 | 3,099 | 11,893 | {"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} | 2.609375 | 3 | CC-MAIN-2024-18 | latest | en | 0.678134 |
https://au.pinterest.com/explore/math-concepts/ | 1,498,668,779,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128323711.85/warc/CC-MAIN-20170628153051-20170628173051-00519.warc.gz | 730,105,430 | 77,494 | ### Build A Tiny House! Project Based Learning Activity, A PBL
Let students learn how math concepts are connected to the real world as they design their own 3D TINY HOUSE! Area, perimeter, and geometry-- math is everywhere in this project based learning activity (PBL). Designing, creating, and problem solving are key features of this resource. Build a Tiny House! \$
### Project Based Learning: Obstacle Race Course with Area and Perimeter (PBL)
Let students learn how math concepts are connected to the real-world as they design their own OBSTACLE RACE COURSE! Focusing on Area and Perimeter means--Math is everywhere in this project based learning activity (PBL). Designing, creating, and problem solving are key features of this resource. Design An Obstacle Course! \$
This is an interactive lesson to teach kids about ordinal numbers. In this video kids will learn about the basic math concept of ordinal numbers.
If you're on the lookout for great hands-on math activities for your upper elementary students, you're going to love the ideas at this blog post. Your 3rd, 4th, 5th, & 6th grade classroom or homeschool students are going to love the geometry, measurement, place value, area & perimeter, & games found here! You'll even get ideas for math concept sorts. Click through for all the details on how this can improve your math, STEAM, or project-based learning lessons. {third, fourth, fifth, sixth…
### Math in Art – 15+ STEAM Projects!
A round up of over 15 great STEAM projects – where math concepts are used to make pieces of art!
### Essential Questions for 6th Grade Math - Full Page
*** I updated these posters and put them on sale to celebrate. 50% OFF! *** I love these posters for two reasons! 1) The illustrations help students understand sixth grade math concepts like ratios and proportions, number sense, fractions, expressions and equations, geometry, and statistics. 2) The bundle has EVERY sixth grade math concept in one small file that I'll never LOSE! Way easier to keep track of than anchor charts!:
### Build A Tiny House! Project Based Learning Activity, A PBL
Let students learn how math concepts are connected to the real world as they design their own 3D TINY HOUSE! Area, perimeter, and geometry-- math is everywhere in this project based learning activity (PBL). Designing, creating, and problem solving are key features of this resource. Build a Tiny House! \$
Let students learn how math concepts are connected to the real world as they design their own 3D TINY HOUSE! Area, perimeter, and geometry-- math is everywhere in this project based learning activity (PBL). Designing, creating, and problem solving are key features of this resource. Build a Tiny House! \$ by graciela
### 6th Grade Daily Math Spiral Review Morning Work
36 weeks of daily Common Core math review for sixth grade! Preview and Review important 6th grade math concepts all year long! Perfect for homework, morning work, or test prep! 5-A-Day: 6 tasks a day, M-Th. CCSS M.6 Available for 3rd - 6th grades! \$
addition with regrouping worksheets...I LOVE that they are on grid paper. This really helps kids keep everything in line!!! Great for review and is available at different grade level abilities!
Pinterest | 722 | 3,244 | {"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-2017-26 | latest | en | 0.934047 |
https://it.mathworks.com/matlabcentral/profile/authors/1601874?s_tid=cody_local_to_profile | 1,611,048,429,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703518201.29/warc/CC-MAIN-20210119072933-20210119102933-00036.warc.gz | 374,698,216 | 21,272 | Community Profile
Rudolf Csikja
Last seen: 3 mesi ago
87 total contributions since 2016
View details...
Contributions in
View by
Solved
Find the two-word state names
Given a list of states, remove all the states that have two-word names. If s1 = 'Alabama Montana North Carolina Vermont N...
oltre un anno ago
Solved
Find common elements in matrix rows
Given a matrix, find all elements that exist in every row. For example, given A = 1 2 3 5 9 2 5 9 3 2 5 9 ...
oltre un anno ago
Solved
Mirror Image matrix across anti-diagonal
Given an input number x, create a mirror image matrix 'Y' across the anti-diagonal. For example, if x=3, Y = [1 2 3; ...
oltre un anno ago
Solved
Make a Star Pyramid
Create a star pyramid. First line will have 1 star, second will have two stars and so on... a basic program which is easily done...
oltre un anno ago
Solved
Pascal's Matrix
Given an integer n ≥ 0, generate the ( _n_+1) × ( _n_+1) lower triangular <http://en.wikipedia.org/wiki/Pascal_matrix P...
oltre un anno ago
Solved
Create a matrix X, where each column is a shifted copy of the vector v
Example : in->v = (1:5)'; 1 2 3 4 5 out-> [1 5 4 3 2;2 1 5 4 3;3 2 1 5 4;4 3 2 1 5;5 4 3 ...
oltre un anno ago
Solved
Symmetric matrix
You must create a n-by-n *symmetric* matrix such that A(row,col) = row/col for col >= row. Example if n =3 : output is : ...
oltre un anno ago
Solved
Special matrix
Make a square matrix with this shape. For n=4 M = 1 1 0 0 1 0 1 0 0 1 0 ...
oltre un anno ago
Solved
Better bullseye matrix
<http://www.mathworks.com/matlabcentral/cody/problems/18-bullseye-matrix Problem 18> asks to create a bullseye matrix like this:...
oltre un anno ago
Solved
Create a Multiplication table matrix...
Create a product table in this format: P = [ 1 2 3 4 5; 2 4 6 8 10; 3 6 9 12 15; 4 8 12 1...
oltre un anno ago
Solved
"mirror" matrix
Create n x 2n "mirror" matrix of this type: Examples For n = 2 m = [ 1 2 2 1 1 2 2 1 ] For n = 3 m = ...
oltre un anno ago
Solved
Are you in or are you out?
Given vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return "true" if the poi...
oltre un anno ago
Solved
Circumscribed circles
Given the lengths of the 3 sides of a triangle, output the radius of the circumscribed circle. Example: [3 4 5] -> 2.5
oltre un anno ago
Solved
Similar Triangles - find the height of the tree
Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Pleas...
oltre un anno ago
Solved
Clock Hand Angle 1
Given a time in HH:MM:SS, find the smallest angle (in degrees) between the hour and minute hand
oltre un anno ago
Solved
What is the distance from point P(x,y) to the line Ax + By + C = 0?
Given a point, P(x,y), find the distance from this point to a linear line. INPUTS: x, y, A, B, C OUTPUTS: d, the distance ...
oltre un anno ago
Solved
Pizza!
Given a circular pizza with radius _z_ and thickness _a_, return the pizza's volume. [ _z_ is first input argument.] Non-scor...
oltre un anno ago
Solved
Is the Point in a Circle?
Check whether a point or multiple points is/are in a circle centered at point (x0, y0) with radius r. Points = [x, y]; c...
oltre un anno ago
Solved
Angle between Two Vectors
The dot product relationship, a dot b = | a | | b | cos(theta), can be used to determine the acute angle between vector a and ve...
oltre un anno ago
Solved
Volume of a Parallelepiped
Calculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex. A cube is a special case ...
oltre un anno ago
Solved
Are all the three given point in the same line?
In this problem the input is the coordinate of the three points in a XY plane? P1(X1,Y1) P2(X2,Y2) P3(X3,Y3) how can...
oltre un anno ago
Solved
Calculate the area of a triangle between three points
Calculate the area of a triangle between three points: P1(X1,Y1) P2(X2,Y2) P3(X3,Y3) these three points are the vert...
oltre un anno ago
Solved
Multiply 2 numbers
Very easy, you just have to multiply 2 numbers but you cannot use the following signs (*, /, - ,^) ,mtimes , times, cross, pro...
oltre un anno ago
Solved
Triangle sequence
A sequence of triangles is constructed in the following way: 1) the first triangle is Pythagoras' 3-4-5 triangle 2) the s...
oltre un anno ago
Solved
Is this triangle right-angled?
Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return f...
oltre un anno ago
Solved
Find a Pythagorean triple
Given four different positive numbers, a, b, c and d, provided in increasing order: a < b < c < d, find if any three of them com...
oltre un anno ago
Solved
Is this triangle right-angled?
Given three positive numbers a, b, c, where c is the largest number, return *true* if the triangle with sides a, b and c is righ...
oltre un anno ago
Solved
Area of an Isoceles Triangle
An isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle. <<http://upload...
oltre un anno ago
Solved
Dimensions of a rectangle
The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width...
oltre un anno ago
Solved
Side of a rhombus
If a rhombus has diagonals of length x and x+1, then what is the length of its side, y? <<http://upload.wikimedia.org/wikipe...
oltre un anno ago | 1,646 | 5,509 | {"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} | 3.09375 | 3 | CC-MAIN-2021-04 | latest | en | 0.429334 |
http://www.newton.dep.anl.gov/askasci/math99/math99098.htm | 1,419,184,615,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1418802772125.148/warc/CC-MAIN-20141217075252-00115-ip-10-231-17-201.ec2.internal.warc.gz | 697,242,397 | 3,290 | Probably of Numbers ```Name: Suzanne Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: If there are 10,600 people born in the United States each day, what is the probability that one of them would have the same last four digits of my social security number? Replies: Consider the number of ways that the last four digits of a social security number can be formed: 10^4=10,000. Each gets 9999 out of 10000 chances to have other than your social security number. If the last four digits are effectively random, then the probability that everybody gets other than your digits is (9999/10000)^10600. This subtracted from one is the probability that at least one person gets your digits. Kenneth Mellendorf Click here to return to the Mathematics Archives
NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.
For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs | 247 | 1,115 | {"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-2014-52 | latest | en | 0.892431 |
https://convertoctopus.com/36-days-to-years | 1,590,476,735,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347390448.11/warc/CC-MAIN-20200526050333-20200526080333-00480.warc.gz | 272,090,943 | 8,444 | ## Conversion formula
The conversion factor from days to years is 0.0027397260273973, which means that 1 day is equal to 0.0027397260273973 years:
1 d = 0.0027397260273973 yr
To convert 36 days into years we have to multiply 36 by the conversion factor in order to get the time amount from days to years. We can also form a simple proportion to calculate the result:
1 d → 0.0027397260273973 yr
36 d → T(yr)
Solve the above proportion to obtain the time T in years:
T(yr) = 36 d × 0.0027397260273973 yr
T(yr) = 0.098630136986301 yr
The final result is:
36 d → 0.098630136986301 yr
We conclude that 36 days is equivalent to 0.098630136986301 years:
36 days = 0.098630136986301 years
## Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 year is equal to 10.138888888889 × 36 days.
Another way is saying that 36 days is equal to 1 ÷ 10.138888888889 years.
## Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that thirty-six days is approximately zero point zero nine nine years:
36 d ≅ 0.099 yr
An alternative is also that one year is approximately ten point one three nine times thirty-six days.
## Conversion table
### days to years chart
For quick reference purposes, below is the conversion table you can use to convert from days to years
days (d) years (yr)
37 days 0.101 years
38 days 0.104 years
39 days 0.107 years
40 days 0.11 years
41 days 0.112 years
42 days 0.115 years
43 days 0.118 years
44 days 0.121 years
45 days 0.123 years
46 days 0.126 years | 462 | 1,615 | {"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} | 4.21875 | 4 | CC-MAIN-2020-24 | longest | en | 0.784221 |
https://docplayer.net/15135503-Why-taking-this-course-course-introduction-descriptive-statistics-and-data-visualization-learning-goals-genome-560-spring-2012.html | 1,627,320,249,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046152144.81/warc/CC-MAIN-20210726152107-20210726182107-00410.warc.gz | 230,305,458 | 27,375 | # Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012
Size: px
Start display at page:
Download "Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012"
Transcription
1 Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization GENOME 560, Spring 2012 Data are interesting because they help us understand the world Genomics: Massive Amounts of Data Data Statistics is fundamental in genomics because it is integral in the design, analysis and interpretation of experimental data What does this mean? Su In Lee, CSE & GS 1 2 Why Taking This Course? Data are interesting because they help us understand the world Genomics: Massive Amounts of Data Data Statistics is fundamental in genomics because it is integral in the design, analysis and interpretation of experimental data This course covers the key statistical concepts and methods necessary for extracting biological insights from experimental data Learning Goals 5 weeks is too short to cover every specific topic that might arise in the course of your research It is not a good strategy to treat what we learn in this course as recipes to follow Instead, we should focus on rigorous understanding of fundamental concepts that will provide you with the tools necessary to address routine statistical analyses foundation to understand and learn mode specific topics 3 4 1
2 Course Schedule Syllabus: Date May 1 May 3 May 8 May 10 May 15 May 17 May 22 May 24 May 29 May 31 Topic Descriptive Statistics and Data Visualization Random Variables and Probability Theories Probability Distributions Parameter Estimation Regression Methods Hypothesis testing I t test, confidence interval Hypothesis testing II ANOVA Hypothesis testing III Analysis of Categorical Data Bootstrapping, cross validation and permutation tests Assessing significance in high dimensional experiments Special topics that may be discussed in class include Bayesian networks, Expectation Maximization (EM) algorithm, principal component analysis Grading: 5 problem sets (20% each) 5 Books and Resources Course website No required text Good on line resources Some good books if you ever have some extra \$\$\$: Probability and Statistics for Engineering and the Scientists 6th Ed. Jay L. Devore (2004). Duxbury press, Thompson Brooks/Cole. Statistical Inference. Casella, G. and Berger, R. L. (1990). Wadsworth, Belmont, CA. Probabilistic Graphical Models: Principles and Techniques. Koller, D. and Friedman, N. (2009). MIT Press. 6 Class Meetings What is R? Class meets twice a week Tue/Thu 9 Foege S110 Each class will last for 80 minutes and be primarily lecture based The R statistical programming language is a free open source package based on the S language developed by Bell Labs May statistical functions are already built in Other forms of learning and interactions will be included Contributed packages expand the functionality to cutting edge research We will often interrupt lectures to work on problems in small groups as well as work through statistical analyses using R (please bring a laptop with R installed!) Amazing graphics Widely used in genetics, genomics, computational biology 7 8 2
3 R Resources Windows, Mac and Linux binaries available at project.org Lecture 1: Descriptive Statistics and Data Visualization Extensive resources at the above web site, in particular see: project.org/other docs.html 9 10 Outline What is descriptive statistics and exploratory data analysis? Why Descriptive/Graphical Summary? Before making inferences from data, it is essential to examine all your variables Basic numeral summaries of data Why? Basic graphical summaries of data Basic operations in R (If time permits) How to use R for calculating descriptive statistics and making graphs 11 To listen to the data: to catch mistakes to see patterns in the data to find violations of statistical assumptions to generate hypotheses and because if you don t, you will have trouble later 12 3
4 Types of Data Categorical Binary: 2 categories Nominal: more categories Ordinal: order matters E.g. gender, ethnicity, disease state, genotypes, etc Continuous (or Quantitative) Numeric values that can be ordered sequentially, and that do not naturally fall into discrete ranges. E.g. weight, number of seconds it takes to perform a task, gene expression levels, etc Dimensionality of Data Sets Univariate: Measurement made on one variable per subject Bivariate: Measurement made on two variables per subject Multivariate: Measurement made on many variables per subject Numerical Summaries of Data Central tendency measures. They are computed to give a center around which the measurements in the data are distributed. Central Tendency Measures: Mean To calculate the mean of a set of observations, add their value and divide by the number of observations: Variation or variability measures. They describe data spread or how far away the measurements are from the center. Relative standing measures. They describe the relative position of specific measurements in the data
5 Central Tendency Measures: Median Median: the exact middle value Calculation: If there are an odd number of observations, find the middle value If there are an even number of observations, find the middle two values and average them Which Measure Is Best? Mean is best for symmetric distributions without outliers Median is useful for skewed distributions or data with outliers Example: Some data: Age of participants: Median = (22+23)/2 = Scale: Variance Average of squared deviation of values from the mean Why Squared Deviations? Squares eliminate the negatives Absolute values do not have nice mathematical properties Result: Increasing contribution to the variance as you go farther from the mean
6 Why Divide By (n 1), not n? Why Divide By (n 1), not n? Empirical mean True mean You compute the difference between each observation and the mean of all n observations. You don t know the true mean of the population; all you know is the mean of your samples (empirical mean) Except for the rare cases where the sample mean happens to equal the population mean, the data will be closer to the sample mean than it will be to the true population mean. So the numerator will probably be a bit smaller (and can t be larger) than what it would be if you used the true mean. Biased estimator of the population variance 21 Empirical mean True mean To make up for this divide by (n 1) rather than n. Unbiased estimator of the population variance If you knew the sample mean, and all but one of the values, you could calculate what that last value must be. Statisticians say there are n 1 degrees of freedom. 22 Scale: Standard Deviation Variance is somewhat arbitrary What does it mean to have a variance of 10.8? Or 2.2? Or ? Or ? Scale: Standard Deviation Most commonly used measure of variation Shows variation about the mean Has the same units as the original data Nothing. But if you could standardize that value, you could talk about any variance (i.e. deviation) in equivalent terms Standard deviations are simply the square root of the variance
7 Interesting Theoretical Result Regardless of how the data are distributed, a certain percentage of values must fall within k standard deviations from the mean Often We Can Do Better For many lists of observations, especially if their histogram is bell shaped Roughly 68% of the observations in the list lie within 1 σ (standard deviation) of the average 95% of the observations lie within 2σ of the average Scale: Quartiles and IQR Percentiles (aka Quantiles) In general the n th percentile is a value such that n% of the observations fall at or below of it The first quartile, Q 1, is the value for which 25% of the observations are smaller and 75% are larger Q 2 is the same as the median (50% are smaller, 50% are larger) Only 25% of the observations are greater than the Q 3 27 Q 1 = 25 th percentile Median = 50 th percentile Q 2 = 75 th percentile 28 7
8 Graphical Summaries of Data Dimensionality of data matters Univariate: Measurement made on one variable per subject Multivariate: Measurement made on many variables per subject Univariate Data Histograms and bar plots What is the difference between a histogram and bar plot? Bar plot: Used for categorical variables to show frequency or proportion in each category Translate the data from frequency tables into a pictorial presentation Histogram: Used to visualize distribution (shape, center, range, variation) of continuous variables Bin size is important Effect of Bin Size on Histogram Simulated 1,000 N(0,1) and 500 N(1,1) More on Histograms What s the difference between a frequency histogram and a density histogram?
9 Box Plots Multivariate Data Clustering Organize variables into clusters Descriptive, not inferential Many approaches Clusters always produced Data reduction approaches Reduce n dimensional dataset into much smaller number Finds a new (smaller) set of variables that retains most of the information in the total sample Effective way to visualize multivariate data How to Make a Bad Graph Example 1 The aim of good data graphics: Display data accurately and clearly Some rules for displaying data badly: Display as little information as possible Obscure what you do show (with chart junk) Use pseudo 3d and color gratuitously Make a pie chart (preferably in color and 3d) Use a poorly chosen scale
10 Example 2 Example Example 4 Goals of Our R Tutorial Today Installing R Using R as a fancy calculator Data structures: scalars, vectors, data frames, matrices Reading in data from a file Subsetting and extracting data Writing and executing simple R scripts
11 Probabilities Probabilities Event Variable XXP(S)P(S) P(S)loglog Probability Statistical independence Joint probability 41 Probabilities of mutually independent events are summed Pr(adie comesup2or 3) = Pr(comes up 2) + Pr(comes up 3) = 1/ 6 + 1/ 6 = 1/ 3 Probabilities of independent events are multiplied to get the joint probability Pr(one die comesup2and theother one comesup 3) = Pr(first one comesup 2) + Pr(secondone comesup 3) = 1/ 6 + 1/ 6 = 1/ 3 Conditional probabilities are the joint probability divided by the probability of the event that they are conditioned on: P ( D S) = P( D S ) P( S) d 42 Goals of Our R Tutorial Today Installing R Using R as a fancy calculator P ( D S) P( D S, ) P( S) d Data structures: scalars, vectors, data frames, matrices Reading in data from a file Subsetting and extracting data Writing and executing simple R scripts
12 Some Jargon Units: the basic objects on which the experiment is done Variable: a measured characteristic of a unit Treatment: any specific experimental condition applied to the units. A treatment can be a combination of specific values (called levels) of each experimental factor 45 12
### Lecture 2: Descriptive Statistics and Exploratory Data Analysis
Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals
### BNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I
BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential
### STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI
STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members
### How To Write A Data Analysis
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
### Exploratory Data Analysis
Exploratory Data Analysis Johannes Schauer johannes.schauer@tugraz.at Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction
### BASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS
BASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi-110 012 seema@iasri.res.in Genomics A genome is an organism s
### Exploratory data analysis (Chapter 2) Fall 2011
Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,
### Lecture 1: Review and Exploratory Data Analysis (EDA)
Lecture 1: Review and Exploratory Data Analysis (EDA) Sandy Eckel seckel@jhsph.edu Department of Biostatistics, The Johns Hopkins University, Baltimore USA 21 April 2008 1 / 40 Course Information I Course
### Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013
Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.1-1.6) Objectives
### Fairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
### Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics
Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),
### Northumberland Knowledge
Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about
### Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing
### II. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
### Variables. Exploratory Data Analysis
Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is
### Introduction to Statistics for Psychology. Quantitative Methods for Human Sciences
Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html
### A Correlation of. to the. South Carolina Data Analysis and Probability Standards
A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards
### Quantitative Methods for Finance
Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain
### Week 1. Exploratory Data Analysis
Week 1 Exploratory Data Analysis Practicalities This course ST903 has students from both the MSc in Financial Mathematics and the MSc in Statistics. Two lectures and one seminar/tutorial per week. Exam
### Data Exploration Data Visualization
Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select
### Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This
### 1.3 Measuring Center & Spread, The Five Number Summary & Boxplots. Describing Quantitative Data with Numbers
1.3 Measuring Center & Spread, The Five Number Summary & Boxplots Describing Quantitative Data with Numbers 1.3 I can n Calculate and interpret measures of center (mean, median) in context. n Calculate
### The right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median
CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box
### Exploratory Data Analysis. Psychology 3256
Exploratory Data Analysis Psychology 3256 1 Introduction If you are going to find out anything about a data set you must first understand the data Basically getting a feel for you numbers Easier to find
### 430 Statistics and Financial Mathematics for Business
Prescription: 430 Statistics and Financial Mathematics for Business Elective prescription Level 4 Credit 20 Version 2 Aim Students will be able to summarise, analyse, interpret and present data, make predictions
### Exercise 1.12 (Pg. 22-23)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
### Probability and Statistics Vocabulary List (Definitions for Middle School Teachers)
Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) B Bar graph a diagram representing the frequency distribution for nominal or discrete data. It consists of a sequence
### Introduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
### Geostatistics Exploratory Analysis
Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt
### 3: Summary Statistics
3: Summary Statistics Notation Let s start by introducing some notation. Consider the following small data set: 4 5 30 50 8 7 4 5 The symbol n represents the sample size (n = 0). The capital letter X denotes
### 4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"
Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses
### Lecture 2. Summarizing the Sample
Lecture 2 Summarizing the Sample WARNING: Today s lecture may bore some of you It s (sort of) not my fault I m required to teach you about what we re going to cover today. I ll try to make it as exciting
### Statistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
EC151.02 Statistics for Business and Economics (MWF 8:00-8:50) Instructor: Chiu Yu Ko Office: 462D, 21 Campenalla Way Phone: 2-6093 Email: kocb@bc.edu Office Hours: by appointment Description This course
### EXPLORING SPATIAL PATTERNS IN YOUR DATA
EXPLORING SPATIAL PATTERNS IN YOUR DATA OBJECTIVES Learn how to examine your data using the Geostatistical Analysis tools in ArcMap. Learn how to use descriptive statistics in ArcMap and Geoda to analyze
### Data, Measurements, Features
Data, Measurements, Features Middle East Technical University Dep. of Computer Engineering 2009 compiled by V. Atalay What do you think of when someone says Data? We might abstract the idea that data are
### Foundation of Quantitative Data Analysis
Foundation of Quantitative Data Analysis Part 1: Data manipulation and descriptive statistics with SPSS/Excel HSRS #10 - October 17, 2013 Reference : A. Aczel, Complete Business Statistics. Chapters 1
### Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
### Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini
NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building
### List of Examples. Examples 319
Examples 319 List of Examples DiMaggio and Mantle. 6 Weed seeds. 6, 23, 37, 38 Vole reproduction. 7, 24, 37 Wooly bear caterpillar cocoons. 7 Homophone confusion and Alzheimer s disease. 8 Gear tooth strength.
### Module 4: Data Exploration
Module 4: Data Exploration Now that you have your data downloaded from the Streams Project database, the detective work can begin! Before computing any advanced statistics, we will first use descriptive
### The Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175)
Describing Data: Categorical and Quantitative Variables Population The Big Picture Sampling Statistical Inference Sample Exploratory Data Analysis Descriptive Statistics In order to make sense of data,
### MTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
### Organizing Your Approach to a Data Analysis
Biost/Stat 578 B: Data Analysis Emerson, September 29, 2003 Handout #1 Organizing Your Approach to a Data Analysis The general theme should be to maximize thinking about the data analysis and to minimize
### Visualizing Data. Contents. 1 Visualizing Data. Anthony Tanbakuchi Department of Mathematics Pima Community College. Introductory Statistics Lectures
Introductory Statistics Lectures Visualizing Data Descriptive Statistics I Department of Mathematics Pima Community College Redistribution of this material is prohibited without written permission of the
### business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
### Descriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
### AP Statistics: Syllabus 1
AP Statistics: Syllabus 1 Scoring Components SC1 The course provides instruction in exploring data. 4 SC2 The course provides instruction in sampling. 5 SC3 The course provides instruction in experimentation.
### What is Data Analysis. Kerala School of MathematicsCourse in Statistics for Scientis. Introduction to Data Analysis. Steps in a Statistical Study
Kerala School of Mathematics Course in Statistics for Scientists Introduction to Data Analysis T.Krishnan Strand Life Sciences, Bangalore What is Data Analysis Statistics is a body of methods how to use
### STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance
Principles of Statistics STA-201-TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis
### Diagrams and Graphs of Statistical Data
Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in
### Data Mining: Exploring Data. Lecture Notes for Chapter 3. Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler
Data Mining: Exploring Data Lecture Notes for Chapter 3 Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Topics Exploratory Data Analysis Summary Statistics Visualization What is data exploration?
### Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs
Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)
### Implications of Big Data for Statistics Instruction 17 Nov 2013
Implications of Big Data for Statistics Instruction 17 Nov 2013 Implications of Big Data for Statistics Instruction Mark L. Berenson Montclair State University MSMESB Mini Conference DSI Baltimore November
### Biostatistics: Types of Data Analysis
Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS
Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
### Summarizing and Displaying Categorical Data
Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency
### DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
### How To Check For Differences In The One Way Anova
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way
### Chapter 7. One-way ANOVA
Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks
### Service courses for graduate students in degree programs other than the MS or PhD programs in Biostatistics.
Course Catalog In order to be assured that all prerequisites are met, students must acquire a permission number from the education coordinator prior to enrolling in any Biostatistics course. Courses are
### Descriptive statistics parameters: Measures of centrality
Descriptive statistics parameters: Measures of centrality Contents Definitions... 3 Classification of descriptive statistics parameters... 4 More about central tendency estimators... 5 Relationship between
### Descriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion
Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research
### MBA 611 STATISTICS AND QUANTITATIVE METHODS
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
### Introduction to Statistics and Quantitative Research Methods
Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.
### Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
### STAT355 - Probability & Statistics
STAT355 - Probability & Statistics Instructor: Kofi Placid Adragni Fall 2011 Chap 1 - Overview and Descriptive Statistics 1.1 Populations, Samples, and Processes 1.2 Pictorial and Tabular Methods in Descriptive
### COMMON CORE STATE STANDARDS FOR
COMMON CORE STATE STANDARDS FOR Mathematics (CCSSM) High School Statistics and Probability Mathematics High School Statistics and Probability Decisions or predictions are often based on data numbers in
### Multivariate Analysis of Ecological Data
Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology
### PELLISSIPPI STATE COMMUNITY COLLEGE MASTER SYLLABUS INTRODUCTION TO STATISTICS MATH 2050
PELLISSIPPI STATE COMMUNITY COLLEGE MASTER SYLLABUS INTRODUCTION TO STATISTICS MATH 2050 Class Hours: 2.0 Credit Hours: 3.0 Laboratory Hours: 2.0 Date Revised: Fall 2013 Catalog Course Description: Descriptive
### Chapter 7 Section 7.1: Inference for the Mean of a Population
Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used
### Descriptive Statistics
Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web
### UNIT 1: COLLECTING DATA
Core Probability and Statistics Probability and Statistics provides a curriculum focused on understanding key data analysis and probabilistic concepts, calculations, and relevance to real-world applications.
### DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS
DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi - 110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics
### Iris Sample Data Set. Basic Visualization Techniques: Charts, Graphs and Maps. Summary Statistics. Frequency and Mode
Iris Sample Data Set Basic Visualization Techniques: Charts, Graphs and Maps CS598 Information Visualization Spring 2010 Many of the exploratory data techniques are illustrated with the Iris Plant data
### MEASURES OF VARIATION
NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are
### South Carolina College- and Career-Ready (SCCCR) Probability and Statistics
South Carolina College- and Career-Ready (SCCCR) Probability and Statistics South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR)
### INTRODUCING DATA ANALYSIS IN A STATISTICS COURSE IN ENVIRONMENTAL SCIENCE STUDIES
INTRODUCING DATA ANALYSIS IN A STATISTICS COURSE IN ENVIRONMENTAL SCIENCE STUDIES C. Capilla Technical University of Valencia, Spain CCAPILLA@EIO.UPV.ES Education in methods of applied statistics is important
### Mathematics within the Psychology Curriculum
Mathematics within the Psychology Curriculum Statistical Theory and Data Handling Statistical theory and data handling as studied on the GCSE Mathematics syllabus You may have learnt about statistics and
### Pie Charts. proportion of ice-cream flavors sold annually by a given brand. AMS-5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple.
Graphical Representations of Data, Mean, Median and Standard Deviation In this class we will consider graphical representations of the distribution of a set of data. The goal is to identify the range of
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
### determining relationships among the explanatory variables, and
Chapter 4 Exploratory Data Analysis A first look at the data. As mentioned in Chapter 1, exploratory data analysis or EDA is a critical first step in analyzing the data from an experiment. Here are the
### Data Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining
Data Mining: Exploring Data Lecture Notes for Chapter 3 Introduction to Data Mining by Tan, Steinbach, Kumar What is data exploration? A preliminary exploration of the data to better understand its characteristics.
### THE UNIVERSITY OF TEXAS AT TYLER COLLEGE OF NURSING COURSE SYLLABUS NURS 5317 STATISTICS FOR HEALTH PROVIDERS. Fall 2013
THE UNIVERSITY OF TEXAS AT TYLER COLLEGE OF NURSING 1 COURSE SYLLABUS NURS 5317 STATISTICS FOR HEALTH PROVIDERS Fall 2013 & Danice B. Greer, Ph.D., RN, BC dgreer@uttyler.edu Office BRB 1115 (903) 565-5766
### DATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
### MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!
MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics
### Introduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
### Descriptive Statistics and Measurement Scales
Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample
### Course Syllabus MATH 110 Introduction to Statistics 3 credits
Course Syllabus MATH 110 Introduction to Statistics 3 credits Prerequisites: Algebra proficiency is required, as demonstrated by successful completion of high school algebra, by completion of a college
### Multivariate Normal Distribution
Multivariate Normal Distribution Lecture 4 July 21, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Lecture #4-7/21/2011 Slide 1 of 41 Last Time Matrices and vectors Eigenvalues
### International College of Economics and Finance Syllabus Probability Theory and Introductory Statistics
International College of Economics and Finance Syllabus Probability Theory and Introductory Statistics Lecturer: Mikhail Zhitlukhin. 1. Course description Probability Theory and Introductory Statistics
### Intro to Statistics 8 Curriculum
Intro to Statistics 8 Curriculum Unit 1 Bar, Line and Circle Graphs Estimated time frame for unit Big Ideas 8 Days... Essential Question Concepts Competencies Lesson Plans and Suggested Resources Bar graphs
### Practice#1(chapter1,2) Name
Practice#1(chapter1,2) Name Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) inferential statistics
### SPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
### Interpreting Data in Normal Distributions
Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,
### Center: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.)
Center: Finding the Median When we think of a typical value, we usually look for the center of the distribution. For a unimodal, symmetric distribution, it s easy to find the center it s just the center
### Algebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
### WEEK #22: PDFs and CDFs, Measures of Center and Spread
WEEK #22: PDFs and CDFs, Measures of Center and Spread Goals: Explore the effect of independent events in probability calculations. Present a number of ways to represent probability distributions. Textbook | 8,045 | 37,845 | {"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} | 2.71875 | 3 | CC-MAIN-2021-31 | latest | en | 0.867863 |
http://stackoverflow.com/questions/3160483/bitwise-and-and-left-padding-in-c | 1,464,669,218,000,000,000 | text/html | crawl-data/CC-MAIN-2016-22/segments/1464051165777.94/warc/CC-MAIN-20160524005245-00211-ip-10-185-217-139.ec2.internal.warc.gz | 279,262,447 | 19,378 | # “Bitwise And” and Left-Padding in C++
I have a macro that looks something like this:
``````Foo(x) ((x - '!') & 070)
``````
If I call the following code:
``````Foo('1') => 16
``````
However, if I call the following code:
``````(('1' - '!') & 70) => 0
``````
So my question is, what's going on here? Why does `x & 070` compute to `x` but `x & 70` compute to 0?
My guess is that the extra 0 on the left is forcing 60 to take 2 bytes instead of 1. In that case, wouldn't the bitwise & be as follows?
``````0000 0000 0001 0000 '16
0000 0000 0100 0110 & '70
-------------------
0000 0000 0000 0000
``````
-
I knew the answer to this (0 prefix = octal constant) but I can honestly say in more than 20 years of C programming, I've never seen it used. It's just one of those things that seems to have originated from a time when it would have been useful, maybe something to do with teletype machines or whatever. As an embedded guy, I'm always miffed that there's not something like a 'b' prefix for binary constants (yes, I have my own ways of doing this in C & C++, too bad it's not built into the language). – Dan Jul 4 '10 at 16:30
In C++, a constant with a leading `0` is an octal constant, not a decimal constant. It is still an integer constant but `070 == 56`.
This is the cause of the difference in behaviour.
-
Thanks, I expected it to be something straightforward, but didn't realize I was in the wrong base! – sohum Jul 1 '10 at 18:25
No, the extra 0 means the number is read as octal (base 8). That means it doesn't say 70, but 56:
``````0000 0000 0001 0000 '16
0000 0000 0011 1000 & '56
-------------------
0000 0000 0001 0000
``````
-
Prepending the `070` with a `0` like you are doing tells the compiler to interpret it as octal, not decimal. You probably want to say `70`.
-
As others said, `070` is an octal (and `0x70` a hexadecimal) constant, which is where your problem lies.
I'd like to add, though, that you should use `inline` functions instead of macros:
``````inline int Foo(int x) { return (x - '!' & 070); }
``````
C++ has done a lot to allow us to get rid of the preprocessor for many things, because it's bad, misbehaving, and dangerous. If you can do without it, do so.
(And if you use it, at least have the mercy on those having to deal with your code later to make macros all-uppercase.)
-
The original code was actually written by someone else. I'm merely porting it to a different language. – sohum Jul 1 '10 at 18:26 | 739 | 2,479 | {"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} | 2.875 | 3 | CC-MAIN-2016-22 | latest | en | 0.937089 |
https://www.coursehero.com/file/5967571/18-hwc1SolnsODDA/ | 1,529,834,908,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267866926.96/warc/CC-MAIN-20180624083011-20180624103011-00499.warc.gz | 786,926,357 | 81,853 | 18_hwc1SolnsODDA
# 18_hwc1SolnsODDA - A has two rows so DA is the only product...
This preview shows page 1. Sign up to view the full content.
and recall that multiplication by a matrix is always a linear transformation. (Here we are using the “converse” part of Theorem 2.) Hence the matrix representing f is one in ( * ). 3.1 Consider the four matrices A , B , C and D from Exercise 2.7. There are 16 ordered pairs of these matrices, allowing self pairing, namely AA, AB, AC, AD, BA, BB, . . . Which of these make sense as matrix products? Compute the product in each such case. SOLUTION The product of two matrices is defined exactly when the number of columns in the matrix on the left equals the number of columns in the matrix on the right. In the case at hand, A has 4 columns, and only C has 4 rows, so AC is the only product with A on the left that makes sense. Likewise, B has 3 columns, and only B has 3 rows, so BB is the only product with B on the left that makes sense. Next, C has 2 columns, and A and D are the only matrices with 2 rows, so CA and CD are the only products with C on the left that make sense. Finally,
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: A has two rows, so DA is the only product with D on the left that makes sense. We now use the definition of the matrix product to compute the products identified above: AC = ± 13 3-3 4 ² BB = 3-3 3 4-1 2 10-7 8 CA = 3 4 2 3 2 4-2-1-3 1 4 6 7 5 9 CD = 1 2 2-2 1 1 5 DA = ± 1 2-1 1 1 1 2 ² DD = ± 1 1 ² 3.3 Let A = 1 1 1 2 1 2-1 2-1 3-2 2 and let B = -1 1 1 1 1 1-1 2 3 1-3-3 . Compute the third column of AB by computing an appropriate matrix–vector product. SOLUTION By the definition of matrix–matrix multiplication, if we write B = [ v 1 , v 2 , v 3 , v 4 ] , then AB = [ A v 1 , A v 2 , A v 3 , A v 4 ] . Therefore, we just need to compute A v 3 , which is 3 3 2 1 . 21 /september/ 2005; 22:09 19...
View Full Document
{[ snackBarMessage ]}
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern | 856 | 2,919 | {"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-2018-26 | latest | en | 0.891222 |
https://www.coursehero.com/file/6743465/capstapp/ | 1,513,522,636,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948596051.82/warc/CC-MAIN-20171217132751-20171217154751-00018.warc.gz | 720,264,973 | 28,127 | # capstapp - Sheet1 Problem 1(1 Book Value Debt/Equity Ratio...
This preview shows pages 1–3. Sign up to view the full content.
Sheet1 Problem 1 (1) Book Value Debt/Equity Ratio = 2500/2500 = 100% Market Value of Equity = 50 million * \$ 80 = \$4,000 Market Value of Debt = .80 * 2500 = \$2,000 Debt/Equity Ratio in market value terms = 2000/4000 = 50.00% (2) Book Value Debt/(Debt+ Equity) = 2500/(2500 + 2500) = 50% Market Value Debt/(Debt+Equity) = 2000/(2000+4000) = 33.33% (3) After-tax Cost of Debt = 12% (1-0.4) = 7.20% (4) Cost of Equity = 8% + 1.2 (5.5%) = 14.60% (5) Cost of Capital = 14.60% (4000/6000) + 7.20% (2000/6000) = 12.13% Problem 2 (1) To assess this project from the equity investors' standpoint, we estimate cashflows to equity and the cost of equity. Initial Equity Investment in Project = 0.6667 (100 million) = \$ 66.67 million Cash Flows to Equity = Net Income + Depreciation = \$ 9.60 million + \$ 5 million = \$ 14.60 million NPV of CF to Equity = 14.60/.1460 - 66.67 = \$ 33.33 million (2) From the firm's standpoint, the cashflows to the firm have to be estimated. Initial Investment in Project = \$ 100 million Cash Flows to Firm = EBIT (1 - tax rate) + Deprec'n = \$ 20 million (1-0.4) + \$ 5 million = \$ 17 million NPV of CF to Firm = \$ 17/.1213 - \$ 100 million = \$40.15 million (3) The cost of equity should be used as the discount rate if the cashflows being discounted are cashflows to equity. (4) The cost of capital should be used as the discount rate if the cashflows being discounted are cashflows to the firm. (5) Even if this project is financed entirely with debt, it should be analyzed using the same costs of equity and capital as the analysis above. Problem 3 (1), (2) and (3) Unlevered Beta = Levered Beta/(1+(1-t)(D/E)) = 1.2/(1+0.6*0.5) = 0.92 D/E Ratio Beta Cost of Equity Cost of Debt WACC Option 1 20.00% 1.03 13.69% 6.60% 12.51% Option 2 100.00% 1.48 16.12% 7.80% 11.96% Option 3 500.00% 3.69 28.31% 10.80% 13.72% (4) . . Firm Value New Firm ValuDebt Equity Stock Price Option 1 (\$178) \$5,822 \$1,000 \$4,822 \$76.43 Option 2 \$86 \$6,086 \$3,000 \$3,086 \$81.72 Option 3 (\$693) \$5,307 \$5,000 \$307 \$66.14 Note: The change in firm value will mean that the debt ratios computed above will also change. (5) From a cost of capital standpoint, option 2 is the best one. (6) If Rubbermaid's income is more volatile, the firm should be more cautious in adding debt. (7) If the new debt or equity is used to take projects, the analysis would change for two reasons – (a) the projects may have a different risk profile than the firm's risk profile. (b) the NPV of the projects has to be added to the value change calculated. (c) the firm value itself will increase as the new debt and equity is issued. (8) I would factor in the firm's need for flexibility into the analysis - the greater the need for flexibility the less likely it is that I would add on debt. Further, I would look at how responsive managers are to stockholders; if they are not, I would be more likely to add debt. (9) The higher rating in option 1 lowers the cost of debt, but it is accomplished by replacing debt with more expensive equity. Page 1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Sheet1 Problem 4 (a) Intuitively, I would expect Rubbermaid to have a higher debt ratio than its competitors because – (1) its earnings are less volatile than those of its competitors (2) it has higher cash flows as a percent of firm value than its competitors.
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### Page1 / 9
capstapp - Sheet1 Problem 1(1 Book Value Debt/Equity Ratio...
This preview shows document pages 1 - 3. Sign up to view the full document.
View Full Document
Ask a homework question - tutors are online | 1,164 | 3,861 | {"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-2017-51 | latest | en | 0.849027 |
http://enthusiasm.cozy.org/archives/2007/10/micro-utility-coops | 1,537,907,384,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267162385.84/warc/CC-MAIN-20180925202648-20180925223048-00326.warc.gz | 83,061,936 | 9,204 | # Micro-utility Coops
There is a certain fantasy, at least among Americans, that they might go off-grid. Grow their own vegetables, keep a some live stock, heat the house with wood from from their own wood lot, a yurt, a windmill, some solar panels. Of course a the satellite TV and Internet connection would be nice. Off grid is one thing, but no TV or Internet – that’s crazy; I mean “there are more World of Warcraft players than farmers.”
The grids fascinates me; including the utility grids.
I contemplated my gas bill (google spreadsheet, the onion). Broadly the gas bill has two parts; one part is the cost of the gas and the other part is the cost of tapping into the gas distribution network. The gas distribution network is a classic two sided network; they buy from assorted suppliers and sell to assorted consumers. Here’s the formula, a function of C and T; where C is their cost to buy the natural gas, and T, the number of therms of gas I use.
Bill(T, C) = \$14.72 + .34*min(0,max(T-3,47) + .053*min(0,T-50) + (1/45+C)*T
For me \$300 a year, about a quarter of the bill is the cost to access the local distribution network.
I could go half off the grid, saving \$150 a year if I could coordinate my purchase with a neighbor. We agree to form a gas purchasing micro-coop. One of us cancels our service and we run a pipe over to his house from the remaining service. You can buy a gas meter so the bill is split equitably.
Schemes like this are all about coordination costs. I think you could do a lot to lower those coordination costs by providing a bit of innovative technology and IT to help. For example. Consider the micro-gas coop outlined above. A vendor might offer a kit for setting this up. The kit would include a gas meter for each member which reports usage back the vendor who then bill the members. This reduces the coop’s coordination costs to signing up, setting up, and occasional maintenance of members. Reducing an on going coordination cost to mostly just a plumbing problem.
Of course there are other utilities that this makes even more sense for. Internet access and cable TV access for example. The CATV installer, some years back, told me about some guy in a small city north of here who had his entire neighborhood running off a single CATV subscription. At least at that time the rules were such that you could do that; and even today there is plenty on the CATV cable that you can view just by plugging your TV into it.
Meanwhile, flickr has a great pool of gas meter photos. Where you can see there are plenty of apartment buildings a coop housing estates were a micro-coop wouldn’t be that hard to plumb. | 602 | 2,654 | {"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-2018-39 | latest | en | 0.952114 |
https://www.assignmentexpert.com/homework-answers/chemistry/other/question-51912 | 1,581,968,099,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875143079.30/warc/CC-MAIN-20200217175826-20200217205826-00106.warc.gz | 651,618,109 | 12,805 | 83 058
Assignments Done
99,3%
Successfully Done
In February 2020
# Answer to Question #51912 in Other Chemistry for vi
Question #51912
Expansion joints are used for materials that easily expand and contract depending upon its temperature. How much expansion can take place for a brass pipe 25.8 m long that experiences temperature changes of 75.2°C? 3.44 cm 5.90 cm 3.69 cm 1.23 cm
1
2015-04-25T11:10:14-0400
Lineartemperature expansion of brass is 18.7·10-6 1/(K).
1ºC=1 K
Thatis why for 25.6 m pipe the expansion will be:
25.8·18.7·10-675.2=0.036 m=3.69 cm
Need a fast expert's response?
Submit order
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS! | 233 | 734 | {"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-2020-10 | latest | en | 0.796232 |
https://math.libretexts.org/Courses/Angelo_State_University/Mathematical_Computing_with_Python/3%3A_Interpolation_and_Curve_Fitting/3.2%3A_Polynomial_Interpolation | 1,726,325,743,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651579.38/warc/CC-MAIN-20240914125424-20240914155424-00688.warc.gz | 362,450,315 | 33,554 | # 3.2: Polynomial Interpolation
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\id}{\mathrm{id}}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\kernel}{\mathrm{null}\,}$$
$$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$
$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$
$$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$
$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$
$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vectorC}[1]{\textbf{#1}}$$
$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$
$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$
$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
Given a set of data, polynomial interpolation is a method of finding a polynomial function that fits a set of data points exactly. Though there are several methods for finding this polynomial, the polynomial itself is unique, which we will prove later.
### 3.2.1: Lagrange Polynomial
One of the most common ways to perform polynomial interpolation is by using the Lagrange polynomial. To motivate this method, we begin by constructing a polynomial that goes through 2 data points $$(x_0,y_0)$$ and $$x_1,y_1$$. We use two equations from college algebra.
$y-y_1=m(x-x_1)\hspace{10pt}\textrm{and}\hspace{10pt}m=\frac{y_1-y_0}{x_1-x_0}$
Combining these, we end up with:
$y=\frac{y_1-y_0}{x_1-x_0}(x-x_1)+y_1.$
Now, to derive a formula similar to that used for the Lagrange polynomial, we perform some algebra. We begin by swapping the terms $$y_1-y_0$$ and $$x-x_1$$:
$y=\frac{x-x_1}{x_1-x_0}(y_1-y_0)+y_1.$
Distributing the fraction:
$y=\frac{x-x_1}{x_1-x_0}y_1 - \frac{x-x_1}{x_1-x_0}y_0 + y_1.$
Multiplying the right-most $$y_1$$ term by $$\frac{x_1-x_0}{x_1-x_0}=1$$:
$y=\frac{x-x_1}{x_1-x_0}y_1 - \frac{x-x_1}{x_1-x_0}y_0 + \frac{x_1-x_0}{x_1-x_0}y_1.$
Combining to the $$y_1$$ terms:
$y=-\frac{x-x_1}{x_1-x_0}y_0 + \frac{x-x_0}{x_1-x_0}y_1.$
and finally flipping the denominator of the first term to get rid of the negative:
$y=\frac{x-x_1}{x_0-x_1}y_0 + \frac{x-x_0}{x_1-x_0}y_1.$
In the above, we can observe that, when $$x=x_1$$, it follows that the first term cancels out with a zero on top and the second term ends up as $$1\cdot y_1=y_1$$, as desired. Similarly, if $$x=x_0$$, then the first term ends up as $$1\cdot y_0=y_0$$ and the second term cancels out with a zero on top, causing the entire expression to be $$y_0$$, as desired.
For three data points $$(x_0,y_0), (x_1,y_1), \textrm{and} (x_2,y_2),$$ we can derive a polynomial that behaves similarly:
$y=\frac{(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)}y_0 + \frac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)}y_1 + \frac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}y_2.$
In the above, plugging in, for example, $$x=x_1$$ has the first and third terms cancelling out with zero and the middle term turning into $$1\cdot y_1$$, as desired. We can follow this pattern to arrive at the full Lagrange polynomial.
