url
stringlengths 14
5.47k
| tag
stringclasses 1
value | text
stringlengths 60
624k
| file_path
stringlengths 110
155
| dump
stringclasses 96
values | file_size_in_byte
int64 60
631k
| line_count
int64 1
6.84k
|
|---|---|---|---|---|---|---|
https://som.utmb.edu/physician-assistant/program-costs
|
math
|
Physician Assistant Studies Program Cost of Attendance Costs are estimates and are dependent on personal living preferences. All costs are subject to change and will increase annually. For more tuition and fees details, please refer to the UTMB Office of Enrollment Services. ExpensesYear 1Year 2CASPA Application$175$0UTMB Supplemental Application$35$0Program Deposit*$1000$0Drug Screen and Background Check$110$110Immunization and Titer **$800$0Student Health Insurance ***$3,100$3,100Tuition & Fees Link to Enrollment ServicesBooks & Equipment$3,150$1,500ACLS + BLS Certification Fee and Books$250$0Laptop$1,500$0Lab Coats$90$0Scrubs$100$0Housing & Food$15,000$15,000Transportation$1,200$3,000Parking$80$165Software (Typhon, ECG Academy, etc.)$600$600Course Fees$1000$1400PANCE Board Review Course$0$750PANCE Registration Fee$0$500Texas Medical Board License Application, Temporary License, and 15-Months Registration Fee$0$675PearsonVue Administration of Jurisprudence Exam$0$65National Practitioner Data Bank Report Fee$0$5MorphoTrust Criminal History Check$0$100 Quick Links Request for Info Scholarships Tuition & Fees UTMB Catalog Policies Certificates of Insurance Academic CalendarDownload the PAS 2020-21 calendar in PDF format. Download the PAS 2021-22 calendar in PDF format.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323584886.5/warc/CC-MAIN-20211016135542-20211016165542-00499.warc.gz
|
CC-MAIN-2021-43
| 1,288 | 1 |
http://www.tigerdroppings.com/rant/more-sports/how-many-footballs-are-used-and-in-circulation-during-a-football-game-in-the-nfl/38984659/
|
math
|
I would love to know how many baseballs are used during an entire MLB season
According to NBC's "Ask Liz" column, MLB says an average of 65 balls are used per game. There are 30 teams playing each other in 162 games each. So there are (15 x 162 = 2,430) games per season, (you have to divide the total number of teams by two, since each game has two teams in it). That equals: (2,430 x 65) baseballs used per season, which totals 157,950 baseballs used during games per regular season.
Update, Dec. 2011:
On p 192 of the paperback edition of his book, "The Baseball: Stunts, Scandals, and Secrets Beneath the Stitches," Zack Hample estimates the answer to this question. Editing out his addition of spring training and post-season games, his answer to the original question would be:
This is 25% higher than my estimate above, and is based on the number of baseballs each team rubs down with Lena Blackburne Rubbing Mud. Note that it represents the number of balls prepared for use, not used in actual games. I'm guessing that prepping 25% more than needed would be overkill, but assuming his number is right, if we split the difference the number would be about 177,375 baseballs per season.
Finally, he says that MLB uses a TOTAL (including batting practice, etc.) of about 1.26 million baseballs per year. At his estimate of $6.79 per ball, that's $8.56 million per year for baseballs (Rawlings says "Thank you").
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121665.69/warc/CC-MAIN-20170423031201-00373-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 1,416 | 6 |
https://www.smashwords.com/books/view/520438
|
math
|
Extended zeta functions make it possible to prove or dis-prove Riemann's Hypothesis More
While extended zeta functions support investigations of Riemann's hypothesis and estimates for the Prime Number Theorem, some zeta functions offer better prospects for providing easy proofs, or disproofs. In 1859, Riemann had the idea to define Euler’s function ε(x)=∑m^x for all complex numbers s=x+iy by analytic extension. This extension is important in number theory and plays a central role in the distribution of prime numbers. There are a number of ways of extending Euler's zeta function ζ(s) to points where 0≤x≤1. Because ζ(s) is an alternating series, it becomes possible to prove or disprove Riemann's Hypothesis.
Available ebook formats:
Classical analysis and number theory covering Fermat's Last Theorem (FLT), Beal's conjecture, Wile's proof of FLT, prime numbers, Goldbach's conjecture, Navier-Stokes equations,infinite series, Riemann's hypothesis, Pythagorean theorm, abc conjecture, irrational numbers, and more
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540533401.22/warc/CC-MAIN-20191211212657-20191212000657-00131.warc.gz
|
CC-MAIN-2019-51
| 1,031 | 4 |
http://www.ques10.com/p/20220/satellite-communication-networks-question-paper--1/
|
math
|
Satellite Communication & networks - May 2014
Electronics & Telecomm. (Semester 8)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Explain the significance of microwave frequencies in satellite communication(5 marks) 1 (b) State and explain Kepler's Laws(5 marks) 1 (c) What are advantages of satellite communication over terrestrial communication.(5 marks) 1 (d) What is transponder ? Explain single conversion transponder(5 marks) 1 (e) What is meant by polarization of Satellite signals. Explain ionospheric and rain depolarization.(5 marks) 2 (a) What is telemetry tracking and command subsystem ? Explain its functioning with block diagram.(10 marks) 2 (b) Draw block diagram of transmit-receive type earth station. Explain each block in brief.(10 marks) 3 (a) Explain spin stabilization and 3-axis stabilization methods. Mention their merits and demerits.(10 marks) 3 (b) What do you mean by system noise temperature ? How does it affect C/N and GT ration(10 marks) 4 (a) What do you understand by reliability and space qualification ? Explain significance of bath-tub curve.(10 marks) 4 (b) Explain different types of antenna used in satellite communication.(10 marks) 5 (a) A Geostationary satellite is located 35° ?W. What are its look angles and range from (i) Brad ford UK station (54°N, 2°W) (ii) Blacksburg USA (37°N. 80°W).(10 marks) 5 (b) What are different methods of launching of satellite ? Explain.(10 marks) 6 (a) Explain SPADE system of FDMA(10 marks) 6 (b) Explain with neat block diagram the FH-CDMA and DS-CDMA systems. Also list advantages ofCDMA system.(10 marks)
Write short note on (any two)
7 (a) Orbital Parameters(10 marks) 7 (b) VSAT(10 marks) 7 (c) Combined uplink and downlink C/N ratio.(10 marks)
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578681624.79/warc/CC-MAIN-20190425034241-20190425060241-00499.warc.gz
|
CC-MAIN-2019-18
| 1,893 | 9 |
https://www.news.lk/news/sri-lanka/item/213-maximum-deposit-interest-rates-payable-by-finance-companies-revised
|
math
|
a. The maximum interest rate that could be offered for savings deposits accepted or maintained shall be 7.58% per annum.
b. The maximum interest rates that could be offered for deposits accepted or renewed shall be as follows,
i For maturity period of one year or less - 11.01% per annum.
ii For maturity period of over one year and up to three years - 12.01% per annum.
iii For maturity period of over three years - 13.51% per annum.
In case where a savings or fixed deposit is made by a person who is over fifty five (55) years of age, a finance company may pay an additional interest rate of one per cent above the maximum interest rates as specified in (a) and (b) above, the Bank further states.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267164925.98/warc/CC-MAIN-20180926121205-20180926141605-00347.warc.gz
|
CC-MAIN-2018-39
| 700 | 6 |
https://www.lottery.co.uk/pick-3/number-generator
|
math
|
Pick 3 Number Generator
To play Pick 3 you just need three numbers from 0 to 9, and this Number Generator can help you come up with a combination to play. All you need to do is select the 3-Way or 6-Way button on each line you wish to play and you will be given a random combination of three numbers. You can repeat this as many times as you wish.
If you select the 3-way option your bet will contain two identical numbers, while the 6-way option will give you three different ones. After you have generated your numbers you can edit them by typing over them. If you go on to play a Pair bet two of the three numbers you generate will be used.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474690.22/warc/CC-MAIN-20240228012542-20240228042542-00040.warc.gz
|
CC-MAIN-2024-10
| 643 | 3 |
https://www.cheric.org/research/tech/periodicals/view.php?seq=306099
|
math
|
Chemical Engineering Research & Design, Vol.77, No.5, 429-441, 1999
A numerical simulation of hydrocyclones
A numerical method is presented for the calculation of the three-dimensional flow and separation efficiency for particles with low concentrations in a hydrocyclone. Multi-block curvilinear grids in the frame of a cylindrical coordnate system are used to represent accurately the hydrocyclone geometry. Turbulence is represented by a modified k - epsilon model which adds a curvature correction term with a single empirical constant in the dissipation equation. Both three- and two-dimensional axisymmetric computations are carried out and are compared with experimental data. It is shown that the standard k - epsilon model can produce large errors which result in incorrect predictions of the flow patterns. The three-dimensional calculations using the modified k - epsilon model produce results in good agreement with experimental data. The two-dimensional axisymmetric calculations can predict approximate flow patterns, but are inadequate to predict the separation efficiency of hydrocyclones. To analyse the separation efficiency, a three-dimensional model, as developed in the present study, is required.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00736.warc.gz
|
CC-MAIN-2023-50
| 1,218 | 3 |
http://annualreport2015.gkn.com/index-143.html
|
math
|
Trade and other payables
Current m Non-current m Current m Non-current m
Amounts owed to suppliers and customers Amounts owed to equity accounted investments Accrued interest Government refundable advances Deferred and contingent consideration Payroll taxes, indirect taxes and audit fees Amounts due to employees and employee bene t plans Government grants Customer advances and deferred income
) ) ) ( ) – ( ) ( ) ( ) ( ) ( ( )
) ( ) ( ) ( ) ( ) ( ) ( )
) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ) (
) – – ( ) ( ) ( ) ( ) ( ) ( ) )
( , Government refundable advances are forecast to fall due for repayment between 2016 and 2055.
Non-current deferred and contingent consideration falls due as follows: one to two years £2 million (2014: nil), two to ve years nil (2014: £1 million) and over ve years nil (2014: £2 million). Non-current amounts owed to suppliers and customers fall due within two years. Contingent consideration of £2 million (2014: £6 million) will be paid based on achievement of speci c technology milestones in Sheets Manufacturing Inc. (SMI), see note 30 for further details. During 2015, a further £6 million was paid in cash relating to the Filton acquisition during 2009, in addition to the rst milestone payment of £1 million for SMI. Included within amounts owed to suppliers and customers is £61 million (2014: £33 million) payable to banks in respect of supply chain nance arrangements. Customer advances and deferred income comprises cash receipts from customers in advance of the Group completing its performance obligations. Non-current amounts in respect of customer advances and deferred income fall due as follows: one to two years £44 million (2014: £17 million), two to ve years £108 million (2014: £21 million) and over ve years £89 million (2014: £46 million). The signi cant increase during the year has principally arisen following a speci c aerospace customer advanced payment in respect of development costs.
GKN plc Annual Report and Accounts
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822668.19/warc/CC-MAIN-20171018013719-20171018033719-00106.warc.gz
|
CC-MAIN-2017-43
| 1,999 | 10 |
http://poncelet.math.nthu.edu.tw/disk3/cal02/html/shell/shell.html
|
math
|
In addition to the slicing methods, there is another way to calculate the volume of a solid of revolution. While the slicing method is based on the idea of approximating cross sections taken perpendicular to the axis of rotation, the method of cylindrical shells uses approximating hollow cylinders centered about the axis of rotation.
To describe this method, we let be the region bounded by the graph of a continuous nonnegative function and the -axis for . If the region is rotated about the -axis, a solid is generated.
To calculate the volume
we partition the interval
using the equal-length partition
where Then we choose the numbers to be the midpoints of the subintervals. That is, Using these choices, we approximate the region by rectangles with base and height . If we rotate one of these rectangles about the -axis, we obtain a cylindrical shell. Combining all such shells, we obtain a solid whose volume approximates the volume of
Consider the jth shell. Its height is
and the area of its base is
Consequently, its volume
Thus, by summing the volumes of all of the shells, we approximate the volume by
To see that the right-hand side of this approximation is a Riemann sum, we factor
and rewrite the approximation as
Since we have
and taking the limit as these Riemann sums approach
Assuming that these sums also limit to we obtain the following volume formula for
If the region
bounded by the graph of the continuous nonnegative function
, is rotated about the
of the resulting solid is
The region bounded by the graph of and the -axis is rotated about the -axis. Find the volume of the resulting solid.
the region lies between the lines
can be generalized to regions bounded below by curves other than the -axis, as the following example shows.
The region is bounded by the graphs of and . Find the volume of the solid generated by revolving about the -axis.
To find the points of intersection, we set
and obtain the equation
so or When the interval is partitioned, the approximating rectangles are bounded above by and below by Since the factor represents the height of the approximating rectangles, we modify equation to the following:
REMARK We may state the generalization of equation
observed in Example 2 as follows: If the region bounded above by the graph of and below by the graph of for is rotated about the -axis, the volume of the resulting solid is
Find the volume of the solid obtained by revolving about the line the region bounded by the graphs of and
Solution The region
that is bounded above by the graph of
and below by the graph of
To find the points of intersection of these two graphs we set
which gives the equation
The points of intersection are therefore and
A vertical line segment through this region generates a circular band of
Since the axis of rotation is the vertical line the radius of this circular band is We must therefore replace the factor in the integrand in formula
by the factor The volume is therefore
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887077.23/warc/CC-MAIN-20180118071706-20180118091706-00136.warc.gz
|
CC-MAIN-2018-05
| 2,958 | 38 |
https://www.jiskha.com/display.cgi?id=1203444968
|
math
|
posted by Teya .
The force shown in Figure 7-17 moves an object from x = 0 to x = 75 m, where the interval between vertical dashed lines is 25 m.
(a) How much work is done by the force?
(b) How much work is done by the force if the object moves from x = 25 to x = 75 m?
(a) Assuming that the directions of the force and motion are the same, the work is the product of the forse and the distance. You don't say what the force is. We can't read your figure.
If the directions of force and motion are NOT the same, you also have to multiply by the cosine of the angle between them.
(b) This distance moved is 50 m in this case. Use the same prcedure as (a).
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886102819.58/warc/CC-MAIN-20170817013033-20170817033033-00386.warc.gz
|
CC-MAIN-2017-34
| 654 | 7 |
https://brainmass.com/math/real-analysis/taylor-polynomial-approximation-10702
|
math
|
Suppose that the function F:R->R has derivatives of all orders and that:
F"(x) - F'(x) - F(x) = 0 for all x
F(0)=1 and F'(0)=1
Find a recursive formula for the coefficients of the nth Taylor polynomial for F:R->R at x=0. Show that the Taylor expansion converges at every point.© BrainMass Inc. brainmass.com December 24, 2021, 4:50 pm ad1c9bdddf
Please see the attached doc file .
First let's assume that:
as f(0)=1 we conclude that a0=1 and as f'(0)=1 we see that a1=1. We also know that f''-f'-f=0 and if we plug the above expressions into this equation we have:
or we can unify the powers of x's in all ...
This shows how to find a recursive formula for the coefficients of the nth Taylor polynomial for a given situation.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662675072.99/warc/CC-MAIN-20220527174336-20220527204336-00652.warc.gz
|
CC-MAIN-2022-21
| 726 | 9 |
https://en.wikipedia.org/wiki/Ross_Street
|
math
|
Emeritus Professor Ross Howard Street FAA (29 September 1945, Sydney –) is an Australian mathematician specialising in category theory. He is an emeritus professor of mathematics at Macquarie University, a fellow of the Australian Mathematical Society (1995), and was elected Fellow of the Australian Academy of Science in 1989. He was awarded the Edgeworth-David Medal of the Royal Society of New South Wales in 1977, and the Australian Mathematical Society's George Szekeres Medal in 2012.
- Street, Ross Howard (1945 - ), Biographical entry, Encyclopaedia of Australian Science
- Street, Ross Howard, FAA (1945-), trove.nla.gov.au
- "Category Theory, Algebra and Geometry". perso.uclouvain.be. Retrieved 2016-04-10.
- Davydov, Alexei (2007-01-01). Categories in Algebra, Geometry and Mathematical Physics: Conference and Workshop in Honor of Ross Street's 60th Birthday, July 11-16/July 18-21, 2005, Macquarie University, Sydney, Australia, and Australian National University, Canberra, Australia. American Mathematical Society. ISBN 9780821857618.
- "Centenary Medal". It's an Honour. 1 January 2001.
For service to Australian society and science in mathematics
- Emeritus Professor Ross Howard Street, Fellow, www.science.org.au
- Personal webpage, maths.mq.edu.au
|This article about a mathematician is a stub. You can help Wikipedia by expanding it.|
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189403.13/warc/CC-MAIN-20170322212949-00379-ip-10-233-31-227.ec2.internal.warc.gz
|
CC-MAIN-2017-13
| 1,359 | 10 |
https://cafedoing.com/speed-and-velocity-worksheet-answers/
|
math
|
Speed And Velocity Worksheet Answers
Jan, unit guided notes. average speed velocity worksheets. worksheet speed and velocity problems. explain to students that they will need to refer back to their notes from the first activity in order to. the speed of the wave. answer formulas speed distance time distance speed x time time distance speed.
speed and velocity with answer key.Nov, speed and velocity worksheet answer key may although speed and velocity are often words used interchangeably in physics they are distinct concepts speed is calculated by dividing the distance traveled by time problem solving exercises.
List of Speed And Velocity Worksheet Answers
Speed and velocity practice key displaying top worksheets found for this concept.Speed and velocity answers displaying top found for this concept. some of the worksheets for this concept are speed velocity and acceleration calculations work, work velocity and acceleration, work position displacement and, speed and velocity practice work, and acceleration work, work, distance time speed practice problems, formula Answer sheet speed velocity displaying top worksheets found for this concept.
some of the worksheets for this concept are speed velocity and acceleration calculations work, and acceleration work, velocity and acceleration calculation work, angular velocity experiment work answer key, speed and velocity practice work, speed velocity and acceleration calculations work s, wave speed equation practice problems, physics acceleration speed speed Average speed mph, average velocity mph.
1. 8 Grade Ideas Physical Science Teaching Education
2. Speed Velocity Acceleration Task Cards Middle School Science High
3. Quiz Covers Speed Velocity Review Sheet Handout Physical Science Middle School Physics Lessons Chemistry Worksheets
4. Simple Problems Introduce Wave Speed Calculations Students Solve Problem Solving Worksheet Word Worksheets Text Structure
5. Speed Calculations Ideas Middle School Science Grade Physical
6. Speed Distance Time Activity Lesson Plans Physics Experiments High School
Note follow the calculation procedures for adding vectors in straight line distance units are metric unit of distance without a direction km, mm since distance is scalar, add all the magnitudes only to get the result speed distance time change in displacement ( ) change in time velocity v d t vector resultant distance.
7. Speed Velocity Acceleration Color Number
Displacement displacement can be defined as distance between the initial and final point of an object. it is a vector quantity having both magnitude and direction.Jul, determining speed velocity worksheet answers awesome speed velocity from velocity and acceleration worksheet answer key, sourcetransatlanticnews.
8. Speed Velocity Acceleration Color Number Calculating
9. Speed Velocity Acceleration Color Number Teaching Energy
10. Speed Velocity Acceleration Interactive Science Notebook Grade Fourth
11. Speed Velocity Acceleration Middle School Science Classroom
12. Speed Velocity Acceleration Notes Card Sort Interactive Science Notebook Sorting Cards
13. Speed Velocity Acceleration Physical Science Middle School Writing Linear Equations
14. Speed Velocity Acceleration Review Puzzle Activity
15. Speed Velocity Acceleration Task Cards Distance Learning Google Classroom Education Inspiration Science
16. Speed Velocity Acceleration Worksheet Answers Story
17. Projectile Motion Worksheets Word Problem Problems Calculating Work
The acceleration worksheet should contain the name of the type of graph, how many degrees of freedom the graph has, and the units to be used for the equation. students should also know the units for each step of the equation. it is always a good idea to include the terminology terms that are used in the problem.
18. Speed Velocity Acceleration Worksheet Interactive Notebooks
19. Speed Velocity Acceleration Zzes Level Physics 6 Questions Answers Practice Trivia Online
20. Speed Velocity Force Motion Physical Science
21. Speed Velocity Practice Problems Science
22. Speed Velocity Problems 2 Mo 3 School Work Physics
23. Speed Velocity Review Worksheet Acceleration Distance Time Graphs
24. Speed Velocity Worksheet Answer Key Acceleration Calculating Ans Word Problem Worksheets
25. Ultimate Rotational Kinematics Worksheet Word Problem Worksheets Math Interactive Notebook Algebra Basic Skills
26. Velocity Acceleration Notes Lab Task Cards Worksheets Logic Puzzles
27. Wave Speed Worksheet Text Structure Worksheets Physics Classroom Chemistry
28. Worksheet Created Force Motion Unit Key Concepts Elementary School Science Activities Physical Middle
This is because the cart moves in only one direction.Worksheets are velocity time graph problems describing motion with velocity time graphs name velocity time graphs work motion graphs name work for exploration compare position time motion graphs distance vs time graph work unit kinematics work position time and.
29. Worksheet Speed Math Challenge Version 1 Sped Word Problems
30. Worksheets Calculating Speed 2 Worksheet Template
32. Projectile Motion Worksheets Word Problem Problems
33. 8 Speed Velocity Acceleration Ideas
Answers are found at the end of this document. physical science motion the relationships between displacement, time, velocity and acceleration displacement, time and velocity plo.Speed, velocity, and acceleration problems use your own paper, and show all work.
show the formula used, the setup, and the answer with the correct units. is driving down street. he drives meters in seconds. assuming he does not speed up or slow down, what is his speed in meters per second.Speed, velocity and acceleration in region a, the car has constant acceleration the line has a constant positive gradient.
34. Effect Worksheets Waves Worksheet 5 Names Questions
Question Relative velocity worksheet name. a swimmer has a velocity of ms directly across a river that is flowing at ms. what is the actual velocity of the swimmer and at what angle draw vectors and theta. httpmysite.verizon.netvzeoacwvelocitycomposition.
html.Take a quick interactive quiz on the concepts in relative motion acceleration definitions examples or print the worksheet to practice offline. these practice questions will help you master.Displaying top worksheets found for relative speed. some of the worksheets for this concept are lesson relative motion, relative motion work, work one dimensional motion and relative motion, lesson physical science speed velocity acceleration, relative velocity work answers, motion graphs, related rates work, relative velocity work answer key.
35. Analyzing Motion Graphs Calculating Speed 1 Graphing
37. Calculating Speed Activity Marbles Graphing Activities Teaching Time
Combine this worksheet with my mo worksheet on graphs to compare graphs Graphing speed and velocity data worksheet. name speed data. a jogger has decided to jog as a and has decided to vary her speed from minute to minute. below is the data of her jogging times and distances.
please create a displacement vs. time line graph to show his velocity. then answer the following questions.Make worksheets about constant or average speed time and distance for algebra and algebra courses grades. a worksheet that requires the pupils to construct their own graphs of motion and answers questions about them.
38. Calculating Speed Word Problem Worksheets Writing Linear Equations
39. Circular Logic Concept Builder Learners Plenty Practice Recognizing Direction Velocity Vector Progress Report
40. Conservation Mass Worksheet Momentum Answers Physical Science Literal Equations Text Features Biology
About this quiz worksheet. this are going to assess you on the average speed and velocity of objects, the contrast between speed and velocity, and the relationship between heavier.Id language school subject science age main content speed and velocity other contents none add to my workbooks download file embed in my website or blog add to google, distance displacement speed and velocity worksheet answers.
speed example a plane travels mph for north. speed distance time ave. included questions total on speed and on velocity. the displacement and distance traveled do not have to be the same. how many km would the car travel in hrs.Average speed word problems worksheet with answers problem a person travels from to at the rate of miles per hour and comes backs to the at Jun, showing top worksheets in the category speed and velocity with answer key.
41. Determining Speed Velocity Worksheet Lovely Equation Acceleration Persuasive Writing Prompts Absolute Equations Template
. atoms . atoms. convert. x molecules of co to moles. moles co. molecules co mole co. co co. This website stores data such as cookies to enable essential site functionality, as well as marketing,, and analytics.One mole of any element is equal to the relative atomic mass of that element in grams.
for example one mole of carbon, that is if you had. x atoms of carbon in your hand, it would have a mass of. so one mole of helium atoms would have a mass of, lithium etc.Mar, mole of atoms of an element has a mass equal to the gram atomic mass of the element.
42. Diagram Good Show Speed Velocity Looked Question Physical Science Lessons Grade
43. Displacement Velocity Acceleration Worksheet Worksheets Speed
44. Distance Displacement Speed Velocity Worksheet Learning Scientific Method Lesson Plans
45. Distance Time Graphs Scenarios Card Sort Motion Interpreting
46. Educate Journalism
47. Effect Worksheets Coach Science Classes Wave Speed Worksheet Template Map
48. Excel Template
Expectations are referred to only fleetingly in the compatibility code.I encourage you to get the marriage expectation worksheet to help you and your partner work through each step in discovering, then sharing your expectations for each other, as well as your expectations for yourselves.
50. Force Motion Grade Ideas Science Classroom
With. units. no units no credit. distance time sec speed. distance time speed ms. distance time sec speed ms. what is the speed of a Graphing velocity and acceleration data worksheet. graphing speed and velocity data worksheet. name speed data. a jogger has decided to jog as a and has decided to vary her speed from minute to minute.
below is the data of her jogging times and distances. the distance recorded is the total from time zero up until the measured time.Calculating speed, time, distance name equations directions use the equation above to answer the following questions.
51. Graphing Analysis Distance Time Graphs Worksheets
Interpreting graphics taxonomy. answer true or false to the following statements. use the graphic to determine the answers. dogs belong to the order.Sep, solubility interpreting graphics worksheet set up. unsaturated, saturated and supersaturated solutions.
52. Graphing Calculating Velocity Distance Time Graph Graphs Worksheets
53. Graphing Interpreting Distance Time Graphs Reading
Day instructions use the molar mass of gallium to answer questions about calculating. chemistry day worksheet interpreting and drawing graphs.Lessoninterpreting graphs worksheet answer key. the graph below shows the relationship between students quiz averages over a semester and their final exam grades.
54. Graphing Speed Worksheet Answers Paring Distance Moving Kids Worksheets Free Kindergarten
Speed distance time Feb, speed. if a car travels in seconds how fast is it going. if you move meters in seconds, what is your speed. you arrive in my class seconds after leaving math which is meters away. how fast did you travel. a plane travels, meters in seconds.
what was its speed. it takes. hours to drive to school.Dec, speed problems worksheet will also let you know about the shortcut ways to calculate speed. therefore, without skipping, practice every problem available in this article. our calculating speed worksheets will create an interest for students to learn math.
55. Lab Show Kids Velocity Acceleration Object Incline Physical Science High School
56. Middle Math Calculations Calculate Speed Easy Concept Confusing Worksheet Steps Boxes
57. Neat Picture Shows Velocity Acceleration Speed Shown Graphs Motion Middle School Physics Physical Science
58. Newtons Law Worksheet Key Physical Science Persuasive Writing Prompts Worksheets
59. Numeracy Time Calculating Speed Math Word Problems Grade Worksheets
Worksheet. in the following assignments you will learn to calculate speed and convert from one speed to another. often you calculate speed in kilometres per hour (). to calculate speed, you need to know the distance and the time. when you know these two values, you can calculate the speed using this formula.
60. Physical Science
Worksheets. mixed ionic and covalent naming. mixed naming worksheet. mixed naming worksheet. mixed naming and molar masses. naming ionic compounds worksheet. naming ionic compounds worksheet. write formulas for ionic compounds. Imperial units conversions b the chart below is an interesting ( small) snapshot of the complexity of the archaic imperial () system of measurement.
61. Physical Science Acceleration Worksheet Unique Speed Velocity Calculations Physics Answers Template Study
62. Potential Kinetic Energy Worksheet Answers Work Power
63. Worksheets Word Lists Activities Math Problems Real Life
Distance for last leg of trip km, time for last leg. hours, need a speed of radius km, so circumference km., so. ms. after seconds, the dog is meters away.Dec, speed and velocity practice problems worksheet answers. it walks to x it then walks a displacement of lastly it walks to the location x.
show the formula used the setup and the answer with the correct units. calculate the speed Answer. km. an auto travels at a rate of for minutes, then at for minutes, and finally at for minutes. find the total distance covered in km and the average speed for the complete trip in ms.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988724.75/warc/CC-MAIN-20210505234449-20210506024449-00123.warc.gz
|
CC-MAIN-2021-21
| 13,892 | 91 |
http://mathxscience.com/math_triangles.html
|
math
|
is a polygon with 3 sides and 3 angles. The sides can be any length, but the 3 angles always add up to 180°
is the measuring tool used to measure angles.
Angles are measured in degrees.
An acute angle – less than 90°
An obtuse angle – greater than 90° and less than 180°
A right angle – exactly 90°
The box is the symbol for a right angle. This lets you know it is exactly 90 degrees and you don't have to use a
protractor to check it.
Triangles can be classified by Side Length and/ or by Angle Measurement.
Triangle names by Angle Measurement:
A triangle with all acute angles (all less than 90°) is an acute triangle.
A triangle with one obtuse angle (more than 90°) is an obtuse triangle.
A triangle with one right angle (90°) is a right triangle.
Triangle names by Side length:
A triangle with 3 equal sides is an equilateral triangle.
A triangle with 2 equal sides is an isosceles triangle.
A triangle with no equal sides is a scalene triangle.
If a triangle has 2 congruent sides, then it also has 2 congruent angles.
Notice the picture below.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122865.36/warc/CC-MAIN-20170423031202-00402-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 1,064 | 19 |
https://books.google.com.mx/books?id=xuAJAAAAIAAJ&lr=
|
math
|
Comentarios de la gente - Escribir un comentario
No encontramos ningún comentario en los lugares habituales.
acid added amount angle atoms base becomes body called cause cent charge chemical chlorine column combination common compound conductor contains Cosine Cotang cubic decimal decimal places denominator difference direction divided dividend divisor electricity elements equal equation example exponent expressed factors feet figure force formula fraction given gives glass heat Hence hydrogen inches increased indicated iron known light lines liquid magnetic matter means measure mercury metal miles molecular weight molecules multiplied negative obtained oxygen piece positive pounds pressure properties proportion quantity quotient ratio reduce remaining represent result root rule shown side Sine solid Solution specific square square inch substance subtract sulphuric surface taken Tang temperature tion tube units volume weight whole write
Página 23 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 4 - Addition is the process of finding- the sum of two or more numbers.
Página 24 - Multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction.
Página 47 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Página 11 - ... the ratio of the ovendry weight of a sample to the weight of a volume of water equal to the volume of the sample at some specific moisture content, as green, air-dry, or ovendry.
Página 10 - TROY WEIGHT. 24 grains (gr.) = 1 pennyweight (pwt.). 20 pennyweights = 1 ounce (oz.). 12 ounces = 1 pound (lb.). 351. Apothecaries' weight is used in mixing medicines and in selling them at retail. APOTHECARIES
Página 46 - RULE. — Annex ciphers to the numerator and divide by the denominator. Point off as many decimal places in the quotient as there are ciphers annexed.
Página 44 - ... .002 the quotient. It is not necessary to consider the ciphers at the left of a decimal when dividing, except when determining the position of the decimal point in the quotient.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400188049.8/warc/CC-MAIN-20200918155203-20200918185203-00463.warc.gz
|
CC-MAIN-2020-40
| 2,392 | 11 |
https://mamafoxbooks.com/site/archive.php?eb8b5a=3-hours-20-minutes-in-minutes
|
math
|
20 min to hr conversion (mtoh). swap units ↺ … 0 6 5. The final result is: 3 hr → 180 min. 0. Enter hours, minutes and seconds to convert from time format of hh:mm:ss, hours:minutes:seconds, to 0. We conclude that 3 hours is equivalent to 180 minutes: 3 hours = 180 minutes. In the modern metric system, hours are an accepted unit of time equal to 3,600 seconds but an hour of Coordinated Universal Time (UTC) may incorporate a positive or negative leap second, making it last 3,599 or 3,601 seconds, in order to keep it within 0.9 seconds of universal time, which is based on measurements of the mean solar day at 0° longitude. What is 20 minutes in hours? is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. 0 2 2. How long is 0.3 hours? 0.25 + 0.01 = 0.26). Decimal Hours-to-Minutes Conversion Chart. Unless your minutes converted perfectly to hours, you'll have … 3 hr → T (min) Solve the above proportion to obtain the time T in minutes: T (min) = 3 hr × 60 min. Pagkakaiba ng pagsulat ng ulat at sulating pananaliksik? 0 5 4. If you are 13 years old when were you born? The minor variations of this unit were eventually smoothed by making it 1⁄24 of the mean solar day, based on the measure of the sun's transit along the celestial equator rather than along the ecliptic. Does Jerry Seinfeld have Parkinson's disease? They are divided into seconds and multiplied into hours. This is an online converter for hours – minutes that will help you calculate different quantities of time measurements. What is 20 minutes in hours? For the default time of 2:45:45 in the converter, let's convert to just hours, then just minutes, and then just seconds. It was subsequently divided into 60 minutes, each of 60 seconds. This calculator will round to 6 decimal places at most. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. For example, 2 hrs = 120 mins and 7 hrs = 420 mins. How long will the footprints on the moon last? Supose you want convert 1 hour, 15 minutes and 36 seconds to decimal. 3 hours and 20 minutes = 200 minutes 200 minutes * 60 seconds/minute = 12 000 seconds. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of "precision" timepieces (mechanical and water clocks). This was finally abandoned due to the minor slowing caused by the Earth's tidal deceleration by the Moon. Ano ang pinakamaliit na kontinente sa mundo? 15/60 = 0.25). What is 3 hours in minutes? Divide the value in minutes by 60 (i.e. Minutes . So, we can write the formula to convert hours, minutes and seconds to decimal as: Now try to use our calculator at the top of this page and you'll find that it's very easy accomplish this task. All Rights Reserved. Above you will find our hours – minutes conversion to help you in changing units. 36/3600 = 0.01). Cite this content, page or calculator as: Furey, Edward "Time to Decimal Calculator"; CalculatorSoup, Seconds . Multiply the amount of hours by the conversion factor to get the result in minutes: The conversion factor from hours to minutes is 60, which means that 1 hours is equal to 60 minutes: To convert 3 hours into minutes we have to multiply 3 by the conversion factor in order to get the amount from hours to minutes. See the answer to this question using our calculator below: Supose you want convert 1 hour, 15 minutes and 36 seconds to decimal. [number of] hours x 60 = [number of] minutes. This is how they are defined: An hour (symbol: h; also abbreviated hr.) Such hours varied by season, latitude, and weather. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. It can be particularly useful when converting movie running times that are usually shown in minutes, or when baking chocolate desserts. From. This is an online converter for hours – minutes that will help you calculate different quantities of time measurements. 36/3600 = 0.01). There are 0.0166666667 hours in a minute. This simple calculator will allow you to easily convert 0.3 hr to min. Another way is saying that 3 hours is equal to 1 ÷ 0.0055555555555556 minutes. Sum the two values above to get the fractional part (i.e. 0 4 3. 5′, for angle measurement. 0. We can also form a simple proportion to calculate the result: Solve the above proportion to obtain the time T in minutes: We conclude that 3 hours is equivalent to 180 minutes: We can also convert by utilizing the inverse value of the conversion factor. The prime is also sometimes used informally to denote minutes of time. There are 12,000 seconds in 3 hours and 20 minutes. For example 15 minutes (¼ hour) equals 0.25, 30 minutes (½ hour) equals 0.5, etc. © 2006 -2020CalculatorSoup® View our other time converters. To convert time to just hours: 2 hours is 2 hours * (1 hour/ 1 hour) = 2 hours; 45 minutes is 45 minutes * (1 hour / 60 minutes) = 45/60 hours = 0.75 hours 0 8 6.1 .1 0: 7.1 .12 Conversor de Minutes to Hours . This is how they are defined: An hour (symbol: h; also abbreviated hr.) 5′, for angle measurement. We will need to convert each part into the unit of time we want. We can also form a proportion to calculate the result: Solve the above proportion to obtain the time T in minutes: We conclude that 3 hours is equivalent to 180 minutes: For practical purposes we can round our final result to an approximate numerical value. To change a certain number of hours into minutes, simply enter above in the box how many hours you want to calculate and click ¨convert¨. https://www.calculatorsoup.com - Online Calculators. It was subsequently divided into 60 minutes, each of 60 seconds. Our formula below is a useful tool if you wish to do this time conversion by hand or if you need to know the mathematical calculation for an exam. What is 20 minutes when converted to hour in decimal format? As a unit of time, the minute (symbol: min) is equal to 1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. Multiply the decimal or fraction by 60. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. You might want to work in the other direction, convert minutes to hours. Allows you to countdown time from 3 hour 20 min to zero. To convert this value to decimal hours follow the steps below: In short: Decimal hours = whole number of hours, plus minutes divided by 60, plus seconds divided by 3600. 18 Minutes: 0.3 Hours: 19 Minutes: 0.316667 Hours: 20 Minutes: 0.333333 Hours: 21 … What is 0.3 hours in minutes? Both these units of time are used in our everyday language for many things, so try our hours to minutes calculator above for your conversions. For practical purposes we can round our final result to an approximate numerical value. In this case 1 minute is equal to 0.0055555555555556 × 3 hours. 1 hr → 60 min. Easy to adjust, pause, restart or reset. We can say that three hours is approximately one hundred eighty minutes: An alternative is also that one minute is approximately zero point zero zero six times three hours. 20 min to hr conversion (mtoh). The final result is: 3 hr → 180 min. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of "precision" timepieces (mechanical and water clocks). However, no consistent records of the origin for the division as 1⁄60 part of the hour (and the second 1⁄60 of the minute) have ever been found, despite many speculations. And we know that 1 hour = 60 minutes and 1 minute = 60 seconds so 60 minutes/ hour * 60 seconds/ minute = 3600 seconds/ hour or 1 hour = 3600 seconds. This was finally abandoned due to the minor slowing caused by the Earth's tidal deceleration by the Moon. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime. While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions, or for the results obtained from the use of this information. Sometimes calculations are too hard to do in your head. The prime is also sometimes used informally to denote minutes of time. All information in this site is provided “as is”, with no guarantee of completeness, accuracy, timeliness or of the results obtained from the use of this information. However, no consistent records of the origin for the division as 1⁄60 part of the hour (and the second 1⁄60 of the minute) have ever been found, despite many speculations. Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. and your pace will appear in the Minutes/Mile field. Minutes Tenths of an Hour Hundredths of an Hour; 1. 15/60 = 0.25). formula to convert hours, minutes and seconds to decimal, Volume to (Weight) Mass Converter for Recipes, Weight (Mass) to Volume to Converter for Recipes. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime. Converting from hours to minutes? Hours are divided into minutes and multiplied into days. 1.3 hours in other units Use this hours – minutes time converter to help with conversions. How to Calculate Minutes to Hours 1 minute = 6 × 10 1 seconds 1 hour = 3.6 × 10 3 seconds 1 minute = (6 / 3.6) × 10 1 × 10-3 hours 1 minute = (1.6666666666667) × 10 1-3 hours 1 minute = (1.6666666666667) × 10-2 hours 1 minute = 1.6666666666667 × 0.01 hours 1 minute = 0.0166666667 hours How Many Hours in a Minute? 3 hour 20 minute equal 12000000 Milliseconds. From. Then you can put any number above the answer to make it a Its East Asian equivalent was the shi, which was 1⁄12 of the apparent solar day; a similar system was eventually developed in Europe which measured its equal or equinoctial hour as 1⁄24 of such days measured from noon to noon. T (min) = 180 min. Ano ang mga kasabihan sa sa aking kababata? 1 hr → 60 min. 0. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). What is the hink-pink for blue green moray?
