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://groups.yahoo.com/neo/groups/primenumbers/conversations/topics/21618?o=1&d=-1
|
math
|
Re: [PrimeNumbers] let me introducte myself and a slightly better approx to pi(x) than Li(x)
- To Compute accurate value of pi(x),please see my book"Prime Numbers" Some Characteristics ISBN 1-4392-4094-9 pages 19-22.
--- On Sat, 7/17/10, pbtoau <PbtoAu@...> wrote:
From: pbtoau <PbtoAu@...>
Subject: Re: [PrimeNumbers] let me introducte myself and a slightly better approx to pi(x) than Li(x)
Date: Saturday, July 17, 2010, 11:53 PM
This is probably just a consequence of Li(x) being larger than pi(x) for the first 300 orders of magnitude or so. Without getting into Riemann zeros and the explicit formula the Riemann approximation does much better than Li(x) with a simple adjustment.
--- In [email protected], Matteo Mattsteel Vitturi <mattsteel@...> wrote:
> Hello Norman.
> Thank you for your reply: I don't think you give me a
> stupid answer and I'm not looking for good approx of pi(x).
> All I
> said happened by chance and, later, I thought to write to this list.
> know a (compicated) formula of pi(x) that takes into account
> non-trivial zeroes of the zeta-function is common-knowledge, but I'm
> naively impressed by the fact that when a "simple number" as x^(1/pi) is
> subtracted to Li(x) then the approximation is improved so much
> (examining the first two millions integers).
> Oh, well: I'm using
> Li(x) = Integral over t from 2 to x of (dt/ln(t))
> For example,
> rounding to the greatest integer, we have
> Li(10)-10^(1/pi) = 4 =
> Li(100)-100^(1/pi) = 25 = pi(100)
> Li(1000)-1000^(1/pi) =
> 168 = pi(1000)
> Li(10000)-10000^(1/pi) = 1227 [that is 2 less than
> Li(100000)-100000^(1/pi) = 9592 = pi(100000)
> = 78563 [that is 65 over pi(1000000)=78498]
> I know that as few as
> three evidence is nothing compared to infinity, and this is the reason
> to ask for your advice.
> Novità dai tuoi amici? Le trovi su Messenger
[Non-text portions of this message have been removed]
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463609598.5/warc/CC-MAIN-20170528043426-20170528063426-00327.warc.gz
|
CC-MAIN-2017-22
| 1,901 | 34 |
https://www.faadooengineers.com/threads/12808-Tech-mahindra-placement-papers
|
math
|
Gender: : Male
Branch: : Computer Science Engineering
City : KolkataSend Friend Request
1. A man starts walking at 3 pm . ha walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way?
Ans: 12 km
2. A grandma has many sons; each son has as many sons as his brothers. What is her age if it?s the product of the no: of her sons and grandsons plus no: of her sons?(age b/w 70 and 100).
3. An electric wire runs for 1 km b/w some no: of poles. If one pole is removed the distance b/w each pole increases by 1 2/6 (mixed fraction). How many poles were there initially?
4. There is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall. There is one each bird sitting on top of both the towers. They fly at a constant speed and time to reach a grain in b/w the towers at the same time. At what distance from the church is the grain?
5. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? on which day the lawyer asks the person to come?
6. There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house ? ( 3 marks)
7. There are 10 Red, 10 Blue, 10 Green, 10 Yellow, 10 White balls in a bag. If you are blindfolded and asked to pick up the balls from the bag, what is the minimum number of balls required to get a pair of atleast one colour ? ( 2 Marks)
Ans :6 balls.
8. Triplet who usually wear same kind and size of shoes, namely, Annie, Danny, Fanny. Once one of them broke a glass in kitchen and their shoe prints were there on floor of kitchen. When their mother asked who broke Annie said, ?I didn?t do it?; Fanny said ?Danny did it?; Danny said ?Fanny is lieing?; here two of them are lieing, one is speaking truth. Can you find out who broke it ? (3 Marks)
Ans : Annie
9. There are total 15 people. 7 speaks french and 8 speaks spanish. 3 do not speak any language. Which part of total people speaks both languages.
10. A jogger wants to save ?th of his jogging time. He should increase his speed by how much %age.
Ans: 33.33 %
11.If A wins in a race against B by 10 mts in a 100 Meter race. If B is behind of A by 10 mts. Then they start running race, who will won?
12. A+B+C+D=D+E+F+G=G+H+I=17 given A=4.Find value of G and H?
Ans: G = 5 E=1
13. One guy has Rs. 100/- in hand. He has to buy 100 balls. One football costs Rs. 15/, One Cricket ball costs Re. 1/- and one table tennis ball costs Rs. 0.25 He spend the whole Rs. 100/- to buy the balls. How many of each balls he bought?