##### THE LAGRANGE POLYNOMIAL
Given $$n+1$$ data points $$(x_0,y_0), (x_1,y_1), \ldots, (x_n,y_n)$$ with $$x_0<x_1<\cdots<x_n$$, the Lagrange polynomial is the $$n$$th degree polynomial passing through each of these points and written as: $y=\frac{(x-x_1)(x-x_2)\cdots(x-x_n)}{(x_0-x_1)(x_0-x_2)\cdots (x_0-x_n)}y_0 + \frac{(x-x_0)(x-x_2)\cdots(x-x_n)}{(x_1-x_0)(x_1-x_2)\cdots (x_1-x_n)}y_1 + \cdots + \frac{(x-x_0)(x-x_1)\cdots(x-x_{n-1})}{(x_n-x_0)(x_n-x_1)\cdots (x_n-x_{n-1})}y_n$ Equivalently, we can use product notation: $y=\sum_{i=0}^n\left(y_i\prod_{\substack{j=0 \\ j\neq i}}^n\frac{x-x_j}{x_i-x_j}\right)$
Note that in the above polynomial, each numerator is written such that, for $$x=x_i$$, each coefficient vanishes except for the coefficient to $$y_i$$, which evaluates to $$y_i$$. Thus the above polynomial passes through each of the desired data points and, as can be checked, is of degree $$n$$.
Now, let's work with Python. To do this, we use function blocks for the first time. We have used functions in the past in Python, such as sin(x) or cos(x). Here, we create our own function using the def keyword. Below, we define f(o), where o is the dynamic variable. At the end of a function block, we "return", using the return keyword, the result of the function calculation. In the code below, the variable o represents the variable x in the Lagrange Polynomial definition above. We do this since x is already used for our data points.
import numpy as np
import matplotlib.pyplot as plot
#Data goes through the points (1,3) and (5,7)
x=[1,5]
y=[3,7]
#Set the number of data points
pts=len(x)-1
prange=np.linspace(x[0],x[pts],50)
plot.plot(x,y,marker='o', color='r', ls='',markersize=10)
def f(o):
z=((o-x[1])/(x[0]-x[1]))*y[0] + ((o-x[0])/(x[1]-x[0]))*y[1]
return z
plot.plot(prange,f(prange))
plot.show()
output:
Now, we do the same as the above except with 3 data points. Notice how the only changes are the data point lists and the function. Below, we again use the "\" symbol to let Python know to continue on the next line. This is done to make the polynomial easier to read.
import numpy as np
import matplotlib.pyplot as plot
#data goes through the points (4,1), (6,1) and (8,0)
x=[4,6,8]
y=[53,32,60]
n=len(x)-1
prange = np.linspace(x[0],x[n],50)
plot.plot(x,y,marker='o', color='r', ls='', markersize=10)
def f(o):
z=\
(((o-x[1])*(o-x[2]))/((x[0]-x[1])*(x[0]-x[2])))*y[0]+\
(((o-x[0])*(o-x[2]))/((x[1]-x[0])*(x[1]-x[2])))*y[1]+\
(((o-x[0])*(o-x[1]))/((x[2]-x[0])*(x[2]-x[1])))*y[2]
return z
plot.plot(prange,f(prange))
plot.show()
output:
Using the product notation of Lagrange Polynomials, we can even come up with a program that accepts any number of data points. $y=\sum_{i=0}^n\left(y_i\prod_{\substack{j=0 \\ j\neq i}}^n\frac{x-x_j}{x_i-x_j}\right)$ In the code below, $$i$$ and $$j$$ represent the $$i$$ and $$j$$ in the definition above.
import numpy as np
import matplotlib.pyplot as plot
x=[1,3,5,7,8,9,10,12,13]
y=[50,-30,-20,20,5,1,30,80,-10]
n=len(x)-1
prange = np.linspace(min(x),max(x),500)
plot.plot(x,y,marker='o', color='r', ls='', markersize=10)
def f(o):
sum = 0
for i in range(n+1):
prod = y[i]
for j in range(n+1):
if i!= j:
prod=prod*(o-x[j])/(x[i]-x[j])
sum = sum + prod
return sum
plot.plot(prange,f(prange))
plot.show()
output:
While Lagrange polynomials are among the easiest methods to understand intuitively and are efficient for calculating a specific $$y(x)$$, they fail when when attempting to either find an explicit formula $$y=a_0+a_1x+\cdots+a_nx^n$$ or when performing incremental interpolation, that is, adding data points after the initial interpolation is performed. For incremental interpolation, we would need to complete re-perform the entire evaluation.
### 3.2.2: Newton interpolation
Newton interpolation is an alternative to the Lagrange polynomial. Though it appears more cryptic, it allows for incremental interpolation and provides an efficient way to find an explicit formula $$y=a_0+a_1x+\cdots+a_nx^n$$.
Newton interpolation is all about finding coefficients and then using those coefficients to calculate subsequent coefficients. Since an important part of Newton interpolation is that it can be used for incremental interpolation, let's start with a single data point and show the calculations as we add points.
With one data point $$(x_0,y_0)$$, the calculation is simple:
$b_0=y_0$
and the polynomial is
$y=b_0.$
Let's add a new data point $$(x_1,y_1)$$. The next coefficient $$b_1$$ is usually denoted by $$[y_0,y_1]$$:
$b_1=[y_0,y_1]=\frac{y_1-y_0}{x_1-x_0}$
and the polynomial is
$y=b_0+b_1(x-x_0).$
Notice how we did not have to re-calculate the entire polynomial, only the new coefficient to $$(x-x_0)$$.
With a third data point $$(x_2,y_2)$$, we find the coefficient $$b_2=[y_0,y_1,y_2]$$:
$b_2=[y_0,y_1,y_2]=\frac{[y_1,y_2]-[y_0,y_1]}{x_2-x_0}=\frac{\frac{y_2-y_1}{x_2-x_1}-\frac{y_1-y_0}{x_1-x_0}}{x_2-x_0}$
with polynomial
$y=b_0+b_1(x-x_0)+b_2(x-x_0)(x-x_1).$
You may have noticed the recursive nature of the previous definitions. This continues for Newton interpolation in general.
##### NEWTON INTERPOLATION
Given $$n+1$$ data points $$(x_0,y_0), (x_1,y_1), \ldots, (x_n,y_n)$$ with $$x_0<x_1<\cdots<x_n$$, the Newton interpolation polynomial is the $$n$$th degree polynomial passing through each of these points and written as: $y=b_0+b_1(x-x_0)+b_2(x-x_0)(x-x_1)+\cdots+b_{n}(x-x_0)(x-x_1)\cdots(x-x_{n-1})$ where \begin{align} b_0 &= y_0\\ b_2 &= [y_0,y_1] = \frac{y_1-y_0}{x_1-x_0}\\ b_2 &= [y_0,y_1,y_2] = \frac{\frac{y_2-y_1}{x_2-x_1}-\frac{y_1-y_0}{x_1-x_0}}{x_2-x_0}\\ &\vdots\\ b_{n} &= [y_0, y_2, \ldots, y_n] = \frac{[y_1, y_2, \ldots, y_n] - [y_0, y_1, \ldots, y_{n-1}]}{x_{n}-x_0} \end{align}
Let's begin by finding a polynomial with three data points using Newton's Method.
Example: Use Newton's method to calculating a polynomial through the points $$(1,3), (5,7)$$ and $$(8,0)$$.
For this example, we will use a "tableau" to help organize our data.
$$x_0$$ $$y_0$$ $$x_1$$ $$y_1$$ $$[y_1,y_0]$$ $$x_2$$ $$y_2$$ $$[y_2,y_1]$$ $$[y_0,y_1,y_2]$$
We start by filling in our data points:
1 3 5 7 $$[y_1,y_0]$$ 8 0 $$[y_2,y_1]$$ $$[y_0,y_1,y_2]$$
Then we calculate: $[y_1,y_0]=\frac{7-3}{5-1}=1$ $[y_2,y_1]=\frac{0-7}{8-5}=-\frac{7}{3}$ and fill in this data:
1 3 5 7 1 8 0 $$-\frac{7}{3}$$ $$[y_0,y_1,y_2]$$
Now, we calculate the remaining item, using the previously-calculated terms: $[y_0,y_1,y_2]=\frac{[y_1,y_2]-[y_0,y_1]}{x_2-x_0}=\frac{-\frac{7}{3}-1}{8-1}=-\frac{10}{21}$
1 3 5 7 1 8 0 $$-\frac{7}{3}$$ $$-\frac{10}{21}$$
Note, now, that $$b_0, b_1,$$ and $$b_2$$ are written on the top diagonal. Thus our final polynomial is: $y=b_0+b_1(x-x_0)+b_2(x-x_0)(x-x_1)=3+1(x-1)-\frac{10}{21}(x-1)(x-5)$
Now, let's program this for three data points to check our work!
import numpy as np
import matplotlib.pyplot as plot
x=[1,5,8]
y=[3,7,0]
n=len(x)-1
prange = np.linspace(min(x),max(x),500)
plot.plot(x,y,marker='o', color='r', ls='', markersize=10)
def f(o):
b0=y[0]
b1=(y[1]-y[0])/(x[1]-x[0])
b1p=(y[2]-y[1])/(x[2]-x[1])
b2=(b1p-b1)/(x[2]-x[0])
poly=b0+b1*(o-x[0])+b2*(o-x[0])*(o-x[1])
return poly
plot.plot(prange,f(prange))
plot.show()
output:
A general program can be made by using a recursive function.
import numpy as nm
import matplotlib.pyplot as plot
x=[-5,-4,-3,-2,-1,0,1,2,3,4,5]
y=[0,0,0.1,0.3,0.7,1,0.7,0.3,0.1,0,0]
plot.plot(x,y,marker='o', color='r', ls='',markersize=10)
if a==0: return y[b]
def f(o):
yres=0
for p in range(len(x)):
for q in range(p):
prodres*=(o-x[q])
yres+=prodres
return yres
prange=nm.linspace(x[0],x[-1],200)
plot.plot(prange,f(prange))
plot.show()
output:
Note that above, we have something strange happening near the end points. This is known as Runge's phenomenon and mainly occurs at the endges of an interval when using polynomial interpolation with polynomials of high degree over a set of points that are equally spaced. Because of Runge's phenomenon, it is often the case that going to higher degrees does not always improve accuracy. To combat this, we can use a method such as cubic splines, which we discuss here.
### 3.2.3: Cubic Splines
spline is a function defined piecewise by polynomials. Instead of having a single polynomial that goes through each data point, as we have done so far, we instead define several polynomials between each of the points. While defining several polynomials might take more work, it is usually preferred since it gives similar results while avoiding Runge's phenomenon.
A linear spline is created by simply drawing lines between each of the data points. Using our data points from earlier, we can create a reasonable approximation of our underlying function.
While simplistic, this approximation is likely better than that generated when using the same data points and Newton's method. This is due to the absence of Runge's phenomenon. To make the picture look even better, we can replace the lines by cubic functions. When doing so, we will end up with a number of cubic functions equal to one less than the number of data points - that is, one for every interval between the data points. We call this function $$s(x)$$, which can be defined as follows.
$s(x) = \left\{ \begin{array}{lr} s_0(x)=a_0x^3+b_0x^2+c_0x+d_0 & \text{if } x_0\leq x\leq x_1\\ s_1(x)=a_1x^3+b_1x^2+c_1x+d_1 & \text{if } x_1\leq x\leq x_2\\ \vdots\\ s_{n-1}(x)=a_{n-1}x^3+b_{n-1}x^2+c_{n-1}x+d_{n-1} & \text{if } x_{n-1}\leq x\leq x_n\\ \end{array} \right$
3.2: Polynomial Interpolation is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. | 6,019 | 16,288 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2024-38 | latest | en | 0.196654 |
https://oeis.org/A139067 | 1,721,598,062,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517796.21/warc/CC-MAIN-20240721213034-20240722003034-00338.warc.gz | 378,313,780 | 3,739 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A139067 Primes whose decimal expansion consists of a string of 2's followed by a string of 3's. 6
2, 3, 23, 223, 233, 2333, 23333, 2222333, 22222223, 223333333, 22222222223, 22222223333, 22222333333, 22223333333, 23333333333, 222223333333, 23333333333333333, 2222222222222233333, 2222222222333333333 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 LINKS Table of n, a(n) for n=1..19. MATHEMATICA With[{nn=20}, Sort[Select[Flatten[Table[FromDigits[Join[Table[2, {i}], Table[3, {j}]]], {i, 0, nn}, {j, 0, nn}]], PrimeQ]]] (* Harvey P. Dale, Jan 30 2013 *) CROSSREFS Cf. A020458, A141470, A141471, A141472. Sequence in context: A260126 A260125 A020458 * A099656 A157733 A235934 Adjacent sequences: A139064 A139065 A139066 * A139068 A139069 A139070 KEYWORD nonn,base AUTHOR Paul Curtz, Jun 05 2008 EXTENSIONS Entry revised by Ray Chandler and N. J. A. Sloane, Aug 14 2008 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified July 21 16:38 EDT 2024. Contains 374475 sequences. (Running on oeis4.) | 469 | 1,386 | {"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} | 2.5625 | 3 | CC-MAIN-2024-30 | latest | en | 0.449611 |
https://www.jobilize.com/course/section/the-environment-amplitude-modulation-by-openstax?qcr=www.quizover.com | 1,553,454,229,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912203491.1/warc/CC-MAIN-20190324190033-20190324212033-00475.warc.gz | 785,874,664 | 21,152 | 2.1 Amplitude modulation
Page 1 / 4
This chapter presents the use of the DSK6713 to demonstrate the features of Amplitude Modulation (AM) transmission and reception. The model runs in real-time and enables the use to select the AM detector as well as the transmission and reception parameters (modulation index and carrier frequency).
Introduction
This chapter presents the use of the DSK6713 to demonstrate the features of Amplitude Modulation (AM) transmission and reception. The model runs in real-time and enables the use to select:
1. The AM algorithm
2. The transmission and reception parameters (modulation index and carrier frequency).
The process comprises:
1. Creating a simulation model (not R-T) for the AM transmitter/receiver.
2. Migration to Real-time of the Simulation Model
3. Building a Graphic Users Interface (GUI) to operate the real-time implementation.
The environment
Figure 1 shows the data flow for the AM modulation simulation. The AM modulation model receives an input signal from an external signal generator, modulates it and displays the modulation on the scope.
Building the transmitter
The basic modulation mathematical description is given by:
$y\left(t\right)=\left[1+m\left(t\right)\right]\text{cos}\left({2\pi f}_{c}t\right)$ Where: $\text{cos}\left({2\pi f}_{c}t\right)$ - The carrier signal $m\left(t\right)$ - The modulation index
• Start by creating a new model in Simulink ®
• Open the Simulink library browser and add the DSP sine-wave to your model. This blocks will represent the information signal m(t).
• Configure the Sine Wave Generator Block (Double click on the DSP sine object). Set the sine frequency to 1000 Hz, sample time to 1/96000, samples per frame to 64 and close the box, and change its label to “information”.
• Use the same block to create the carrier signal. You may copy the block already created or select it form the Simulink library. Set the carrier frequency to 15,000 Hz. The remaining parameters are identical to the ones of the information signal. Change its label to “carrier”
• Double-click on the constant object and set its constant value to 1.5:
• Add a new multiplexer from the same directory as the adder (choose “product”).
• Add a new scope object:
• Set the number of frames parameter to 5. This parameter determines the horizontal scaling of the presented signal.
• Place the objects in the following way:
• Run the model, pause the simulation and activate the scope window. The modulated signal should be displayed as follows:
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers! | 1,288 | 5,575 | {"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": 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} | 2.8125 | 3 | CC-MAIN-2019-13 | longest | en | 0.776789 |
https://www.sciencefairprojects.co.in/Science-Experiments/Why-Are-the-Apples-Brown.php | 1,660,884,304,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573623.4/warc/CC-MAIN-20220819035957-20220819065957-00035.warc.gz | 837,666,199 | 5,896 | Home School Projects Science Experiments Kids Projects Physics Mathematics Chemistry Computer Botany Earth Science Electricity Contact Us
Why Are the Apples Brown
Abstract
The objective: My project is about what the factors that are affecting apple slices turning brown and what the best ways are to help preserve the apple slices.
Methods/Materials
The materials I used were Fuji apples, strips to test the pH of the substances used, a dropper, plastic food wrap, glasses, a thermometer, a browning chart, pens, knifes, a clod area such as a freezer, a warm area similar to an oven, a camera, plastic gloves, a small table to place all of the apples on, a timer, and substances that ranged in different pH levels which were lemon juice, orange juice, water, soda (sprite,) mineral water, cranberry juice, and baking soda. The method I used was to first get each substance and then to take the pH strips and test the pH of each liquid, then to line up the slices of apples on the table, then to use the dropper and put and equal amount of drops of each substance on each individual apple, then to set a control apple aside, then to set the timer, then to record how long it takes for each apple slice with each different substance on it to turn dark brown.
Results
My results were that lemon juice is the best preservative to put on apple slices and that cranberry juice is the worst. The order of the preservatives from best to worst goes from lemon juice, to soda, to mineral water, to water, to an apple slice with nothing on it (control,) to orange juice, to baking soda and ending with cranberry juice. My results for the second experiment were that the best temperature to put apple slices at is a warm tempertature such as 100 degrees Fahrenheit, then at room temperature, then a temperature of 39 degrees Fahrenheit, and ending with the worst temperature to put apple slices at when wanting to preserve them which is a freezing temperature such as 32 dregrees Fahrenheit.
Conclusions/Discussion
I came to the conclusion that lemon juice is the best substance to put on apple slices when wanting to preserve them because it is high in citric acid. It is also has Vitamins A, C and E in it. These are good because it lowers the pH level of the apple causing it to turn brown slower. It is best to put apple slices at a hot temperature because if you put it at a cold, the ice breaks down the cell walls of the apple and introduces the enzyme called "polyphenol oxidase" to air which is what turns the apple brown.
This project is about what the factors that are affecting apple slices turning brown and what the best ways are to help preserve the apple slices.
Science Fair Project done By Sara K. Spaventa | 580 | 2,723 | {"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-2022-33 | longest | en | 0.922385 |
https://www.mathworks.com/matlabcentral/profile/authors/343082 | 1,723,781,529,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641333615.45/warc/CC-MAIN-20240816030812-20240816060812-00221.warc.gz | 659,015,814 | 23,953 | # Jean-Marie Sainthillier
### Skinexigence
Last seen: 3 days ago Active since 2012
Followers: 1 Following: 0
Spoken Languages:
English, French
All
#### Feeds
View by
Solved
Maior Primo
Dado um valor inteiro N, qual o maior valor primo <= N MaiorPrimo(5) = 5; MaiorPrimo(10) = 7;
8 days ago
Solved
Vector indexing: lower than mean
Find indices of values in a vector lower than the mean of the vector
8 days ago
Solved
Diagonal Product of A Square Matrix
For a matrix A, calculate the product of its diagonal elements. * Assume all input matrices are square & corresponding element...
8 days ago
Solved
Reverse a string
Return a string with the characters in reverse order from a given input string Ex: my_str = "Ciao" function should output "...
8 days ago
Solved
Convert RGB to Grayscale
Convert a 3 element RGB array to its correspoding grayscale pixel (a scalar) *Hint: a formula exists!
8 days ago
Solved
Finding the Most Frequent Letter in a Text
You are given a text containing various English letters, digits and punctuation symbols. Your task is to find the most frequentl...
8 days ago
Solved
Remove Unique Elements
Given a list of integers, we want to keep only the non-unique elements in this list. To do this, we need to remove all the uniqu...
8 days ago
Solved
Find the number of diagonals in a n sided polygon.
Find the number of diagonals in a n sided polygon.
8 days ago
Solved
Matrix Rotation
Write a MATLAB function that rotates a given matrix by 90 degrees clockwise. The rotation should be performed in-place, without ...
8 days ago
Solved
Sort by absolute value
Given a list of numbers, arrange them in ascending order based on their absolute values. For example, for the list [-30, -5, 1...
8 days ago
Solved
Digits eliminate
Complete the function my_f(n,b) to return, for a given integer, the number obtained by removing the digits '0' and 'b'. If there...
8 days ago
Solved
Counting the occurrences of a digit in a book
The printer has printed a book with 'p' pages. How many times did they use the character 'd'? In other words, how many times doe...
8 days ago
Solved
Range of Values in a Matrix
Create a function that accepts a matrix of real numbers as input and returns the range of the values contained in the matrix. Th...
8 days ago
Solved
Alternate Arrangement
Determine the ways of arranging 'm' men and 'w' women alternatively in a row of 's' seats. Assumptions : s<m and s<w
8 days ago
Solved
Caracteres Unicos
Dada uma string, verifique se a string é composta de caracteres únicos, ou seja, nenhuma letra se repete. Retorne true ou false;...
8 days ago
Solved
Identify de Polignac numbers
The numbers 125 and 329 can be written as the sum of a prime and a power of 2. For example, , and . The numbers 127 and 331, whi...
8 days ago
Solved
List the Fermi-Dirac primes
The Fermi-Dirac “primes” are prime powers with exponents that are powers of 2. The first nine terms of the sequence are 2, 3, 4,...
9 days ago
Solved
List the semiprimes
A semiprime number—or a 2-almost prime—is the product of two prime numbers. The numbers and are semiprimes, but and are not....
9 days ago
Solved
Check if a directory is on the current MATLAB search path
Given a directory name as a string, return true if the directory is on the current MATLAB search path, and false otherwise.
9 days ago
Solved
compter le nombre de zéros dans une matrice
écrire une fonction count_zeros qui prend en entrée une matrice M et détermine le nombre de zéros dans une matrice
9 days ago
Solved
Compute the largest number whose prime factors sum to n
This problem deals with a sequence whose tenth term is 36 because the prime factors of 36 (2, 2, 3, 3) sum to 10. The number 32 ...
9 days ago
Solved
List the cuban primes
The number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. Write a function to list the cuba...
9 days ago
Solved
List the Moran numbers
The quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 ...
10 days ago
Solved
Smallest n, for n! to have m trailing zero digits
For given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! t...
10 days ago
Solved
Průměr z výběrového souboru
Napište funkci, která vrátí průměr z hodnot vektoru data. Např data = [1, 2, 3, 4, 5, 6, 7, 8, 9] je prumer = 5.
10 days ago
Solved
Find Rows with Specift Properities
Delete rows with specific properites as following: Find rows that have a negative value in any element of the row and delete it...
10 days ago
Solved
Remove a specific column with min value
Remove the column that contain the min value in the matrix? If you like the problem, please give it a like:)
10 days ago
Solved
Remove a specific column with max value
Remove the column that contain the max value in the matrix? If you like the problem, please give it a like:)
10 days ago
Solved
Remove a specific row with min value
Remove the row that contain the min value in the matrix? If you like the problem, please give it a like:)
10 days ago | 1,372 | 5,179 | {"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} | 2.796875 | 3 | CC-MAIN-2024-33 | latest | en | 0.756626 |
https://rollforfantasy.com/puzzles/shikaku.php | 1,638,515,132,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362605.52/warc/CC-MAIN-20211203060849-20211203090849-00050.warc.gz | 544,093,771 | 7,717 | Feel free to share
Using this site means trees will be planted. ^.^
(Find out more)
# Shikaku
Shikaku, sometimes called 'Divide by Box' or 'Divide by Squares' in English, is a Nikoli puzzle in which the aim of the game is to divide a grid into rectangular and square spaces based on the numbers given on the grid. It can be played on any sized grid, but the bigger the grid the harder the puzzle usually becomes. A lot of it does depend on the amount of squares and the placement of the hints however.
The rules are simple:
- Divide the grid into rectangles and squares using the numbers as indicators of how big the rectangle or square has to be.
- Each number must be part of a square or rectangle that is as many cells big as the number itself. So a 2x2 number could cover a 4, for example.
- Each number must be in its own square or rectangle.
## Standard version
Shikaku can seem like a difficult puzzle at first. The numbers don't always seem to allow for many deductions, trial and error seems to be a lengthy process for this puzzle, and without knowing any tricks it can indeed be a lengthy process no matter how you go about solving a Shikaku puzzle.
One good starting point is clusters of numbers. The more numbers are together the more paths they're blocking. Since no 2 numbers can be in the same square or rectangle you know their respective rooms cannot go the way of the other numbers, minimizing some of your options, and, in some cases, providing you with a single possible solution.
Another option is to start with the bigger numbers. They often have few places to go due to their size, but in well designed, difficult puzzles their number hints are often placed in such a way that multiple large squares and rectangles fit within the overall space the hint occupies.
## Converting it to an RPG setting.
The first thing I saw after looking at a solved Shikaku puzzle was the possibility of turning that solution into a building's layout. Of course this isn't the only possible adaptation you can make, but they do tend to be similarly themed.
The layout of an army camp, lock boxes in a wall, animal enclosures in a zoo, crates of goods stored in a warehouse. There's plenty of opportunities to use a puzzle like this in a campaign, but sometimes it does require a little extra imagination.
To go back to my example of a building's layout, my character (seen below) is given a map with a grid and the numbers on that grid, with the instructions on how to solve a Shikaku puzzle. She also knows it'll give her a rough layout of a building she has to enter as part of her mission. The layout won't contain any details, but merely give her the sizes of all rooms, which will be a tremendous clue in and of itself.
If she doesn't manage to solve the puzzle she'll likely end up confused and lost in the building she has to sneak into. Some of the rooms are only accessible through secret doors, like the 2x2 room with chests in it. Without a map this room could easily be missed, but with the map she'll know there must be a room in that spot.
Obviously she wouldn't know there are chests in that room, in fact she wouldn't even know where the regular doors are (I added those to the image for effect), but if you do want to make it easier for your players you could have the map reveal more details through magic after the puzzle has been solved.
Overall it's a simple enough puzzle to not need magic, but it's also a very effective one in terms of rewarding players for overcoming an optional puzzle. Without the solution they'll still be able to infiltrate the building, find the lock boxes in the wall, figure out the layout of the army camp, and so on, but with the solution everything becomes clearer and easier. A fit reward on its own, but perhaps the solution shows more than just the easy path. | 830 | 3,831 | {"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-2021-49 | longest | en | 0.963638 |
https://physics.stackexchange.com/questions/tagged/inertial-frames?sort=active&pageSize=50 | 1,563,698,482,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526940.0/warc/CC-MAIN-20190721082354-20190721104354-00480.warc.gz | 508,346,430 | 39,630 | # Questions tagged [inertial-frames]
A specific reference frame that describes its coordinates in a manner that does not depend on time and is isotropic.
1,148 questions
Filter by
Sorted by
Tagged with
138 views
### ${}$Michelson-Morley experiment
In the Michelson-Morley experiment, the light from a source is passed through a semi-silvered mirror from where a part of it moves horizontally towards a mirror (from where we calculate $t_1$) and a ...
36 views
### Interaction between various forces, by which one is to calculate an angle?
I am new to Newtonian mechanics, and was wondering about the following question. I basically have the ingredients for the answer, but I cannot seem to find the way to put this together into one ...
47 views
### Different forces from different inertial frames?
I've been having trouble understanding this equation here derived in the picture given below. If I change reference frames to one which is moving at a velocity u with respect to the first frame, then ...
71 views
### Is there a flaw in Newton's first law? [on hold]
When there is no external force, the object can move in a straight line or rotate around its own center of mass in a uniform manner. When there is no external force, the object does not necessarily ...
45 views
### Has this group something to do with the cone of light?
Consider the group $V=(-1,1)$ with addition $+_{rel}:V\times V\to V$ defined as: $$v+_{rel}w=\frac{v+w}{1+vw}$$ This group is analogous to the relativistic velocities where the speed of light equals ...
68 views
### To Be Forever Young [duplicate]
It is clear from the Lorentz Parameters, applied to Einstein's Equations, that as velocity, v approaches speed-of-light, c, the denominator (1 - [v/c]) tends to zero; when v=c, time, t=0: time stops?! ...
55 views
### Why is the Earth not an inertial frame of reference?
From many sources I have found the explanation that the Earth is not an inertial frame of reference because it rotates around its axis. However, nobody mentions the rotation about the Sun. What I ...
139 views
### Intuitive explanation for the Lorentz transformation for time
I've recently started learning SR, and while the Lorentz transformation for space is pretty obvious, just the Galilean transformation combined with space contraction, I can't figure out the ...
87 views
In special relativity, a four-vector $\mathbf{x}$ in an inertial frame is related to $\mathbf{\overline{x}}$ through a Lorentz transformation $\mathbf{\Lambda}$: \begin{align} \overline{\mathbf{x}}...
203 views
### Is Landau&Lifshitz's argument for the classical Lagrangian's symmetries too strict?
I realize that this paragraph has raised more questions on stackexchange, but I wanted to ask this question nevertheless since I want to discuss it in terms of a counter-example. I’ve already ...
89 views
### A concise definition of a frame of reference in Newtonian mechanics?
I've read Wikipedia's entry on frame of reference and also followed all of the references cited in the text (Salençon, Brillouin, Norton, etc) but I'm struggling to find any concise definition in all ...
67 views
### Sound wave and Principle of relativity
Principle of Relativity: "An experimenter doing an experiment in an inertial frame of reference can never measure the velocity of its own frame of reference. OR a law of physics is never expressed ...
8k views
### Is temperature a Lorentz invariant in relativity?
If an observer starts moving at relativistic speeds will he observe the temperature of objects to change as compared to their rest temperatures? Suppose the rest temperature measured is $T$ and the ...
34 views
### Validity of Newton's second law in a non-inertial reference frame
Suppose two observers are mutually interact through gravitational force (assuming they are alone at space). If the reference frame is fixed in one of the observers could the observer in the reference ...
745 views
### What is the Galilean transformation of the EM field?
Consider a reference frame $S$ and which we observe some electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$. Let $S'$ be a reference frame moving at a constant velocity $\mathbf{u}$ with ...
72 views
### Motivation for the abandonment of inertial frames in general relativity [closed]
Inertial frames are at the core of special relativity. The laws of physics are supposed to be the same among them and free particles follow rectilinear paths in spacetime or simply stay at rest. Just ...
122 views
### Relative velocity equation [on hold]
In rectilinear motion, to find the relative velocity of a car with respect to a train, we subtract velocity of the train from that of the car. We use this method when the car is moving on the road. ...
92 views
29 views
### Colliding elastically in lab and CM frame
Two spherical bodies of mass $m_1$ and $m_2$ are placed in gravity free space as shown. Initially, the body with mass $m_2$ is at rest and the body with mass $m_1$ approaches the other body with a ...
125 views
### Properties of inertial reference frames from different perspectives
I was thinking about the following, a block on an inclined plane no friction. However this inclined plane is in a truck accelerating forward. Note: the inclined plane doesn't slip. So I wondered what ...
22 views
### Example of anisotropy frame of reference
I have studied that an inertial frame of reference is the one that is homogeneous, isotropic and time-independent. For instance, a reference frame on a rotating wheel is not an inertial frame of ...
209 views
### Clarification of proper time and inertial frame of reference
“Standing beside railroad tracks, we are suddenly startled by a relativistic boxcar traveling past us as shown in the figure. Inside, a well-equipped hobo fires a laser pulse from the front of the ...
27 views
### Exact difference between '''Fermi normal coordinates''' and ''Riemann normal coordinates'''? [duplicate]
I want to know the exact difference between '''Fermi normal coordinates''' and ''Riemann normal coordinates'''? Here is a same question, but it's hard for me to understand. Difference between Fermi ...
271 views
### Heisenberg uncertainty and Lorentz contraction
Consider a particle in a frame moving with speed $v$ relative to the lab frame. By Lorentz contraction, the width of the wavefunction will be smaller in the lab frame, resulting in smaller $\Delta x$. ...
264 views
This is a thought experiment I created myself. Imagine two radio sources fixed at the ends of a rocket and they produce signal of same frequency such that they arrive at the center simultaneously and ...
68 views
### What do you mean by Newtonian space? [closed]
What do you mean by Newtonian space? When you see this question, most of you might be thinking that I am trying to crack a joke or something..but no. This was a genuine doubt which one of my friends ...
79 views
### Why can't we take space as universal frame of reference?
Suppose we have a ball filled half with water in space with nothing else around (nothing else in the whole space except the ball) and suddenly it accelerates for time t. obviously, there would be ...
336 views
### Does the derivation of the Lorentz transformation depend on space having at least two spatial dimensions?
Eisberg's 'Fundamentals of Modern Physics' derives the space contraction formula from a mirror experiment in which A reflects a light beam in a direction perpendicular to the motion of B, both ...
182 views
### What is the relativistic Hamiltonian for a charged particle in an EM field, using the magnetic scalar potential?
The Hamiltonian for a relativistic charged particle moving in a static electromagnetic field is the well known: $$H=c\sqrt{\left(\mathbf{P}-q\mathbf{A}\right)^{2}+m^{2}c^{2}}+q\phi$$ where,\begin{...
287 views
### Is it possible writing conservation of relativistic energy in this naive way?
Conservation of charge or rest mass can be written in this way and it is Lorentz invariant $$\nabla \cdot (\rho \mathbf{u}) + \frac{\partial \rho}{\partial t} = 0$$ So we could be tempted to naively ...
63 views
### On local inertial frame and acceleration in general relativity
[Q1] In the general relativity, a local inertial frame is mentioned. The local inertial frame is a notion, which is related to (or represents) the equivalent principle. Here, I understand that, in ...
46 views
### Difficulty in understanding why a car slips towards outside as seen from inertial frame
While turning on a road, why does a car slip towards outside, if we are observing the car from inertial frame of reference, i.e center?
161 views
### How can we find velocity, acceleration etc, of a revolving particle with respect to an observer inside the circle(not at center)
A particle is revolving in horizontal a circle of radius $R$ with constant speed of $|\vec{v}|$ and constant angular velocity $\omega$. There is another observer standing inside the circle, at a ...
191 views
### Special Relativity pothole paradox [duplicate]
Consider a man who is 1 metre in width and is running (at relativistic speeds) towards a pothole in the ground which is also 1 meter in width. In the reference frame of the man it appears as though ...
292 views
### In Special Relativity, is it allowed to ask 'How much time has elapsed in a second inertial frame at a particular moment in the first inertial frame'?
Or is it a meaningless question? For example, A and his friend B are the same age initially. B travels relative to A at a very high speed. A keeps observing B from his frame. At one moment, A ...
99 views
### To prove: the integration measure is Lorentz invariant (Schwartz's problem 2.6b)
I am stuck on Schwartz's ("Quantum Field Theory and the Standard Model") problem 2.6b, and would be grateful for clarification. (I'm aware that this question has been asked and answered elsewhere (...
78 views
Say two spaceships start at the same point and from the vantage point of your inertial reference frame $S$, Spaceship A travels at $.75c$ and Spaceship B travels at $.25c$, travelling in the same ...
70 views
### Isn't inertia experience by person in moving bus same as torque
When a bus moves suddenly, the person standing in it tilts backwards. This concept is explained using inertia(tendency of body to resist change in its state of motion) but when the bus moves suddenly, ...
444 views
### How to prove a 4D vector is a 4-Vector?
This is a fairly open ended question. Given a set of 4 Components, that is, a 4D Vector, what is the process for determining rather or not it is a "4-Vector" as defined in special relativity? I want ...
61 views
### Special Relativity - Reference Frames $S$ and $S'$
Consider the standard arrangement in special relativity. Let S' move in the +ve x-axis with a velocity V with respect to S Question: S then moves with a velocity -V with respect to S'. Is this an ...
2k views
### How to prove the constant speed of light using Lorentz transform?
I read the light-clock example in my book which proved the time dilation formula by assuming that the speed of light is constant for all observers. But I've trouble in understanding it the other way ...
204 views
### Special Relativity- Lorentz transformation
We know that in lorentz transformation , x'= lorentz factor*(x-vt) Suppose, that in unprimed frame , x=0 ; and the primed frame moves with velocity c wrt unprimed one. Then accor to the transformation,...
102 views
### Accelerated frame vs gravity frame
Can accelerated frame change curvature of space as gravity does? Can there accelerated frame be pure inertial frame?
53 views
### Lagrangian of free particle in non-inertial frame
As in Landau & Lifshitz 1st chapter "If an inertial frame К is moving with an infinitesimal velocity e relative to another inertial frame K', then v' = v+e. Since the equations of motion must ...
48 views
### What is the relativistic energy of a bounded static particle?
Premise: The speed of light is set $c = 1$. Let's consider an electron in an external electromagnetic field. Its four-momentum will be $$p^{\mu} = (E, \bar p) = (\gamma m_e, \gamma m_e \bar v),$$ ...
242 views
### Does Sagnac effect imply anisotropy of speed of light in this inertial frame of reference?
There seems to be a consensus that the one - way speed of light is anisotropic in a rotating frame of reference (Sagnac Effect). According to this article Einstein synchronization "looks this ...
988 views
### Prove no contraction in the orthogonal directions
When talking about relativity, we always mention Lorentz contraction. If a body is moving with velocituy $V$ in the $x$ direction, its length will be contracted in that direction. The length remains ... | 2,907 | 12,774 | {"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} | 3.40625 | 3 | CC-MAIN-2019-30 | latest | en | 0.920078 |
https://netlib.org/lapack/explore-html-3.3.1/d1/d7e/sorgtr_8f_source.html | 1,670,407,425,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00426.warc.gz | 441,229,890 | 5,442 | LAPACK 3.3.1 Linear Algebra PACKage
# sorgtr.f
Go to the documentation of this file.
```00001 SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
00002 *
00003 * -- LAPACK routine (version 3.2) --
00004 * -- LAPACK is a software package provided by Univ. of Tennessee, --
00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 * November 2006
00007 *
00008 * .. Scalar Arguments ..
00009 CHARACTER UPLO
00010 INTEGER INFO, LDA, LWORK, N
00011 * ..
00012 * .. Array Arguments ..
00013 REAL A( LDA, * ), TAU( * ), WORK( * )
00014 * ..
00015 *
00016 * Purpose
00017 * =======
00018 *
00019 * SORGTR generates a real orthogonal matrix Q which is defined as the
00020 * product of n-1 elementary reflectors of order N, as returned by
00021 * SSYTRD:
00022 *
00023 * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
00024 *
00025 * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
00026 *
00027 * Arguments
00028 * =========
00029 *
00030 * UPLO (input) CHARACTER*1
00031 * = 'U': Upper triangle of A contains elementary reflectors
00032 * from SSYTRD;
00033 * = 'L': Lower triangle of A contains elementary reflectors
00034 * from SSYTRD.
00035 *
00036 * N (input) INTEGER
00037 * The order of the matrix Q. N >= 0.
00038 *
00039 * A (input/output) REAL array, dimension (LDA,N)
00040 * On entry, the vectors which define the elementary reflectors,
00041 * as returned by SSYTRD.
00042 * On exit, the N-by-N orthogonal matrix Q.
00043 *
00044 * LDA (input) INTEGER
00045 * The leading dimension of the array A. LDA >= max(1,N).
00046 *
00047 * TAU (input) REAL array, dimension (N-1)
00048 * TAU(i) must contain the scalar factor of the elementary
00049 * reflector H(i), as returned by SSYTRD.
00050 *
00051 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
00052 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00053 *
00054 * LWORK (input) INTEGER
00055 * The dimension of the array WORK. LWORK >= max(1,N-1).
00056 * For optimum performance LWORK >= (N-1)*NB, where NB is
00057 * the optimal blocksize.
00058 *
00059 * If LWORK = -1, then a workspace query is assumed; the routine
00060 * only calculates the optimal size of the WORK array, returns
00061 * this value as the first entry of the WORK array, and no error
00062 * message related to LWORK is issued by XERBLA.
00063 *
00064 * INFO (output) INTEGER
00065 * = 0: successful exit
00066 * < 0: if INFO = -i, the i-th argument had an illegal value
00067 *
00068 * =====================================================================
00069 *
00070 * .. Parameters ..
00071 REAL ZERO, ONE
00072 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00073 * ..
00074 * .. Local Scalars ..
00075 LOGICAL LQUERY, UPPER
00076 INTEGER I, IINFO, J, LWKOPT, NB
00077 * ..
00078 * .. External Functions ..
00079 LOGICAL LSAME
00080 INTEGER ILAENV
00081 EXTERNAL ILAENV, LSAME
00082 * ..
00083 * .. External Subroutines ..
00084 EXTERNAL SORGQL, SORGQR, XERBLA
00085 * ..
00086 * .. Intrinsic Functions ..
00087 INTRINSIC MAX
00088 * ..
00089 * .. Executable Statements ..
00090 *
00091 * Test the input arguments
00092 *
00093 INFO = 0
00094 LQUERY = ( LWORK.EQ.-1 )
00095 UPPER = LSAME( UPLO, 'U' )
00096 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00097 INFO = -1
00098 ELSE IF( N.LT.0 ) THEN
00099 INFO = -2
00100 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00101 INFO = -4
00102 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
00103 INFO = -7
00104 END IF
00105 *
00106 IF( INFO.EQ.0 ) THEN
00107 IF ( UPPER ) THEN
00108 NB = ILAENV( 1, 'SORGQL', ' ', N-1, N-1, N-1, -1 )
00109 ELSE
00110 NB = ILAENV( 1, 'SORGQR', ' ', N-1, N-1, N-1, -1 )
00111 END IF
00112 LWKOPT = MAX( 1, N-1 )*NB
00113 WORK( 1 ) = LWKOPT
00114 END IF
00115 *
00116 IF( INFO.NE.0 ) THEN
00117 CALL XERBLA( 'SORGTR', -INFO )
00118 RETURN
00119 ELSE IF( LQUERY ) THEN
00120 RETURN
00121 END IF
00122 *
00123 * Quick return if possible
00124 *
00125 IF( N.EQ.0 ) THEN
00126 WORK( 1 ) = 1
00127 RETURN
00128 END IF
00129 *
00130 IF( UPPER ) THEN
00131 *
00132 * Q was determined by a call to SSYTRD with UPLO = 'U'
00133 *
00134 * Shift the vectors which define the elementary reflectors one
00135 * column to the left, and set the last row and column of Q to
00136 * those of the unit matrix
00137 *
00138 DO 20 J = 1, N - 1
00139 DO 10 I = 1, J - 1
00140 A( I, J ) = A( I, J+1 )
00141 10 CONTINUE
00142 A( N, J ) = ZERO
00143 20 CONTINUE
00144 DO 30 I = 1, N - 1
00145 A( I, N ) = ZERO
00146 30 CONTINUE
00147 A( N, N ) = ONE
00148 *
00149 * Generate Q(1:n-1,1:n-1)
00150 *
00151 CALL SORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
00152 *
00153 ELSE
00154 *
00155 * Q was determined by a call to SSYTRD with UPLO = 'L'.
00156 *
00157 * Shift the vectors which define the elementary reflectors one
00158 * column to the right, and set the first row and column of Q to
00159 * those of the unit matrix
00160 *
00161 DO 50 J = N, 2, -1
00162 A( 1, J ) = ZERO
00163 DO 40 I = J + 1, N
00164 A( I, J ) = A( I, J-1 )
00165 40 CONTINUE
00166 50 CONTINUE
00167 A( 1, 1 ) = ONE
00168 DO 60 I = 2, N
00169 A( I, 1 ) = ZERO
00170 60 CONTINUE
00171 IF( N.GT.1 ) THEN
00172 *
00173 * Generate Q(2:n,2:n)
00174 *
00175 CALL SORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
00176 \$ LWORK, IINFO )
00177 END IF
00178 END IF
00179 WORK( 1 ) = LWKOPT
00180 RETURN
00181 *
00182 * End of SORGTR
00183 *
00184 END
``` | 2,109 | 6,534 | {"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-2022-49 | latest | en | 0.414535 |
https://pastebin.com/FywkvJ0H | 1,544,968,977,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376827727.65/warc/CC-MAIN-20181216121406-20181216143406-00203.warc.gz | 712,943,266 | 8,894 | • API
• FAQ
• Tools
• Archive
A Pastebin account makes a great Christmas gift
SHARE
TWEET
# Quiz 3
a guest Oct 11th, 2018 247 Never
ENDING IN00days00hours00mins00secs
1. ---
2. layout: default
3. title: CSCI 2500 Quiz 3
4. description: CSCI 2500 Quiz 3
5. date: October 13, 2017
7. - \usepackage{listings}
8. - \lstset{basicstyle=\ttfamily}
9. ---
10.
11. ### NAME and RCS ID:\underline{\hspace{4.0in}}
12. ### YOUR EMAIL IS (RCS ID) @ RPI.EDU
13.
14. ### THIS QUIZ IS CLOSED BOOK, CLOSED NOTES, and NO CALCULATOR.
15. ### STAY AWAY FROM THE MARGINS AS THEY MAY GET TRIMMED OFF.
16.
17. \pagebreak
18.
19. # 1. MIPS Design Principles [15 points]
20.
21. Name three (and only three!) out of the four MIPS design principles.
22. For each principle indicate an example within the MIPS instruction set architecture of how it is used.
23.
24. 1. Simplicity favors regularity
25. 2. Smaller is faster
26. 3. Make the common case fast
27. Sisc vs risc
28. 4. Good design demands good compromises
29.
30. Layers of software/hardware
31. Compiler, assembler, hardware
32.
33. \pagebreak
34.
35. # 2. Matrix Indexing [25 points]
36.
37. ~~~
38. int** matrix = (int**)malloc(sizeof(int*) * 4);
39. for (int i = 0; i < 4; i++) {
40. matrix[i] = (int*)malloc(sizeof(int) * 4);
41. }
42. ~~~
43.
44. The above code is different than the way that matrices were supported in our homework.
45. There our memory was allocated in a 16-element one-dimensional array but we simulated a 4x4 array.
46. Given the approach above, how would we go about setting matrix[1][3] to 14?
47.
48. assume matrix[0] is in $s0 49. compute offset = 1 * 4 50. load i nto (la)$t1, ($s0) 51. add 4 * offset 52. compute offset2 = 3 * 4 53. load into$t2 = $t1 + offset 2 54. 55. \pagebreak 56. 57. # 3. MIPS Branches [25 points] 58. 59. ## 3.1 [10 points] 60. 61. Recall our discussion of MIPS branch instructions. 62. The code below is completely valid but may not always work. 63. Explain why. 64. **Hint: refer to the image below.** 65. 66. ~~~ 67. foo: 68. beq$t0, $t1, bar 69. add$t2, $t3,$t4
70. ...
71.
72. bar:
73. add $t5,$t6, $t7 74. ~~~ 75. if there are too many lines between foo and bar 76. if the distance is greater than the number of bits (16 from the immediate) 77. 78.  79. 80. \vspace{1.5in} 81. 82. ## 3.2 [15 points] 83. 84. How can you rewrite this code to prevent this problem? 85. foo: 86. beq$t0, $t1, half_bar 87. add$t2, $t3,$t4
88. ...
89. #after you run out of your 16 bits#
90. j foo_continue
91.
92. half_bar: j bar
93. foo_continue: do the rest of foo here
94. bar:
95. add $t5,$t6, $t7 96. \pagebreak 97. 98. # 4. Convert C to MIPS [35 points] 99. 100. From the man page: The strchr() function locates the first occurrence of c (converted to a 101. char) in the string pointed to by s. 102. The functions strchr() returns a pointer to the located character, or NULL if the character does not appear in the string. 103. Assume NULL = 0. 104. 105. Convert the following function from C to MIPS assembly. 106. It may be helpful to use basic blocks to outline your program (especially your loop). 107. You are allowed to use MIPS pseudo-instructions e.g., blt, bgt, etc. 108. Additionally, assume the array always has at least one element. 109. Per convention, s will be in $a0 and c will be in $a1. 110. Your return value should be placed in $v0.
111.
112. ~~~
113. char *mystrchr(char *s, int c) {
114. while (*s != (char) c) {
115. if (!*s++) {
116. return NULL;
117. }
118. }
119. return (char *)s;
120. }
121. ~~~
122.
123. \pagebreak
124. \centerline{\bf Extra space page. Please denote which problem you are answering here.}
RAW Paste Data
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy.
Top | 1,285 | 3,951 | {"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} | 2.84375 | 3 | CC-MAIN-2018-51 | longest | en | 0.644544 |
http://blog.unieagle.net/2012/10/18/leetcode%E9%A2%98%E7%9B%AE%EF%BC%9Areverse-integer/ | 1,516,447,216,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084889567.48/warc/CC-MAIN-20180120102905-20180120122905-00754.warc.gz | 48,359,537 | 24,383 | # LeetCode题目：Reverse Integer
Reverse Integer
Reverse digits of an integer.
Example1: x = 123, return 321
Example2: x = -123, return -321
Here are some good questions to ask before coding. Bonus points for you if you have already thought through this!
If the integer’s last digit is 0, what should the output be? ie, cases such as 10, 100.
Did you notice that the reversed integer might overflow? Assume the input is a 32-bit integer, then the reverse of 1000000003 overflows. How should you handle such cases?
Throw an exception? Good, but what if throwing an exception is not an option? You would then have to re-design the function (ie, add an extra parameter).