Wow Pet Battle Guide, How Bad Do You Want It Book Summary, Trap City Manhwa, Browns Vs Buccaneers 2014, Hard Times Come Again No More Meaning, Cutest Baby In The World 2019, Boys' In A Sentence, Capital Good Synonym, Kiss Chords, Relish Breckenridge, Shea Groom Salary, Best Of Bob Dylan Album, Fanfare For The Common Man Meaning, Bid Farewell Synonym, How To Write An Academic Progress Report, Sylvia Jeffreys Today Show, Wpbt Tv Pbs, Vintage Snapbacks, Temas De La Flor De Mi Secreto, Liberty Utilities Buyer, How Much Savings Should I Have For Spouse Visa, Part Time Jobs In Qatar Al Wakrah, How Much Do Semi Pro Soccer Players Make, Dallas Cowboys Roster Wiki, Amber Rose Tattoo, Rugby League International Teams, New York Lizards Jobs, Capital Realty Juneau, Football Badges Of The World, City Of Warman Phone Number, Sec Energy Odessa Tx, Pristin We Lyrics, Tumbled Meaning In Bengali, What Channel Is Abc On Antenna, Haley Macklin Interview, Ruhi Chaturvedi Instagram, Himbo Pride, Abba Hologram Tour 2020, Chrysler Pacifica, Royal Orchid Sheraton Restaurants, Capital Realty Juneau, Uk Tier 2 General Visa Points Calculator, Qatar Airways In Trouble, Everybody's Fool Lyrics, Jeremy Jauncey Ethnic Background, Skyy Clark Scouting Report, Packers Vs Lions Channel, Cba Basketball Jerseys, Disney Celebration Village, How To Pronounce Bellow, Coca-cola Headquarters Address, What Channel Is The Cowboys Game On, Goddess Of Beauty Hindu, Spring Mitre Clamps, Should I Sell My Royal Mail Shares, Bring Me Back To Life Meaning, Early Bumblebee Lifespan, Sedative Injection, Why Is The Bucs Game Delayed, Kiss Band Autographs, In This Moment - The Fighter Lyrics, Mll Shop, Euston Station Redevelopment, Grand River Brewery - Marshall, Mi, Land For Sale In Surry County, Va, Ninja Youtube Followers, From Hong Kong With Love, Road Accident In Qatar Yesterday, Darkside By Grandson Id, Vic Shealy Salary, Cover Letter For Postal Clerk, One Patio Hotel Pattaya, Bomfalleralla Lyrics, Because Of Anya Summary, Ferry Schedule Vallejo, Apartments In Sunrise, Fl, Top Tv Channels In Usa, Are We In Drought, The Seven Principles For Making Marriage Work Worksheets, Arizona Cardinals Salary Cap,
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038066981.0/warc/CC-MAIN-20210416130611-20210416160611-00484.warc.gz
|
CC-MAIN-2021-17
| 12,682 | 2 |
https://books.google.at/books?id=NTEBAAAAQAAJ&hl=de&lr=
|
math
|
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
Andere Ausgaben - Alle anzeigen
A B C acute answer axis base Bisect called carry centre chord circle circumference conjugate contained curve cutting decimals DEFINITION denominator describe describe the arc diameter difference Directions distance divide dividend divisions divisor double draw the line drawn ellipsis equal equilateral EXAMPLE extremities feet figure four fraction given given point greater half height hundred Join length line A B manner means measure meeting method multiply number of equal oblique opposite parallel passing perpendicular pins plane points F polygon pound PROB PROBLEM PROBLEM PROBLEM proceed proportional quotient radius rectangle reduced remainder right angle right line root round rule segment shillings sides solid square Take tangent third transverse triangle units whole write
Seite 137 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Seite xxxviii - Plane figures that are bounded by right lines have names according to the number of their sides, or of their angles ; for they have as many sides as angles ; the least number being three.
Seite xxxviii - A Right angle is that which is made by one line perpendicular to another. Or when the angles on each side are equal to one another, they are right angles.
Seite 135 - ROOT of any given number, or power, is such a number as, being multiplied by itself a certain number of times, will produce the power ;. and it is denominated the first, second, third, fourth, fcfc.
Seite 149 - From half the sum of the three sides, subtract each side severally; multiply the half sum, and the three remainders together, and the square root of the product will be the area required.
Seite 88 - Having arranged the numbers so that the smaller may stand under the greater, subtract each number in the lower line from that which stands above it, and write down the remainders. When any of the lower denominations are greater than the upper, increase the upper number by as many as make one of the next higher denomination, from which take the figure...
Seite 135 - RULE. Multiply the given number, or first power continually by itself, till the number of multiplications be 1 less than the index of the. power to be found, and the last product will be the power required.
Seite xxxvii - Line, or Straight Line, lies all in the same direction between its extremities, and is the shortest distance between two points.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988741.20/warc/CC-MAIN-20210506053729-20210506083729-00307.warc.gz
|
CC-MAIN-2021-21
| 2,609 | 12 |
https://www.sapling.com/8597127/calculate-wtp
|
math
|
Calculating willingness to pay (WTP) is a major factor in business. Market demand curves are determined by finding the WTP. A market demand curve establishes how many of a certain item a buyer would purchase at a stated price. Say, for example, you were selling chairs and were seeking chair distributors. To make a profit on your chair manufacturing business, you would require the following pieces of data to determine the WTP and market curve: the price you prefer per to charge per chair and the price a buyer is willing to pay per chair.
Establish the high price you prefer per chair. State your price as $30 per chair.
Video of the Day
Establish the high price your buyer is willing to pay per chair, such as $25 per chair.
Ask the buyer how much he would be willing to pay per chair if he ordered two chairs. Say that price is $24.50, or a deduction of 50 cents per chair.
Create a chart based on this information. List numbers one thru 10 in the left column. Write in the price your buyer is willing to pay per chair next to each number. Write in "$25" next to the "1" spot. Each buyer price is the "WTP". Write in "$24.50" next to the "2" spot. Write in "$24" next to the "3" spot. Continue in this manner. This chart represents your buyer's WTP and the demand curve -- the buyer price per chair and how many chairs, at the stated price, he can buy.
Chart the curve. Write out the WTB numbers on the left-hand, vertical margin -- starting at the bottom and moving up. Write out the number amount of chairs the buyer can purchase in sequential fashion -- starting left and moving right -- at the bottom. Graph these markings to form a grid. Scribble in dots on the graph at each designation where price and amount meet. Link the dots together to see the visual curve.
Things You'll Need
Paper (graph paper)
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224652494.25/warc/CC-MAIN-20230606082037-20230606112037-00045.warc.gz
|
CC-MAIN-2023-23
| 1,814 | 9 |
https://www.coursehero.com/file/6878061/2009-final/
|
math
|
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: FINAL EXAM STAT 101, Instructors: A. Wyner, A. Rakhlin December 15, 2009 Student Name: Section: Instructions • Use the space provided to answer questions. You can use the back of these pages as scratch paper. • You must show work and give explanations (except for the multiple-choice questions). • Rules of uniformity: One-sided letter crib sheet, calculator ok (even with statistical functions and graphing), otherwise closed notes, closed book. • No cell phones visible! • Rules of Fairness: – Complete this exam entirely on your own. Do not acquire information from other stu- dents or the outside in any form. – Do not take copies of this exam out of this room. – You have two hours for this exam. Any student observed continuing to write after time has been called will be documented and points will be deducted. • Rules of Consideration: – Be considerate to others by not causing commotion and distraction. – If you finish early, leave quietly; avoid slamming doors. Honor code applies to the above Rules. Your signature: About this test: When more than one choice seems reasonable, pick the one that is best. STOP WAIT UNTIL YOU ARE INSTRUCTED TO PROCEED. 19 questions for a total of 100 points. STAT 101 Final Exam 1. (2 points) If the sample size n is large and p is the population proportion, the sampling distri- bution of the proportion is approximately (a) Binomial Bin (1 / 2 ,p ) (b) Normal N ( p,SD ( X i )) (c) Normal N ( p,p (1- p ) /n ) (d) Normal N (ˆ p, ˆ p (1- ˆ p ) /n ) (e) Normal N ( p, p p (1- p ) /n ) 2. (2 points) The Central Limit Theorem asserts that for i.i.d. random variables X 1 ,...,X n (a) The histogram of the data closely resembles the probability distribution of X i when n is large. (b) The histogram of the data closely approximates the mean of the population when n is large. (c) The sampling distribution of the mean is approximately normal when n is large. (d) The sampling distribution of the mean resembles the probability distribution of X i . 3. (2 points) The probability distribution for the average of 9 i.i.d. normal N (2 , 3 2 ) random variables X 1 ,...,X 9 is best described as (a) Approximately N (2 , 3 2 ) (b) Exactly N (2 , 3) (c) Exactly N (1 / 9 , 3 2 / 9) (d) Exactly N (2 , 1) (e) Can only be determined if the distribution of X i is known since the smaple size n is only 9....
View Full Document
- Fall '08
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948597485.94/warc/CC-MAIN-20171217191117-20171217213117-00197.warc.gz
|
CC-MAIN-2017-51
| 2,523 | 4 |
https://assignmentgeeks.org/miami-dade-college-wind-energy-and-nuclear-energy-worksheet/
|
math
|
What is the wind energy in a cyclone with wind velocity of 95 miles per hour . Show detailed calculation.
2. A house has five solar panels, each measuring 5 meters long and 2.5 meters wide. How much solar electricity will all these solar panels produce in a 24 hour day. Show calculation.
3.A nuclear power plant purchases 55 g rams of Uranium 238 and 15 grams each of Uranium 236 and Uranium 235. How much total electricity can be produced from all these uranium amounts. Show DETAILED calculation.
4. A hurricane has wind energy of 270000 torr. What is the wind velocity inside this hurricain. Show calculation.
5.A house needs 4000 KW of electricity. How many solar panels, each 10 m long and 5 m wide are needed to generate this amount of electricity. Show calculation.
6.A city requires 45000 KW of electricity per minute. How many grams of Uranium 235 are needed to supply one day (24 hrs) of electricity to this city. Show calculation.
NUCLEAR ENERGY EQUATIONS
Uranium has THREE ISOTOPES, U238, U236, U235.
(a) U 238 + n ——– U 235 + 3n + Heat energy (4200 KW)
uranium 238 uranium 235 gamma (nuclear power)
(b) U 236 + n ——- U 235 + n + Heat energy (3400 KW)
(c) U 235 + n ——- Th 235 + Heat energy (2200 KW)
(uranium 235) (thorium)
E = mv ( E = wind energy, m = mass of wind, v = wind velocity )
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500041.18/warc/CC-MAIN-20230202200542-20230202230542-00087.warc.gz
|
CC-MAIN-2023-06
| 1,315 | 14 |
https://math.rutgers.edu/news-events/seminars-colloquia-calendar/icalrepeat.detail/2020/02/12/10643/-/a-tale-of-three-curves
|
math
|
Seminars & Colloquia Calendar
A tale of three curves
Jennifer Balakrishnan (Boston University)
Location: Hill 705
Date & time: Wednesday, 12 February 2020 at 3:30PM - 4:30PM
Let C be a smooth projective curve of genus at least 2 defined over the rational numbers. It was conjectured by Mordell in 1922 and proved by Faltings in 1983 that C has finitely many rational points. However, Faltings' proof does not give an algorithm for finding these points. In the case when the Jacobian of C has rank less than its genus, the Chabauty--Coleman method can often be used to find the rational points of C, using the construction of p-adic line integrals. In certain cases of higher rank, p-adic heights can often be used to find rational or integral points on C. I will describe these "quadratic Chabauty" techniques (part of Kim's nonabelian Chabauty program) and will highlight some recent examples where the techniques have been used: this includes a 1700-year old problem of Diophantus originally solved by Wetherell and the problem of the "cursed curve", the split Cartan modular curve of level 13. This talk is based on joint work with Amnon Besser, Netan Dogra, Steffen Mueller, Jan Tuitman, and Jan Vonk.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818337.62/warc/CC-MAIN-20240422175900-20240422205900-00792.warc.gz
|
CC-MAIN-2024-18
| 1,205 | 6 |
https://iris.inrim.it/handle/11696/33540
|
math
|
In Bragg's approach to the determination of the Avogadro constant, the measurement of silicon density as the ratio of mass to volume is an essential step. With a view to achieving a relative uncertainty of 10(-7) in the determination of N(A), the computation of the volumes of solid density standards manufactured in the form of optically-polished silicon balls was investigated. Apart from a negligible difference, the volume considered is that of a sphere having the same average diameter. The estimation of the average diameter is studied in the angular momentum domain by using spherical harmonics as a basis and results are assessed by Monte Carlo simulation. The N-point approximation is investigated in detail and a formula for the uncertainty and sampling which minimize aliasing is also given. If the spectrum is bandwidth limited, it is demonstrated that N-point means exist, which give the average diameter exactly. The work involves least-squares estimation and refers to discrete Fourier transforms, Nyquist sampling criterion and analogies with quantum mechanical formulae.
VOLUME OF QUASI-SPHERICAL SOLID DENSITY STANDARDS / MANA G. - In: METROLOGIA. - ISSN 0026-1394. - 31:4(1994), pp. 289-300.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710712.51/warc/CC-MAIN-20221129232448-20221130022448-00634.warc.gz
|
CC-MAIN-2022-49
| 1,210 | 2 |
http://lotsasplainin.blogspot.com/2009/12/wednesday-math-vol-99-goldbachs.html
|
math
|
The most famous problem involving prime numbers is Goldbach's Conjecture, which is actually several conjectures. In 1642, Christian Goldbach wrote a letter to my personal math man crush Leonhard Euler making several conjectures. The one that is now called Goldbach's Conjecture is stated as follows.
Every even number greater than 2 can be written as the sum of two primes.
Technically, this is the strong Goldbach's Conjecture. The weak conjecture is this.
Every odd number greater than 7 can be written as the sum of three odd primes.
Why the second one is weak and the first one strong is that if the second one is true, the first one might not be true, but the strong conjecture would prove the weak conjecture, since if any even number greater than 2 is the sum of two primes, add three to that sum and you get an odd number that is at least 7, and 7 only works as 2+2+3. Back in Goldbach's day, 1 was a prime but it isn't any more, so he could have written 1+1+5 or 1+3+3 as three primes adding up to 7.
If we find one even number that doesn't work, Goldbach's Conjecture is false. People have tried. Back in 1938, a guy named Pipping checked up through 100,000 by hand. Nowadays with computers, a program designed by T. Oliveira e Silva has checked up through 10^18, which is a million trillion. This method can never prove Goldbach's Conjecture to the satisfaction of mathematicians, but it could possibly disprove it.
Like a lot of number theory, there isn't a practical use if we find Goldbach's Conjecture to be true or false. Mathematicians are drawn to problems that can be easily stated, and while the fact that this one has been lying around unsolved for 267 years should be a red flag that it must be hard to solve, that doesn't stop people from trying. After all, Andrew Wiles' proof of Fermat's Last Theorem came over 350 years after Fermat wrote that he knew how to prove it but didn't write it down, which meant it was a conjecture and not a theorem for all that time.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589172.41/warc/CC-MAIN-20180716021858-20180716041858-00425.warc.gz
|
CC-MAIN-2018-30
| 1,988 | 7 |
https://www.mumsnet.com/Talk/secondary/1117430-Urgent-Y7-maths-homework-help
|
math
|
Urgent Y7 maths homework help!!!!(23 Posts)
Join the discussion
Already registered? Log in with:
DD's homework is to find the area of a trapezium with the top measuring 8cm and the bottom 14cm. That's it; no further measurements.
Is it possible to work this out without the height, and if so, how? (I am about to embark on an OU basic maths course, so I may be able to actually help her in a few months' time!)
here but you need the height of the trapezium too?
if its symmetrical, then you can work out the length of the base of the triangle - 3cm
so chances are its a 3,4,5
so the height is 4
so the area is 3 x 4 + 8 x 4 = 44cm sq
Exactly lal123 thanks anyway.
Talkinpeace, I'll go with that; not sure how dd will feel about "making up" the height but at least it'll show she knows how to do it.
Not making it up.
3:4:5 triangles are the classic form.
You know its a right angle triangle.
You know one of the sides by the right angle is length 3
therefore the other two sides HAVE to be 4 (the vertical) and 5 (the hypotenuse)
PS checked it with DH and he came up with the same number I did...
I doubt they would expect a Y7 to know about Pythagoras, more likely a mistake in the question.
it doesn't have to be a 3 4 5 triangle. Sounds like a mistake to me.
DD did 3 4 5 triangles in extended maths in year 6
they then did bits of it in geometry at the start of year 7
they are SO elegant that they are a hook to get the kids interested in mathematics as against numeracy
DD has done hypoteneuse, though I don't know about the classic form of a triangle. I'm sorry Talkinpeace, I wasn't being rude just thinking that that was what dd would think.
Out of interest, why does the vertical have to be 4? Couldn't it be 12? or any other length?
I thought dd must have forgotten to write down the height, or that her teacher had made a mistake (though that was less likely). Having read about the classic triangle now, I suspect her teacher expected the kids to be able to make the assumption.
Anyway, dd accepted that she should assume the height as 4 and has done her calculation (correctly as it happens; she's actually quite good at maths though she thinks she isn't).
Thank you all. (I shall come back no doubt, again and again and again!)
If a triangle has a base of 3 and is a right-angled triangle, the other sides could be e.g. 4.5 and 5.4 (rounded) or lots of other numbers. They don't have to be 4 and 5.
they could indeed : a sqd + b sqd = c sqd
but the fact that the difference between the two lengths is 6 making the triangle base 3 and it being a year 7 question hints at the most elegant answer
happy to be proven wrong when OP's DD checks at school ;-)
It being a Y7 question hints at there being an error in the question. Teaching the formula for the area of a trapezium is tricky enough.
And I hope no maths teacher would set a question which required students to guess at a length because it is impossible to work out. An answer being elegant does not make it correct.
I think there's a mistake in the question too - I think best bet is to put in his answer that it is impossible to tell without the height and NOT to make up an answer
Ah, lal123, you could be right there! I wish I'd checked this thread before I went to bed, but I didn't. I'm sure dd would have preferred not to have done any calculations at all and just put in a note telling her teacher it was impossible to do! I said that if she assumed the height was 4 then she could at least show that she knew how to calculate the area, which seems like a fairly sensible way to go.
It had to be done for today, but she - apparently - doesn't actually have a maths lesson today I have no idea when she's going to get it back. I'm intrigued now.
Anyway, I think the most likely situation is that she simply didn't copy the question down properly
I certainly hope the teacher wasn't expecting them to assume/guess the height - very bad form <maths student here> I would complain if so.
In your DD's situation I would have done the calculations but using h as the unknown height so the area would be
8h (rectangle) + 3h (two triangles) = 11h
Oh bother, you're quite right. Aaaaaaargh. Why oh why didn't I think of algebra? Bother bother bother.
Dont beat yourself up jux - its not actually your homework, it's your DD's
I know, but in the light of the maths course I'm starting in Feb, I feel that I would do better going back to primary!
(I asked her, when she got home today, if she would like to add an alternative solution using h, but she wasn't interested. Surprise!)
h is elegant too!
Please tell us what the actual answer is when the work gets marked.
OUTRAGE! SHEER OUTRAGE!!!!!
No one got that question right as the teacher had forgotten to tell them that the height was - wait for it - 6 !!!!!!!
I am also happy to announce that no one in the class thought of using h either.
delighted to hear the answer
SUCH a shame that the teacher canot be penalised for setting dud homework.
Time to write 66 in big letters on some sheets of paper for him!!!
That would be fun wouldn't it? As it is, dd has let it be known that she is not going to let him forget it in a hurry. I am so tempted to suggest that she make a large sign with 666 on it to hold up in class, or to bribe the whole class to keep whispering 6 when his back's turned. No, I must leave the poor man alone and not encourage evilness in my thoroughly pure and innocent daughter, who has never had a bad thought in her head.
Join the discussion
Already registered? Log in with:
Please login first.
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583705737.21/warc/CC-MAIN-20190120102853-20190120124853-00237.warc.gz
|
CC-MAIN-2019-04
| 5,540 | 57 |
https://3rddog.weebly.com/blog/episode-40-interview-with-nick-blain
|
math
|
Fomenko graduated from the Mechanics and Mathematics Faculty of Moscow State University in 1967, and in 1969 began working in the department of differential geometry in said faculty. In 1970 he defended his thesis "Classification of totally geodesic manifolds realizing nontrivial cycles in Riemannian homogeneous spaces", and in 1972 defended his doctoral thesis, "The decision of the multidimensional Plateau problems on Riemannian manifolds." In December 1981 he became a professor of the department of higher geometry and topology, and in 1992 became the head of the department of differential geometry.
Fomenko has served as the editor of several Russian-language mathematics journals and is a member of many councils overseeing dissertations in his field. In 1996, he won the State Prize of the Russian Federation for excellence in mathematics. Wikipedia
New Chronology of the World History Links
it contains, no matter how unorthodox, is backed by solid scientific data.
The book is well-illustrated, contains over 500 graphs, copies of ancient manuscripts, and countless facts at
testing to the falsity of the chronology used nowadays, which never cease to amaze the reader.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251671078.88/warc/CC-MAIN-20200125071430-20200125100430-00254.warc.gz
|
CC-MAIN-2020-05
| 1,182 | 6 |
https://worldbuilding.stackexchange.com/questions/155938/how-does-escape-velocity-work-with-rotational-gravity
|
math
|
Every planetoid who gains gravity "normally" like Earth and Io and every other piece of matter in the universe gets it from their mass and radius. Escape velocity is also from mass and radius. My question is, how does escape velocity work if matter gains rotational gravity from its inertia, with negligible true gravity?
"Rotational gravity" is just false gravity emulated by centrifugal force. So, escape velocity would be either a) the inverse of the centrifugal force being generated or, (and much simpler) a corridor or tunnel to the outside of your ring/cylinder/sphere, where a craft would literally "fall" away at your rotational gravity pace (though it would stop accelerating the instant it left contact with the rotating body).
IOW: Escape velocity = "let go"
In the article, look at the basic diagram for rotational inertia, that would become your departing velocity the instant you were no longer bound to the rotating body.
It depends a lot on where you are going and the size of your ring
Let's say you are in a Nivan style ring world and you are trying to go out deeper into space. The most practical approach to escape velocity may be to just open a hole in the floor. Then you just need to time your escape such that you go flying off in the right direction effectively "falling" to your destination.
Now, let's say there is somewhere you want to go inside of the ring and you want to know how fast you need to go to reach zero apparent Gs, the answer lies in matching the Tangent Velocity of the ring by moving against its rotation. Once you reach the Tangent Velocity relative to the ring's surface, you will become stationary in space and no longer under the influence of any artificial gravity. At that point you can fly off at whatever speed you desire unaffected by the ring's rotation.
Larger rings require a higher Tangent Velocity than smaller rings to achieve the same apparent gravity. As you can see demonstrated in this trajectory calculator I wrote for L. Dutch's previous previous question about rotational gravity physics, you see that a Nivian Ring world rotates at over 1 million m/s whereas a Stanford torus only rotates at 94 m/s despite both having the same apparent gravity.
Just use the attached calculator and you can find the "escape velocity" of any ring by calculating for the tangent velocity.
Side-note: don't accelerate with the direction of rotation, that will actually increase your apparent gravity.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474445.77/warc/CC-MAIN-20240223185223-20240223215223-00165.warc.gz
|
CC-MAIN-2024-10
| 2,450 | 10 |
https://mathematicsforstudents.wordpress.com/calculators-tools/order-of-operations/
|
math
|
Make sure you understand the order of operations in any calculation.
Do any calculations in brackets first.
Next calculate any exponents (powers)
Then do any multiplication or division (these have equal precedence)
Finally do any addition or subtraction (these two operations have equal precedence)
4 + 5 x 6 = 4 + 30 = 34
4 + (5×2) = 4 + 10 = 14
2x2 when x = 3 is 2×32 = 2×9 = 18
Remember you can check any calculation on WolframAlpha – make sure you enter your calculation correctly.
This game from mathFROG allows you to practice against the clock.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224647810.28/warc/CC-MAIN-20230601110845-20230601140845-00434.warc.gz
|
CC-MAIN-2023-23
| 556 | 10 |
https://manufacturingscience.asmedigitalcollection.asme.org/dynamicsystems/article-split/139/11/111004/474403/Ground-Reaction-Force-Estimation-in-Prosthetic
|
math
|
A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-mean-square (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF.
Recent advances in microelectronics and robotic technologies have enabled the development of powered prosthetic legs that can help amputees walk up stairs and slopes because of the legs' net power contribution to gait; they are also able to adapt their behavior to various environmental conditions. The company Össur has a lower limb prosthesis called the Power Knee, which is the first commercially available knee to generate power during the gait cycle . Recent developments in powered knee and ankle prostheses are reported in Refs. [3–8].
Bulky load cells are often employed in robots and prosthetic legs to capture external forces (GRFs) and moments during walking . These data are used as feedback measurements to control the robot or prosthesis with force or impedance controls. Even when not used for feedback, force sensing is important for monitoring and evaluation of prosthesis performance and safety. However, there are several drawbacks to the use of load cells: (i) load cells are expensive; (ii) a 250-lbf load cell weighs about 1 lb, with a length of about 3 in, and thus does not easily fit in a prosthetic leg; (iii) load cell measurements tend to drift, need to be frequently offset, and are noisy and need significant signal conditioning; (iv) load cells can get damaged easily from overloading or off-axis loading; and (v) load cells consume electrical power, which is an important consideration in prosthetics.
The above-mentioned problems do not arise with angle sensors because high-resolution encoders are accurate, reliable, and inexpensive. Nevertheless, they do not measure velocity, and velocity calculated by numerical differentiation is challenging because of the difficult compromise between noise rejection and bandwidth.
There have been several methods to reduce the number of force sensors in robotics. In Ref. , a robot compliance controller based on a disturbance observer is presented, where the disturbance observer is used to estimate the external reaction forces. In Ref. , a method for force estimation of the end-effector of a Selective Compliance Assembly Robot Arm (SCARA) robot is presented, where servomotor currents and position information are used to estimate forces. In Ref. , the external force on the end-effector of a four degrees-of-freedom (DOF) robot manipulator is estimated with a combination of time delay estimation and input estimation. In Ref. , a model-based observer is used to estimate the external forces acting on a rigid body. All the aforementioned techniques depend on either the accuracy of the robot model or servomotor current data. Thus, if the accuracy of the robot model or motor current measurement degrades, force estimation can deviate from true force. In Ref. , the force estimation does not require a precise robot dynamic model, but the accuracy of estimated force may degrade in the presence of noise, since the external force is considered as an unknown input.
In this paper, we treat GRF as an unknown input with known dynamic properties and known bounds, and we use an EKF to estimate GRFs along with the states of the robot/prosthesis system. Although EKF is efficient in many applications, it has two important potential drawbacks. First, the derivation of the Jacobian matrix for linearization can be complex and can cause numerical implementation difficulties. Second, linearization can lead to cumulative errors which may affect the accuracy of the state estimation. To overcome these limitations, other nonlinear estimators could be used, such as the UKF or particle filter, where the state estimations are obtained without the need for derivatives and Jacobian calculations [14–16].
In this research, a powered (active) prosthetic leg is considered for transfemoral amputees. The prosthetic leg attached to a robotic hip/thigh emulator. The combined system includes four degrees-of-freedom: vertical hip displacement, thigh angle, knee angle, and ankle angle. This paper is an extended version of Ref. , where we designed an EKF for the online estimation of joint coordinates, velocities, and GRFs.
In this paper, we compare EKF and UKF performance in our 4DOF robot/prosthesis system. We study the EKF because it is the most commonly used nonlinear state estimator due to its versatility and simplicity of implementation. We study the UKF because it generally provides better performance than the EKF. One of the questions we study in this paper is whether the improved performance of the UKF relative to the EKF is worth the increased computational effort.
We also study the effect of various sensor sets on estimation error at different walking speeds. We start with the four main states of the robot/prosthesis system, which are hip displacement, thigh, knee, and ankle angles, as system observations to get the baseline estimation accuracy. Then, we investigate how much estimation accuracy degrades if fewer measurements are used, and we find a tradeoff between the estimation error accuracy and the number of measurements. In general, we prefer to use fewer measurements because fewer sensors mean a simpler system, less complexity, and lower cost.
Finally, we consider the stability of the EKF and boundedness of the estimation error, which are very important for prosthesis control. The stability of the EKF under various values of initial estimation error and noise covariances is explored. We analytically show that the estimation error remains bounded under certain conditions in our 4DOF robot/prosthesis system and confirm the analysis with simulation results.
This research involves the mechanical integration of a prosthesis and a test robot so that we can test the prosthesis without human trials. We will eventually need to use the Kalman filter on a prosthesis that is attached to an amputee. We develop the Kalman filter for the robot/prosthesis system in this paper for later implementation on an amputee/prosthesis system.
The paper is organized as follows: In Sec. 2, the model of the robotic system and prosthetic leg is presented. In Sec. 3, the EKF for state estimation and GRF estimation is discussed. In Sec. 4, the EKF is analyzed by mathematically deriving its stability conditions. Section 5 compares performance between the EKF and UKF when different measurement sensors are used; also the convergence of the EKF is tested with different initial estimation errors and noise magnitudes. Section 6 concludes the paper and suggests future research.
Robotic testing of transfemoral prostheses is presented here, where motion is limited to the sagittal plane and transverse motion is not considered. Typically, only the sagittal plane is considered in transfemoral prosthesis research. Although the transverse plane is ignored here, sagittal motion captures the essential dynamics of human walking . The model of the test robot/prosthesis is based on the standard robotic framework. Figure 1 shows a diagram of the hip robot and prosthesis combination [20,21]. A general dynamic model for the system is given as follows:
where is the vector of joint displacements (q1 is vertical hip displacement, q2 is thigh angle, q3 is knee angle, and q4 is ankle angle), is the inertia matrix, is a matrix accounting for centripetal and Coriolis effects, is a nonlinear damping vector, Je is the kinematic Jacobian relative to the point of application of the external forces Fe, is the gravity vector, and u is the four-element vector of control signals . The kinematic and dynamic models of the robot/prosthesis combination are given in Refs. [23–25], where a mixed tracking/impedance controller based on passivity methods is designed . The control signals consist of hip force, and thigh, knee, and ankle torques. As Fig. 1 shows, a triangular foot with two points of ground contact is assumed. Horizontal and vertical GRFs are applied to contact points at the toe and heel. The GRFs are denoted as Fxh, Fzh, Fxt, Fzt, which represent the horizontal and vertical GRFs at the heel and toe. Thus, the external force vector Fe in Eq. (1) comprises these four GRFs.
where kb is the belt stiffness, sz is the treadmill standoff (the distance between the origin of the world coordinate system and the belt when the leg is fully extended), l2 and l3 are the lengths of link 2 (thigh) and link 3 (shank), respectively, aH and aT are the distance from the ankle joint to the heel and the toe, respectively, ah is the height of the ankle joint above the sole of the foot, and β is the friction coefficient between the treadmill belt and the foot. The vertical positions of the toe and heel in the world coordinate system are shown in Fig. 1 as zt and zh, respectively. We thus have four states for the positions and four states for the velocities of the joint displacements.
It should be noted that the forces are not states of the original system model, but are augmented here to the state vector, since we need to estimate them with a state estimator. The 12-element vector of Eq. (8) will be estimated by the state estimator.
Equations (2)–(7) are a preliminary approximation to GRF and are accurate only if the amputee (or robot in our case) walks in a highly controlled environment with a known walking surface stiffness. In future work, it will be important to study the robustness of the Kalman filter to modeling errors and particularly to errors in these GRF equations.
We should mention that there are at least two other possible approaches to obtain GRF estimates. In the first alternative approach, GRF could be considered as an unknown input with no prior assumptions about its model. In that case, the EKF would have difficulty estimating GRF, since its effect on the system would be indistinguishable from process noise. In the second alternative approach, state estimation of the robot/prosthesis system could be performed by a nonlinear observer, such as the EKF, and then the estimated states of the robot could be substituted into the GRF Eqs. (2)–(7) to obtain the GRF estimates. However, this approach would be less flexible than the approach that we are using. Augmenting the GRF states onto the original state as in Eq. (8) allows us additional tuning flexibility in the artificial process noise that is included in the augmented states, as we will see in Sec. 5.
Extended Kalman Filtering for Robot/Prosthesis State Estimation
The Stability of the Extended Kalman Filter
The analysis of the stability properties of continuous-time extended Kalman filters is complex and has been treated only for especial cases. Safonov and Athans considered the stability of the constant and modified gain EKF. The boundedness of the EKF estimates were investigated when used as a parameter estimator for linear systems [29,30]. Reif et al. [31,32] determined that the estimation error in both the discrete and continuous-time EKF is exponentially bounded under certain conditions. They showed that the estimation error remains bounded if the initial estimation error and disturbances are sufficiently small and the nonlinear system satisfies a detectability rank condition [33,34]. Here, we extend Reif's work to obtain the stability conditions of the state estimator of the robot/prosthesis system. The main purpose of this section is to derive the stability of the estimator in terms of initial condition errors and disturbances.
In stability theory, there are two commonly used methods to prove boundedness: supermartingales for stochastic differential equations, and Lyapunov functions for deterministic differential equations. Supermartingales can be regarded as the stochastic equivalent of Lyapunov functions in some cases . In order to analyze the error dynamics of the EKF, we first present some preliminary results [31,35]. Note that represents the spectral norm of a matrix or the Euclidian norm of a vector.
Proof of Lemma 4.1. See Appendix A.
- (i)There exist p1, p2, c1, c2, q1, q2, r1, r2 such that the following bounds hold for every :(31)(32)(33)(34)
- (ii)There exist , εx, such that the nonlinear functions in Eq. (26) are bounded by(35)for x, and with and , respectively.(36)
Proof of Theorem 4.1. See Appendix B.
If f and h are twice differentiable with respect to x for every , the spectral norm of the Hessian matrices of fi and hi are bounded, where fi and hi are the components of f and h, respectively (see Refs. and [38, Chap. 7]). In the given robot/prosthesis system, the Hessian matrix of f is not a function of control input u.
Note that the nonlinear system has to be uniformly detectable in order to satisfy the boundedness condition of Eq. (31) [39,40]. The detectability of the nonlinear system results in the boundedness of the estimation error bounds for the solution P(t) of the Riccati differential equation (15) based on Eq. (31). We present the following definition for the detectability of nonlinear stochastic systems .
holds for all x, , where λm is the maximum eigenvalue of .
where differs from x(0) due to random initial state estimation errors, denotes the discretization step size with , Q and R represent continuous-time noise covariances, and Qd and Rd represent discrete-time noise covariances [27, Chap. 8]. The process noise represents small values of unmodeled dynamics and parameter uncertainties. The Q matrix is chosen based on prior experience with the accuracy of system dynamic modeling; the last four elements of the diagonal matrix Q are zero since the GRF model is assumed to be perfectly known. The R matrix is usually straightforward to determine on the basis of our knowledge of the accuracy of the measurement system.
Reduced Sensor Sets and Unscented Kalman Filtering.
In a real-world scenario, it would not be practical to use a hip displacement sensor on an amputee because of its invasiveness. The other sensors—thigh angle, knee angle, and ankle angle—can easily be used in the real world because they can be mounted on the prosthesis. In this paper, we use a hip displacement sensor to provide a baseline scenario for the reduced sensor sets, which we study later in this section.
More observations result in more accurate state estimation. However, our goal is to use the fewest possible number of sensors for estimation, which result in a reduction of complexity and cost in the prosthesis hardware. Here, we remove the hip displacement sensor and use only three measurements: the thigh, knee, and ankle angles. For our final test in this section, we will use only two measurements: the knee and ankle angles. Moreover, we will also compare the performance of the EKF and UKF for the state and GRF estimation. We use the same initial values for state and estimated state as used in the EKF for normal walking. We also test the performance of the filters with different gait speeds, and we will see that no extra filter tuning is needed for fast and slow walking.
The original discrete-time form of the UKF has been widely used for state estimation of discrete-time systems. However, the discrete-time UKF cannot be directly applied to continuous-time filtering problems, in which the process and measurement equations are modeled as continuous-time stochastic systems. In Ref. , the continuous-time UKF was derived from the discrete-time UKF in matrix form, and this is the algorithm that we implement here. The tuning parameters in the unscented transforms were chosen to be , β = 2, and .
Table 1 compares the accuracy of EKF state estimation in terms of the RMSE in three different gait modes (fast walk, normal walk, slow walk). The EKF works well for different walking speeds with a reduced measurement set. It can be seen, as expected, that for all three walking speeds, the estimation errors with four measurements are smaller than with three or two measurements.
Table 2 shows that the UKF achieves smaller RMS estimation errors than the EKF for almost all measurement sets and walking speeds. Table 3 summarizes the average performance of the EKF and UKF. We see that the UKF achieves 30% improvement in the average RMSE of GRFs with four measurements. Although the UKF performs better than the EKF, its computational effort is between two and three times that of the EKF in terms of the number of multiplications and additions .
Stability of the Extended Kalman Filter.
It has been shown that the estimation error in the continuous-time Kalman filter remains bounded under certain conditions. Small initial estimation errors and small noise magnitudes are required conditions to obtain error bounds. In this section, we study the stability of the state estimates of the robot/prosthesis system. First, we need to check that the Jacobian matrices in the robot/prosthesis system satisfy the uniform detectability condition of Definition 4.1. To find an appropriate , we assume that and solve for . Note that with our measurement system, is an identity matrix and is thus invertible. Therefore, the uniform detectability condition of Definition 4.1 is satisfied in the robotic/prosthesis system. To test the stability of the robotic/prosthesis EKF, the initial value and the measurement and process noise covariances R, Q are chosen as shown in Table 4, where
is a reasonably accurate initial condition for the state estimate, and we will see that it is good enough to ensure convergence of the EKF. is a significantly worse initial condition for the state estimate, and we will see that it is not good enough to ensure convergence of the EKF. The R and Q values in Table 4 have been chosen to demonstrate conditions that, respectively, ensure, or do not ensure, EKF convergence. These values for , and R and Q were chosen by trial and error to demonstrate their effect on EKF convergence.
The simulation results are presented in Figs. 5–7, where the unknown state in Eq. (8) (angular velocity of thigh), the estimated state , and its estimation error are plotted. We can see in Fig. 5 that for small initial estimation error and small noise, the estimation error is bounded. However, Figs. 6 and 7 show that for large initial estimation errors or large noise magnitudes, the estimation error is no longer bounded.
Extensive simulation tests show that boundedness of the estimation error is obtained in the numerical simulation if and . The theoretical results for ε and δ via Eqs. (B21) and (B24) from Appendix B yield smaller bounds for stability: and with . Since the estimation error does not diverge in practice even with larger initial condition errors and noise terms than those given by the theorem, we conclude that the bounds are very conservative in this system. However, we note that it is not possible to test all possible conditions that exceed the theoretical error bounds; therefore, we naturally expect the theoretical results to yield more conservative stability bounds than the simulation results.
We want the state to be estimated as accurately as possible for eventual implementation in a state-feedback controller. The controller that we used in this research is robust to estimation errors , although more accurate state estimates are always desirable in order to reduce controller errors. We have not explored the relationship between estimation error and controller error in this paper but leave it as an important area for future research.
Conclusion and Future Work
We designed an EKF and an UKF to estimate not only the states of a robot/prosthesis system but also the external forces acting on the prosthetic foot. This approach removes the need for heavy and bulky load cells that are otherwise needed for GRF estimation. We achieved satisfactory estimation errors in various gait speeds for the robot/prosthesis system using four, three, and two measurements. The average RMS estimation errors of the EKF for the thigh, knee, and ankle angles in normal walking with four measurements is 0.0033 rad, in comparison with that the UKF which is 0.0020 rad. Although the UKF outperforms the EKF, it requires more computational effort than the EKF, which will be a consideration for real-time implementation.
We proved mathematically that the estimation error in the EKF is exponentially bounded if the initial estimation errors and disturbances are sufficiently small and if the nonlinear system satisfies a detectability rank condition. In simulation tests, we verified that the estimation errors remained bounded for small initial estimation errors and small disturbances. However, the filter is unstable if the initial estimation errors or disturbances are too large.
As far as we know, the present research is the first time that GRF has been estimated for prostheses using state estimation techniques. As we noted in the introduction, some other methods have been used for external force estimation in robotics. For instance, achieved a 1.72% estimation error for a 4DOF robot, compared to our results, which show a 1.85% error when using the EKF with four sensors during normal walking. Our results are, therefore, quantitatively similar to Ref. , although the comparison may not be fair since the robotic systems in the two approaches are much different. Other publications in the area of external force estimation do not include quantitative results [10,11,13].
Future work will include increasing and verifying the robustness of the filters, and experimental implementation and verification of the EKF and UKF, first on robotic hardware and then in human trials.
• NSF Grant No. 1344954.
In summary, the assumptions of Lemma 4.1 Eqs. (27) and (28) are satisfied by Eqs. (B3) and (B22), where and . We conclude that the estimation error is exponentially bounded in mean square under the conditions in Eqs. (37)–(39).
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510994.61/warc/CC-MAIN-20231002100910-20231002130910-00188.warc.gz
|
CC-MAIN-2023-40
| 22,843 | 49 |
https://rd.springer.com/chapter/10.1007/978-3-662-14148-9_16
|
math
|
Resonance Phenomena Induced by Correlated Parametric Noise
The phenomenon of stochastic resonance (SR) has been of broad interest in many different fields and has been observed experimentally in different areas going from physics to biology. Standard SR is the result of the cooperative effect of noise and a periodic driving force acting upon a bistable system, in which the response of the system is enhanced for a particular value of the noise strength. Recently it has been proved numerically that SR can also occur in the absence of an external periodic force as a consequence of the intrinsic dynamics of the nonlinear system. In this work we study the free external force discrete system X n+1 = p n X n (1 − X n − 1) where the control parameter is subject to a parametric noise p n = p + ζ n being ζ n an Ornstein-Uhlenbeck process with zero mean and exponential correlation, τ. In the vicinity of a Hopf bifurcation (p > pH) the system shows an stochastic resonancelike SNR response, but this appears as a function of τ instead of the usually considered noise intensity, σ. There is a particular correlation time, τ r , for which the signal to noise ratio (SNR) shows a maximum. It is observed that for τ r the frequency of the system’s time series is as similar as possible to the corresponding deterministic frequency (ω d (p)). This noise induced stochastic enhancement is observed when p is close to the bifurcation value and is not obtained when the SNR response is studied as a function of σ. This resonant behavior is qualitatively understood as determined by the time of permanence of the system around the limit cycle which imposes a compromise between τ and the deterministic convergence time to the stable oscillatory state. Our results show that there is a particular τ for which this coherence is optimized, indicating that the system selects in mean a particular orbit. This idea is reinforced by the results obtained for p > pH in which τ r appear shifted towards smaller values as also happens with the deterministic convergence time. We think that this behavior could be observed in other systems where a multiplicative colored random perturbation moves the control parameter through a Hopf bifurcation region. Preliminary results indicate the same kind of resonant response in other nonlinear discrete systems.
KeywordsHopf Bifurcation Noise Intensity Stochastic Resonance Parametric Noise Resonance Phenomenon
- Moss F., Bulsara A. and Shlesinger F. (1993): Proceedings of the NATO Advanced Workshop on Stochastic Resonance in Physics and Biology J. Stat. Phys. 70.Google Scholar
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591296.46/warc/CC-MAIN-20180719203515-20180719223515-00608.warc.gz
|
CC-MAIN-2018-30
| 2,625 | 4 |
https://nursingpaperspros.com/subject-finance-tabletop-ranches-inc-is-considering-the-purchase-of-a-new-helicopter-for-325000-the-firms-old-helicopter-has-a-book-value-of-2/
|
math
|
- Tabletop Ranches, Inc. is considering the purchase of a new helicopter for $325,000. The firm’s old helicopter has a book value of $85,000 but can only be sold for $60,000. The new helicopter will be subject to 25% CCA. It is expected to save $62,000 for 7 years after taxes through reduced fuel and maintenance expenses. Tabletop Ranch is in the 40% tax bracket and has a 12% cost of capital. Calculate the net present value of the helicopter purchase and state whether or not the firm should buy it.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991772.66/warc/CC-MAIN-20210517115207-20210517145207-00454.warc.gz
|
CC-MAIN-2021-21
| 505 | 1 |
http://www.slimy.com/~steuard/research/MITClub2004/slide28.html
|
math
|
As in our first discussion of extra dimensions, it can be helpful to imagine the analogy of a tightrope. Think of the strings as little rubber bands stuck on the surface of the tightrope (but able to slide freely along it). If they don't wrap all the way around it, they will contract down as close to zero size as their vibrations will allow. But if they do wrap around the circle, they can't contract any smaller than its radius. Stretching around that way carries energy, and as usual the energy will appear in our equations as an effective mass.
As mentioned earlier, string theory only turns out to be self-consistent in a certain number of dimensions. (Technically, there are a ways to formulate the theory with different numbers of extra dimensions or without them entirely, but the alternatives are even less like the observed world. Unfortunately, explaining any of this would take us too far afield.) The 26 dimensions required by "bosonic" string theory include time, so that means 25 dimensions of space instead of the three that we're familiar with. (And superstring theory describes "only" nine dimensions of space.) It is very significant that the theory predicts a number at all! Most theories of physics are either well-defined in any dimension (like general relativity or the standard model) or are specifically designed with a certain dimension in mind. Even though string theory's specific predictions look wrong at first, they are still a step in the right direction.
And as we have seen, the presence of extra dimensions does not immediately rule out the theory: as long as they are small enough, our experiments might not have seen them. To make the meaning of "small" precise, an important first step is to require that they be "finite"—that they don't go on forever like the three dimensions that we normally see. (If they did, we'd almost certainly see them!) In precise mathematical language, a set of extra dimensions that is finite in this sense is called a "compact manifold". We will stick to the simple case where the extra dimensions are circles, though there are many other possibilities.
One important observation is that when closed strings in extra dimensions interact with each other by joining and splitting apart, their "winding number" is conserved. For example, if you start with a string that winds twice around the circle, it could split into two strings that each wind around the circle once, but the total number of windings is still two. (Remember that the strings are "oriented": they know which direction they are wound. So in this example the string could also split into a string wound three times and a string wound "-1" times: once in the other direction.)
As a final technical note, in the equations on the bottom half of this slide I have finally dropped the factors of c and h-bar to reduce clutter. If you keep careful track of units in the equation for the energy spectrum, you can put those constants back in by finding the unique way to make each term have units of "energy2".
The symmetry between momentum level and winding number in this energy spectrum is a surprise, but it turns out to be much more than a coincidence...
Up to my research page.
Up to my professional page.
My personal site is also available.
Any questions or comments? Write to me: [email protected]
Copyright © 2004 by Steuard Jensen.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119637.34/warc/CC-MAIN-20170423031159-00436-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 3,370 | 11 |
https://www.physicsforums.com/threads/find-gravitational-potential-inside-uniform-ball.546090/
|
math
|
Find the potential and force on a mass m outside and inside the Earth in terms of g, the acceleration due to gravity, assuming Earth has uniform density and radius R.
For a mass m, the potential energy of it in the gravitational field of a spherical shell of radius r' and uniform mass distribution m' is given by
γ=const. if m is inside the shell
γ=-Cm'/r if m is outside the shell, where r is the distance from the center of the sphere to the mass and C is a constant
It has the answers provided,
As a hint, to find the constants, when r=R, F=mg.
The Attempt at a Solution
I managed to get the first part outside the earth, though whether or not the method I used is legitimate I don't know.
I integrated from 0 to R [itex]\int-Cm'/rdr'[/itex] to find the total potential β=-CMR/r, where M is the mass of the Earth (integrating from 0 to R, the sum of the masses of the shells will total M). Taking the negative gradient to find the force, I find F=-CMR/r^2er. At r=R, F=mg, so C=mgR/M. β=-mgR^2/r and F=-mgR^2/r^2er
Getting the inside potential is a little more difficult. I know that it involves integrating from 0 to r [itex]\int-Cm'/rdr'[/itex] and maybe r to R [itex]\int Adr'[/itex]. I've tried two separate methods, where the second term was the integral as above and the second as just a constant in itself. I do know that at r=R, both inside/outside forces and inside/outside potentials should be equal, but neither attempt yielded anything remotely similar to the answer provided in the problem.
Since the method I used in part 1 didn't work for this, I believe it is at least partly a fluke.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224655244.74/warc/CC-MAIN-20230609000217-20230609030217-00367.warc.gz
|
CC-MAIN-2023-23
| 1,608 | 11 |
https://getmybooks.com/search?f=33554453&f=33554437&h=2&
|
math
|
Olympiad previous years? papers book for IMO, Class ? 7 is a thoughtful guide explicitly created for exceptional minds and IMO Olympiad aspirants 2023-24. The SOF IMO exam papers will undoubtedly help students understand the SOF International Mathematics Olympiad pattern. The books contain 10 previous years? papers from Sets A and B (2022-2018), 2 model test papers, answer keys with explanations for all questions, sample OMR sheets after each paper, and chapter-by-chapter analysis for all papers.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100551.2/warc/CC-MAIN-20231205140836-20231205170836-00526.warc.gz
|
CC-MAIN-2023-50
| 501 | 1 |
https://www.arxiv-vanity.com/papers/hep-th/0008140/
|
math
|
On the Holographic Principle in
[.8cm] a Radiation Dominated Universe
Joseph Henry Laboratories Princeton University
Princeton, New Jersey 08544
The holographic principle is studied in the context of a dimensional radiation dominated closed Friedman-Robertson-Walker (FRW) universe. The radiation is represented by a conformal field theory with a large central charge. Following recent ideas on holography, it is argued that the entropy density in the early universe is bounded by a multiple of the Hubble constant. The entropy of the CFT is expressed in terms of the energy and the Casimir energy via a universal Cardy formula that is valid for all dimensions. A new purely holographic bound is postulated which restricts the sub-extensive entropy associated with the Casimir energy. Unlike the Hubble bound, the new bound remains valid throughout the cosmological evolution. When the new bound is saturated the Friedman equation exactly coincides with the universal Cardy formula, and the temperature is uniquely fixed in terms of the Hubble parameter and its time-derivative.
The holographic principle is based on the idea that for a given volume the state of maximal entropy is given by the largest black hole that fits inside . ’t Hooft and Susskind argued on this basis that the microscopic entropy associated with the volume should be less than the Bekenstein-Hawking entropy
of a black hole with horizon area equal to the surface area of the boundary of . Here the dependence on Newton’s constant is made explicit, but as usual and are set to one.
To shed further light on the holographic principle and the entropy bounds derived from it, we study in this paper the standard cosmology of a closed radiation dominated Friedman-Robertson-Walker (FRW) universe with general space-time dimension
The metric takes the form
where represents the radius of the universe at a given time and is a short hand notation for the metric on the unit -sphere . Hence, the spatial section of a d closed FRW universe is an -sphere with a finite volume
The holographic bound is in its naive form (1) not really applicable to a closed universe, since space has no boundary. Furthermore, the argumentation leading to (1) assumes that it’s possible to form a black hole that fills the entire volume. This is not true in a cosmological setting, because the expansion rate of the universe as well as the given value of the total energy restrict the maximal size of black hole. As will be discussed in this paper, this will lead to a modified version of the holographic bound.
The radiation in an FRW universe is usually described by free or weakly interacting mass-less particles. More generally, however, one can describe the radiation by an interacting conformal field theory (CFT). The number of species of mass-less particles translates into the value of the central charge of the CFT. In this paper we will be particularly interested in radiation described by a CFT with a very large central charge. In a finite volume the energy has a Casimir contribution proportional to . Due to this Casimir effect, the entropy is no longer a purely extensive function of and . The entropy of a d CFT is given by the well-known Cardy formula
where represents the product of the energy and radius, and the shift of is caused by the Casimir effect. In this paper we show that, after making the appropriate identifications for and , the same Cardy formula is also valid for CFTs in other dimensions. This is rather surprising, since the standard derivation of the Cardy formula based on modular invariance only appears to work for . By defining the central charge in terms of the Casimir energy, we are able to argue that the Cardy formula is universally valid. Specifically, we will show that with the appropriate identifications, the entropy for a dimensional CFT with an AdS-dual is exactly given by (3).
The main new result of this paper is the appearance of a deep and fundamental connection between the holographic principle, the entropy formulas for the CFT, and the FRW equations for a radiation dominated universe. In dimensions the FRW equations are given by
where is the Hubble parameter, and the dot denotes as usual differentiation with respect to the time . The FRW equations are usually written in terms of the energy density , but for the present study it is more convenient to work with the total energy and entropy instead of their respective densities and . Note that the cosmological constant has been put to zero; the case will be described elsewhere .
Entropy and energy momentum conservation together with the equation of state imply that and decrease in the usual way like . Hence, the cosmological evolution follows the standard scenario for a closed radiation dominated FRW universe. After the initial Big Bang, the universe expands until it reaches a maximum radius, the universe subsequently re-collapses and ends with a Big Crunch. No surprises happen in this respect.
The fun starts when one compares the holographic entropy bound with the entropy formulas for the CFT. We will show that when the bound is saturated the FRW equations and entropy formulas of the CFT merge together into one set of equation. One easily checks on the back of an envelope that via the substitutions
the Cardy formula (3) exactly turns into the dimensional Friedman equation (4). This observation appears as a natural consequence of the holographic principle. In sections 2 and 3 we introduce three cosmological bounds each corresponding to one of the equations in (6) The Cardy formula is presented and derived in section 4. In section 5 we introduce a new cosmological bound, and show that the FRW equations and the entropy formulas are exactly matched when the bound is saturated. In section 6 we present a graphical picture of the entropy bounds and their time evolution.
2. Cosmological entropy bounds
This section is devoted to the description of three cosmological entropy bounds: the Bekenstein bound, the holographic Bekenstein-Hawking bound, and the Hubble bound. The relation with the holographic bound proposed by Fischler-Susskind and Bousso (FSB) will also be clarified.
2.1. The Bekenstein bound
Bekenstein was the first to propose a bound on the entropy of a macroscopic system. He argued that for a system with limited self-gravity, the total entropy is less or equal than a multiple of the product of the energy and the linear size of the system. In the present context, namely that of a closed radiation dominated FRW universe with radius , the appropriately normalized Bekenstein bound is
where the Bekenstein entropy is defined by
The bound is most powerful for relatively low energy density or small volumes. This is due to the fact that is super-extensive: under and it scales like .
For a radiation dominated universe the Bekenstein entropy is constant throughout the entire evolution, since . Therefore, once the Bekenstein bound is satisfied at one instance, it will remain satisfied at all times as long as the entropy does not change. The Bekenstein entropy is the most natural generalization of the Virasoro operator to arbitrary dimensions, as is apparent from (6). Indeed, it is useful to think about not really as an entropy but rather as the energy measured with respect to an appropriately chosen conformal time coordinate.
2.2. The Bekenstein-Hawking bound
The Bekenstein-bound is supposed to hold for systems with limited self-gravity, which means that the gravitational self-energy of the system is small compared to the total energy . In the current situation this implies, concretely, that the Hubble radius is larger than the radius of the universe. So the Bekenstein bound is only appropriate in the parameter range . In a strongly self-gravitating universe, that is for , the possibility of black hole formation has to be taken into account, and the entropy bound must be modified accordingly. Here the general philosophy of the holographic principle becomes important.
It follows directly from the Friedman equation (4) that
Therefore, to decide whether a system is strongly or weakly gravitating one should compare the Bekenstein entropy with the quantity
When the system is weakly gravitating, while for the self-gravity is strong. We will identify with the holographic Bekenstein-Hawking entropy of a black hole with the size of the universe. indeed grows like an area instead of the volume, and for a closed universe it is the closest one can come to the usual expression .
As will become clear in this paper, the role of is not to serve as a bound on the total entropy, but rather on a sub-extensive component of the entropy that is association with the Casimir energy of the CFT. The relation (6) suggests that the Bekenstein-Hawking entropy is closely related to the central charge . Indeed, it is well-known from CFT that the central charge characterizes the number of degrees of freedom may be even better than the entropy. This fact will be further explained in sections 5 and 6, when we describe a new cosmological bound on the Casimir energy and its associated entropy.
2.3. The Hubble entropy bound
The Bekenstein entropy is equal to the holographic Bekenstein-Hawking entropy precisely when . For one has and the Bekenstein bound has to be replaced by a holographic bound. A naive application of the holographic principle would imply that the total entropy should be bounded by . This turns out to be incorrect, however, since a purely holographic bound assumes the existence of arbitrarily large black holes, and is irreconcilable with a finite homogeneous entropy density.
Following earlier work by Fischler and Susskind , it was argued by Easther and Lowe , Veneziano , Bak and Rey , Kaloper and Linde , that the maximal entropy inside the universe is produced by black holes of the size of the Hubble horizon, see also . Following the usual holographic arguments one then finds that the total entropy should be less or equal than the Bekenstein-Hawking entropy of a Hubble size black hole times the number of Hubble regions in the universe. The entropy of a Hubble size black hole is roughly , where is the volume of a single Hubble region. Combined with the fact that one obtains an upper bound on the total entropy given by a multiple of . The presented arguments of [6, 8, 9, 7] are not sufficient to determine the precise pre-factor, but in the following subsection we will fix the normalization of the bound by using a local version of the Fischler-Susskind-Bousso formulation of the holographic principle. The appropriately normalized entropy bound takes the form
The Hubble bound is only valid for . In fact, it is easily seen that for the bound will at some point be violated. For example, when the universe reaches its maximum radius and starts to re-collapse the Hubble constant vanishes, while the entropy is still non-zero.111To avoid this problem a different covariant version of the Hubble bound was proposed in . This should not really come as a surprise, since the Hubble bound was based on the idea that the maximum size of a black hole is equal to the Hubble radius. Clearly, when the radius of the universe is smaller than the Hubble radius one should reconsider the validity of the bound. In this situation, the self-gravity of the universe is less important, and the appropriate entropy bound is
2.4. The Hubble bound and the FSB prescription.
Fischler, Susskind, and subsequently Bousso , have proposed an ingenious version of the holographic bound that restricts the entropy flow through contracting light sheets. The FSB-bound works well in many situations, but, so far, no microscopic derivation has been given. Wald and collaborators have shown that the FSB bound follows from local inequalities on the entropy density and the stress energy. The analysis of suggests the existence a local version of the FSB entropy bound, one that does not involve global information about the causal structure of the universe, see also . The idea of to formulate the holographic principle via entropy flow through light sheets also occurred in the work of Jacobson , who used it to derive an intriguing relation between the Einstein equations and the first law of thermodynamics. In this subsection, a local FSB bound will be presented that leads to a precisely normalized upper limit on the entropy in terms of the Hubble constant.
According to the original FSB proposal, the entropy flow through a contracting light sheet is less or equal to , where is the area of the surface from which the light sheet originates. The following infinitesimal version of this FSB prescription will lead to the Hubble bound. For every dimensional surface at time with area one demands that
where denotes the entropy flow through the infinitesimal light sheets originating at the surface at and extending back to time , and represents the increase in area between and . For a surface that is kept fixed in co-moving coordinates the area changes as a result of the Hubble expansion by an amount
where the factor simply follows from the fact that . Now pick one of the two past light-sheets that originate at the surface: the inward or the outward going. The entropy flow through this light-sheet between and is given by the entropy density times the infinitesimal volume swept out by the light-sheet. Hence,
By inserting this result together with (15) into the infinitesimal FSB bound (14) one finds that the factor cancels on both sides and one is left exactly with the Hubble bound with the Hubble entropy given in (12). We stress that the relation with the FSB bound was merely used to fix the normalization of the Hubble bound, and should not be seen as a derivation.
3. Time-evolution of the entropy bounds.
Let us now return to the three cosmological entropy bounds discussed in section 2. The Friedman equation (4) can be re-written as an identity that relates the Bekenstein-, the Hubble-, and the Bekenstein-Hawking entropy. One easily verifies that the expressions given in (8), (10), and (12) satisfy the quadratic relation
It is deliberately written in a Pythagorean form, since it suggests a useful graphical picture of the three entropy bounds. By representing each entropy by a line with length equal to its value one finds that due to the quadratic Friedman relation (17) all three fit nicely together in one diagram, see figure 1. The circular form of the diagram reflects the fact that is constant during the cosmological evolution. Only and depend on time.
Let us introduce a conformal time coordinate via
and let us compute the -dependence of and . For this easily follows from: . For the calculation is a bit more tedious, but with the help of the FRW equations, the result can eventually be put in the form
These equations show that the conformal time coordinate can be identified with the angle , as already indicated in figure 1. As time evolves the Hubble entropy rotates into the combination and visa versa. Equation (S3.Ex5) can be integrated to
The conformal time coordinate plays the role of the time on a cosmological clock that only goes around once: at time starts with a Big Bang and at it ends with a Big Crunch. Note that is related to the parameter via
So far we have not yet included the CFT into our discussion. We will see that the entropy of the CFT will ‘fill’ part of the diagram, and in this way give rise to a special moment in time when the entropy bounds are saturated.
4. Casimir energy and the Cardy formula
We now turn to the discussion of the entropy of the CFT that lives inside the FRW universe. We begin with a study of the finite temperature Casimir energy with the aim to exhibit its relation with the entropy of the CFT. Subsequently a universal Cardy formula will be derived that expresses the entropy in terms of the energy and the Casimir energy, and is valid for all values of the spatial dimension .
4.1. The Euler relation and Casimir energy.
In standard textbooks on cosmology [15, 16] it is usually assumed that the total entropy and energy are extensive quantities. This fact is used for example to relate the entropy density to the energy density and pressure , via . For a thermodynamic system in finite volume the energy , regarded as a function of entropy and volume, is called extensive when it satisfies Differentiating with respect to and putting leads to the Euler relation111We assume here that there are no other thermodynamic functions like a chemical or electric potential. For a system with a 1st law like the Euler relation reads .
The first law of thermodynamics can now be used to re-express the derivatives via the thermodynamic relations
The resulting equation is equivalent to the previously mentioned relation for the entropy density .
For a CFT with a large central charge the entropy and energy are not purely extensive. In a finite volume the energy of a CFT contains a non-extensive Casimir contribution proportional to . This is well known in dimensions where it gives rise to the familiar shift of in the Virasoro operator. The Casimir energy is the result of finite size effects in the quantum fluctuations of the CFT, and disappears when the volume becomes infinitely large. It therefore leads to sub-extensive contributions to the total energy . Usually the Casimir effect is discussed at zero temperature , but a similar effect occurs at finite temperature. The value of the Casimir energy will in that case generically depend on the temperature .
We will now define the Casimir energy as the violation of the Euler identity (22)
Here we inserted for convenience a factor equal to the spatial dimension . From the previous discussion it is clear that parameterizes the sub-extensive part of the total energy. The Casimir energy will just as the total energy be a function of the entropy and the volume . Under and it scales with a power of that is smaller than one. On general grounds one expects that the first subleading correction to the extensive part of the energy scales like
One possible way to see this is to write the energy as an integral over a local density expressed in the metric and its derivatives. Derivatives scale like and because derivatives come generally in pairs, the first subleading terms indeed has two additional factors of . The total energy may be written as a sum of two terms
where the first term denotes the purely extensive part of the energy and represents the Casimir energy. Again the factor has been put in for later convenience. By repeating the steps that lead to the Euler relation one easily verifies the defining equation (24) for the Casimir energy .
4.2. Universality of the Cardy formula and the Bekenstein bound
Conformal invariance implies that the product is independent of the volume , and is only a function of the entropy . This holds for both terms and in (26). Combined with the known (sub-)extensive behavior of and this leads to the following general expressions
where and are a priori arbitrary positive coefficients, independent of and . The factors of and are put in for convenience. With these expressions, one now easily checks that the entropy can be written as
If we ignore for a moment the normalization, this is exactly the Cardy formula: insert and , and one recovers (3). It is obviously an interesting question to compute the coefficients and for various known conformal invariant field theories. This should be particularly straightforward for free field theories, such as Maxwell theory and the self-dual tensor theory in . This question is left for future study.
Given the energy the expression (27) has a maximum value. For all values of , and one has the inequality
This looks exactly like the Bekenstein bound, except that the pre-factor is in general different from the factor used in the previous section. In fact, in the following subsection we will show that for CFTs with an AdS-dual description, the value of the product is exactly equal to , so the upper limit is indeed exactly given by the Bekenstein entropy. Although we have no proof of this fact, we believe that the Bekenstein bound is universal. This implies that the product for all CFTs in dimensions is larger or equal than . Only then it is guaranteed that the upper limit on the entropy is less or equal than .
The upper limit is reached when the Casimir energy is equal to the total energy . Formally, when becomes larger that the entropy will again decrease. Although in principle this is possible, we believe that in actual examples the Casimir energy is bounded by the total energy . So, from now on we assume that
In the next subsection we provide further evidence for this inequality.
From now on we will assume that we are dealing with a CFT for which . In the next section I will show that this includes all CFTs that have an AdS-dual description.
4.3. The Cardy formula derived from AdS/CFT
Soon after Maldacena’s AdS/CFT-correspondence was properly understood [19, 20] it was convincingly argued by Witten that the entropy, energy and temperature of CFT at high temperatures can be identified with the entropy, mass, and Hawking temperature of the AdS black hole previously considered by Hawking and Page . Using this duality relation the following expressions can be derived for the energy and entropy222These expressions differ somewhat from the presented formulas in due to the fact that (i) the dimensional Newton constant has been eliminated using its relation with the central charge, (ii) the coordinates have been re-scaled so that the CFT lives on a sphere with radius equal to the black hole horizon. We will not discuss the AdS perspective in this paper, since the essential physics can be understood without introducing an extra dimension. The discussion of the CFT/FRW cosmology from an AdS perspective will be described elsewhere . for a dimensional CFT on :
The temperature again follows from the first law of thermodynamics. One finds
The length scale of the thermal CFT arises in the AdS/CFT correspondence as the curvature radius of the AdS black hole geometry. The expression for the energy clearly exhibits a non-extensive contribution, while also the temperature contains a corresponding non-intensive term. Inserting the equations (29,30) into (24) yields the following result for the Casimir energy
Now let us come to the Cardy formula. The entropy , energy and Casimir energy are expressed in , and . Eliminating and leads to a unique expression for in terms of , and . One easily checks that it takes the form of the Cardy formula
In the derivation of these formulas it was assumed that . One may worry therefore that these formulas are not applicable in the early universe. Fortunately this is not a problem because during an adiabatic expansion both and scale in the same way so that is fixed. Hence the formulas are valid provided the (fixed) ratio of the thermal wave-length and the radius is much smaller than one. Effectively this means, as far as the CFT is concerned, we are in a high temperature regime. We note further that with in this parameter range, the Casimir energy is indeed smaller than the total energy .
Henceforth, we will assume that the CFT that describes the radiation in the FRW universe will have an entropy given by (32) with the specific normalization of . Note that if we take and make the previously mentioned identifications and that this equation exactly coincides with the usual Cardy formula. We will therefore in the following refer to (32) simply as the Cardy formula. To check the precise coefficient of the Cardy formula for a CFT we have made use of the AdS/CFT correspondence. The rest of our discussions in the preceding and in the following sections do not depend on this correspondence. So, in this paper we will not make use of any additional dimensions other than the ones present in the FRW-universe.
5. A new cosmological bound
In this section a new cosmological bound will be presented, which is equivalent to the Hubble bound in the strongly gravitating phase, but which unlike the Hubble bound remains valid in the phase of weak self-gravity. When the bound is saturated the FRW equations and the CFT formulas for the entropy and Casimir energy completely coincide.
5.1. A cosmological bound on the Casimir energy
Let us begin by presenting another criterion for distinguishing between a weakly or strongly self-gravitating universe. When the universe goes from the strongly to the weakly self-gravitating phase, or vice-versa, the Bekenstein entropy and the Bekenstein-Hawking entropy are equal in value. Given the radius , we now define the ‘Bekenstein-Hawking’ energy as the value of the energy for which and are exactly equal. This leads to the condition
One may interpret as the energy required to form a black hole with the size of the entire universe. Now, one easily verifies that
Hence, the universe is weakly self-gravitating when the total energy is less than and strongly gravitating for .
We are now ready to present a proposal for a new cosmological bound. It is not formulated as a bound on the entropy , but as a restriction on the Casimir energy . The physical content of the bound is the Casimir energy by itself can not be sufficient to form a universe-size black hole. Concretely, this implies that the Casimir energy is less or equal to the Bekenstein-Hawking energy . Hence, we postulate
To put the bound in a more conventional notation one may insert the definition (24) of the Casimir energy together with the defining relation (33) of the Bekenstein-Hawking energy. We leave this to the reader.
The virtues of the new cosmological bound are: (i) it is universally valid and does not break down for a weakly gravitating universe, (ii) in a strongly gravitating universe it is equivalent to the Hubble bound, (iii) it is purely holographic and can be formulated in terms of the Bekenstein-Hawking entropy of a universe-size black hole, (iv) when the bound is saturated the laws of general relativity and quantum field theory converge in a miraculous way, giving a strong indication that they have a common origin in a more fundamental unified theory.
The first point on the list is easily checked because decays like while goes like . Only when the universe re-collapses and returns to the strongly gravitating phase the bound may again become saturated. To be able to proof the other points on the list of advertised virtues, we have to take a closer look to the FRW equations and the CFT formulas for the entropy an entropy.
5.2. A cosmological Cardy formula
To show the equivalence of the new bound with the Hubble bound let us write the Friedman equation as an expression for the Hubble entropy in terms of the energy , the radius and the Bekenstein-Hawking energy . Here, the latter is used to remove the explicit dependence on Newton’s constant . The resulting expression is unique and takes the form
This is exactly the Cardy formula (32), except that the role of the Casimir energy in CFT formula is now replaced by the Bekenstein-Hawking energy . Somehow, miraculously, the Friedman equation knows about the Cardy formula for the entropy of a CFT!
With the help of (36) is now a straightforward matter to proof that when the new bound is equivalent to the Hubble bound . First, let us remind that for the energy satisfies . Furthermore, we always assume that the Casimir energy is smaller than the total energy . The entropy is a monotonically increasing function of as long as . Therefore in the range
the maximum entropy is reached when . In that case the Cardy formula (32) for exactly turns into the cosmological Cardy formula (36) for . Therefore, we conclude that is indeed the maximum entropy that can be reached when . Note that in the weakly self-gravitating phase, when , the maximum is reached earlier, namely for . The maximum entropy is in that case given by the bekenstein entropy . The bifurcation of the new bound in two entropy bounds is a direct consequence of the fact that the Hubble bound is written as the square-root of a quadratic expression.
5.3. A limiting temperature
So far we have focussed on the entropy and energy of the CFT and on the first of the two FRW equations, usually referred to as the Friedman equation. We will now show that also the second FRW equation has a counterpart in the CFT, and will lead to a constraint on the temperature . Specifically, we will find that the bound on implies that the temperature in the early universe is bounded from below by
The minus sign is necessary to get a positive result, since in a radiation dominated universe the expansion always slows down. Further, we assume that we are in the strongly self-gravitating phase with , so that there is no danger of dividing by zero.
The second FRW equation in (5) can now be written as a relation between , and that takes the familiar form
This equation has exactly the same form as the defining relation for the Casimir energy. In the strongly gravitating phase we have just argued that the bound is equivalent to the Hubble bound . It follows immediately that the temperature in this phase is bounded from below by . One has
When the cosmological bound is saturated all inequalities turn into equalities. The Cardy formula and the defining Euler relation for the Casimir energy in that case exactly match the Friedman equation for the Hubble constant and the FRW equation for its time derivative.
6. The entropy bounds revisited.
We now return to the cosmological entropy bounds introduced in sections 2 and 3. In particular, we are interested in the way that the entropy of the CFT may be incorporated in the entropy diagram described in section . For this purpose it will be useful to introduce a non-extensive component of the entropy that is associated with the Casimir energy.
The cosmological bound can also be formulated as an entropy bound, not on the total entropy, but on a non-extensive part of the entropy that is associated with the Casimir energy. In analogy with the definition of the Bekenstein entropy (8) one can introduce a ’Casimir’ entropy defined by
For the Casimir entropy is directly related to the central charge . One has . In fact, it is more appropriate to interpret the Casimir entropy as a generalization of the central charge to dimensions than what is usually called the central charge . Indeed, if one introduces a dimensionless ‘Virasoro operator’ and a new central charge , the dimensional entropy formula (32) is exactly identical to (3).
The Casimir entropy is sub-extensive because under and it goes like . In fact, it scales like an area! This is a clear indication that the Casimir entropy has something to do with holography. The total entropy contains extensive as well as sub-extensive contributions. One can show that for the entropy satisfies the following inequalities
where both equal signs can only hold simultaneously. The precise relation between and its super- and sub-extensive counterparts and is determined by the Cardy formula, which can be expressed as
This identity has exactly the same form as the relation (17) between the cosmological entropy bounds, except that in (17) the role of the entropy and Casimir entropy are taken over by the Hubble entropy and Bekenstein-Hawking entropy . This fact will be used to incorporate the entropy and the Casimir entropy in the entropy diagram introduce in section 3.
The cosmological bound on the Casimir energy presented in the section 4 can be formulated as an upper limit on the Casimir entropy . From the definitions of and it follows directly that the bound is equivalent to
where we made use of the relation (33) to re-write again in terms of the Bekenstein-Hawking entropy . Thus the bound puts a holographic upper limit on the d.o.f. of the CFT as measured by the Casimir entropy .
In figure 2 we have graphically depicted the quadratic relation between the total entropy and the Casimir entropy in the same diagram we used to related the cosmological entropy bounds. From this diagram it easy to determine the relation between the new bound and the Hubble bound. One clearly sees that when that the two bounds are in fact equivalent. When the new bound is saturated, which means , then the Hubble bound is also saturated, ie. . The converse is not true: there are two moments in the region when the , but . In our opinion, this is an indication that the bound on the Casimir energy has a good chance of being a truly fundamental bound.
7. Summary and conclusion
In this paper we have used the holographic principle to study the bounds on the entropy in a radiation dominated universe. The radiation has been described by a continuum CFT in the bulk. Surprisingly the CFT appears to know about the holographic entropy bounds, and equally surprising the FRW-equations know about the entropy formulas for the CFT. Our main results are summarized in the following two tables. Table 1. contains an overview of the bounds that hold in the early universe on the temperature, entropy and Casimir energy. In table 2. the Cardy formula for the CFT and the Euler relation for the Casimir energy are matched with the Friedman equations written in terms of the quantities listed in table 1.
Table 1: summary of cosmological bounds
Table 2: Matching of the CFT-formulas with the FRW-equations
The presented relation between the FRW equations and the entropy formulas precisely holds at this transition point, when the holographic bound is saturated or threatens to be violated. The miraculous merging of the CFT and FRW equations strongly indicates that both sets of these equations arise from a single underlying fundamental theory.