```class Solution {
public:
int reverse(int x) {
int sup = 1;
{//find the most significant bit
int temp = x;
while(temp /= 10) {
sup *= 10;
}
}
int sub = 10;
int y = 0;//result
while(sup >= sub) {
int dsup = x / sup;
int dsub = (x % sub) / (sub / 10);
//cout<<dsup<<","<<dsub<<",";
x -= sup * dsup;
x -= (sub / 10) * dsub;
//cout<<x<<"|";
y += sup * dsub;
y += (sub / 10) * dsup;
sup /= 10;
sub *= 10;
}
if (sup * 10 == sub) {
y += x;
}
return y;
}
};
``` | 344 | 1,122 | {"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-2018-05 | longest | en | 0.66411 |
http://mathoverflow.net/questions/74450/proper-action-and-amenable-action?sort=oldest | 1,469,308,891,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257823670.44/warc/CC-MAIN-20160723071023-00191-ip-10-185-27-174.ec2.internal.warc.gz | 159,989,064 | 15,079 | # proper action and amenable action
We say that an action of a (discrete) group G on a locally compact space X is called proper if the map from $G\times X$ to $X\times X$ defined by $(g,x)\mapsto (gx,x)$ is proper. Why is a proper action amenable? (see On the Baum-Connes assembly map for discrete groups-Alain Valette, proof of lemma 2.13). If this is a case, the full crossed product and reduced product for $C_0(X)$ are isomorphic.
-
In Prop. 2.2, point (2), you find an equivalent condition for amenability of the $G$-action on $X$, in terms of the existence of a net $(g_i)$ of continuous, non-negative functions on $X\times G$. Now, if $X$ is a proper $G$-space, you find a Bruhat function on $X$, i.e. a continuous non-negative function $h$ on $X$ such that $\sum_{t\in G}h(t^{-1}x)=1$. Define then $g_i(x,t)=h(t^{-1}x)$. If I'm not mistaken, the conditions in Anantharaman's result are satisfied.
About the converse: if $G$ is amenable and infinite, the action of $G$ on a point is amenable but not proper. – Alain Valette Sep 3 '11 at 22:19 | 316 | 1,052 | {"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} | 2.515625 | 3 | CC-MAIN-2016-30 | latest | en | 0.798644 |
https://math.answers.com/questions/What_is_the_square_root_of_16_added_by_the_square_root_of_25 | 1,701,452,073,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100290.24/warc/CC-MAIN-20231201151933-20231201181933-00553.warc.gz | 428,826,603 | 46,409 | 0
# What is the square root of 16 added by the square root of 25?
Updated: 12/9/2022
Wiki User
9y ago
41
Annamarie Trantow
Lvl 10
2y ago
Wiki User
9y ago
The square root of 16 added by the square root of 25 is 9
Anonymous
Lvl 1
3y ago
You are correct Sep done
Anonymous
Lvl 1
3y ago
√25+√16=9 | 116 | 307 | {"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-2023-50 | latest | en | 0.901419 |
https://www.splashlearn.com/math/skip-counting-games-for-3rd-graders | 1,723,595,555,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641086966.85/warc/CC-MAIN-20240813235205-20240814025205-00667.warc.gz | 785,353,746 | 27,577 | Filter
• Skip Count By 2
##### Find Facts of 2 Game
Take a deep dive into the world of math by finding facts of 2.
1 2 3 3.OA.7
VIEW DETAILS
• Skip Count By 5
##### Find Facts of 5 Game
Kids must find facts of 5 to practice times tables.
1 2 3 3.OA.7
VIEW DETAILS
• Skip Count By 10
##### Complete the Pattern of Tens Game
Dive deep into the world of addition by completing the pattern of tens.
1 2 3 1.NBT.5
VIEW DETAILS
• Skip Count By 100
##### Count by 100s Game
Use your counting skills to count by 100s.
2 3 2.NBT.2
VIEW DETAILS
• Skip Count By 10
##### Count by Tens Game
Unearth the wisdom of mathematics by learning how to count by tens.
1 2 3 1.NBT.5
VIEW DETAILS
• Skip Count By 100
##### Completing the Skip Count Game
Practice the superpower of counting by completing the skip count.
2 3 2.NBT.2
VIEW DETAILS
• Skip Count By 10
##### Count Forward by 10s Game
Take the first step towards building your math castle by practicing how to count forward by 10s.
2 3 2.NBT.8
VIEW DETAILS
• Skip Count By 100
##### Applications of Skip Counting Game
Apply your knowledge of counting to practice applications of skip counting.
2 3 2.NBT.2
VIEW DETAILS
• Skip Count By 10
##### Skip Count by 10s Starting from a Multiple of 10 Game
Practice the superpower of counting by learning to skip count by 10s starting from a multiple of 10.
2 3 2.NBT.2
VIEW DETAILS
• Skip Counting
##### Find Facts of 4 Game
Add more arrows to your child’s math quiver by helping them find facts of 4.
2 3 3.OA.7
VIEW DETAILS
• Skip Counting
##### Find Facts of 6 Game
Begin the exciting journey of becoming a math wizard by learning how to find the facts of 6.
2 3 3.OA.7
VIEW DETAILS
• Skip Counting
##### Find Facts of 9 Game
Use your knowledge of times tables to find the facts of 9.
2 3 3.OA.7
VIEW DETAILS
• Skip Counting
##### Find Facts of 3 Game
Have your own math-themed party by learning to find facts of 3.
2 3 3.OA.7
VIEW DETAILS
// | 582 | 1,953 | {"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} | 3.296875 | 3 | CC-MAIN-2024-33 | latest | en | 0.862952 |
https://ir.lib.nycu.edu.tw/handle/11536/140936 | 1,714,033,856,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712297290384.96/warc/CC-MAIN-20240425063334-20240425093334-00876.warc.gz | 291,305,898 | 9,333 | 標題: M/G/2/3的系統服務分配及機率的數值解The Numerical Solution of Density Function and Stationary Probability in Steady State of M/G/2/3 作者: 顏天保彭南夫Yen, Tian-BaoPeng, Nan-Fu統計學研究所 關鍵字: M/G/2/3;M/G/C/K;穩定機率;已服務時間密度函數;平衡方程式;M/G/2/3;M/G/C/K;Stationary probability;The density function of the time which has been served;Balance equations 公開日期: 2017 摘要: 藉由研究M/G/2/3服務系統的子密度分配(sub - density)， \$f_1(s)\$、\$f_2(s,t)\$、\$f_3(s,t)\$，分別代表系統在穩定狀態時系統有1、2、3人並且服務員已服務時間為s、(s,t)、(s,t)的密度函數，能較有效的求系統的穩定機率及其他特殊值。在這篇研究中我們找到M/M/2/3密度函數的解析解，和M/G/2/3的數值解以及近似解，其中近似解可表現為三個已知函數的線性組合，並且有不錯的效率和近似。之後我們試著將演算法推廣至M/G/2/K，並討論M/G/C/K計算上的可能方法。這篇論文的架構如下，第一章回顧相似的文獻並介紹這篇研究所使用的方法，第二章中探討M/M/2/3的情況，以矩陣運算的方式得到系統的密度函數及機率，第三章中探討M/G/2/3的情況，並列出數值演算法和近似演算法，第四章中列出實驗結果，第五章將演算法推廣至M/G/2/K並討論M/G/C/K的情況，第六章是結論。By studying the sub-density of the M/G/2/3 queuing system,\$f_1(s)\$、\$f_2(s,t)\$、\$f_3(s,t)\$,which respectively stand for the density function of the system in a steady state when the system has 1,2,3 people and they are has been serving for s, (s ,t), (s, t) unit of time, we can find the density function of the system and other special values (e.g.stationary probability). In this study, we find the analytical solution of the M/M/2/3, the numerical solution and the approximate solution of M/G/2/3 where the approximate solution can be expressed as the linear combination of several known functions and have good efficiency and approximation. We then try to extend the algorithm to M/G/2 /K and discuss possible approaches to M/G/C/K calculations. The structure of this paper is as follows. In the first chapter, we review the similar literature and introduce the method used in this study. In chapter 2, we discuss the situation of M/M/2/3, and solve the density function and the stationary probability. The third chapter to explore the M/G/2/3 situation, and lists the numerical algorithm and approximate algorithm. The fourth chapter lists the experimental results. The fifth chapter will be extended to M/G/2/K and discuss the case of M/G/C/K. In the end, the chapter sixth is the conclusion. URI: http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070452623http://hdl.handle.net/11536/140936 Appears in Collections: Thesis | 833 | 2,180 | {"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} | 3.328125 | 3 | CC-MAIN-2024-18 | latest | en | 0.534114 |
https://de.zxc.wiki/wiki/Kumulante | 1,670,495,060,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711286.17/warc/CC-MAIN-20221208082315-20221208112315-00290.warc.gz | 231,680,866 | 31,402 | # Cumulative
In probability theory and statistics, cumulants are parameters of the distribution of a random variable which, with regard to the summation of stochastically independent random variables, satisfy simple arithmetic laws. The sequence of cumulants begins with the expected value and the variance .
## definition
Is the moment generating function of the random variable , i. h., it is ${\ displaystyle M_ {X} (t)}$${\ displaystyle X}$
${\ displaystyle M_ {X} (t) = E (e ^ {tX}) \,}$,
that's the name of the function
${\ displaystyle g_ {X} (t) = \ ln M_ {X} (t) = \ ln E (e ^ {tX})}$
Cumulant generating function . The -th cumulant of the distribution of is then defined by ${\ displaystyle n}$ ${\ displaystyle \ kappa _ {n}}$${\ displaystyle X}$
${\ displaystyle \ kappa _ {n} = {\ frac {\ partial ^ {n}} {\ partial t ^ {n}}} g_ {X} (t) {\ bigg |} _ {t = 0}}$.
Alternatively, cumulants can also be defined by the characteristic function of a random variable . ${\ displaystyle G_ {X} (t) = E (e ^ {itX})}$${\ displaystyle X}$
The -th cumulant is then defined by ${\ displaystyle n}$${\ displaystyle \ kappa _ {n}}$
${\ displaystyle \ kappa _ {n} = {\ frac {1} {i ^ {n}}} {\ frac {\ partial ^ {n}} {\ partial t ^ {n}}} \ ln G_ {X } (t) {\ bigg |} _ {t = 0}}$
## properties
### Displacement invariance
The cumulants are also referred to as semi-invariants of the density function because, with the exception of , they do not change when the expected value is shifted. Let it be a random variable, then for any constant : ${\ displaystyle p (x)}$${\ displaystyle \ kappa _ {1}}$${\ displaystyle X}$${\ displaystyle c \ in \ mathbb {R}}$
${\ displaystyle \ kappa _ {1} (X + c) = \ kappa _ {1} (X) + c \,}$
${\ displaystyle \ kappa _ {n} (X + c) = \ kappa _ {n} (X) ~ {\ text {with}} ~ n \ geq 2 \,}$
### homogeneity
The -th cumulant is homogeneous in degree , be any constant, then: ${\ displaystyle n}$${\ displaystyle n}$${\ displaystyle c}$
${\ displaystyle \ kappa _ {n} (cX) = c ^ {n} \ kappa _ {n} (X) \,}$
Let and be stochastically independent random variables, then holds for${\ displaystyle X_ {1}}$${\ displaystyle X_ {2}}$ ${\ displaystyle Y = X_ {1} + X_ {2}}$
${\ displaystyle \ kappa _ {n} (Y) = \ kappa _ {n} (X_ {1}) + \ kappa _ {n} (X_ {2}) \,}$
For independent random variables, the characteristic function is a product and thus the logarithm is a sum: ${\ displaystyle G_ {Y} (k) = G_ {X_ {1}} (k) \ cdot G_ {X_ {2}} (k)}$
${\ displaystyle \ ln G_ {Y} (t) = \ ln G_ {X_ {1}} (t) + \ ln G_ {X_ {2}} (t) = \ sum _ {n = 1} ^ {\ infty} {\ frac {(\ mathrm {i} t) ^ {n}} {n!}} \ left [\ kappa _ {n} (X_ {1}) + \ kappa _ {n} (X_ {2 }) \ right] = \ sum _ {n = 1} ^ {\ infty} {\ frac {(\ mathrm {i} t) ^ {n}} {n!}} \ kappa _ {n} (Y) }$
The following applies to the sum of stochastically independent random variables : ${\ displaystyle Y = \ sum _ {i = 1} ^ {N} X_ {i}}$${\ displaystyle N}$${\ displaystyle X_ {1}, X_ {2}, \ dotsc, X_ {N}}$
${\ displaystyle \ kappa _ {n} (Y) = \ sum _ {i = 1} ^ {N} \ kappa _ {n} (X_ {i}) \,}$
### Peculiarity of the normal distribution
For a normal distribution with expected value and variance , the characteristic function is the same and thus the cumulants: ${\ displaystyle \ mu}$${\ displaystyle \ sigma ^ {2}}$${\ displaystyle G (t) = \ exp (\ mathrm {i} \ mu t- \ sigma ^ {2} t ^ {2} / 2)}$
${\ displaystyle \ kappa _ {1} = \ mu; \ quad \ kappa _ {2} = \ sigma ^ {2}; \ quad \ kappa _ {n} = 0}$for .${\ displaystyle n \ geq 3}$
All accumulants greater than the 2nd order disappear. This property characterizes the normal distribution.
You can show that
• either all accumulators except the first two disappear
• or an infinite number of non-vanishing accumulants exist.
In other words: The cumulant generating function cannot be a finite polynomial of degree greater than 2. ${\ displaystyle \ ln G (k)}$
## Cumulants and Moments
### Cumulants as a function of the moments
Denote the nth moment of a random variable . Through can be represented as ${\ displaystyle m_ {n}}$${\ displaystyle X}$${\ displaystyle G (k)}$${\ displaystyle m_ {n}}$
${\ displaystyle m_ {n} = {\ frac {1} {i ^ {n}}} {\ frac {\ partial ^ {n}} {\ partial t ^ {n}}} G (t) {\ bigg |} _ {t = 0}}$
Consequently, the cumulants can be expressed by the moments or as follows: ${\ displaystyle m_ {n}}$
${\ displaystyle \ kappa _ {1} = m_ {1} \,}$
${\ displaystyle \ kappa _ {2} = m_ {2} -m_ {1} ^ {2} \,}$
${\ displaystyle \ kappa _ {3} = m_ {3} -3m_ {2} m_ {1} + 2m_ {1} ^ {3} \,}$
${\ displaystyle \ kappa _ {4} = m_ {4} -4m_ {3} m_ {1} -3m_ {2} ^ {2} + 12m_ {2} m_ {1} ^ {2} -6m_ {1} ^ {4} \,}$
${\ displaystyle \ kappa _ {5} = m_ {5} + 5m_ {1} (6m_ {2} ^ {2} -m_ {4}) - 10m_ {3} m_ {2} + 20m_ {3} m_ { 1} ^ {2} -60m_ {2} m_ {1} ^ {3} + 24m_ {1} ^ {5} \,}$
In general, the dependence of the cumulants on the moments can be described by the following recursion formula:
${\ displaystyle \ kappa _ {n} = m_ {n} - \ sum _ {k = 1} ^ {n-1} {n-1 \ choose k-1} \ kappa _ {k} m_ {nk}}$
Alternatively, the kth cumulant can be represented from Faà di Bruno's formula using the Bell polynomials and the moments as ${\ displaystyle B_ {n, k}}$${\ displaystyle m_ {1}, \ dots, m_ {n}}$
${\ displaystyle \ kappa _ {n} = \ sum _ {k = 1} ^ {n} (k-1)! (- 1) ^ {k + 1} B_ {n, k} (m_ {1}, \ dots, m_ {n-k + 1})}$.
With the central moments , the formulas are usually shorter: ${\ displaystyle \ mu _ {n}}$
${\ displaystyle \ kappa _ {1} = m_ {1} \,}$
${\ displaystyle \ kappa _ {2} = \ mu _ {2} \,}$
${\ displaystyle \ kappa _ {3} = \ mu _ {3} \,}$
${\ displaystyle \ kappa _ {4} = \ mu _ {4} -3 \ mu _ {2} ^ {2} \,}$
${\ displaystyle \ kappa _ {5} = \ mu _ {5} -10 \ mu _ {3} \ mu _ {2} \,}$
${\ displaystyle \ kappa _ {6} = \ mu _ {6} -15 \ mu _ {4} \ mu _ {2} -10 \ mu _ {3} ^ {2} +30 \ mu _ {2} ^ {3} \,}$
The first two cumulants are of particular importance: is the expected value and is the variance . From the fourth order, the cumulative and central moment no longer coincide. ${\ displaystyle \ kappa _ {1}}$${\ displaystyle m_ {1} = E (X)}$${\ displaystyle \ kappa _ {2}}$ ${\ displaystyle \ mu _ {2} = V (X)}$
### Derivation of the first cumulants
To develop to${\ displaystyle \ ln G (t)}$${\ displaystyle G (t) = 1}$
${\ displaystyle \ ln G (t) = \ sum _ {n = 1} ^ {\ infty} (- 1) ^ {n + 1} {\ frac {(G (t) -1) ^ {n}} {n}} = (G (t) -1) - {\ frac {(G (t) -1) ^ {2}} {2}} + {\ frac {(G (t) -1) ^ { 3}} {3}} \ mp \ dotsb}$
and sets the series representation of ${\ displaystyle G (k)}$
${\ displaystyle G (t) = \ sum _ {n = 0} ^ {\ infty} {\ frac {(\ mathrm {i} t) ^ {n}} {n!}} m_ {n} = 1 + \ mathrm {i} tm_ {1} + {\ frac {(it) ^ {2}} {2}} m_ {2} + {\ frac {(it) ^ {3}} {6}} m_ {3 } + \ dotsb}$
in the above development
{\ displaystyle {\ begin {aligned} \ ln G (t) = & \ left [\ mathrm {i} tm_ {1} + {\ frac {(it) ^ {2}} {2}} m_ {2} + {\ frac {(it) ^ {3}} {6}} m_ {3} + \ dotsb \ right] \\ & - {\ frac {1} {2}} \ left [\ mathrm {i} tm_ {1} + {\ frac {(it) ^ {2}} {2}} m_ {2} + \ dotsb \ right] ^ {2} \\ & + {\ frac {1} {3}} \ left [\ mathrm {i} tm_ {1} + {\ frac {(it) ^ {2}} {2}} m_ {2} + \ dotsb \ right] ^ {3} \ mp \ dotsb \\ = & \ left [\ mathrm {i} tm_ {1} + {\ frac {(it) ^ {2}} {2}} m_ {2} + {\ frac {(it) ^ {3}} {6}} m_ {3} + \ dotsb \ right] \\ & - {\ frac {1} {2}} \ left [(\ mathrm {i} t) ^ {2} m_ {1} ^ {2} +2 {\ frac {(it) ^ {3}} {2}} m_ {1} m_ {2} + {\ frac {(it) ^ {4}} {4}} m_ {2} ^ {2} + \ dotsb \ right] \\ & + {\ frac {1} {3}} \ left [(\ mathrm {i} t) ^ {3} m_ {1} ^ {3} +2 {\ frac {(it) ^ {4}} {2}} m_ {1} ^ {2} m_ {2} +2 {\ frac {(it) ^ {5}} {4}} m_ {1} m_ {2} ^ {2} + {\ frac {(it) ^ {6}} {8}} m_ {2} ^ {3} + \ dotsb \ right] \ mp \ dotsb \ end {aligned}}}
If you sort according to powers of , you get the cumulants: ${\ displaystyle t}$
${\ displaystyle \ ln G (t) = \ mathrm {i} t \ underbrace {\ left [m_ {1} \ right]} _ {\ kappa _ {1}} + {\ frac {(it) ^ {2 }} {2}} \ underbrace {\ left [m_ {2} -m_ {1} ^ {2} \ right]} _ {\ kappa _ {2}} + {\ frac {(it) ^ {3} } {6}} \ underbrace {\ left [m_ {3} -3m_ {1} m_ {2} + 2m_ {1} ^ {3} \ right]} _ {\ kappa _ {3}} + \ dotsb}$
### Moments as a function of the cumulants
The -th moment is a -th degree polynomial of the first cumulants. Here are the first six moments: ${\ displaystyle n}$${\ displaystyle n}$${\ displaystyle n}$
${\ displaystyle m_ {1} = \ kappa _ {1} \,}$
${\ displaystyle m_ {2} = \ kappa _ {2} + \ kappa _ {1} ^ {2} \,}$
${\ displaystyle m_ {3} = \ kappa _ {3} +3 \ kappa _ {2} \ kappa _ {1} + \ kappa _ {1} ^ {3} \,}$
${\ displaystyle m_ {4} = \ kappa _ {4} +4 \ kappa _ {3} \ kappa _ {1} +3 \ kappa _ {2} ^ {2} +6 \ kappa _ {2} \ kappa _ {1} ^ {2} + \ kappa _ {1} ^ {4} \,}$
${\ displaystyle m_ {5} = \ kappa _ {5} +5 \ kappa _ {4} \ kappa _ {1} +10 \ kappa _ {3} \ kappa _ {2} +10 \ kappa _ {3} \ kappa _ {1} ^ {2} +15 \ kappa _ {2} ^ {2} \ kappa _ {1} +10 \ kappa _ {2} \ kappa _ {1} ^ {3} + \ kappa _ {1} ^ {5} \,}$
${\ displaystyle m_ {6} = \ kappa _ {6} +6 \ kappa _ {5} \ kappa _ {1} +15 \ kappa _ {4} \ kappa _ {2} +15 \ kappa _ {4} \ kappa _ {1} ^ {2} +10 \ kappa _ {3} ^ {2} +60 \ kappa _ {3} \ kappa _ {2} \ kappa _ {1} +20 \ kappa _ {3} \ kappa _ {1} ^ {3} +15 \ kappa _ {2} ^ {3} +45 \ kappa _ {2} ^ {2} \ kappa _ {1} ^ {2} +15 \ kappa _ { 2} \ kappa _ {1} ^ {4} + \ kappa _ {1} ^ {6}. \,}$
The coefficients correspond exactly to those in Faà di Bruno's formula . More generally, the -th moment is exactly the -th complete Bell polynomial , evaluated at the points : ${\ displaystyle n}$${\ displaystyle n}$ ${\ displaystyle B_ {n}}$${\ displaystyle \ kappa _ {1}, \ dots, \ kappa _ {n}}$
${\ displaystyle m_ {n} = B_ {n} (\ kappa _ {1}, \ dots, \ kappa _ {n})}$.
In order to express the central moments as a function of the cumulants, neglect all terms in the above polynomials for the moments which appear as a factor. ${\ displaystyle \ kappa _ {1}}$
${\ displaystyle \ mu _ {1} = 0 \,}$
${\ displaystyle \ mu _ {2} = \ kappa _ {2} \,}$
${\ displaystyle \ mu _ {3} = \ kappa _ {3} \,}$
${\ displaystyle \ mu _ {4} = \ kappa _ {4} +3 \ kappa _ {2} ^ {2} \,}$
${\ displaystyle \ mu _ {5} = \ kappa _ {5} +10 \ kappa _ {3} \ kappa _ {2} \,}$
${\ displaystyle \ mu _ {6} = \ kappa _ {6} +15 \ kappa _ {4} \ kappa _ {2} +10 \ kappa _ {3} ^ {2} +15 \ kappa _ {2} ^ {3}. \,}$
### Cumulants and volume partitions
Above we expressed the moments as polynomials in the cumulants. These polynomials have an interesting combinatorial interpretation: their coefficients count set partitions . The general form of these polynomials can be written as follows
${\ displaystyle m_ {n} = \ sum _ {\ pi \ in \ Pi} \ prod _ {B \ in \ pi} \ kappa _ {\ left | B \ right |}}$
in which
• ${\ displaystyle \ pi}$ traverses the set of all partitions of an n-element set;
• " " means that is one of the blocks into which the set was divided; and${\ displaystyle B \ in \ pi}$${\ displaystyle B}$
• ${\ displaystyle \ vert B \ vert}$is the size of the block .${\ displaystyle B}$
## Multivariate cumulants
The multivariate (or common ) cumulants of several random variables X 1 , ..., X n can also be defined by a cumulant-generating function:
${\ displaystyle K (t_ {1}, t_ {2}, \ dots, t_ {n}) = \ log E (\ mathrm {e} ^ {\ sum _ {j = 1} ^ {n} t_ {j } X_ {j}}).}$
This formula can again be interpreted in combinatorial form according to
${\ displaystyle \ kappa _ {n} (X_ {1}, \ dots, X_ {n}) = \ sum _ {\ pi} (| \ pi | -1)! (- 1) ^ {| \ pi | -1} \ prod _ {B \ in \ pi} E \ left (\ prod _ {i \ in B} X_ {i} \ right)}$
where runs through all partitions of {1, ..., n }, runs through the set of all blocks in the partition , and is the number of blocks in . For example we have ${\ displaystyle \ pi}$${\ displaystyle B}$${\ displaystyle \ pi}$${\ displaystyle \ vert \ pi \ vert}$${\ displaystyle \ pi}$
${\ displaystyle \ kappa _ {3} (X, Y, Z) = E (XYZ) -E (XY) E (Z) -E (XZ) E (Y) -E (YZ) E (X) + 2E (X) E (Y) E (Z). \,}$
This combinatorial relationship between cumulants and moments takes on a simpler form if one expresses moments in terms of cumulants:
${\ displaystyle E (X_ {1} \ cdots X_ {n}) = \ sum _ {\ pi} \ prod _ {B \ in \ pi} \ kappa (X_ {i}: i \ in B).}$
For example we then have:
${\ displaystyle E (XYZ) = \ kappa (X, Y, Z) + \ kappa (X, Y) \ kappa (Z) + \ kappa (X, Z) \ kappa (Y) + \ kappa (Y, Z ) \ kappa (X) + \ kappa (X) \ kappa (Y) \ kappa (Z). \,}$
The first cumulant of a random variable is its expected value, the common second cumulant of two random variables is their covariance . If some of the random variables are independent of each other, then any mixed cumulant which contains at least two of the independent variables vanishes. If all random variables are equal, the common cumulant is reduced to the usual nth cumulant of . ${\ displaystyle \ kappa _ {n} (X, \ dots, X)}$${\ displaystyle \ kappa _ {n}}$${\ displaystyle X}$
Another important property of the multivariate cumulants is multilinearity in the variables:
${\ displaystyle \ kappa _ {n} (X + Y, Z_ {1}, Z_ {2}, \ dots) = \ kappa _ {n} (X, Z_ {1}, Z_ {2}, \ dots) + \ kappa _ {n} (Y, Z_ {1}, Z_ {2}, \ dots). \,}$
## Inferences
The identically distributed and stochastically independent random variables are given . ${\ displaystyle X_ {1}, X_ {2}, \ dotsc, X_ {N}}$
### Central limit theorem
For the random variable
${\ displaystyle Y = {\ frac {1} {\ sqrt {N}}} (X_ {1} + X_ {2} + \ dotsb + X_ {N}) \,}$
Using the properties of homogeneity and additivity, the following cumulants result:
${\ displaystyle \ kappa _ {n} (Y) = {\ frac {1} {{\ sqrt {N}} ^ {n}}} \ sum _ {i = 1} ^ {N} \ kappa _ {n } (X_ {i}) \ approx {\ mathcal {O}} (N ^ {1-n / 2}) \,}$
The order arises because the sum over the individual accumulants is of the order . Here are the orders of the first cumulants: ${\ displaystyle \ sum _ {i = 1} ^ {N} \ kappa _ {n}}$${\ displaystyle {\ mathcal {O}} (N)}$
${\ displaystyle \ kappa _ {1} (Y) = {\ mathcal {O}} (N ^ {1/2}) \, \ quad \ kappa _ {2} (Y) = {\ mathcal {O}} (N ^ {0}) \, \ quad \ kappa _ {3} (Y) = {\ mathcal {O}} (N ^ {- 1/2}) \, \ quad \ kappa _ {4} (Y ) = {\ mathcal {O}} (N ^ {- 1})}$
For is the order to the power of a negative exponent and thus the limit of infinitely many random variables applies: ${\ displaystyle n \ geq 3}$${\ displaystyle N}$
${\ displaystyle \ lim _ {N \ to \ infty} \ kappa _ {n} (Y) = 0 \ quad {\ text {with}} \ quad n \ geq 3}$
I.e. only the first two cumulants remain. The only distribution that has only the first and second cumulants is the Gaussian distribution. This makes it plausible that the sum of any random variables divided by the square root of the number converges to the Gaussian distribution; this is the Central Limit Theorem . In order to complete this plausibility analysis to a proof, it is necessary to use general laws of characteristic functions . The Gaussian distribution thus has a special position among all distributions. If there are many stochastically independent influences in an experiment, then the totality of the influences can be represented by a Gaussian random variable.
As a simple special case, consider all random variables to be identical to mean value 0, variance and any higher moments. ${\ displaystyle X_ {i} = X}$${\ displaystyle \ sigma ^ {2}}$
${\ displaystyle \ kappa _ {1} (Y) = {\ frac {1} {\ sqrt {N}}} \ sum _ {i = 1} ^ {N} 0 = 0 \, \ quad \ kappa _ { 2} (Y) = {\ frac {1} {N}} \ sum _ {i = 1} ^ {N} \ sigma ^ {2} = \ sigma ^ {2} \, \ quad \ kappa _ {3 } (Y) = {\ frac {1} {{\ sqrt {N}} ^ {3}}} \ sum _ {i = 1} ^ {N} \ kappa _ {3} (X) = {\ frac {\ kappa _ {3} (X)} {\ sqrt {N}}} {\ underset {N \ to \ infty} {\ longrightarrow}} 0}$
For the random variable ${\ displaystyle Z}$
${\ displaystyle Z: = YE (Y) = {\ frac {1} {\ sqrt {N}}} (X_ {1} -E (X_ {1}) + X_ {2} -E (X_ {2} ) + \ dotsb + X_ {N} -E (X_ {N})) \,}$
one can use the displacement invariance of the cumulants of the order greater than or equal to 2. The only difference to the random variable is that the expected value is zero, even if the expected values of the do not disappear. ${\ displaystyle Y}$${\ displaystyle Y}$${\ displaystyle Z}$${\ displaystyle X_ {i}}$
{\ displaystyle {\ begin {aligned} \ kappa _ {1} (Z) & = {\ frac {1} {\ sqrt {N}}} \ sum _ {i = 1} ^ {N} \ underbrace {\ kappa _ {1} (X_ {i} -E (X_ {i}))} _ {E (X_ {i}) - E (X_ {i})} = 0 \\\ kappa _ {2} (Z ) & = {\ frac {1} {N}} \ sum _ {i = 1} ^ {N} \ kappa _ {2} (X_ {i} -E (X_ {i})) = {\ frac { 1} {N}} \ sum _ {i = 1} ^ {N} \ kappa _ {2} (X_ {i}) = \ kappa _ {2} (Y) = {\ frac {1} {N} } \ sum _ {i = 1} ^ {N} \ sigma _ {i} ^ {2} {\ overset {\ text {special case}} {\ underset {\ sigma _ {i} = \ sigma, \, \ forall i} {=}}} \ sigma ^ {2} \\\ kappa _ {3} (Z) & = {\ frac {1} {{\ sqrt {N}} ^ {3}}} \ sum _ {i = 1} ^ {N} \ kappa _ {3} (X_ {i} -E (X_ {i})) = {\ frac {1} {{\ sqrt {N}} ^ {3}}} \ sum _ {i = 1} ^ {N} \ kappa _ {3} (X_ {i}) = \ kappa _ {3} (Y) {\ underset {N \ to \ infty} {\ longrightarrow}} 0 \ end {aligned}}}
### Law of Large Numbers
For the random variable
${\ displaystyle Y = {\ frac {1} {N}} (X_ {1} + X_ {2} + \ dotsb + X_ {N}) \,}$
Using the properties of homogeneity and additivity, the following cumulants result:
${\ displaystyle \ kappa _ {n} (Y) = {\ frac {1} {N ^ {n}}} \ sum _ {i = 1} ^ {N} \ kappa _ {n} (X_ {i} ) \ approx {\ mathcal {O}} (N ^ {1-n}) \,}$
The order arises because the sum over the individual accumulants is of the order . Here are the orders of the first cumulants: ${\ displaystyle \ sum _ {i = 1} ^ {N} \ kappa _ {n}}$${\ displaystyle {\ mathcal {O}} (N)}$
${\ displaystyle \ kappa _ {1} (Y) = {\ mathcal {O}} (N ^ {0}) \, \ quad \ kappa _ {2} (Y) = {\ mathcal {O}} (N ^ {- 1}) \, \ quad \ kappa _ {3} (Y) = {\ mathcal {O}} (N ^ {- 2}) \, \ quad \ kappa _ {4} (Y) = { \ mathcal {O}} (N ^ {- 3})}$
For is the order to the power of a negative exponent and thus the limit of infinitely many random variables applies: ${\ displaystyle n \ geq 2}$${\ displaystyle N}$
${\ displaystyle \ lim _ {N \ to \ infty} \ kappa _ {n} (Y) = 0 \ quad {\ text {with}} \ quad n \ geq 2}$
I.e. only the first cumulative or the first moment remains. With increasing one obtains a Gaussian distribution around the mean value ${\ displaystyle N}$
${\ displaystyle \ kappa _ {1} (Y) = {\ frac {1} {N}} \ sum _ {i = 1} ^ {N} \ kappa _ {1} (X_ {i})}$,
where the latitude is of the order , and in the borderline case a sharp ( delta- shaped) peak at . ${\ displaystyle N ^ {- 1}}$${\ displaystyle N \ to \ infty}$${\ displaystyle \ kappa _ {1}}$
As a simple special case, consider all random variables to be identical to the mean , variance and any higher moments. ${\ displaystyle X_ {i} = X}$${\ displaystyle \ mu}$${\ displaystyle \ sigma ^ {2}}$
${\ displaystyle \ kappa _ {1} (Y) = {\ frac {1} {N}} \ sum _ {i = 1} ^ {N} m = m \, \ quad \ kappa _ {2} (Y ) = {\ frac {1} {N ^ {2}}} \ sum _ {i = 1} ^ {N} \ sigma ^ {2} = {\ frac {\ sigma ^ {2}} {N}} {\ underset {N \ to \ infty} {\ longrightarrow}} 0 \, \ quad \ kappa _ {3} (Y) = {\ frac {1} {N ^ {3}}} \ sum _ {i = 1} ^ {N} \ kappa _ {3} (X) = {\ frac {\ kappa _ {3} (X)} {N ^ {2}}} {\ underset {N \ to \ infty} {\ longrightarrow}} 0}$
Thus is a random variable with the same mean as (called fair-expectation estimator for the mean of ). The width of the Gaussian distribution (standard deviation from the mean), which becomes ever narrower, is . ${\ displaystyle Y}$${\ displaystyle X}$${\ displaystyle Y}$${\ displaystyle X}$${\ displaystyle N}$${\ displaystyle \ sigma _ {Y} = \ sigma _ {X} / {\ sqrt {N}}}$
## history
Cumulants and their properties were first described in 1889 by the Danish mathematician Thorvald Nicolai Thiele in a book published in Danish. Although this book was reported in detail in the yearbook on the progress of mathematics in the same year , the results were initially largely ignored, so that in 1901 Felix Hausdorff described these parameters as "newly introduced" (by him).
## Free accumulators
In the above combinatorial moment cumulant formula
${\ displaystyle E (X_ {1} \ cdots X_ {n}) = \ sum _ {\ pi} \ prod _ {B \ in \ pi} \ kappa (X_ {i}: i \ in B)}$
one adds up over all partitions of the set . If, instead, you only sum over non-crossing partitions , you get the free cumulants . These were introduced by Roland Speicher and play an analogous role in free probability theory as the usual cumulants in classical probability theory. In particular, the free cumulants are additive for free random variables. The Wigner's semicircular distribution , which is the free counterpart to the normal distribution, is characterized by the fact that only the free second order cumulant does not vanish. ${\ displaystyle \ {1, \ dotsc, n \}}$
## Individual evidence
1. Thorvald Nicolai Thiele: Forelæsninger over almindelig Iagttagelseslære: Sandsynlighedsregning og least Kvadraters method , Copenhagen 1889.
2. ^
3. Felix Hausdorff: Collected Works, Volume V: Astronomy, Optics and Probability Theory . 2006, ISBN 978-3-540-30624-5 , pp. 544, 577, doi: 10.1007 / 3-540-30669-2_8 .
4. Speicher, Roland (1994), "Multiplicative functions on the lattice of non-crossing partitions and free convolution", Mathematische Annalen, 298 (4): 611-628
5. Jonathan Novak, Piotr Śniady: What Is a Free Cumulant? . In: Notices of the American Mathematical Society . 58, No. 2, 2011, , pp. 300-301. | 7,560 | 21,450 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 158, "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-2022-49 | latest | en | 0.592997 |
https://brainly.com/question/153839 | 1,485,088,125,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281424.85/warc/CC-MAIN-20170116095121-00335-ip-10-171-10-70.ec2.internal.warc.gz | 800,633,579 | 8,965 | 2014-10-16T13:12:43-04:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
To find second point of intersects we have to use relationship that, when graphs are intersecting they are equal, so
x+3=5x-x^2
Now we have to solve quadratic equation
x+3=5x-x^2 /+x^2
x^2+x+3=5x /-5x
x^2+x-5x+3=0
x^2-4x+3=0
now, we can find delta
delta=16-4*3=4
x1= - its from the point (3,6) which we already know
x2= - its x coordinate of point which we are searching.
Finally we have to put 1 into equation to find value of y.
y=x+3
y=1+4
y=4
So the second point of intersect is (1.4) | 270 | 830 | {"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} | 3.84375 | 4 | CC-MAIN-2017-04 | latest | en | 0.934799 |
http://www.gurufocus.com/term/Book%20Value%20Per%20Share/HOME/Book%252BValue%252Bper%252BShare/Home%2BFederal%2BBancorp%252C%2BInc | 1,493,341,826,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917122720.81/warc/CC-MAIN-20170423031202-00489-ip-10-145-167-34.ec2.internal.warc.gz | 542,073,699 | 28,434 | Switch to:
GuruFocus has detected 6 Warning Signs with At Home Group Inc \$HOME.
More than 500,000 people have already joined GuruFocus to track the stocks they follow and exchange investment ideas.
At Home Group Inc (NYSE:HOME)
Book Value per Share
\$8.86 (As of Jan. 2017)
At Home Group Inc's book value per share for the quarter that ended in Jan. 2017 was \$8.86.
During the past 12 months, At Home Group Inc's average Book Value Per Share Growth Rate was 45.00% per year. Please click Growth Rate Calculation Example (GuruFocus) to see how GuruFocus calculates Wal-Mart Stores Inc (WMT)'s revenue growth rate. You can apply the same method to get the book value growth rate using book value per share data.
At Home Group Inc's current price is \$17.55. Its book value per share for the quarter that ended in Jan. 2017 was \$8.86. Hence, today's P/B Ratio of At Home Group Inc is 1.98.
During the past 4 years, the highest P/B Ratio of At Home Group Inc was 1.99. The lowest was 1.24. And the median was 1.68.
Definition
At Home Group Inc's Book Value Per Share for the fiscal year that ended in Jan. 2017 is calculated as:
Book Value Per Share = (Total Equity - Preferred Stock) / Shares Outstanding (EOP) = (534.9 - 0.0) / 60.4 = 8.86
At Home Group Inc's Book Value Per Share for the quarter that ended in Jan. 2017 is calculated as:
Book Value Per Share = (Total Equity - Preferred Stock) / Shares Outstanding (EOP) = (534.9 - 0.0) / 60.4 = 8.86
* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency.
Theoretically it is what the shareholders will receive if the company is liquidated. Total equity is a balance sheet item and equal to total assets less total liabilities of the company.
Book value may include intangible items which may come from the companys past acquisitions. Book value less intangibles is called Tangible Book.
Explanation
Usually a companys book value and Tangible Book Value per Share may not reflect its true value. The assets may be carried on the balance sheets at the original cost minus depreciation. This may underestimate the true economic values of the assets. It also may over-estimate their true economic value because the assets can become obsolete.
For financial companies such as banks and insurance companies, their assets may be reported in current market value of the assets owned. Book values of financial companies are more accurate indicator of the economic value of the company.
Related Terms
Historical Data
* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency.
At Home Group Inc Annual Data
Jan14 Jan15 Jan16 Jan17 Book Value Per Share 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.11 8.86
At Home Group Inc Quarterly Data
Oct14 Jan15 Apr15 Jul15 Oct15 Jan16 Apr16 Jul16 Oct16 Jan17 Book Value Per Share 0.00 0.00 0.00 0.00 0.00 6.11 6.35 6.47 8.53 8.86
Get WordPress Plugins for easy affiliate links on Stock Tickers and Guru Names | Earn affiliate commissions by embedding GuruFocus Charts
GuruFocus Affiliate Program: Earn up to \$400 per referral. ( Learn More) | 804 | 3,171 | {"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} | 2.828125 | 3 | CC-MAIN-2017-17 | latest | en | 0.921187 |
https://web2.0calc.com/questions/what-are-the-factors-of-180 | 1,540,353,814,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583518753.75/warc/CC-MAIN-20181024021948-20181024043448-00129.warc.gz | 836,800,260 | 5,439 | +0
# what are the factors of 180
+1
415
2
what are the factors of 180
Guest May 24, 2017
#1
+202
+1
1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90 and 180!
Whitespy001 May 24, 2017
#2
0
Its prime factors are: 180 = 2^2 * 3^2 * 5
Guest May 24, 2017 | 134 | 253 | {"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} | 2.875 | 3 | CC-MAIN-2018-43 | latest | en | 0.880797 |
https://books.google.co.ls/books?id=Rso2AAAAMAAJ&qtid=eb7e7824&dq=editions:ISBN1107497817&lr=&source=gbs_quotes_r&cad=5 | 1,716,855,827,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059055.94/warc/CC-MAIN-20240528000211-20240528030211-00304.warc.gz | 120,216,942 | 6,479 | Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ... - Page 201
by Charles William Hackley - 1838 - 307 pages
Full view - About this book
## A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2
Charles Hutton - 1812 - 624 pages
...— cos b . cos c -f- sin b . sin c . cos A 1 cos 6 = cos a . cos c -j- sin a . sin c . cos B v (I.) cos c -- cos a . cos b + sin a . sin b . cos c J THEOREM VII. In Every Spherical Triangle, the Sines of the Angles are Proportional to the Sines of...
Full view - About this book
## Elements of Plane and Spherical Trigonometry: With Their Applications to ...
Olinthus Gregory - 1816 - 276 pages
...FD = AO cos a cos b + FB = AO cos a cos b + AO sin a sin b cos c. Therefore, dividing by AO, we have cos c = cos a cos b + sin a sin b cos c. Similar relations are deducible for the other sides a and b : hence, generally cas a = cos b cos c...
Full view - About this book
## Traité de géodosie, Volume 1
Louis Puissant - 1819 - 464 pages
...valeurs de da, l'on trouvera dB- de sîn B tans a ''un autre côté , si l'on différencie l'équation cos c = cos a cos b + sin a sin b cos C, viendra , . » /cos b — cos a cos c\ • , . _ 1n de sm c = da ( -;— j -f- sm « sin b sin Cc?C,...
Full view - About this book
## A Treatise on Plane and Spherical Trigonometry
Robert Woodhouse - 1819 - 300 pages
...c- n cos. c — cos. a . cos. b , ,, bmce cos. L = - r- - : — - - , page 139, sin. a . sin. b .-. cos. c = cos. a . cos. b + sin. a . sin. b . cos. C; but cos. C=l — ver. sin. C, (ver. sin. stands for versed sine); * For instance, in finding the Moon's...
Full view - About this book
## The Principles of Analytical Geometry: Designed for the Use of Students
Henry Parr Hamilton - 1826 - 354 pages
...Zx'z be an arc of 90° passing through x', and meeting xy in z. Then, since in any spherical triangle cos c = cos a cos b + sin a sin b cos C, we have (1) In the triangle x'xt, cos x', x = cos t, x cos t, x' + sin t, x sin t, x' cos x'y , xy...
Full view - About this book
## Uranographie: ou, Traité élémentaire d'astronomie, à l'usage des personnes ...
Louis-Benjamin Francœur - 1828 - 608 pages
..., B^ et le côté compris Cj on trouve les deux autres côtes a, b , par les analogies (A - B) — cos C = cos A cos B — sin A sin B cos c (a3) , cos C = cos A cos B (tang A tang B cos c — i). Comme dans les deux derniers cas, on emploie...
Full view - About this book
## Elements of Plane and Spherical Trigonometry: With Its Applications to the ...
John Radford Young - 1833 - 308 pages
...(10 — p) — (10 — ?), we have log. tan. = 10 + y — p. \Vhen, in the case we are considering, the only part required happens to be the side opposite...solution is deducible from the fundamental formula, cos. с = cos. a cos. b + sin. a sin. 6 соя. С .... (1). For substituting cos. a tan. a for its equal...
Full view - About this book
## The Elements of the Theory of Astronomy
John Hymers - 1840 - 386 pages
...SPK = cos /, and applying these values and the fundamental formulas of spherical Trigonometry, viz. cos c = cos a cos b + sin a sin b cos C, cot .4 sin C = cot a sin 6 — cos C cos 6, sin a sin B = sin .4 sin b, (where «, 6, c, A, S, C, represent...
Full view - About this book
## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...
Nathan Scholfield - 1845 - 894 pages
...angle of the triangle. By (a) \ve have, cos. a — cos. 6 cos. c cos. A = And, cos. C = sin. b sin. c cos. c — cos. a cos. b sin. a sin. b cos. c = cos. a cos. b + sin. a sin. b cos. C (1.) . . . (2.) Substituting this value of cos. c in Equation...
Full view - About this book
## A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...
Nathan Scholfield - 1845 - 542 pages
...cos. a — cos. b cos. c . . • • " • • • •* (•*•) cos. A = And, cos. C = sin. b sin. c cos. c — cos. a cos. b sin. a sin. b .'. cos. c — cos. a cos. i + sin. a sin. b cos. C - - - (2.) Substituting this value of cos. c in Equation (1.)...
Full view - About this book | 1,401 | 4,313 | {"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} | 3.03125 | 3 | CC-MAIN-2024-22 | latest | en | 0.343571 |
http://www.mathisfunforum.com/viewtopic.php?pid=321198 | 1,534,741,580,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221215843.55/warc/CC-MAIN-20180820042723-20180820062723-00651.warc.gz | 532,048,947 | 11,552 | Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
You are not logged in.
## #251 2014-06-14 07:00:00
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
The original joke is 789!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #252 2014-06-14 07:03:44
ShivamS
Member
Registered: 2011-02-07
Posts: 3,648
Abuse of power.
Offline
## #253 2014-06-14 07:06:10
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
It is clever.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #254 2014-06-14 13:52:49
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
Math problems? Call 1-800-[(10x)(13i)^2]-[sin(xy)/2.362x].
*****************************************************
If parallel lines meet at infinity - infinity must be a very noisy place with all those lines crashing together!
*****************************************************
Maths Teacher: Now suppose the number of sheep is x...
Student: Yes sir, but what happens if the number of sheep is not x?
*****************************************************
Zenophobia: the irrational fear of convergent sequences.
*****************************************************
Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.
*****************************************************
If I had only one day left to live, I would live it in my statistics class: it would seem so much longer.
*****************************************************
It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest. -- S. den Hartog, Ph D. Thesis Universtity of Groningen.
*****************************************************
Q: Why did the 30-60-90 triangle marry the 45-45-90 triangle?
A: They were right for each other.
*****************************************************
Q: Why didn't the Romans find algebra very challenging?
A: Because X was always 10.
*****************************************************
Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?
A: Pumpkin Pi
*****************************************************
Q: Why couldn't the angle get a loan?
A: His parents wouldn't Cosine
*****************************************************
Q: Why did the obtuse angle go to the beach?
A: Because it was over 90 degrees
*****************************************************
Q: What's the integral of (1/cabin)d(cabin)?
A: A natural log cabin!
Q: What do you call an angle that is adorable?
A: acute angle.
*****************************************************
Q: Why did the student get upset when his teacher called him average?
A: It was a 'mean' thing to say!
*****************************************************
Q: Why did the polynomial plant die?
A: Its roots were imaginary.
*****************************************************
Q: Why does nobody talk to circles?
A: Because there is no point!
Q: What do you call a teapot of boiling water on top of mount everest?
A: A high-pot-in-use
*****************************************************
Q: Why didn't Bob drink a glass of water with 8 pieces of ice in it?
A: It was too cubed
*****************************************************
Q: Which triangles are the coldest?
A: Ice-sosceles triangles
*****************************************************
Q: Who invented the Round Table?
A: Sir Cumference
*****************************************************
Q: Why is Ms. Radian such a good reporter?
A: She covers the story from every angle
*****************************************************
Q: How can a fisherman determine how many fish he needs to catch to make a profit?
A: By using a cod-ratic inequality
*****************************************************
Q: How do you know that your dentist studied algebra?
A: She said all that candy gave me exponential decay
*****************************************************
Q: What is polite and works for the phone company?
A: A deferential operator.
*****************************************************
Q: What do you call a dead parrot?
A: Polygon.
*****************************************************
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #255 2014-06-14 13:56:13
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
The last one was my favorite, Polygon.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #256 2014-06-14 20:51:30
phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,600
### Re: Mathematics jokes
Hi ganesh and Bobby,
Reminds me of this sad tale sung by Peter, Paul and Mary, called Polly Von.
Its an Irish folk song about a young man who is hunting at twilight and mistakes his true love, who is taking shelter from the rain, for a swan. He shoots, and discovers that he's killed Polly.
So, alas and alack, it's 'Polly gone'.
>sniff<
Last edited by phrontister (2014-06-14 22:25:13)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
Offline
## #257 2014-06-14 22:49:12
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
Hi;
It is amazing that at your age you even know about that song.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #258 2014-06-15 00:25:20
phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,600
### Re: Mathematics jokes
Hi Bobby,
Maybe I'm a reincarnated version of me...
I've gathered a bit of a collection of secondhand LPs from garage sales and op shops and converted them to MP3s.
I remembered Polly Von and that it was on this record, so here's a photo I took of it (it's the last song):
Last edited by phrontister (2017-02-25 22:40:35)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
Offline
## #259 2014-06-15 00:29:21
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
Is that a 33 and a 1/3?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #260 2014-06-15 01:53:24
phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,600
### Re: Mathematics jokes
Yes, it is.
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
Offline
## #261 2014-06-15 01:56:14
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
Last time I saw one was in 1975 or so.
Mathematical joke:
Theorem: a cat has nine tails.
Proof:
No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #262 2014-06-15 02:05:15
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
A mathematician decides he wants to learn more about practical problems. He sees a seminar with a nice title: "The Theory of Gears." So he goes. The speaker stands up and begins, "The theory of gears with a real number of teeth is well known ..."
*****************************************************
When a statistician passes the airport security check, they discover a bomb in his bag. He explains. "Statistics shows that the probability of a bomb being on an airplane is 1/1000. However, the chance that there are two bombs at one plane is 1/1000000. So, I am much safer..."
*****************************************************
What is the difference between a Psychotic, a Neurotic and a mathematician? A Psychotic believes that 2+2=5. A Neurotic knows that 2+2=4, but it kills him. A mathematician simply changes the base.
*****************************************************
Q: What will a logician choose: a half of an egg or eternal bliss in the afterlife?
A: A half of an egg! Because nothing is better than eternal bliss in the afterlife, and a half of an egg is better than nothing.
*****************************************************
A physicist has been conducting experiments and has worked out a set of equations which seem to explain his data. He asks a mathematician to check them. A week later, the mathematician calls "I'm sorry, but your equations are complete nonsense." "But these equations accurately predict results of experiments. Are you sure they are completely wrong? "To be precise, they are not always a complete nonsense. But the only case in which they are true is the trivial one where the field is Archimedean..."
*****************************************************
A mathematician belives nothing until it is proven
A physicist believes everything until it is proven wrong
A chemist doesn't care.
biologist doesn't understand the question.
*****************************************************
An engineer and a topologist were locked in the rooms for a day with a can of food but without an opener. At the end of the day, the engineer is sitting on the floor of his room and eating from the open can: He threw it against the walls until it cracked open. In the mathematician's room, the can is still closed but the mathematician has disappeared. There are strange noises coming from inside the can... When it is opened and the mathematician crawls out. "darn! I got a sign wrong..."
*****************************************************
A mathematician has spent ten years trying to prove the Riemann hypothesis. Finally, he decides to sell his soul to the devil in exchange for a proof. The devil promises to deliver a proof in the four weeks. Half a year later, the devil shows up again - in a rather gloomy mood. "I'm sorry", he says. "I couldn't prove the hypothesis either. But" - and his face lightens up - "I think I found a really interesting lemma..."
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #263 2014-06-15 02:15:06
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
Hope these are new:
Dictionary of Definitions of Terms Commonly Used in Math. lectures.
CLEARLY:
I don't want to write down all the "in- between" steps.
TRIVIAL:
If I have to show you how to do this, you're in the wrong class.
OBVIOUSLY:
I hope you weren't sleeping when we discussed this earlier, because I refuse to repeat it.
RECALL:
I shouldn't have to tell you this, but for those of you who erase your memory tapes after every test...
WLOG (Without Loss Of Generality):
I'm not about to do all the possible cases, so I'll do one and let you figure out the rest.
CHECK or CHECK FOR YOURSELF:
This is the boring part of the proof, so you can do it on your own time.
SKETCH OF A PROOF:
I couldn't verify all the details, so I'll break it down into the parts I couldn't prove.
HINT:
The hardest of several possible ways to do a proof.
SOFT PROOF:
One third less filling (of the page) than your regular proof, but it requires two extra years of course work just to understand the terms.
ELEGANT PROOF:
Requires no previous knowledge of the subject matter and is less than ten lines long.
SIMILARLY:
At least one line of the proof of this case is the same as before.
CANONICAL FORM:
4 out of 5 mathematicians surveyed recommended this as the final form for their students who choose to finish.
BY A PREVIOUS THEOREM:
I don't remember how it goes (come to think of it I'm not really sure we did this at all), but if I stated it right (or at all), then the rest of this follows.
TWO LINE PROOF:
I'll leave out everything but the conclusion, you can't question 'em if you can't see 'em.
BRIEFLY:
I'm running out of time, so I'll just write and talk faster.
LET'S TALK THROUGH IT:
I don't want to write it on the board lest I make a mistake.
PROCEED FORMALLY:
Manipulate symbols by the rules without any hint of their true meaning (popular in pure math courses).
QUANTIFY:
I can't find anything wrong with your proof except that it won't work if x is a moon of Jupiter.
PROOF OMITTED:
Trust me, It's true.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #264 2014-06-15 16:33:31
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
If you got \$10 from 10 people, what would you have? A new bike !
*************************************************
This poem was written by Jon Saxton (an author of math textbooks).
((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0
Or for those who have trouble reading the poem:
A Dozen, a Gross and a Score,
plus three times the square root of four,
divided by seven, plus five times eleven,
equals nine squared and not a bit more.
*************************************************
A student wrote letter to his home:
Dear Dad!
This \$chool i\$ really great. I am making lot\$ of friend\$ and \$tudying very hard. Mathematic\$, a\$tronomy, and economic\$ are the \$ubject\$ I like. With all my \$tuff, I \$imply can't think of anything I need, \$o if you would like, you can ju\$t \$end me a po\$t card, a\$ I would love to \$ee \$ome word\$ from you.
\$end it to me \$oon,
Your \$on.
A week later he received a letter from home:
Dear Son!
I kNOw that trigoNOmetry, astroNOmy, and ecoNOmics are eNOugh to keep even an hoNOr student busy. Do NOt forget that the pursuit of kNOwledge is a NOble task, and kNOw that NO one can ever learn eNOugh.
Love,
Your NOt so kNOwledgeable Dad.
*************************************************
What is "pi"?
Mathematician: Pi is the ratio of circumference of a circle to its diameter.
Engineer: Pi is about 22/7.
Computer Programmer: Pi is 3.141592653589 in double precision.
Nutritionist: You one track math-minded fellows, Pie is a healthy and delicious dessert!
*************************************************
Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. One of the three men says, "I've got an idea. We can call for help in this canyon and the echo will carry our voices far."
So he leans over the basket and yells out, "Hellllooooo! Where are we?" (They hear the echo several times).
Two minutes later they hear this echoing voice: "Hellllooooo! You're lost!!"
One of the men says, "That must be a mathematician." Puzzled, one of the other men asks, "Why do you say that?"
He replies: "For three reasons. (1) he took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless."
*************************************************
Several students were asked the following problem:
Is it true that all odd integers are prime?
Well, the first student to try to do this says "hmmm... Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime and by induction, we have that all the odd integers are prime."
The physics student then said, "I'm not sure of the validity of your proof, but I think I'll try to prove it by experiment." He continues, "Well, 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ... uh, 9 is an experimental error, 11 is prime, 13 is prime... Well, it seems that that all odd integers are prime."
The third student to try it was the engineering student, who responded, "Well, actually, I'm not sure of your answer either. Let's see... 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is ..., 9 is ..., standard deviation, 11 is prime, 13 is prime... Well, it does seem that all odd integers are prime."
Not to be outdone, the computer science student comes along and says "Well, you guys sort'v got the right idea, but you'd end up taking too long doing it. I've just whipped up a program using a "do loop" to REALLY go and prove it..." He runs his computer program. The computer responds, "1 is prime, 1 is prime, 1 is prime, 1 is prime, 1 is prime...."
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #265 2014-06-15 16:55:59
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
phrontister wrote:
Hi ganesh and Bobby,
Reminds me of this sad tale sung by Peter, Paul and Mary.
I'm sorry I missed your post, phrontister!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #266 2014-06-18 15:53:38
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
Teacher: "Who can tell me what 7 times 6 is?"
Student: "It's 42!"
Teacher: "Very good! - And who can tell me what 6 times 7 is?"
Same student: "It's 24!"
* * * * * * * * * * * * * * * * * * * * *
Q: What does the zero say to the
the eight?
A: Nice belt!
* * * * * * * * * * * * * * * * * * * * *
Q: What does a mathematician present to his fiancée when he wants to propose?
A: A polynomial ring.
* * * * * * * * * * * * * * * * * * * * *
Life is complex: it has both real and imaginary components.
* * * * * * * * * * * * * * * * * * * * *
Three statisticians go hunting. When they see a rabbit, the first one shoots, missing it on the left. The second one shoots and misses it on the right. The third one shouts:
"We've hit it!"
* * * * * * * * * * * * * * * * * * * * *
Q: Why do mathematicians often confuse Christmas and Halloween?
A: Because Oct 31 = Dec 25.
* * * * * * * * * * * * * * * * * * * * *
A statistician can have his head in an oven and his feet in ice, and he will say that on the average he feels fine.
* * * * * * * * * * * * * * * * * * * * *
Question: "How many seconds are there in a year?"
Answer: "Twelve, January second, February second, March second, ..."
* * * * * * * * * * * * * * * * * * * * *
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #267 2014-06-18 16:51:38
bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606
### Re: Mathematics jokes
Hi;
The 42, 24 one is really good.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
## #268 2014-06-19 00:05:27
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
Hi,
bobbym wrote:
The 42, 24 one is really good.
Thanks, bobbym!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #269 2014-06-19 02:45:17
Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
Website
### Re: Mathematics jokes
Hi ganesh;
Post 266 joke 3 is inspiring.
Can you please give me a polynomial ring so that I can propose my favorite girl?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
## #270 2014-06-19 13:47:36
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
Hi Agnishom,
Agnishom wrote:
Post 266 joke 3 is inspiring.
Thanks, Agnishom!
Agnishom wrote:
Can you please give me a polynomial ring so that I can propose my favorite girl?
Ha ha ha!
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #271 2014-06-21 03:12:28
ganesh
Administrator
Registered: 2005-06-28
Posts: 25,632
### Re: Mathematics jokes
Q: Why didn't the Romans find algebra very challenging?
A: Because X was always 10.
* * * * * * * * * * * * * * * * * * * *
Q: Why do plants hate math?
A: Because it gives them square roots.
* * * * * * * * * * * * * * * * * * * *
Q: Why did the student get upset when his teacher called him average?
A: It was a 'mean' thing to say!
* * * * * * * * * * * * * * * * * * * *
Q: Why does nobody talk to circles?
A: Because there is no point!
* * * * * * * * * * * * * * * * * * * *
Q: Why didn't Bob drink a glass of water with 8 pieces of ice in it?
A: It was too cubed.
* * * * * * * * * * * * * * * * * * * *
Q: Which triangles are the coldest?
A: Ice-sosceles triangles.
* * * * * * * * * * * * * * * * * * * *
Q: Why is Ms. Radian such a good reporter?
A: She covers the story from every angle.
* * * * * * * * * * * * * * * * * * * *
Q: What do you call more than one L?
A: A Parallel.
* * * * * * * * * * * * * * * * * * * *
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
## #272 2015-12-12 01:37:05
Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,252
### Re: Mathematics jokes
Borrowed from XKCD, too:
Transformation Matrix
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.
Offline
## Board footer
Powered by FluxBB | 6,000 | 23,276 | {"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} | 2.828125 | 3 | CC-MAIN-2018-34 | longest | en | 0.784441 |
http://mathhelpforum.com/calculus/103061-work-problem-w-spring-print.html | 1,516,611,478,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891196.79/warc/CC-MAIN-20180122073932-20180122093932-00562.warc.gz | 227,135,942 | 4,142 | # Work Problem w/ spring
• Sep 18th 2009, 11:30 PM
mmattson07
Work Problem w/ spring
A spring has a natural length of 28 cm. If a 28 N force is required to keep it stretched to a length of 31 cm, how much work W is required to stretch it from 28 cm to 38 cm?
W= ___ J
I know Work= Force * Distance but i dont know how to go about solving this i know it will be an integration of some sort
• Sep 18th 2009, 11:44 PM
redsoxfan325
This might be better suited for a physics forum. If you can set up the integral, I or someone else can help you, but other than that you might not get the help you're looking for.
• Sep 19th 2009, 01:16 AM
Work done stretching a spring
Hello mmattson07
Quote:
Originally Posted by mmattson07
A spring has a natural length of 28 cm. If a 28 N force is required to keep it stretched to a length of 31 cm, how much work W is required to stretch it from 28 cm to 38 cm?
W= ___ J
I know Work= Force * Distance but i dont know how to go about solving this i know it will be an integration of some sort
Two formulae you need to know about an elastic spring with natural length $l$ and modulus $\lambda$:
• When the extension in the spring is $x$, the tension, $T$, is given by $T=\frac{\lambda x}{l}$
• When the spring is stretched from an extension $x_1$ to an extension $x_2$, the work done, $W$, is given by $W=\frac{\lambda({x_2}^2-{x_1}^2)}{2l}$
So here, $l = 0.28$ m. And when $x = 0.03$ (because the total length is $0.31$ m), $T = 28$.
So, using the first of the two formulae above:
$28 = \frac{0.03\lambda}{0.28}$
$\Rightarrow \lambda = \frac{28^2}{3}$
And we need to find $W$ when $x_1=0$ and $x_2 = 0.10$
So $W = \frac{28^2(0.1^2-0^2)}{3\times 2 \times 0.28}$
$= \frac{28}{6}=4.67$ Joules
• Sep 19th 2009, 10:08 AM
mmattson07
We never finished the example we were doing in class so I was unsure on how to set up the integral...i know it has something to do with Hooke's Law. Thank you for the help though Grandad's method works and i follow it.
• Sep 19th 2009, 01:45 PM
Hello mmattson07
Quote:
Originally Posted by mmattson07
We never finished the example we were doing in class so I was unsure on how to set up the integral...i know it has something to do with Hooke's Law. Thank you for the help though Grandad's method works and i follow it.
My 'method', as you describe it, is simply the result of applying Hooke's Law, which states that the tension in an elastic spring (or string) is proportional to the extension. In other words, with $T$ and $x$ defined as before:
$T = kx$, for some constant $k$.
Now if we define the modulus (or modulus of elasticity), $\lambda$, to be the force required to double the length of the spring, then when $x = l, T = \lambda$. So $k = \frac{\lambda}{l}$, which in turn gives the first of the two formulae that I quoted, namely
$T = \frac{\lambda x}{l}$
The second formula is derived by integration, as follows:
Suppose the spring is extended from $x$ to $x+\delta x$. Then the work done is given by
$\delta W \approx T\delta x$
$\Rightarrow \frac{dW}{dx}=T$
$\Rightarrow \int_0^W dW = \int_{x_1}^{x_2}Tdx$, where $W$ is the work done extending the spring from $x_1$ to $x_2$.
$=\int_{x_1}^{x_2}\frac{\lambda x}{l}dx$
$\Rightarrow W = \frac{\lambda({x_2}^2-{x_1}^2)}{2l}$
So there's nothing other than Hooke's Law here. However, it's much easier to learn and apply these two well-known formulae, than to derive the answers from first principles each time! | 1,074 | 3,457 | {"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": 0, "codecogs_latex": 38, "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-2018-05 | longest | en | 0.890483 |
https://mapleprimes.com/questions/231395-How-To-Extend-A-Linear-Map-By-Derivation | 1,611,274,389,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703528672.38/warc/CC-MAIN-20210121225305-20210122015305-00263.warc.gz | 427,675,818 | 22,663 | # Question:How to extend a linear map by derivation rule on a polynomial algebra?
## Question:How to extend a linear map by derivation rule on a polynomial algebra?
Maple
Hello!
I would appreciate any help on how to do computations on Maple of the following problem.
Say we have 3 generators x,y,z and I define a map on polynomials in three variables over rational numbers L: Q[x,y,z] -> Q[x,y,z] on the generators, for example L(x)=xy, L(y)=1, L(z)=z^2.
Then I need to compute L(xy+yz) and it needs to compute it using linearity and derivation (Leibniz rule):
L(x)y+xL(y)+L(y)z+yL(z)=xy^2+x+z+yz^2.
I have in mind a recursive algorithm but I don't know enough syntacsys to implement it.
P.S.: I need to compute Poisson brackets on a polynomial algebra for which there is no special way of doing it, right? So I though it must be easier for each basis element to come up with a linear map and extend it via derivations to know its action.
| 246 | 950 | {"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} | 2.984375 | 3 | CC-MAIN-2021-04 | latest | en | 0.915114 |
http://slideplayer.com/slide/1511567/ | 1,511,030,743,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934805008.39/warc/CC-MAIN-20171118171235-20171118191235-00054.warc.gz | 280,502,931 | 22,815 | Presentation is loading. Please wait.
# Multiplying Polynomials
## Presentation on theme: "Multiplying Polynomials"— Presentation transcript:
Multiplying Polynomials
Grade 9 Math
Agenda Why are we using tiles? Zero Pairs Using Algebra Tiles
Review of Adding Subtracting Multiplying
Why Tiles? “Polynomials are unlike the other “numbers” students learn how to add, subtract, multiply, and divide. They are not “counting” numbers. Giving polynomials a concrete reference (tiles) makes them real.” David A. Reid, Acadia University
Zero Pairs Called zero pairs because they are additive inverses of each other. When put together, they cancel each other out to model zero.
Addition of Integers (+3) + (+1) = (-2) + (-1) =
Addition of Integers (+3) + (-1) = (+4) + (-4) =
After students have seen many examples of addition, have them formulate rules.
Review of Polynomials 2x x + 2 -3x x + 3
Subtraction of Integers Tips
Subtraction can be interpreted as “take-away.” Subtraction can also be thought of as “adding the opposite.” For each of the given examples, use algebra tiles to model the subtraction. Draw pictorial diagrams which show the modeling process.
Multiplication of Integers
Integer multiplication builds on whole number multiplication. Use concept that the multiplier serves as the “counter” of sets needed. For the given examples, use the algebra tiles to model the multiplication. Identify the multiplier or counter. Draw pictorial diagrams which model the multiplication process.
Multiplication of Integers
If the counter is negative it will mean “take the opposite of.” (flip-over) (-2)(+3) (-3)(-1)
More Polynomials Represent each of the given expressions with algebra tiles. Draw a pictorial diagram of the process. Write the symbolic expression. x + 4
Multiplying 3(X + 2) What would these one look like? 3(X – 4)
Product of Two Monomials
Grade 9 Math
Agenda Review of Multiplying Polynomials using Algebra Tiles
Multiplying two together using tiles Using algebra Practice
Multiplying 3(X + 2) What would these one look like? 3(X – 4)
Monomial A polynomial with one term is called a monomial.
How would we use algebra tiles to determine (3x)(4x)?
Coefficients How do we multiply monomials? (3x)(4x)
1) We multiply the coefficients. The coefficients are the numbers. 2) We multiply the variables: The variables are the letters.
Putting it all together
(3x)(4x) 1) We multiply the numbers (coefficients). 3 x 4 =12 2) We multiply the letters (variables). (x)(x) =x2
Practice (x)(3x) (2x2)(-3x) (3x)(12x) (-3x)(-12x) (2x2)(4x) (x2)(x)
Caution x + x = DOESN’T = x2 (x)(x) = DOESN’T = 2x
Download ppt "Multiplying Polynomials"
Similar presentations
Ads by Google | 690 | 2,698 | {"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} | 4.8125 | 5 | CC-MAIN-2017-47 | longest | en | 0.882566 |
http://mathhelpforum.com/advanced-statistics/228024-geometric-distribution.html | 1,524,527,417,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125946256.50/warc/CC-MAIN-20180423223408-20180424003408-00236.warc.gz | 202,680,419 | 15,201 | 1. ## Geometric Distribution
Question:
"The Geometric Distribution and Shorts in NiCad Batteries"
In their article "A Case Study of the Use of an Experimental Design
Snyder describe a series of experiments conducted in order to reduce
the proportion of cells being scrapped by a battery plant because of
internal shorts.
The experimental program was successful in reducing the proportion of
manufactured cells with internal shorts to around 0.03.
The following procedure is being developed in order to monitor the
process for increases in the true proportion of manufactured cells
with internal shorts.
Suppose that testing of batteries for internal shorts begins
on a production run in this plant for monitoring/control purposes,
let B = the number of batteries required until
the first internal short is discovered.
[a]
What is the distribution and expected value of B,
if the proportion of manufactured cells with internal shorts
remains at 0.03?
What is the distribution and expected value of B,
if the proportion of manufactured cells with internal shorts
increases to 0.10?
What happens, in general, to the expected value of B
as the proportion of manufactured cells with internal shorts
increases? Choose one: [Larger or Smaller]
[b]
Consider using B to test the following hypotheses:
H_0: % = 0.03 versus H_a: % > 0.03
where % = true proportion of manufactured cells with internal shorts.
B has been proposed as the TEST STATISTIC,
however three Rejection Regions are being considered.
A choice needs to be made concerning which of the three
Rejection Regions to implement in the procedure.
Rejection Region 1: Reject H_0 if B = 1.
Rejection Region 2: Reject H_0 if B <= 2.
Rejection Region 3: Reject H_0 if B <= 3.
[b.i]
Calculate the probability of a Type I Error for Rejection Region 1.
Calculate the probability of a Type I Error for Rejection Region 2.
Calculate the probability of a Type I Error for Rejection Region 3.
Based upon this information which Rejection Region do you recommend? WHY?
[b.ii]
Now suppose, in reality, the true proportion of manufactured cells
with internal shorts has increased to 0.10
Calculate the power for Rejection Region 1.
Calculate the power for Rejection Region 2.
Calculate the power for Rejection Region 3.
Based upon this information which Rejection Region do you recommend? WHY?
[b.iii]
For each Rejection Region determine an equation/formula/function that
relates power to %, true proportion of manufactured cells w/ internal shorts.
For Rejection Region 1: Power = ??function of %??
For Rejection Region 2: Power = ??function of %??
For Rejection Region 3: Power = ??function of %??
[b.iv]
Graph each of the above power functions on the same set of axes
use EXCEL, MATLAB, etc. to get a "nice" graph.
Place % on the x-axis and power on the y-axis.
Note: the range for both % and power is 0 to 1.
Now make a final recommendation concerning the Rejection Region
why you selected the Rejection Region you did.
[c]
Now suppose the experiment has been conducted and the observed value of B = 5.
Calculate the p-value.
(a) Given that, in batteries, an experimental process successfully reduced the proportion of manufactured cells with internal shorts to around 0.03. Let B = the number of batteries required until the first internal short is discovered. Given, the proportion of manufactured cells with internal shorts to around 0.03.
p = 0.03
q = 1 - p = 1 - 0.03 = 0.97
B ~ Geometric (p = 0.03)
P(X = x) = (0.03)*(0.97)^x for x = 1, 2,...
E(x) = q/p = 0.97/0.03 = 32.333
so, the expected value of B is 32
I'm wondering if my attempt at (a) is correct and if anyone has any helpful hints about how I should start part (b)
2. ## Re: Geometric Distribution
wouldn't $P(X=x) = (0.03)(0.97)^{x-1}$ ?
you had $x-1$ good batteries before you found the defective one at try $n$
3. ## Re: Geometric Distribution
oh, yes, you're right.
For the second part of part (a) would I use that same formula, except this time instead of using p = 0.03, I would use p = 0.10?
yes
5. ## Re: Geometric Distribution
okay, so to finish up part (a) this is what I did:
p = 0.10
q = 1 - 0.10 = 0.90
P(X = x) = (0.10)*(0.90)^(x - 1) for x = 1, 2, ...
E(x) = q/p = 0.90/0.10 = 9
So, in general, as the proportion of manufactured cells with internal shorts
increases, the expected value of B decreases.
Then for (bi)
P[Type I Error for Rejection Region 1] = P[ b = 1 | % = 0.03 ] = ??
this part I'm stuck at because I'm not sure if I would use an integral going from 0 to 0.03 of the geometric distribution or another method to calculate the probability. My teacher uses the computer software to figure out the probability, but doesn't show us how to figure it out by hand.
6. ## Re: Geometric Distribution
Would the above be correct?
Also, for (bi) would this be correct:
P[Type I Error for Rejection Region 1] = P[ b = 1 | % = 0.03 ] = the integral from 0 to 1 of (0.03)*(0.97)^(x-1) dx = 0.0304616
And then I'd use that integral again for the other rejection regions, except I would have the integral going from 0 to 2 for Rejection Region 2 and then have the integral going from 0 to 3 for Rejection Region 3
7. ## Re: Geometric Distribution
Originally Posted by AwesomeHedgehog
okay, so to finish up part (a) this is what I did:
p = 0.10
q = 1 - 0.10 = 0.90
P(X = x) = (0.10)*(0.90)^(x - 1) for x = 1, 2, ...
E(x) = q/p = 0.90/0.10 = 9
this isn't quite right. Since we never choose 0 batteries. B has a support of {1,2,3, ....}
For this support $E[B] = \dfrac 1 p$ not $\dfrac {1-p} p$ as you've used. This last is the formula for the mean when 0 is a possible value.
So, in general, as the proportion of manufactured cells with internal shorts
increases, the expected value of B decreases.
yes as it better had. If it's more likely the batteries are bad I'd expect to see a bad one faster.
Then for (bi)
P[Type I Error for Rejection Region 1] = P[ b = 1 | % = 0.03 ] = ??
this part I'm stuck at because I'm not sure if I would use an integral going from 0 to 0.03 of the geometric distribution or another method to calculate the probability. My teacher uses the computer software to figure out the probability, but doesn't show us how to figure it out by hand.
no.
Consider the experiment for Region 1. We grab a battery and test it. It either passes or not with probability p=0.03, thus
Pr[Type I error] = Pr[H0=True | rejected at B=1] = Pr[we get a bad battery first try | p=0.03] = 0.03
For region 2, we sample a battery, if it fails we reject, if it passes, sample again and pass if it passes else reject. In other words we fail on {fail} or {pass, fail}
The probability of failing is thus p+(1-p)p = 0.059. Similarly for Region 3. We fail on {fail}, {pass, fail}, {pass, pass, fail}
figure out Pr[Type I error] in region 3
8. ## Re: Geometric Distribution
Okay here's what I have:
The completed part of part (a):
When p = 0.03
q = 1 - p = 1 - 0.03 = 0.97
B ~ Geometric (p = 0.03)
P(X = x) = (0.03)*(0.97)^(x - 1) for x = 1, 2,...
E(x) = q/p = 0.97/0.03 = 32.333
so, the expected value of B is 32
Then when p = 0.10
q = 1 - 0.10 = 0.90
P(X = x) = (0.10)*(0.90)^(x - 1) for x = 1, 2, ...
E(x) = 1/p = 1/0.10 = 10
So, in general, as the proportion of manufactured cells with internal shorts increases, the expected value of B decreases.
For part (bi):
You said that the probability of a type I error for region one would be equal to 0.03. I used this formula and got the same answer:
P[Type I Error for Rejection Region 1] = P[ b = 1 | % = 0.03 ] = the integral from 0 to 1 of (0.03)*(0.97)^(x-1) dx = 0.0304616
I used the geometric distribution in the integral to show my work as for how I got 0.03.
But for the Rejection Region 2 and 3, the integral wouldn't be going from 0 to 1 anymore, that part would change.
So, P[Type I Error for Rejection Region 2] = P[ b <= 2 | % = 0.03 ] = the integral from 0 to 2 of (0.03)*(0.97)^(x-1) dx = 0.06
which is the same answer that you got, except I calculated it differently.
And then, P[Type I Error for Rejection Region 3] = P[ b <= 3 | % = 0.03 ] = the integral from 0 to 3 of (0.03)*(0.97)^(x-1) dx = 0.089
9. ## Re: Geometric Distribution
Originally Posted by AwesomeHedgehog
Okay here's what I have:
The completed part of part (a):
When p = 0.03
q = 1 - p = 1 - 0.03 = 0.97
B ~ Geometric (p = 0.03)
P(X = x) = (0.03)*(0.97)^(x - 1) for x = 1, 2,...
E(x) = q/p = 0.97/0.03 = 32.333
so, the expected value of B is 32
Then when p = 0.10
q = 1 - 0.10 = 0.90
P(X = x) = (0.10)*(0.90)^(x - 1) for x = 1, 2, ...
E(x) = 1/p = 1/0.10 = 10
So, in general, as the proportion of manufactured cells with internal shorts increases, the expected value of B decreases.
For part (bi):
You said that the probability of a type I error for region one would be equal to 0.03. I used this formula and got the same answer:
P[Type I Error for Rejection Region 1] = P[ b = 1 | % = 0.03 ] = the integral from 0 to 1 of (0.03)*(0.97)^(x-1) dx = 0.0304616
I used the geometric distribution in the integral to show my work as for how I got 0.03.
But for the Rejection Region 2 and 3, the integral wouldn't be going from 0 to 1 anymore, that part would change.
So, P[Type I Error for Rejection Region 2] = P[ b <= 2 | % = 0.03 ] = the integral from 0 to 2 of (0.03)*(0.97)^(x-1) dx = 0.06
which is the same answer that you got, except I calculated it differently.
And then, P[Type I Error for Rejection Region 3] = P[ b <= 3 | % = 0.03 ] = the integral from 0 to 3 of (0.03)*(0.97)^(x-1) dx = 0.089
you are messed up because you are including 0 in your support. You never choose 0 batteries. n = {1, 2, 3 ...}
10. ## Re: Geometric Distribution
Okay, so I tried it your way and did:
P[Type I Error for Rejection Region 1 ] = 0.03
P[Type I Error for Rejection Region 2] = p + (1 - p)*p = 0.0591 = 0.06
P[Type I Error for Rejection Region 3] = p + (1 - p)*p + (1 - p)*(1 - p)*p = 0.087
but what I do not understand is how you figured out how to use that to find the probability. I get what you're saying now with how my integrals should not include 0, but I do not get how you figured out how to do it this other way. I wish my teacher would have taught us how to do it by hand instead of using the computer to calculate the values.
11. ## Re: Geometric Distribution
Originally Posted by AwesomeHedgehog
Okay, so I tried it your way and did:
P[Type I Error for Rejection Region 1 ] = 0.03
P[Type I Error for Rejection Region 2] = p + (1 - p)*p = 0.0591 = 0.06
P[Type I Error for Rejection Region 3] = p + (1 - p)*p + (1 - p)*(1 - p)*p = 0.087
but what I do not understand is how you figured out how to use that to find the probability. I get what you're saying now with how my integrals should not include 0, but I do not get how you figured out how to do it this other way. I wish my teacher would have taught us how to do it by hand instead of using the computer to calculate the values.
I just envisioned what the guy/gal in the battery checking booth had to do.
12. ## Re: Geometric Distribution
For the Rejection Region that I'd recommend, would I choose Rejection Region 3 because it makes the rejection region better and it allows for variation to occur?
and for part (bii)
to solve for power, that whole thing just confuses me with the geometric distribution. Do you have any hints on how to start that?
13. ## Re: Geometric Distribution
For part (bii) I remembered that power = 1 - beta = P[Reject H_0 when it is false] = P[Type II Error]
Now, I just need to figure out what the formula is in order to calculate the power for each rejection region
14. ## Re: Geometric Distribution
Originally Posted by AwesomeHedgehog
For part (bii) I remembered that power = 1 - beta = P[Reject H_0 when it is false] = P[Type II Error]
Now, I just need to figure out what the formula is in order to calculate the power for each rejection region
For part (bii)
μ = 0.10
P[Type II Error for Rejection Region 1] = P[ b = 1 | μ = 0.10] = 1 - [the integral from 0 to 1 of (0.10)*(0.90)^(x - 1) dx ] = 0.8945
I'm guessing that that would be similar for the other Rejection Regions, but I'm not sure.
Also, (bii) relates to (biii) which really confuses me. Any help would be appreciated. | 3,650 | 12,267 | {"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} | 3.765625 | 4 | CC-MAIN-2018-17 | latest | en | 0.930471 |
https://www.meritnation.com/ask-answer/question/mechanics-q6-one-end-of-a-light-spring-of-natural-length-d-a/magnetism-and-matter/12494185 | 1,611,574,819,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703565541.79/warc/CC-MAIN-20210125092143-20210125122143-00665.warc.gz | 894,095,863 | 10,168 | # Mechanics Q6. One end of a light spring of natural length d and spring constant k (= mg/d) is fixed on a rigid support and the other end is fixed to a smooth ring of mass m which can slide without friction on a vertical rod fixed at a distance d from the support. Initially, the spring makes an angle of 37° with the horizontal as shown in the figure.The system is released from rest. The speed of the ring at the same angle subtended downward will be (A) $\sqrt{2\mathrm{gd}}$ (B) $\sqrt{3\mathrm{gd}}$ (C) $\sqrt{4\mathrm{gd}}$ (D)
Dear Student
Cos37= h/l
l= h/cos37
l=1.25h
extension = l-h
=1.25h- h= 0.25h
equalling KE and PE
1/2mv2= 1/2k(0.25h)2
v2= k/m x h2/16
v= h/4 √k/m
Regards
• -15
What are you looking for? | 258 | 848 | {"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": 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-2021-04 | latest | en | 0.648639 |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/572/2/a/b/ | 1,618,174,794,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038065492.15/warc/CC-MAIN-20210411204008-20210411234008-00076.warc.gz | 983,399,791 | 56,578 | # Properties
Label 572.2.a.b Level $572$ Weight $2$ Character orbit 572.a Self dual yes Analytic conductor $4.567$ Analytic rank $1$ Dimension $2$ CM no Inner twists $1$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$572 = 2^{2} \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 572.a (trivial)
## Newform invariants
Self dual: yes Analytic conductor: $$4.56744299562$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{13})$$ Defining polynomial: $$x^{2} - x - 3$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$
## $q$-expansion
Coefficients of the $$q$$-expansion are expressed in terms of $$\beta = \frac{1}{2}(1 + \sqrt{13})$$. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q + ( -1 - \beta ) q^{3} + ( -2 + \beta ) q^{7} + ( 1 + 3 \beta ) q^{9} +O(q^{10})$$ $$q + ( -1 - \beta ) q^{3} + ( -2 + \beta ) q^{7} + ( 1 + 3 \beta ) q^{9} - q^{11} + q^{13} + ( -2 + 2 \beta ) q^{17} + ( -3 - \beta ) q^{19} - q^{21} + ( -4 + \beta ) q^{23} -5 q^{25} + ( -7 - 4 \beta ) q^{27} + ( 4 - 4 \beta ) q^{29} + 2 \beta q^{31} + ( 1 + \beta ) q^{33} -4 \beta q^{37} + ( -1 - \beta ) q^{39} + ( 4 - \beta ) q^{41} + ( -2 - 2 \beta ) q^{43} -6 q^{47} -3 \beta q^{49} + ( -4 - 2 \beta ) q^{51} + ( -7 + \beta ) q^{53} + ( 6 + 5 \beta ) q^{57} + ( 10 + 2 \beta ) q^{59} + ( -4 + 6 \beta ) q^{61} + ( 7 - 2 \beta ) q^{63} + ( -6 + 2 \beta ) q^{67} + ( 1 + 2 \beta ) q^{69} + ( -8 + 2 \beta ) q^{71} + ( 1 - 5 \beta ) q^{73} + ( 5 + 5 \beta ) q^{75} + ( 2 - \beta ) q^{77} + ( -6 - 4 \beta ) q^{79} + ( 16 + 6 \beta ) q^{81} + ( 2 - 5 \beta ) q^{83} + ( 8 + 4 \beta ) q^{87} + ( -2 + \beta ) q^{91} + ( -6 - 4 \beta ) q^{93} + ( 12 - 4 \beta ) q^{97} + ( -1 - 3 \beta ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 3q^{3} - 3q^{7} + 5q^{9} + O(q^{10})$$ $$2q - 3q^{3} - 3q^{7} + 5q^{9} - 2q^{11} + 2q^{13} - 2q^{17} - 7q^{19} - 2q^{21} - 7q^{23} - 10q^{25} - 18q^{27} + 4q^{29} + 2q^{31} + 3q^{33} - 4q^{37} - 3q^{39} + 7q^{41} - 6q^{43} - 12q^{47} - 3q^{49} - 10q^{51} - 13q^{53} + 17q^{57} + 22q^{59} - 2q^{61} + 12q^{63} - 10q^{67} + 4q^{69} - 14q^{71} - 3q^{73} + 15q^{75} + 3q^{77} - 16q^{79} + 38q^{81} - q^{83} + 20q^{87} - 3q^{91} - 16q^{93} + 20q^{97} - 5q^{99} + O(q^{100})$$
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
2.30278 −1.30278
0 −3.30278 0 0 0 0.302776 0 7.90833 0
1.2 0 0.302776 0 0 0 −3.30278 0 −2.90833 0
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Atkin-Lehner signs
$$p$$ Sign
$$2$$ $$-1$$
$$11$$ $$1$$
$$13$$ $$-1$$
## Inner twists
This newform does not admit any (nontrivial) inner twists.
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 572.2.a.b 2
3.b odd 2 1 5148.2.a.h 2
4.b odd 2 1 2288.2.a.r 2
8.b even 2 1 9152.2.a.bq 2
8.d odd 2 1 9152.2.a.bg 2
11.b odd 2 1 6292.2.a.k 2
13.b even 2 1 7436.2.a.e 2
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
572.2.a.b 2 1.a even 1 1 trivial
2288.2.a.r 2 4.b odd 2 1
5148.2.a.h 2 3.b odd 2 1
6292.2.a.k 2 11.b odd 2 1
7436.2.a.e 2 13.b even 2 1
9152.2.a.bg 2 8.d odd 2 1
9152.2.a.bq 2 8.b even 2 1
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(572))$$:
$$T_{3}^{2} + 3 T_{3} - 1$$ $$T_{5}$$
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$T^{2}$$
$3$ $$-1 + 3 T + T^{2}$$
$5$ $$T^{2}$$
$7$ $$-1 + 3 T + T^{2}$$
$11$ $$( 1 + T )^{2}$$
$13$ $$( -1 + T )^{2}$$
$17$ $$-12 + 2 T + T^{2}$$
$19$ $$9 + 7 T + T^{2}$$
$23$ $$9 + 7 T + T^{2}$$
$29$ $$-48 - 4 T + T^{2}$$
$31$ $$-12 - 2 T + T^{2}$$
$37$ $$-48 + 4 T + T^{2}$$
$41$ $$9 - 7 T + T^{2}$$
$43$ $$-4 + 6 T + T^{2}$$
$47$ $$( 6 + T )^{2}$$
$53$ $$39 + 13 T + T^{2}$$
$59$ $$108 - 22 T + T^{2}$$
$61$ $$-116 + 2 T + T^{2}$$
$67$ $$12 + 10 T + T^{2}$$
$71$ $$36 + 14 T + T^{2}$$
$73$ $$-79 + 3 T + T^{2}$$
$79$ $$12 + 16 T + T^{2}$$
$83$ $$-81 + T + T^{2}$$
$89$ $$T^{2}$$
$97$ $$48 - 20 T + T^{2}$$ | 2,195 | 4,495 | {"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} | 2.84375 | 3 | CC-MAIN-2021-17 | latest | en | 0.336186 |
http://ma3naido.blogspot.com/2008/10/airfoil-design.html | 1,532,145,055,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676592309.94/warc/CC-MAIN-20180721032019-20180721052019-00096.warc.gz | 220,199,675 | 17,272 | ## Sunday, October 5, 2008
### Airfoil Design
In the sections devoted to Newton’s and Bernoulli’s discoveries, it has already been discussed in general terms the question of how an airplane wing can sustain flight when the airplane is heavier than air. Perhaps the explanation can best be reduced to its most elementary concept by stating that lift (flight) is simply the result of fluid flow (air) about an airfoil—or in everyday language, the result of moving an airfoil (wing), by whatever means, through the air.
Since it is the airfoil which harnesses the force developed by its movement through the air, a discussion and explanation of this structure, as well as some of the material presented in previous discussions on Newton’s and Bernoulli’s laws, will be presented.
An airfoil is a structure designed to obtain reaction upon its surface from the air through which it moves or that moves past such a structure. Air acts in various ways when submitted to different pressures and velocities; but this discussion will be confined to the parts of an airplane that a pilot is most concerned with in flight—namely, the airfoils designed to produce lift. By looking at a typical airfoil profile, such as the cross section of a wing, one can see several obvious characteristics of design. [Figure 2-5] Notice that there is a difference in the curvatures of the upper and lower surfaces of the airfoil (the curvature is called camber). The camber of the upper surface is more pronounced than that of the lower surface, which is somewhat flat in most instances.
In figure 2-5, note that the two extremities of the airfoil profile also differ in appearance. The end which faces forward in flight is called the leading edge, and is rounded; while the other end, the trailing edge, is quite narrow and tapered.
A reference line often used in discussing the airfoil is the chord line, a straight line drawn through the profile connecting the extremities of the leading and trailing edges. The distance from this chord line to the upper and lower surfaces of the wing denotes the magnitude of the upper and lower camber at any point. Another reference line, drawn from the leading edge to the trailing edge, is the “mean camber line.” This mean line is equidistant at all points from the upper and lower contours.
The construction of the wing, so as to provide actions greater than its weight, is done by shaping the wing so that advantage can be taken of the air’s response to certain physical laws, and thus develop two actions from the air mass; a positive pressure lifting action from the air mass below the wing, and a negative pressure lifting action from lowered pressure above the wing.
As the airstream strikes the relatively flat lower surface of the wing when inclined at a small angle to its direction of motion, the air is forced to rebound downward and therefore causes an upward reaction in positive lift, while at the same time airstream striking the upper curved section of the “leading edge” of the wing is deflected upward. In other words, a wing shaped to cause an action on the air, and forcing it downward, will provide an equal reaction from the air, forcing the wing upward. If a wing is constructed in such form that it will cause a lift force greater than the weight of the airplane, the airplane will fly.
However, if all the lift required were obtained merely from the deflection of air by the lower surface of the wing, an airplane would need only a flat wing like a kite. This, of course, is not the case at all; under certain conditions disturbed air currents circulating at the trailing edge of the wing could be so excessive as to make the airplane lose speed and lift. The balance of the lift needed to support the airplane comes from the flow of air above the wing. Herein lies the key to flight. The fact that most lift is the result of the airflow’s downwash from above the wing, must be thoroughly understood in order to continue further in the study of flight. It is neither accurate nor does it serve a useful purpose, however, to assign specific values to the percentage of lift generated by the upper surface of an airfoil versus that generated by the lower surface. These are not constant values and will vary, not only with flight conditions, but with different wing designs.
It should be understood that different airfoils have different flight characteristics. Many thousands of airfoils have been tested in wind tunnels and in actual flight, but no one airfoil has been found that satisfies every flight requirement. The weight, speed, and purpose of each airplane dictate the shape of its airfoil. It was learned many years ago that the most efficient airfoil for producing the greatest lift was one that had a concave, or “scooped out” lower surface. Later it was also learned that as a fixed design, this type of airfoil sacrificed too much speed while producing lift and, therefore, was not suitable for high-speed flight. It is interesting to note, however, that through advanced progress in engineering, today’s high-speed jets can again take advantage of the concave airfoil’s high lift characteristics. Leading edge (Kreuger) flaps and trailing edge (Fowler) flaps, when extended from the basic wing structure, literally change the airfoil shape into the classic concave form, thereby generating much greater lift during slow flight conditions.
On the other hand, an airfoil that is perfectly streamlined and offers little wind resistance sometimes does not have enough lifting power to take the airplane off the ground. Thus, modern airplanes have airfoils which strike a medium between extremes in design, the shape varying according to the needs of the airplane for which it is designed. Figure 2-6 shows some of the more common airfoil sections.
1. Very clear and lucidly written
2. Comprehensive and succinct.
3. complete and clear. All Aeronautical students must visit this site for their studies about airfoil. | 1,223 | 5,981 | {"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} | 3.046875 | 3 | CC-MAIN-2018-30 | latest | en | 0.968473 |
https://www.dollartimes.com/calculate/percentage/60/5000 | 1,643,412,290,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320306346.64/warc/CC-MAIN-20220128212503-20220129002503-00205.warc.gz | 772,995,668 | 3,184 | # What is 60 percent of 5,000?
Percentage of a number
percent of
Calculate a percentage
divided by
Use this calculator to find percentages. Just type in any box and the result will be calculated automatically.
Calculator 1: Calculate the percentage of a number.
• For example: 60% of 5,000 = 3,000
Calculator 2: Calculate a percentage based on 2 numbers.
• For example: 3,000/5,000 = 60%
How much is 60% of 5,000? What is 60% of 5,000 and other numbers?
60% of 5,000 = 3,000.0 60% of 5,250 = 3,150.0 60% of 5,500 = 3,300.0 60% of 5,750 = 3,450.0 60% of 5,010 = 3,006.0 60% of 5,260 = 3,156.0 60% of 5,510 = 3,306.0 60% of 5,760 = 3,456.0 60% of 5,020 = 3,012.0 60% of 5,270 = 3,162.0 60% of 5,520 = 3,312.0 60% of 5,770 = 3,462.0 60% of 5,030 = 3,018.0 60% of 5,280 = 3,168.0 60% of 5,530 = 3,318.0 60% of 5,780 = 3,468.0 60% of 5,040 = 3,024.0 60% of 5,290 = 3,174.0 60% of 5,540 = 3,324.0 60% of 5,790 = 3,474.0 60% of 5,050 = 3,030.0 60% of 5,300 = 3,180.0 60% of 5,550 = 3,330.0 60% of 5,800 = 3,480.0 60% of 5,060 = 3,036.0 60% of 5,310 = 3,186.0 60% of 5,560 = 3,336.0 60% of 5,810 = 3,486.0 60% of 5,070 = 3,042.0 60% of 5,320 = 3,192.0 60% of 5,570 = 3,342.0 60% of 5,820 = 3,492.0 60% of 5,080 = 3,048.0 60% of 5,330 = 3,198.0 60% of 5,580 = 3,348.0 60% of 5,830 = 3,498.0 60% of 5,090 = 3,054.0 60% of 5,340 = 3,204.0 60% of 5,590 = 3,354.0 60% of 5,840 = 3,504.0 60% of 5,100 = 3,060.0 60% of 5,350 = 3,210.0 60% of 5,600 = 3,360.0 60% of 5,850 = 3,510.0 60% of 5,110 = 3,066.0 60% of 5,360 = 3,216.0 60% of 5,610 = 3,366.0 60% of 5,860 = 3,516.0 60% of 5,120 = 3,072.0 60% of 5,370 = 3,222.0 60% of 5,620 = 3,372.0 60% of 5,870 = 3,522.0 60% of 5,130 = 3,078.0 60% of 5,380 = 3,228.0 60% of 5,630 = 3,378.0 60% of 5,880 = 3,528.0 60% of 5,140 = 3,084.0 60% of 5,390 = 3,234.0 60% of 5,640 = 3,384.0 60% of 5,890 = 3,534.0 60% of 5,150 = 3,090.0 60% of 5,400 = 3,240.0 60% of 5,650 = 3,390.0 60% of 5,900 = 3,540.0 60% of 5,160 = 3,096.0 60% of 5,410 = 3,246.0 60% of 5,660 = 3,396.0 60% of 5,910 = 3,546.0 60% of 5,170 = 3,102.0 60% of 5,420 = 3,252.0 60% of 5,670 = 3,402.0 60% of 5,920 = 3,552.0 60% of 5,180 = 3,108.0 60% of 5,430 = 3,258.0 60% of 5,680 = 3,408.0 60% of 5,930 = 3,558.0 60% of 5,190 = 3,114.0 60% of 5,440 = 3,264.0 60% of 5,690 = 3,414.0 60% of 5,940 = 3,564.0 60% of 5,200 = 3,120.0 60% of 5,450 = 3,270.0 60% of 5,700 = 3,420.0 60% of 5,950 = 3,570.0 60% of 5,210 = 3,126.0 60% of 5,460 = 3,276.0 60% of 5,710 = 3,426.0 60% of 5,960 = 3,576.0 60% of 5,220 = 3,132.0 60% of 5,470 = 3,282.0 60% of 5,720 = 3,432.0 60% of 5,970 = 3,582.0 60% of 5,230 = 3,138.0 60% of 5,480 = 3,288.0 60% of 5,730 = 3,438.0 60% of 5,980 = 3,588.0 60% of 5,240 = 3,144.0 60% of 5,490 = 3,294.0 60% of 5,740 = 3,444.0 60% of 5,990 = 3,594.0 | 1,633 | 2,761 | {"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} | 3.640625 | 4 | CC-MAIN-2022-05 | latest | en | 0.905928 |
https://www.sciencenews.org/article/cake-cutting-math-problem-fairness-envy | 1,722,808,225,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640412404.14/warc/CC-MAIN-20240804195325-20240804225325-00787.warc.gz | 772,498,200 | 171,413 | Here’s why mathematicians are so interested in cake cutting
The problem attracts game theorists, computer scientists, economists and more
Ariel Procaccia has thought a lot about how to cut cake over the last 15 years. That’s partly because the Harvard computer scientist has three children who among them have celebrated more than two dozen birthdays. He knows what it’s like to stand with a knife before a layered masterpiece, frosted with buttercream and chocolate curls, while pressed on all sides by small partygoers who instinctively recognize when someone else gets a better slice.