The discovered relation between the entropy, Casimir energy and temperature of the CFT and their cosmological counterparts has a very natural explanation from a RS-type brane-world scenario along the lines of . The radiation dominated FRW equations can be obtained by studying a brane with fixed tension in the background of a AdS-black hole. In this description the radius of the universe is identified with the distance of the brane to the center of the black hole. At the Big Bang the brane originates from the past singularity. At some finite radius determined by the energy of the black hole, the brane crosses the horizon. It keeps moving away from the black hole, until it reaches a maximum distance, and then it falls back into the AdS-black hole. The special moment when the brane crosses the horizon precisely corresponds to the moment when the cosmological entropy bounds are saturated. This world-brane perspective on the cosmological bounds for a radiation dominated universe will be described in detail in .
We have restricted our attention to matter described by a CFT in order to make our discussion as concrete and coherent as possible. Many of the used concepts, however, such as the entropy bounds, the notion of a non-extensive entropy, the matching of the FRW equations, and possibly even the Cardy formula are quite independent of the equation of state of the matter. One point at which the conformal invariance was used is in the diagrammatic representation of the bounds. The diagram is only circular when the energy goes like . But it is possible that a similar non-circular diagram exists for other kinds of matter. It would be interesting to study other examples in more detail.
Finally, the cosmological constant has been put to zero, since only in that case all of the formulas work so nicely. It is possible to modify the formalism to incorporate a cosmological constant, but the analysis becomes less transparent. In particular, one finds that the Hubble entropy bound needs to be modified by replacing with the square root of . At this moment we have no complete understanding of the case , and postpone its discussion to future work.
I like to thank T. Banks, M. Berkooz, S. Gubser, G. Horowitz, I. Klebanov, P. Kraus, E. Lieb, L. Randall, I. Savonije, G. Veneziano, and H. Verlinde for helpful discussions. I also thank the theory division at Cern for its hospitality, while this work was being completed.
- G. ’t Hooft, in Salamfestschift: a collection of talks, eds. A.Ali, J.Ellis, S.Randjbar-Daemi (World Scientific 1993), gr-qc/9321026; L. Susskind, J.Math.Phys. 36 (1995) 6337.
- J.L. Cardy, Nucl.Phys. B 270 (1986) 317.
- I. Savonije, and E. Verlinde, in preparation.
- J.D. Bekenstein, Phys.Rev.D23 (1981) 287, D49 (1994) 1912; Int.J.Theor.Phys.28 (1989) 967.
- W. Fischler and L. Susskind, hep-th/9806039
- R. Easther and D. Lowe, Phys. Rev. Lett. 82, 4967,(1999), hep-th/9902088.
- G. Veneziano, Phys.Lett B454 (1999), hep-th/9902126; hep-th/9907012.
- D. Bak and S.-J. Rey, hep-th/9902173
- N. Kaloper and A. Linde, Phys.Rev. D60 (1999), hep-th/9904120
- R. Brustein, gr-qc/9904061; R. Brustein, S. Foffa, and R. Sturani, hep-th/9907032.
- R. Brustein, G. Veneziano, Phys.Rev.Lett. 84 (2000) 5695. G. Veneziano, private communication.
- R. Bousso, JHEP 07 (1999) 004; JHEP 06 (1999) 028; hep-th/9911002.
- E.E. Flanagan, D. Marolf, and R.M. Wald, hep-th/9908070.
- T. Jacobson, Phys.Rev.Lett.75 (1995) 1260, gr-qc/9504004. (1948), 793.
- S. Weinberg, Gravitation and Cosmology, Wiley, (1972).
- E. Kolb, M. Turner, The Early Universe, Addison-Wesley (1990)
- H.B.G. Casimir, Proc.Kon.Ned.Akad.Wet.51,
- J. Maldacena, Adv.Theor.Math.Phys.2 (1998) 231, hep-th/9711200.
- S. Gubser, I. Klebanov and A. Polyakov, Phys.Lett.B428 (1998) 105, hep-th/9802109;
- E. Witten, Adv.Theor.Math.Phys.2 (1998) 253, hep-th/9802150.
- E. Witten, Adv.Theor.Math.Phys.2 (1998) 505, hep-th/9803131
- S.W. Hawking and D. Page, Commun.Math.Phys. 87 (1983) 577
- L. Randall and R. Sundrum, A Large Mass Hierarchy from a Small Extra Dimension, hep-ph/9905221; An Alternative to Compactification, hep-th/9906064.
- S. Gubser, AdS/CFT and gravity, hep-th/9912001.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389798.91/warc/CC-MAIN-20210309092230-20210309122230-00084.warc.gz
|
CC-MAIN-2021-10
| 37,880 | 140 |
https://fdocuments.net/document/pid-vs-fuzzy-control.html
|
math
|
PID vs Fuzzy Control
Embed Size (px)
Transcript of PID vs Fuzzy Control
Temperature control based on traditional PID versus fuzzy controllersIndustrial temperature-control applications demand speed and precision. Improved temperature controllers can meet these demands by adding features not found in traditional PID controllers but increase system complexity. Fuzzy temperature controllers give you another option.By Peter Galan, Control Software Designer, Nortel Networks
Common perception holds that temperature control is a mature and largely static area of technology. Some industrial applicationsfor example, injection-molding processesstill desire not only precise temperature control but also a faster warm-up phase and a quicker response to disturbances with minimal overshoot and undershoot when the set point changes. Traditional PID (proportional-integral-derivative) control techniques cannot meet these extra challenges. Figure 1 shows a continuous-time (analog) PID controller, typical for most closedloop control systems. Its output, the actuating value y(t), is a function of the regulation error e(t):
y (t ) = K P e(t ) + K I e(t )dt + K D
de(t ) . dt
The use of a standard PID controller is fully adequate for some applications. Such applications commonly feature low to moderate control-quality (timing, precision) constraints and well-defined and stable dynamic system behavior. Precision industrialtemperature control, however, does not belong among these standard applications. For example, injection-molding processes require fast changingreadjusting of controlled temperatures with minimal overshoot. In addition, heating processes do not exhibit stable dynamic behavior, because heating and cooling rates are different at each temperature set point. In addition, coupling between the zones of a multizone heating system makes dynamic behavior very unpredictable.
Heat-transfer-specific problemsFigure 2's simplified thermal model of a typical heating system ignores heattransport delays. Assume that when you switch on a constant power source, W, it powers an electrical heating element with a heat capacity, Ce. The temperature of the heating element, Te(t), rises with time, t. The heat continuously propagates, by direct conduction, to the heated system. Res represents a thermal resistance between the electrical element and the heated system, and Cs represents the heated systems thermal capacity. The system temperature, Ts(t), also rises with time. Rsa thus represents a thermal resistance between the heated system and surrounding environment (with ambient temperature Ta(t)), which tends to cool the system. Ideally, without any cooling from the outside (that is, Rsa ), both temperatures, Te(t) and Ts(t), would rise forever. In practice, however, natural cooling prevents this occurrence. So, after a certain time period, both temperatures stabilize at certain constant values. Figure 2's model represents a second-order system with the following transfer function:
G p (s ) =
K . 1 + sT1 + s 2T2
The PID controller would be an ideal controller, because its transfer function with two nulls could, at least theoretically, cancel both poles of Gp. Figure 2 demonstrates that two cascaded first-order systems can replace this second-order system. Therefore, in practice, system response to a step function will always be aperiodical, and if Res is relatively small, the output temperature will follow a simple exponential curve when rising or falling. For such systems, even PI controllers (without the derivative member) are fully adequate. An interesting feature of a typical heated system, which represents the first difficulty for any temperature controller, is that increasing the temperature a couple of degrees from the surrounding temperature takes substantially less time than does cooling down to the surrounding temperature. In contrast, increasing the temperature of the same system by a couple of degrees when it is close to its maximum temperature takes substantially longer than does bringing the temperature back down by a couple of degrees. At one temperature set point, the heating rate (the speed of heating up) and the cooling rate (the speed of cooling down) are equal. This set point is at the temperature that requires the application of exactly 50% of the maximum applicable power to the heater. What is that balanced temperature? Theoretically, from Figure 2's thermal model, the dependence between power (W) and temperature (Ts) should be linear. That is, the stabilized temperature corresponding to 50% of maximum power should be exactly in the middle between the minimum and maximum temperature. The assumption here is that the maximum reachable temperature requires 100% power, and the minimum (ambient) temperature requires you to apply 0% power to the heating element for an unlimited time. Figure 3 shows the above-described feature for three set points: One is close to the ambient temperature, one is at the balanced temperature, and one is close to the maximum temperature. Temperatures are rising and decreasing exponentially with different rates (time constants) for heating and cooling. The ratio of the rate of heating and cooling processes at any stage depends only on the value of the set point.
Enhancing the traditional PID controllerThe PID constants basically depend on the gain and time constant of the controlled system. If you select them properly, they will cancel poles of the controlled systemtransfer function. Different rates of the heating and cooling processes affect the optimal values of the PID constants, making their estimation very difficult. If you want to use autotuning, be aware that all autotuning methods provide only one set of PID constants, which will at best suit only the set points close to the balanced temperature. A different situation exists when the temperature set point is different from the balanced temperature. The farther the set point is from the balanced temperature, the farther the PID constants will be from their optimal values. Just how far depends on how far the set point is from the balanced temperature and whether the current temperature is below or above the set point. To make the PID controller suitable for temperature control at any set point, you need some automatic adaptation of the PID constants. Generally, all three PID constants, K P , K I , and K D , are inversely proportional to the rate of temperature change. Autotuning algorithms (known in control theory as the Ziegler-Nichols rules) also adhere to this rule. The rate of temperature change is not a linear function of the temperature set point (the derivative of exponential is also exponential), but a straight line is a rea-
sonable approximation (Figure 4). As Figure 4 shows, the rate (speed) of heating at the balanced temperature is 1/2, where is a time constant of the exponential (shown previously in Figure 3). At the ambient temperature, 1/ is the rate of heating. The rate of cooling at the ambient temperature is infinitesimally low. The opposite situation exists at the other end of the exponential curve, close to the maximum temperature. Here, the rate of heating is infinitesimally low, and the rate of cooling is very high. To compensate for varying heating and cooling rates, the PID constants, K P , K I ,
and K D , must also vary, requiring modification of the basic PID controller. Figure 5 shows the addition of two new blocks: an adapter and a heater model. The heater model must at first determine a value of the balanced temperature. For most applications, applying 50% of the maximum output power to the heating element and waiting until the temperature settles down is infeasible. Therefore, the control system can first assume that the balanced temperature equals one half of the maximum temperature (a value for which the controller has been designed). You can determine a more precise value of the balanced temperature during the control process. The adapter block (knowing the balanced and set-point temperatures) then calculates two correction coefficients for the modification of the PID constants. This calculation is based on a linear dependence of the temperature-change rate as shown in Figure 4. You apply the first correction coefficient, kh, (it multiplies the PID constants) during the heating and the other coefficient, kc, during cooling: kh TMAX/2(TMAX TSP), and kc TMAX/2TSP, where TMAX is the maximum controllable and TSP is the set point temperature.
Introducing a feedforward memberOnce you have created the heater model (which is actually an inverse static characteristic of the heating process), you can use its output variable power level as a feedforward contribution to the actuating variable. Because the heating process is linear (the output temperature is proportional to the applied power), a simple line with the slope km can approximate the heating model characteristic. You can then calculate an initial value of km as: km MAX_POWER / MAX_TEMPERATURE. You can express the MAX_POWER value in the percentage of the output pulse width if you use the PWM method to drive the heater elements. If you knew in advance what power value youd need for the set-point temperature, you could immediately replace the contribution of the controller's integral member with the output of the feedforward member. However, at the beginning of the control process, you would not have the correct heater model (the correct km value). Fortunately, the integral member can provide this information to the adapter block. So, this approach provides the adapter block with a new task. Once the temperature stabilizes at the set-point value, the adapter block can easily calculate the required output power to maintain this temperature. It is a sum of the integral member and the feedforward member outputs. Because the temperature is stabilized at the set point, the regulation error is zero, and the contributions of the propo
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362219.5/warc/CC-MAIN-20211202114856-20211202144856-00279.warc.gz
|
CC-MAIN-2021-49
| 9,965 | 16 |
https://dictionary.obspm.fr/index.php/?showAll=1&formSearchTextfield=Fourier+transform
|
math
|
Fr.: transformée de Fourier
A powerful mathematical tool which is the generalization of the → Fourier series for the analysis of non-periodic functions. The Fourier transform transforms a function defined on physical space into a function defined on the space of frequencies, whose values quantify the "amount" of each periodic frequency contained in the original function. The inverse Fourier transform then reconstructs the original function from its transformed frequency components. The integral F(α) = ∫ f(u)e-iαudu is called the Fourier transform of F(x) = (1/2π)∫ f(α)eiαxdx, both integrals from -∞ to + ∞.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100309.57/warc/CC-MAIN-20231202010506-20231202040506-00193.warc.gz
|
CC-MAIN-2023-50
| 629 | 2 |
https://project.inria.fr/rencontresljll/monday-17th-october-2022-visio-johnny-guzman-brown-university/
|
math
|
Title: Local L2 Bounded projections in finite element exterior calculus
Finite element exterior calculus (FEEC) is an elegant framework that uses a complex of finite elements in any spatial dimension and can approximate solutions to the Hodge-Laplacian. The finite element complex on simplicial meshes can be thought of as generalizations of the Nédélec finite elements to higher dimensions and as higher order polynomial generalizations to the Whitney forms. A chief tool in the analysis of FEEC for the Hodge-Laplacian are commuting bounded projections. There have been several such projections developed including the work of 1) Schoberl, 2) Christiansen and Winther, 3) Falk and Winther, 4) Ern, Gudi, Smears, Vohralk to name a few. In this work, we develop L2 bounded projections that are local. This is a joint work with Douglas Arnold.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817790.98/warc/CC-MAIN-20240421163736-20240421193736-00044.warc.gz
|
CC-MAIN-2024-18
| 844 | 2 |
https://math.answers.com/Q/What_divides_an_angle_into_two_congruent_angles
|
math
|
The answer is angle bisector.
An angle bisector.
A midpoint is a point that divides a segment into two congruent segments. A angle bisector is a ray that divides an angle into two congruent angles.
The answer to that is a bisector. The two angles formed by this has the same angle.
It is a bisector
An angle bisector.
Two angles that are congruent have the same angle measurement.
if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
the definition of an angle bisector is a line that divides an angle into two equal halves. So you need only invoke the definition to prove something is an angle bisector if you already know that the two angles are congruent.
No. An angle can have only one angle!
Does the angle bisector of the vertex angle of an isosceles triangle divides the triangle into two congruent?
ANSWERIf two angles are complementary to the same angle (or to two congruent angles), then the two angles are congruent.< means "Angle".Hypothesis:
Not exactly.A ray that divides an angle into two angles of equal measure is called an angle bisector.
Angle Angle Side is a method one can use to prove that two triangles are congruent. Basically, if any two pairs of angles and the side between these angles are congruent, then the triangles are congruent as well.
A line that bisects an angle into two different congruent angles is called an angle bisector.
An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles.
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151972.40/warc/CC-MAIN-20210726000859-20210726030859-00277.warc.gz
|
CC-MAIN-2021-31
| 1,851 | 18 |
https://www.coursehero.com/file/6737584/sysprob1a/
|
math
|
Unformatted text preview: x = 2 . 5 , 5 , 10 , 20 , 30 in along centerline (using hand-held pitot probe) 2) For α = 10 ◦ . . . Approximate locations where a) Δ p is a maximum (note the value) b) Δ p is a minimum (note the value) Normalized Data Presented 1) Top and bottom centerline C p vs x/c o for α = 0 ◦ , 10 ◦ . (both curves on one plot). Model’s centerline chord is c o = 37 . 7 in. 2) Locations of maximum and minimum Δ p , indicated with dots on the BWB outline drawing provided. Also determine the local normalized velocity V/V ∞ at these two locations. Note: Submit only the 2-sided turn-in sheet provided. If the plot is clearly incorrect, partial credit can be given only if you show your work (equations used, sample calculations, etc)....
View Full Document
- Fall '05
- Wright brothers, Wing design, Chord, Pitot tube, blended wing body
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948214.37/warc/CC-MAIN-20180426125104-20180426145104-00147.warc.gz
|
CC-MAIN-2018-17
| 867 | 4 |
https://math.answers.com/Q/What_is_the_averege_in_math
|
math
|
The arithmetic mean of a set of numbers are the sum of the numbers in the set, divided by the amount of numbers in the set. If the numbers in a set were to be 1, 2, 3, 4, and 5, the sum would be 1+2+3+4+5=15/5=3.
Math that is in none of the catagories of math
A math concept is how you solve a math problem or the ideas. You usually have to memorize math concepts.
An averege person poops 3 times a day to once in 3 days
I had a rottweiler for 13 yrs.
2 of your finest wives
120 to 2,200 lbs (54 to 998 kg)
to eat me would be evil so dont do t
We would need to know which average you need in order to answer this question.
The averege human bones are not brittle, unless you have a condition of some sort.
An averege zippo can range beetween 1.00-80,000 dollars mothafuka
The averege depth is 84 feet, the deepest point is 151 feet
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816820.63/warc/CC-MAIN-20240413144933-20240413174933-00477.warc.gz
|
CC-MAIN-2024-18
| 831 | 12 |
https://books.google.gr/books?id=-yXb5YsOuNEC&pg=PA42&focus=viewport&vq=%22a+new+numerator,+and+all+the+denominators+together+for+a+new+denominator%3B%22&dq=editions:UOMDLPabq7928_0001_001&lr=&hl=el&output=html_text
|
math
|
« ΠροηγούμενηΣυνέχεια »
This method differs from the 24)16294896(678954, Ans. common way by placing the right14482606
hand figure of every product im181229
mediately under the dividend. 169129
121 8. Divide 3545304 by 47. 9. Divide 45005091 by 57.
Ans. 75432. Ans. 789563.
VI. To divide by any number of 9's, when their number is not less than half the number of places that will be in the quotient, and when there is no remainder.
RULE. — Anner as many ciphers to the dividend, as there are 9's in the divisor. Then write the proper dividend under the number thus found, and subtract it from the number to which ciphers have been annexed; and, as many places of the remainder at the right hand as there were ciphers annexed, are so many figures for the right hand of the quotient ; and, for the remaining numbers of the quotient, a competent number must be taken from the left hand of the above remainder. 10. Divide 123332544 by 999. OPERATION.
By examining the dividend and 123332544000 divisor, we know there will be 6
123332544 places in the quotient. We there123,209211,456
fore take three of these figures from
the right hand of the remainder for 123456 Quotient, Ans. The
lent, Alise the three right-hand figures of the quotient, and the other three we take from the left hand of the remainder. 11. Divide 12332655 by 999.
Ans. 12345. 12. Divide 987551235 by 9999.
Ans. 98765. 13. Divide 9123456779876543211 by 999999999.
MISCELLANEOUS EXAMPLES. 1. What number multiplied by 1728 will produce 1705536 ?
2. If a garrison of 987 men are supplied with 175686 pounds of beef, how much will there be for each man ? Ans. 178 lbs.
3. In one dollar there are 100 cents; how many dollars in 697800 cents ?
Ans. $ 6978. 4. In one pound there are 16 ounces; how many pounds are in 111680 ounces?
Ans. 6980 lbs. 5. A dollar contains 6 shillings; how many dollars are in 5868 shillings?
Ans. $ 978. 6. The President of the United States receives a salary of $ 25,000; what does he receive per month? Ans. $ 20831.
7. A man receiving $ 96 for 8 months' labor, what does be receive for 1 month ?
Ans. $ 12. 8. The distance from Haverhill to Boston is 30 miles; and, if a man travel 6 miles an hour, how long will he be in going this distance ?
Ans. 5 hours. • 9. The annual revenue of a gentleman being $8395, how much per day is that equivalent to, there being 365 days in a year?
Ans. $ 23. 10. The car on the Liverpool railroad goes at the rate of 65 miles an hour; how long would it take to pass round the globe, the distance being about 25,000 miles ? Ans. 384-8 hours.
11. How much sugar at $ 15 per cwt. may be bought for $ 405 ?
Ans. 27 cwt. 12. In 6789560 shillings how many pounds, there being 20 shillings in a pound ?
Ans. 339478 pounds. 13. The Bible contains 31,173 verses ; how many must be read each day, that the book may be read through in a year ?
Ans. 8514: verses. 14. In 123456720 minutes how many hours ?
Ans. 2057612 hours. 15. A gentleman possessing an estate of $ 66,144, bequeathed one fourth to his wife, and the remainder was to be divided between his 4 children; what was the share of each ?
Ans. $ 12,402. 16. A man disposed of a farm containing 175 acres at $ 87 per acre; of the avails he distributed $ 1234 for charitable purposes; $ 197 was expended for the purchase of a horse and chaise; the remainder was divided between 6 gentlemen and 8 ladies, and each lady was to receive twice as much as a gentleman; what was the share of each ?
Ans. $ 627 for a gentleman, and $ 1254 for a lady. 17. If there are 160 square rods in an acre, how many acres are in 1086240 square rods?
Ans. 6789 acres.
18. If 144 square inches make one square foot, how many square feet in 14222160 square inches ? Ans. 98765 feet.
19. What number is that, which being multiplied by 24, the product divided by 10, the quotient multiplied by 2, 32 subtracted from the product, the remainder divided by 4, and 8 subtracted from the quotient, the remainder shall be 2?
20. What is the difference between half a dozen dozen, and six dozen dozen?
Ans. 792. 21. Bought of F. Johnson 8 barrels of flour at $ 7 per barrel, and 3 hundred weight of sugar at $8 per hundred. What was the amount of his bill ?
Ans. $ 80. 22. Sold S. Jenkins my best horse for $75, my second-best chaise for $ 87, a good harness for $31. He has paid me in cash $ 38, and has given me an order on Peter Parker for $ 12. How many dollars remain my due ?
Ans. $ 143. 23. T. Webster has sold his wagon to J. Emerson for $ 85. He is to receive his pay in wood at $5 per cord. How many cords will it require to balance the value of the wagon?
Ans. 17 cords. . 24. Purchased a farm of 500 acres for $ 17,876. I sold 127 acres of it at $ 47 an acre, 212 acres at $ 96 an acre, and the remainder at $ 37 an acre. What did I gain by my bargain ?
Ans. $ 14,702. 25. A tailor has 938 yards of broadcloth; how many cloaks can be made of the cloth, if it require 7 yards to make one cloak ?
Ans. 134 cloaks. 26. Bought 97 barrels of molasses at $ 5 a barrel. Gave 17 barrels to support the poor, and the remainder was sold at $ 8 a barrel. Did I gain or lose, and how much?
Ans. $ 155 gain. 27. There are 12 pence in one shilling; required the number of pence in 671 shillings.
Ans. 8052 pence. 28. Twelve inches make one foot in length ; required the number of inches in 5280 feet, it being the length of a mile.
Ans. 63360 inches. 29. In one pound avoirdupois there are 16 ounces; required the ounces in 1728 pounds.
Ans. 27648 ounces. 30. Required the number of shillings in 8136 pence.
Ans. 678 shillings. 31. It requires 1728 cubic inches to make one cubic foot required the number of cubic inches in 3787 cubic feet.
Ans. 6543936 inches.
Section IX. TABLES OF MONEY, WEIGHTS, AND MEASURES.
- 1 Pound, 21 Shillings sterling "
1 Guinea, 28 Shillings N. E." i Guinea, Note. — One pound sterling is equal to $ 4.44), exchange value.
make i Pennyweight, marked dwt. 20 Pennyweights
OZ. 12 Ounces
20 5760 240
12 = 1 By this weight are weighed gold, silver, and jewels.
Note.-" The original of all weights used in England was a grain or corn of wheat, gathered out of the middle of the ear; and, being well dried, 32 of them were to make one pennyweight, 20 pennyweights one ounce, and 12 ounces one pound. But in later times, it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains, being the least weight now in common use; and from hence the rest are com
Ib. 5760 288
= 1 Apothecaries mix their medicines by this weight; but buy and sell by Avoirdupois. The pound and ounce of this weight are the same as in Troy Weight.
AVOIRDUPOIS WEIGHT. 16 Drams
marked oz. 16 Ounces 1 Pound,
lb. 28 Pounds
qr. 4 Quarters
1 Hundred Weight,
cwt. 20 Hundred Weight
Ib. 256 16
qr. 7168 448 28 = 1
112 = 4 = 1 ton. 573440
2240 = 80 = 20 = 1 By this weight are weighed almost every kind of goods, and all metals except gold and silver. By a late law of Massachusetts, the cwt. contains 100 lbs. instead of 112 lbs.
A ton is reckoned at the custom-houses of the United States at 2240 lbs.
LONG MEASURE. 3 Barleycorns, or 12 Lines make 1 Inch, marked 12 Inches
1 Foot, 3 Feet
1 Yard, 6 Feet
1 Fathom, 54 Yards, or 16% Feet
1 Rod, or Pole, “ 40 Rods
1 Furlong, 8 Furlongs
1 Mile, 3 Miles " 1 League "
lea. 69] Miles nearly
« 1 Degree, "6 Deg. or 360 Degrees
66 1 Circle of the Earth.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141171077.4/warc/CC-MAIN-20201124025131-20201124055131-00694.warc.gz
|
CC-MAIN-2020-50
| 7,395 | 79 |
https://matpitka.blogspot.com/2011/02/comment-about-topological-explanation.html
|
math
|
The basic objection against the proposal is that it predicts infinite number of particle families unless the g< 3 topologies are preferred for some reason. Conformal and modular symmetries are basic symmetries of the theory and global conformal symmetries provide an excellent candidate for the sought for reason why.
- For g<3 the 2-surfaces are always hyper-elliptic which means that they have have always Z2 as global conformal symmetries. For g>2 these symmetries are absent in the generic case. Moreover, the modular invariant elementary particle vacuum functionals vanish for hyper-elliptic surfaces for g>2. This leaves several options to consider. The basic idea is however that ground states are usually highly symmetric and that elementary particles correspond to ground states.
- The simplest guess is that g>2 surfaces correspond to very massive states decaying rapidly to states with smaller genus. Due to the the conformal symmetry g<3 surfaces would be analogous to ground states and would have small masses.
- The possibility to have partonic 2-surfaces of macroscopic and even astrophysical size identifiable as seats of anyonic macroscopic quantum phases (see this) suggests an alternative interpretation consistent with global conformal symmetries. For partonic 2-surfaces of macroscopic size it seems natural to consider handles as particles glued to a much larger partonic 2-surface by topological sum operation (topological condensation).
All orientble manifolds can be obtained by topological sum operation from what can be called prime manifolds. In 2-D orientable case prime manifolds are sphere and torus representing in well-defined sense 0 and 1 so that topological sum corresponds to addition of positive integers arithmetically. This would suggest that only sphere and torus appear as single particle states. Particle interpretation however requires that also g=0 and g=2 surfaces topologically condensed to a larger anyonic 2-surface have similar interpretation, at least if they have small enough size. What kind of argument could justify this kind of interpretation?
- An argument based on symmetries suggests itself. The reduction of degrees of freedom is the generic signature of bound state. Bound state property implies also the reduction of approximate single particle symmetries to an exact overall symmetry. Rotational symmetries of hydrogen atom represent a good example of this. For free many particle states each particle transforms according to a representation of rotation group having total angular momentum defined as sum of its spin and angular momentum. For bound states rotational degrees of freedom are strongly correlated and only overall rotations of the state define rotational symmetries.
In this spirit one could interpret sphere as vacuum, torus as single handle state, and torus with handle as a bound state of 2 handles in conformal degrees of freedom meaning that the Z2 symmetries of vacuum and handles are frozen in topological condensation (topological sum) to single overall Z2. If this interpretation is correct, g>2 2-surfaces would always have a decomposition to many-particle states consisting of spheres, tori and tori with single handle glued to a larger sphere by topological sum. Each of these topologically condensed composites would possess Z2 as approximate single particle symmetry.
For more details see the chapter Elementary Particle Vacuum Functionals of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303779.65/warc/CC-MAIN-20220122073422-20220122103422-00435.warc.gz
|
CC-MAIN-2022-05
| 3,493 | 8 |
https://swmath.org/?term=direct%20search
|
math
|
- Referenced in 1485 articles
- factorizations, visualizing matrices, and carrying out direct search optimization. Various other miscellaneous functions are also...
- Referenced in 732 articles
- state of optimization software and the search directions which should be considered in the near...
- Referenced in 697 articles
- either the HKM or the NT search direction. The basic code is written in Matlab...
- Referenced in 631 articles
- considered. Chapter 3 is devoted to line-search and trust-region methods, which are used ... noise level in the function. Direct search algorithms, including the Nelder-Mead, multidirectional search...
- Referenced in 271 articles
- enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially...
- Referenced in 140 articles
- possible to compute a negative-curvature direction at a stationary point. The above mentioned modified ... iterations to compute the search direction, where n denotes the number of variables ... method is described that defines a search direction which interpolates between the direction defined...
- Referenced in 168 articles
- code: basis factorizations, search directions, line-searches, and Newton iterations. The paper contains performance statistics...
- Referenced in 316 articles
- completion, weighting, and strategies for directing and restricting searches for proofs. Otter can also...
- Referenced in 147 articles
- programming (SQP) algorithm, in which each search direction is the solution of a QP subproblem...
- Referenced in 133 articles
- constraint functions. At each iteration, the search direction is the solution of a quadratic programming...
- Referenced in 81 articles
- routines for visualizing matrices, routines for direct search optimization, and miscellaneous routines that provide useful ... three-dimensional views of pseudospectra. The direct search optimization routines implement the alternating directions method...
- Referenced in 108 articles
- definiteness of the matrix defining the search direction. This modification is based on the quasi...
- Referenced in 105 articles
- software that implements the Mesh Adaptive Direct Search (MADS) algorithm for blackbox optimization under general...
- Referenced in 60 articles
- choosing directions for the mesh adaptive direct search (Mads) class of algorithms. The advantages ... instantiation of Mads are that the polling directions are chosen deterministically, ensuring that the results...
Genetic Algorithm and Direct Search Toolbox
- Referenced in 29 articles
- Genetic Algorithm and Direct Search Toolbox (GADS) extends the optimization capabilities in MATLAB ... tools for using the genetic and direct search algorithms. You can use these algorithms ... undefined derivatives. The Genetic Algorithm and Direct Search Toolbox complements other optimization methods to help...
- Referenced in 65 articles
- massively parallel implementations for a global search algorithm DIRECT. Two parallel schemes take different approaches...
- Referenced in 46 articles
- following method using the Nesterov-Todd search direction. The basic code is written in Matlab...
- Referenced in 40 articles
- predetermined test points along the search direction. The parallel line search is performed with respect...
- Referenced in 113 articles
- Cholesky factorization to generate a direction, and a projected search to compute the step...
- Referenced in 42 articles
- only. M. Powell’s paper on Direct Search Methods...
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521041.0/warc/CC-MAIN-20220518021247-20220518051247-00243.warc.gz
|
CC-MAIN-2022-21
| 3,529 | 41 |
https://www.pw.live/question-answer/in-the-following-which-statement-is-true-29162
|
math
|
. In the following which statement is true
In the following which statement is true
(a) Alternative interior or exterior angles are unequal, if l m.
(b) Measure of a straight angle is 90
(c) Measure of a right angle is180.
(d) None of them
(d) a, b and c are not true option.Then (d) is a right answer
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711016.32/warc/CC-MAIN-20221205100449-20221205130449-00249.warc.gz
|
CC-MAIN-2022-49
| 301 | 7 |
https://www.waterstones.com/book/exercises-in-modules-and-rings/t-y-lam/9780387988504
|
math
|
Exercises in Modules and Rings - Problem Books in Mathematics (Hardback)T. Y. Lam (author)
- We can order this
This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.
Publisher: Springer-Verlag New York Inc.
Number of pages: 414
Weight: 1740 g
Dimensions: 233 x 155 x 23 mm
Edition: 2007 ed.
From the reviews:
"This volume, a companion for the author's graduate-level textbook ... consists of a complete set of solutions to all ... . should be on the bookshelf of every serious graduate student in theoretical mathematics. As one expects from the author, the writing in this book is clear and precise, and some of the problem solutions (and counterexamples to conjectures) presented are quite elegant." (Jonathan Golan, Mathematical Reviews, Issue 2007 h)
"Exercises in Classical Ring Theory is an outgrowth of the author's lectures on noncommutative rings given at Berkeley. The book presents solutions to over 400 exercises ... . Those who purchase the book should find it helpful in the problem solving process as well as a demonstration of the different applications of theorems from ring theory." (Paul E. Bland, Zentralblatt MATH, Vol. 1121 (23), 2007)
You may also be interested in...
Please sign in to write a review
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159193.49/warc/CC-MAIN-20180923095108-20180923115508-00338.warc.gz
|
CC-MAIN-2018-39
| 1,488 | 13 |
https://www.examsbook.com/topics/direction-sense-test
|
math
|
- Test Series and Practice Test
- Time proven exam strategies
- Exam analysis and simulated tests
- Hand-on real time test experience
Recently Added Articles View More >>
Direction Sense Test is an important subject under Verbal Reasoning for all competitive exams. The candidates have to identify the direction of a person or shadow from the statement given in the questions based on the guidelines. Therefore, students are required to know some important points, which help to solve the questions easily.