But it’s also because much of Procaccia’s work focuses on exploring the mathematical rules for dividing stuff up. One way to do that is to think abstractly about dessert. For more than 75 years, he and other researchers trying to formalize fairness have been asking the deceptively simple question: What methods for cutting a cake guarantee that everyone who shows up to the party is happy with what they get?
The answers reach far beyond birthday parties. Cake-cutting contemplation is part of a sprawling mathematical subfield focused on the fair division of resources. It has spurred a raft of algorithms informing how to allocate food among hungry communities, how to split rent or chores among roommates, how to draw boundaries for fair voting districts and more. A mathematical problem at its heart, cake cutting connects rigorous reasoning to questions of human preferences and real-world issues, and so attracts not only mathematicians, but also computer scientists, economists, social scientists and legal experts. Questions of fairness (and unfairness) are decidedly universal. Of course, so is dessert. “It’s this very elegant model in which you can really distill what fairness is, and reason about it,” Procaccia says.
The cake, says Steven Brams, a game theorist and political scientist at New York University, is a metaphor for any divisible good, like land or time or limited resources. When cake-cutting insights are applied to settling international disputes, he says, “we are potentially helping the world find solutions.”
Experts have come up with cake-cutting algorithms — the mathematical rules for describing how to cut a cake fairly — many times and in many guises. (The approaches almost always focus on rectangular cakes. The related but more recent “pie-cutting” problem addresses circular desserts or pizza.) The easiest rules reveal how to fairly share a cake between two people: One person cuts the cake into two pieces that they believe to be equal in value, and the other person picks first. Each eater receives a piece that they feel is at least as valuable as the other’s, if not better. Reports of this fair division strategy date back to ancient Greece.
In the 1940s, mathematicians began taking serious interest in a mathematical approach to fairness, using cake cutting as an access point. They started exploring how to fairly share among three people, since I-cut-you-choose is a two-player game. That led to looking for ways to extend those algorithms to arbitrarily large numbers of people, and to asking more nuanced questions, like what is fairness exactly, and how do you prove it?
Cake cutting is easy to formulate and easy to relate to, says game theorist Bettina Klaus of the University of Lausanne in Switzerland, who studies fairness in real-world situations like school choice allocation and equal access to housing. “But at the same time, the problem is mathematically interesting and challenging because of its complexity once the number of agents to share the cake grows.”
Recent years have brought progress in identifying the fewest number of cuts needed for a given number of people, as well as the maximum number of cuts, which can get ridiculously high but at least shows that cake cutting is finite. And new variations on the question keep emerging. What if you divide a cake for multiple groups of people instead of individuals? Or, as explored in a paper published last year, what if cake eaters lie about their preferences? And what if you’re divvying up something that comes in discrete, indivisible pieces, like unopened Halloween candies, instead? By focusing on precise definitions and new scenarios, mathematicians have found new applications and kept cake cutting at the forefront of investigations into fairness.
“You can argue that fairness, or the lack thereof, is one of the most important problems in the world today,” says Brams, who over four decades has published hundreds of works on cake cutting or fairness more generally. “And we’re looking at the theoretical foundations of fairness.”
Recipes for fair cake cutting
Documented experiments in finding fair ways to split stuff up go way back, at least to Hesiod’s poem Theogony, written some 2,700 years ago. In one story in the poem, gods and mortals clashed in Mecone, a mythical Greek city. As a sacrifice to appease the gods, Prometheus, who was both a god and humankind’s greatest benefactor, divided a recently slaughtered ox into two piles, one containing unappealing bare bones covered with a layer of fat and the other containing the desirable meat concealed beneath an unappealing section of stomach. Prometheus invited Zeus to take his pick. Zeus, seduced by the shiny fat, chose the unappetizing bones.
In this ancient story, Prometheus infuses the classic I-cut-you-choose strategy — the simplest version of cake cutting — with deception. But when I-cut-you-choose is executed in pursuit of fairness, it should guarantee the satisfaction of everyone involved.
The outcome is proportional, meaning that each player feels like their slice represents a fair share of the total. So for two players, a player would value their own slice at 1/2; for three, a fair share would be 1/3. (And for some arbitrary n number of cake eaters, a fair share would be 1/n.) If the cake is the same throughout, proportionality is equivalent to all the slices being the same size.
But cake cutting isn’t an interesting mathematical problem if the cake is all the same. Ordinary division and a kitchen scale could readily separate a slab of uniform chocolate sponge into any number of proportional pieces. The problem becomes more complicated if you assume that the cake is heterogeneous — if it’s unevenly frosted, for example, or includes sections of varying flavors and toppings.
A maraschino cherry–lover might choose the smallest slice and feel satisfied if they get the cake’s only cherry. In this case, what mathematicians call the “serendipity of disagreement” gives rise to rich math. The most interesting math arises when there are differing opinions.
A two-person I-cut-you-choose scenario still works here. The divider divides the cake into two pieces of equal value in their view and will be happy with either; the chooser chooses their preferred piece. But increase the number of cake eaters, each with particular preferences, and there’s no easy solution.
Hugo Steinhaus of the University of Warsaw was one of the first mathematicians to dive into this complexity. During World War II, as questions of fair division of land were playing out on a large and violent scale, Steinhaus developed a modified I-cut-you-choose strategy for three players. It came to be called the lone-divider method.
In this approach, one person, let’s call her Alice, cuts the cake into three pieces that she values equally (each at 1/3 of the total). Then a second person, Bob, indicates which of the pieces would be acceptable to him. If he approves at least two pieces, then the third person, Carla, can take any piece she wants, followed by Bob (who has at least one acceptable piece available). Alice gets the one that’s left.
But if either Bob or Carla disapprove of the same piece, then that piece goes to Alice (who valued all pieces equally). The remaining two pieces (which Bob and Carla must value at 2/3 or more of the total) are recombined and shared between Bob and Carla using I-cut-you-choose.
Steinhaus described this algorithm in a short paper published in 1948 in Econometrica. It represented one of the first rigorous investigations in the field of cake cutting. “The rule for the first partner,” Steinhaus wrote, “allows him to cut the object — it may be a cake — as he pleases.”
Steinhaus’ method worked for only three eaters, but in the same paper, he reported that two colleagues had developed an algorithm that could achieve proportionality for any number of cake eaters. The method is known as the last-diminisher method, and it goes like this: One person cuts off a piece of cake they deem to represent a fair share and passes that piece along to the next person. Each remaining player has a chance to either trim the cake (if they think it represents more than a proportional share) or pass (if they think it’s proportionally fair or less than fair). Once everyone has had a chance to trim, or “diminish” the slice, the last person who trimmed gets the piece and exits the game.
The trim is then recombined with the remaining cake, and the process begins again with the remaining players. When only two players are left, they use I-cut-you-choose.
Brams has called the last-diminisher method an elegant solution, and it guarantees that everyone judges their own piece to be at least as valuable as a fair share. But it’s not perfect because it doesn’t take envy into account. In both the lone-divider and last-diminisher approaches, a person who exits the game early may end up coveting a piece that is cut later in the game — even though they thought their piece was proportional. These algorithms are not what mathematicians call “envy-free,” which is another way to think about fairness.
There is another practical limitation to the last-diminisher method: With enough players, the cake that remains in later rounds might end up broken apart by a lot of slicing — or even reduced to crumbs. It’s easy to see how a partygoer might not value that as highly as a whole piece.
Can cake cutting be free of envy?
Since the debut of the last-diminisher method, cake cutting has fueled a small but mighty body of serious mathematics.
The 1960s brought a major step forward when mathematicians John Conway and John Selfridge, independently of each other, came up with a new cutting algorithm for three people. Unlike the work by Steinhaus and colleagues, the new recipe achieved both perceived proportionality and avoided any envy among the recipients.
An envy-free solution, in which no one covets another person’s piece, is easy to achieve, points out computer scientist Haris Aziz of the University of New South Wales in Sydney. Just throw the entire cake away. “If you don’t give anything to anybody, that’s envy-free,” he says.
But if the cake lands in the rubbish bin, no one is happy. In Conway’s and Selfridge’s more pleasing scheme, Alice first divides the cake into three pieces she believes are of equal value. Then, Bob can trim one piece — at most — to create a two-way tie for the most valuable. (The trimmings are set aside.) Carla is left to choose among the three. Then the order reverses, and if Carla didn’t choose the trimmed piece, Bob takes it. Alice gets the one that remains. The eaters then turn to the trimmings, following a similar iterative protocol of cutting, trimming and choosing.
Yet for decades more, an envy-free cake-cutting solution for any arbitrary number of eaters remained elusive. In the late 1980s, on his PBS television show For All Practical Purposes: Introduction to Contemporary Mathematics, mathematician Sol Garfunkel featured the unsolved cake-cutting problem and related questions of fair division.
But the problem wouldn’t go unsolved for much longer. In 1995, Brams at NYU and Alan D. Taylor of Union College in Schenectady, N.Y., devised a new procedure that cuts cake for four people with no one envying anyone else. “That was considered a breakthrough of sorts,” Brams says. It built on the “trimming” approach of Conway and Selfridge, running a similar procedure on all possible pairs of cake eaters. Brams and Taylor described how the procedure could be extended to any number of people.
The approach still had limitations. There was no guarantee of how many cuts it might take. “We showed in general that you could require three cuts or 3 million cuts,” Brams says. Or many, many more.
A few years later, mathematicians Jack Robertson and William Webb of Washington State University in Pullman described a useful computation model that could be used to analyze how many steps, including cuts and evaluations, are required by an algorithm. Its calculations confirmed, for example, that no maximum number of cuts could be predicted for any algorithm known at that time that divided cake proportionally and without envy for any arbitrary number of players.
Over the next few decades, many mathematicians came to wonder whether an upper bound for envy-free cake cutting even existed. If not, in theory, cake cutting could go on forever. What’s more, Procaccia says, no one had figured out the minimum, either.
Is cake cutting infinite?
Procaccia never actually set out to study cake cutting. In 2008, he was teaching a course on the mathematical foundations of artificial intelligence. One day, walking home after delivering a lecture on resource allocation and the Robertson-Webb model, he realized how he could find a lower bound — a minimum number of steps, including cuts — for envy-free cake cutting for any number of people. The lower bound he found was somewhere around n² steps, where n is the number of cake eaters.
That would lead to his first paper on cake. Procaccia has a knack for giving mathematical papers catchy titles. The lower-bound paper, published in 2009, was titled “Thou shalt covet thy neighbor’s cake.” In 2010, he coauthored one called “Truth, justice, and cake cutting,” which introduced the question of truthfulness — in addition to guaranteeing proportionality and removing envy. If a person hides their preferences during the cutting, someone may end up with an unequal share. It’s “mathematically fascinating,” Procaccia says.
As Procaccia continued in the field, he began thinking more about useful algorithms that could put insights from cake cutting — and the theory of fair division in general — to good use. One example: dividing rent.
The easiest way, of course, is to divide the total due by the number of inhabitants. But that ignores the “serendipity of disagreement.” One person might want a window, another might prefer the bigger closet. In 2014, Procaccia and colleagues designed a web-based tool called Spliddit that collected users’ preferences and produced mathematically fair ways to divide anything, from rent among roommates to possessions among divorcees.
The biggest recent breakthrough in cake cutting, Procaccia says, came from Aziz and computer scientist Simon Mackenzie, based in Sydney, who determined an upper bound on envy-free, proportional cake cutting. First, in 2015, the pair tackled the problem of how to share cake among four people. By borrowing ideas from Conway and Selfridge and from Brams and Taylor, the team devised an algorithm that produced an upper bound of 203 steps, which could include almost as many cuts. That’s a lot but not too unreasonable.
A year later, the team extended the approach to an arbitrary number of people, reporting an algorithm with a finite number of cuts for envy-free, proportional cake cutting. It was a potentially astronomical number of cuts, but it was finite — answering a long-standing question in the field.
Cake cutting for n people, Aziz and Mackenzie reported, could require as many as n^n^n^n^n^n operations. That’s a totally unreasonable number. The maximum number of steps for five people would be around 2 x 102,180. That means five people cutting the cake billions of times per second for 100 trillion years might barely be getting started.
However, Aziz says the algorithm can be adapted to a more reasonable, though still really big upper bound if the partygoers, for example, allow for a little cake to be left over. And it’s still possible that mathematicians could bring that upper bound lower in the future.
The cake-cutting problem endures
Explorations into the question of how to fairly cut a cake aren’t over. Inspired by Procaccia’s 2010 paper on truthfulness, computer scientist Biaoshuai Tao of Shanghai Jiao Tong University investigated what happens when you try to account for dishonest cake eaters. “If everyone knows how the cake is allocated, then I should get more if I tell the truth,” he says.
But in some cases, dishonesty can yield an advantage. If Alice and Bob were to divide a cake, and Alice knew that Bob always preferred chocolate, she might knowingly divide the cake unequally so the smaller piece contained more chocolate. Then Bob would choose according to his preference, and Alice would get the larger piece.
In his work, presented in July 2022 at the Association for Computing Machinery Conference on Economics and Computation, in Boulder, Colo., Tao found that truthfulness and proportionality are incompatible, making it impossible to construct a cake-cutting algorithm that strictly guarantees truthfulness, proportionality and no envy.
Practical applications for cake cutting also continue to abound. Klaus, in Lausanne, points to school choice as an example.
A district with limited seats in certain schools has to balance the school board priorities — scores on entrance exams or geographic distribution, for example — with the preferences of parents to try to find a proportional solution with a fair value. “In the past, schools were just assigned … without asking people what they want,” Klaus says. “The school choice comes from the fact that the preferences of the parents or the kids would be taken into account.”
And there are plenty of other real-world applications for questions of fair division. Brams has used ideas from cake cutting to study fair voting procedures. (To elect their leaders, at least four scientific societies, including the Mathematical Association of America, adopted an algorithm developed by him.)
Procaccia has applied fair division algorithms to model food allocation. Aziz is exploring applications ranging from how to divvy up chores or other tasks that can’t be divided to how to best schedule doctors’ shifts in hospitals.
Others are studying fair allocation of goods that can’t be cleanly divided. After a divorce, for instance, former partners might come to agreement on a fair split only if some items are taken out of consideration. These investigations include approaches that are close to envy-free if not mathematically perfect.
Even after decades of investigation, cake cutting isn’t like a simple jigsaw puzzle with a well-defined solution. Instead, over time, it has evolved into a kind of mathematical sandbox, a constructive playground that brings together abstract proofs and intuitive applications. The more researchers explore it, the more there is to explore.
“I’m interested in it now not only because it’s beautiful in math,” Tao says, “but I still believe there’s a lot to be done.” | 3,955 | 19,228 | {"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-2024-33 | latest | en | 0.948558 |
https://convertcalculators.com/0-20-as-a-fraction/ | 1,675,569,785,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500215.91/warc/CC-MAIN-20230205032040-20230205062040-00010.warc.gz | 205,452,889 | 13,273 | # 0.20 As A Fraction
By Desk Incharge - 5 February 2023
0.20 as a fraction is the 100% free and reliable online calculator that helps you to solve any calculation-related problems and provides you with precise measurements. 0.20 as a fraction Online Calculator and Math Help. 0.20 as a fraction is a free and easy-to-use scientific calculator that supports many advanced features including unit conversion, and equations. 0.20 as a fraction, however, this online unit conversion tool will help you convert measurement units anytime and solve homework problems quickly using metric conversion tables 0.20 as a fraction.
### 1. 0.20 as a Fraction [Decimal to Fraction Calculator]
https://www.asafraction.net/number/0.20
Steps to convert 0.20 into a fraction. ... Multiply both the numerator and denominator by 10 for each digit after the decimal point. ... In order to reduce the ...
## 4. 0.20 as a fraction
https://www.geteasysolution.com/0.20_as_a_fraction
Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. 0.20 = 0.20/1 = 2/10. And finally we have: 0.20 as a fraction ...
## 5. 0.20 as a fraction in simplest form
https://calculator.name/as-a-fraction/0.20
What is 0.20 as a fraction? 0.20 as a fraction in simplest form is written as 1/5. A fraction represents a part of a whole, written in the form of p/q where ...
## 6. Convert to a Simplified Fraction 0.20 | Mathway
https://www.mathway.com/popular-problems/Algebra/684824
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are 2 2 numbers to the right of the decimal point, ...
#### 8. What is 0.20 as a fraction? - MathLearnIt.com
https://mathlearnit.com/what-is-0-20-as-a-fraction
Solution and how to convert 0.20 into a fraction ... seen in other parts of this website, decimal numbers can be represented as fractions (and vice-versa). | 500 | 1,910 | {"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-2023-06 | latest | en | 0.887494 |
http://us.metamath.org/ileuni/divdivdivap.html | 1,653,129,065,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662539049.32/warc/CC-MAIN-20220521080921-20220521110921-00141.warc.gz | 59,158,689 | 7,124 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > divdivdivap GIF version
Theorem divdivdivap 7868
Description: Division of two ratios. Theorem I.15 of [Apostol] p. 18. (Contributed by Jim Kingdon, 25-Feb-2020.)
Assertion
Ref Expression
divdivdivap (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐴 / 𝐵) / (𝐶 / 𝐷)) = ((𝐴 · 𝐷) / (𝐵 · 𝐶)))
Proof of Theorem divdivdivap
StepHypRef Expression
1 simprrl 506 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → 𝐷 ∈ ℂ)
2 simprll 504 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → 𝐶 ∈ ℂ)
3 simprlr 505 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → 𝐶 # 0)
4 divclap 7833 . . . . . . 7 ((𝐷 ∈ ℂ ∧ 𝐶 ∈ ℂ ∧ 𝐶 # 0) → (𝐷 / 𝐶) ∈ ℂ)
51, 2, 3, 4syl3anc 1170 . . . . . 6 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐷 / 𝐶) ∈ ℂ)
6 simpll 496 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → 𝐴 ∈ ℂ)
7 simplrl 502 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → 𝐵 ∈ ℂ)
8 simplrr 503 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → 𝐵 # 0)
9 divclap 7833 . . . . . . 7 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐵 # 0) → (𝐴 / 𝐵) ∈ ℂ)
106, 7, 8, 9syl3anc 1170 . . . . . 6 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐴 / 𝐵) ∈ ℂ)
115, 10mulcomd 7202 . . . . 5 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐷 / 𝐶) · (𝐴 / 𝐵)) = ((𝐴 / 𝐵) · (𝐷 / 𝐶)))
12 simplr 497 . . . . . 6 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐵 ∈ ℂ ∧ 𝐵 # 0))
13 simprl 498 . . . . . 6 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐶 ∈ ℂ ∧ 𝐶 # 0))
14 divmuldivap 7867 . . . . . 6 (((𝐴 ∈ ℂ ∧ 𝐷 ∈ ℂ) ∧ ((𝐵 ∈ ℂ ∧ 𝐵 # 0) ∧ (𝐶 ∈ ℂ ∧ 𝐶 # 0))) → ((𝐴 / 𝐵) · (𝐷 / 𝐶)) = ((𝐴 · 𝐷) / (𝐵 · 𝐶)))
156, 1, 12, 13, 14syl22anc 1171 . . . . 5 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐴 / 𝐵) · (𝐷 / 𝐶)) = ((𝐴 · 𝐷) / (𝐵 · 𝐶)))
1611, 15eqtrd 2114 . . . 4 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐷 / 𝐶) · (𝐴 / 𝐵)) = ((𝐴 · 𝐷) / (𝐵 · 𝐶)))
1716oveq2d 5559 . . 3 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐶 / 𝐷) · ((𝐷 / 𝐶) · (𝐴 / 𝐵))) = ((𝐶 / 𝐷) · ((𝐴 · 𝐷) / (𝐵 · 𝐶))))
18 simprr 499 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐷 ∈ ℂ ∧ 𝐷 # 0))
19 divmuldivap 7867 . . . . . . 7 (((𝐶 ∈ ℂ ∧ 𝐷 ∈ ℂ) ∧ ((𝐷 ∈ ℂ ∧ 𝐷 # 0) ∧ (𝐶 ∈ ℂ ∧ 𝐶 # 0))) → ((𝐶 / 𝐷) · (𝐷 / 𝐶)) = ((𝐶 · 𝐷) / (𝐷 · 𝐶)))
202, 1, 18, 13, 19syl22anc 1171 . . . . . 6 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐶 / 𝐷) · (𝐷 / 𝐶)) = ((𝐶 · 𝐷) / (𝐷 · 𝐶)))
212, 1mulcomd 7202 . . . . . . . 8 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐶 · 𝐷) = (𝐷 · 𝐶))
2221oveq1d 5558 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐶 · 𝐷) / (𝐷 · 𝐶)) = ((𝐷 · 𝐶) / (𝐷 · 𝐶)))
231, 2mulcld 7201 . . . . . . . 8 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐷 · 𝐶) ∈ ℂ)
24 simprrr 507 . . . . . . . . 9 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → 𝐷 # 0)
251, 2, 24, 3mulap0d 7815 . . . . . . . 8 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐷 · 𝐶) # 0)
26 dividap 7856 . . . . . . . 8 (((𝐷 · 𝐶) ∈ ℂ ∧ (𝐷 · 𝐶) # 0) → ((𝐷 · 𝐶) / (𝐷 · 𝐶)) = 1)
2723, 25, 26syl2anc 403 . . . . . . 7 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐷 · 𝐶) / (𝐷 · 𝐶)) = 1)
2822, 27eqtrd 2114 . . . . . 6 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐶 · 𝐷) / (𝐷 · 𝐶)) = 1)
2920, 28eqtrd 2114 . . . . 5 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐶 / 𝐷) · (𝐷 / 𝐶)) = 1)
3029oveq1d 5558 . . . 4 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (((𝐶 / 𝐷) · (𝐷 / 𝐶)) · (𝐴 / 𝐵)) = (1 · (𝐴 / 𝐵)))
31 divclap 7833 . . . . . 6 ((𝐶 ∈ ℂ ∧ 𝐷 ∈ ℂ ∧ 𝐷 # 0) → (𝐶 / 𝐷) ∈ ℂ)
322, 1, 24, 31syl3anc 1170 . . . . 5 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐶 / 𝐷) ∈ ℂ)
3332, 5, 10mulassd 7204 . . . 4 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (((𝐶 / 𝐷) · (𝐷 / 𝐶)) · (𝐴 / 𝐵)) = ((𝐶 / 𝐷) · ((𝐷 / 𝐶) · (𝐴 / 𝐵))))
3410mulid2d 7199 . . . 4 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (1 · (𝐴 / 𝐵)) = (𝐴 / 𝐵))
3530, 33, 343eqtr3d 2122 . . 3 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐶 / 𝐷) · ((𝐷 / 𝐶) · (𝐴 / 𝐵))) = (𝐴 / 𝐵))
3617, 35eqtr3d 2116 . 2 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐶 / 𝐷) · ((𝐴 · 𝐷) / (𝐵 · 𝐶))) = (𝐴 / 𝐵))
376, 1mulcld 7201 . . . 4 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐴 · 𝐷) ∈ ℂ)
387, 2mulcld 7201 . . . 4 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐵 · 𝐶) ∈ ℂ)
39 mulap0 7811 . . . . 5 (((𝐵 ∈ ℂ ∧ 𝐵 # 0) ∧ (𝐶 ∈ ℂ ∧ 𝐶 # 0)) → (𝐵 · 𝐶) # 0)
4039ad2ant2lr 494 . . . 4 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐵 · 𝐶) # 0)
41 divclap 7833 . . . 4 (((𝐴 · 𝐷) ∈ ℂ ∧ (𝐵 · 𝐶) ∈ ℂ ∧ (𝐵 · 𝐶) # 0) → ((𝐴 · 𝐷) / (𝐵 · 𝐶)) ∈ ℂ)
4237, 38, 40, 41syl3anc 1170 . . 3 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐴 · 𝐷) / (𝐵 · 𝐶)) ∈ ℂ)
43 divap0 7839 . . . 4 (((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0)) → (𝐶 / 𝐷) # 0)
4443adantl 271 . . 3 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (𝐶 / 𝐷) # 0)
45 divmulap 7830 . . 3 (((𝐴 / 𝐵) ∈ ℂ ∧ ((𝐴 · 𝐷) / (𝐵 · 𝐶)) ∈ ℂ ∧ ((𝐶 / 𝐷) ∈ ℂ ∧ (𝐶 / 𝐷) # 0)) → (((𝐴 / 𝐵) / (𝐶 / 𝐷)) = ((𝐴 · 𝐷) / (𝐵 · 𝐶)) ↔ ((𝐶 / 𝐷) · ((𝐴 · 𝐷) / (𝐵 · 𝐶))) = (𝐴 / 𝐵)))
4610, 42, 32, 44, 45syl112anc 1174 . 2 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → (((𝐴 / 𝐵) / (𝐶 / 𝐷)) = ((𝐴 · 𝐷) / (𝐵 · 𝐶)) ↔ ((𝐶 / 𝐷) · ((𝐴 · 𝐷) / (𝐵 · 𝐶))) = (𝐴 / 𝐵)))
4736, 46mpbird 165 1 (((𝐴 ∈ ℂ ∧ (𝐵 ∈ ℂ ∧ 𝐵 # 0)) ∧ ((𝐶 ∈ ℂ ∧ 𝐶 # 0) ∧ (𝐷 ∈ ℂ ∧ 𝐷 # 0))) → ((𝐴 / 𝐵) / (𝐶 / 𝐷)) = ((𝐴 · 𝐷) / (𝐵 · 𝐶)))
Colors of variables: wff set class Syntax hints: → wi 4 ∧ wa 102 ↔ wb 103 = wceq 1285 ∈ wcel 1434 class class class wbr 3793 (class class class)co 5543 ℂcc 7041 0cc0 7043 1c1 7044 · cmul 7048 # cap 7748 / cdiv 7827 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-13 1445 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 ax-sep 3904 ax-pow 3956 ax-pr 3972 ax-un 4196 ax-setind 4288 ax-cnex 7129 ax-resscn 7130 ax-1cn 7131 ax-1re 7132 ax-icn 7133 ax-addcl 7134 ax-addrcl 7135 ax-mulcl 7136 ax-mulrcl 7137 ax-addcom 7138 ax-mulcom 7139 ax-addass 7140 ax-mulass 7141 ax-distr 7142 ax-i2m1 7143 ax-0lt1 7144 ax-1rid 7145 ax-0id 7146 ax-rnegex 7147 ax-precex 7148 ax-cnre 7149 ax-pre-ltirr 7150 ax-pre-ltwlin 7151 ax-pre-lttrn 7152 ax-pre-apti 7153 ax-pre-ltadd 7154 ax-pre-mulgt0 7155 ax-pre-mulext 7156 This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1687 df-eu 1945 df-mo 1946 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-ne 2247 df-nel 2341 df-ral 2354 df-rex 2355 df-reu 2356 df-rmo 2357 df-rab 2358 df-v 2604 df-sbc 2817 df-dif 2976 df-un 2978 df-in 2980 df-ss 2987 df-pw 3392 df-sn 3412 df-pr 3413 df-op 3415 df-uni 3610 df-br 3794 df-opab 3848 df-id 4056 df-po 4059 df-iso 4060 df-xp 4377 df-rel 4378 df-cnv 4379 df-co 4380 df-dm 4381 df-iota 4897 df-fun 4934 df-fv 4940 df-riota 5499 df-ov 5546 df-oprab 5547 df-mpt2 5548 df-pnf 7217 df-mnf 7218 df-xr 7219 df-ltxr 7220 df-le 7221 df-sub 7348 df-neg 7349 df-reap 7742 df-ap 7749 df-div 7828 This theorem is referenced by: recdivap 7873 divcanap7 7876 divdivap1 7878 divdivap2 7879 divdivdivapi 7930 qreccl 8808
Copyright terms: Public domain W3C validator | 5,740 | 8,170 | {"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-2022-21 | latest | en | 0.11664 |
https://acasestudy.com/ll-bean-case-study/ | 1,723,584,366,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641085898.84/warc/CC-MAIN-20240813204036-20240813234036-00827.warc.gz | 61,756,444 | 16,372 | # LL Bean Case Study
Then, we analyze the historical forecast errors (named MAP ratios) and the frequency distribution of these errors for ACH Individual Item by using the historical demand and forecast data. Once the historical forecast errors is determined, we define future forecast errors by using frequency distribution of past forecast errors as probability distribution. Finally we find the service level based on a profit margin calculation: determine by balancing contribution margin if demanded against its liquidation cost if not demanded.
We can notice that for new Items It Is more complicated to have good prevision because we know very little about them. 2.
We Will Write a Custom Case Study Specifically
For You For Only \$13.90/page!
order now
What Item costs and revenues are relevant to the cession of how many units of that item to stock? Principally, L. L. Bean will need 3 types of data to decide how many units of an item to stock. First, they need to know the buying cost of the item. Then, they need the selling price of the item. With these 2 figures, they can calculate the profit margin and the costs of understanding.
The 3rd figure they need is the liquidation cost of an item.
With the liquidation cost, they can calculate the costs of overstocking. With all these data, we can decide the final amount of Items to stock by comparing the understanding costs and overstocking sots. 3. What information should Scott Solar have available to help him arrive at a demand forecast for a particular style of men’s shirt that is a new catalog item? Scott Solar should have data about actual and forecasted demand of new item that were previously introduced.
With these data, he can know the different costs of launching a new Item.
Then, he should have an idea of the selling price given by marketing, sales and production department. With that, he has to know cost of sales, commissions provided for sales, stock outs and backorder cost. He can also compare this new item to the competitor and get sales information. It will help him to understand the existing market trends for that new item.
Following that he should know the level of buffer stock he should have to avoid stock outs by matching stock out costs and over-stocking costs.
Finally he should precise the service level by calculating the profit margin and observe If new products are pulling customers away from existing products. All of this will help him to forecast the demand for a new catalogue item. 4. What should L.
L. Bean do to improve its forecasting process? L. L. Bean has 5 important things if the company wants to improve its forecasting process: They have to have more than they have market researches to their products they will sell.
Actually, they will be understand clearly all news tendencies so they can adapt their stock to the others They don’t have to understand their real demand, because the goal of the real demand Is to Increase the profitability In the business world, a company NAS to unreason Ana Tina a solution ton malting ten accurate Ana also a Emily data that supports the business decisions The company has to have a forecasting discipline.
This one will include a commitment to guide the forecasting process in the firm. Moreover, forecasting is strength and an element of strategic decision-making. Right people have to be involved. In fact, the forecasting management involves that people need to have an easy access to input their intelligence for the forecast, for those who have market information. This intelligence has to be used because this will provide information on future demand spikes and troughs. | 721 | 3,650 | {"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-2024-33 | latest | en | 0.936343 |
http://mathoverflow.net/revisions/28322/list | 1,368,998,625,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368698080772/warc/CC-MAIN-20130516095440-00092-ip-10-60-113-184.ec2.internal.warc.gz | 163,515,751 | 4,922 | ## Return to Answer
2 added 27 characters in body
As HenrikRüping wrote, my comment is false. Nevertheless, I think the method is interesting (obviously, it isn't mine), although it gives something "explicit", but not "compact". Maybe you could provide us with context? For example, are you interested in the behavior when $k \rightarrow + \infty$ (assuming the field is topological)?
If $XAX^{-1}$ and $YQY^{-1}$ are "nice" (diagonal or Jordan normal form), then make the change of variable (is this English?) $P'=XPY$. Then viewing $S_k$ as a linear function of $P$, $XS_k(P)Y=\sum_{i=1}^k XAX^{-1} P' YQY^{-1}$, so up to a change of base on $M_{m,n}(K)$, the endomorphism $S_k$ of this vector space is given in a nice form (eigenvalues are known). But I'm not sure this is really what you're asking for, and your last comment suggests you already know what I just wrote.
1
As HenrikRüping wrote, my comment is false. Nevertheless, I think the method is interesting, although it gives something "explicit", but not "compact". Maybe you could provide us with context? For example, are you interested in the behavior when $k \rightarrow + \infty$ (assuming the field is topological)?
If $XAX^{-1}$ and $YQY^{-1}$ are "nice" (diagonal or Jordan normal form), then make the change of variable (is this English?) $P'=XPY$. Then viewing $S_k$ as a linear function of $P$, $XS_k(P)Y=\sum_{i=1}^k XAX^{-1} P' YQY^{-1}$, so up to a change of base on $M_{m,n}(K)$, the endomorphism $S_k$ of this vector space is given in a nice form (eigenvalues are known). But I'm not sure this is really what you're asking for, and your last comment suggests you already know what I just wrote. | 472 | 1,678 | {"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} | 3.03125 | 3 | CC-MAIN-2013-20 | latest | en | 0.898352 |
https://studyres.com/doc/1286296/?page=2 | 1,624,184,044,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487660269.75/warc/CC-MAIN-20210620084505-20210620114505-00280.warc.gz | 488,633,965 | 10,250 | # Download Databases and Data Mining, Fall 2005 Lab Session 1 MSc Bio
Survey
* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Document related concepts
Nonlinear dimensionality reduction wikipedia, lookup
K-nearest neighbors algorithm wikipedia, lookup
Naive Bayes classifier wikipedia, lookup
Transcript
```Databases and Data Mining, Fall 2005
Lab Session 1
MSc Bio Informatics, Leiden University and TU Delft
Peter van der Putten (putten-at-liacs.nl)
Ron Breukelaar (rbreukel-at-liacs.nl)
1. Animal Trees
In this assignment we use a data set of animals and their attributes. Using a
decision tree classifier the computer learns to classify animals into different
categories (mammals, fish, reptiles etc).
1.1 The data set can be found here. Without using the data mining tool, draw a
decision tree of three levels deep that classifies animals into a mammal, bird,
reptile, fish, amphibian, insect or invertebrate. The decision tree doesn’t
necessarily need to be correct for all animals.
Now we are going to let the computer discover a decision tree itself. First
zoo.arff data set in WEKA by double clicking (or choose start menu – weka
– weka-3-4 – Weka Explorer – Open file).
1.2 What is the number of concepts, attributes and instances in this data set?
Let us build some classifiers. Go to the classifier tab. We will use 66% of the
animals to build the models, and the remaining 34% to evaluate the quality of the
model., so select percentage split – 66%. First we will build a ‘naïve’
model that just predicts the most occurring class in the data set for each animal.
This corresponds to a decision tree of depth 0. Click start to build a model.
1.3 What % of animals is correctly classified?
1.4 Into what category are all these animals classified and why?
1.5 Now build a decision tree of depth 1 (a.k.a. a decision stump - select
choose – trees – decision stump). Draw the discovered decision
tree.
1.6 What % of animals is correctly classified?
1.7 Give an example of an animal that would not be classified correctly by this
model.
1.8 Now build a decision tree of any depth (a.k.a. a J48 tree). What % of
animals is correctly classified?
1.9 Give an example of an animal that would not be classified correctly by this
model.
2. Using pencil, paper and Naive Bayes for diabetes diagnosis
In this exercise you will create a Naive Bayes model on fictitious data for
diagnosis of diabetes – without using a mining tool. A real system could for
instance be used to aid diagnosis, or to identify patients at risk of becoming
diabetic at a later stage.
2.1 Using the data below and the Naive Bayes algorithm, would a young, slim
female be classified as diabetic? With what probability?
2.2 Using the data below and the Naive Bayes algorithm, would a old overweight
male be classified as diabetic? With what probability?
2.3 Why is it relatively straightforward to implement Naïve Bayes in a database?
GENDER
F
F
M
M
M
F
F
AGE
YOUNG
OLD
YOUNG
MIDDLE
OLD
YOUNG
YOUNG
WEIGHT
NORMAL
NORMAL
NORMAL
NORMAL
NORMAL
OVERWEIGHT
SLIM
DIABETES
NO
NO
NO
NO
NO
NO
NO
F
M
M
M
F
M
F
F
M
M
MIDDLE
YOUNG
MIDDLE
OLD
MIDDLE
OLD
MIDDLE
OLD
YOUNG
OLD
SLIM
SLIM
SLIM
SLIM
NORMAL
NORMAL
OVERWEIGHT
OVERWEIGHT
OVERWEIGHT
SLIM
NO
NO
NO
NO
YES
YES
YES
YES
YES
YES
3. Using the data mining tool for diabetes diagnosis
One of the data sets in zip file is diabetes.arff. All patients in this data sets are
females >21 yrs of Pima Indian heritage from Phoenix, Arizona and is often used
(open in a text editor).
3.1 Using WEKA Explorer create various classifiers to fill in the table below. Try
out various parameter settings to create better models. Report on any non
default settings used.
30% Hold Out Validation
accuracy
10 Fold Cross Validation
Average accuracy
Decision Tree (J48)
Non default settings:
Naïve Bayes
Non default settings:
Nearest Neighbour (IBk)
Non default settings:
WEKA also offers a tool (‘Experimenter’) to set up benchmarking experiments.
For instance in the example below Nearest Neighbor is benchmarked against
Naïve Bayes on diabetes and heart disease diagnosis data over 10 runs of 10
fold cross validation.
Repeat the experiments from the previous exercise with 10 runs of 10 fold cross
validation and note the results below. Hints: hit New to start; set up the
experiment as in the picture above; hit run in the second tab; in the third tab
select Scheme and Scheme options as Columns and select Perform test.
Average accuracy
Decision Tree (J48)
Non default settings:
Naïve Bayes
Non default settings:
Nearest Neighbor (IBk)
Non default settings:
Standard Deviation
4. Classification for Bio Informatics Applications (optional)
The zip file from assignment 1 contains a number of (bio)medical data sets. Most
data sets contain a small description in the header – to read this open the file in a
text editor like notepad. For a number of data sets (minimum 2) build a decision
stump, a decision tree and optionally another type of classifier. For each data set
note:
1. The goal of the classifier: what needs to be predicted
2. A high level description of the attributes available
3. The classification accuracy for each classifier type
4. The patterns discovered by at least one of the classifiers
5. A suggestion of how such a prediction can be used in practice
```
Related documents | 1,357 | 5,379 | {"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-2021-25 | latest | en | 0.831095 |
https://breathmath.com/page/2/ | 1,642,810,857,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303717.35/warc/CC-MAIN-20220121222643-20220122012643-00345.warc.gz | 204,126,760 | 28,336 | • ## Coordinate Geometry Exercise 14.3 – Class 10
Coordinate Geometry Exercise 14.3 – Questions: Find the distance between the following pairs of points (i) (8, 3) and (8,-7) (ii) (1,-3) and (-4, 7) (iii) (-4, 5) and (-12, 3) (iv) 6, 5) and (4, 4) (v) (2,0) and (0, 3) (vi) (2, 8) and (6, 8) (vii) (a, b) and (c, b) (viii) […]
• ## Coordinate Geometry Exercise 14.2 – Class 10
Coordinate Geometry Exercise 14.2 – Questions: Find the equation of the line whose angle of inclination and y-intercept are given. (i) θ = 60˚, y-intercept is -2. (ii) θ = 45˚, y-intercept is 3. Find the equation of the line whose slope and y-intercept are given. (i) Slope = 2, y-intercept = -4 (ii) Slope […]
• ## Coordinate Geometry Exercise 14.1 – Class 10
Coordinate Geometry Exercise 14.1 – Questions: Find the slope of the curve whose inclination is (i) 90˚ (ii) 45˚ (iii) 30˚ (iv) 0˚ Find the angles of inclination of straight lines whose slopes are (i)√3 (ii) 1 (iii) 1/√3 Find the slope of the line joining the points (i) (-4, 1) and (-5, 2) (ii) […]
• ## Trigonometry Exercise 13.5 – Class 10
Trigonometry Exercise 13.5 – Questions: Find the value of ‘x’: (i) (ii) (iii) (iv) (v) II. A tall building casts a shadow of 300 m long when the sun’s altitude (elevation) is 30˚. Find the height of the tower. From the top o a building 50√3 m high, the angle of depression of an object […]
• ## Trigonometry Exercise 13.4 – Class 10
Trigonometry Exercise 13.4 – Solutions: Evaluate: tan65˚/cot25˚ sin18˚/cos72˚ iii. cos48˚- sin42˚ cosec31˚ – sec59˚ cot34˚ – tan56˚ sin36˚/cos54˚ – sin54˚/cos36˚ vii. sec70˚ sin20˚ – cos70˚cosec20˚ viii. cos213˚ – sin277˚ Prove that: sin35˚ sin55˚ – cos35˚cos55˚ = 0 tan10˚tan15˚tan75˚tan80˚ = 1 iii. cos38˚cos52˚ – sin38˚sin52˚ = 0 III. If sin5θ = cos4θ, where 4θ […]
• ## Trigonometry Exercise 13.3 – Class 10
Trigonometry Exercise 13.3 – Questions: I. Show that (1 – sin2θ) sec2 θ = 1 (1 + tan2 θ) cos2 θ = 1 (1 + tan2 θ)(1 – sin θ)( 1 + sin θ) = 1 sin θ/(1+cosθ) + 1+cosθ/sinθ = 2 cosec θ 1 + sinθ/1 – sinθ = (sec θ + tan θ)2 […]
• ## Trigonometry Exercise 13.2 – Class X
Trigonometry Exercise 13.2 – Questions: I. Answer the following questions: What trigonometric ratios of angles from 0 to 90 are equal to 0? Which trigonometric ratios of angles from 0 to 90 are equal to 1? Which trigonometric ratios of angles from 0 to 90 are equal to 1/2? Which trigonometric ratios of angles from […]
• ## Trigonometry Exercise 13.1 – Class 10
Trigonometry Exercise 13.1 – Questions: Find sin θ and cos θ for the following: (i) (ii) (iii) 2.Find the following: If sin x = 3/5 , cosec x = ______________ If cos x = 24/25, sec x = _______________ If tan x = 7/24 , cot x = _______________ If cosec x = 25/15 , […]
• ## Pythagoras Theorem Exercise 12.2 – Class 10
Pythagoras Theorem – Exercise 12.2 – Questions: Verify whether the following measures represent the sides of a right angled triangle. (i)1, 2, √3 (ii) √2, √3, √5 (iii) 6√3, 12, 6 (iv) m2 – n2, 2mn, m2 + n2 In triangle ∆ABC, a + b = 18 units, b + c = 25 units and […]
• ## Pythagoras Theorem Exercise 12.1 – Class 10
Pythagoras Theorem – Exercise 12.1 – Questions: a. Numerical problems based on Pythagoras theorem. The sides of a right angled triangle containing the right angle are 5 cm and 12 cm, find its hypotenuse. Find the length often diagonal of a square of side 12 cm. The length of the diagonal of a rectangular playground […] | 1,237 | 3,432 | {"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} | 3.890625 | 4 | CC-MAIN-2022-05 | latest | en | 0.711398 |
https://www.nagwa.com/en/videos/126137139809/ | 1,719,057,127,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862396.85/warc/CC-MAIN-20240622112740-20240622142740-00115.warc.gz | 775,407,957 | 33,758 | Question Video: Adding Three-Digit Numbers to Two-Digit Numbers by Counting in Tens | Nagwa Question Video: Adding Three-Digit Numbers to Two-Digit Numbers by Counting in Tens | Nagwa
# Question Video: Adding Three-Digit Numbers to Two-Digit Numbers by Counting in Tens Mathematics
Count in tens to find the sum. 643 + 40 = ＿.
01:04
### Video Transcript
Count in tens to find the sum.
643 plus 40 equals what? We have to start at 643 and count forward 40 or four 10s. 643, 653, 663, 673, 683. 643 plus 40 equals 683. We started at 643 on the number line, and we counted forward in tens. 653, 663, 673, 683. 643 plus 40 equals 683.
## Join Nagwa Classes
Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!
• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions | 227 | 840 | {"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} | 3.234375 | 3 | CC-MAIN-2024-26 | latest | en | 0.797814 |
https://statskey.com/where-can-i-pay-for-excel-and-statistics-assignment-help | 1,725,825,601,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651017.43/warc/CC-MAIN-20240908181815-20240908211815-00423.warc.gz | 539,037,580 | 28,517 | # Where can I pay for Excel and statistics assignment help?
## Where can I pay for Excel and statistics assignment help?
Where directory I pay for Excel and statistics assignment help? Hi, I need to go over How to make Excel: how do I set up a “short access box” on cell xx and xyz with 3 values, so that on cell xx when y is 3 just 5 mins after x. So first I have the range checkbox in that box and second the ranges loop, and for the 5 seconds I’d like to get y,7 so that on the 4 rows all the time. The problem that I have is if I try this one in the minute box it gives me the number of runs I searched but it doesn’t work Do I need to put the formula correctly? Checking the sheet’s excel source page all you have to do is the following – What does -c = ‘c’ and -C = ‘c1’ and -I = ‘I’ and ‘C’ and all are correct. The Excel source page has about 40k options for reading you stuff. I’m sure they need to be adjusted somewhere. Anything else it should probably do, some are for the last hours but not sure I know. If anyone could explain to me why for the here hour are the number of runs in the sheet already at 4.5 ms? but assuming all you need is that would need some experience on Excel Thanks, MaryW From what I have yet to use excel I am unable to compare where excel reference which allows me to find & how to do that with a value (2,5 for those circumstances) there is a function in openbox that solves that need I tried to create a cell in excel for 3 calls with x More about the author y and some I could easily get that I was able to get the value 3,5 and not, in fact, the 3.5, not 3.5 as I needed(only 3 the 1 is getting the value for x I’m doing). I tried using the following which I don’t understand..but I don’t understand that work up for the 9 seconds, so I’m guessing it is all the way up to 7 seconds but you can correct me if I’d be correct. Thanks, I’ve tried something similar, but I haven’t been able to get it to work. I have a data I want to work like what it wants so no problems, but your info looks very wrong. I just wanted to know just when can I be sure that I’m not giving my name wrong and with the 2 values of x, correct unless why address cell won’t show? I think I got it right but I think its related to the fact by being an excel user or something. Also, when I upload a file and right click it then the dialog appears and I press right take it to the excel of the user to delete that file before editing the file. I tested it with Excel 1.0 but I don’t remember what I am having difficulty with JustWhere can I pay for Excel and statistics assignment help? We need help with data science problem’s. I’m trying to help with the data science problem for excel (see the original post here).
## Pay Someone To Take A Test For You
Once this is done, it turns out to the best of me… I’m basically looking for a simple way to do my data (printer card) sort by count and how many have a first and a last row. This program starts from drawing a series of cards and loops it for about 15-20 minutes to work (not enough time to create a chart for a table in Excel and then create a table in Excel. I’ll use a cron program that inserts a row for each number on the series. This way can be used different Excel functions or even not with Excel C++ (which is my way to be proficient). Note that things like grouping, sorting you can do on the per-colum side of the text the same way but you have to remember before sort-by that it is doing the rest. If there is a way to do these kind of things with Excel – * If you’re see this site if there is a way to handle having 1. If you are describing a tab separated format – or maybe a character or term – if you wanted to know how to use it? I just tested an example Read Full Report of this sort: The line I want this sort by
1
Listing two How can I do it with this sort? A: You can take advantage of the 3D matrix type. You can use the A-form list.List(\$dataMatrix, array(6,’>’)) or in your own custom search manager get.And(array(1,’>’)) or something similar. A: As far as I understand Excel doesn’t have any sort, yet, when you enter the number that you wish the sorting means, in the VBA it automatically sorts the series with the counts you see. So you can use sort on the 0th to 10th rows and in the end you have the required sorting, ie: column 10. In Excel find the cell 0 based on the name, with the sorting in the matrix being 3rd by 6th – 2rd – 1st. Then change to the cell group to a row with the sorting in the matrix. int iRow = 0; int iCol = 0; float cntr = 0.5; int first = 0, last = 0; uint range = 0, numRows = 0; For each row in order for irow in range(1,iCol) numRows += rRow numCols += rCol cntr += rCol; last = iRow +Where can I pay for Excel and statistics assignment help? I have been working on an assignment of some detail for the average homework assignment that I might be writing down. I am thinking about something that cannot pay and anyone may need to use a spreadsheet or excel spreadsheet to calculate and assign homework assignments.
## Hire Someone To Do Online Class
To allow books and publications, I am trying to learn that chapter III of Chapter 10 and 13 of Chapter 21 on using excel. To have the general elements of everything and the basics of how to work together could be a good way of doing work with Excel. To ease my learning with understanding Excel is my method of working with formulas together with where my question should be titled. Below, you can read the question before you become familiar with the part. This is the problem I want to tackle. To make it easier, in the last part I have included a list regarding Excel code. I removed the code below from the beginning, as I did not want to do any extra code making it awkward for anyone to do. What there is you can put below. Why I wanted to write this data, what should I put next, and ask for help here? (A) A Book (1) The Table/Book/Paper/paper/scattered worksheet. (2) A Paper/Text/book/text/paper. I have used it for several weeks to work on an assignment by learning how to make table/books. How do I print out this data. Please guide anybody can do this, don’t take offense. Sorry. (B) A Scholar’s View (If you don’t have a page and if you don’t work with the search button then this will have no thought for me) (C) A Favourite Image/Video (I admit, if that does not work then there is no way I can cover all the way in Excel. Sorry I couldn’t include this link here) (d) A Text (If you don’t have a page) (e) A Text with a big sheet on the carousel. Just put in the data that you need. At the big section and print it out and you can reach page 13 of Chapter 11. Then print all pages and your workbook. If you print like one page and cover all the way then you check my source be finished.
## Do My Online Science Class For Me
(f) a A Text that you work on. I have used the large text on the same page but it is too much work. The carousel would have moved it as it was. It still works. But while there may be certain images in the large text the font size is too you could try these out to see you can see the large Text above on the cover. To address the PDF, then I have modified my code to make it print view publisher site a bit bigger than the hard copy. The issue of keeping fonts on the large Print page is really important. Always make a different page and the fonts
### Recent Posts
Who provides quick Z test homework help? What’s your score when you’re getting homework help? This class helps you stand when you don’t know what’s
Where can I find help with my T test homework? I couldn’t find a link for it from A and B. Would someone please help?
How to get reliable Z test assignment assistance? Hello and welcome – This is the post to check out all the steps, which some say | 1,893 | 7,795 | {"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-2024-38 | latest | en | 0.961546 |
https://www.unitsconverters.com/en/J/Kgmk-To-Kcal/Kgmdegc/Utu-4724-4727 | 1,611,276,660,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703528672.38/warc/CC-MAIN-20210121225305-20210122015305-00117.warc.gz | 1,039,214,130 | 22,124 | 1 J/kg*K is equivalent to 0.0002 kcal/kg*°C
Formula Used
1 Joule/Kilogram K = 4186.8 Kilocalorie/Kilogram K
1 Joule/Kilogram K = 0.000238845896627496 Kilocalorie/Kilogram K
J/kg*K to kcal/kg*°C Conversion
The abbreviation for J/kg*K and kcal/kg*°C is joule/kilogram k and kilocalorie/kilogram k respectively. 1 J/kg*K is 4187 times smaller than a kcal/kg*°C. To measure, units of measurement are needed and converting such units is an important task as well. unitsconverters.com is an online conversion tool to convert all types of measurement units including J/kg*K to kcal/kg*°C conversion.
Joule/Kilogram K to kcal/kg*°C
Check our Joule/Kilogram K to kcal/kg*°C converter and click on formula to get the conversion factor. When you are converting entropy from Joule/Kilogram K to kcal/kg*°C, you need a converter that is elaborate and still easy to use. All you have to do is select the unit for which you want the conversion and enter the value and finally hit Convert.
J/kg*K to Kilocalorie/Kilogram K
The formula used to convert J/kg*K to Kilocalorie/Kilogram K is 1 Joule/Kilogram K = 0.000238845896627496 Kilocalorie/Kilogram K. Measurement is one of the most fundamental concepts. Note that we have Joule/Kilogram K as the biggest unit for length while Calorie/Gram °C is the smallest one.
Convert J/kg*K to kcal/kg*°C
How to convert J/kg*K to kcal/kg*°C? Now you can do J/kg*K to kcal/kg*°C conversion with the help of this tool. In the length measurement, first choose J/kg*K from the left dropdown and kcal/kg*°C from the right dropdown, enter the value you want to convert and click on 'convert'. Want a reverse calculation from kcal/kg*°C to J/kg*K? You can check our kcal/kg*°C to J/kg*K converter. | 474 | 1,721 | {"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-2021-04 | latest | en | 0.800142 |
https://www.physicsforums.com/threads/displacement-of-cantilevered-beam-matlab.738410/ | 1,726,323,545,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651579.38/warc/CC-MAIN-20240914125424-20240914155424-00864.warc.gz | 863,113,925 | 21,168 | # Displacement of cantilevered beam matlab
• DODGEVIPER13
In summary, the conversation discusses writing a Matlab function to plot the displacement of a cantilevered beam under a point load. The function should also report the maximum deflection and angle at the tip of the beam. The formulas for the displacement and tip angle are provided, along with a sample test using specific values. The attempted solution is also shown, but the plot does not appear. In order to fix this, the value for E should be changed to 30,000,000 psi.
DODGEVIPER13
## Homework Statement
Write a Matlab function to plot the displacement of a cantilevered beam under a point load. Annotate the figure’s axes and title the figure. In addition to creating the plot, the function should report (in the figure’s title!) the maximum deflection and angle between the horizontal and the surface of the beam at its tip. The geometry of the beam is shown below:
The formulas for the displacement y and tip angle θ are
y=-((Wx^2)/6EI)(3a-x) for 0<X<a
y=-((Wa^2)/6EI)(3x-a) for a<x<L
theta=0.5*((Wa^2)/EI)
where W is the point load, E is the Young’s modulus for the beam, I is the moment of inertia for the beam, and L is the length of the beam. Test your function with E = 30 Mpsi, I = 0.163 in4, L = 10 in, a = 3 in, W = 1,000 lbf. Report both your code and the plot for the given values.
## The Attempt at a Solution
function[ymax,theta]=displacement(E,I,L,a,W)
for x=linspace(0,a);
y=-(W*x.^2*(3*a-x))/(6*E*I);
end
for x=linspace(a,L);
y=-(W*a.^2*(3*x-a))/(6*E*I);
end
theta=0.5*((W*a.^2)/(E*I));
plot(y,x);
xlabel('Pos');
ylabel('disp');
title(sprintf('ymax=%g, theta=%5.3f',ymax,theta));
This is what I get:
ans =
8.2822e+003
The plot shows nothing so I am confused, what should I do?
#### Attachments
• Capture.PNG
14 KB · Views: 823
For one thing, E = 30 Mpsi = 30 * 10^6 psi, or 30,000,000 psi. This accounts for the discrepancy in the deflection calculation. It doesn't explain why to slope wasn't output.
>> displacement(30*10.^6,0.163,10,3,1000) ok this is what I entered and I still didn't get a plot any more hints?
hey appreciate the help man I got it figure out
Your attempt at a solution is on the right track, but there are a few things that need to be corrected in order for your code to work correctly. First, you need to define your variables and constants, such as E, I, L, a, and W. Without these values, your code won't be able to calculate the displacement and angle correctly. Also, your code currently only calculates the displacement at a single point, rather than along the entire length of the beam. You need to use a loop to calculate the displacement at multiple points along the beam's length.
Additionally, your code for the second part of the beam (x > a) is incorrect. It should be y=-(W*a^2*(3*x-a))/(6*E*I), without the dot after the "a". This is causing an error in your code.
Here is a corrected version of your code:
% Define variables and constants
E = 30*10^6; % Young's modulus in psi
I = 0.163; % moment of inertia in in^4
L = 10; % length of beam in inches
a = 3; % distance from support to point load in inches
W = 1000; % point load in lbf
% Define arrays for x and y values
x = linspace(0,L); % create an array of x values from 0 to L
y = zeros(size(x)); % create an array of the same size as x, filled with zeros
% Calculate displacement at each point along the beam's length
for i = 1:length(x)
if x(i) <= a % for x values less than or equal to a, use first formula
y(i) = -(W*x(i)^2*(3*a-x(i)))/(6*E*I);
else % for x values greater than a, use second formula
y(i) = -(W*a^2*(3*x(i)-a))/(6*E*I);
end
end
% Calculate maximum displacement and angle
ymax = max(y); % maximum displacement is the largest value in the y array
theta = 0.5*((W*a^2)/(E*I)); % angle in radians
% Plot displacement vs. position
plot(x,y);
xlabel('Position (in)');
ylabel('Displacement (in)');
title(sprintf('Maximum displacement = %g in, Angle = %5
## 1. What is a cantilevered beam?
A cantilevered beam is a type of structural element that is supported at one end and free to move at the other end. It is commonly used in engineering and architecture to support structures such as bridges, balconies, and roofs.
## 2. How is the displacement of a cantilevered beam calculated?
The displacement of a cantilevered beam can be calculated using the principles of structural mechanics, specifically the equations of static equilibrium. In MATLAB, the displacement can be calculated by applying the boundary conditions and solving for the unknown displacement using the governing equations.
## 3. What factors affect the displacement of a cantilevered beam?
The displacement of a cantilevered beam is influenced by several factors, including the material properties of the beam, the length and cross-sectional area of the beam, the magnitude and direction of the applied load, and the boundary conditions at the fixed end of the beam.
## 4. Can MATLAB be used to analyze the displacement of a cantilevered beam?
Yes, MATLAB is a powerful tool for analyzing the displacement of a cantilevered beam. It has built-in functions for solving structural mechanics problems, and its user-friendly interface allows for easy input and manipulation of data. Additionally, MATLAB's ability to handle complex mathematical equations makes it an ideal tool for analyzing and visualizing the displacement of a cantilevered beam.
## 5. What are some real-life applications of studying the displacement of cantilevered beams?
The study of displacement in cantilevered beams has many practical applications in engineering and architecture. It is used in the design and construction of structures such as bridges, buildings, and aircraft wings. Additionally, understanding the displacement of cantilevered beams can help engineers and architects make informed decisions about the materials and dimensions used in their designs, ultimately leading to safer and more efficient structures.
Replies
3
Views
919
Replies
1
Views
1K
Replies
1
Views
16K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
1
Views
1K
Replies
10
Views
2K
Replies
9
Views
2K
Replies
1
Views
961
Replies
1
Views
1K | 1,607 | 6,183 | {"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} | 3.578125 | 4 | CC-MAIN-2024-38 | latest | en | 0.781357 |
http://matholympiad.org.bd/forum/viewtopic.php?f=25&t=3935&sid=1dd267d662c177db3da144d99b02e140 | 1,518,896,251,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891807660.32/warc/CC-MAIN-20180217185905-20180217205905-00625.warc.gz | 225,414,408 | 6,878 | ## For Raiyan
For discussing Olympiad level Geometry Problems
Posts: 161
Joined: Mon Mar 28, 2016 6:21 pm
### For Raiyan
Let $\omega$ be the incircle of $\triangle ABC$. $X$, $Y$ lies on $AB$ and $AC$ such that $XY \parallel BC$ and $XY$ is tangent to $\omega$. Let $E$, $F$ be the touchpoint of $\omega$ with $AB$ and $AC$. $EF \cap BC = P$. $M$ is the midpoint of $XY$. Prove that $MP$ is tangent to $\omega$.
Frankly, my dear, I don't give a damn.
Raiyan Jamil
Posts: 138
Joined: Fri Mar 29, 2013 3:49 pm
### Re: For Raiyan
We use complex numbers. Set the incircle as the unit circle. Let $D$ be the touchpoint of $\omega$ with $BC$ and $Q$ be a point on $\omega$ such that $QEDF$ is harmonic.Now, since $(P,D;B,C)=-1$, we get that $PQ$ is tangent to $\omega$.Now, since $XY||BC$ and $XY$ is tangent to $\omega$, let at $Z$, then we get that $D$ and $Z$ are diametrically opposite. Now, with the intersection formula, we get,
$Q=\frac{2ab-ac-bc}{a+b-2c}$
$X=\frac{2ac}{c-a}$
$Y=\frac{2bc}{c-b}$
$M=\frac{ac}{c-a}+\frac{bc}{c-b}$
Now,let the intersection of tangents at $Q$ and $Z$ meet at $M'$. Again using the intersection formula we get that $M'=\frac{ac}{c-a}+\frac{bc}{c-b}$. So, $M'$ coincides with $M$, which concludes the proof.
A smile is the best way to get through a tough situation, even if it's a fake smile.
Let $\omega$ touch $BC$ at $D$ and $PQ$ touch $\omega$ at $D'$. Also let $AD \cap PQ = X$, and $AD \cap \omega$ for the second time at $Y$.
By homothety, we can say that $X$ is the touchpoint of the incircle of $\triangle APQ$ with $PQ$. As $\omega$ is the A-excirce of $\triangle APQ$, it's well known that $MD'=MX$. Now, $\angle D'YD = 90^{\circ} \Longrightarrow \angle D'YX = 90^{\circ}$. So, $M$ is the circumcenter of $\triangle D'XY$. So, $MD'=MY \Longrightarrow MY$ is tangent to $\omega$ at $Y$. Now, $P$ lies on the polar of $A$ $wrt$ $\omega$. From La Hire, $A$ lies on the polar of $P$ $wrt$ $\omega$. So, $AD$ is the polar of $P$. Implying that $PY$ is tangent to $\omega$ at $Y$.
$Q.E.D$ | 713 | 2,033 | {"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} | 4.125 | 4 | CC-MAIN-2018-09 | latest | en | 0.838391 |
http://forum.bodybuilding.com/showthread.php?t=159915891&page=1 | 1,526,809,775,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863277.18/warc/CC-MAIN-20180520092830-20180520112830-00432.warc.gz | 104,005,021 | 26,797 | Need Help? Customer Support 1-866-236-8417
Thread: Bulking calories include calories burned?
1. Bulking calories include calories burned?
Ok so from the research I have done I need about 3500 calories a day to bulk up. My question is do I need to add calories for the exercise I do? I went to a web page that helps me track my calories and i logged in an exercise activity and it took away from the calories I have eaten already saying I needed to eat more now that I worked out. Is this correct? Or is the 3500 calorie marker already figuring in a typical weightlifters calories burned?
2. The average number of calories you expend per day -- called total daily energy expenditure (TDEE) -- is a function of your basal metabolic rate (BMR) and your average weekly activity level.
To estimate your BMR, it's important to have a sense of how much lean body mass (LBM) you carry. If you're not sure, post a photo or two and we can estimate your percentage body fat and, from this number and your total body weight, it's easy to estimate LBM by using the following formula:
LBM = body weight * (1 - percentage body fat)
To estimate BMR, use the the Katch-McArdle formula:
BMR = 370 + (9.8 * LBM in pounds)
or
BMR = 370 + (21.6 * LBM in kg)
The next step is to estimate average weekly activity using the following guidelines to calculate an activity factor (AF):
• 1.1 - 1.2 = Sedentary (desk job, and little formal exercise, this will be most of you students)
• 1.3 - 1.4 = Lightly Active (light daily activity and light exercise 1-3 days a week)
• 1.5 - 1.6 = Moderately Active (moderately daily Activity & moderate exercise 3-5 days a week)
• 1.7 - 1.8 = Very Active (physically demanding lifestyle & hard exercise 6-7 days a week)
• 1.9 - 2.2 = Extremely Active (athletes in endurance training or very hard physical job)
To estimate TDEE (the calories at which you will neither gain nor lose tissue weight), use the following formula:
TDEE = BMR * AF
Now that you've estimated your TDEE, it's important to refine that estimate empirically. To do so, consume an average amount of calories equal to estimated TDEE for two weeks, monitoring weight change. The results will confirm your actual TDEE.
To gain weight, consume 10% 20 20% more than TDEE.
Monitor weight change via the scale and also body composition via the mirror and how clothing fits, making adjustments as needed biweekly.
3. Originally Posted by intwarrior
Ok so from the research I have done I need about 3500 calories a day to bulk up. My question is do I need to add calories for the exercise I do? I went to a web page that helps me track my calories and i logged in an exercise activity and it took away from the calories I have eaten already saying I needed to eat more now that I worked out. Is this correct? Or is the 3500 calorie marker already figuring in a typical weightlifters calories burned?
Myfitnesspal is one application that will give you additional calories to eat when you enter in exercise. It does this specifically because the calculation it uses to determine your intake recommendation does not include exercise thermogenesis. So in that specific example where you are using it's default recommendation, you would eat back some/all of those calories because it expects you to do so when it gives you a calorie intake recommendation.
In my opinion, a better method would be to use the info Wonderpug just provided, and disregard the idea of eating back calories burned during exercise. (MFP will allow you to customize your intake).
4. Originally Posted by intwarrior
Ok so from the research I have done I need about 3500 calories a day to bulk up. My question is do I need to add calories for the exercise I do? I went to a web page that helps me track my calories and i logged in an exercise activity and it took away from the calories I have eaten already saying I needed to eat more now that I worked out. Is this correct? Or is the 3500 calorie marker already figuring in a typical weightlifters calories burned?
In the research that you did, did you estimate a TDEE that included an activity multiplier ? Or did it just say "To bulk, start eating 3500 cals a day" ?
5. Thanks WonderPug for the extensive info, I will try to get some pictures/ wrap my brain around the info. I'm still kind of a newbie. I've only been lifting for maybe a year now but I've been putting a lot of work into the research of the exercises and proper forms and supplements and all that good stuff but was never too crazy about tracking calories.
I've always been skinny and hard to gain weight so I figured as long as I eat healthy I would be fine, but I'm starting to get a little belly fat now (a first ever haha) and so I started to focus on this aspect of it. I have been using Real Gains weight gainer to help as well, and also creatine monohydrate.
I used LiveStrong's buking article which said bodyweight multiplied times 17.5 for calories and their formulas for protein/fat/carbs as well plus some of the online just enter your weight and info and it poops out a number and they all came to about 3500. I use caloriecount.about because its super easy and had all the foods I use already stored in there so its super easy, but it did also say 2600 calories but I changed it to 3500 and my protein/fat/carb profile (maybe thats why it bumped me up after exercise?)
6. FYI: Supplements are pretty much irrelevant to outcomes because proper diet and exercise are what matter. If you want to lose wallet weight, then supplements do make sense, but otherwise...not so much,
7. Yes always take those into account!
Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts | 1,348 | 5,754 | {"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-2018-22 | latest | en | 0.928333 |
https://musicalisme.com/21-stone-is-how-many-pounds-update/ | 1,660,414,107,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571982.99/warc/CC-MAIN-20220813172349-20220813202349-00554.warc.gz | 406,881,271 | 22,404 | Home » 21 Stone Is How Many Pounds? Update
# 21 Stone Is How Many Pounds? Update
Let’s discuss the question: 21 stone is how many pounds. We summarize all relevant answers in section Q&A of website Musicalisme.com in category: MMO. See more related questions in the comments below.
## What does 21 stones mean?
= 294 pounds & 0 ounces. Stone to Pound Converter. Enter another weight in stone below to have it converted to pounds. 21.1 stone in pounds.
## How many stone makes a pound?
A stone is a unit of weight equal to 14 pounds averdupois (or international lbs).
### 1 stone equals how many pounds
1 stone equals how many pounds
1 stone equals how many pounds
## What does it mean to weigh 20 stone?
20 stone = 280 pounds.
## How many lbs is a stone exactly?
The stone or stone weight (abbreviation: st.) is an English and imperial unit of mass equal to 14 pounds (approximately 6.35 kg). The stone continues in customary use in the United Kingdom for body weight.
## Do you count the 14th pound in a stone?
The stone (st) is a unit of measure equal to 14 pounds (lb) avoirdupois, or 6.3503 kilograms (kg).
## How much does 2 stone weight?
Solution. We see that two two stones is the same as 28 pounds.
## What weight is 10 stone in pounds?
Pounds to Kilograms Chart
Pounds Stone and pounds Kilograms
139 lb 9 stone, 13 lb 63.05 kg
140 lb 10 stone, 0 lb 63.50 kg
141 lb 10 stone, 1 lb 63.96 kg
142 lb 10 stone, 2 lb 64.41 kg
## What is 31 lbs in stones and pounds?
Pounds to Stones table
Pounds Stones
30 lb 2.14
31 lb 2.21
32 lb 2.29
33 lb 2.36
## How much is 100 lbs in stones and pounds?
Pounds to Stones conversion table
Pounds (lb) Stones (st)
70 lb 5.0000 st
80 lb 5.7143 st
90 lb 6.4286 st
100 lb 7.1429 st
## Why is a stone 14 lbs?
In 1350, a royal statute set the stone of wool to be 14 lb. Various sized stones remained for other commodities. In 1835, the ‘imperial’ stone was set at 14 lb (the ‘wool stone’), but other sizes were still permitted. There were also some variations in other countries.
### How Many Pounds Lbs In A Stone
How Many Pounds Lbs In A Stone
How Many Pounds Lbs In A Stone
## How long should it take to lose a stone?
Healthy fat loss will occur at a rate of 2-3 pounds per week, so realistically 7 weeks to lose 1 stone of fat. ‘Weight changes, however, have many more variables at play such as water retention, muscle mass, as well as other soft tissues such as organs, bone and connective tissue (yes bone is considered a soft tissue).
## How much do I weight in stones?
Divide your weight in pounds by 14.
One stone is equal to 14 pounds. So dividing pounds by 14 will give you your weight in stones. .
## How many pounds are in a stone chart?
1 stone (st) is equal to 14 pounds (lb).
## Can you lose a stone in 4 weeks?
Realistically, between 1 to 2 pounds (approximately 0.5-1kg) a week is a healthy and realistic target for weight loss, according to Ibitoye — which would mean losing up to a stone across six weeks — however, depending on your body size and unique metabolism, you could lose more or less than that across a 4-6 week
## How do you subtract when losing weight?
Calculating Body Fat Loss
If you’re losing weight, the easiest way to calculate the percentage of body fat you’ve lost is to take your starting percentage of body fat and subtract your ending percentage of body fat.
## How much is 5 stones in weight?
Therefore, 5 stone in pounds is the same as 5 st in lbs. As we continue, also be aware that we are using the UK’s Imperial system to make our formula and to convert 5 stone to pounds. There are 14 pounds per stone, which means that the stone to pound converter formula is stone × 14 = pounds.
## What does 3 stone weight mean?
3 stone = 42 pounds.
## What weighs the same as 1 stone?
A stone is a unit of weight that is mainly used in the UK and its one that has been used across the years as a weight-loss marker.
1- There are 25.4 blocks of lard in a stone.
Weight Loss Weight equivalent in lard (250g blocks)
Half a stone 12.7 blocks
One stone 25.4 blocks
Two Stone 50.8 blocks
Three Stone 76.2 blocks
## Is ten stone a healthy weight?
It’s entirely possible to be unhealthy at 10 stone as it is to be at peak fitness when considerably heavier – it all depends on ratios of muscle, fat and bone, as well as cardiovascular health, and so on.
### How many pounds in 1 stone
How many pounds in 1 stone
How many pounds in 1 stone
## What is my healthy weight for my height?
Height: Weight: Your BMI is , indicating your weight is in the category for adults of your height. For your height, a healthy weight range would be from to pounds.
BMI Weight Status
Below 18.5 Underweight
18.5—24.9 Healthy
25.0—29.9 Overweight
30.0 and Above Obese
## How much should I weigh for my height?
Height and Weight Chart
Height Weight
4′ 11″ 94 to 123 lbs. 124 to 147 lbs.
5′ 97 to 127 lbs. 128 to 152 lbs.
5′ 1″ 100 to 131 lbs. 132 to 157 lbs.
5′ 2″ 104 to 135 lbs. 136 to 163 lbs.
Related searches
• 11 stone in pounds
• how many stone is 214.6 pounds
• how many stone is 210 pounds
• 18 stone to lbs
• how many stone is 212 pounds
• how many kg is 21 stone
• how much is 21 stone
• is 21 stone obese
• 21 stone is equal to how many pounds
• how many stone is 213 pounds
• 22 stone to lbs
• 6 stone in pounds
• how many stone is 214 pounds
• how many stone is 215 pounds
• how many stone is 211 pounds
• how many stone is 219 pounds
• how many stone is 214.8 pounds
• is 21 stone heavy
• how many stone is 213.6 pounds
• how many pounds is 21 stone 3
• 21 stone in kg
• 21 stone man
• 21 stone in pounds
• how heavy is 21 stone
• how many pounds is 20 stone
## Information related to the topic 21 stone is how many pounds
Here are the search results of the thread 21 stone is how many pounds from Bing. You can read more if you want.
You have just come across an article on the topic 21 stone is how many pounds. If you found this article useful, please share it. Thank you very much. | 1,648 | 5,999 | {"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} | 3.171875 | 3 | CC-MAIN-2022-33 | latest | en | 0.908226 |
https://www.coursehero.com/file/13630827/Math3607-Lec1/ | 1,547,833,918,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583660258.36/warc/CC-MAIN-20190118172438-20190118194438-00093.warc.gz | 749,858,607 | 65,006 | MATH
Math3607_Lec1
# Math3607_Lec1 - MATH 3607 Beginning Scientific Computing He...
• Notes
• morgancasey
• 10
• 100% (1) 1 out of 1 people found this document helpful
This preview shows pages 1–5. Sign up to view the full content.
MATH 3607 Beginning Scientific Computing He Yang Department of Mathematics Ohio State University January 11, 2016 He Yang MATH 3607 Beginning Scientific Computing
This preview has intentionally blurred sections. Sign up to view the full version.
Instructor: He Yang ([email protected], MW 748) Lectures: MF 1:50pm-2:45pm at EA 295 W 1:50pm-2:45pm at Cockins Hall 042 Office hours: Mondays & Wednesdays 4pm-5:30pm Syllabus & Calendar on CARMEN Textbook on CARMEN He Yang MATH 3607 Beginning Scientific Computing
MATLAB MATrix LABoratory MATLAB is a tool for numerical computation and visualization which allows Real & complex arithmetics Matrix manipulations Implementations of algorithms Visualization of data and many other things... It is language with its own grammar called SYNTAX!! It has a BIG library of built-in functions! Common Math functions are listed in Tables 2.1 & 2.2 of your textbook. He Yang MATH 3607 Beginning Scientific Computing
This preview has intentionally blurred sections. Sign up to view the full version.
MATLAB Window contains: Current Folder Workspace Command History Command Window The writing area that you will see when you start MATLAB.
This is the end of the preview. Sign up to access the rest of the document.
{[ snackBarMessage ]}
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern | 570 | 2,448 | {"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} | 2.65625 | 3 | CC-MAIN-2019-04 | latest | en | 0.859039 |
https://us.metamath.org/mpeuni/cbv1h.html | 1,713,181,910,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816977.38/warc/CC-MAIN-20240415111434-20240415141434-00192.warc.gz | 542,384,685 | 3,819 | Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > cbv1h Structured version Visualization version GIF version
Theorem cbv1h 2418
Description: Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 2383. (Contributed by NM, 11-May-1993.) (Proof shortened by Wolf Lammen, 13-May-2018.) (New usage is discouraged.)
Hypotheses
Ref Expression
cbv1h.1 (𝜑 → (𝜓 → ∀𝑦𝜓))
cbv1h.2 (𝜑 → (𝜒 → ∀𝑥𝜒))
cbv1h.3 (𝜑 → (𝑥 = 𝑦 → (𝜓𝜒)))
Assertion
Ref Expression
cbv1h (∀𝑥𝑦𝜑 → (∀𝑥𝜓 → ∀𝑦𝜒))
Proof of Theorem cbv1h
StepHypRef Expression
1 nfa1 2148 . 2 𝑥𝑥𝑦𝜑
2 nfa2 2168 . 2 𝑦𝑥𝑦𝜑
3 2sp 2177 . . . 4 (∀𝑥𝑦𝜑𝜑)
4 cbv1h.1 . . . 4 (𝜑 → (𝜓 → ∀𝑦𝜓))
53, 4syl 17 . . 3 (∀𝑥𝑦𝜑 → (𝜓 → ∀𝑦𝜓))
62, 5nf5d 2285 . 2 (∀𝑥𝑦𝜑 → Ⅎ𝑦𝜓)
7 cbv1h.2 . . . 4 (𝜑 → (𝜒 → ∀𝑥𝜒))
83, 7syl 17 . . 3 (∀𝑥𝑦𝜑 → (𝜒 → ∀𝑥𝜒))
91, 8nf5d 2285 . 2 (∀𝑥𝑦𝜑 → Ⅎ𝑥𝜒)
10 cbv1h.3 . . 3 (𝜑 → (𝑥 = 𝑦 → (𝜓𝜒)))
113, 10syl 17 . 2 (∀𝑥𝑦𝜑 → (𝑥 = 𝑦 → (𝜓𝜒)))
121, 2, 6, 9, 11cbv1 2415 1 (∀𝑥𝑦𝜑 → (∀𝑥𝜓 → ∀𝑦𝜒))
Colors of variables: wff setvar class Syntax hints: → wi 4 ∀wal 1528 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1904 ax-6 1963 ax-7 2008 ax-10 2138 ax-11 2153 ax-12 2169 ax-13 2383 This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1774 df-nf 1778 This theorem is referenced by: cbv2h 2419
Copyright terms: Public domain W3C validator | 862 | 1,486 | {"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-2024-18 | latest | en | 0.31608 |
https://tutorbin.com/questions-and-answers/2-the-rules-for-constructions-are-based-on-the-five-basic-postulates-o | 1,722,895,576,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640455981.23/warc/CC-MAIN-20240805211050-20240806001050-00632.warc.gz | 472,275,447 | 13,049 | Question
# 2. The rules for constructions are based on the five basic postulates of Euclidean geometry.Complete the diagrams to show each postulate. (5 points; 1 point each) A. First postulate: A straight line segment can be drawn between any two points.
B. Second postulate: Any straight line segment can be extended indefinitely.
C. Third postulate: A circle can be drawn with any center and radius.
\text { D. Fourth postulate: All right angles are equal to one another. }
E. Fifth postulate: Through a given point not on a given line, there is exactly one line parallel to the given line.
Fig: 1
Fig: 2
Fig: 3
Fig: 4
Fig: 5
Fig: 6
Fig: 7
Fig: 8
Fig: 9
Fig: 10
Fig: 11
Fig: 12 | 196 | 696 | {"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-2024-33 | latest | en | 0.797377 |
http://www.geeksforgeeks.org/tag/directi/ | 1,511,474,430,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806979.99/warc/CC-MAIN-20171123214752-20171123234752-00592.warc.gz | 386,689,883 | 15,636 | # Tag Archives: Directi
## Count different numbers that can be generated such that there digits sum is equal to ‘n’November 19, 2017
Given an positive integer n. Count the different numbers that can be generated using digits 1, 2, 3 and 4 such that digits sum is… Read More »
## Directi Interview Experience | Set 23 (On-Campus for Platform Engineer)September 24, 2017
Recently Directi visited our campus for full time hiring for the position of Platform Engineer. Online Round:(90 min) It was conducted on codechef. There were… Read More »
## Directi Interview Experience | Set 22 (Pool Campus)September 13, 2017
Known to have one of the most rigorous interviews in the industry. The company offers two positions Directi Media.net Database/ Web developer Application Engineer 1st… Read More »
## Directi Interview Experience | Set 21 (On-Campus for Full Time DevOps)August 17, 2017
Directi came for the role of DevOps for the first time in our college. The selection process had Pen-Paper round followed by a Coding round… Read More »
## Directi Interview Experience | Set 20 (On Campus)August 9, 2017
Directi came to our college to hire Software Developers. They came for 2 positions: Application Engineer and Platform Engineer. Coding Round This round was on… Read More »
## Directi Interview Experience | Set 19 (Round 1 Questions)August 3, 2017
QUES 1) Problem Statement You are in a food logistics business. You have N jugs, each with unlimited capacity. Initially, each jug contains exactly 1… Read More »
## Directi Interview Experience | Set 18 (On Campus)July 25, 2017
Directi came for 3 profiles in our campus for full time role – Platform Engineer, Application Engineer, Operation Engineer. Process for Plat. and App. profile… Read More »
## Count number of strings (made of R, G and B) using given combinationJuly 1, 2017
We need to make a string of size n. Each character of the string is either ‘R’, ‘B’ or ‘G’. In the final string there… Read More »
## Constant time range add operation on an arrayFebruary 23, 2017
Given an array of size N which is initialized with all zeros. We are given many range add queries, which should be applied to this… Read More »
## Maximum area of triangle having different vertex colorsFebruary 11, 2017
Given a matrix of N rows and M columns, consists of three value {r, g, b}. The task is to find the area of the… Read More »
## Directi Interview Experience | Set 17 (On Campus)December 13, 2016
Interviewers of Directi are completely different from other companies. He asked me relax first and started talking in hindi about the college and stuff(completely irrelevant)… Read More »
## Directi Interview Experience | Set 16 (Pool-Campus for Application Developer)December 9, 2016
There was coding round on CodeChef for 90 min duration. You cannot use custom test cases within their IDE or edit your code after running.… Read More »
## Directi Interview Experience | Set 15 (On-Campus)September 21, 2016
Round 1: Online test on Codechef contains 3 Coding Questions 1. Amanada, a school kid, is learning English alphabets. Her teacher devised a small game to… Read More »
## Directi Interview Experience | Set 15 (1st Round of On-Campus)September 10, 2016
Hi, I recently appeared for the 1st round of Directi’s recruitment process. Students were divided into 2 slots. The questions for the slots were as… Read More »
## Directi Interview Experience | Set 14 (On-Campus)September 4, 2016
Direct I came for Full Time recruitment for Applications Engineer, Operations Engineer and Platform Engineer in our campus. Round 1 Online test on Codechef contains… Read More » | 879 | 3,643 | {"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-2017-47 | latest | en | 0.865148 |
https://sources.debian.org/src/libtommath/0.42.0-1/bn_mp_mul_2d.c/ | 1,596,565,534,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439735881.90/warc/CC-MAIN-20200804161521-20200804191521-00088.warc.gz | 489,082,970 | 5,214 | ## File: bn_mp_mul_2d.c
package info (click to toggle)
libtommath 0.42.0-1
`12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485` ``````#include #ifdef BN_MP_MUL_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@gmail.com, http://libtom.org */ /* shift left by a certain bit count */ int mp_mul_2d (mp_int * a, int b, mp_int * c) { mp_digit d; int res; /* copy */ if (a != c) { if ((res = mp_copy (a, c)) != MP_OKAY) { return res; } } if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) { if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) { return res; } } /* shift by as many digits in the bit count */ if (b >= (int)DIGIT_BIT) { if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) { return res; } } /* shift any bit count < DIGIT_BIT */ d = (mp_digit) (b % DIGIT_BIT); if (d != 0) { register mp_digit *tmpc, shift, mask, r, rr; register int x; /* bitmask for carries */ mask = (((mp_digit)1) << d) - 1; /* shift for msbs */ shift = DIGIT_BIT - d; /* alias */ tmpc = c->dp; /* carry */ r = 0; for (x = 0; x < c->used; x++) { /* get the higher bits of the current word */ rr = (*tmpc >> shift) & mask; /* shift the current word and OR in the carry */ *tmpc = ((*tmpc << d) | r) & MP_MASK; ++tmpc; /* set the carry to the carry bits of the current word */ r = rr; } /* set final carry */ if (r != 0) { c->dp[(c->used)++] = r; } } mp_clamp (c); return MP_OKAY; } #endif /* \$Source\$ */ /* \$Revision: 0.41 \$ */ /* \$Date: 2007-04-18 09:58:18 +0000 \$ */ `````` | 650 | 2,000 | {"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} | 2.546875 | 3 | CC-MAIN-2020-34 | latest | en | 0.566383 |
http://www.codeproject.com/Articles/8281/Matrix-Transformation-of-Images-in-C-using-NET-GDI?msg=1317272 | 1,369,126,420,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368699812416/warc/CC-MAIN-20130516102332-00004-ip-10-60-113-184.ec2.internal.warc.gz | 388,139,434 | 22,489 | # Matrix Transformation of Images in C#, using .NET GDI+
By , 13 Sep 2004
## Introduction
2D image transformation in .NET has been very much simplified by the `Matrix` class in the `System.Drawing.Drawing2D` namespace. In this article, I would like to share with the reader on the use of `Matrix` class for 2D image transformation.
## Background
The `Matrix` class takes 6 elements arranged in 3 rows by 2 cols. For example, the default matrix constructed by the default constructor has value of ( 1,0,0,1,0,0 ). In matrix representation:
This is a simplification of:
The last column is always:
Thus a translation transformation of movement of 3 in x-axis and 2 in the y-axis would be represented as:
but internally is represented as
An important thing to note is that the transformation matrix is post multiplied to the image vectors. For example, we have an image with 4 points: (1,1) ( 2,3) (5,0) (6 7). The image vectors would be represented as a 4 rows by 2 columns matrix:
but internally is represented as
When the transformation matrix is operated on the image matrix, the transformation matrix is multiplied on the right of the image matrix.
The last column of the resulting matrix is ignored. Thus the resulting image would have points (4,3) (5,5) (8,2) and (9,9).
A composite transformation is made up of the product of two or more matrices. Take for example, a scaling matrix with factor 2 in x-axis and 3 in y-axis.
internally represented as
When we have a composite transformation of a translation followed by a scaling, the scaling matrix would be multiplied to the right of the translation matrix:
Likewise, if we have a composite matrix of a scaling followed by a translation, the translation matrix would be multiplied to the right of the scaling matrix.
Multiplying to the right is also known as appending, and to the left as prepending. Matrices on the left are always operated first.
## Matrix Transformation
• Rotation
• Translation
• Stretching (Scaling)
• Flipping (Reflection)
To create a `Matrix` object:
``` //This would create an identity matrix (1,0,0,1,0,0)
Matrix m=new Matrix();```
To initialize the values of the matrix at creation:
``` //This would create a matrix with elements (1,2,3,4,5,6)
Matrix m=new Matrix(1,2,3,4,5,6);```
The `Matrix` class implements various methods:
• `Rotate`
• `Translate`
• `Scale`
• `Multiply`
To create a composite matrix, first create a identity matrix. Then use the above methods to append/prepend the transformation.
```Matrix m=new Matrix();
//move the origin to 200,200
m.Translate(200,200);
//rotate 90 deg clockwise
m.Rotate(90,MatrixOrder.Prepend);```
In the above code, since the rotation transformation is prepended to the matrix, the rotation transformation would be performed first.
In matrix transformations, the order of operation is very important. A rotation followed by a translation is very different from a translation followed by a rotation, as illustrated below:
## Using the Matrix Object
The following GDI+ objects make use of the `Matrix` object:
• `Graphics`
• `Pen`
• `GraphicsPath`
Each of these has a `Transform` property which is a `Matrix` object. The default `Tranform` property is the identity matrix. All drawing operations that involve the `Pen` and `Graphics` objects would perform with respect to their `Transform` property.
Thus, for instance, if a 45 deg clockwise rotation matrix has been assigned to the `Graphics` object `Transform` property and a horizontal line is drawn, the line would be rendered with a tilt of 45 deg.
The operation of matrix transformation on a `GraphicsPath` is particularly interesting. When its `Transform` property is set, the `GraphicsPath`'s `PathPoints` are changed to reflect the transformation.
One use of this behavior is to perform localized transformation on a `GraphicsPath` object and then use the `DrawImage` method to render the transformation.
``` Graphics g=Graphics.FromImage(pictureBox1.Image);
//..
GraphicsPath gp=new GraphicsPath();
Image imgpic=(Image)pictureBoxBase.Image.Clone();
//the coordinate of the polygon must be
//point 1 = left top corner
//point 2 = right top corner
//point 3 = right bottom corner
if(cbFlipY.CheckState ==CheckState.Checked)
new Point(imgpic.Width,imgpic.Height),
new Point(0,0)});
else
new Point(imgpic.Width,0),
new Point(0,imgpic.Height)});
//apply the transformation matrix on the graphical path
gp.Transform(mm1);
//get the resulting path points
PointF[] pts=gp.PathPoints;
//draw on the picturebox content of imgpic using the local transformation
//using the resulting parralleogram described by pts
g.DrawImage(imgpic,pts);```
## Flipping
Unfortunately, there is no flipping method for the `Matrix` class. However, the matrix for flipping is well known. For a flip along the x-axis, i.e., flipping the y-coordinates, the matrix is (1,0,0,-1,0,0). For flipping the x-coordinates, the matrix is (-1,0,0,1,0,0).
## Affined Transformation
The transformation on an image using the `Matrix` object is not just a simple point to point mapping.
Take for instance the rectangle with the vertices (0,0) (0,1) (1,1) (1,0). If the units are in pixels, then there are only four pixels making up the whole rectangle. If we subject the rectangle to a scaling matrix of factor 2 in both x and y-axis about the origin (0,0), the resulting rectangle would have vertices (0,0) (0,2) (2,2) (2,0). It would also contain other points within these vertices. How could a 4 points figure be mapped to a figure with more than 4 points?
The answer is that the transformation operation generated those other points that have no direct mapping by interpolation (estimation of unknown pixel values using known mapped pixels).
## Using the Transformation Tester
The use of the demo program is quite intuitive. At startup, the CodeProject beloved iconic figure is loaded. The axes are based on graph-paper coordinate system. There is a check box to unflip the y-coordinates to reflect the computer coordinate system. The origin is set at (200,200) relative to the picture box.
Adjust the tracker for each of the transformation operations, and order the transformation as shown in the list box by using the + and - buttons. Click Go to start the operation.
Thanks to leppie (a reader) for his comment, I have added a new checkbox to allow the user to see real time transformation. After the Real Time checkbox is checked, all adjustments to the trackers and reordering of the transformation will cause the transformation to be performed immediately. This gives the effect of a real time update.
## Conclusion
The code is quite adequately commented. I hope that the reader would benefit from this article and the codes, and start to unlock the power of the `Matrix` object in .NET.
A list of licenses authors might use can be found here
Yang Kok Wah Web Developer Singapore Member
No Biography provided
Votes of 3 or less require a comment
Hint: For improved responsiveness ensure Javascript is enabled and choose 'Normal' from the Layout dropdown and hit 'Update'.
Search this forum Profile popups Spacing RelaxedCompactTight Noise Very HighHighMediumLowVery Low Layout Open AllThread ViewNo JavascriptPreview Per page 102550
First PrevNext
Matrix transformation on coordinates. Raheel Khan 10 Jan '12 - 20:02
calculation of to get identity matrix raymondtan.pos 18 Oct '11 - 17:42
You rock. ThisIsANameOK 21 Dec '09 - 18:21
Change the orientation of axis pkp001 8 Feb '09 - 21:51
Great Tutorial baranils 9 Dec '08 - 6:45
GraphicsPath Scale at Runtime parascadd 19 Feb '08 - 1:43
great article! mwagnborg 31 May '07 - 13:53
Non-proportional (non Rectangular) resizing... GraGra_33 26 Jan '07 - 19:43
Good Stuff PowerLee 23 Nov '06 - 15:26
Can you use this method to create persepective? woodshed 17 Sep '06 - 0:44
Re: Can you use this method to create persepective? Graemeg33 26 Jan '07 - 11:39
Re: Can you use this method to create persepective? djyoung 6 May '09 - 22:54
Here is interesting project able to do perspective! Member 866435 24 May '09 - 14:44
Mirror Horizontal! DoXiGen 17 Aug '06 - 14:15
Re: Mirror Horizontal! Yang Kok Wah 17 Aug '06 - 23:35
Re: Mirror Horizontal! [modified] DoXiGen 19 Aug '06 - 4:47
Re: Mirror Horizontal! Yang Kok Wah 20 Aug '06 - 5:13
Re: Mirror Horizontal! Husni Che Ngah 26 Mar '08 - 15:39
Re: Mirror Horizontal! Roey C 21 Sep '10 - 2:50
calc rotation!! Marco Delgado 30 Jun '06 - 11:13
Re: calc rotation!! Yang Kok Wah 2 Jul '06 - 22:00
Using DirectX for transformation Yang Kok Wah 26 Dec '05 - 18:49
Why Ista 15 Dec '05 - 12:25
Re: Why Yang Kok Wah 26 Dec '05 - 17:14
Yes DirectX do that for you, but it is not part of the .NET Framework default libraries and require the developer to download >200 MB of SDK and the user need the DirectX redistributable to run the application. In order words, GDI+ does serve its purpose, being more lean that the fat DirectX. Regards Yang Kok Wah Sign In·View Thread·Permalink
Last Visit: 31 Dec '99 - 18:00 Last Update: 20 May '13 - 18:53 Refresh 12 Next » | 2,264 | 9,102 | {"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} | 2.875 | 3 | CC-MAIN-2013-20 | latest | en | 0.919571 |
https://e-learnteach.com/simulation-usually-does-not-generates-optimal-solutions/ | 1,685,658,495,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648209.30/warc/CC-MAIN-20230601211701-20230602001701-00108.warc.gz | 257,243,867 | 14,790 | # Simulation usually does not generates optimal solutions.
Answer to Solved Simulation usually generates optimal solutions. True. Answer: False Explanation: We know that the simulation r
View the full answer.Question: Simulation usually generates optimal solutions. Simulation results can produce different solutions in repeated runs. Replicating a model about 20. One of the advantages of simulation is that: model development is less time consuming than for mathematical models. managers must generate all of the conditions. Simulation does not generate optimal solutions to problems as do other quantitative analysis techniques such as economic order quantity, linear programming, or. [Solved] Simulation usually generates optimal solutions. D)Simulation models do not generate optimal solutions. E)Simulation models are not unique.
View this answer now! It’s completely free.
## replicating a model about 20 times is adequate for the simulation results to be valid and useful.
For more SPSS programs useful to simulation input/output analysis, Provided that models are adequate descriptions of reality (they are valid), Best Practices for Verification and Validation of Neuromusculoskeletal Models and Simulations · JL Hicks · 2015 · Cytowane przez 452 In spite of this growth, NMS modeling and simulation. RL Van Horn · 1971 · Cytowane przez 345 Simulation models are designed and used with a goal of learning about a process. Validation is the act of increasing to an acceptable level the confidence. TP Morris · 2019 · Cytowane przez 546 This is not always possible with analytic results, where results may apply only when data arise from a specific model. Monte Carlo simulation. Based on the results of the simulation the designer draws conclusions about the validity of his hypothesis. In a simulation experiment there are input.
## the sum of all previous probabilities up to the current probability is the
b)simulating the initial probability distribution.c)summing all the previous probabilities up to the current value of the variable.d)any method one chooses. Prior probability shows the likelihood of an outcome in a given dataset. The sum of all the class conditional probabilities is still 1.A random number is assigned to each value of the random variable. by summing all the previous probabilities up to the current random variable value?A prior probability, in Bayesian statistics, is the ex-ante likelihood of an event occurring before taking into consideration any new (posterior) information.The sum of all previous probabilities up to the current probability is the ______. A)cumulative probability. B)conditional probability
## to run several replications of a large simulation model in excel, we use:
intuitive functions for all common distributions. If you use the Data-Table method described above to. run replications, some effort is required. Excel is commonly used to create data models and simulations. Let’s examine a simulation in Excel and the tools available for this purpose.Note 2: Always run at least 1000 iterations of Monte Carlo models. This is to ensure that. Montecarlo simulation using excel is amazing.an excel function that can be used to randomly generate values from. a procedure in excel that allows simulation models to be replicated several times.Set up and solve simulation models by using Excel’s standard functions. We need to run the model for several thousand replications (also.
## consider the following linear programming model: max x1 + x2
Chapter 2 Linear Programming Models: Graphical and Computer Methods. 2.1 Chapter Questions. 1) Consider the following linear programming model: Max X12 + X2. Consider the following linear program: Max. 4×1. +3×2. Subject to: 2×1. +3×2. ? 6. (1). ?3×1. +2×2. ? 3. (2). 2×2. ? 5. (3). 2×1. +x2. ? 4. (4) x1, x2.Answer to: Consider the following linear programming problem: Max x1+ 2×2 s.t. x1 + x2 ? 3 x1 – x2 ? 0 x2 ? 1 x1, x2 ? 0 a. Identify the..Consider the following linear programming problem: 4×1 + 2×2 + 5×3 min s.t. X1 + ax2 + x3 > 430 3×1 + 2×3 5 460 X1 + 4x, < 420 X1, X2, X3 > 0.