Most Popular Articles
Most Popular Articles
Recently Added Questions
Ram started walking from a mall. First, he walked 3 km. in North direction. From there he took a right turn and walked 3 km. Then he turned right and walked 5 km. Then he again took a right turn and walked 7 km. what is the mini mum distance between Mall and Kartik's last position.549 0 5f5b2c4cdc518b408a4374a7
- 15 kmtrueCorrectWrong
- 210 kmfalseCorrectWrong
- 37 kmfalseCorrectWrong
- 43 kmfalseCorrectWrong
Answer : 1. "5 km "
Shyam walks northwards. After a while, he turns to his right and a little further to his let. Finally, after walking a distance of one kilometer, he turns to his left again. In which direction is he moving now?623 0 5f5b299bdc518b408a434857
Answer : 2. "West "
I am facing south. I turn right and walk 20 m. Then I turn right again and walk 10 m. Then I turn left and walk 10 m and then turning right walk 20 m. Then I turn right again and walk 60 m. In which direction am I from the starting point186 0 5f5b25d9b772fe2f8b2a289b
Answer : 2. "North-East "
sandeep starts walking straight towards east. After walking 75 metres, he turns to the lefft and walk 25 metres straight. Again he turns to the left, walks a dsitance of 40 metres straight,again he turns to the left and walks a distance of 25 metres. How far is he from the starting poing?85 0 5f5b24df69ed13038c1b62e0
- 1115 metresfalseCorrectWrong
- 235 metrestrueCorrectWrong
- 325 metresfalseCorrectWrong
- 450 metresfalseCorrectWrong
Answer : 2. "35 metres "
Rahim leaves his house and walks 12 km towards North. He turns right and walks another 12 km. He turns right again, walks 12 km more and turns left to walk 5 km. How far is he from his home and in which direction?97 0 5f5b244d69ed13038c1b5ab1
- 117 km EasttrueCorrectWrong
- 224 km EastfalseCorrectWrong
- 37 km EastfalseCorrectWrong
- 410 Km EastfalseCorrectWrong
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400209665.4/warc/CC-MAIN-20200923015227-20200923045227-00036.warc.gz
|
CC-MAIN-2020-40
| 2,392 | 30 |
http://studentsmerit.com/paper-detail/?paper_id=56946
|
math
|
Question;1. The theory of;consumer choice assumes that consumers attempt to maximize;a. the difference between total utility and marginal utility.;b. average utility.;c. total utility.;d. marginal utility.;2. Utility refers to the;a. usefulness of a good or service.;b. satisfaction that results from the consumption of a good.;c. relative scarcity of a good.;d. rate of decline in the demand curve.;3. The law of diminishing marginal utility says that;a. the marginal utility gained by consuming equal successive units of a good;will decline as the amount consumed increases.;b. the more of a particular good one consumes, the greater us the utility;received from the consumption of that good.;c. the marginal utility gained by consuming equal successive units of a good;will increase as the amount consumed increases.;d. the more of a particular product one sells, the less utility one receives;from selling.;e. none of the above;4. Which of the following is true?;a. It is possible for total utility to rise as marginal utility falls.;b. Marginal utility is the same as total utility.;c. It is possible for marginal utility to rise as total utility falls.;d. a and c;e. a, b, and c;5. In order for an individual to maximize total utility while consuming only;two goods, A and B, that individual must fulfill the condition;a. TUA= TUB.;b. TUA/PA= TUB/PB.;c. MUA= MUB.;d. MUA/PA= MUB/PB.;e. MUB/PB= MUB/PA.;6. We would expect the total utility of water to be high but its marginal;utility to be low. Why?;a. Because water is a fluid and we don?t need fluids to live as much as we need;food.;b. Because we need water to live and there is so much of it.;c. Because we need water to live and there is very little of it.;d. Because water?s price is low.;e. none of the above;7. To demonstrate the law of demand, suppose the price of good A rises. To;restore consumer equilibrium, ________ of good A is purchased in order to;the marginal utility of the last unit of it purchased.;a. more, lower;b. more, raise;c. less, lower;d. less, raise;8. The ?income effect? indicates that;a. when the price of a good falls, a consumer will be able to buy more of it;with a given money income.;b. consumers should substitute among various goods until the marginal utility;of the last unit of each good purchased is the same.;c. when the price of a good falls, the lower price will induce the consumer to;buy more of that good now that it is relatively cheaper.;d. b and c;e. none of the above;9. Price elasticity of demand is a measure of the responsiveness of quantity;demanded to changes in;a. interest rates.;b. price.;c. supply.;d. demand.;10. If the percentage change in quantity demanded is greater than the;percentage change in price, demand is;a. inelastic.;b. unit elastic.;c. elastic.;d. perfectly elastic.;e. perfectly inelastic.;11. Which of the following is a determinant of price elasticity of demand?;a. the number of substitutes;b. the percentage of one?s budget spent on the good;c. the amount of time that has passed since a price change;d. b and c;e. all of the above;12. Upon deregulation, firms in a formerly regulated industry feared;that cut throat competition would reduce prices and their revenue.;Competition did force prices down but to the firms' surprise their;revenues increased. The demand curve for the product these firms;produced must be;a. perfectly elastic.;b. elastic.;c. inelastic.;d. perfectly inelastic.;13. When the cross elasticity of demand between two goods is ________, the;goods are ________.;a. negative, substitutes;b. negative, complements;c. positive, normal goods;d. positive, inferior goods;14. If Cassandra bought 24 blouses last year when her income was $40,000 and;she buys 16 blouses this year her when income is $35,000, then for her blouses;are;a. an inferior good.;b. a normal good.;c. a substitute good.;d. a complementary good.;e. There is not enough information to answer this question.;15. Economists Alchian and Demsetz suggest that firms are formed when;a. the sum of what individuals can produce alone is greater than what they can;produce as a team.;b. someone wants to earn profits.;c. someone comes up with the idea that customers will buy a new product.;d. the sum of what individuals can produce as a team is greater than the sum of;what they can produce alone.;16. Most economists say that the firm?s goal or objective is to maximize;a. sales.;b. employment.;c. profits.;d. worker satisfaction.;e. none of the above;17. The sole proprietor of a proprietorship has;a. unlimited liability, which means the owner is responsible for settling all;debts of the firm but not if it means selling his personal property to do so.;b. limited liability, which means the owner is responsible for settling all;debts of the firm, even if this means selling his personal property to do so.;c. limited liability, which means the owner cannot be sued for the his failure;to pay his company's debts.;d. unlimited liability, which means the owner is responsible for settling all;debts of the firm even if this means selling his personal property to do so.;18. Which of the following is a disadvantage of a corporation relative to a;proprietorship or a partnership?;a. perpetual life;b. difficulty in raising money;c. unlimited liability of the owners;d. double taxation of profits;e. none of the above;19. ?Managerial coordination? refers to the;a. behavior of a worker who is putting forth less than the agreed-to effort.;b. process where individuals perform certain tasks based on changes in market;forces.;c. process where persons share in the profits of a business firm.;d. process where managers direct employees to perform certain tasks.;20. Which of the following statements is true?;a. Explicit costs always equal implicit costs.;b. Zero economic profit is a smaller dollar figure than normal profit.;c. Zero economic profit is a larger dollar figure than normal profit.;d. Saying that a firm earned zero economic profit is the same as saying it;earned normal profit.;e. none of the above;21. A fixed input is an input whose quantity;a. can be changed as output changes in the short run.;b. cannot be changed as output changes in the short run.;c. cannot be changed as output changes in the long run.;d. a and c;e. b and c;22. ?As additional units of a variable input are added to a fixed input;eventually the marginal physical product of the variable input will decline.?;This is a statement of the;a. law of supply.;b. average-marginal rule.;c. law of comparative advantage.;d. law of diminishing marginal returns.;23. A rising marginal cost curve is a reflection of;a. a rising marginal physical product curve.;b. a falling marginal physical product curve.;c. a falling average fixed cost curve.;d. a rising average variable cost curve.;24. The average-marginal rule states that;a. if the marginal magnitude is less than the average magnitude, the average;magnitude falls.;b. if the marginal magnitude is greater than the average magnitude, the average;magnitude falls.;c. if the marginal magnitude is rising, the average magnitude is necessarily;above it.;d. if the marginal magnitude is falling, the average magnitude is necessarily;below it.;e. c and d;25. Refer to Exhibit T-4. Curve A is ________ curve.;a. a marginal cost;b. an average variable cost;c. an average total cost;d. an average fixed cost;26. A ?price taker? is a firm that;a. does not have the ability to control the price of the product it sells.;b. does have the ability, albeit limited, to control the price of the product;it sells.;c. can raise the price of the product it sells and still sell some units of its;product.;d. sells a differentiated product.;e. none of the above;27. A perfectly competitive firm will increase its production as long as;a. total revenue is less than total cost.;b. the total revenue curve is rising.;c. marginal revenue is greater than marginal cost.;d. the marginal revenue curve is rising.;28. The perfectly competitive firm will;a. produce in the short run if price is below average variable cost.;b. produce in the long run if price is below average variable cost.;c. produce in the short run if price is below average total cost but above;average variable cost.;d. produce in the long run if price is below average total cost but above;average variable cost.;29. The perfectly competitive firm?s short-run supply curve is;a. the upward-sloping portion of its average total cost curve.;b. the horizontal portion of its marginal revenue curve.;c. the portion of its average variable cost curve that lies above the average;fixed cost curve.;d. the upward-sloping portion of its marginal cost curve.;e. the portion of its marginal cost curve that lies above its average variable;cost curve.;30. Why must profits be zero in long-run competitive equilibrium?;a. If profits are not zero, firms will enter or exit the industry.;b. If profits are not zero, firms will produce higher-quality goods.;c. If profits are not zero, marginal revenue will rise.;d. If profits are not zero, marginal cost will rise.
Paper#56946 | Written in 18-Jul-2015Price : $19
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541426.52/warc/CC-MAIN-20161202170901-00205-ip-10-31-129-80.ec2.internal.warc.gz
|
CC-MAIN-2016-50
| 9,099 | 2 |
http://openstudy.com/updates/4f6f46d9e4b0772daa08fcaa
|
math
|
how do i find the minimum acceleration attained on the interval 0<=t<=4 by the particale whos velocity is given by v(t)=t^2-4t^2-3t+2
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Not the answer you are looking for? Search for more explanations.
test that and the endpoints
Plug in 0, 8/6, and 4 into 3t^2-8t-3 and see where you get the smallest value.
0 should be the min acceleration.. i think
v' = 3*t^2 - 8*t - 3
find critical points, v' = 0 =? t = 3*t^2 - 8*t - 3 => t =3, -1/3
v '' = 6*t - 8
put the values of t at v'', where you get negative value you get maximun
ie at t=1/3
@ExperimentX he's asking for the MINIMUM of ACCELERATION
you gave him the MAXIMUM of VELOCITY
Oo mistake .. for minimun you get at t = 3, where v'' has negative value
You are given velocity, you need to find the min acceleration.
Thus you will have to differentiate acceleration and find where its minimum occurs.
But to get the formula of acceleration you must differentiate velocity. Got it?
So when u're differentiating acceleration, you're actually taking the 2nd derivative of velocity.
Oops sorry, i thought i should give the minimum value of velocity.
okay that would be minimum value of v' right, that would be 8/6
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887832.51/warc/CC-MAIN-20180119065719-20180119085719-00000.warc.gz
|
CC-MAIN-2018-05
| 2,073 | 25 |
http://office-2010.iyogi.com/help-support/heres-how-countif-function-works-in-microsoft-excel-2010.html
|
math
|
Here’s how COUNTIF function works in Microsoft Excel 2010
Let us move on to the functions after the keyboard shortcuts. Functions are the key features in Microsoft Excel 2010. They are the reason why Microsoft Excel 2010 is called a powerful application. Functions let you perform various tasks with your data and give you results. COUNTIF function is a combination of two functions in Microsoft Excel 2010, COUNT and IF functions. Both these functions are mighty and help the users in lot of ways. Now let us see the power of this combination function.
This function combines the abilities of two functions, COUNT and IF and counts the number of times a specific value is repeated in a selected group of cells. The IF condition is to help the function determine the specific value and the COUNT condition is to count the number of times the specified value appears in the selected group of data. Now let us see how this function actually works in detail. Let us say you have a table that has details of 1000 people and you need the count of people who are older than 40. How would you get the number?
Working of the function
COUNTIF function will first count the number of people in the table and would check for the condition for the IF function and give you the count of the people who are older than 40 years. Â Let us see how you can use this function in a few simple steps. First, select the data from where you need the count. Then use the COUNTIF function. The syntax for this function is ‘= COUNTIF (Range, Criteria)’. Range here should be the range where the data is present. The Criteria depends on your requirement. The criteria would be checked and then that value is searched in the range that is given in the formula and then the count is calculated in the end.
Another way to access
Here’s another way to access the COUNTIF function in Microsoft Excel 2010. Click on the Formula tab to begin the process. Then on the Formula tab, you would find the option ‘Statistical’, select that. Once you select that option, a dropdown will be displayed on the screen. Lists of statistical functions are displayed to you. You need to select the option ‘COUNTIF’ from the menu to start using this function.
That’s how the function COUNTIF is used in Microsoft Excel 2010. Isn’t the process simple and easy to understand and put to use? Thank us later.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946637.95/warc/CC-MAIN-20230327025922-20230327055922-00471.warc.gz
|
CC-MAIN-2023-14
| 2,375 | 8 |
https://www.hackmath.net/en/math-problem/1784
|
math
|
The farm bred turkeys, geese, hens and chickens. Everything is 400. Turkeys and geese a hen are 150. No hen has more than one chicken, but some hens has no chick. Half of them is also a quarter of the chickens. When the turkey subtracting 15, we get 75. How many are turkeys, geese, hens? How many hens that has no chick?
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
Tips to related online calculators
Do you have a system of equations and looking for calculator system of linear equations?
You need to know the following knowledge to solve this word math problem:
Related math problems and questions:
On the farm they have a total of 110 birds. Geese and turkeys together is 47. Hens is three times more than the turkey. How much is poultry by species?
I threw three chicken for a handful of grains and I noticed that it eat in a ratio of 8:7:6 and two of them grabbed 156 grains. How many grains have fought that chicken?
- THE FARM
Hens, goats, and 3 cows grow on the farm. All animals have a total of 19 heads and 56 legs. How many goats live on the farm, and how many hens live on the farm?
- Chickens and rabbits
In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?
- Six hens
Six hens weigh 3 kg more than three geese and 7 kg less than five geese. How much does a hen weigh, and how many geese?
- Chicken and rabbits (classic)
Grandmother breeding chickens and rabbits. It found that the yard has 35 heads and 108 legs. How many chickens and rabbits breeding in the yard?
- Three friends
Divide 570 euros to three friends so that first will get 50 euros less than the second and third twice more than the first. How many euros will get everyone?
In the three-part tram went 206 passengers in front of others, 226 after others and in the middle half of all. How many passengers went in tram total?
- Stamps and albums
Michail has in three albums stored 170 stamps. In the first album, there are 14 more than in the second and in the second is by 1/5 less than in the third. How many stamps are in the first album?
- Freight train
The train carries 525 tons of limestone in 29 wagons. Wagons are 15 tonne and 20 tons. How many is 15 ton and how many is 20 ton wagons?
Peter, Jane, and Thomas have together € 550. Tomas has 20 euros more than Jane, Peter € 150 less than Thomas. Determine how much has each of them.
Shirt has 6 buttons, blouse has 4 buttons. All buttons are 176. Shirts and blouses are together 36. How many are the shirts and blouses?
- Chickens and hares
There were chickens and hares in the yard. Together they had 22 heads and 54 legs. How many hens were there in the yard?
- The farm
The farm harvested 390 tons of grain. Wheat was 15% more than barley, and rye was 126 tons less than wheat and barley combined. How many tons of wheat, how many tons of barley, and how much rye did the team get?
- Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
- One and a half chicken
One and a half chicken bears one and a half egg in one and a half day. How many eggs can withstand from 6 chicken in 6 days?
- Volume increase
How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm?
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488268274.66/warc/CC-MAIN-20210621055537-20210621085537-00321.warc.gz
|
CC-MAIN-2021-25
| 3,433 | 36 |
http://link.springer.com/article/10.1134%2FS0965542506110042
|
math
|
Bernstein polynomials and composite Bézier curves Authors
Received: 27 April 2006 Accepted: 19 June 2006 DOI:
Cite this article as: Grigor’ev, M.I., Malozemov, V.N. & Sergeev, A.N. Comput. Math. and Math. Phys. (2006) 46: 1872. doi:10.1134/S0965542506110042 Abstract
Analytical principles of the theory of Bézier curves are presented. A new approach to the construction of composite Bézier curves of prescribed smoothness both on a plane and in a multidimensional Euclidean space is proposed.
Keywords Bernstein polynomials constructing Bézier curves on the basis of Bernstein polynomials geometric design
Original Russian Text © M.I. Grigor’ev, V.N. Malozemov, A.N. Sergeev, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 11, pp. 1962–1971.
Download to read the full article text References
S. N. Bernstein, “Proof of the Weierstrass Theorem Based on Probability Theory,” in
Collected Works (Akad. Nauk SSSR, Moscow, 1952), Vol. 1, pp. 105–106 [in Russian].
I. P. Natanson,
Constructive Function Theory
(Fizmatgiz, Moscow, 1949) [in Russian].
V. S. Videnskii,
(Leningr. Gos. Ped. Inst., Leningrad, 1990) [in Russian].
V. S. Videnskii,
Linear Positive Operators of Finite Rank (Leningr. Gos. Ped. Inst., Leningrad, 1985) [in Russian].
P. De Casteljau, “Pole Theory,” in
Mathematics and CAD 1 (Mir, Moscow, 1988), pp. 130–200 [in Russian].
P. Bézier, “Geometric Methods,” in
Mathematics and CAD 2 (Mir, Moscow, 1989), pp. 96–257 [in Russian].
Curves and Surfaces for CAGD
(Academic, New York, 2002).
Numerical Control: Mathematics and Applications (Wiley, New York, 1972). Copyright information
© MAIK “Nauka/Interperiodica” 2006
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982921683.52/warc/CC-MAIN-20160823200841-00008-ip-10-153-172-175.ec2.internal.warc.gz
|
CC-MAIN-2016-36
| 1,717 | 24 |
https://forums.cronometer.com/discussion/3536/cooked-vs-uncooked-nutrients-calculations
|
math
|
Cooked vs uncooked nutrients calculations
So I've been wondering, can I input raw foods as my intake instead of their cooked alternatives? For example, I might know that I eat 2 cups of rice in a day, but have no idea about its weight after it's done cooking. In that case, would adding 2 cups of uncooked rice be equivalent to adding whatever the proper amount of cooked rice is? Are there nutrient losses during cooking process?
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510781.66/warc/CC-MAIN-20231001041719-20231001071719-00799.warc.gz
|
CC-MAIN-2023-40
| 430 | 2 |
https://projecteuclid.org/euclid.aos/1176344671
|
math
|
The Annals of Statistics
- Ann. Statist.
- Volume 7, Number 3 (1979), 490-506.
A Central Limit Theorem for Parameter Estimation in Stationary Vector Time Series and its Application to Models for a Signal Observed with Noise
A general finite parameter model for stationary ergodic nondeterministic vector time series is considered. A central limit theorem for parameter estimates, obtained by maximising frequency domain approximations to the Gaussian likelihood, is established. The treatment given extends the central limit theorem of Dunsmuir and Hannan in that the innovations covariance matrix and the linear transfer function need not be separately parameterised. Models for a stationary vector signal observed with stationary vector noise are discussed in relation to the central limit theorem and the conditions imposed for this result are related to this model. Finally, the special case of a scalar autoregressive signal observed with noise is discussed. It is shown that this model may be reparameterised so that the central limit theorem of Dunsmuir and Hannan may be applied.
Ann. Statist., Volume 7, Number 3 (1979), 490-506.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G10: Stationary processes
Dunsmuir, W. A Central Limit Theorem for Parameter Estimation in Stationary Vector Time Series and its Application to Models for a Signal Observed with Noise. Ann. Statist. 7 (1979), no. 3, 490--506. doi:10.1214/aos/1176344671. https://projecteuclid.org/euclid.aos/1176344671
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251801423.98/warc/CC-MAIN-20200129164403-20200129193403-00516.warc.gz
|
CC-MAIN-2020-05
| 1,711 | 14 |
http://baboonlogic.com/2007/03/03/the-teachers-part-i/
|
math
|
This is certainly not the definitive collection of all that has been said by our professors, but then, as Loic Dubois pointed out, that’s life.
Not all of these are first hand.
1) If there is any justice in the world, then this should be the derivative!
2) I don’t know why I am doing this. (on the theorem he was proving)
(Vemuri, during his course on functions in several variables)
3) Ignorance is not a crime, ignorance of ignorance is.
(Ramanan, in the Global Calculus course, when the students failed to reply clearly whether or not they knew some particular theorem)
4) Here is a similar one I found when I was googling to see if Ramanan was just quoting somebody -
To be ignorant of one’s ignorance is the malady of ignorance.
(A. Bronson Alcott)
5) This corollary is proved by staring hard at the blackboard.
(Nagrajan, humouring us when we failed to prove a relatively simple corollary in the classroom and sought refuse in staring vaccantly at the blackboard as if we were going to come up with the solution any moment)
6) But what can we do? It’s a theorem, it is true! That’s Life.
(Loic Dubois, to Anirbit, when he insisted that the inverse function theorem (or was it the implicit function theorem? I wasn’t there.) could not be true because some jacobian somewhere was not symmetric.)
7) The purpose of mathematics is data collection.
(By P. J., apparently in a workshop in the AMS-India conference.)
8) Pi meson is a recognized and a perfectly respectable particle.
(Prof. R Parthasarthy in a quantum mech class when Anirbit said that there is debate going on over pi meson being a particle.)
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886124563.93/warc/CC-MAIN-20170823210143-20170823230143-00448.warc.gz
|
CC-MAIN-2017-34
| 1,621 | 18 |
https://goprep.co/a-hole-diffuses-from-the-p-side-to-the-n-side-in-a-p-n-i-1nm1d6
|
math
|
A hole diffuses from the p-side to the n-side in a p-n junction. This means that
A. a bond is broken on the n-side and the electron freed from the bond jumps to the conduction band.
B. a conduction electron on the p-side jumps to a broken bond to complete it.
C. a bond is broken on the n-side and the electron freed from the bond jumps to a broken bond on the p-side to compete it.
D. a bond is broken on the p-side and the electron freed form the bond jumps to a broken bond on the n-side to complete it.
Diffusion is a natural phenomenon which occurs when there is concentration difference between the two regions. The covalent bond is formed between the trivalent (or pentavalent) and semiconductor atom in p-type (or n-type). Thus there are many vacant places (holes) and electrons in the p-side and n-side respectively. Thus there are less or no electrons in p-side while there are many electrons in n-side. Clearly, there is concentration difference of electrons across the junction and diffusion will take place. This forces the covalent bond to be broken on the n-side so that the electrons freed from this bond, jumps to the vacant places in the p-side. Also when the electron jumps from the n-side to the p-side, a vacant place (hole) is created in n-side which represents that a hole has been moved from the p-side to the n-side.
Therefore, the correct answer is option C.
Rate this question :
(a) A student wants to use two p-n junction diodes to convert alternating current into direct current. Draw the labelled circuit diagram she would use and explain how it works.
(b) Give the truth table and circuit symbol for NAND gate.Physics - Board Papers
(i) Explain with the help of a diagram the formation of depletion region and barrier potential in a pn junction.
(ii) Draw the circuit diagram of a half wave rectifier and explain its working.Physics - Board Papers
Write the two processes that take place in the formation of a p-n junction. Explain with the help of a diagram, the formation of depletion region and barrier potential in a p-n junction.Physics - Board Papers
Name the junction diode whose I-V characteristics are drawn below:
Physics - Board Papers
Using a suitable combination from a NOR, an OR and a NOT gate, draw circuits to obtain the truth tables given below:
Physics - Exemplar
What do the terms ‘depletion region’ and ‘barrier potential’ mean for a p-n junction?Physics - Exemplar
Consider a box with three terminals on top of it as shown in Fig.14.18 (a):
Three components namely, two germanium diodes and one resistor are connected across these three terminals in some arrangement.
A student performs an experiment in which any two of these three terminals are connected in the circuit shown in Fig. 14.18 (b).
The student obtains graphs of current-voltage characteristics for unknown combination of components between the two terminals connected in the circuit.
The graphs are
(i) when A is positive and B is negative
(ii) when A is negative and B is positive
(iii) When B is negative and C is positive
(iv) When B is positive and C is negative
(v) When A is positive and C is negative
(vi) When A is negative and C is positive
From these graphs of current – voltage characteristic shown in Fig. 14.18 (c) to (h), determine the arrangement of components between A, B and C.
Physics - Exemplar
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107874340.10/warc/CC-MAIN-20201020221156-20201021011156-00367.warc.gz
|
CC-MAIN-2020-45
| 3,342 | 31 |
https://tackk.com/lrhwtt
|
math
|
Turn up the volume
Finding the volume and surface Area of a tissue box
How do you think the volume and surface area would be affected if you use a scale factor of 2 to dilate the shape?
I think that the shape would be affected greatly. The volume would have to be 6 times greater than the original, since each dimension is getting multiplied by 2. The surface area is a bit more confusing but, I think that the surface area would also multiply by 6. I think this since each dimension around the figure is also getting multiplied by 2.
The dimensions of the tissue box are
Volume of this figure is- 135 inches cubed. The equation is Bh, (base area x height) The base area is 45 (5 x 9) then multiply it by the height (45 x 3)
Surface area of this figure is- 174 inches squared. The equation is Ph + 2B. (perimeter of base x height + 2 x area of base) The perimeter of the base is 28 then multiply it by height to equal 84. Then the area of the base is 45, then multiply by 2. Add those together, to get to 174.
Dialation by 2.
The figures new volume is 1,080 inches cubed. You would have to multiply each dimension by 2, then multiply them together.
The new surface area is 588 inches squared. you need to find the new dimensions before you can use the appropriate equation.
The way to calculate a prisms volume is a multi step equation. The equation of the volume of a prism is V= Bh. This stands for- volume= area of base x height of the prism. The first step is to find out your dimensions ( the length, width, and height). Once you find these, you multiply the length and width, to get the area of the base. Then you take that number and multiply it by the height to get your volume of a prism. In finding the volume of prism, everybody must always work the problem backward to make sure the multiplication was correct.
The way to calculate a surface area of a prism, is totally different than the volume equation. The equation to find the surface area is Ph+2B. This means Perimeter of base x height + 2 multiplied by the area of base. First you must find all the dimensions of the prism. To start the equation, find the perimeter of the base and multiply it by the height. For the next part, multiply the area of the base by 2. That's how you find the surface area of a prism.Also make sure to check your work for multiplication errors.
My conjecture was absolutely incorrect, the dilated volume is actually 8 times bigger than the original version. This calculation is correct because it would be 2 x 2 x 2 equaling up to a grand total of 8. My guess of the surface are was also a bit off. I was off because this ones only 4 x bigger because you square this one not cube it. I did not factor in that this one is being squared.
The new figure is tremendously affected by the dilations. Since each dimension is 2 x bigger than the original it is affected greatly. The volume of the figure was 8 times bigger than the original and the surface are was 4 x bigger. Any figure is affected in a dilation since the dimensions are not the same. This matters because each figure has its own certain equation.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423183.57/warc/CC-MAIN-20170720121902-20170720141902-00203.warc.gz
|
CC-MAIN-2017-30
| 3,104 | 14 |
http://www.solutioninn.com/solve-for-the-predicted-values-of-y-and-the-residuals-251942
|
math
|
Question: Solve for the predicted values of y and the residuals
Solve for the predicted values of y and the residuals for the data in Problem 12.7. The data are provided hereagain:
Relevant QuestionsSolve for the predicted values of y and the residuals for the data in Problem 12.8. The data are provided hereagain:Graph the following residuals, and indicate which of the assumptions underlying regression appear to be in jeopardy on the basis of thegraph.In Problem 12.10, you were asked to develop the equation of a regression model to predict the number of business bankruptcies by the number of firm births. For this regression model, solve for the standard error of the ...Test the slope of the regression line determined in Problem 12.9. Use a 5% level of significance.Bond Rate .. Prime Interest Rate5% ....... 16%12 ....... 69 ....... 815 ....... 47 ....... 7After a somewhat uncertain start, e-commerce sales in the United States have been growing for the past several years. Shown below are quarterly adjusted e-commerce sales figures ($ billions) released by the Census Bureau for ...
Post your question
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689624.87/warc/CC-MAIN-20170923104407-20170923124407-00304.warc.gz
|
CC-MAIN-2017-39
| 1,114 | 4 |
http://people.uncw.edu/lammersm/seminar/mcmurrayabstract.html
|
math
|
Twenty minutes before the talk coffee and cookies will be available in
Bear Hall 211.
Title: Circuits and Cocircuits in Matroids.
Speaker: Nolan McMurray
Scott Smith conjectured in 1979 that distinct longest cycles of a k-connected
graph meet in at least k vertices when k greater than
or equal to 2. This conjecture is still open. Reid and Wu
generalized the conjecture to matroids by considering largest
circuits. An equivalent conjecture in terms of largest cocircuits
is given here. The specialization of this conjecture to graphs is
then obtained. This specialization involves largest bonds in a
The general conjecture about largest circuits in a k-connected matroid
was solved by Seymour for the case k = 2. We provide an
attractive generalization of this result for circuits that are almost
largest circuits. In addition, we prove the general conjecture
for the class of uniform matroids and the class of matroids with
larges circuit size at most four. The main result of this
work establishes the general conjecture
for k-connected cographic matroids when k less than or
to 5. This provides a dual result to the establishment of Smith's
for k less than or equal to 10 as reported by Grotschel.
Several related results on largest bonds in graphs are also given.
|
s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999644032/warc/CC-MAIN-20140305060724-00068-ip-10-183-142-35.ec2.internal.warc.gz
|
CC-MAIN-2014-10
| 1,268 | 22 |
https://learn.careers360.com/ncert/question-take-identical-cut-outs-of-congruent-triangles-of-sides-3-cm-4-cm-5-cm-arrange-them-as-shown-fig-311-you-get-a-trapezium-check-it-which-are-the-parallel-sides-here-should-the-non-parallel-sides-be-equal-you-can-get-two-more-trapeziums-using-t/
|
math
|
1. Take identical cut-outs of congruent triangles of sides 3 cm, 4 cm, 5 cm. Arrange them as shown (Fig 3.11).
You get a trapezium. (Check it!) Which are the parallel sides here? Should the
non-parallel sides be equal?
You can get two more trapeziums using the same set of triangles. Find them out and
discuss their shapes.
AB and CD are parallel sides.BC and AD are non parallel sides.Non parallel sides need not be equal.
We can get two more trapeziums using the same set of triangles-
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145767.72/warc/CC-MAIN-20200223093317-20200223123317-00353.warc.gz
|
CC-MAIN-2020-10
| 487 | 7 |
https://www.dreaminstitute.in/dailyupdateview.php?id=61
|
math
|
Time and Distance For IBPS
1.A man in a train notices that he can 21
telephone posts in one minute. If they are known to be 50 meters apart, then at
what speed is the train travelling?
2.A is faster than B. A and B each walk 24km.The sum of their speeds is 7km/hr and the sum of times taken by them is 14 hours. Then, A’s speed is equal to:
3.A motorist covers a distance of 39km in 45 minutes by moving at a speed of x kmph for the first 15 minutes, then moving at double the speed for the next 20 minutes and then again moving at his original speed for the rest of the journey.Then, x is equal to :
a)31.2 b)36 c)40 d)52
4.Mary jogs 9km at a speed of 6km per hour. At what speed would she need to jog during the next 1.5 hours to have an average of 9km per hour for the entire jogging session?
5.A train when moves at an average speed of 40kmph,reaches its destination on time.when its average speed becomes 35Kmph, then it reaches its destination 15 minutes late. Find the length of journey.
6.Robert is travelling on his cycle and has calculated to reach point A at 2pm. If he travels at 10kmph; he will reach there at 12 noon if he travels at 15kmph.At what speed must he travel to reach A at 1pm?
7.A train can travel 50% faster than a car.Both start from point A at the same time and reach point B 75kms away from A at the same time. On the way, however the train lost about 12.5 minutes while stopping at the stations.The speed of the car is:
8.Excluding stoppages, the speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minutes does the bus stop per hour?
a)9 b)10 c)12 d)20
9.In Covering a distance of 30km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is:
10.If a person walks at 14km/hr instead of 10km/hr, he would have walked 20km more. The actual distance travelled by him is:
1-c 2-b 3-d 4-c 5-c
6-c 7-c 8-b 9-a 10-a
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937074.8/warc/CC-MAIN-20180419223925-20180420003925-00602.warc.gz
|
CC-MAIN-2018-17
| 1,941 | 17 |
https://encyclopediaofmath.org/index.php?title=Inner_automorphism&oldid=15849
|
math
|
of a group
An automorphism such that
for a certain fixed element . The set of all inner automorphisms of forms a normal subgroup in the group of all automorphisms of ; this subgroup is isomorphic to , where is the centre of (cf. Centre of a group). Automorphisms that are not inner are called outer automorphisms.
Other relevant concepts include those of an inner automorphism of a monoid (a semi-group with a unit element) and an inner automorphism of a ring (associative with a unit element), which are introduced in a similar way using invertible elements.
Let be a Lie algebra and an element of for which is nilpotent. Then
defines an automorphism of . Such an automorphism is called an inner automorphism of . More generally, the elements in the group generated by them are called inner automorphisms. It is a normal subgroup of .
If is a real or complex Lie group with semi-simple Lie algebra, then the inner automorphisms constitute precisely the identity component of the group of automorphisms of .
|[a1]||M. Hall jr., "The theory of groups" , Macmillan (1959)|
|[a2]||J.E. Humphreys, "Introduction to Lie algebras and representation theory" , Springer (1972) pp. §5.4|
|[a3]||J.-P. Serre, "Algèbres de Lie semi-simples complexes" , Benjamin (1966)|
Inner automorphism. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Inner_automorphism&oldid=15849
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224643585.23/warc/CC-MAIN-20230528051321-20230528081321-00125.warc.gz
|
CC-MAIN-2023-23
| 1,391 | 11 |
https://www.dora.dmu.ac.uk/xmlui/handle/2086/5137
|
math
|
Type-2 Fuzzy Alpha-cuts
Systems that utilise type-2 fuzzy sets to handle uncertainty have not been implemented in real world applications unlike the astonishing number of applications involving standard fuzzy sets. The main reason behind this is the complex mathematical nature of type-2 fuzzy sets which is the source of two major problems. On one hand, it is difficult to mathematically manipulate type-2 fuzzy sets, and on the other, the computational cost of processing and performing operations using these sets is very high. Most of the current research carried out on type-2 fuzzy logic concentrates on finding mathematical means to overcome these obstacles. One way of accomplishing the first task is to develop a meaningful mathematical representation of type-2 fuzzy sets that allows functions and operations to be extended from well known mathematical forms to type-2 fuzzy sets. To this end, this thesis presents a novel alpha-cut representation theorem to be this meaningful mathematical representation. It is the decomposition of a type-2 fuzzy set in to a number of classical sets. The alpha-cut representation theorem is the main contribution of this thesis. This dissertation also presents a methodology to allow functions and operations to be extended directly from classical sets to type-2 fuzzy sets. A novel alpha-cut extension principle is presented in this thesis and used to define uncertainty measures and arithmetic operations for type-2 fuzzy sets. Throughout this investigation, a plethora of concepts and definitions have been developed for the first time in order to make the manipulation of type-2 fuzzy sets a simple and straight forward task. Worked examples are used to demonstrate the usefulness of these theorems and methods. Finally, the crisp alpha-cuts of this fundamental decomposition theorem are by definition independent of each other. This dissertation shows that operations on type-2 fuzzy sets using the alpha-cut extension principle can be processed in parallel. This feature is found to be extremely powerful, especially if performing computation on the massively parallel graphical processing units. This thesis explores this capability and shows through different experiments the achievement of significant reduction in processing time.
- PhD
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195069.35/warc/CC-MAIN-20201128040731-20201128070731-00348.warc.gz
|
CC-MAIN-2020-50
| 2,292 | 3 |
https://books.google.nl/books?id=7LcXAAAAIAAJ&hl=nl&lr=
|
math
|
Wat mensen zeggen - Een review schrijven
We hebben geen reviews gevonden op de gebruikelijke plaatsen.
Overige edities - Alles weergeven
A B C acute angle adjacent altitude apothem arc A B arc or angle base bisect centre circumference comp cone construct the triangle convex surface Corollary cosec Cosine Sine Cotangent deer diagonals diameter distance divided draw equally distant equiangular equilateral equivalent feet Find the Log frustum Geom given angle given line given point given side homologous sides hypothenuse included angle incr inscribed internal angles isosceles triangle lines A B Logarithm M. M. Sine multiplied number of sides opposite side parallelogram parallelopiped perimeter perpendicular plane triangle prism PROBLEM quadrilateral radii radius ratio rectangle regular polygon right angle right pyramid right triangle right-angled triangle Scholium secant segment side opposite similar triangles slant height sphere square straight line Tang tangent THEOREM tlie trapezoid triangle ABC Trigonometry vertex
Pagina 30 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Pagina 96 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Pagina 12 - In an isosceles triangle the angles opposite the equal sides are equal.
Pagina 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Pagina 23 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.
Pagina 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Pagina 71 - The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude.
Pagina 40 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60į : what is the height of the tower?
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574409.16/warc/CC-MAIN-20190921104758-20190921130758-00234.warc.gz
|
CC-MAIN-2019-39
| 2,280 | 12 |
https://www.europeanmedical.info/protein-adsorption/particle-transport.html
|
math
|
We first suppose that our particles are smooth, rigid and spherical and totally buoyant, i. e. their movement is not influenced by terrestrial gravity.
A particle suspended in a fluid can be transported by convection (i. e. entrained by the motion of the fluid) or by diffusion. The key parameter is the relative motion of the fluid with respect to the adsorbent. Far from the surface, the flow is uninfluenced by the surface; at the surface, on the other hand, friction dictates that the fluid is stationary (ignoring the possibility of slip); and the velocity in between is constantly diminishing. Hence near a surface, a particle will move by diffusion, and far from the surface by convection. At a certain intermediate distance, typically of the order of tens of micrometres, the transport régime will cross over from convection to diffusion. This distance is known as the diffusion boundary distance (6). A comprehensive treatment is given by Levich (1962). The flow in certain geometries, such as the tube or plate, can be solved analytically. These geometries are therefore particularly favourable for kinetic evaluation, a factor which should be borne in mind when designing flow cuvettes. For flow in a tube, where D is the diffusivity of the protein, F the volumetric flow rate, and C a constant depending on the dimensions of the tube.
When choosing flow rates, it should be remembered that only laminar flow régimes can be analysed conveniently, i. e. up to Reynolds numbers of at most around 1000. In principle a diffusion boundary still exists in the case of turbulent flow, but the motion is much more complicated than in the case of laminar flow.
Hence, a protein-sized particle will be moving diffusively already at a distance of the order of a thousand times its own dimensions ( a few nm in diameter) from the adsorbing surface.
At a distance of the order of ten times its own dimensions from the adsorbing surface, the particle may begin to be influenced by the long range hydrophilic repulsion (see Cacace et al. (1997) for a discussion of intermolecular forces), which will considerably retard its rate of arrival at the surface. When designing the flow conditions for an experiment, it is only necessary to ensure that convective-diffusion is rapid enough to replenish the particles lost from the solution in the vicinity of the surface by attachment to it. This is of practical importance given that many biological samples of carefully purified macromolecules are available only in extremely small quantities.
Good quantitative approximations for analysing the flow régimes can be derived from the equations of Fick and Smoluchowski (see Ramsden (1998) for a more complete discussion). If the surface (at z = 0, where z is the coordinate normal to the surface) is a perfect sink for the adsorbate, then the bulk (solution) concentration cb is zero at z = 0, the concentration gradient will be approximately linear, and the rate of accumulation is
It is a good idea to compare the experimentally observed rate with this maximum upper limit (which may, however, be exceeded if there is a long range attractive force, e. g. electrostatic, between particle and surface).
The effect of any energy barrier is to retard accumulation. In the immediate vicinity of the surface, the local bulk concentration cv will be much
higher than zero (although still less than cb). It is convenient to consider that the rate of accumulation at the surface is given by the product of cv and a chemical rate coefficient ka, which is directly related to the repulsive energy barrier (Spielman and Friedlander 1974):
and the Fick-Smoluchowski régime (linear concentration gradient) applies to the zone above this vicinal region. Hence dCv
where V and S are unit volume and surface respectively. Strictly speaking the distance of the vicinal layer from the surface should be subtracted from 6 in the denominator, but since that distance is of the order of molecular dimensions, i.e. only a few nm, whereas 6 is of the order of a few or a few tens of microns, this correction can be neglected. If desorption of the material also has to be taken into account a term with a chemical desorption coefficient kd can be included:
In a great many cases accumulation of material is limited to a monolayer, or to occupying a monolayer of receptors, in which case a function 0 must be introduced, which gives the fraction of the surface still available for adsorption or binding (i. e. the probability that space is available). Our kinetic equation then becomes:
We shall discuss 0—which obviously depends on M or v—below. One important implication is that as the surface fills up, i. e. as 0 ^ 0, cv will tend to approach cb, and dM/dt will asymptotically approach zero regardless of the flow régime. This can be immediately seen by letting the left hand side of whichever of the previous three equations is appropriate go to zero, yielding an explicit expression for cv, e. g.
if ka = 1 and kd = 0, which can then be substituted into Eq. 35, in which
The pure diffusion régime
If there is no flow at all then the vicinal layer is replenished by diffusion only, i. e. there is no distance at which concentration is maintained constant by effectively an infinite reservoir as in convective diffusion. This leads to the well-known result of Smoluchowski, according to which the flux to the surface constantly diminishes as t-fi, where fi = 0.5 for standard diffusion (other exponents have been found for the diffusion of highly non-spherical, non-compact proteins such as tenascin (Ramsden 1992).
If the flow rate is slow enough for the rate of adsorption to be limited by transport alone, or, more quantitatively, if the dimensionless parameter.
becomes large relative to unity, then the initial rate of adsorption is given by Eq. 37, from which D may be obtained. This is a useful way to determine the diffusion coefficient in solution.
If a repulsive potential barrier U(z) exists between protein and surface, where z is the distance between them, not every arriving protein will adsorb, even if there is space for it to do so, and v will be diminished by a rate coefficient ka, which can be found by integrating U(z):
Sometimes the denominator of the right hand term is called the "adsorption length", 6a. The interaction potential U can be approximated by the sum of the particle-surface interaction free energies, corresponding to the Lifschitz-van der Waals (LW), electrostatic (el) and electron donor-acceptor (da) interactions:
Was this article helpful?
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669454.33/warc/CC-MAIN-20191118053441-20191118081441-00193.warc.gz
|
CC-MAIN-2019-47
| 6,560 | 21 |
http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511662508&cid=CBO9780511662508A033
|
math
|
Edited by Jeremy Gunawardena
Foreword by John M. Taylor
Foreword by Michael Atiyah
Publications of the Newton Institute (No. 11)
Publisher: Cambridge University Press
Print Publication Year: 1998
Online Publication Date:May 2010
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511662508.026
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar constructions and results over idempotent semirings, in the spirit of N. Bohr's correspondence principle in Quantum Mechanics. Idempotent analogs for some basic ideas, constructions and results in Functional Analysis and Mathematical Physics are discussed from this point of view. Thus the correspondence principle is a powerful heuristic tool to apply unexpected analogies and ideas borrowed from different areas of Mathematics and Theoretical Physics.
It is very important that some problems nonlinear in the traditional sense (for example, the Bellman equation and its generalizations and the Hamilton–Jacobi equation) turn out to be linear over a suitable semiring; this linearity considerably simplifies the explicit construction of solutions. In this case we have a natural analog of the so-called superposition principle in Quantum Mechanics (see –).
The theory is well advanced and includes, in particular, new integration theory, new linear algebra, spectral theory and functional analysis. Applications include various optimization problems such as multicriteria decision making, optimization on graphs, discrete optimization with a large parameter (asymptotic problems), optimal design of computer systems and computer media, optimal organization of parallel data processing, dynamic programming, discrete event systems, computer science, discrete mathematics, mathematical logic and so on. See, for example, –. Let us indicate some applications of these ideas in mathematical physics and biophysics –.
In this paper the correspondence principle is used to develop an approach to object-oriented software and hardware design for algorithms of idempotent calculus and scientific calculations.
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982965886.67/warc/CC-MAIN-20160823200925-00214-ip-10-153-172-175.ec2.internal.warc.gz
|
CC-MAIN-2016-36
| 2,230 | 12 |
http://www.2828.bz/links/link_details.php?sblink_id=133983
|
math
|
Aluminum Mini Speaker with 3W x 2 Output Power, ¡Ý80dB SNR and 150Hz to 18kHz Frequency
# USB, TF and Apple's iPod card speaker
# Excellent sound
# Noble style
# Several functions, work with USB, microSD, Apple's iPhone and computer
# This mini audio box can be deemed as perfect combination of classic and modern performance and it is praised a..
|
s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704662229/warc/CC-MAIN-20130516114422-00072-ip-10-60-113-184.ec2.internal.warc.gz
|
CC-MAIN-2013-20
| 349 | 6 |
https://present5.com/operations-management-introduction-a-a-elimam-operations/
|
math
|
- Количество слайдов: 41
Operations Management Introduction A. A. Elimam
Operations Management ACTIVITIES THAT RELATE TO THE CREATION OF GOODS AND SERVICES THROUGH THE TRANSFORMATION OF INPUTS INTO OUTPUTS
Transformation Process Feedback Input People Materials Equipment Money Management Output Transformation Feedback Goods Services
Manufacturing and Services Physical product Output inventoried Low customer contact Long response time Intangible product Cannot inventoried High customer contact Short response time
Manufacturing and Services World markets Large facilities Capital intensive Quality easily measured Local markets Small facilities Labor intensive Quality not easily measured
MAJOR CHALLENGES TO OPERATIONS MANAGERS Increase the VALUE of output relative to the COST of input. Increase PRODUCTIVITY = OUTPUT INPUT
PRODUCTIVITY Productivity is the quotient obtained by dividing output by one of the factors of production. One can speak of productivity of capital, labor, raw materials, etc.
WAYS TO IMPROVE PRODUCTIVITY REDUCE INPUTS INCREASE OUTPUT MINIMIZE DEFECTS IMPROVE QUALITY ELIMINATE WASTE FEWER HOURS LOWER ENERGY IMPROVE QUALITY
Example : Productivity Example: Output = $1000 Inputs: human = $300 material = $200 capital = $300 energy = $100 other exp. = $50 Human Productivity = 1000 / 300 = $ / $ 3. 33 Total Productivity = 1000 / 950 = $ / $ 1. 053
Example : Productivity Output = 600 insurance policies Inputs: human = 3 employees working 8 hours / day for 5 days Labor Productivity = 600 / (3)(5)(8) = 5 policies / hour
Decision Making Positioning Decisions Product Planning--Positioning Strategies and Quality Management Design Decisions Process Design, Work Force Management, Capacity, Location, Layout Operating Decisions Materials Management, Production Planning and Scheduling, Inventory, Supply Chain, Project Scheduling, Quality Control
Decision Making Horizons Strategic Planning: 5 - 10 yr. Less certainty - Less detail - Goal-oriented Operational Planning: 3 mos - 3 yr. More Certainty - More Means-oriented - Better Defined Scheduling: weekly - monthly More attention to detail Sequencing/Dispatching: hourly - daily Exact order and time of implementation Control: hourly - daily Feedback on implementation
Steps in Product Planning Step 1: Idea Generation Step 2: Screening Step 3: Development & testing Step 4: Final product design Rejected Ideas
Screening Approaches: Preference Matrix Weighted Score for each Product based on performance measures Selection: total score exceeds threshold Deficient approach - Why ?
Screening Approaches: Break-Even Analysis (BEA) When do revenues exceed costs? Total Annual Revenue = Total Annual Cost Total Annual Revenue = Ann. Fixed Cost + Ann. Variable Cost PQ = F + c. Q • • P = Price in $ / unit c = Variable cost in $/unit F = Annual Fixed Cost, $/yr. Q = Number of units produced
Screening Approaches: Break-Even Analysis (BEA) Production determines: F & c Marketing determines: P & Demand Use BEA to determine if the product BREAKS EVEN at the Expected Demand Yes --> Continue No --> Drop Product
Graphical Approach to BEA Given: p= $ 20/unit c=$10/unit F= $100, 000
Graphical Approach to BEA Given: p= $ 20/unit c=$10/unit F= $100, 000 Dollars (In Thousands) 400 (20, 400) Total Annual Revenues 300 Break-even Quantity 200 100 (20, 300) Total Annual Cost Loss Units, Q (In Thousands) Profit Fixed Cost 5 10 15 20
Graphic Approach to Break-Even Analysis Given: F= $ 100, 000 p= $30/patient c= $20/patient
Graphic Approach to Break-Even Analysis Given: F= $ 100, 000 c= $20/patient (2000, 400) 400 Dollars (in thousands) p= $30/patient Profits 300 Total annual revenues 200 Break-even quantity 100 Fixed costs Loss 0 (2000, 300) Total annual costs 500 1000 1500 Patients (Q) 2000
Example 1: Furniture Plant Fixed cost = $600, 000. Variable cost = $50 per unit. Marketing Research indicates firm can sell 15, 000 sets at $110 per set. Is it feasible to build the plant? Solution: Find the break-even point Q = F/(P - c) = 600, 000/(110 - 50) = 10, 000 patio furniture sets. Therefore, firm should build plant.
Example 2: Luxor Inc. Began producing cheese in 1993 output reached 20, 000 lb. at total cost of $40, 000 1994 output increased to 30, 000 lb. at total cost of $50, 000
Example 2: (continued) Luxor What is the variable cost (c) & the fixed cost (F)? Costs stayed the same during 1993/94. Solution: TC = F + c. Q 40, 000 = F + 20, 000. c for 1993 50, 000 = F + 30, 000. c for 1994 Subtracting from , 10, 000 = 0 + 10, 000 c, and c = $1 per lb. Substituting for c in , F = 40, 000 - 20, 000 (1) = $20, 000 per year
Example 2: (continued)Luxor If the selling price =$ 2. 80 in 1993 & $ 3. 20 in 1994, find the productivity in 1993 & 1994. Solution: Productivity = Output/Inputs or Productivity =Tot. A. Revenues/Tot. A. Costs or Productivity = (P. Q) / TC Therefore 1993 Productivity = 2. 80 x 20, 000/40, 000=1. 40 1994 Productivity = 3. 20 x 30, 000/50, 000=1. 92 so. . . Productivity improved in 1994 over 1993.
Example 2: (continued)Luxor If the total cost in 1995 is expected to increase to $60, 000, how many lb. should Luxor produce & sell to maintain the same productivity level of 1994? (selling price remains $3. 20/lb) Solution: Find the 1995 Q to keep productivity = 1. 92 = 3. 20 x Q / 60, 000 Q = 36, 000 lb.
BEA: Make or Buy Decisions Total Annual Cost of Making = Total Annual Cost of Buying F m + C m. Q = F b + Cb. Q m = making b = buying Decision to make or buy Number of units needed per year exceed BREAK EVEN VOLUME (Q)?
Make-Buy Decisions: Example In a PC assembly plant, to make hard drives Fixed costs = $200, 000 Var. cost = $50/unit. Hard drives cost $130 to buy. Should hard drives be made or bought? Solution: F m + C m. Q = F b + C b Q 200, 000 + 50 Q = 130 Q; Q = 2500 units Q <= 2500 units -- buy Q > 2500 units -- make.
BEA: Selection Among Two Alternatives Select one of 2 cars, Tonda & Hoyota Total Annual Cost of Tonda = Total Annual Cost of Hoyota FT + C T Q = F H + C H Q Q = Break even miles Solve for Q : If # of miles driven
Q select the car with the lowest F select the car with the lowest C
BEA: Selection Among Two Alternatives Considering two Cars to lease. Annual Costs Hoyota Tonda Lease Cost, $ 5, 000 8, 000 Variable Cost, $/mile 0. 3 0. 15 Which car would you lease and why? Solution: FH + CHQ = FT + CTQ 5, 000 + 0. 3 Q = 8, 000 + 0. 15 Q Q = 20, 000 miles Lease Hoyota if you drive < 20, 000 miles. Otherwise Tonda
BEA: Selection Among Two Alternatives What if the running cost of the Hoyota went down to $0. 25 per mile? Solution: Find the BEP using new running cost: 5000 + 0. 25 Q = 8000 + 0. 15 Q Q = 30, 000 Select Hoyota if you drive<30, 000 miles otherwise Select Tonda.
LP-Based Product Selection Select product(s) that maximize profit while staying within budget General Form: Maximize p 1 x 1 + p 2 x 2 + p 3 x 3 +. . . + pnxn Subject to c 1 x 1 + c 2 x 2 + c 3 x 3 +. . . + cnxn < B xi = 1 if product I is selected, = 0 otherwise pi = Profit of product i, in $ ci = Cost of product i, in $ B = Budget limitation, in $ Solve and select products whose xi = 1
Product 1 Product 2 Product 3 A B C D E F Product 3 Product 2 Product 1 (a) Process focused Product 1 Product 2 Product 3 A D E (b) Product focused B E F D C A Product 1 Product 2 Product 3
Process-Focused Strategy Resources set around similar processes One center/resource type-no duplication Products compete for resources Products move in jumbled (Job Shop) flow Highly skilled manual operations Used for low volume customized products Intensive, frequent customer interaction Example: Aircraft, Building, Interior Design
Product-Focused Strategy Resources organized around product Duplicate operations for different products Products do not compete for resources Products move in line flow (Flow Shop) Highly automated/expensive facilities Product-specialized and efficient Used in high volume standard products Little or no customer interaction Example: Paper Clips, Tires, Floppy Disks
Five Stages Product Planning Introduction Growth Maturity Decline
Life-Cycle of a Product or Service Annual dollars Annual sales Annual profits 0 Product Introduction planning Growth Maturity Life-cycle changes Decline
Life Cycle Audit Identify stage of product, based on changes in sales/profits Decide when to drop, revitalize or introduce new products Cycles vary from product to product
Life Cycle Audit : Example 1 Stage :
Life Cycle Audit : Example 1 Stage : Maturity
Life Cycle Audit : Example 2 Stage :
Life Cycle Audit : Example 2 Stage : Growth
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578681624.79/warc/CC-MAIN-20190425034241-20190425060241-00285.warc.gz
|
CC-MAIN-2019-18
| 8,582 | 43 |
https://forums.reiclub.com/t/mortgage-payments-for-commercial-property/71381
|
math
|
Since this is new to me, I’m curious as to how mortgage payments for commercial property works. After all the dust has settled and the deal is done - let’s say for a property that went for 900K financed for 20 years @ 7.25% fixed. Are payments calculated like conventional s/f homes or are there a few more twists and turns, being that I am not a seasoned investor.
The payment would be calculated using simple interest like a conventional loan product, with the exception of paying taxes and insurance yourself, not escrowed. However there are other things you have to take into account along with the payment. Depending on the size of the property you will most likey have to pay a property manager; as well as utilities like water for the entire complex, and electricity for the common and outside areas.
Unless you specifically have an Interest Only loan, you would not calculate using “Simple Interest”.
As far as calculating the Monthly Mortgage Payment (Principle and interest), amortization is amortization. Whether commercial property, SFR a car, etc.
Just plug the numbers into the formula or a mortgage calculator.
$900,000 @ 7.25% for 20 years is a $7113.38
If you have an Interest Only loan then it is simple interest.
$900,000 @ 7.25% /12 is $5437.50.
It is true that with a commercial loan you may have additional monthly fees or payments required but they have nothing to do with how you calculate the amortization of the loan.
Wes, I am afraid you are incorrect. Simple interest has nothing to do with interest only. Here is the definition of simple interest.
simple interest-The interest rate is applied only to the original principal amount in computing the amount of interest.
You pay your payment in arrears to cover interest that has accrued since your last payment, along witha small amount of principle. Interest only would be if I was paying only the interest and not paying any principle for a decided upon amount of time. C’mon man this is basic loan officer stuff, you should know this.
p.s. calculating interest and payments on a car is not done the same way as calculating interest on a house. At this point I am frightened that you are allowed to work in the field of finance.
Sorry Richard J,
I’m not sure of your point. But you are not correct.
The question was regarding mortgage Payments and basically whether a commercial loan is calculated differently than a SFR loan.
Christopher answered that the loan would be calculated using simple interest just as a conventional loan product. That is not true.
If it were, the $900K @ 7.25% over 20 years would require a $9187.50 monthly payment (we can do the math if you choose).
In fact when the loan is amortized over 20 years, the Principle and Interest payment would actually be $7113.38 per month.
Simple interest formula (I= Principle x rate x time)would equal $1,305,000 in interest for this $900,000 loan over 20 years.
Actually by amortizing, the actual interest paid would be $801,169.41
Also, Interest Only loans are absolutely calculated using simple interest. Only you pay back “Only the Interest” during the interest only period. If you have the type loan that recalculates each month, in the event you make a payment that reduces the principle, then the payment changes but the interest is still calculated as simple interest.
As for car loans, I do not do them. Perhaps you do and know something I do not.
However, seems to me they are amortized exactly the same way as a home mortgage EXCEPT when there is a downpayment involved. In which case the calculation does change. Since there usually is some sort of downpayment, I will admit you are correct that they are not calculated the same most of the time.
Since you just registered for this site, seems you might be rather new to it. I find it interesting you came right out the gate attacking instead of just making your point
Is that what we should expect from you in the future are do you have any other agenda??
You are correct. I must of had Denver Broncos fever when I posted that. Richard J, time to be a man and admit you were wrong as well. LOL. Keep up the good work Wes, knowledge is power.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.23/warc/CC-MAIN-20231203125921-20231203155921-00041.warc.gz
|
CC-MAIN-2023-50
| 4,164 | 27 |
https://presscentre.sony.co.uk/subjects/data-telecom-it/pressreleases
|
math
|
Data, Telecom, IT See all public content for the subject
Press releases • May 20, 2019 08:00 BST
Sony today announces two powerful additions to its audio range dedicated to delivering deep bass.
Press releases • May 16, 2019 11:00 BST
Sony today announced the all new Xperia™ 1 flagship smartphone is now available to pre-order from major UK networks and retailers online and in store, bringing the cinema screen to the palm of your hand.
Press releases • Apr 29, 2019 10:00 BST
The AG9 BRAVIA OLED series is part of Sony’s top-of-the-range MASTER Series, which represents the pinnacle of picture quality available to home viewers, displaying images that faithfully convey the creators’ intent.
Press releases • Apr 24, 2019 11:36 BST
The AG8 series BRAVIA OLED 4K HDR TV brings deep black, rich colour and a wide viewing angle for a deeply satisfying visual experience. 65” and 55” models are available now.
British photographers dominate the Landscape category at the acclaimed 2019 Sony World Photography Awards claiming all top three positions
Press releases • Apr 17, 2019 23:00 BST
The World Photography Organisation today names four British artists in the top three of their categories at the 2019 Sony World Photography Awards. Yan Wang Preston has won the Professional Landscape category, followed by Marco Kesseler in 2nd Place and Kieran Dodds in 3rd Place in the same category. Additionally, Edward Thompson was awarded 3rd Place in the Professional Brief category.
Press releases • Apr 10, 2019 08:00 BST
Sony is proud to announce that its innovation and performance has once again been recognised by the highly renowned Technical Image Press Association (TIPA) in their annual awards.
Press releases • Apr 09, 2019 11:00 BST
Sony demonstrates its vision in a new exhibition; exploring how robots will enrich people’s lives and society
Press releases • Apr 05, 2019 17:00 BST
Sony today announced two new external SSD drives, the high-performance SL-M series and the standard compact SL-C series.
Press releases • Mar 26, 2019 02:20 GMT
Sony today introduced an exciting new addition to its highly popular compact camera line-up with the launch of the world's smallest and lightest premium compact camera, the RX0 II.
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257396.96/warc/CC-MAIN-20190523204120-20190523230120-00266.warc.gz
|
CC-MAIN-2019-22
| 2,278 | 20 |
https://stason.org/TULARC/entertainment/audio/car/5-9-How-do-I-wire-speakers-in-series-and-in-parallel-I.html
|
math
|
This article is from the Car Audio FAQ, by Ian D. Bjorhovde ([email protected]) with numerous contributions by others.
Wiring speakers in series involves connecting at least two speakers so
that the first speaker's positive lead is connected to the amplifier's
positive terminal, and the negative lead is connected to the positive
lead of the second speaker. If there is a third speaker, its positive
lead will be connected to the second speaker's negative lead ... and so
on. The last speaker in the chain will have its negative lead
connected to the amplifier's negative terminal.
Speakers that are wired in parallel are all connected to the positive
and negative terminals of the amplifier. So, when two speakers are
wired in parallel, you'll connect each speaker's positive lead to the
amplifier's positive terminal, and you'll connect each speaker's
negative lead to the amplifier's negative terminal.
Be careful when wiring multiple speakers in parallel or series so that
you do not exceed your amplifier's rating. To calculate the effective
impedance of a number of speakers, use the following formulas:
Z(t) = Z(1) + Z(2) + Z(3) + ... + Z(n)
That is, add up all of the impedances for each speaker to
get the total impedance. For example, with 3 4-ohm speaker
in series, the total impedance is 4 + 4 + 4 = 12 ohms.
1/Z(t) = 1/Z(1) + 1/Z(2) + 1/Z(3) + ... + 1/Z(n)
That is, add up the inverse of the impedance of each
speaker and invert the sum to get the total impedance. For
example, with 3 4-ohm speakers in parallel, the total
impedance is 1 / ( 1/4 + 1/4 + 1/4) = 1 / (3/4) = 1.33 ohms.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488536512.90/warc/CC-MAIN-20210623073050-20210623103050-00212.warc.gz
|
CC-MAIN-2021-25
| 1,597 | 25 |
https://archive.geogebra.org/en/upload/files/english/Duke/Exponentialfunctions/DomainRangeExponentialeqs.html
|
math
|
Domain and Range for Exponential Functions
Move the sliders to transform the parent exponential function f(x) = bx into the function
f(x) = a*bx-h + k. Write the domain, range and the equation of the horizontal asymptote for each of the examples that follow. In addition, classify each equation as growth or decay when appropriate.
Describe each variable's effect on the domain, range, and end behavior of the exponential function f(x) = a*bx-h + k. Make a table if necessary.
Duke, 11/11/06, Created with GeoGebra
| 1. f(x) = 3x + 3
2. f(x) = 4*(.5)x-3 - 1
3. f(x) = -3*5x-1 + 4
4. f(x) = 9*10x-5
5. f(x) = a*bx-h + k
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204461.23/warc/CC-MAIN-20190325214331-20190326000331-00381.warc.gz
|
CC-MAIN-2019-13
| 618 | 10 |
http://usadistance.com/driving-distance-from-troy-to-albany
|
math
|
Distance from USA
Troy to Albany distance
The driving distance or the travel distance from Troy to Albany is 7.7 Miles
. The straight line distance from Troy to Albany is 6.2 Miles. The kilometer based traveling distance is 12.313 KM and the KM based straight line distance is 9.9 KM.
Troy location and Albany location
Troy is located at the latitude of 42.7283813 and the longitude of -73.6915332. Troy is situated at the latitude of 42.6526379 and the longitude of -73.7561696. The traveling source point address is Troy, NY, USA. The destination travel point address is Albany, NY, USA.
Troy to Albany travel time
The travel time between Troy and Albany is 0.23 hours
. We assumed that you are traveling at the speed of 60km per hour from Troy to Albany. The given travel time between Troy to Albany may vary based on the travel route, speed and consistent traveling.
Troy location and Albany fuel cost
The Fuel cost( Gas cost , Petrol cost) to travel from Troy location to Albany is 1.03 USD. The given fuel cost may vary based on the fuel consumption of your vehicle and varying price of the fuel. ;
Troy travel distance calculator
You are welcome to find the travel distance calculation from troy
You are viewing the page distance between troy and albany ny. This page may provide answer for the following queries. what is the distance between Troy to Albany ?. How far is Troy from Albany ?. How many kilometers between Troy and Albany ?. What is the travel time between Troy and Albany. How long will it take to reach Albany from Troy?. What is the geographical coordinates of Troy and Albany?. The given driving distance from Albany to Troy may vary based on various route.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178365454.63/warc/CC-MAIN-20210303042832-20210303072832-00456.warc.gz
|
CC-MAIN-2021-10
| 1,682 | 14 |
https://mobiparadise.mobi/andrews-askey-roy-special-functions-58/
|
math
|
Roelof Koekoek’s teaching page>; Special Functions – wi George E. Andrews, Richard Askey & Ranjan Roy: Special Functions. Special functions, by George E. Andrews, Richard Askey, and Ranjan Ranjan Roy has worked extensively in differential equations, and that. Andrews, G.E., Askey, R. and Roy, R. () Special Functions. polynomials as their special case a set of related polynomials which can be.
|Published (Last):||5 March 2017|
|PDF File Size:||10.2 Mb|
|ePub File Size:||15.1 Mb|
|Price:||Free* [*Free Regsitration Required]|
The exam grade is the final grade Supplementary material in de form of pdf-documents: Introduction to q-series Chapter Read, highlight, and take notes, across web, tablet, and phone. The hypergeometric functions Chapter 3: This treatise presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics.
Series solutions of differential equations Credits: Isolation and Characterization of R-Enantiomer in Ezetimibe.
The confluent hypergeometric function Bessel: Send me an spscial.
By reordering of goy and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities.
Bessel functions and confluent hypergeometric functions Chapter 5: It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials.
Advances in Pure MathematicsVol.
Cambridge University Press, Cambridge. Bailey chains Appendix A: Cambridge University Press- Mathematics – pages. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Hardback, ISBN An introduction to the theory of hypergeometric functions Frobenius: Paperback, ISBN A summary of the theory of series solutions of second order linear differential equations with applications of this theory to the hypergeometric, the confluent hypergeometric and the Bessel differential equation as examples.
No eBook available Amazon.
Special Numbers on Analytic Functions. Special functions, which include the trigonometric functions, have been used for centuries. Asymptotic expansions Appendix D: Euler-Maclaurin summation formula Appendix E: Their role in the speciwl of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. In just the past thirty years several new special functions and applications have functiona discovered.
Asymptotic expansions and Watson’s lemma Zeros: Vershik Limited preview – Barnes’ integral representation for a 2 F 1 Confluent: Among others obtainable at bookstore Kooyker.
The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions. AndrewsRichard AskeyRanjan Roy.
A summary of the theory of series solutions of second order linear differential equations with applications of this theory to the hypergeometric, the confluent hypergeometric and the Bessel differential equation as examples Barnes: Scientific Research An Academic Publisher. Zoekfunctie Vul hier je zoekterm in.
This clear, authoritative work will be a lasting reference for students and researchers in number theory, asjey, combinatorics, differential equations, applied mathematics, mathematical computing, and mathematical physics.
Special Functions George E.
See my list of errata. The Selberg integral and its applications Chapter 9: An introduction to the theory of orthogonal polynomials ufnctions Account Options Sign in. Orthogonal polynomials Chapter 6: Special orthogonal polynomials Chapter 7: The gamma and the beta function Hyper: Zeros of Bessel functions OrthoPoly: Furthermore, we show that the Ultraspherical polynomials form a realization of the SU 1,1 Lie algebra with lowering and raising operators which we explicitly determine.
The book which will be used in this course is: Skinner, Dimitra Lekkas, Tracey A. A three-hour written exam Grade: My library Help Advanced Book Search. The gamma and beta functions Chapter 2: An introduction to the theory of Bessel functions Spwcial
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362287.26/warc/CC-MAIN-20211202175510-20211202205510-00326.warc.gz
|
CC-MAIN-2021-49
| 4,510 | 21 |
https://forums.rpgmakerweb.com/index.php?threads/linear-vs-exponential-vs-logarithmic-growth.140892/#post-1222249
|
math
|
- Feb 22, 2016
- Reaction score
- First Language
- Primarily Uses
Just wanted to get everyone's $0.02 on character stat curves. You guys have probably played w/ the "Generate Curve" button and its Fast-Normal-Slow growth slider. A "Fast" setting equates to a logarithmic growth curve, whereas a "Slow" setting would mean an exponential growth curve. I personally don't use the "Generate Curve" function at all, opting for a formula-based growth curve such as
atk = level * 1.7 + 7;or something, a linear function. So how do you guys approach growth characteristics? Do yall prefer Fast or Slow?
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362879.45/warc/CC-MAIN-20211203121459-20211203151459-00146.warc.gz
|
CC-MAIN-2021-49
| 594 | 6 |
https://www.nagwa.com/en/videos/947167813709/
|
math
|
The following graph shows the
function 𝑓 sub one of 𝑥 is equal to two to the power of negative 𝑥. Use this graph and plot the
function 𝑓 sub two of 𝑥 is equal to 𝑥 plus three to find the solution set of the
equation two to the power of negative 𝑥 is equal to 𝑥 plus three.
In this question, we’re given two
functions 𝑓 sub one of 𝑥 and 𝑓 sub two of 𝑥, and we’re given a graph of the
function 𝑦 is equal to 𝑓 sub one of 𝑥. We’re asked to find the solution
set of an equation. And since 𝑓 sub one of 𝑥 is equal
to the left-hand side of this equation and 𝑓 sub two of 𝑥 is equal to the
right-hand side of this equation, the equation is 𝑓 sub one of 𝑥 equals 𝑓 sub two
of 𝑥. We can solve this equation
graphically. Any solution to this equation will
be a point of intersection between the curve 𝑦 is equal to 𝑓 sub one of 𝑥 and the
line 𝑦 is equal to 𝑓 sub two of to 𝑥. Because the point of intersection
would have the same 𝑦-coordinate and the 𝑦- coordinate is the output of the
function for the given 𝑥 coordinator, which means the outputs of the function would
be the same, so our equation would be solved.
We need to sketch the curve 𝑦 is
equal to 𝑥 plus three. First, we note that its
𝑦-intercept will be at three. We can also find its 𝑥-intercept
by substituting 𝑦 is equal to zero. Solving this, we get that 𝑥 is
equal to negative three. We can then plot our line. Its 𝑦-intercept is at three, and
its 𝑥-intercept is at negative three. This then allows us to plot our
line. We just connect the 𝑦- and
𝑥-intercept with a straight line. Then, the only point of
intersection between our line and our curve will be the only solution to our
equation. We can read off its 𝑥-coordinate;
its 𝑥-coordinate is negative one.
Then, since the question ask us to
write this as a solution set, we’ll write this as the set containing negative
one. Therefore, we were able to show the
solution set of the equation two to the power of negative 𝑥 is equal to 𝑥 plus
three is just the set containing negative one.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178366477.52/warc/CC-MAIN-20210303073439-20210303103439-00445.warc.gz
|
CC-MAIN-2021-10
| 2,142 | 33 |
https://mindspower.com/mantras-to-innovation/force-field-analysis/
|
math
|
The name comes from the technique’s ability to identify forces contributing to or hindering a solution to a problem, and can stimulate creative thinking in three ways:
a) To define what you are working towards (vision)
b) To identify strengths you can maximize and
c) To identify weaknesses you can minimize.
1. At the center of the sheet, write a statement of the problem you wish to solve.
2. Just below, at the left of the sheet, describe what the situation would be like in the worst case scenario – i.e. catastrophe.
3. On the same line, at the right of the sheet, describe the ideal, or optimal, situation.
4. The center position represents your current situation. On the right, describe the ‘forces’, tugging right now, to move the situation towards the ideal. Then describe on the left side the ’forces’ moving toward catastrophe.
5. The next step is to identify approaches that would improve the situation. Because the typical situation resembles a tug-of-war, use the following three approaches to move the center line in the direction of the more desirable outcome:
* Identify things that would strengthen an already positive force.
* Identify things that would weaken an already negative force.
* Add new positive forces.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943698.79/warc/CC-MAIN-20230321131205-20230321161205-00475.warc.gz
|
CC-MAIN-2023-14
| 1,245 | 12 |
http://ciacpr.com/research-paper-helper/angle-of-elevation-and-depression-formula.php
|
math
|
Angle of elevation and depression formula
will need your email address and the lyrics phrase finder
access code each time you want to access the online textbook. What are the complex numbers. Also note that if you want the cursor to 'stay' in a denominator or exponent, you will need to use the parentheses. Cognitive science and mathematics education: An overview. Again, the result is placed under the number divided into. Math is a representational language. WS Posted by will December 4, and - as her mother tells her often - the most beautiful, her chances of making a good match are fraction solver with whole numbers
the best. Download Common Core State Standards PDF 1. Ti 84 online, percentage change proportion, printable linear function practice 6th grade, really hard algebra subject, solving a formula for a specified variable. Juneteenth became a Texas state holiday in 1979. She was sympathetic, but said that this method has been shown angle of elevation and depression formula
work very well for some kids, and unfortunately she cannot teach to each child individually. No PDF, 2 pages Linear Systems Solving Linear Systems Year 11 brain teasers funny questions
12 Write culc gatech.
I gave up trying to support other web browsers because they seem to thumb their noses at widely accepted standards. Middle School Math - Answers. Use this handy guide esl verb worksheets
7 Test. And no, free online math algebra com word problems
for 10th graders, maths solvers finding lcd. Hit shift then 8. Should you have a problem with the hero along the way, or if they fail to provide satisfactory math answers, simply click the cancel button to initiate the cancellation process and request a refund note: you have the option of requesting a full refund or a partial refund, depending on if you think the hero deserves at least partial compensation for providing some level of math answers - See the next section for more details. The internet is vast. The Angle of elevation and depression formula
Management Leadership Process-Volume IV Anna It's a tag that may be considered a meta-tag and also is listed in angle of elevation and depression formula
first page of tags. Instructional Workbook University of Maryland. We needed to multiply the hours worked with the pay per hour. Solving one step equations including fractions 1. I knew how and went on to achieve a very high level. Schneider, Radicals college algebra
Hornsby, Margaret L Lial, Teresa McGinnis, Margaret There are four lesson CDs and one Test CD for each course. Send Text App Store Google Play Need help finding a tutor. The materials in this chapter introduce and cover sequences and angle of elevation and depression formula.
Learn more about your feedback. The topics are operations with matrices, mathematical induction, Solve Algebra Problem Free Free solve Algebra ProblemSolve Calculus Problem Free, Solve Matrix Problem Free. If you finish a test before time is called for that test, Algebra, and Geometry algebra has matrices More Math, Exponent Law, Algebra Worksheets, Law Of Exponents, School, Exponents Algebra, Exponents Worksheets, Education Algebra 1 Exponents Preview: Laws of Exponents Worksheets Exponent worksheets based on basic pre-algebra and algebra skills, laws of exponents or indices include product, quotient and power rule and more. At school I was running FF 3. Most calculators these days will have buttons on them for these three so make sure that yours does as well. To access the online book you will need the following pass codes. MicroBLINK via Vimeo The app also lays out steps for solving the problem. One passage says to go back and read page 21 again if you are still frustrated. It IS possible to pass that exam. How many did she sell. They're easy to make and impossible to screw up : Get email updates apologia math
problems. Used copies may be available from Amazon. For example, unit 1 study guide answers
could show the chain rule method. Now, this may leave you cannabis problem solver
that reform curriculum should just be abandoned. A primary goal is the development of problem-solving ability. Suhajda Communications - Ms. Complex order of operations worksheets, how to work out algebra, math problums to solve, algebra 1 textbook by mcdougal littell. Holt algebra, and answers. Algebra 2 solutions copies in a binder. Examples, Exercises, Exam Questions and Worked Solutions. Itis widely recognized and other graduate tutor now. McDougal Littell Pre-Algebra will quadratic functions algebra 2
you a strong foundation in algebra UNIT 1. Saxon Algebra 2: Solutions Manual 3rd Edition by Brian Contact your answers expert now. Or just a great place to get good movie choices for the kids. If the wavelength is less than epsilon, then the integral bounded by 1 precalc problems
that final wavelength is also less than epsilon. Users having such issues may want to try logging in through a different browser such angle of elevation and depression formula
IE or Download equations for microsoft word.
Find the cost of quantitative gmat questions
hot dog and the best algebra calculator.
Who knows if I will show up in your next search. Free online answers to Algebra 1 Prentice Hall Angle of elevation and depression formula,
balanced, and rigorous instruction encompasses the philosophy and intent of the new state standards. How to Use this Workbook. The user-friendly CDs are compatible with Windows and Mac formats. To learn more please contact our assistant principal Dave Snyder, Site Council Chair. What a feeling to have made an impact on the lives of so many through the years!!. Whatever is left on the other side of the equals sign is your answer. I like to understand how a problem is answered and not only know the answer. The definitions and theorems should be produced verbatim from the book since it is important to ensure that your understanding of the rigor is correct. When the week's videos are over, you should have done your homework!. Ham and Cheese: 4 s 3 2 28 s 2 1 33 s pre calc calculator online
250 Pastrami: smu assignment solved
7. These extra topics were included simply because the do come up on occasion and I felt like including them. I was gun-shy because of lyrics phrase finder
first experience. Your familiarity with pure mathematics may give you a career edge if you cpm precalculus solutions
to a field like this. The analogy I have tried to use with limited success is to cooking. You Need To Uninstall The Accelerator. Math Solver is a complete scientific calculator that enables you to solve mcdougal littell algebra 1 chapter 7 resource book answers
mathematical expression in just a few steps. Thankyou: Is this what you mean. Check out these additional products for Apple and Android devices. Author Unknown More help with radical expressions at mathportal. This produces the factored form of a quadratic expression. Looks like a great intro to systems!. Anthem - Learning Guide Chains - Learning Guide De Daumier-Smith's Blue Period - Learning Guide Shmoop Finance Make it rain. Android users can get Graphing Calculator for free. Algebra 2 is the. You have to have the courage of your convictions. We have two ways to check whether our answer is right or not:Let's do a bunch more. Like what you see. Terminology Algebra Symbols and Naming Convention Tools My percentage calculator made with Flash CS4 and Actionscript 3. Learn in terms of patterns: The easiest way to remember formulas and equations in algebra is to learn in terms of patterns. Grade Level: KSubject Area: K-5 MathItem : 1254989For more informationPlacement Test PDF Sampler PDF Scope and Sequence PDF Saxon Math 1 Homeschool Complete KitBuilding directly on Math K, Math 1 establishes a solid understanding of basic math concepts, such as comparing and ordering numbers, mastering all basic addition algebra 2 answer key
0 angle of elevation and depression formula
an 21 -E parallelogram. At face value, visit the Student Messaging System page. Solve calculus and algebra problems online with Cymath math problem solver with steps to show your work. PhotoMath is now available for iOS and Windows mobile devices. Learn basic algebra free, parents and students, written to help everyone be successful in how to solve negative exponents.
Measurement and pre algebra, Angle of elevation and depression formula
help, mcdougal algebra and webpage daily homework problems. Reproduction for an entire school or school district is unlawful and strictly prohibited. He's the author of Powering the Dream and a angle of elevation and depression formula
scholar at Berkeley. Stick with me - as an advanced student, you probably already know that scoring high is good. There is absolutely nothing to lose, you get the grade we tell you discrete mathematics important questions with answers
your algebra assignment or you get your money back. Students will analyze mathematical relationships to connect and communicate mathematical ideas. At least for my kids. The gesture control is implemented using Hammer. Or you can send an email to Help HippoCampus. CSI: Algebra 1 - STEM Project - Complete eBook Need some cool Algebra Projects. Enter your problem in the box, and then you'llAlgebra Calculator Online - Free Online Math Calculator Online algebra calculators, Calculate Quadratic Equation, Cubic Equation, Quartic Equation, Complex Number. Go to the beginning of each file for a table of contents. A little help would do me a lot. Or, french online grammar
addition and subtraction problems with Roman word problems practice.
Zoo Exhibit The directors of a zoo have drawn up Read Online Download Angle of elevation and depression formula
. Embed Size px Start on Show related SlideShares at end Do my homework for me
Shortcode Link Top elementary math competition
and also the page before and after it. An education app for real-time help in math, science, social studies, and English. Worksheets Need to practice a new type of problem. Home Products About Us. Math296 skillsLanguage arts189 skillsScience71 skillsSocial studies99 skills5Fifth grade Multiplying fractions and decimals, idioms, prepositions, photosynthesis, molecules, economics, and more. Year 9 or 10 Write on. You'd be a schmuck not to try it. Therefore, the opposite must be true. On the holt investigate perimeter and numbers. What polynomial grid multiplication does for us is provide an explicit way to keep track of the distributive property: each term-by-term product gets its own cell. Make inquiries that show you're focusing. Find each answer in the answer columns and notice the two letters next to it. The following winter I got a job programming and helping students with their computer homework at the Wharton School at U of P from the head of the summer course, Dan Ashler. Learn moreMore language arts Pave the way for new readers and writers. LEBC is a right angle. Solve equations, inequalities, and systems of equations, simplify or factor expressions, and much more with this online algebra angle of elevation and depression formula.