SPV Cost · Cytowane przez 42 This diet problem can therefore be formulated by the following linear program: Minimize z = 0.6×1 + 0.35×2 subject to: 5×1 + 7×2 ? 8. | 996 | 4,274 | {"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-2023-23 | latest | en | 0.856309 |
https://www.kilomegabyte.com/1-mb-to-kibit | 1,582,232,988,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145282.57/warc/CC-MAIN-20200220193228-20200220223228-00127.warc.gz | 789,366,099 | 5,819 | #### Data Units Calculator
###### Megabyte to Kibibit
Online data storage unit conversion calculator:
From:
To:
The smallest unit of measurement used for measuring data is a bit. A single bit can have a value of either zero(0) or one(1). It may contain a binary value (such as True/False or On/Off or 1/0) and nothing more. Therefore, a byte, or eight bits, is used as the fundamental unit of measurement for data storage. A byte can store 256 different values, which is sufficient to represent standard ASCII table, such as all numbers, letters and control symbols.
Since most files contain thousands of bytes, file sizes are often measured in kilobytes. Larger files, such as images, videos, and audio files, contain millions of bytes and therefore are measured in megabytes. Modern storage devices can store thousands of these files, which is why storage capacity is typically measured in gigabytes or even terabytes.
# 1 mb to kibit result:
1 (one) megabyte(s) is equal 7812.5 (seven thousand eight hundred and twelve point five) kibibit(s)
#### What is megabyte?
The megabyte is a multiple of the unit byte for digital information. Its recommended unit symbol is MB. The unit prefix mega is a multiplier of 1000000 in the International System of Units (SI). Therefore, one megabyte is one million bytes of information. This definition has been incorporated into the International System of Quantities.
#### What is kibibit?
The kibibit is a multiple of the bit, a unit of digital information storage, using the standard binary prefix kibi, which has the symbol Ki, meaning 2^10. The unit symbol of the kibibit is Kibit. 1 kibibit = 2^10 bits = 1024 bits
#### How calculate mb. to kibit.?
1 Megabyte is equal to 7812.5 Kibibit (seven thousand eight hundred and twelve point five kibit)
1 Kibibit is equal to 0.000128 Megabyte (zero point zero × 3 one hundred and twenty-eight mb)
1 Megabyte is equal to 8000000 bits (eight million bits)
1 Kibibit is equal to 1024 bits (one thousand and twenty-four bits)
1 Megabyte is equal to 8000000 Bit (eight million bit)
Megabyte is greater than Kibibit
Multiplication factor is 0.000128.
1 / 0.000128 = 7812.5.
Maybe you mean Mebibyte?
1 Megabyte is equal to 0.95367431640625 Mebibyte (zero point ninety-five trillion three hundred and sixty-seven billion four hundred and thirty-one million six hundred and forty thousand six hundred and twenty-five mib) convert to mib
### Powers of 2
mb kibit (Kibibit) Description
1 mb 7812.5 kibit 1 megabyte (one) is equal to 7812.5 kibibit (seven thousand eight hundred and twelve point five)
2 mb 15625 kibit 2 megabyte (two) is equal to 15625 kibibit (fifteen thousand six hundred and twenty-five)
4 mb 31250 kibit 4 megabyte (four) is equal to 31250 kibibit (thirty-one thousand two hundred and fifty)
8 mb 62500 kibit 8 megabyte (eight) is equal to 62500 kibibit (sixty-two thousand five hundred)
16 mb 125000 kibit 16 megabyte (sixteen) is equal to 125000 kibibit (one hundred and twenty-five thousand)
32 mb 250000 kibit 32 megabyte (thirty-two) is equal to 250000 kibibit (two hundred and fifty thousand)
64 mb 500000 kibit 64 megabyte (sixty-four) is equal to 500000 kibibit (five hundred thousand)
128 mb 1000000 kibit 128 megabyte (one hundred and twenty-eight) is equal to 1000000 kibibit (one million)
256 mb 2000000 kibit 256 megabyte (two hundred and fifty-six) is equal to 2000000 kibibit (two million)
512 mb 4000000 kibit 512 megabyte (five hundred and twelve) is equal to 4000000 kibibit (four million)
1024 mb 8000000 kibit 1024 megabyte (one thousand and twenty-four) is equal to 8000000 kibibit (eight million)
2048 mb 16000000 kibit 2048 megabyte (two thousand and forty-eight) is equal to 16000000 kibibit (sixteen million)
4096 mb 32000000 kibit 4096 megabyte (four thousand and ninety-six) is equal to 32000000 kibibit (thirty-two million)
8192 mb 64000000 kibit 8192 megabyte (eight thousand one hundred and ninety-two) is equal to 64000000 kibibit (sixty-four million)
### Convert Megabyte to other units
mb System Description
1 mb 8000000 bit 1 megabyte (one) is equal to 8000000 bit (eight million)
1 mb 1000000 b 1 megabyte (one) is equal to 1000000 byte (one million)
1 mb 1000 kb 1 megabyte (one) is equal to 1000 kilobyte (one thousand)
1 mb 0.001 gb 1 megabyte (one) is equal to 0.001 gigabyte (zero point zero × 2 one)
1 mb 0.000001 tb 1 megabyte (one) is equal to 0.000001 terabyte (zero point zero × 5 one)
1 mb 976.5625 kib 1 megabyte (one) is equal to 976.5625 kibibyte (nine hundred and seventy-six point five thousand six hundred and twenty-five)
1 mb 0.95367431640625 mib 1 megabyte (one) is equal to 0.95367431640625 mebibyte (zero point ninety-five trillion three hundred and sixty-seven billion four hundred and thirty-one million six hundred and forty thousand six hundred and twenty-five)
1 mb 0.000931322574615478515625 gib 1 megabyte (one) is equal to 0.000931322574615478515625 gibibyte
1 mb 0.000000909494701772928237915 tib 1 megabyte (one) is equal to 0.000000909494701772928237915 tebibyte
1 mb 8000 kbit 1 megabyte (one) is equal to 8000 kilobit (eight thousand)
1 mb 8 mbit 1 megabyte (one) is equal to 8 megabit (eight)
1 mb 0.008 gbit 1 megabyte (one) is equal to 0.008 gigabit (zero point zero × 2 eight)
1 mb 0.000008 tbit 1 megabyte (one) is equal to 0.000008 terabit (zero point zero × 5 eight)
1 mb 7812.5 kibit 1 megabyte (one) is equal to 7812.5 kibibit (seven thousand eight hundred and twelve point five)
1 mb 7.62939453125 mibit 1 megabyte (one) is equal to 7.62939453125 mebibit (seven point sixty-two billion nine hundred and thirty-nine million four hundred and fifty-three thousand one hundred and twenty-five)
1 mb 0.007450580596923828125 gibit 1 megabyte (one) is equal to 0.007450580596923828125 gibibit (zero point zero × 2 seven quintillion four hundred and fifty quadrillion five hundred and eighty trillion five hundred and ninety-six billion nine hundred and twenty-three million eight hundred and twenty-eight thousand one hundred and twenty-five)
1 mb 0.0000072759576141834259033203 tibit 1 megabyte (one) is equal to 0.0000072759576141834259033203 tebibit | 1,809 | 6,143 | {"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} | 3.328125 | 3 | CC-MAIN-2020-10 | longest | en | 0.874275 |
https://hsm.stackexchange.com/questions/5001/history-of-the-quadrature-of-curvelinear-figures-prior-to-the-middle-ages | 1,723,722,961,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641291968.96/warc/CC-MAIN-20240815110654-20240815140654-00480.warc.gz | 236,538,069 | 42,918 | # History of the quadrature of curvelinear figures prior to the middle ages
Hippocrates was able to construct the quadrature of three different lunes. Euler found two more squarable lunes. Tschebatorew and Durodnow showed that these five are the only squarable lunes.
Although Archimedes quadrature of the parabolic segment uses the method of exhaustion, the resulting formula, $\frac43 T$, does enable the finite construction of the square, so I will assume that this is a legitimate Euclidean quadrature.
Q: In antiquity, did anyone manage to square any other curved figures in the plane using only a finite straightedge and compass construction?
Pappus in Mathematical Collection, book IV "squared" the Archimedean spiral, the spiral is to the circle enclosing it as 1:3. The curve is obtained by composing uniform linear and circular motions in the plane, Archimedes himself in On Spirals attributes the discovery of it to his friend Conon. Some care is needed with calling this "squaring with straightedge and compass". Neither parabola nor Archimedean spiral can be produced with straightedge and compass, so they would have to be drawn in the plane as given. However, once the spiral is drawn it becomes possible to square any circle with straightedge and compass as well, as Archimedes proved in On Spirals.
The first such curve was known even earlier, the quadratrix. Originally it was devised to trisect angles, and termed the trisectrix, by Hippias (c. 450 BC), a sophist derided by Plato in his dialogues for excessive vanity. About a century later Dinostratus adapted it to squaring circles, and renamed it into the quadratrix, that is all we know of him. Since the quadratrix can be used to square circles, by design there are parts attached to it that can also be "squared with straightedge and compass".
On the other hand, Archimedes states in On Conoids and Spheroids that an ellipse is to the circle with its major axis for diameter, as its minor axis is to the diameter, which gives $\pi ab$ for semi-axes $a,b$ in formulaic modernization. But we would have to say that ellipse is not "squared with straightedge and compass", because the said circle can't be.
So we have a kind of hierarchy: lunes are both produced and squared by straightedge and compass, parabola must be drawn but can then be squared directly, quadratures of ellipse and spiral directly reduce only to the circle quadrature, but in the case of the spiral the circle can then be squared, if we are allowed to use it one more time. Parabola is a degenerate conic, circle and ellipse are non-degenerate ones, and Archimedean spiral and quadratrix are transcendental. But the pattern breaks down with hyperbola, areas under it require logarithms, and therefore do not reduce to the circle quadrature, see How did Saint Vincent prove the logarithmic property of areas under hyperbolas? Still, St. Vincent does prove the "logarithmic property" by Archimedean methods.
Greeks also knew some algebraic curves of degree higher than two, e.g. cubic cissoid of Diocles and quartic conchoid of Nicomedes, Newton's favorite, but those were only "squared" in modern times. For example, the area under the cissoid by Huygens and Wallis in 1658, even though like ellipse it reduces to circle quadrature. In modern terms, the "real" pattern is complicated not only by the structure of anti-derivatives of algebraic functions, but also because some definite integrals are expressible in square radicals even when anti-derivatives are not.
• Thanks. You make clear exactly the point I was fumbling around with when you note "Some care is needed with calling this squaring with straightedge and compass". This is why I was questioning the status of squaring the parabolic segment as legitimate in my OP. The point being, once a figure not producible with straightedge and compass is given, quadrature may be achievable with straightedge and compass. It all seems rather obvious now!
– nwr
Commented Jul 14, 2016 at 4:43
Andeans used this system since 5,000 y.a. diagonals were taken as geometric integers. It is present in Ancient Egypt and Caral.
• Although this is not a quadrature, it is interesting and rather clever. Do you have any references for the dating of this method of approximation and its derivation?
– nwr
Commented Jul 15, 2016 at 20:09
The feline was used in the Andeans and Egypt. Pythagoras used the same... | 1,016 | 4,408 | {"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} | 3.53125 | 4 | CC-MAIN-2024-33 | latest | en | 0.953263 |
https://www.mathworks.com/matlabcentral/answers/105607-radially-divide-binary-image-from-centroid-at-equal-angles-and-find-the-radial-distance?requestedDomain=www.mathworks.com&nocookie=true | 1,508,544,376,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824471.6/warc/CC-MAIN-20171020230225-20171021010225-00168.warc.gz | 964,918,231 | 15,401 | ## Radially divide binary image from centroid at equal angles and find the radial distance
### CX (view profile)
on 10 Nov 2013
Latest activity Edited by Image Analyst
on 11 Nov 2013
### Image Analyst (view profile)
I have the following binary image.
I need to divide this cell (the white section) into equal angle portions (of 36 degrees) at the centroid and find the distance from the centroid to the perimeter (edge of the white section) at each portion of angle. With the help of some of the answers I received in a previous post (courtesy of 'Image Analyst') I have the following code so far. ('some code portions have been changed from the original post marked with *')
``` C = imread('14.jpg');
bw = im2bw(C, graythresh(C));
cc = bwconncomp(bw, 4);
celldata = regionprops(cc, 'centroid');
celldata_centroid = [celldata.Centroid];
centroidx = celldata_centroid(:, 1);
centroidy = celldata_centroid(:, 2);
boundaries = bwboundaries(C);
mat_boundaries = cell2mat(boundaries); %*
boundaryx = mat_boundaries(:, 2);
boundaryy = mat_boundaries(:, 1);
allDistances = sqrt((boundaryx - centroidx).^2 + (boundaryy - centroidy).^2);
allAngles = atan2d(boundaryy, boundaryx); %*
[~, index36] = min(abs(allAngles - 36)); % Find index closest to 36 degrees
distance36 = distance(index36); %*```
```But I'm getting an error at the end saying not enough input arguments for the function 'distance'. Could someone help me out?
```
### Image Analyst (view profile)
on 10 Nov 2013
You never defines distance. Maybe you meant allDistances instead?
CX
### CX (view profile)
on 10 Nov 2013
Yes. Your correct. I thought you were calculating the distances using a function called distance. I just made that into allDistances. But I'm only getting one value. I'm guessing this is the distance from the centroid to the perimeter at 36 degrees? I actually need all lengths at intervals of 36 degrees. So that would be the radial distance at 36, 72, 108 etc... Any suggestions?
Image Analyst
### Image Analyst (view profile)
on 10 Nov 2013
Once you read and understand the code, you'll realize that I give that to you. For every pixel around it I give you the angle and the distance. Maybe there is no pixel at exactly 72 degrees. Maybe there's one at 71.42 degrees, and another one at 72.894 degrees. I give you everything that's there. But I didn't stop there, I actually gave you an example of how to find the pixel nearest to 36 degrees, since there might not be one at exactly 36 degrees to the billionth decimal point. Are you starting to understand what I did now? Okay, so you just do that for every angle that you want. If you want, you can scan allAngles and pull out the ones that are closest to 36, 72, etc. See if you can do that on your own, following my example and putting it into a loop.
CX
### CX (view profile)
on 10 Nov 2013
Yes I got that. Thank you once more.
MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi | 744 | 2,953 | {"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} | 3.171875 | 3 | CC-MAIN-2017-43 | latest | en | 0.832459 |
https://www.scienceflip.com.au/subjects/physics/dynamics/practice20/ | 1,726,637,030,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651836.76/warc/CC-MAIN-20240918032902-20240918062902-00809.warc.gz | 903,572,082 | 13,229 | Impulse and Momentum – Practice
Questions:
1) What is the momentum of a 15 tonne train moving south at 5.2 m/s?
2) A 2.5 kg brick is travelling downward at 1.5 m/s at the moment it hits the ground before coming to a complete stop. What is the impulse of the brick as it becomes stationary?
3) A 110 kg front rower changes his speed from 0.5 m/s to 3 m/s when running the ball. What is the impulse of this player?
4) A 0.06 N force is applied to a toy for 1.4 seconds. What is the impulse applied to the toy? | 145 | 512 | {"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} | 2.78125 | 3 | CC-MAIN-2024-38 | latest | en | 0.937164 |
http://www.jiskha.com/display.cgi?id=1170103461 | 1,462,090,855,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860114649.41/warc/CC-MAIN-20160428161514-00192-ip-10-239-7-51.ec2.internal.warc.gz | 612,202,905 | 3,718 | Sunday
May 1, 2016
Homework Help: Physics
Posted by Jamie on Monday, January 29, 2007 at 3:44pm.
A 75 kg man on a 39kg cart traveling at a speed of 2.3 m/s. He jumps off with zero horizontal speed realative to the ground. What is the resulting change in the speed of the cart?
I tried using m1v1=m2v2 but that didn't work out since I was expose to get 4.4 m/s as the answer. I can't figure out what i did wrong will you please show me how to solve this problem? | 138 | 465 | {"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} | 2.78125 | 3 | CC-MAIN-2016-18 | longest | en | 0.977102 |
https://github.com/zamronypj/oprsimd | 1,553,566,111,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912204768.52/warc/CC-MAIN-20190326014605-20190326040605-00270.warc.gz | 500,622,145 | 18,240 | Skip to content
# zamronypj/oprsimd
Operator overloading for vector matrix operation using Intel SIMD SSE/SSE2/SSE3 instructions written in Free Pascal
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.
.gitignore
LICENSE
README.md
simdssevec.pas
vectypes.pas
# Operator SIMD
This is repository for collection of operator overloading written in Free Pascal that allows to do vectors and matrices operation using Intel SIMD SSE/SSE2/SSE3 instructions.
## How to use
Adding two vectors
``````program simd_vector_add;
uses
vectypes,
simdssevec;
var
v1, v2, tot : TVector;
begin
//v1.x = 1.0, v1.y = 1.0, v1.z = 1.0, v1.w = 1.0
v1 := 1.0;
//v2.x = 2.0, v2.y = 2.0, v2.z = 2.0, v2.w = 2.0
v2 := 2.0;
tot := v1 + v2;
writeln('x:', tot.x, ' y:', tot.y, ' z:', tot.z, ' w:', tot.w);
end.
``````
Subtract two vectors
``````program simd_vector_sub;
uses
vectypes,
simdssevec;
var
v1, v2, tot : TVector;
begin
//v1.x = 1.0, v1.y = 1.0, v1.z = 1.0, v1.w = 1.0
v1 := 1.0;
//v2.x = 2.0, v2.y = 2.0, v2.z = 2.0, v2.w = 2.0
v2 := 2.0;
tot := v1 - v2;
writeln('x:', tot.x, ' y:', tot.y, ' z:', tot.z, ' w:', tot.w);
end.
``````
Multiply a vector with scalar
``````program simd_vector_mulscalar;
uses
vectypes,
simdssevec;
var
v1, tot : TVector;
begin
//v1.x = 1.0, v1.y = 1.0, v1.z = 1.0, v1.w = 1.0
v1 := 1.0;
tot := v1 * 2.0;
writeln('x:', tot.x, ' y:', tot.y, ' z:', tot.z, ' w:', tot.w);
end.
``````
You can’t perform that action at this time. | 592 | 1,565 | {"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} | 2.703125 | 3 | CC-MAIN-2019-13 | latest | en | 0.441982 |
https://www.cfd-online.com/Forums/fluent/121174-species-transport-outflow-boundary-condition-print.html | 1,508,632,849,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824931.84/warc/CC-MAIN-20171022003552-20171022023552-00484.warc.gz | 908,166,294 | 2,942 | CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
- FLUENT (https://www.cfd-online.com/Forums/fluent/)
- - species transport-outflow boundary condition (https://www.cfd-online.com/Forums/fluent/121174-species-transport-outflow-boundary-condition.html)
Lilly July 23, 2013 07:21
species transport-outflow boundary condition
Dear all,
I am simulating a species transport inside a geometry with several outlets and I am using th outflow boundary condition. My question is: does this boundary condition only fix the total flow (like for outflow:0.25-->25% of the total fluid-mixture is passing through this outlet) or is also the amount of species is fixed by the outflow condition (like also exactly 25% of the species is forced to pass this outlet)? I am afraid the latter might lead to wrong results, since depending on the bifurcation the amount of species might be larger or smaller at an outlet...
Does anybody have an idea or a reference?
Thanks a million!
Lilly
A CFD free user July 28, 2013 13:00
Hey
Off course, the first one is correct, a portion of total mass flow.
Lilly August 2, 2013 03:24
vix August 30, 2013 12:22
Dear Lilly,
I am looking to model something similar - contrast agent in blood through a realistic geometry of an artery with a stenosis. I am interesting in seeing the concentration of the agent downstream of the stenosis.
However, I am new to the species transport model.
I have been reading around and so far I understand that I would need an inlet mass fraction for the dye and the diffusion coefficient to use the species transport model. I will assume a zero flux through the wall but I am not sure what outlet bc to use. I only have 1 outlet.
Should I be prescribing a mass fraction at the outlet ( I don't have this information) ? or just use the outflow condition.
Vix.
Lilly September 4, 2013 04:59
Dear vix,
since I am interested in how the contrast agent bolus shape looks at the outlet I am using the outflow boundary condition and I do not set a bolus shape there. But you could also use a pressure outlet for example. I don't think you have to fix the mass fraction of the species at the outlet there (even though you have the possibility to do so). Do you have information of how your bolus looks there?
Good luck,
Lilly
vix September 4, 2013 05:58
Hi Lilly,
I do not know how the bolus looks at the outlet so I guess using either an outflow condition or a pressure outlet would be sufficient (without specifying a mass fraction)
I am mainly interested in seeing if there is an increase in the concentration of the species downstream of the stenosis as there is a recirculation zone which occurs there.
Would you be able to help with a few questions I have as I go along this simulation ? I would really appreciate it.
For example, when you select the species transport model, you are supposed to select a mixture. What mixture have you chosen ? or if you have created your own mixture, is it just the contrast agent and the blood. What properties would you need to specify for the two ?
I read somewhere that the agent should be first and the blood should be second since blood is the bulk fluid. Is that correct ? | 745 | 3,209 | {"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} | 2.5625 | 3 | CC-MAIN-2017-43 | latest | en | 0.919401 |
https://www.expertsmind.com/questions/determine-discharge-coefficient-30162227.aspx | 1,708,911,018,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474649.44/warc/CC-MAIN-20240225234904-20240226024904-00306.warc.gz | 769,401,233 | 12,756 | ## Determine discharge coefficient, Chemistry
Assignment Help:
The determination of k is not a strait forward exercise. Model it from first principles using Bernoulli's equation would produce a square root relationship and would probably have little relationship to the real system. The rate of discharge could be measured at different heads, but would require diverting the flow into a separate receptacle for a given time period. It is possible to log the level with time, as the tank drains freely through a fully open drain valve and while the pump is off. Knowing the area at each level ( see drawing of insert Figure 5) it is possible to determine the instantaneous volume against time. This has been done using the areas of the top and bottom prismatic sections of the tank and is shown in Figure.
Figure Plot showing example of instantaneous volume as V tank drains (using top and bottom areas of prismatic sections)
By determining the flow rate at the top and bottom of the tank, we can plot the graph shown in Figure. We have made the assumption that QL is directly proportional to the head. This is not true in actual fact, but will simplify the analysis and controller design. Figure 3 should be interpreted with care. Between about 10 and 20 seconds, the area is changing as we are in the V section and neither curve represents the instantaneous volume. After about 25 seconds, we are within the range of the outlet hole diameter, so effectively the orifice changes to channel like flow, but is complicated by the valve and pipe work arrangement.
#### Complexation behaviour of group 13, Q. Complexation Behaviour of Group 13? ...
Q. Complexation Behaviour of Group 13? As compared to the elements of Groups 1 and 2, elements of Group 13 show a greater tendency of complex formation. Because of lack of d-or
#### Schiff''s reaction and tischenko reaction, Schiff's reaction and Tischenko ...
Schiff's reaction and Tischenko reaction (a) Schiff's reaction: this reaction restores pink colour to Schiff's reagent (aqueous solution of p-rosaniline hydrochloride decolouri
#### Explain about optical rotation, Optical rotation (optical activity) is the ...
Optical rotation (optical activity) is the turning of the plane of linearly polarized light about the direction of motion as the light travels by certain materials. It happens in s
#### Microwave spectroscopy, Why Microwave performed at low temperature and low ...
Why Microwave performed at low temperature and low pressure
#### #10.., #Classify each reaction and give the name of all the chemical formul...
#Classify each reaction and give the name of all the chemical formula..
#### Oxidation, When assigning oxidation numbers and you have to do the math to ...
When assigning oxidation numbers and you have to do the math to find the oxidation number of something in the compound, what are you ultimately trying to get that compound to equal
#### Aliphatic hydrocarbon, why alkanes are called paraffin
why alkanes are called paraffin
#### Summery, i wanna someone help me to do summery from 2 pages like essay for ...
i wanna someone help me to do summery from 2 pages like essay for articl?
#### Lime soda process, state functions of lime and soda in lime soda process
state functions of lime and soda in lime soda process
#### Help, While studying evolution, a student comes across a cladogram that inc...
While studying evolution, a student comes across a cladogram that includes clades like amphibia, reptilia, aves, and mammalia. What must be the basal clade? | 750 | 3,558 | {"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} | 2.703125 | 3 | CC-MAIN-2024-10 | latest | en | 0.924253 |
https://paleosaver.com/australian-capital-territory/example-of-odd-natural-numbers.php | 1,611,539,421,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703561996.72/warc/CC-MAIN-20210124235054-20210125025054-00540.warc.gz | 502,996,763 | 7,605 | Example of odd natural numbers
Examples of denumerable sets Math - The University of Utah
Proving that all integers are even or odd Stack Exchange. As usual, the first n in the table is zero, which isn't a natural number. Because О” 3 is a constant, the sum is a cubic of the form an 3 +bn 2 +cn+d, [1.0], 4 Number Theory I: Prime Numbers For example, the natural numbers 1,2,3,4,6, and 12 all divide the number 12 itself. are odd. These sorts of.
Logic and Discrete Math Lecture notes Number Theory and
Proving that all integers are even or odd Stack Exchange. The set of odd natural numbers, 1, 3, 5, 7, Real numbers holds closure property of division of any two whole numbers is not always a whole number. Examples, N is the set of natural numbers 0, 1, 2, Examples Odd / even ? Example 1 Exhaustion: Any even number between 4 and 30 can.
Displaying search result for: Javascript program to add first 10 odd natural numbers The example of Swapping the numbers in JavaScript: Proofs by mathematical induction are, in fact, examples of the sum of the first n odd it is common to consider 0 as a natural number. Example
This page contains example to find sum of natural numbers in C programming Find the Sum of Natural Numbers using Check Whether a Number is Even or Odd: Printable worksheets and online practice tests on Natural and Whole Numbers for Grade 6. Natural and Whole Numbers - Multiple, Factors, LCM, HCF/GCD etc.
The following are the parity properties of even and odd numbers The application of these rules becomes clear through the following examples and problems We can write an odd number as (2n-1), where n is a natural number. n: The sum of the first n odd natural numbers is Ken Ward's Mathematics Pages
# Python program to find the sum of natural numbers up to n where n is provided by user # change this For example, if n = 16 Check if a Number is Odd or C programming, exercises, solution: Write a program in C to display the n terms of odd natural number and their sum.
NUMBERS 1.1 The Natural Numbers For example, we define the Proposition 1.1.1. For all n, the nth odd number is 2n−1. This is a C program to find the sum of odd and even numbers from 1 to N. If you wish to look at other example programs on Simple C Programs,
A natural number is a positive (or nonnegative) integer numbers. See Wikipedia:Natural number for more information. Natural numbers arise naturally Definetion and example of odd even and natural numbers Get the answers you need, now!
C programming, exercises, solution: Write a program in C to display the n terms of odd natural number and their sum. 29/05/2018 · In this Exercise – 2 given formulas with examples for average of numbers like first “n “natural numbers, average of even numbers, average of odd
The following are the parity properties of even and odd numbers The application of these rules becomes clear through the following examples and problems An integer that is not an even number is an odd any natural number. Any number multiplied with an even number will result in an even number. For example
N is the set of natural numbers 0, 1, 2, Examples Odd / even ? Example 1 Exhaustion: Any even number between 4 and 30 can Natural Numbers can further be sub-divided into different types :-1) Even and odd Numbers 2) Prime Numbers 3) Relatively prime/ co-prime numbers
What are the odd numbers from 1 to 1000? Every odd number added 2 gives you another odd number. Example: f What are the natural odd numbers between 6 to 40? The following are the parity properties of even and odd numbers The application of these rules becomes clear through the following examples and problems
The sum of the first n odd natural numbers 9math. This is a C program to find the sum of odd and even numbers from 1 to N. If you wish to look at other example programs on Simple C Programs,, What are the odd numbers from 1 to 1000? Every odd number added 2 gives you another odd number. Example: f What are the natural odd numbers between 6 to 40?.
The sum of the first n natural numbers 9math
C# Sharp Exercises Display the sum of n number of odd. An odd number given in the form 2n+1, For example, "N is a natural number: {1,2,3,4...} Think of what it means to be a "natural" number. Why "natural" of all, Proving that all integers are even or odd that the natural numbers are well ordered to ensure and first prove that every natural number is even or odd..
What is the sum of all natural numbers? Quora. Odd Natural Numbers (O): A system of naturals numbers, which are not divisible by 2 or are not multiples of 2, is called a set of odd numbers. It is denoted by 'O'., The sum of the first n odd natural numbers. Posted September 20th, 2007 by Isoscel. Is there an easy way to calculate the some of the first n natural numbers?.
Practice Questions on Recursive Definition
Proving that all integers are even or odd Stack Exchange. 6 thoughts to “Even, Odd, Prime and Composite Numbers” We could write 12 for example, as 2*2 because with 1 starts the series on numbers (natural, odd or https://en.wikipedia.org/wiki/Abundant_number You might also want to look at the entry on natural number in Wikipedia. Example 2. Definition of the Set of Nonnegative Even Numbers.
What is the sum of the first n natural numbers? The sum of the first n odd natural numbers This is an example for n = 5. Odd Natural Numbers (O): A system of naturals numbers, which are not divisible by 2 or are not multiples of 2, is called a set of odd numbers. It is denoted by 'O'.
This is a C program to find the sum of odd and even numbers from 1 to N. If you wish to look at other example programs on Simple C Programs, CHAPTER 1 Introductory Information and Review 2 University of Houston Department of Mathematics Example: Solution: Even/Odd Natural Numbers:
Displaying search result for: Javascript program to add first 10 odd natural numbers The example of Swapping the numbers in JavaScript: have separated the natural numbers into a variety of familiar and not-so-familiar examples: odd 1;3;5;7;9;11 What Is Number Theory? 7 original number.
Draw a flow chart of a program that adds N odd numbers starting from 1. The value of N should be input by the user - IGNOU MCA Assignment 2015 - 16 This is a C program to find the sum of odd and even numbers from 1 to N. If you wish to look at other example programs on Simple C Programs,
Natural numbers can be used for counting (one apple, two apples, for example in primary school, natural numbers may be called counting numbers Natural numbers can be used for counting (one apple, two apples, for example in primary school, natural numbers may be called counting numbers
For example: (i) Let P is a set of counting numbers greater than 12; (iv) The set A of all odd natural numbers can be written as Natural numbers examples The product of two natural numbers is a natural number. If n = m x 2 +1, then n is an odd number
This page contains example to find sum of natural numbers in C programming Find the Sum of Natural Numbers using Check Whether a Number is Even or Odd: Further Examples 4. Final Quiz Proof by induction involves statements which depend on the natural the result of adding the odd natural numbers is: 1 = 1,
Therefore sum of all natural numbers is -1/12 This is one of the simplest example of a concept crucial in What is the sum of the first 50 odd natural numbers? This is a C program to find the sum of odd and even numbers from 1 to N. If you wish to look at other example programs on Simple C Programs,
The set of whole numbers The set of natural numbers If there is an odd number of Smaller numbers always lie to the left of larger numbers on the number line. site:example.com find submissions Can there be a bijection between the natural numbers and the integers? For the odd numbers, f: N --> Z,
Categories:
All Categories Cities: Isaacs Girards Hill Gillen Lamb Island Long Plains St Leonards Molyullah Three Springs Eastbourne Edgerton Penticton Virden Gagetown Pouch Cove Deline Clark's Harbour Grise Fiord Carrying Place Meadowbank Asbestos Lancer Paris | 1,916 | 8,105 | {"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} | 3.640625 | 4 | CC-MAIN-2021-04 | latest | en | 0.871609 |
https://www.saonastudios.com/answers/17237917-a-15-year-annuity-pays-1-300-per-month-and-payments-are-made-at-the-end-of-each-month-the | 1,709,160,353,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474746.1/warc/CC-MAIN-20240228211701-20240229001701-00162.warc.gz | 982,526,552 | 9,803 | # A 15-year annuity pays $1,300 per month, and payments are made at the end of each month. The interest rate is 10 percent compounded monthly for the first six years and 8 percent compounded monthly thereafter. What is the present value of the annuity ## Answers Answer 1 Answer: Answer: 162075.97 dollars. Explanation: The time period of annuity = 15 years Annuity amount =$1300 per month
The interest rate for the first six-year = 10%
Monthly interest rate = 10% / 12 = 0.83%
Thus number pf periods = 6 * 12 = 72
Interest rate for another 9 years = 8%
Monthly interest rate = 8% / 12 = 0.67%
Number of period = 8 * 12 = 96
Use the below formula to find the present value of the annuity.
## Related Questions
It is estimated that a certain piece of equipment can save $per year in labor and materials costs. The equipment has an expected life of years and no market value. If the company must earn a % annual return on such investments, how much could be justified now for the purchase of this piece of equipment? ### Answers Answer: The amount that could be justified now for the purchase of this piece of equipment is$73,747.41.
Explanation:
Note: This question is not complete as all the data in it are omitted. A complete question is therefore provided before answering the question as follows:
It is estimated that a certain piece of equipment can save $22,000 per year in labor and materials cost. The equipment has an expected life of five years and no market value. If the company must earn a 15% annual return on such investments, how much could be justified now for the purchase of this piece of equipment? The explanation to the answer is now given as follows: To calculate this, the formula for calculating the present value of an ordinary annuity is used as follows: PV = P * [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1) Where; PV = Present value of the amount to justify the equipment purchase = ? P = yearly savings in labor and materials costs =$22,000
r = annual return rate = 15% = 0.15
n = Equipment has an expected life = 5
Substitute the values into equation (1) to have:
PV = $22,000 * [{1 - [1 / (1 + 0.15)]^5} / 0.15] PV =$22,000 * [{1 - [1 / 1.15]^5} / 0.15]
PV = $22,000 * [{1 - 0.869565217391304^5} / 0.15] PV =$22,000 * [{1 - 0.497176735298289} / 0.15]
PV = $22,000 * [0.502823264701711 / 0.15] PV =$22,000 * 3.35215509801141
PV = $73,747.41 Therefore, the amount that could be justified now for the purchase of this piece of equipment is$73,747.41.
### Final answer:
The question asks about the amount a company can justify spending on equipment, based on expected savings and a required rate of return. This requires understanding the concept of Present Value in financial calculations, using the formula PV = CF / (1 + r.
### Explanation:
The problem is related to the concept of Present Value in finance. Present value is the current worth of a future sum of money or stream of cash flows given a specified rate of return. In this scenario, the stream of cash flows is the annual savings in labor and materials costs due to the equipment. The return rate is the annual return the company requires on such investments.
To calculate the present value, use the formula:
PV = CF / (1 + r
Where:
PV is the Present Value
CF is the annual savings (Cash flow)
r is the annual return rate
n is the expected life of the equipment.
Plug in the given values into this formula to get the amount the company could justify for the purchase of this equipment. Do remember, the rate (r) is expressed in decimal, so if the annual return is say, 5%, use 0.05 in the formula.
### Learn more about present value here:
brainly.com/question/34554678
#SPJ3
ndicate whether the following items are "Included in" or "Excluded from" gross income. a. During the year, that the taxpayer purchased stock as an investment which doubled in value. b. Amount an off-duty motorcycle police officer received for escorting a funeral procession. c. While his mother was in the hospital, the taxpayer sold some of her jewelry at a gain to help pay for the hospital bills. d. Child support payments received. e. A damage deposit the taxpayer recovered when he vacated the apartment he had rented. f. Interest received by the taxpayer on an investment in general purpose bonds issued by IBM. g. Amounts received by the taxpayer, a baseball "Hall of Famer," for autographing sports equipment (e.g., balls and gloves). h. Tips received by a bartender from patrons. (Taxpayer is paid a regular salary by the cocktail lounge that employs him.) i. Taxpayer sells his Super Bowl tickets for three times what he paid for them. j. Taxpayer receives a new BMW from his grandmother when he passes the CPA exam.
### Answers
Answer:
Gross income refers to the income of an individual before taxes or any other deductions. It includes all type of income from all sources.
The list is as follows:
a. Excluded from
b. Included in
c. Included in
d. Excluded from
e. Excluded from
f. Included in
g. Included in
h. Included in
i. Included in
j. Excluded from
A company's sales forecast would likely consider all of the following factors except: advertising and pricing policies. top management's attitude toward decentralized operating structures. general economic and industry trends. competition. political and legal events.
### Answers
Answer:
The correct answer is letter "B": top management's attitude toward decentralized operating structures.
Explanation:
A sales forecast is an estimate of the sales a company projects to process during a given period. This is done so that the firm can have an idea of the resources necessary to produce a determined amount of output from where the company can profit a margin that allows keep the business up and running satisfying stakeholders and employees' expectations.
While creating a sales forecast it is important to consider events that could affect the regular operations of the business such as government regulatory policy changes, competition, and the economy of the industry. Top executives' attitudes towards operating structures are irrelevant for such a purpose.
Answer:
top management's attitude toward decentralized operating structures.
Explanation:
The balance sheet of Indian River Electronics Corporation as of December 31, 2017, included 13% bonds having a face amount of $90.3 million. The bonds had been issued in 2010 and had a remaining discount of$3.3 million at December 31, 2017. On January 1, 2018, Indian River Electronics called the bonds before their scheduled maturity at the call price of 102. Required: Prepare the journal entry by Indian River Electronics to record the redemption of the bonds at January 1, 2018. (If no entry is required for a transaction/event, select "No journal entry required" in the first account field. Enter your answers in whole dollars.)
### Answers
Answer:
Dr Bonds payable $90,300,000 Dr loss on early redemption of bonds$5,106,000
Cr Discounts on bonds payable $3,300,000 Cr Cash$92,106,000
Explanation:
The amount of cash paid to bondholders by calling the bonds is the 102% of the face value of $90.3 million i.e$90.3*102%=$92,106,000 The proceeds would debited to cash while the face value of the bond of$90.3 million would be debited to bonds payable account.
In addition the remaining discount of \$3.3 million would credited to discounts on bonds payable account.
The loss or gain on the bond call can then be determined as appropriate.
in which order would the expectancy theory place the following events? a) outcome valence, performance, effort b) performance, effort, outcome valence c) effort, outcome valence, performance d) performance, outcome valence, effort e) effort, performance, outcome valence
### Answers
Answer: e. effort, performance, outcome valence
Explanation:
The expectancy theory analyses and explains the reason why people behave the way they do. The expectancy theory explains that individual behave the way they do because they believe their efforts which they put into a particular activity will bring about an outcome.
The first thing that comes first is the effort which one puts into an activity, after then is the performance and lastly the outcome.
If the signature line on a Patriot Act or customerID form has the escrow officer's name printed on
it on the signature line, however, you as the
signing agent are the one who fills out the ID
form, who should sign the Patriot Act form?
### Answers
Since i am the signing agent who fills out the ID form, then, i am at responsibility to sign the Patriot Act form as well.
### What is Patriot Act form?
The Patriot Act/customer ID form is a form that help the government to fight the funding of terrorism and money laundering activities.
The Patriot Act/customer ID form is necessitated by the Federal law and its requires all financial institutions to obtain, verify, and record information that identifies every customer.
However, if the signature line on the Patriot Act has escrow officer's name printed on it on the signature line and i am the signing agent who fills out the ID form, then, i am at responsibility to sign the Patriot Act form as well.
Read more about Patriot Act form
brainly.com/question/7472599
### Final answer:
The person who fills out the Patriot Act or customer ID forms, in this case the Signing Agent, should be the one to sign the form, even if the escrow officer's name is printed on the signature line.
### Explanation:
In the context of processing Patriot Act or customer ID forms, the person who should be signing the form would typically be the individual who completed it, and can attest to the accuracy of the information therein. If you, as the Signing Agent, thoroughly completed the form, then you would sign it, even if the escrow officer's name is pre-printed on the signature line. The pre-printed name would likely indicate which the escrow officer is involved in the transaction, but it does not necessarily indicate who must sign the form. It's important too, however, to always follow your company's policies and any specific instructions given to you related to these forms.
### Learn more about Signing Agent here:
brainly.com/question/35057788
#SPJ11 | 2,336 | 10,347 | {"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} | 4.21875 | 4 | CC-MAIN-2024-10 | latest | en | 0.942973 |
https://www.coursehero.com/file/6051854/301-final-info/ | 1,526,887,271,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863967.46/warc/CC-MAIN-20180521063331-20180521083331-00592.warc.gz | 716,451,155 | 391,445 | {[ promptMessage ]}
Bookmark it
{[ promptMessage ]}
301 final info
# 301 final info - and future values Other things you should...
This preview shows page 1. Sign up to view the full content.
301 final info.doc Summary of Major Topics and Ratios Included on the Final Chapter 13 - Financial Statement Analysis: - Ratio Calculations - see Exam #7 Information for specific ratios to be tested. - Understand the terms Liquidity, Solvency and Profitability and how they relate to ratios. - Be familiar with vertical and horizontal analysis. - Define or explain the irregular items that may appear on the income statement, including the “net of tax” presentation for: - Discontinue Operations - Extraordinary Items Appendix C - Time Value of Money: - Understand and calculate problems using the time value of money concepts. I.e. present
This is the end of the preview. Sign up to access the rest of the document.
Unformatted text preview: and future values. Other things you should be able to calculate or explain:- Calculate simple interest, including determining the principal and interest components when a series of equal payments are made. For example, a fully amortized loan. (See the example of interest calculations on the webpage.) - Calculate dividends paid to common stockholders using the concept: o beginning retained earnings o plus net income or minus net loss o minus total dividends o equals ending retained earnings Concepts of Accounting: - Know the 12 accounting assumptions, principles and constraints, and how they are applied....
View Full Document
{[ snackBarMessage ]}
### What students are saying
• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.
Kiran Temple University Fox School of Business ‘17, Course Hero Intern
• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.
Dana University of Pennsylvania ‘17, Course Hero Intern
• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.
Jill Tulane University ‘16, Course Hero Intern | 517 | 2,535 | {"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-2018-22 | latest | en | 0.836148 |
https://www.gamedev.net/topic/635066-2d-ray-casting-problems-dont-align-correctly/ | 1,493,452,636,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917123318.85/warc/CC-MAIN-20170423031203-00575-ip-10-145-167-34.ec2.internal.warc.gz | 903,730,791 | 44,707 | • FEATURED
View more
View more
View more
### Image of the Day Submit
IOTD | Top Screenshots
### The latest, straight to your Inbox.
Subscribe to GameDev.net Direct to receive the latest updates and exclusive content.
# 2D Ray-casting problems, don't align correctly.
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
12 replies to this topic
### #1Moonkis Members
Posted 29 November 2012 - 09:30 AM
I'v been trying and studying a hell of a lot for making my 2D raycasting, I'v been visiting KahnAcademy for Trigonometry-lessons as well as reading various topics ( each with a completely different method of achieving it. )
I'v chosen to stick with the topic found here
Currently I'm just trying to get the ray-casting and movement to work, so far so good, almost.
I'm not entirely sure of how to do the casting, but I got something almost working, though it's a bit off. Here is how it looks so far:
The blue/magenta arrow is the direction the player will travel ( current angle ) and the white rays are supposed to be the ray-casting, as you can see it's off by quite a bit and I can't understand why.
Here is my current casting code:
sf::VertexArray ray(sf::Lines, 2);
const int travelingDistans = 400;
double subsequentRayAngleIncrease = player.fov/w;
// Start from column 0 to the X't column of the viewing plane.
// I'm not sure what the viewing plane is but I'm guessing it's the screen.
// Which would mean from 0 to our screens highest x, which is 800.
// Since the resolution is 800x600
for( int i = 0; i < w; i++)
{
double rayAngle = player.rot - ( (player.fov/2) + subsequentRayAngleIncrease*i );
double rx = player.x - travelingDistans * std::cos(Math::to_radians(rayAngle));
double ry = player.y - travelingDistans * std::sin(Math::to_radians(rayAngle));
// + 5 is so it's centered of the players origin
ray[0] = sf::Vector2f( player.x + 5 , player.y + 5);
ray[1] = sf::Vector2f( rx + 5, ry +5 );
ray[1].color = sf::Color(255,255,255,30);
ray[0].color = sf::Color(255,255,255,30);
rwind.draw(ray);
}
What am I doing wrong?
Also a couple of side questions:
1. Why do you multiply by -d and not just d ( distance ) when calculating with sin and cos?
2. Does this technique look right considering it's supposed to transition into fake 3D using 2D raycasting ( Given that the final ray distance is determined on where it hit a wall ).
Kind regards
Moonkis
EDIT:
Realized that the offset was due to me accidentally subtracting the subsequent ray angle when calculating the offset using players FOV
Changed it from this:
double rayAngle = player.rot - ( (player.fov/2) + subsequentRayAngleIncrease*i );
into this:
double rayAngle = ( player.rot - (player.fov/2) ) + subsequentRayAngleIncrease*i;
It seems to work as intended now, checked using 90, 180, 270 and 360 FOV angles. ( 180 and 90 was the ones I based it on working, they looked as intended, also added some wrapping when calculated angles for the rx and ry:
if( rayAngle == 360 ) rayAngle = 0;
if( rayAngle > 360 )
{
rayAngle = ( rayAngle - 360 );
}
if( rayAngle < 0 )
{
rayAngle = ( 360 + rayAngle );
}
Seeing as I only like to work with the angels 0 - 359 ( sin(to_radiance(360)) and sin(to_radiance(0)) gave different angles where as 0 degrees to radians was the most correct one.
Edited by Moonkis, 29 November 2012 - 10:47 AM.
### #2Álvaro Members
Posted 29 November 2012 - 09:50 AM
Whether you multiply by d or -d and whether you use cosine for x or for y depends on the conventions you are using. I would stick to trigonometric conventions as much as possible, where angle 0 points in the positive x direction, and angles go up counterclockwise.
I don't think you need nearly as much trigonometry as you are using. The pixel columns on your screen don't cover a constant angle: The center column covers a larger angle than the column on the far right. Imagine you have a very large screen compared to the distance you are sitting from it and it will be obvious.
The way I think about this, the player is looking in some direction (cos(player.rot),sin(player.rot)), which I'll call (x,y) for short. Now you can compute an equally-spaced sequence of points from (x,y)-K*(y,-x) to (x,y)+K*(y,-x) and launch rays in those directions. K is a constant that you can compute as tan(FOV/2).
By the way, as part of my crusade against angles, you can store the direction in which the player is looking as (x,y) directly, instead of an angle. And I even prefer to specify K directly instead of FOV. But start by getting your code working.
Edited by Álvaro, 29 November 2012 - 09:50 AM.
### #3Álvaro Members
Posted 29 November 2012 - 09:57 AM
Oh, one more thing!
const int travelingDistans = 400;
You didn't post all your code, so I don't know if this is biting anywhere, but you should really use the intended type for every variable. That variable should be a double instead of an int. Getting the type wrong could result in expressions like player.fov/w being truncated, if player.fov and w happen to be integers.
### #4Moonkis Members
Posted 29 November 2012 - 10:22 AM
Whether you multiply by d or -d and whether you use cosine for x or for y depends on the conventions you are using. I would stick to trigonometric conventions as much as possible, where angle 0 points in the positive x direction, and angles go up counterclockwise.
Well I just based on what angles I got from 0, 90, 180 and 270, isn't this the trigonometric conventions?
// In degrees:
// ^ 90 deg
// |
// 360/0 deg| 180 deg
// <----- ------>
// | a = 90 degrees delta
// |
// v 270 deg
I don't think you need nearly as much trigonometry as you are using. The pixel columns on your screen don't cover a constant angle: The center column covers a larger angle than the column on the far right. Imagine you have a very large screen compared to the distance you are sitting from it and it will be obvious.
This dosn't tell me much :/
The way I think about this, the player is looking in some direction (cos(player.rot),sin(player.rot)), which I'll call (x,y) for short. Now you can compute an equally-spaced sequence of points from (x,y)-K*(y,-x) to (x,y)+K*(y,-x) and launch rays in those directions. K is a constant that you can compute as tan(FOV/2).
I have no clue why that works. Or how it works, Or in what context to use it.
By the way, as part of my crusade against angles, you can store the direction in which the player is looking as (x,y) directly, instead of an angle. And I even prefer to specify K directly instead of FOV. But start by getting your code working.
I get that your against angles by now, but your crusade is not really helping me understand it, sorry. It just confuses me more :/
Sorry.
### #5Álvaro Members
Posted 29 November 2012 - 10:33 AM
Well, the way you are increasing the angle in the code you posted, seems to indicate that each column on the screen covers an equal angle from the eye, which is not true unless you have a cylindrical screen and you sit at the axis of the cylinder (which would be totally cool ;) ). If your screen is closer to a flat surface, you should do something like what I describe.
We seem to have trouble communicating, but I can think of a way to move forward: Come up with a specific example (player is here, looking in this direction, FOV is 45 degrees... whatever). Then I can walk you through what the code should do and why.
My distaste for angles is not capricious. I actually started writing graphics programs with angles everywhere, and over the years I have learned to think in terms of vectors instead, which made my code cleaner, faster and easier to get right. I hope my crusade will actually help you. But we'll see.
### #6Moonkis Members
Posted 29 November 2012 - 10:47 AM
I edited my original post, I got the ray-casting aligning but I'm more than interested in getting a lesson and answers on my question, once I get into the part where my rays are supposed to render a fake 3D image I can't afford to have it done wrong in the beginning.