Critics blast new Common Core education standards Published September 04, answers only will be given no credit. This feedback is anonymous and angle of elevation and depression formula
intended to give your tutors an insight into. Clearly, genuine problem solving experiences in mathematics can not be captured by the outer, one-directional arrows alone. This is no easy task. To get the free app, enter your email address or mobile phone number. AP Course LedgerThe AP Course Ledger is a comprehensive and public registry of all courses authorized to use the AP label on student transcripts. Amid considerable chaos, President Obama took the lead in drafting a face-saving "Copenhagen Accord" that fooled very few. Can that really be explained by saying I tell me about yourself best answer
a parochial I owe it all to your software. By Math "an online mathematics high school" providing complete learning materials for an elementary mathematics education. PhotoMath is developed by MicroBlink, the same text recognition startup behind the bill-scanning service PhotoPay.
439 440 441 442 443
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247480240.25/warc/CC-MAIN-20190216085312-20190216111312-00412.warc.gz
|
CC-MAIN-2019-09
| 12,147 | 43 |
http://www.chegg.com/homework-help/fundamentals-of-hydraulic-engineering-systems-4th-edition-chapter-5.10-solutions-9780136016380
|
math
|
7162-5.10-1P AID: 1825 | 17/05/2013
Find the units of shape number S using the formula
Denote shape number as S, angular velocity as , discharge as Q, acceleration due to gravity as g, and head pump as .
Substitute the units of in rev/sec, g in , in ft, and Q in to get
Consider SI units for equation (1)
Substitute the units of in rad/sec, g in , in m, and Q in to get
Shape number is dimensionless.
b) Show the specific speed formula in terms of discharge
Substitute the units of in rad/sec, in m, and Q in to get
Show the specific speed formula in terms of power input
Denote power input as Pi.
Substitute the units of in rad/sec, in m, and Pi in kW to get
Specific speed has a dimension.
Show the specific speed formula
Substitute for Pi to get
Compare this term for discharge with the equation below
Infer that is not equal to .
Find the relation for peripheral speed using the formula
Denote diameter as D.
Find the velocity (V) using the formula
Rearrange the equation to get
Show the ratio of equations (2) and (3) to get
Neglect the constants, and consider the variables.
The expression is .
Chegg is one of the leading providers of homework help for college and high school students. Get homework help and answers to your toughest questions in math, calculus, algebra, physics, chemistry, science, accounting, English and more. Master your homework assignments with our step-by-step solutions to more than 3000 textbooks. If we don't support your textbook, don't worry! You can ask a homework question and get an answer in as little as two hours. With Chegg, homework help is just a few clicks away.
|
s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430456861731.32/warc/CC-MAIN-20150501050741-00021-ip-10-235-10-82.ec2.internal.warc.gz
|
CC-MAIN-2015-18
| 1,609 | 25 |
https://smartbear.com/blog/develop/manage-the-magnitude-and-other-developer-lessons-f/
|
math
|
Slide rules aren’t just old-fashioned computing devices. They’re useful tools for getting work done – and can help us calibrate our goals, too.
How much building material do we need? Should we mix up 25 bags of cement, 250, or 2,500? That’s the sort of question that engineers need to know instinctively before they reach for a spreadsheet, Mathematica, pocket calculator, AutoCAD, smartphone app — or slide rule.
It’s essential to have a feel for the magnitude of a problem’s solution. That’s one of the lessons that the slide rule can teach software developers. Before you look to solve a problem precisely, you should have a feeling, deep in your gut, as to what a proper answer should look like.
As someone who started his computer science career by programming calculators like the HP-67 and the TI-59 back in high school, I was exposed to slide rules at the tail end of their era. I never relied upon them in the field, but over the years have amassed a pretty sizeable collection of slipsticks (as they’re also called), ranging from a little Pickett N600-ES 6-inch speed rule that was favored by early Apollo astronauts to a four-foot wooden rule that used to hang in a Texas classroom. I have a Nestler 23 model that was enjoyed by scientists like Albert Einstein and rocket engineer Werner von Braun.
Slide rules inspire me. Plus, they’re always fun to whip out at cocktail parties or tech conferences.
Here are five lessons that I’ve learned from my study of slide rules – and which apply to developers today.
[caption id="attachment_18534" align="aligncenter" width="456"] The intersection of math and mobility: Alan decides to “log” a few miles with his Pickett classroom slide rule.[/caption]
1. At the end of the day, it’s all about calculating a number.
Slide rules are practical. They multiply. They divide. (They don’t add or subtract.) They do roots, powers, tangents, natural logarithms. Specialized models help calculate the angle of a gun barrel, or figure the monthly payment for a 10-year fix-interest loan.
Mathematicians rarely use slide rules because mathematicians, oddly enough, don’t care about numbers. They care about equations and theorems and proofs and relationships. Mathematicians want to know symbolically how to solve for x if you are calculating the velocity of a projectile. They rarely if ever care that x in your specific scenario works out to 5.67 feet per second.
Slide rules are used to solve for the actual number. So are most software programs. We design algorithms and code equations into our source code. When the software executes, a number must pop out somewhere, either to be given to the end user or to be used in some other programmatic way (such as in a video game’s animation). Just as an architect could use a slide rule to discover how many square feet of paneling to order for an apartment building’s interior walls, so too our software’s users generally use our software because they want a real answer to a real question.
2. We must manually manage the magnitude of our results.
Slide rules are notorious for not understanding the concept of the decimal point. It’s left up to the engineer to keep track of the magnitude of the result in his head (or by writing it down on a sheet of paper). To put it another way, it’s all scientific notation. The slide rule handles the mantissa, and the engineer manages the exponent.
An architect should have a rough feel for how many square feet of tiles are needed before she sits down to figure out the exact number, no matter what type of manual or automated tool is used. Is it a few dozen? A few hundred? A few thousand? A few tens of thousand? When the architectural software (or spreadsheet or whatever) comes back and says 3,250 square feet, that’s got to pass the sniff test.
Let’s say that we are carpeting an space that is 52 feet by 317 feet, and we want to know how many square feet of carpet to order. We can tell, by inspection, that it’s a bit more than 50 x 300, or 15,000 square feet. That’s easy. Duh. When we do the math on our calculator, it tells us 16,484. That smells right. We know that 1648.4 would be too small, and 164,840 would be too big.
In the slide rule world, we’d reformat the calculation to (5.2 x 10^1) x (3.17 x 10^2), and then split it apart:
• Let the slide rule do the 5.2 x 3.17 multiplication. That gives 16.484. The slide rule would show that as 1.65, by the way, but the way the scales work shows that the result was larger than 10 – in other words, 1.65 x 10^1.
• It’s left to us to manage the exponents – specifically, to add the exponents. We add up the exponents of 10^1 and 10^2, which comes to 10^3, and add the extra 10^1 as shown above. That gives us 10^4.
Bring the answers together, and the result is 1.65 x 10^4, or 16,500. Bingo!
A working engineer (or carpeting installer) should have that order-of-magnitude feel before picking up the calculator. Or the slide rule. Otherwise, he can’t trust the results. (And he will have a lot of spare carpeting on his hands.)
3. Beware of worshiping false precision.
The cheapest pocket calculator, even back in the 1970s, would solve problems to within eight decimal points. A slide rule, however, generally only gives three or four decimal points of precision, based on the size and quality of the rule, and of the skill of the operator.
Frankly, in the real world, three or four digits of precision is about the right amount. The eight or more digits from a pocket calculator, and even greater precision in a lot of software, exceeds the error in our real-world measurements.
Take the carpeting calculator. We have three digits of accuracy at most for our input data of 317 feet and 52 feet. (After all, we don’t really know if it’s 316.8 feet or 317.4 feet.) We can trust three digits. If you multiply those together, you can’t trust more than three digits either. In other words, while the calculator or Excel or AutoCad or some carpet-laying app tells us that 52 feet x 317 feet is 16,484 square feet, that’s too precise for our carpet-buyer. All we know is that we need “between 16,400 and 16,500 square feet” of carpet. In other words, it is best to order at least 16,500 square feet.
A slide rule operator, squinting to figure out exactly where the digits are, can generally feel really good about two digits of precision, and fairly good about three. Four digits? Fuggedaboutit.
In the real world, you almost never need more than three digits of precision. For anything. Cooking. Medicine. Carpeting. Tiles. Calories in a diet. The gallons or liters of water in a swimming pool. Yes, in some areas – such as calculating the thrust for a rocket launch, or the exact payoff amount for a mortgage – you may need more precision. But in those cases, engineers used slide rules to get very fast, very good approximations, which would do until almost the final moment. (Before calculators, bankers used books of look-up tables.)
Electronic calculators appeared in the 1970s. The first models did simple addition, subtraction, multiplication, and division, and they started edging out adding machines. When models from Hewlett-Packard and Texas Instruments started doing square roots, exponents, logarithms, and trigonometry, those so-called “slide rule” calculators killed the real slide rules. Electronic calculators were faster, they didn’t require the skills that slide rules required, and they took care of managing the magnitude. Calculators also appeared to be more accurate, with their eight digits of precision. From a numerical perspective, they indeed were more accurate.
However, working engineers knew that it was false precision: In real-world problems, the extra digits were meaningless. Today, we have forgotten that.
4. We have to understand, at a visceral and visual level, how the math works.
My slide rule collection has dozens of models. Some are quite simple. Others, like my Pickett Model 14 (designed for the U.S. military’s field artillery) have specialized calculation scales. One of my slide rules has more than 34 scales!
When you have a pocket calculator, or use spreadsheet functions like atanh (calculate the inverse hyperbolic tangent), you push a button and there’s a result. You may know what an inverse hyperbolic tangent is, or you may not; perhaps you are copying the formula or algorithm out of a book.
With a slipstick, you may also be working a problem out of a textbook, professional handbook, or field guide. However, you’re unlikely to get the right answer unless you not only know what that math operation is, but also how the scale works and how it relates to the real world. (Many slide rule manufacturers created wonderful instruction books for their instruments.)
It’s my own gut feel, but I think that seeing the calculation, and actually performing the calculation yourself gives the operator a better feel for whether it’s the right calculation and what it means.
If you are coding math-library functions into your algorithms, do you truly understand what the library does, how it works, its limitations, and its precision? Do you know how to verify if is returning a result that fits the real world? And in a larger sense, even when you aren’t working with mathematical calculations: How do you know when you have the right answer? Does it mean you are asking the right questions? It is something to think about.
5. Math is fun – and math is fundamental.
The term “computer” used to mean a person who did computation – that is, calculations. Once upon a time, many of us used computers primarily for math. That was in the era of punch cards, of course – long before computers were used for data processing, for document management, for image processing (which of course is math), office automation (Excel – math again), communication (email), social networking, and ultimately, of course, watching cat videos on YouTube.
When I started programming, what I had access to were programmable calculators — and so most of my programs were math oriented. In the 1970s and 1980s, I wrote and shared many programs with the HP and TI community, most of which were oriented around number theory and geometry, such as calculating areas of arbitrary polygons or finding the most efficient ways to generate Pythagorean triples. Great fun. When I moved over to bigger machines, including IBM mainframes, again, much of my work involved math.
Whether today we are using computers to navigate Facebook’s social graph, or launching Google’s search algorithm with a query on our smartphone, running MATLAB or asking merging photos using high-dynamic-range imaging, math is still at the heart of our computing experience. It’s just hidden. Playing with slide rules reminds us where we came from.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107887810.47/warc/CC-MAIN-20201025041701-20201025071701-00210.warc.gz
|
CC-MAIN-2020-45
| 10,845 | 38 |
https://projecteuclid.org/journals/annals-of-probability/volume-33/issue-1/The-arctic-circle-boundary-and-the-Airy-process/10.1214/009117904000000937.full
|
math
|
We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp’s conjecture concerning the structure of the tiling at the center of the Aztec diamond.
"The arctic circle boundary and the Airy process." Ann. Probab. 33 (1) 1 - 30, January 2005. https://doi.org/10.1214/009117904000000937
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573533.87/warc/CC-MAIN-20220818215509-20220819005509-00611.warc.gz
|
CC-MAIN-2022-33
| 482 | 2 |
https://thetextchemistry.org/qa/what-is-the-y-intercept-in-an-equation.html
|
math
|
What is Y intercept of a line?
Where a line crosses the y-axis of a graph..
What is the easiest way to find the Y intercept?
To find the x-intercept of a given linear equation, plug in 0 for ‘y’ and solve for ‘x’. To find the y-intercept, plug 0 in for ‘x’ and solve for ‘y’. In this tutorial, you’ll see how to find the x-intercept and the y-intercept for a given linear equation.
What is the Y intercept in a problem?
In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the “slope-intercept form”.
What is the Y intercept of y =- 3x 2?
1 Answer. The slope is 3 and the y-intercept is 2 or (0, 2).
What is Y intercept of a graph?
It’s called the “y intercept” and it’s the y value of the point where the line intersects the y- axis. For this line, the y-intercept is “negative 1.” You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038066568.16/warc/CC-MAIN-20210412023359-20210412053359-00196.warc.gz
|
CC-MAIN-2021-17
| 1,212 | 10 |
https://jiyuushikan.org/probability-of-a-union-b-union-c/
|
math
|
Learning ObjectivesTo learn how some events are normally expressible in regards to other occasions. To learn how to use unique formulas for the probcapacity of an event that is expressed in terms of one or more other events.
The enhance of an eventThe occasion does not occur. A in a sample space S, denoted Ac, is the repertoire of all outcomes in S that are not elements of the set A. It synchronizes to negating any type of summary in words of the event A.
You are watching: Probability of a union b union c
Two occasions linked through the experiment of rolling a single die are E: “the number rolled is even” and also T: “the number rolled is higher than two.” Find the enhance of each.
In the sample space S=1,2,3,4,5,6 the matching sets of outcomes are E=2,4,6 and T=3,4,5,6. The complements are Ec=1,3,5 and also Tc=1,2.
In words the complements are explained by “the number rolled is not even” and also “the number rolled is not greater than 2.” Of course simpler descriptions would be “the number rolled is odd” and “the number rolled is less than three.”
If tbelow is a 60% possibility of rain tomorrow, what is the probability of fair weather? The obvious answer, 40%, is an circumstances of the adhering to basic dominance.
Find the probcapacity that at leastern one heads will certainly appear in 5 tosses of a fair coin.
Identify outcomes by lists of five hs and ts, such as tthtt and hhttt. Although it is tedious to list them all, it is not hard to count them. Think of utilizing a tree diagram to do so. Tbelow are 2 choices for the first toss. For each of these tright here are 2 selections for the second toss, hence 2×2=4 outcomes for two tosses. For each of these 4 outcomes, tright here are 2 possibilities for the 3rd toss, for this reason 4×2=8 outcomes for three tosses. Similarly, tbelow are 8×2=16 outcomes for four tosses and also finally 16×2=32 outcomes for 5 tosses.
Let O signify the occasion “at least one heads.” There are many type of methods to obtain at leastern one heads, however just one means to fail to execute so: all tails. Therefore although it is tough to list all the outcomes that develop O, it is easy to compose Oc=ttttt. Due to the fact that tright here are 32 equally most likely outcomes, each has actually probcapability 1/32, so P(Oc)=1∕32, hence P(O)=1−1∕32≈0.97 or about a 97% possibility.
The intersection of eventsBoth events occur. A and B, denoted A ∩ B, is the repertoire of all outcomes that are elements of both of the sets A and B. It synchronizes to combining descriptions of the two events making use of the word “and.”
To say that the occasion A ∩ B occurred suggests that on a particular trial of the experiment both A and also B arisen. A visual representation of the interarea of events A and also B in a sample space S is offered in Figure 3.4 "The Interarea of Events ". The intersection coincides to the shaded lens-shaped region that lies within both ovals.
Figure 3.4 The Intersection of Events A and B
In the experiment of rolling a single die, discover the interarea E ∩ T of the occasions E: “the number rolled is even” and also T: “the number rolled is greater than two.”
The sample area is S=1,2,3,4,5,6. Because the outcomes that are prevalent to E=2,4,6 and T=3,4,5,6 are 4 and also 6, E∩T=4,6.
In words the intersection is defined by “the number rolled is even and also is greater than two.” The only numbers between one and also 6 that are both even and also greater than two are 4 and 6, matching to E ∩ T offered above.
A single die is rolled.Suppose the die is fair. Find the probcapacity that the number rolled is both also and greater than two. Suppose the die has actually been “loaded” so that P(1)=1∕12, P(6)=3∕12, and the continuing to be 4 outcomes are equally most likely with one an additional. Now uncover the probability that the number rolled is both even and also greater than two.
In both cases the sample room is S=1,2,3,4,5,6 and the occasion in question is the interarea E∩T=4,6 of the previous instance.Since the die is fair, all outcomes are equally most likely, so by counting we have actually P(E∩T)=2∕6.
The indevelopment on the probabilities of the six outcomes that we have so much isOutcome123456Probablity112pppp312
Due to the fact that P(1)+P(6)=4∕12=1∕3 and also the probabilities of all six outcomes include up to 1,P(2)+P(3)+P(4)+P(5)=1−13=23
Therefore 4p=2∕3, so p=1∕6. In particular P(4)=1∕6. ThereforeP(E∩T)=P(4)+P(6)=16+312=512
Events A and B are mutually exclusiveEvents that cannot both take place at when. if they have no aspects in common.
For A and B to have actually no outcomes in common implies precisely that it is difficult for both A and B to occur on a solitary trial of the random experiment. This gives the adhering to rule.
Probability Rule for Mutually Exclusive Events
Events A and also B are mutually exclusive if and also just ifP(A∩B)=0
Any event A and its match Ac are mutually exclusive, yet A and also B can be mutually exclusive without being complements.
In the experiment of rolling a single die, discover three choices for an event A so that the occasions A and also E: “the number rolled is even” are mutually exclusive.
Since E=2,4,6 and we want A to have no facets in prevalent via E, any kind of event that does not contain any kind of even number will certainly execute. Three selections are 1,3,5 (the enhance Ec, the odds), 1,3, and 5.
The union of eventsOne or the various other occasion occurs. A and B, denoted A ∪ B, is the repertoire of all outcomes that are facets of one or the various other of the sets A and B, or of both of them. It corresponds to combining descriptions of the two events using the word “or.”
To say that the occasion A ∪ B developed implies that on a particular trial of the experiment either A or B occurred (or both did). A visual representation of the union of occasions A and B in a sample room S is offered in Figure 3.5 "The Union of Events ". The union coincides to the shaded area.
Figure 3.5 The Union of Events A and also B
In the experiment of rolling a solitary die, uncover the union of the events E: “the number rolled is even” and T: “the number rolled is better than two.”
Due to the fact that the outcomes that are in either E=2,4,6 or T=3,4,5,6 (or both) are 2, 3, 4, 5, and also 6, E∪T=2,3,4,5,6. Note that a result such as 4 that is in both sets is still provided just once (although strictly speaking it is not incorrect to list it twice).
In words the union is explained by “the number rolled is also or is greater than two.” Eincredibly number in between one and also six other than the number one is either even or is greater than two, corresponding to E ∪ T given over.
A two-kid family members is schosen at random. Let B signify the occasion that at least one boy is a boy, let D represent the event that the genders of the 2 children differ, and also let M signify the occasion that the genders of the 2 kids match. Find B ∪ D and B∪M.
A sample area for this experiment is S=bb,bg,gb,gg, wbelow the initially letter denotes the sex of the firstborn boy and also the second letter denotes the gender of the second child. The events B, D, and also M areB=bb,bg,gb D=bg,gb M=bb,gg
Each outcome in D is currently in B, so the outcomes that are in at leastern one or the various other of the sets B and also D is simply the collection B itself: B∪D=bb,bg,gb=B.
Every outcome in the totality sample room S is in at least one or the other of the sets B and also M, so B∪M=bb,bg,gb,gg=S.
The following Additive Rule of Probability is a beneficial formula for calculating the probcapacity of A∪B.
The next instance, in which we compute the probcapability of a union both by counting and by making use of the formula, reflects why the last term in the formula is essential.
Two fair dice are thrvery own. Find the probabilities of the following events:both dice present a 4 at least one die reflects a four
As was the situation via tossing 2 the same coins, actual experience dictates that for the sample room to have equally most likely outcomes we need to list outcomes as if we might distinguish the two dice. We might imagine that among them is red and the various other is green. Then any kind of outcome have the right to be labeled as a pair of numbers as in the following screen, where the first number in the pair is the variety of dots on the top face of the green die and also the second number in the pair is the number of dots on the optimal confront of the red die.111213141516212223242526313233343536414243444546515253545556616263646566 There are 36 equally likely outcomes, of which precisely one corresponds to two fours, so the probcapability of a pair of fours is 1/36.
From the table we deserve to view that there are 11 pairs that correspond to the occasion in question: the six pairs in the fourth row (the green die mirrors a four) plus the additional 5 pairs various other than the pair 44, already counted, in the fourth column (the red die is four), so the answer is 11/36. To check out exactly how the formula gives the same number, let AG represent the event that the green die is a 4 and let AR represent the event that the red die is a four. Then clearly by counting we get P(AG)=6∕36 and P(AR)=6∕36. Because AG∩AR=44, P(AG∩AR)=1∕36; this is the computation in component (a), of course. Thus by the Additive Rule of Probcapacity,P(AG∪AR)=P(AG)+P(AR)−P(AG−AR)=636+636−136=1136
A tutoring company specializes in preparing adults for high school equivalence tests. Among all the students seeking aid from the service, 63% need aid in mathematics, 34% require help in English, and also 27% need aid in both math and also English. What is the percentage of students that require assist in either mathematics or English?
Imagine selecting a student at random, that is, in such a means that eextremely student has actually the very same possibility of being selected. Let M signify the event “the student requirements aid in mathematics” and let E signify the event “the student requirements help in English.” The information given is that P(M)=0.63, P(E)=0.34, and P(M∩E)=0.27. The Additive Rule of Probcapability givesP(M∪E)=P(M)+P(E)−P(M∩E)=0.63+0.34−0.27=0.70
Keep in mind how the naïve reasoning that if 63% need aid in mathematics and also 34% need aid in English then 63 plus 34 or 97% need aid in one or the various other offers a number that is also huge. The percentage that need aid in both topics need to be subtracted off, else the people needing assist in both are counted twice, when for needing aid in mathematics and also when aobtain for needing help in English. The simple sum of the probabilities would certainly work if the occasions in question were mutually exclusive, for then P(A∩B) is zero, and provides no distinction.
Volunteers for a disaster relief initiative were classified according to both specialty (C: building, E: education and learning, M: medicine) and also language capability (S: speaks a single language fluently, T: speaks two or more langueras fluently). The outcomes are shown in the complying with two-method classification table:
The initially row of numbers means that 12 volunteers whose specialty is construction stop a single language fluently, and 1 volunteer whose specialty is building and construction speaks at leastern two languperiods fluently. Similarly for the other two rows.
A volunteer is selected at random, meaning that each one has an equal possibility of being chosen. Find the probability that:his specialty is medication and also he speaks two or even more languages; either his specialty is medicine or he speaks 2 or more languages; his specialty is something other than medication.
When indevelopment is presented in a two-way classification table it is typically convenient to adjoin to the table the row and also column totals, to create a new table like this:
The probcapability sought is P(M∩T). The table shows that tbelow are 2 such people, out of 28 in all, hence P(M∩T)=2∕28≈0.07 or about a 7% opportunity.
The probability sought is P(M∪T). The third row total and also the grand full in the sample provide P(M)=8∕28. The second column complete and also the grand total give P(T)=6∕28. Hence utilizing the result from component (a),P(M∪T)=P(M)+P(T)−P(M∩T)=828+628−228=1228≈0.43
or about a 43% opportunity.
This probcapacity have the right to be computed in 2 ways. Since the occasion of interest deserve to be perceived as the occasion C ∪ E and the occasions C and E are mutually exclusive, the answer is, using the initially 2 row totals,P(C∪E)=P(C)+P(E)−P(C∩E)=1328+728−028=2028≈0.71
On the other hand also, the event of interemainder deserve to be believed of as the enhance Mc of M, therefore making use of the value of P(M) computed in part (b),P(Mc)=1−P(M)=1−828=2028≈0.71
Key TakeawayThe probcapacity of an event that is a enhance or union of events of recognized probability deserve to be computed using formulas.
For the sample room S=a,b,c,d,e determine the enhance of each event offered.A=a,d,e B=b,c,d,e S
For the sample room S=r,s,t,u,v identify the complement of each event given.R=t,u T=r ∅ (the “empty” set that has actually no elements)
The sample room for 3 tosses of a coin isS=hhh,hht,hth,htt,thh,tht,tth,ttt
Define eventsH:at least one head is observedM:more heads than tails are oboffered List the outcomes that make up H and M. List the outcomes that consist of H ∩ M, H ∪ M, and Hc. Assuming all outcomes are equally likely, find P(H∩M), P(H∪M), and also P(Hc). Determine whether or not Hc and also M are mutually exclusive. Explain why or why not.
For the experiment of rolling a single six-sided die as soon as, specify eventsT:the number rolled is threeG:the number rolled is four or better List the outcomes that comprise T and G. List the outcomes that comprise T ∩ G, T ∪ G, Tc, and also (T∪G)c. Assuming all outcomes are equally likely, uncover P(T∩G), P(T∪G), and also P(Tc). Determine whether or not T and G are mutually exclusive. Exsimple why or why not.
A unique deck of 16 cards has actually 4 that are blue, 4 yellow, 4 green, and 4 red. The four cards of each color are numbered from one to 4. A single card is attracted at random. Define eventsB:the card is blueR:the card is redN:the number on the card is at most 2 List the outcomes that comprise B, R, and also N. List the outcomes that make up B ∩ R, B ∪ R, B ∩ N, R ∪ N, Bc, and also (B∪R)c. Assuming all outcomes are equally most likely, find the probabilities of the occasions in the previous part. Determine whether or not B and also N are mutually exclusive. Exsimple why or why not.
In the conmessage of the previous problem, define eventsY:the card is yellowI:the number on the card is not a oneJ:the number on the card is a two or a four List the outcomes that make up Y, I, and J. List the outcomes that make up Y ∩ I, Y ∪ J, I ∩ J, Ic, and also (Y∪J)c. Assuming all outcomes are equally most likely, discover the probabilities of the events in the previous part. Determine whether or not Ic and also J are mutually exclusive. Exordinary why or why not.
The Venn diagram offered mirrors a sample space and also 2 occasions A and B. Suppose P(a)=0.13, P(b)=0.09, P(c)=0.27, P(d)=0.20, and P(e)=0.31. Confirm that the probabilities of the outcomes add up to 1, then compute the following probabilities.
P(A). P(B). P(Ac) 2 ways: (i) by finding the outcomes in Ac and also adding their probabilities, and (ii) utilizing the Probcapacity Rule for Complements. P(A∩B). P(A∪B) 2 ways: (i) by finding the outcomes in A ∪ B and adding their probabilities, and (ii) using the Additive Rule of Probability.
The Venn diagram provided shows a sample space and 2 occasions A and also B. Suppose P(a)=0.32, P(b)=0.17, P(c)=0.28, and also P(d)=0.23. Confirm that the probabilities of the outcomes add approximately 1, then compute the complying with probabilities.
P(A). P(B). P(Ac) two ways: (i) by finding the outcomes in Ac and adding their probabilities, and (ii) utilizing the Probcapacity Rule for Complements. P(A∩B). P(A∪B) 2 ways: (i) by finding the outcomes in A ∪ B and also including their probabilities, and (ii) utilizing the Additive Rule of Probability.
Confirm that the probabilities in the two-way contingency table include as much as 1, then use it to find the probabilities of the occasions indicated.
P(A), P(B), P(A∩B). P(U), P(W), P(U∩W). P(U∪W). P(Vc). Determine whether or not the events A and also U are mutually exclusive; the events A and also V.
Confirm that the probabilities in the two-means contingency table add approximately 1, then usage it to discover the probabilities of the occasions suggested.
P(R), P(S), P(R∩S). P(M), P(N), P(M∩N). P(R∪S). P(Rc). Determine whether or not the events N and also S are mutually exclusive; the occasions N and also T.
Make a statement in simple English that defines the match of each occasion (execute not sindicate insert the word “not”).In the roll of a die: “5 or more.” In a roll of a die: “an also number.” In two tosses of a coin: “at leastern one heads.” In the random selection of a college student: “Not a freshguy.”
Make a statement in plain English that describes the complement of each event (carry out not sindicate insert the word “not”).In the roll of a die: “2 or much less.” In the roll of a die: “one, three, or four.” In two tosses of a coin: “at the majority of one heads.” In the random selection of a college student: “Neither a freshguy nor a senior.”
The sample room that defines all three-boy households according to the genders of the youngsters through respect to birth order isS=bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg.
For each of the complying with occasions in the experiment of picking a three-boy family members at random, state the complement of the occasion in the simplest possible terms, then discover the outcomes that comprise the event and its match.At leastern one kid is a girl. At the majority of one son is a girl. All of the kids are girls. Exactly two of the children are girls. The first born is a girl.
The sample space that describes the two-means classification of citizens according to gender and also opinion on a political problem isS=mf,ma,mn,ff,fa,fn,
wright here the initially letter denotes sex (m: male, f: female) and the second opinion (f: for, a: against, n: neutral). For each of the complying with events in the experiment of picking a citizen at random, state the enhance of the occasion in the easiest feasible terms, then find the outcomes that consist of the occasion and its enhance.The person is male. The person is not in favor. The perkid is either male or in favor. The perkid is female and neutral.
A tourist that speaks English and also Germale but no other language visits a region of Slovenia. If 35% of the residents soptimal English, 15% soptimal Germale, and 3% sheight both English and Gerguy, what is the probability that the tourist will certainly be able to talk with a randomly encountered resident of the region?
In a particular country 43% of all automobiles have airbags, 27% have actually anti-lock brakes, and also 13% have both. What is the probcapability that a randomly selected auto will have both airbags and anti-lock brakes?
A manufacturer examines its documents over the last year on a component component got from exterior suppliers. The breakdvery own on source (supplier A, supplier B) and also high quality (H: high, U: usable, D: defective) is shown in the two-means contingency table.
The record of a part is selected at random. Find the probcapability of each of the adhering to events.The part was defective. The part was either of high top quality or was at least usable, in two ways: (i) by including numbers in the table, and also (ii) making use of the answer to (a) and also the Probability Rule for Complements. The component was defective and came from supplier B. The component was defective or came from supplier B, in 2 ways: by finding the cells in the table that correspond to this event and also adding their probabilities, and (ii) using the Additive Rule of Probability.
Individuals with a details clinical problem were classified according to the visibility (T) or absence (N) of a potential toxin in their blood and also the onset of the condition (E: at an early stage, M: midselection, L: late). The breakdvery own according to this classification is presented in the two-way contingency table.
One of these people is selected at random. Find the probcapability of each of the adhering to occasions.The perkid knowledgeable beforehand onset of the problem. The oncollection of the problem was either midarray or late, in 2 ways: (i) by including numbers in the table, and also (ii) using the answer to (a) and also the Probability Rule for Complements. The toxin is present in the person’s blood. The perchild proficient at an early stage oncollection of the problem and also the toxin is present in the person’s blood. The person knowledgeable early onset of the condition or the toxin is present in the person’s blood, in two ways: (i) by finding the cells in the table that correspond to this occasion and including their probabilities, and also (ii) utilizing the Additive Rule of Probability.
The breakdown of the students enrolled in a university course by class (F: freshman, So: sophoeven more, J: junior, Se: senior) and scholastic significant (S: scientific research, mathematics, or design, L: liberal arts, O: other) is presented in the two-way classification table.
A student enrolled in the course is schosen at random. Adsign up with the row and also column totals to the table and also usage the broadened table to discover the probcapability of each of the following occasions.The student is a freshguy. The student is a liberal arts major. The student is a freshguy liberal arts major. The student is either a freshguy or a liberal arts significant. The student is not a liberal arts significant.
The table relates the response to a fund-increasing appeal by a college to its alumni to the variety of years since graduation.
See more: Why Was Ray Charles Banned From Georgia, Was Ray Charles Banned From Georgia
An alumnus is selected at random. Adjoin the row and column totals to the table and also usage the expanded table to discover the probcapability of each of the complying with events.The alumnus responded. The alumnus did not respond. The alumnus graduated at leastern 21 years earlier. The alumnus graduated at leastern 21 years back and responded.
The sample room for tossing three coins isS=hhh,hht,hth,htt,thh,tht,tth,ttt List the outcomes that correspond to the statement “All the coins are heads.” List the outcomes that correspond to the statement “Not all the coins are heads.” List the outcomes that correspond to the statement “All the coins are not heads.”
H=hhh,hht,hth,htt,thh,tht,tth, M=hhh,hht,hth,thh H∩M=hhh,hht,hth,thh, H∪M=H, Hc=ttt P(H∩M)=4∕8, P(H∪M)=7∕8, P(Hc)=1∕8 Mutually exclusive because they have no facets in common.
B=b1,b2,b3,b4, R=r1,r2,r3,r4, N=b1,b2,y1,y2,g1,g2,r1,r2 B∩R=∅, B∪R=b1,b2,b3,b4,r1,r2,r3,r4, B∩N=b1,b2, R∪N=b1,b2,y1,y2,g1,g2,r1,r2,r3,r4, Bc=y1,y2,y3,y4,g1,g2,g3,g4,r1,r2,r3,r4, (B∪R)c=y1,y2,y3,y4,g1,g2,g3,g4 P(B∩R)=0, P(B∪R)=8∕16, P(B∩N)=2∕16, P(R∪N)=10∕16, P(Bc)=12∕16, P((B∪R)c)=8∕16 Not mutually exclusive because they have an aspect in common.
P(A)=0.38, P(B)=0.62, P(A∩B)=0 P(U)=0.37, P(W)=0.33, P(U∩W)=0 0.7 0.7 A and also U are not mutually exclusive because P(A∩U) is the nonzero number 0.15. A and also V are mutually exclusive bereason P(A∩V)=0.
“All the children are boys.”
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055601.25/warc/CC-MAIN-20210917055515-20210917085515-00498.warc.gz
|
CC-MAIN-2021-39
| 23,938 | 93 |
https://drupal.mpiwg-berlin.mpg.de/einstein_virtuell/SC-66497905_MOD-1521014061_SEQ732862291_SL202196634_en.html
|
math
|
Relativitaet auf dem Pruefstand
The inertial mass is a measure how much resistance an object exhibits if an external force is acting on it. The gravitational mass determines the weight of an object due to the gravitational field.
The fact that both masses are the same is known since long. As a consequence of this so called weak equivalence in a vacuum all objects are falling with the same speed, irrespective of their material properties.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711016.32/warc/CC-MAIN-20221205100449-20221205130449-00403.warc.gz
|
CC-MAIN-2022-49
| 441 | 3 |
http://marmotadventures.com/php/picture.php?2005-06-28,2,1
|
math
|
by Stormy on June 28, 2005
Carlsbad Caverns National Park is a pretty big place and Carlsbad Caverns isn't the only cave on their property. Wild and semi-wild cave tours are offered to other caves on park property.
Read the entire story.
|Out in the desert is a pretty incredible cave. It's dark in there. Be ready for that.|
(taken by Max on June 28, 2005)
|home back reload feedback |
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370518767.60/warc/CC-MAIN-20200403220847-20200404010847-00336.warc.gz
|
CC-MAIN-2020-16
| 421 | 6 |
https://economics.stackexchange.com/questions/4472/intuition-behind-comparative-advantange
|
math
|
I already read and ask NOT about pp 52-54, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw. I understand such numerical examples that corroborate Comparative Advantage, but how can I intuit comparative advantage? I wish to quash my need to revisit these numerical examples to recollect this idea. i start with definitions from pp 52 and 53 (supra):
absolute advantage = the ability to produce a good using fewer inputs than another producer
comparative advantage = the ability to produce a good at a lower opportunity cost than another producer
First, ... comparative advantage is clearly counter-intuitive. ... Secondly, the theory is easy to confuse with ... the theory of absolute advantage. The logic behind absolute advantage IS quite intuitive. This confusion between these two concepts leads many people to think that they understand comparative advantage when in fact, what they understand is absolute advantage.
However, instead of assuming, as Adam Smith did, that England is more productive in producing one good and Portugal is more productive in the other; [David] Ricardo assumed that Portugal was more productive in both goods. Based on Smith's intuition, then, it would seem that trade could not be advantageous, at least for England.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816586.79/warc/CC-MAIN-20240413051941-20240413081941-00519.warc.gz
|
CC-MAIN-2024-18
| 1,264 | 5 |
https://www.bartleby.com/questions-and-answers/find-the-most-general-antiderivative-of-fx7x28x2.-note-any-arbitrary-constants-used-must-be-an-upper/898daedf-b07f-45f1-bcfe-53223852c4ef
|
math
|
Find the most general antiderivative of f(x)=−7x^2+8x−2.
Note: Any arbitrary constants used must be an upper-case "C".
An anti derivative of a function f is a differentiable function, whose derivative should be equal to the original function f.
That is, the reverse process of differentiation is used here.
The reverse process of differentiation is integration.
So, integral of a function is also called as an anti derivative of that function.
The given function is,
Obtain the anti derivative of ...
Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*See Solution
Q: 3x4 y‴+9x4 =5xy′+5x5 y″+9lnx Determine the order of the differential equation shown above.
A: The given differential equation is,
Q: How do I show the correct solution for the differential equation? I know the answer is D.
A: First we separate the variables
Q: Find the area of the region described. -4x and xIn 3 The region bounded by y e. ye X The area of the...
A: We first draw a rough sketch of y=e^x, y=e^-4x and x=ln 3And find the region bounded by them.
Q: 3 dx = 1 2x 8 In 국 5 -4 In 2 In을 -2 In -8 In LOn LOn
A: Obtain the value of the integral as follows.The given integral is,
Q: Find the area, in square units, bounded by f(x)=3x+5 and g(x)=2x+1 over the interval [0,12]. Do not ...
A: Area of region between f(x) and g(x) over the interval [0,12] is computed as follows.
Q: 1000 Find the marginal cost when q = 10. 9 The average coste for producing q units of a product is g...
A: The average cost c is given by ,
Q: find the volume aquired by taking by region bound by y=x^2 and y=x^4 and rotating it around x=-1
A: To calculate the volume bounded by the curve y=x2 and y=x4 which is rotating about the line x=-1. No...
Q: How do I choose my g(u,v) and h(u,v)?
A: The double integral is given by,
Q: The heat flow vector field for conducting objects is F=−k∇T, where T(x,y,z) is the temperature in t...
A: Assume k = 1.Then the vector field becomes, F = −∇T.Find ∇T as follows.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250619323.41/warc/CC-MAIN-20200124100832-20200124125832-00457.warc.gz
|
CC-MAIN-2020-05
| 2,045 | 27 |
https://www.wordaz.com/Functions.html
|
math
|
Definition of Functions. Meaning of Functions. Synonyms of Functions
Here you will find one or more explanations in English for the word Functions. Also in the bottom left of the page several parts of wikipedia pages related to the word Functions and, of course, Functions synonyms and on the right images related to the word Functions.
Definition of Functions
functionFluent Flu"ent, n.
1. A current of water; a stream. [Obs.]
2. [Cf. F. fluente.] (Math.) A variable quantity, considered
as increasing or diminishing; -- called, in the modern
calculus, the function or integral.
Meaning of Functions from wikipedia
key, a type of key on computer keyboards Function
model, a structured representation
- In mathematics, hyperbolic functions
of the ordinary trigonometric functions defined
for the hyperbola rather
than on the circle: just as...
set. Typical examples
or from the real numbers
to real numbers. Functions
- mathematics, the trigonometric functions
(also called circular functions
, angle functions
or goniometric functions
) are real functions which relate
- the Bessel functions
are mostly smooth functions
of α. The most important cases
are when α is an integer
or half-integer. Bessel functions
- trigonometric functions
(occasionally also called arcus functions
, antitrigonometric functions
or cyclometric functions
) are the inverse functions
of the trigonometric...
- collisions). Hash functions
to (and often confused
with) checksums, check
digits, fingerprints, lossy
compression, randomization functions
- analytic function
is a function
that is locally given
by a convergent power
series. There exist
both real analytic functions
and complex analytic functions
- f(x) = y and g(y) = x. Not all functions
have inverse functions
that do are called
invertible. For a function
f: X → Y to have an inverse, it...
- flexibility. Higher order executive functions require
use of multiple basic executive functions
and include planning
Recent Searches ...
Related images to Functions
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738950.61/warc/CC-MAIN-20200813014639-20200813044639-00168.warc.gz
|
CC-MAIN-2020-34
| 2,002 | 56 |
http://gocututoludaxaqyc.polkadottrail.com/write-a-fraction-in-lowest-terms-calculator-1686916869.html
|
math
|
So dividing gives us Therefore, can be reduced to. Fractions can undergo many different operations, some of which are mentioned below. An alternative to using this equation in cases where the fractions are uncomplicated would be to find a least common multiple and then add or subtract the numerators as one would an integer.
Both parts of the fraction need to be divisable by the same figure then that will give you a lower term. Would you like to make it the primary and merge this question into it?
To clear a named set of saved entries, click or tap the Data tab, select the saved data record from the drop-down menu, and then tap or click the Clear button. Divide 16 by 3: When possible this calculator first reduces an improper fraction to lowest terms before finding the mixed number form.
The factors of 24 are 1, 2, 4, 6, 8, 12, and Reduce fractions to their simplest form. Divide both the numerator by the same number and the result will be a fraction reduced to its lowest terms. Speak it out loud.
If your device keypad does not include a decimal point, use this popup keypad to enter decimal numbers where applicable. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined.
Work the division the fraction represents, leaving your answer in remainder form. You can then save any changes to your entries by simply clicking the Save button while the data record is selected. For example, if we are told to express with a denominator of 12, we know that in order for the denominator to equal 12, we have to multiply the original denominator by 4.
That depends on the instructions you get and your ultimate goal. To continue with the example given: Either way, your math life will be a lot easier if you get into the habit of reducing all of those fractions to lowest terms.
Either way, you end up with: Depending on the complexity of the fractions, finding the least common multiple for the denominator can be more efficient than using the equations.
Look for Common Factors Examine both numbers, or make a list, to find their factors: If a person were to eat 3 slices, the remaining fraction of the pie would therefore be 5 8 as shown in the image to the right.
If the field includes a grid icon, tapping the icon will open a popup keypad which will include only the characters allowed in the field. How do you put a fraction in lowest terms? This calculator will also simplify improper fractions into mixed numbers. Find the GCF of the numerator and denominator.
Converting Improper Fractions to Mixed Numbers Should you keep improper fractions the way they are, or convert them into a mixed number? A summary of these explanations, along with any additional term explanations, can also be found under the Terms tab.
How to Convert an Improper Fraction to a Mixed Number Divide the numerator by the denominator Write down the whole number result Use the remainder as the new numerator over the denominator.
If the GCF is greater than 1, divide each term by that number. To reduce fractions to the lowest terms, you must find the highest number that will divide into both the numerator and the denominator.
Divide by the Greatest Common Factor Divide both numerator and denominator by the greatest common factor or, to think of it another way, factor that number out of both numerator and denominator and then cancel it.Fractions in Lowest Terms A fraction is said to written using lowest terms if its numerator and denominator are relatively prime, that is, they To write 6 9 in lowest terms, divide both the numerator and denominator by the greatest common factor, in this case 3: 6.
If a given fraction is not reduced to lowest terms, you can find other equivalent fractions by dividing both numerator and denominator by the same number. What is an equivalent fraction? How to know if two fractions are equivalent?
Jul 18, · Reducing a Fraction to Lowest Terms. Here I look at reducing a fraction to lowest terms. I do not take the shortest route, but show how I often perform the simplification if no one is watching!
Reducing a fraction – in order to reduce a fraction to its lowest terms, we must find the greatest common factor for the numerator and denominator.
If we are given, we see that the common factors of 15 and 30 are 3, 5 and 15, of which 15 is the greatest. This page will show you how to reduce a fraction to lowest terms.
Type your numerator and denominator (numbers only please!) into the boxes, then click the button. To write a fraction in lowest terms, you need to identify any common divisors between the numerator and denominator.Download
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999620.99/warc/CC-MAIN-20190624171058-20190624193058-00419.warc.gz
|
CC-MAIN-2019-26
| 4,616 | 19 |
http://www.integrare.net/in-excel/info-rounding-of-the-output-value-in-msexcel-2003.php
|
math
|
Rounding Of The Output Value In MsExcel 2003
As a reminder, the ROUND function uses =1/3 in each of the three cells A1:A3. 14, even though 12.1 is clearly closer to 12 than to 14. You can use the MROUND function to find outLike this article?IEEE Floating Point StandardThe section describes the 2003 made via this site.
fixed at 1022 and the mantissa is assumed to be between 0 and 1. Next, it is rounded down the http://www.integrare.net/in-excel/fixing-rounding-in-excel.php value Excel Mround ALL purchases totaling over numbers, they store fractional numbers as binary fractions. Of course, for most numbers,
Decimal_places of decimal places that you want to display. + x*8 + x*16 etc) where x is the state of the bit. Excel MsExcel values in its calculations, rather than the underlying numbers.You may have only two decimal places displayed on the
If the numbers you are roundingof 10 to which you want to round. How To Use Round Function In Excel With Formula The number stored in the exponent bits is the actual in or earlier), this tip may not work for you.However, I really need to round some valuesbit level, in a later section of this article.
The difference is that the ROUNDUP function always rounds up the value specified EXCEL DASHBOARD REPORTS Rounding Numbers in Excel | | Information Helpful? When the exponent bits are all zero, the exponent is treated as being function will round the expression so that the last digit is an even number.Use the ROUNDUP function.Enter your address and click "Subscribe." Subscribe (Your e-mail address using that number of digits.
Since the mantissa is always greater than or equal to 1, only in approximation of 0.4, since it cannot be stored exactly. How To Round Decimals In Excel can enable from Calculate tab on the Options dialog (Tools menu).Or, you want to round a number to to a Multiple Current Special! Instead of the ROUND function, youElectrical And Electronic Engineers) standard for floating point numbers.
Home tab, in the Number group, click Increase Decimal or Decrease Decimal .The number 10 is represented in binary asIf the bit Rounding this would be4024CCCCCCCCCCCC The first 0 is the sign bit.Excel's ROUND() function is designed over here MsExcel Decimals on the Format toolbar, to the right of $ % , symbols.
Although this may seem to defy every week in ExcelTips, a free productivity newsletter.He is president of Sharon Parqbuilding powerful, robust, and secure applications with Excel. This site https://www.techonthenet.com/excel/formulas/round_vba.php here: http://excelribbon.tips.net/T012083 ExcelTips is your source for cost-effective Microsoft Excel training.You can also pass a negative value for the number of decimal places, 2003 the following: The ROUND function utilizes round-to-even logic.
It can be used as Associates, a computer and publishing services company. This is called an "unnormalized" number, and iscontain only 6 items.Enter your address and click in [decimal_places] ) Parameters or Arguments expression A numeric expression that is to be rounded.
Both ROUNDUP and ROUNDDOWN take the same$59.95 Instant Buy/Download, 30 Day Money Back Guarantee & Free Excel Help for LIFE! + 1/8 ) that is exactly equal to 0.4. Excel Round To Nearest 100 older menu interface of Excel here: Rounding to Two Significant Digits.This allows extremely small numbers to with 2 as their num_digits arguments in cells B5 and B7, respectively.
Discover More Associates, a computer and publishing services company.Discover More Subscribe FREE SERVICE: Get tips like number rounded to a specified number of digits.If the bit of Excel rounds the number to the left of the decimal point.As a binaryyou want to round to a multiple of a number that you specify.
Discover More Rounding Up to the Next Half When processing data it function is part of the Analysis ToolPak Add-In for Excel. Excel Round To Nearest 5 how the value 0 is stored in a double.Even with this accuracy, many numbers are represented in design decisions and make the most of Excel's powerful features.Spreadsheet" shows how to maximize your Excel experience using in Excel.
Purchases MUST be of can control the number of decimal places displayed without affecting the actual number.In the example, you are not really adding 0.3 + 0.3 + 0.3,Discover MoreOn a worksheet Select the cells that you want to format.For example, using the ROUNDDOWN function to rounddoesn't work that great if you are rounding non-whole values.
The second is same result, 3.14, as does using the ROUND function with 2 as its second argument.more information about these functions. How To Round Numbers In Excel Without Formula the number 1/10 = 0.1 in binary form.
This degree of accuracy is unnecessary for to round a number. Please read our ROUND function (WS) page if you are looking for thenear fraction Use the ROUND function.Change the number of decimal places displayed without changing the number works for negative values, as well.) ExcelTips is your source for cost-effective Microsoft Excel training. So please be carefulare not displayed to their full values.
explains how to use the Excel ROUND function (in VBA) with syntax and examples. Since the mantissa is 52 bits, plus the implied ones bit, the precision of thea number down, and ROUNDUP always rounds a number up. Complete Excel Excel Training Course for Excel 97 - Excel 2003, only $145.00. Roundup Function In Excel the names of people) are routinely marked as incorrect by Word's spell checker. of This matters when you add some numbers androunded and the desired number of decimal places.
Subscribe FREE SERVICE: Get tips like this may get even more decimal places! Does the answer change if dealingFree Business Forms Free Calendars OUR COMPANY Sharon Parq Associates, Inc. You can find a version of this tip for the Excel Round To Nearest 1000 the examples shown represent only a very small list of possible scenarios.The result would appear to bea VBA function (VBA) in Excel.
The ROUND function is a built-in function in some statistical analysis that he was doing. Less Let's say you want to round a number to themagazine articles to his credit, Allen Wyatt is an internationally recognized author. Check out Professionala product in crates of 18 items. So before using this function, please read they are displayed via Tools>Options - Calculation and check Precision as displayed.
If the number of digits is negative, it by 18 is 11.333, and you will need to round up.
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201812.2/warc/CC-MAIN-20190318232014-20190319014014-00516.warc.gz
|
CC-MAIN-2019-13
| 6,473 | 20 |
https://blisswrite.org/2021/08/25/expert-answeraccounting-3230-exercises-4-spring-2014/
|
math
|
Solved by verified expert :Accounting 3230Exercises #4Spring 2014Part 1:Blue Sapphire Inc. issues 2,500 shares of $1 par value common stock and 1,000 shares of $50 par value preferred stock for a lump sum of $275,000.Instructions:a) Prepare the journal entry for the issuance when the market value of the common shares is $95 each and the market value of the preferred is $60 each.b) Prepare the journal entry for the issuance when only the market value of the common stock is known and it is $90 per share.Part 2:The outstanding capital stock of Jersey Brands Corporation consists of 10,000 shares of $75 par value, 10% preferred and 25,000 shares of $1 par value common.Instructions:Assuming that the company has net income of $250,000, all of which is to be paid out in dividends, and that preferred dividends were not paid during the current year r or the past year, state how much each class of stock should receive under each of the following conditions.a) The preferred stock is noncumulative and fully participating.b) The preferred stock is cumulative and nonparticipating.c) The preferred stock is cumulative and fully participating.Part 3:On January 1, 20X2, Archie Game Corporation issued 15 year, $50,000,000 face value 4% bonds at par. Each $1,000 bond is convertible into 20 shares of Archie Game Corporation common stock. None of the bonds were converted in 20X2. Archie Game Corporation’s net income in 20X2 was $8,680,00 and its tax rate was 30%. The company had 2,650,000 shares of common stock issued and outstanding throughout 20X2.Instructions:a) Compute diluted earnings per share for 20X2.b) Compute diluted earnings per share for 20X2 assuming the same facts as above, except that $50,000,000 of 6% convertible preferred stock was issued instead of the bonds. Each $1000 preferred share is convertible into 2 shares of Archie Game Corporation common stock.
Expert answer:Accounting 3230 Exercises #4 Spring 2014
How it works
- Paste your instructins in the instructions box. You can also attach an instructions file
- Select the writer category, deadline, education level and review the instructions
- Make a payment for the order to be assignment to a writer
- Download the paper after the writer uploads it
Will the writer plagiarize my essay?
You will get a plagiarism-free paper and you can get an originality report upon request.
Is this service safe?
All the personal information is confidential and we have 100% safe payment methods. We also guarantee good grades
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00677.warc.gz
|
CC-MAIN-2023-14
| 2,497 | 11 |
https://wikimili.com/en/Quantum_topology
|
math
|
|Part of a series on|
Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology.
Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associated with topological spaces and the related embedding of one space within another such as knots and links in three-dimensional space. This bra–ket notation of kets and bras can be generalised, becoming maps of vector spaces associated with topological spaces that allow tensor products.
Topological entanglement involving linking and braiding can be intuitively related to quantum entanglement.
In quantum mechanics, bra–ket notation, or Dirac notation, is ubiquitous. The notation uses the angle brackets, "" and "", and a vertical bar "", to construct "bras" and "kets". A ket looks like "". Mathematically it denotes a vector, , in an abstract (complex) vector space , and physically it represents a state of some quantum system. A bra looks like "", and mathematically it denotes a linear functional , i.e. a linear map that maps each vector in to a number in the complex plane . Letting the linear functional act on a vector is written as .
In mathematics, any vector space V has a corresponding dual vector space consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
In quantum computing, a qubit or quantum bit is the basic unit of quantum information—the quantum version of the classical binary bit physically realized with a two-state device. A qubit is a two-state quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include: the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property which is fundamental to quantum mechanics and quantum computing.
In mathematics, topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters ψ and Ψ.
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined together so that it cannot be undone, the simplest knot being a ring. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of upon itself ; these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.
A topological soliton or "toron" occurs when two adjoining structures or spaces are in some way "out of phase" with each other in ways that make a seamless transition between them impossible. One of the simplest and most commonplace examples of a topological soliton occurs in old-fashioned coiled telephone handset cords, which are usually coiled clockwise. Years of picking up the handset can end up coiling parts of the cord in the opposite counterclockwise direction, and when this happens there will be a distinctive larger loop that separates the two directions of coiling. This odd looking transition loop, which is neither clockwise nor counterclockwise, is an excellent example of a topological soliton. No matter how complex the context, anything that qualifies as a topological soliton must at some level exhibit this same simple issue of reconciliation seen in the twisted phone cord example.
In gauge theory and mathematical physics, a topological quantum field theory is a quantum field theory which computes topological invariants.
A qutrit is a unit of quantum information that is realized by a quantum system described by a superposition of three mutually orthogonal quantum states.
In physics, a topological quantum number is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topological considerations. Most commonly, topological quantum numbers are topological invariants associated with topological defects or soliton-type solutions of some set of differential equations modeling a physical system, as the solitons themselves owe their stability to topological considerations. The specific "topological considerations" are usually due to the appearance of the fundamental group or a higher-dimensional homotopy group in the description of the problem, quite often because the boundary, on which the boundary conditions are specified, has a non-trivial homotopy group that is preserved by the differential equations. The topological quantum number of a solution is sometimes called the winding number of the solution, or, more precisely, it is the degree of a continuous mapping.
In physics, topological order is a kind of order in the zero-temperature phase of matter. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders cannot change into each other without a phase transition.
In theoretical physics, topological string theory is a version of string theory. Topological string theory was first thought of and is studied by physicists such as Edward Witten and Cumrun Vafa.
In category theory, a branch of mathematics, dagger compact categories first appeared in 1989 in the work of Sergio Doplicher and John E. Roberts on the reconstruction of compact topological groups from their category of finite-dimensional continuous unitary representations. They also appeared in the work of John Baez and James Dolan as an instance of semistrict k-tuply monoidal n-categories, which describe general topological quantum field theories, for n = 1 and k = 3. They are a fundamental structure in Samson Abramsky and Bob Coecke's categorical quantum mechanics.
For any complex number written in polar form, the phase factor is the complex exponential factor (eiθ). As such, the term "phase factor" is related to the more general term phasor, which may have any magnitude. The phase factor is a unit complex number, i.e., of absolute value 1. It is commonly used in quantum mechanics.
In physics, a state space is an abstract space in which different "positions" represent, not literal locations, but rather states of some physical system. This makes it a type of phase space.
The topological entanglement entropy or topological entropy, usually denoted by γ, is a number characterizing many-body states that possess topological order.
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces.
This is a glossary for the terminology often encountered in undergraduate quantum mechanics courses.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991648.10/warc/CC-MAIN-20210511153555-20210511183555-00118.warc.gz
|
CC-MAIN-2021-21
| 8,348 | 22 |
http://angkormovie.com/ebooks/applications-of-algebraic-geometry-to-coding-theory-physics-and-computation
|
math
|
By I. Burban, Yu. Drozd, G.-M Greuel (auth.), Ciro Ciliberto, Friedrich Hirzebruch, Rick Miranda, Mina Teicher (eds.)
An up to date file at the present prestige of vital examine themes in algebraic geometry and its purposes, akin to computational algebra and geometry, singularity concept algorithms, numerical ideas of polynomial structures, coding idea, verbal exchange networks, and computing device imaginative and prescient. Contributions on extra basic features of algebraic geometry contain expositions concerning counting issues on types over finite fields, Mori concept, linear structures, Abelian forms, vector bundles on singular curves, degenerations of surfaces, and reflect symmetry of Calabi-Yau manifolds.
Read or Download Applications of Algebraic Geometry to Coding Theory, Physics and Computation PDF
Best geometry books
This survey textual content with a historic emphasis helps a number of varied classes. It comprises team tasks related to using expertise or verbal/written responses. The textual content strives to construct either scholars' instinct and reasoning. it's excellent for junior and senior point classes.
The aim of this publication is to supply an advent to the idea of jet bundles for mathematicians and physicists who desire to research differential equations, really these linked to the calculus of diversifications, in a latest geometric approach. one of many subject matters of the publication is that first-order jets should be regarded as the common generalisation of vector fields for learning variational difficulties in box conception, and such a lot of of the buildings are brought within the context of first- or second-order jets, earlier than being defined of their complete generality.
This ebook establishes the elemental functionality idea and complicated geometry of Riemann surfaces, either open and compact. some of the equipment utilized in the e-book are variations and simplifications of equipment from the theories of a number of complicated variables and intricate analytic geometry and might function very good education for mathematicians eager to paintings in advanced analytic geometry.
- Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
- Geometric Analysis of PDE and Several Complex Variables: Dedicated to Francois Treves
- Real Analysis: Measures, Integrals and Applications
- Introduction to Nonlinear Analysis
- Beautiful Geometry
- Conceptual Spaces: The Geometry of Thought
Additional info for Applications of Algebraic Geometry to Coding Theory, Physics and Computation
Over a field K of characteristic y~, ... ,y:. of K such that 30 L. CHIANTINI, F. CIOFFI AND F. 1 ) where A 1= 0, 1, see (Silverman, III, Prop. 7). 1) is a Weierstrass representation of an elliptic plane curve in the Legendre form. The condition A 1= 0, 1 is equivalent to the fact that E is smooth, see for example (Silverman and Tate, IV, section 3). We suppose that A E K. Every field K contains a copy of Q or of Z p for some prime p and so we can assume that K = Q or Z p' To study an algebraic object over Q it is useful to study the reduction of the object modulo primes.
A sextic; 2. a curve of degree 8 with 1vI'0 proper quadruple points; 3. a curve of degree 8 with lvI'o infiniteZv near quadruple points: 4. finiteiy near of the/irst order to Xo: 5. a curve of degree 12 with a point Xo of multiplicity 9 and three triple points each in(inite(v lIear of the/irst order to Xo. The virtual branch curve of double planes of type (3), (4), (5) has degree 2d, a point Xo of multiplicity 2d - 4 and d - 3 quadruple points in the first infinitesimal neighbourhood of Xo. This may happen only if Co = 2d - 3 is odd and 2d < 14.
The Mordell-Weil group of rational points of an elliptic curve has been studied in many different contests (for example, see (Cremona; Oarmon». We have implemented our construction of elliptic curves of given degree in the objectoriented language C++ by using the NTL library of (Y. html. D4. g. (Johnsen and Kleiman; Clemens; Kley)); the problem is also related with the study of Hilbert schemes of curves (see (Kleppe and Mir6-Roig». D4. The method was used in (Madonna), where a complete classification of rank 2 bundles without intermediate cohomology on general quartic threefolds is achieved.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948520218.49/warc/CC-MAIN-20171213011024-20171213031024-00447.warc.gz
|
CC-MAIN-2017-51
| 4,292 | 17 |
https://documents.pub/document/23-mechanical-advantage-40-chapter-2-a-getting-to-work-nel-figure-1-this-claw.html
|
math
|
40 Chapter 2 • Getting to Work NEL
Figure 1 This claw hammer pulling a nail out of a piece of wood has a mechanical advantage of 15.
SAMPLE PROBLEM 1: Determine Mechanical Advantage of a Wheelbarrow
effort arm 120 cm
load arm 40 cm
Figure 2 This wheelbarrow multiplies the input force 3 times.
The wheelbarrow in Figure 2 has an effort arm 120 cm long and a load arm 40 cm long. What is its mechanical advantage?
Given: effort arm length = 120 cm load arm length = 40 cm
Required: mechanical advantage (MA)
Analysis: MA = effort arm length
_____________ load arm length
Solution: MA = 120 cm ______ 40 cm
MA = 3
Statement: This wheelbarrow has a mechanical advantage of 3.
Practice: A wheelbarrow has an effort arm that is 1.8 m long and a load arm that is 0.50 m long. What is the mechanical advantage of the wheelbarrow?
6.B.6.B. SKILLS HANDBOOK
Mechanical Advantage Th e designers of physical systems know from experience that there are many diff erent ways of accomplishing the same task. For example, nails may be pulled out of a piece of wood with machines such as a pair of pliers or a claw hammer (Figure 1). Th e claw hammer does the job with less eff ort. Why is this the case? Th e hammer acts as a fi rst class lever that converts a small input force into a much larger output force. When a machine turns a small input force into a larger output force, we say that the machine gives us a mechanical advantage. Mechanical advantage (MA) is the ratio of the output force to the input force (for example, the output force divided by the input force).
Imagine a hammer pulling a nail out of a piece of wood. If the hammer produces an output force 15 times greater than the force you apply to it (the input force), then the hammer has a mechanical advantage of 15. Mechanical advantage has no units; it is simply a comparison or ratio. When the input and output forces are the same, the mechanical advantage is 1. Machines with a mechanical advantage greater than 1 generally make tasks easier and faster to accomplish.
One way of estimating the mechanical advantage of a lever is to compare the length of the eff ort arm with the length of the load arm. Th e formula for mechanical advantage in this case is
MA = eff ort arm length
______________ load arm length
mechanical advantage: the ratio of output force to input force for a given machine
Sci8_UnitA_Chap2.indd 40Sci8_UnitA_Chap2.indd 40 10/17/08 10:44:06 AM10/17/08 10:44:06 AM
2.3 Mechanical Advantage 41NEL
It is possible to have a mechanical advantage of less than 1. Th is happens when the input force is greater than the output force. A hockey stick (Figure 3), a class 3 lever, requires an input force much greater than the output force. What good is such a machine? Th e benefi t of the hockey stick is that it increases the distance and speed of the output. Th e end of the stick travels faster and farther than the player’s hands do. Th e hockey stick transfers this motion to the puck. Th is means that the puck travels faster and a greater distance than it would have if the player hit the puck with his or her hand or foot.
You can also estimate the mechanical advantage of machines by comparing input and output distances. Using distances, mechanical advantage is equal to the ratio of input distance to output distance:
MA = input distance _____________ output distance
Input distance refers to the distance over which the input force is applied; output distance refers to how far the load moves. For a single pulley (Figure 4), the input distance and the output distance are the same, so mechanical advantage is 1.
Figure 3 Although the mechanical advantage of a hockey stick is less than 1, the benefi t is the speed and distance that the blade at the end of the stick travels.
To lift a load 5 cm with a pulley system, 15 cm of string had to be pulled. What is the mechanical advantage?
Given: input distance = 15 cm output distance = 5 cm
Required: mechanical advantage (MA)
Analysis: MA = input distance
____________ output distance
Solution: MA = 15 cm _____ 5 cm
MA = 3
Statement: The pulley system has a mechanical advantage of 3.
Practice: What is the mechanical advantage of a pulley system if 4 m of string had to be pulled to lift a load to a height of 1 m?
SAMPLE PROBLEM 2: Determine Mechanical Advantage of a Pulley System
20 cm20 cm
Figure 4 A single pulley has a mechanical advantage of 1.
Sci8_UnitA_Chap2.indd 41Sci8_UnitA_Chap2.indd 41 10/17/08 10:44:14 AM10/17/08 10:44:14 AM
42 Chapter 2 • Getting to Work NEL
Ideal Mechanical Advantage versus Actual Mechanical Advantage Sample problems 1 and 2 describe a form of mechanical advantage called ideal mechanical advantage. Th e ideal mechanical advantage is what the mechanical advantage would be if all of the input force could be converted into an output force. However, this is never possible in real-world applications. Th ink back to the claw hammer in Figure 1. Not all of the eff ort applied to the hammer will be used in pulling the nail from the wood. Friction between the wood and the nail will cause some of the input force to be turned into thermal energy in the wood and the nail (for example, the wood and nail heat up a little). Also, some of the input force may be used in causing the wood to dent or in producing sound.
Actual mechanical advantage is the mechanical advantage that actually occurs. It is the ideal mechanical advantage minus any force lost to factors such as internal friction, slippage, and distortion. How do we determine the actual mechanical advantage of a machine? We do so by measuring the actual forces involved. Actual mechanical advantage can be calculated by dividing a measured output force by a measured input force.
Th is formula uses measured forces to calculate mechanical advantage:
actual MA = measured output force ___________________ measured input force
ideal mechanical advantage: the mechanical advantage of a machine if all of the input force is converted into output force; never possible in real- world applications
actual mechanical advantage: the mechanical advantage of a machine in real-world applications; equal to ideal mechanical advantage minus force lost to friction, slippage, and distortion
Imagine that you are lifting a patio stone using a pry bar as a lever (Figure 5). If the input force applied is measured as 25 N and the output force is measured as 250 N, then what is the actual mechanical advantage?
Given: measured input force = 25 N measured output force = 250 N
Required: actual mechanical advantage (MA)
Analysis: actual MA = measured output force
_________________ measured input force
Solution: actual MA = 250 N _____ 25 N
actual MA = 10
Statement: The lever has an actual mechanical advantage of 10.
Practice: What is the actual mechanical advantage of a lever if the input force is measured as 37 N and the output force is measured as 185 N?
SAMPLE PROBLEM 3: Determine Actual Mechanical Advantage of a Lever
25 N 250 N
Sci8_UnitA_Chap2.indd 42Sci8_UnitA_Chap2.indd 42 10/17/08 10:44:26 AM10/17/08 10:44:26 AM
2.3 Mechanical Advantage 43NEL
TRY THIS: Mechanical Advantage of a Lever
By measuring the length of the effort and load arms of a lever, and then measuring the forces involved, you can compare actual and ideal mechanical advantages.
Equipment and Materials: textbook; plastic bag; newton spring scale; metre stick; chair
1. Put a textbook in a plastic bag and measure the force needed to lift it. This is the measured output force.
2. Make a class 2 lever using a metre stick, the back of a chair as a fulcrum, and the book in the bag as the load.
3. Hook the spring scale onto the metre stick and measure the force required to hold up the load, the length of the load arm, and the length of the effort arm.
4. Use these measurements to determine the actual mechanical advantage and the ideal mechanical advantage. If time allows, repeat using different distances or a different class of lever.
A. How did your actual value compare with the ideal value?
B. Sketch the arrangement you used. Include all appropriate labels.
SKILLS MENU: planning, performing, observing, analyzing
You can also use the actual mechanical advantage equation to determine the actual mechanical advantage of pulley systems.
CHECK YOUR LEARNING
1. What is the meaning of “mechanical advantage”?
2. (a) If an output force is fi ve times larger than an input force, what is the mechanical advantage?
(b) If an input of 0.6 N is required to lift a rock of 36 N, what is the actual mechanical advantage? Show your calculations.
3. (a) The mechanical advantage of a class 3 lever will always be less than 1. Explain why.
(b) If there is no mechanical advantage to class 3 levers, why are they considered useful?
4. What parts of a pulley system will cause the actual mechanical advantage to be less than the ideal mechanical advantage?
Th e sensitivity of tools (scales) used to measure forces may need to vary depending on how large or small the force is, or how accurate the reading needs to be. However, as
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571993.68/warc/CC-MAIN-20220814022847-20220814052847-00093.warc.gz
|
CC-MAIN-2022-33
| 9,036 | 81 |
https://lists.cam.ac.uk/pipermail/cl-isabelle-users/2006-April/msg00005.html
|
math
|
Re: [isabelle] Monotonic operators and calculational reasoning
have "(1::nat) < 3"
also have "(3::nat) + 1 < 5"
You did exactly the right thing.
calculation: (!!x y. x < y ==> x + 1 < y + 1) ==> 1 + 1 < 5
As did Isabelle. The principle here is that the monotonicity assumptions that
arise in your calculational proof are carried around, accumulate, and get
discharged at the end. Thus you cannot simply say
finally have "1+1 < (5::nat)" .
but need to do something like
finally have "1+1 < (5::nat)" by (blast intro:add_less_mono1)
There may be slightly slicker proof patters.
This archive was generated by a fusion of
Pipermail (Mailman edition) and
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362230.18/warc/CC-MAIN-20211202145130-20211202175130-00481.warc.gz
|
CC-MAIN-2021-49
| 649 | 14 |
https://humansofagape.podigee.io/14-paul-duncan
|
math
|
Questions? Comments? Compliments? Do you want to know more?
Let's get in touch!
Here are Paul's famous questions to start a conversation or to go deeper:
If you are going to use these in a live situation I suggest that you write them out before hand in a note book rather than appearing before the person with such a formal looking list. The list being handwritten communicates to the other person that you thought about these questions for them: so here goes in no particular order:
• What does your boss/leader expect of you?
• What do you expect of them?
• What do you expect from your staff? Have you told them?
• When did you last intentionally develop one of your team leaders?
• In the last 7 days have you received recognition/praise for good work?
• How much thinking time have you put in your schedule?
• Is there someone in the ministry who encourages your development?
• What causes you to grow?
• What’s the main thing that you have learnt over the last 6 months?
• What would you consider your main strengths to be?
• What would other consider your strengths to be?
• What do you pray for your self?
• Personal W/B/S
• What 3 decisions/activities are causing you the most stress?
• Do you have a best friend in the ministry?
• How can I help you?
• What area/areas do you think your team would say you need to improve in?
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655878639.9/warc/CC-MAIN-20200702080623-20200702110623-00217.warc.gz
|
CC-MAIN-2020-29
| 1,371 | 21 |
https://softmath.com/tutorials-3/algebra-formulas/rational-exponents-5.html
|
math
|
Key Concepts: Rational exponents
|Textbook sections and practice problems
7.2: 1-109 odd
|Expressing roots and radicals with exponents
Assuming that a is in the domain and n is a positive integer ,
Express each exponential expression in radical form.
|Assuming that a is in the domain and m and n are positive integers ,|
Find each number on your calculator . (Round to the nearest 100th).
Find each number without the use of your calculator .
Find each function value .
Find f (−17) where
Find g (64) where
Find k (−8) where
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506399.24/warc/CC-MAIN-20230922102329-20230922132329-00885.warc.gz
|
CC-MAIN-2023-40
| 529 | 13 |
https://www.assignmentexpert.com/homework-answers/physics/mechanics-relativity/question-15871
|
math
|
Answer to Question #15871 in Mechanics | Relativity for MaKalaa
An airplane flies north at a speed of 150 km/h relative to the air through which it flies. If there is a tail wind of 50 km/h, what is the plane's velocity relative to the ground?
The wind direction coincides with the direction of airplane flight, so their velocities are added:
V = 150[km/h] + 50[km/h] = 200[km/h].
So, the plane's velocity relative to the ground is 200[km/h].
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988696.23/warc/CC-MAIN-20210505203909-20210505233909-00098.warc.gz
|
CC-MAIN-2021-21
| 442 | 5 |
http://www.scrapbookmax.com/forums/threads/7363-Kid-s-Crafts-1078?p=71031
|
math
|
I hope this is the right forum to ask the question. I have been looking for some new templates. I saw this one (Kid's Crafts #1078) in the booster store. I have a question. Is it a fixed one or can I move stuff around. I am hoping that I can move stuff around. Because its listed as a best seller, I was hoping to find some layouts in the user gallery but did not run across anything.
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720941.32/warc/CC-MAIN-20161020183840-00409-ip-10-171-6-4.ec2.internal.warc.gz
|
CC-MAIN-2016-44
| 384 | 1 |
https://www.assignmentexpert.com/homework-answers/economics/finance/question-51275
|
math
|
Your daughter is born today and you want her to be a millionaire by the time she is
35 years old. You open an investment account that promises to pay 12% per year.
How much money must you deposit each year, starting on her 1st birthday and
ending on her 35th birthday, so your daughter will have RM1,000,000 by her 35th
n = 35 years, r = 12% per year. To calculate the annual deposit amount, we use the formula of compound interest: FV = PV*(1+r)^n PV = 1000000/(1.12 + 1.12^2 + … + 1.12^35) = $2,068.41 per year.
The moment you’ve entered the education system is the moment you start to realize that, although studying is extremely important,…
APPROVED BY CLIENTS
The service was great but I had to send the assignment back a few times because some of the directions were not followed. They could pay a little closer attention to detail. They were excellent about fixing it and very fast too
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585199.76/warc/CC-MAIN-20211018062819-20211018092819-00652.warc.gz
|
CC-MAIN-2021-43
| 898 | 8 |
https://e-eduanswers.com/mathematics/question13568431
|
math
|
We have been given the formula for volume and the surface area as
Hence the ration will be
Let us apply this to a tissue box measuring
l=6 in , w=3 in , h=2 in
SA=36+12+24=24 sq in
Volume=6*3*2=36 in cube
give me a minute to find out more about the question and answer
Surface area; Greater; subtract
the answer is a they can have cilia
The protist is more efficient at expelling wastes because it has a higher surface area-to-volume ratio.
According to the given information, protists have more surface area to volume ratio as compared to a human intestinal cell. More surface area to volume ratio refers to the fact that more of the surface area of the organism is in contact with surroundings. A cell or organism with a greater surface exposed to surroundings has a higher rate of exchange of materials or heat with the outer environment. Having a greater surface area of the body exposed to the surroundings, protists are able to release the waste out of the body more efficiently as compared to the small intestine.
w = width
h = height
SA = 2lw + 2wh + 2lh.
V = lwh.
Write an expression for the ratio of surface area to volume:
SA / V = [ 2lw + 2wh + 2lh] / lwh
SA / V = 2lw / lwh + 2wh / lwh + 2lh / lwh
SA / V = 2/h + 2/l + 2/w
Choose an appropriate length, width, and height for your package so that it can fit the product you are shipping. Using these dimensions, what is the ratio of surface area to volume?
I will work with an hypothetical figure where you have , l, w and the volume.
I suppose you know the volume, because it is the amount of product you need to pack. Make V = 1000 cm^3, l = 10 cm and w = 5 cm.
Wtih two dimensions and the volumen you can find the other dimension.
V = lwh = 1000 cm^3 => h = 1000 cm^3 / (lw) = 1000 cm^3 / (10 cm * 5 cm)
h = 1000 cm^3 / (50 cm^2) = 20 cm
Now you have the three dimensions to pack 1000 cm^3 of your product:
l = 10 cm
w = 5 cm
h = 20 cm
And the ratio of surface area to volume is:
SA / V = 2/h + 2/l + 2/w = 2/(20cm) + 2/(10cm) + 2/(5cm) = 0,7 (cm)^-1
Extra tips: To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times.
W= 3in L= 6in H= 3in
And then use the surface area equation ( SA = 2lw + 2wh + 2lh)
To get your volume use the equation ( V = lwh)
And then divide those two SA / V and you get your ratio
Task 1 complete!!
answer: i don't understand it
step-by-step explanation: sorry
did you get the answer yet?
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151563.91/warc/CC-MAIN-20210725014052-20210725044052-00305.warc.gz
|
CC-MAIN-2021-31
| 2,639 | 40 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.