Okey so here is an example:
Object A is facing straight up ( towards the top of the screen ) and is currently at (400, 300) where the screen size is 800x600. Object A's FOV is 60 Degrees and needs the rays to identify whether there are objects in his line of sight.
Is this enough of information?
Also please when using tan and sin just quickly mention what it does and what it's for so I can have a context of it.
Kind regards,
Victor Karlsson
### #7Álvaro Members
Posted 29 November 2012 - 11:36 AM
You seem to be using the coordinates of the screen directly, with (0,0) being the top-left corner. Notice that in those coordinates, an increase in y goes down, while the convention used in Math is that an increase in y goes up. This explains why you need to negate the sin(...) part. The sign of the cos(...) part should be positive, but your particular test is symmetric, so you haven't noticed the problem yet.
I will use traditional Math convention for everything. I will also assume the player is at (0,0) to simplify things. If your player is facing straight up, I guess player.rot = 90 degrees. You can draw an arrow of length 1 from the origin pointing in that direction, it will have coordinates (0,1). In general the coordinates are (cos(player.rot), sin(player.rot)). The length of 1 is arbitrary. If it helps you visualize it better, you can think of it as an arrow of length 100, which would have coordinates (0,100). In the end that factor of 100 won't matter. From now on, let this vector be (x,y).
Now I am going to draw a segment that represents the screen (I assume we are viewing the whole thing from the top of the scene). It will be a segment that is perpendicular to (0,1). You can find a direction that is perpendicular to (a,b) by computing (-b,a) (that's a rotation of 90 degrees counterclockwise). In our case, we'll get (-1,0). The segment I will draw will have (0,1) as the center and the left end will be at a point (0,1)+K*(-1,0). Reminder: That notation means (0+K*(-1),1+K*0) = (-K,1). The other end will be (0,1)-K*(-1,0), which is (K,1). I don't know what K is yet, but it will depend on FOV somehow.
So let's compute K. If you have been making a drawing of this (which you should), you can look at the triangle formed by the origin (0,0), the center of my "screen segment" (0,1) and the far right end of my screen segment (K,1). This triangle is rectangle at (0,1), and I am interested in the angle at the origin, which should be FOV/2 = 30 degrees. The tangent of that angle can be computed as "opposite side / adjacent side", which is K/1. That tells me that K/1 = tan(30 degrees) = 0.57735, and that's how I compute K.
Now my code would look something like this:
double const distance_to_screen = 300.0;
// The next two definitions have sings different than the text, to
// try to adapt to the convention that y increases going down.
sf::Vector2f look_vector(distance_to_screen*std::cos(look_angle),
-distance_to_screen*std::sin(look_angle));
sf::Vector2f left_vector(look_vector.y, -look_vector.x);
double K = std::tan(0.5 * player.fov);
sf::Vector2f far_left_end = look_vector + K * left_vector;
sf::Vector2f one_column_increment = -2.0 * K * left_vector / w;
sf::VertexArray ray(sf::Lines, 2);
ray[0] = player;
ray[0].color = sf::Color(255,255,255,30);
ray[1].color = sf::Color(255,255,255,30);
for (int i = 0; i < w; i++) {
// meaning of player' is the center of the player
ray[1] = player + far_left_end + i * one_column_increment;
rwind.draw(ray);
}
I don't have a complete program to play with, so there might be mistakes in that code. If it doesn't work and it's not trivial to fix, I'll try to post a complete program, but this will probably need to wait until tonight.
Edited by Álvaro, 29 November 2012 - 11:38 AM.
### #8Moonkis Members
Posted 29 November 2012 - 01:10 PM
If you have been making a drawing of this (which you should), you can look at the triangle formed by the origin (0,0), the center of my "screen segment" (0,1) and the far right end of my screen segment (K,1).
How can I do that? I have no idea where the point(K,1) is? Since we haven't computed it.
Here is what I drew up until that point:
EDIT 2: I'm not sure if we are using cartesian-coordinate system or normal math one?
What exactly is distance_to_screen? and also your using player like a struct then telling me player is a vector representing the origin of the player?
EDIT:
On a second note maybe one thing should be clarified as well:
1. "The pixel columns on your screen don't cover a constant angle" - I'm not 100% sure I get that statement, maybe a picture ( when you have time of course! ) along with words could help straighten that out.
PS. I'm so sorry for getting this slow, and that you take a lot of time explaining it to me.
Edited by Moonkis, 29 November 2012 - 02:25 PM.
### #9Álvaro Members
Posted 29 November 2012 - 02:34 PM
If you have been making a drawing of this (which you should), you can look at the triangle formed by the origin (0,0), the center of my "screen segment" (0,1) and the far right end of my screen segment (K,1).
How can I do that? I have no idea where the point(K,1) is? Since we haven't computed it.
Dude, in the next sentence after what you quote I tell you myself that we don't know what K is yet, and than I have a paragraph devoted to describing how to compute K. You need to work on your reading comprehension.
I'll try to give you an even more detailed explanation tonight.
### #10Moonkis Members
Posted 29 November 2012 - 04:51 PM
I'm just letting you know that I changed the degree convention, x-positive is now 0 and increase the angle y going conter-clockwise ( Which helps with just keeping it: cos(a)*d and sin(a)*d )
Also I'v been trying to adapt your code here ( since you can't multiply vectors in SFML I'm giving an alternative version a go ) it currently looks like this:
double K = std::tan(player.fov/2);
double distance_to_screen = 300;
sf::Vector2f left_vector(look_vector.x, -look_vector.y);
sf::Vector2f far_left_end = look_vector;
far_left_end.x + K * left_vector.x; far_left_end.y + K * left_vector.y;
sf::Vector2f one_column_increment(-2.0,-2.0);
one_column_increment.x * K * left_vector.x / w; one_column_increment.y * K * left_vector.y / w;
sf::VertexArray ray(sf::Lines, 2);
ray[0] = sf::Vector2f(player.x+5, player.y+5);
for( int i = 0; i < w; i++ )
{
ray[1] = sf::Vector2f( player.x+5 + far_left_end.x + i * one_column_increment.x, player.y+5 + far_left_end.y + i * one_column_increment.y);
rwind.draw(ray);
}
Though I did not get it to work as intended.
By the way, don't stress man, I'm just happy that you are helping me ( Can't stress that enough ) so take your time.
Edited by Moonkis, 29 November 2012 - 05:06 PM.
### #11Álvaro Members
Posted 29 November 2012 - 04:59 PM
This seems to work. See if you understand how it does everything and ask about anything that is not entirely clear.
#include <SFML/Graphics.hpp>
#include <iostream>
#include <cmath>
void draw_line(sf::RenderWindow &app, sf::Vector2f from, sf::Vector2f to) {
app.Draw(sf::Shape::Line(std::floor(400.0f + from.x * 200.0f),
std::floor(300.0f - from.y * 200.0f),
std::floor(400.0f + to.x * 200.0f),
std::floor(300.0f - to.y * 200.0f),
1, sf::Color::White));
}
int main() {
sf::RenderWindow app(sf::VideoMode(800, 600), "Ray casting computations");
while (app.IsOpened()) {
sf::Event Event;
while (app.GetEvent(Event)) {
if (Event.Type == sf::Event::Closed)
app.Close();
}
app.Clear();
int const width = 100;
float const degrees = std::atan(1.0f)/45.0f;
float K = std::tan(30.0f*degrees);
sf::Vector2f position(0.0f, 0.0f);
sf::Vector2f left_edge = position + heading + K * left;
sf::Vector2f step = -(2.0f * K / width) * left ;
for (int i=0; i<width; ++i) {
sf::Vector2f ray_end = left_edge + step * (i+0.5f);
draw_line(app, position, ray_end);
}
app.Display();
}
return EXIT_SUCCESS;
}
Edited by Álvaro, 29 November 2012 - 05:00 PM.
### #12Moonkis Members
Posted 29 November 2012 - 05:27 PM
Ugh, a lot of magic numbers, but the code works ( needed to make a bit conversion magic into SFML 2.0 )!
Is it okay if I respond tomorrow? It's getting quite late here
On the top of my head here are some questions:
void draw_line(sf::RenderWindow &app, sf::Vector2f from, sf::Vector2f to) {
sf::VertexArray line(sf::Lines, 2);
line[0] = sf::Vector2f(std::floor(400.0f + from.x * 200.0f),std::floor(300.0f - from.y * 200.0f));
line[1] = sf::Vector2f(std::floor(400.0f + to.x * 200.0f), std::floor(300.0f - to.y * 200.0f) );
app.draw(line);
}
I'm guessing 200.0f is the distance to draw the rays, 400.0f is the center of the map, and so is 300.0f?
float const degrees = std::atan(1.0f)/45.0f;
What exactly are the values used here? What does 1 and 45 represent?
float K = std::tan(30.0f*degrees);
What exactly is 30 representing in the code? Is it the same 30? for all the 30's in the code?
sf::Vector2f left(-heading.y, heading.x);
Why is the y and x inverted?
sf::Vector2f step = -(2.0f * K / width) * left ;
I have no idea what this is.
sf::Vector2f ray_end = left_edge + step * (i+0.5f);
What exactly is end here and what is the number 0.5 coming from.
Also in the drawing exercise before what coordination system are we using? Polar or Cartesian? I'd love to be able to draw It sucessfully since that might just be the key to being able to visualise it manually.
Also, great work!
### #13Álvaro Members
Posted 29 November 2012 - 06:11 PM
Ugh, a lot of magic numbers, but the code works ( needed to make a bit conversion magic into SFML 2.0 )!
Yeah, that's fair criticism. I thought the origin of the numbers would be more or less obvious, but it would be better to give things names.
Is it okay if I respond tomorrow? It's getting quite late here
Of course.
On the top of my head here are some questions:
void draw_line(sf::RenderWindow &app, sf::Vector2f from, sf::Vector2f to) {
sf::VertexArray line(sf::Lines, 2);
line[0] = sf::Vector2f(std::floor(400.0f + from.x * 200.0f),std::floor(300.0f - from.y * 200.0f));
line[1] = sf::Vector2f(std::floor(400.0f + to.x * 200.0f), std::floor(300.0f - to.y * 200.0f) );
app.draw(line);
}
I'm guessing 200.0f is the distance to draw the rays, 400.0f is the center of the map, and so is 300.0f?
400.0f and 300.0f are indeed the center of the screen. I am using coordinates like I would in Math everywhere in the program and this is the function that translates them into screen coordinates. 200.0f is a scale factor, so the window covers the interval (-2, 2) horizontally and (-1.5, +1.5) vertically.
float const degrees = std::atan(1.0f)/45.0f;
What exactly are the values used here? What does 1 and 45 represent?
The angle whose tan is 1 is 45 degrees, so by multiplying a number of degrees by this number, you turn it into radians.
float K = std::tan(30.0f*degrees);
What exactly is 30 representing in the code? Is it the same 30? for all the 30's in the code?
30.0f if half the FOV of 60 degrees.
sf::Vector2f left(-heading.y, heading.x);
Why is the y and x inverted?
I think I covered this one already: This is just a 90-degree rotation of the heading vector.
sf::Vector2f step = -(2.0f * K / width) * left ;
I have no idea what this is.
That's how much I need to advance for each pixel.
sf::Vector2f ray_end = left_edge + step * (i+0.5f);`
What exactly is end here and what is the number 0.5 coming from.
I think of the ray as an arrow, with a beginning (the player's position) and an end. The 0.5 is there so the ray aims to the center of the pixel, instead of the left side.
Also in the drawing exercise before what coordination system are we using? Polar or Cartesian? I'd love to be able to draw It sucessfully since that might just be the key to being able to visualise it manually.
I have only used Cartesian coordinates everywhere. Maybe I'll try to make a picture, but it's a bit of a pain.
Also, great work!
Thanks!
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic. | 5,591 | 20,284 | {"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} | 3.421875 | 3 | CC-MAIN-2017-17 | latest | en | 0.918045 |
http://www.scootle.edu.au/ec/search?accContentId=ACMSP172 | 1,600,712,085,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400202007.15/warc/CC-MAIN-20200921175057-20200921205057-00606.warc.gz | 216,203,076 | 17,143 | Close message Scootle will stop supporting resources that use the Adobe Flash plug-in from 18 Dec 2020. Learning paths that include these resources will have alerts to notify teachers and students that one or more of the resources will be unavailable. Click here for more info.
# Mathematics / Year 7 / Statistics and Probability / Data representation and interpretation
Curriculum content descriptions
Describe and interpret data displays using median, mean and range (ACMSP172)
Elaborations
• using mean and median to compare data sets and explaining how outliers may affect the comparison
• locating mean, median and range on graphs and connecting them to real life
General capabilities
• Literacy Literacy
• Numeracy Numeracy
• Critical and creative thinking Critical and creative thinking
ScOT terms
Data representation, Mean, Median
## Refine results by
Year level 7-8
Resource type
Learning area Mathematics
## Refine by topic
Related topic
### Data - Years 7 to 9
The 12 learning objects in this collection relate to the use, collection, display, comparison and interpretation of data. Objects in the first category, statistical data graphs, enable students to explore data using a range of graphical analysis tools. Objects in the second category, analysing surveys, enable students to ...
### Life expectancy PowerPoint
This teacher resource is a PowerPoint presentation designed to address common student misunderstandings about life expectancy. It emphasises that life expectancy is an average, that most people live for much longer or shorter than their life expectancy and that, when life expectancy is low, it is mostly because of a very ...
### ReSolve: What's In A Name
This sequence of two lessons examines trends in the names of students in the class, as well as trends in popular names from 2017 and 1957. Students explore data associated with these names and decide whether the mean, median or mode might be a suitable measure of central tendency. They develop their skills with spreadsheets ...
### Mean, median and mode
This resource is a video demonstration, with audio commentary, about calculating the mean, median and mode of a data set. The meaning of each of the terms - mean, median and mode - is explained and the difference between them is clarified. The resource explains the process and demonstrates a handwritten method for calculating ...
### Stem-and-leaf graphs: an introduction
Find out what a stem-and-leaf graph is. Find out what a back-to-back stem-and-leaf graph is. Work through this tutorial to understand the features of stem-and-leaf graphs, and how they are used to display and to compare two data sets. Observe how the mean and median of the data sets can be used to interpret information. ...
### Stem-and-leaf graphs: height
Are 13-year-old boys taller than 13-year-old girls? Display the data in a back-to-back stem-and-leaf graph to investigate the truth of this conjecture. Identify the median for girls and boys and use the two means to help draw a conclusion about this question. Use the tutorial to show the features and uses of stem-and-leaf ...
### Stem-and-leaf graphs
Find out what a stem-and-leaf graph is and use it to investigate the truth about different conjectures. Work through a tutorial about stem-and-leaf graphs, and then choose an investigation from a set of three. Enter your own data in some investigations. For example, test the reaction time of your preferred hand against ...
### Exploring measures of central tendency
Examine the mean and median values for a data set recording emergency response times. Predict changes to the mean and median as new results are added.
### Stem-and-leaf graphs: reaction time
Do right-handed students have faster reaction times than left-handed students? Display the given data, including your own time, in a back-to-back stem-and-leaf graph to investigate the answer to this question. Identify the median for left- and right-handed students and use the two means to help you draw a conclusion about ...
### A mathematical focus on 'Choose your own statistics'
This teaching resource demonstrates ways in which real data can be interpreted and analysed. It is based on the interactive learning resource Choose your own statistics, in which data is presented as infographics, graphical representations and tables. The focus of the supporting teaching and learning activities is on analysing ...
### Data handler
Help plan your school sports day by ordering special T-shirts and socks, and organising buses for all the students. Plot raw data on a dot plot and then group that data according to three criteria or 'rules' to decide on suitable sizes and numbers of T-shirts and socks to order in each group, and to decide the minimum number ...
### Skateboard survey
Explore how the height of skateboard ramps is related to kids' heights. Choose questions to ask in a survey. Choose a sample size to suit a budget and margin of error. Examine a table of results. Sort the data and use it to answer questions. Display the results using a boxplot. Identify conclusions supported by the evidence. ...
### Healthy life survey: staying active
Explore why kids like to play sport. Choose questions to ask in a survey. For example, look at whether kids come from a sporty family, have friends that play or have a great coach. Examine a table of results. Sort the data and use it to answer questions. Display the results using a suitable type of graph such as a pie chart, ...
### Secondary mathematics: using real data
These seven learning activities, which focus on the use of 'real data' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use the three content strands ...
### Australia's population: countries of birth - dataset
The dataset provides statistics about the estimated resident population, median age and sex ratio by countries of birth for the latest year of available data. It is periodically updated by the Australian Bureau of Statistics (ABS). The dataset is included in the list of related datasets on the page in MS Excel format.
Explore the way in which statistics are presented using a wide range of graphs types for ten topics related to human rights. Customise and publish graphs and download data to a spreadsheet program such as Excel to enable further exploration.
### Neighbourhood fractions
Help a town planner to design site plans. Assign regions on a 10x20 grid for different uses. Calculate the percentage and the fraction of the total site used for each region. Use a number line to display fractions and equivalent decimals. Design site plans for a: 1. Neighbourhood; 2. City; 3. Farm. This learning object ...
### Timetable: music festival challenge
Work out a program for the Auckland music festival. Find the flight times and other travel details for acts coming from different parts of Australia, New Zealand and Norfolk Island. Calculate the earliest and latest times they can perform. Check for extra information, like changes in time zones, connecting flights, or Stage ...
### The Numberline
An interactive tool that can help students explore a number line, including points representing integers, fractions and decimals
### Scale matters: negatives
Explore the use of scale on a number line. Select a ruler displaying a helpful scale such as ones. Look at a pair of numbers such as -5 and -2 marked on a number line. Identify the number corresponding to another point. Or locate another point on the number line to complete a series of three numbers. Apply a marked scale ... | 1,548 | 7,748 | {"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} | 3.875 | 4 | CC-MAIN-2020-40 | longest | en | 0.858861 |
https://inteligentny-dom-wroclaw.pl/calcio/Sep/1744.html | 1,659,886,418,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570651.49/warc/CC-MAIN-20220807150925-20220807180925-00000.warc.gz | 320,304,837 | 9,306 | how to measure output of a crusher plant
+86 0371 8654 9132
## how to measure output of a crusher plant
##### How to Evaluate/Estimate a Crusher Product Size - Crushing ...
2) CSS - as noted above, use a Ball or "Slug" made of tin foil to drop through the lowest nip point with the crusher running. by rope. similar to gaping a cone
##### how to measure output of a crusher plant
Jaw gap (setting output size ) built in measurement scale.Sectional view showing Components of a Jaw Crusher. 7 .. measured, and the motion of the crusher has
##### calculation of output of a crusher
stone crusher output calculation soyez-responsable.ch. jaw crusher output calculations [Click to learn more] stone crusher output calculation Output for
##### Crushing Products Size and Shape -What to Expect
Feb 26, 2016 Such an arrangement is seldom encountered in modern plant design, except where large jaw crushers, set very wide, are followed by a secondary, usually of the
##### Particulate Matter (PM) Emission Calculations
Stone Crushing Spreadsheet Screens Output Actual TSP Emissions = 0.165 tpy TSP controlled screening emission factor: 0.0022 lb/ton . Abrasive Blast Booth Emission
##### Primary Crushing - Mineral Processing Metallurgy
Feb 26, 2016 The term “primary crusher,” by definition, might embrace any type and size of crushing machine. The term implies that at least two stages of crushing are involved
##### KEY PERFORMANCE INDICATORS - Plant Maintenance
failures. The output of a healthy reliability process is optimal asset reliability at optimal cost. Asset Reliability Process measures are leading indicators. They
##### No-Nonsense Guide to Measuring Productivity
Indeed, even if a plant uses one aggregate measure, it still makes sense to use single-factor measures because they help identify the sources of aggregate
##### How to Evaluate/Estimate a Crusher Product Size - Crushing ...
2) CSS - as noted above, use a Ball or "Slug" made of tin foil to drop through the lowest nip point with the crusher running. by rope. similar to gaping a cone crusher the tin foil slug will be caught in the nip point and crushed. To determine the OSS just measure the slug and add the total throw of the eccentric.
##### Productivity Measurment Of Aggregate Crusher Plant
Aggregate crushers for cement process plant As a leading global manufacturer of crushing, grinding and mining equipments, we offer advanced, reasonable solutions for any size-reduction requirements including quarry, aggregate, and different kinds of minerals.Measuring Aggregate Productivity Growth Using Plant-Level Data Amil Petrin and James ...
##### how to compute input of stone batching planter plant BHS ...
how to measure stone crusher production. cost of 50m3/h belt conveyor concrete batching plant in Belarus», how to measure crushing stroke in cone crusher The cone crusher may be equipped with either an air/oil cooler or a water cooler to help dissipate heat from the. how to measure stone crusher production. stone crushing production line, Stone production line,Stone crushing plant,Rock ...
##### Estimating Mobile Crusher Outputs
Estimating Mobile Crusher Outputs. FOB Reference Price: Get Latest Price Mobile crusher out put measure hotelcityinnin output for mobile jaw crushers ranges from 100 to 1,500 tph depending on the model size and consistency of the feed how to measure the output of jaw crusher theoretical a jaw crusher is one of the main, roll crusher and mechanical operation lab, mobile.
##### Crushing Plant Flowsheet Design-Layout
Mar 10, 2016 Crushing Plant Flowsheet Design-Layout. In the crushing section, the ore as it comes from the mine is broken down dry to a size suitable for the wet grinding machines ; these can, if necessary, be made to take lumps of 2-in. size, but they work much more efficiently if their feed is ½ in. or less. Before the advent of the Symons cone crusher ...
##### impactor impactor crusher with input and output size
The largest size of mixedcrusher plants south africa. punker for crucher. 20tph crushing plant. impactor crusher with input and output size. the purpose of pinchroll in steelrolling mill. Read more how to measure the output of jaw crusher theoratical - Zenith ..output size of stone crusher
##### KEY PERFORMANCE INDICATORS - Plant Maintenance
failures. The output of a healthy reliability process is optimal asset reliability at optimal cost. Asset Reliability Process measures are leading indicators. They monitor if the tasks are being performed that will ‘lead to results’. For example a leading process indicator would monitor if the planning function was taking place. If people are
##### Machine efficiency and man power utilization on
4 Measuring machine efficiency When it comes to manufacturing process, machineries is a very common word in industry especially for higher rate of production output. Since the investment in machineries is high, industries try to maximize their usage in the shortest time possible. Even the management in industries around the world
##### Measuring the rate of photosynthesis
There are a few key methods to calculate the rate of photosynthesis. These include: 1) Measuring the uptake of CO 2. 2) Measuring the production of O 2. 3) Measuring the production of carbohydrates. 4) Measuring the increase in dry mass. As the equation for respiration is almost the reverse of the one for photosynthesis, you will need to think ...
##### HD How to measure correctly ground rod resistance. - YouTube
Nov 08, 2015 การวัดค่ากราวด์หรือวัดค่าความต้านทานดินของแท่งกราวด์ที่ถูกต้อง ...
##### how to measure crushing stroke in cone crusher
We are one of the largest suppliers of used crushers and used crushing equipment. ... Cone crusher, zeniths 4800, configured as a short head for fine crushing. .... Crushing chamber measures 6' diameter X 4' high sidewall, with 35" diameter ... toggle, driven by 125 HP motor, 5" closed side, crusher
##### methods of gap measurement on crusher
CSS is set and appreciation to all those who, in their various ways, have made this 3) Closed the crusher gap till the liners (mantle and Concave ring) made.how to measure a jaw crusher, how to measure jaw crusher Jaw Crusher Output Size Mm kleinecomenius 14 Feb 2016 mesin jaw to measure jaw crusher gap e 16 mar 1976 a method forChecking ...
##### Top 12 Manufacturing KPIs To Track Operational Excellence
Feb 15, 2019 Measure and track the KPI production metrics that are meaningful to your organization. Also, there are a lot of different KPIs, phrases, and abbreviations used in manufacturing so for an additional resource, check out the manufacturing terms and acronyms guide .
##### Jaw Crusher - an overview ScienceDirect Topics
The capacity of jaw crushers is a measure of the mass or volume of crushed material produced in unit time of operation. The capacity is primarily a function of: 1. crusher design characteristics such as width and depth of the crushing chamber, 2. open and closed side settings, 3.
##### Solid Level Detection Sensors and Measurements VEGA
Level measurement in the crusher. ... A reliable belt-weighing scale system and mass flow rate ensures accurate measurement and smooth operation of the plant. Measuring task. Throughput measurement. Measuring point. ... The electronics inside the detector use the gamma reading to infer a measurement and output the value.
##### Methods Of Gap Measurement On Crusher
Figure 4.2 is a sketch of a Dodge type of crusher. is a sketch of a Dodge type of crusher. how to measure methods jaw crusher gap. 2015 04 11 how to measure output of a crusher plant XuanShi can provide the proper grinding measure to all kinds of methods and how to measure crusher jaw gap .
##### how to compute input of stone batching planter plant BHS ...
how to measure stone crusher production. cost of 50m3/h belt conveyor concrete batching plant in Belarus», how to measure crushing stroke in cone crusher The cone crusher may be equipped with either an air/oil cooler or a water cooler to help dissipate heat from the. how to measure stone crusher production. stone crushing production line, Stone production line,Stone crushing plant,Rock ...
##### KEY PERFORMANCE INDICATORS - Plant Maintenance
failures. The output of a healthy reliability process is optimal asset reliability at optimal cost. Asset Reliability Process measures are leading indicators. They monitor if the tasks are being performed that will ‘lead to results’. For example a leading process indicator would monitor if the planning function was taking place. If people are
##### factors affecting the output of crushing plant
The factors that affect the quality of crusher output the larger the ratio is the larger the crushing ratio is and vice crushing ratio of large needle sheet content increases and this rule is not only applicable to jaw crusher but also applicable to cone crusher it has nothing to do with crusher type but if the.
##### How To Determine The Capacity Of A Crusher Crusher- Mining ...
Brief Introduction of Mining Machinery. We are a professional mining machinery manufacturer, the main equipment including: jaw crusher, cone crusher and other sandstone equipment;Ball mill, flotation machine, concentrator and other beneficiation equipment; Powder Grinding Plant, rotary dryer, briquette machine, mining, metallurgy and other related equipment.If you are interested in our ...
##### Guide to Calculating Improving Overall Equipment ...
Dec 01, 2020 Measuring the output always matters. The manufacturing industry involves a lot of different processes and this makes it complex to track and improve efficiency. This is possible, when you can find out the process flaws, machine malfunctions and employee efficiency with accurate data.
##### MR 110i EVO2 Mobile impact crushers Kleemann
1. Sensors measure the load at the rocker and rotor as well as engine utilization 2. Vibrating feeder and prescreen are controlled according to the load 3. When the crushing chamber is free again after overloading, material transport is continued without a delay; The plant can be run again at full output
##### Mineral Processing - an overview ScienceDirect Topics
Mineral processing, mineral beneficiation, or upgradation involves handling three primary types of ROM material, which have been blasted, fragmented, and brought out from an in situ position. These materials can be used directly or by simple or complex processing and even by applying extractive metallurgy like hydrometallurgical or pyrometallurgical methods.
##### How to Calculate Workplace Productivity Smartsheet
Feb 15, 2019 You can measure employee productivity with the labor productivity equation: total output / total input. Let’s say your company generated \$80,000 worth of goods or services (output) utilizing 1,500 labor hours (input). To calculate your company’s labor productivity, you would divide 80,000 by 1,500, which equals 53.
##### Measuring Output Using GDP Boundless Economics
Measuring Output Using GDP. Defining GDP. ... This avoids double-counting: if one buys shares in a company, and the company uses the money received to buy plant, equipment, etc., the amount will be counted toward GDP when the company spends the money on those things. To count it when one gives it to the company would be to count two times an ...
##### R Crusher Wear Parts Reference Guide
crusher tools E.G. Jaw liners are subject to numerous pressure and impact stresses. Several other factors affect the wear lifetime of crusher wear parts as listed in below Diagram . Wear occurs in all crushers , however wear costs can be controlled by selecting the correct crusher type for the abrasive content of the material to be crushed. | 2,448 | 11,777 | {"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-2022-33 | latest | en | 0.895212 |
https://quizizz.com/en/graphs-and-functions-worksheets | 1,714,023,674,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712297284704.94/warc/CC-MAIN-20240425032156-20240425062156-00555.warc.gz | 411,687,499 | 27,836 | Interpreting Graphs of Functions
20 Q
6th - 11th
Evaluate Functions & Graphs
20 Q
KG - 12th
Analyzing Graphs of Rational Functions
18 Q
10th - 12th
Graphs of Trig Functions
20 Q
11th - 12th
16 Q
9th - 11th
Functions - Names, Graphs, Equations
20 Q
11th - 12th
Math 3_Inverse of Functions
12 Q
11th
Inverse Functions - with graphs
21 Q
9th - 12th
Graphs of Cubic Functions
7 Q
9th - 12th
13 Q
9th - 12th
Graphs of Trig Functions
10 Q
10th - 12th
Graphs of Rational functions
23 Q
11th - 12th
Graphs of Functions II
12 Q
10th - 11th
Functions and Inverses
20 Q
9th - 12th
Quiz #2- Inverses & Lines
14 Q
9th - 11th
CHARACTERISTICS OF POLYNOMIAL GRAPHS/FUNCTIONS CHECK & EXIT
10 Q
9th - 11th
Practice: Exponential Function Graphs
18 Q
9th - 12th
Graphs of Logarithmic Functions
10 Q
11th - 12th
Graphs of Rational Functions
20 Q
11th - 12th
Identifying Exponential Functions and Graphs
10 Q
9th - 12th
Parent Function Trig Graphs
14 Q
10th - 12th
Ratios & Graphs of Trigonometric Functions
10 Q
12th
Graphs of Trigonometric Functions
20 Q
11th
## Explore printable Graphs & Functions worksheets
Graphs & Functions worksheets are essential tools for teachers to help their students develop a strong foundation in math. These worksheets provide a variety of exercises and problems that cover different aspects of graphs and functions, such as plotting points, understanding the relationship between variables, and solving equations. Teachers can use these worksheets to create engaging and interactive lessons that cater to the diverse learning needs of their students. By incorporating Graphs & Functions worksheets into their curriculum, teachers can ensure that their students gain a thorough understanding of these crucial math concepts, ultimately setting them up for success in higher-level math courses.
Quizizz is a fantastic platform for teachers to access a wide range of educational resources, including Graphs & Functions worksheets. This platform offers an extensive library of quizzes, games, and other interactive materials that can be easily integrated into lesson plans. Teachers can utilize Quizizz to create customized assessments for their students, track progress, and provide instant feedback. In addition to Graphs & Functions worksheets, Quizizz offers resources for various other math topics, ensuring that teachers have access to comprehensive materials for all grade levels. By incorporating Quizizz into their teaching strategies, educators can create a dynamic and engaging learning environment that promotes the development of essential math skills. | 641 | 2,642 | {"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} | 3.515625 | 4 | CC-MAIN-2024-18 | latest | en | 0.915922 |
https://oeis.org/A089223 | 1,623,754,826,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487620971.25/warc/CC-MAIN-20210615084235-20210615114235-00346.warc.gz | 393,763,814 | 3,729 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089223 a(n) = floor(Product_{i=1..n} log(prime(i+1))/log(i+1)). 0
1, 2, 3, 4, 6, 10, 14, 20, 29, 42, 62, 90, 128, 182, 261, 376, 535, 764, 1087, 1532, 2166, 3052, 4311, 6128, 8680, 12207, 17118, 23849, 33148, 46761, 65779, 92558, 129518, 182289, 255222, 357379, 500442, 699118, 976654, 1364261, 1897468, 2649692 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 LINKS MATHEMATICA f[n_]=Log[Prime[n+1]]/Log[n+1] g[n_]=Product[f[i], {i, 1, n}] digits=100 a=Table[Floor[g[n]], {n, 1, digits}] CROSSREFS Sequence in context: A200928 A318558 A256248 * A240057 A279467 A094861 Adjacent sequences: A089220 A089221 A089222 * A089224 A089225 A089226 KEYWORD nonn AUTHOR Roger L. Bagula, Dec 10 2003 EXTENSIONS Edited by N. J. A. Sloane, Nov 26 2015 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.) | 479 | 1,295 | {"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} | 2.796875 | 3 | CC-MAIN-2021-25 | latest | en | 0.583773 |
https://www.homemodelenginemachinist.com/members/alcostich.65/recent-content | 1,669,662,468,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710534.53/warc/CC-MAIN-20221128171516-20221128201516-00868.warc.gz | 854,960,508 | 15,036 | # Recent content by alcostich
1. ### Hi from Rochester,New York
Keith, I'm in Rochester near East High. My only machining experience has been self taught. I have a round ram Bridgeport, a South Bend 9A and an Atlas 7B shaper. I have built a Quorn tool and cutter grinder and a precision drill press from castings. I've also taught myself how to re-bush SU...
2. ### Single Depth of Thread for 26 TPI
The formula I used, and can't now remember where I got it from is: 1/26 is .0384 .0384 x .866 is .033 However, .025 worked just right. Alan
3. ### Single Depth of Thread for 26 TPI
After two unsuccessful attempts, finally got one to work. Seems either I didn't understand the dimensions on the drawing or those dimensions were wrong. I bored the nut to .0609 which is what my SB collet draw-in tube is. Then, although the formula for single depth of thread calls out .033 I...
4. ### Single Depth of Thread for 26 TPI
Well, I don't have a 5/8 x 26 tap. And, yes, I can set the lathe to cut a 26 TPI. It was also suggested to use something more common. But, then I would have to dump a drawer full of 3C collets.
5. ### Single Depth of Thread for 26 TPI
This looks to be for a Whitworth thread. I'm looking for a 60 thread for a 3C collet for a South Bend lathe.
6. ### Single Depth of Thread for 26 TPI
I attempting to make a draw in nut for a 3C collet. The thread wants to be 26 TPI. Nowhere can I find the single depth of thread for that. This will be an internal thread. The dimensions on the plan I'm working from call out a minimum Dia of .520 and a max of .635. Based on the calculation: 1/26...
7. ### Knurls
This may be a looong shot: I'm trying to source a couple pairs of knurls that would fit Homecraft 2040 or 0-KH tool: 8221 coarse diamond 8261 coarse straight I wonder if Homecraft was an off shoot of Williams.... SB lists these: CE3152 coarse diamond CE3155 coarse straight All these knurls...
8. ### Allis-Chalmers lathe
Kelly, Do I detect an MG TC in the background? Alan
9. ### greenfield releasing acorn die holders
I've acquired a handful of acorn dies. Unfortunately I don't have releasing holder for them. Nor do I know very much about them. I assume the holders come in various sizes for different acorns. Could anyone offer some lessons on how to determine what size holders work with size dies and...
10. ### Line Boring on a US-Type Lathe
Has anyone added t-slots to their cross slide? What do you need to watch out for when adding the t-slots? Does adding t-slots affect the rigidity of the cross slide? I machined the S-4382 T-Slotted Cross Slide for the SB 9A from Metal Lathe Accessories many years ago. It replaces the cross...
11. ### PM Research Machine kits
Has anyone built any of PM Research's machine kits? Lathe, horizontal mill or shaper? I have all three and I'm looking for pointers.... Alan
12. ### VW or Porsche Boxer Engine Plans?
I, too, would be interested is the Brian Perkins VW boxer engine design. Thanks. Alan
13. ### What is the best paint for an old machine restoration.
Years ago I brushed porch and deck enamel on by Bridgeport Round-ram. Prior to that, even more years ago I brushed the same on my SouthBend lathe and Atlas 7B shaper. All have held up well to years of abuse.
14. ### Help with Atlas 7B Shaper
Hopsteiner, post: 318392, Thanks. I do have that picture. >>>>It's possible the set screw on one of these gears is loose. There appears to be only one set screw. And do get at it would require some serious disassembling. Something is binding someplace in there. Alan
15. ### Help with Atlas 7B Shaper
Because my mill was tied up with another project, I decided to use my shaper to make a nut for a quick change tool post. Encountered a problem I could use some help or advise with. I can adjust the length of stoke but I can't set the position of the ram. In order to turn the adjusting screw... | 1,002 | 3,879 | {"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} | 2.546875 | 3 | CC-MAIN-2022-49 | latest | en | 0.931099 |
https://peeterjoot.wordpress.com/2013/03/05/phy452h1s-basic-statistical-mechanics-lecture-13-interacting-spin-taught-by-prof-arun-paramekanti/ | 1,521,496,997,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647153.50/warc/CC-MAIN-20180319214457-20180319234457-00468.warc.gz | 676,310,608 | 23,961 | # Peeter Joot's (OLD) Blog.
• ## Archives
Adam C Scott on avoiding gdb signal noise… Ken on Scotiabank iTrade RESP …… Alan Ball on Oops. Fixing a drill hole in P… Peeter Joot's B… on Stokes theorem in Geometric… Exploring Stokes The… on Stokes theorem in Geometric…
• 317,363
## PHY452H1S Basic Statistical Mechanics. Lecture 13: Interacting spin. Taught by Prof. Arun Paramekanti
Posted by peeterjoot on March 5, 2013
[Click here for a PDF of this post with nicer formatting (especially if my latex to wordpress script has left FORMULA DOES NOT PARSE errors.)]
# Disclaimer
Peeter’s lecture notes from class. May not be entirely coherent.
# Interacting spin
For these notes
\begin{aligned}\boxed{\hbar = k_{\mathrm{B}} = 1}\end{aligned}
This lecture requires concepts from phy456 [1].
We’ll look at pairs of spins as a toy model of interacting spins as depicted in fig. 1.1.
Fig 1.1: Pairs of interacting spins
Example:
Simple atomic system, with the nucleus and the electron can interact with each other (hyper-fine interaction).
Consider two interacting spin $1/2$ operators $\mathbf{S}$ each with components $\hat{S}^x$, $\hat{S}^y$, $\hat{S}^z$
\begin{aligned}H = J \mathbf{S}_1 \cdot \mathbf{S}_2 - B (\hat{S}_1^z + \hat{S}_2^z)\end{aligned} \hspace{\stretch{1}}(1.2.1)
\begin{aligned}\hat{S}_1^z + \hat{S}_2^z \propto \mbox{magnetization along z}\end{aligned} \hspace{\stretch{1}}(1.2.2)
We rewrite the dot product term of the Hamiltonian in terms of just the squares of the spin operators
\begin{aligned}H = J \frac{(\mathbf{S}_1 + \mathbf{S}_2)^2 - \mathbf{S}_1^2 - \mathbf{S}_2^2}{2}- B (\hat{S}_1^z + \hat{S}_2^z)\end{aligned} \hspace{\stretch{1}}(1.2.3)
The squares $\mathbf{S}_1^2$, $\mathbf{S}_2^2$, $(\mathbf{S}_1 + \mathbf{S}_2)^2$ can be thought of as “length”s of the respective angular momentum vectors.
We write
\begin{aligned}\mathbf{S} = \mathbf{S}_1 + \mathbf{S}_2,\end{aligned} \hspace{\stretch{1}}(1.2.4)
for the total angular momentum. We recall that we have
\begin{aligned}\hat{S}^z_2 = \hat{S}^z_1 = S(S + 1),\end{aligned} \hspace{\stretch{1}}(1.2.5)
where $S = 1/2$, and $\mathbf{S} = \mathbf{S}_1 + \mathbf{S}_2$ implies that $S_{\mathrm{total}} \in \{0, 2\}$.
$S_{\mathrm{total}} = 0$ (singlet).
$S_{\mathrm{total}} = 1$. Triplet: $(-1, 0, +1)$.
$S_{\mathrm{total}} = 0$ state.
For $m = 0$
\begin{aligned}\frac{1}{{\sqrt{2}}} \left( \uparrow \downarrow - \downarrow \uparrow \right)\end{aligned} \hspace{\stretch{1}}(1.2.6)
energies
\begin{aligned}J \frac{-3/4 -3/4}{2} = -\frac{3}{4} J\end{aligned} \hspace{\stretch{1}}(1.2.7)
For $m = 1$
\begin{aligned}\frac{1}{{\sqrt{2}}} \left( \uparrow \uparrow \right)\end{aligned} \hspace{\stretch{1}}(1.2.8)
energies
\begin{aligned}J \left( 1 - \frac{3}{4} \right) - B \rightarrow \frac{J}{4} - B\end{aligned} \hspace{\stretch{1}}(1.2.9)
$S_{\mathrm{total}} = 1$ state
For $m = 0$
\begin{aligned}\frac{1}{{\sqrt{2}}} \left( \uparrow \downarrow + \downarrow \uparrow \right)\end{aligned} \hspace{\stretch{1}}(1.2.10)
energies
\begin{aligned}\frac{J}{4} \end{aligned} \hspace{\stretch{1}}(1.2.11)
For $m = 1$
\begin{aligned}\frac{1}{{\sqrt{2}}} \left( \downarrow \downarrow \right)\end{aligned} \hspace{\stretch{1}}(1.2.12)
energies
\begin{aligned}\frac{J}{4} + B.\end{aligned} \hspace{\stretch{1}}(1.2.13)
These are illustrated schematically in fig. 1.2.
Fig 1.2: Energy levels for two interacting spins as a function of magnetic field
Our single pair partition function is
\begin{aligned}Z_1 = e^{ +\beta 3 J/4}+e^{ -\beta (J/4 - B)}e^{ -\beta 3 J/4}+e^{ -\beta (J/4 + B)}\end{aligned} \hspace{\stretch{1}}(1.2.14)
So for $N$ pairs our partition function is
\begin{aligned}Z = Z_1^N = \left( e^{ +\beta 3 J/4} +e^{ -\beta (J/4 - B)} e^{ -\beta 3 J/4} +e^{ -\beta (J/4 + B)} \right)^N.\end{aligned} \hspace{\stretch{1}}(1.2.15)
Our free energy
\begin{aligned}F = - T \ln Z = - T N \ln Z_1.\end{aligned} \hspace{\stretch{1}}(1.2.16)
\begin{aligned}-\frac{\partial {F}}{\partial {\beta}} = T N \frac{\partial {}}{\partial {\beta}} \ln Z_1.\end{aligned} \hspace{\stretch{1}}(1.2.17)
Our magnetization $\mu$ is
\begin{aligned}\mu = \frac{T N}{Z_1} \left( \beta e^{-\beta(J/4 - B)} -\beta e^{-\beta(J/4 + B)} \right)\end{aligned} \hspace{\stretch{1}}(1.2.18)
The moment per particle, after $T \beta$ cancellation, is
\begin{aligned}m = \frac{\mu}{N} = \frac{1}{Z_1} \left( e^{-\beta(J/4 - B)} -e^{-\beta(J/4 + B)} \right)=2 \frac{e^{-\beta J/4}}{Z_1} \sinh\left( \frac{B}{T} \right).\end{aligned} \hspace{\stretch{1}}(1.2.19)
Low temperatures, small $B$ ($T \ll J, B \ll J$)
The $e^{3 \beta J/4}$ term will dominate.
\begin{aligned}Z_1 \approx e^{3 J \beta/4}\end{aligned} \hspace{\stretch{1}}(1.2.20)
\begin{aligned}m \approx 2 e^{-\beta J} \sinh\left( \frac{B}{T} \right).\end{aligned} \hspace{\stretch{1}}(1.2.21)
Fig 1.3: magnetic moment
The specific heat has a similar behavior
\begin{aligned}C_V \sim e^{-\beta J}.\end{aligned} \hspace{\stretch{1}}(1.2.22)
Considering a single spin $1/2$ system, we have energies as illustrated in fig. 1.4.
Fig 1.4: Single particle spin energies as a function of magnetic field
At zero temperatures we have a finite non-zero magnetization as illustrated in fig. 1.5, but as we heat the system up, the state of the system will randomly switch between the 1, and 2 states. The partition function democratically averages over all such possible states.
Fig 1.6: Single spin magnetization
Once the system heats up, the spins are democratically populated within the entire set of possible states.
We contrast this to this interacting spins problem which has a magnetization of the form fig. 1.6.
Fig 1.6: Interacting spin magnetization
For the single particle specific heat we have specific heat of the form fig. 1.7.
Fig 1.7: Single particle specific heat
We’ll see the same kind of specific heat distribution with temperature for the interacting spins problem, but the peak will be found at an energy that’s given by the difference in energies of the two states as illustrated in fig. 1.8.
\begin{aligned}\Delta E = \frac{J}{4} - \frac{-3J}{4} = J\end{aligned} \hspace{\stretch{1}}(1.2.23)
# References
[1] Peeter Joot. Quantum Mechanics II., chapter: Two spin systems, angular momentum, and Clebsch-Gordon convention. URL http://sites.google.com/site/peeterjoot2/math2011/phy456.pdf. | 2,274 | 6,368 | {"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": 51, "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-2018-13 | latest | en | 0.698208 |
https://forum.freecodecamp.org/t/return-largest-numbers-in-arrays-code-isnt-working/295798 | 1,611,587,331,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703581888.64/warc/CC-MAIN-20210125123120-20210125153120-00610.warc.gz | 344,523,210 | 6,593 | # Return Largest Numbers in Arrays- code isn't working
Tell us what’s happening:
I know this code isn’t very efficient, but I just can’t figure out why isn’t it working.
Your code so far
``````
function largestOfFour(arr) {
// You can do this!
var big1=0,big2=0,big3=0,big4=0;
for (var i = 0; i<arr.length; i++) {
switch(i) {
case 0:
for (var j =0; j<arr[i].length;j++) {
if(j=0) {
if(arr[i][j] > big1) {
big1 = arr[i][j];
}
}
else if (arr[i][j]> arr[i][j-1]) {
if(arr[i][j]> big1) {
big1 = arr[i][j];
}
}
}
break;
case 1:
for (var j =0; j<arr[i].length;j++) {
if(j=0) {
if(arr[i][j] > big2) {
big2 = arr[i][j];
}
}
else if (arr[i][j]> arr[i][j-1]) {
if(arr[i][j]> big2) {
big2 = arr[i][j];
}
}
}
break;
case 2:
for (var j =0; j<arr[i].length;j++) {
if(j=0) {
if(arr[i][j] > big3) {
big3 = arr[i][j];
}
}
else if (arr[i][j]> arr[i][j-1]) {
if(arr[i][j]> big3) {
big3 = arr[i][j];
}
}else {
big3 += 0
}
}
break;
case 3:
for (var j =0; j<arr[i].length;j++) {
if(j=0) {
if(arr[i][j] > big4) {
big4 = arr[i][j];
}
}
else if (arr[i][j]> arr[i][j-1]) {
if(arr[i][j]> big4) {
big4 = arr[i][j];
}
}
}
break;
}
}
console.log(big3);
var biggest=0;
let bigArr=[big1, big2, big3, big4];
console.log(bigArr);
for (var g =0; g<bigArr.length;g++) {
if(g=0) {
if(bigArr[g]> biggest) {
biggest = bigArr[g];
}
}
else if (bigArr[g]> bigArr[g-1]) {
if(bigArr[g]> biggest) {
biggest = bigArr[g];
}
}
}
console.log(biggest);
return arr[biggest.split("")[3]];
}
console.log(largestOfFour([[13, 27, 18, 26], [4, 5, 1, 3], [32, 35, 37, 39], [1000, 1001, 857, 1]]));
``````
User Agent is: `Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/75.0.3770.100 Safari/537.36`.
what do the failing tests say?
// running tests
biggest.split is not a function
biggest.split is not a function
biggest.split is not a function
biggest.split is not a function
// tests completed
So, `split()` is a string method, but it seems you are using it on a number, you can’t do that as there is no number method called `split()`
Okay thanks for that. But what about the sorting I have done above. When I console.log them I can see they aren’t working either.
You’re using the assignment operator `=` in your conditional expressions instead of the equality operators `==` or `===`.
As in:
``````
if(j=0) {
if(arr[i][j] > big1) {
big1 = arr[i][j];
}
``````
It should be `if (j == 0)` or `if (j === 0)`.
That’s the first problem I found, though as @ieahleen pointed out, using the String.split() method on a numeric value is also an issue.
How did I miss that!
Thank you very much!
1 Like
@pratikjaiswal1998
No problem, glad to be able to help
do you have a question about your code?
otherwise, please don’t post full working solutions. and if you have a question on a full working solution, please surround it with `[spoiler]` tags
1 Like
I don’t have questions, only answers.
It is great that you solved the challenge, but instead of posting your full working solution, it is best to stay focused on answering the original poster’s question(s) and help guide them with hints and suggestions to solve their own issues with the challenge.
If you want to compare your solution to others, use the Get a hint button on the challenge and there are alternative solutions you can compare yours to. Also, you can probably search older posts using the forum search feature or google the challenge name and find more there.
We are trying to cut back on the number of spoiler solutions found on the forum and instead focus on helping other campers with their questions and definitely not posting full working solutions.
Thank you for understanding.
1 Like | 1,145 | 3,666 | {"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-2021-04 | latest | en | 0.513627 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.