14. The distance between Station Atena and Station Barcena is 90 miles. A train starts from Atena towards Barcena. A bird starts at the same time from Barcena straight towards the moving train. On reaching the train, it instantaneously turns back and returns to Barcena. The bird makes these journeys from Barcena to
the train and back to Barcena continuously till the train reaches Barcena. The bird finally returns to Barcena and rests. Calculate the total distance in miles the bird travels in the following two cases:
(a) The bird flies at 90 miles per hour and the speed of the train is 60 miles per hour.
(b) the bird flies at 60 miles per hour and the speed of the train is 90 miles per hour
Ans: time of train=1hr.so dist of bird=60*1=60miles
15. A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match.
(a) How many players participate in the tournament if 15 matches are totally played?
(b) How many matches are played in the tournament if 50 players totally participate?
16.When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?
17. In a soap company a soap is manufactured with 11 parts. For making one soap you will get 1 part as scrap. At the end of the day u have 251 such scraps. From that how many soaps can be manufactured?
18. There is a 5digit no. 3 pairs of sum is eleven each. Last digit is 3 times the first one. 3 rd digit is 3 less than the second.4 th digit is 4 more than the second one. Find the digit.
Ans : 25296.
19. Fifty percent of the articles in a certain magazine are written by staff members. Sixty percent of the articles are on current affairs. If 75 percent of the articles on current affairs are written by staff members with more than 5 years experience of journalism, how many of the articles on current affairs are written by journalists with more than 5 years experience? 20 articles are written by staff members. Of the articles on topics other than current affairs, 50 percent are by staff members with less than 5 years experience.
20. Is xy > 0 ?
x/y < 0
x + y < 0
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948530668.28/warc/CC-MAIN-20171213182224-20171213202224-00348.warc.gz
|
CC-MAIN-2017-51
| 4,970 | 37 |
https://lessmagazine.com/what-does-a-thousand-square-foot-mean/
|
math
|
The area of a surface, such as a floor or a plot of land, is measured in thousand square feet. A 1,000 square foot area can take many different forms.
An area’s square footage is estimated in a variety of ways depending on its shape. A square or rectangular space’s square footage can be calculated by multiplying the width by the length of the space.
A space that is 50 feet long and 20 feet wide, for example, could be 1,000 square feet. A 1,000-square-foot triangular space with one right angle and a length of 40 feet and a width of 50 feet might also be used.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335254.72/warc/CC-MAIN-20220928113848-20220928143848-00674.warc.gz
|
CC-MAIN-2022-40
| 568 | 3 |
https://mcqlearn.com/math/g10/multiplication-of-matrices-mcqs.php
|
math
|
Class 10 math Practice Tests
Class 10 Math Online Tests
The Book Multiplication of matrices Multiple Choice Questions (MCQ Quiz) with answers, multiplication of matrices MCQ Quiz PDF download to study online 10th grade math certificate courses. Solve Matrices and Determinants Multiple Choice Questions and Answers (MCQs), Multiplication of Matrices quiz answers PDF for school certificate. The e-Book Multiplication of Matrices MCQ App Download: multiplicative inverse of matrix, types of matrices, solution of simultaneous linear equations, addition and subtraction of matrices test prep for school certificate.
The MCQ: The law which does not hold in multiplication of matrices is known as PDF, "Multiplication of Matrices" App Download (Free) with distributive law, inverse law, associative law, and commutative law choices for school certificate. Study matrices and determinants quiz questions, download Amazon eBook (Free Sample) for online degrees.
MCQ: The law which does not hold in multiplication of matrices is known as
MCQ: If the number of rows in A matrix are equal to the number of column in B matrix, then A and B are comfortable for
MCQ: If A(BC) = (AB)C, then with respect to multiplication this law is called
Download 10th Grade Math Quiz App, 8th Grade Math MCQ App, and 9th Grade Math MCQs App to install for Android & iOS devices. These Apps include complete analytics of real time attempts with interactive assessments. Download Play Store & App Store Apps & Enjoy 100% functionality with subscriptions!
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100705.19/warc/CC-MAIN-20231207221604-20231208011604-00745.warc.gz
|
CC-MAIN-2023-50
| 1,526 | 8 |
http://www.slideshare.net/Nuumero1/velocity-and-accelaration
|
math
|
Tips & Tricks
Velocity and accelaration
Like this document? Why not share!
motion velocity accelaration and di...
Libro ribeiro, lair -_el_ã©xito_no_...
by Coach YLICH TARAZONA
Эстония. Южная Эстония. Культурный ...
by Агентство лечебно...
Autoestima; Origen, Formación y Des...
by Coach YLICH TARAZONA
Chapter 2-radar equation
by Rima Assaf
Email sent successfully!
Show related SlideShares at end
Velocity and accelaration
Feb 14, 2014
Comment goes here.
12 hours ago
Are you sure you want to
Your message goes here
Be the first to comment
Be the first to like this
Number of Embeds
No notes for slide
Velocity and accelaration
1. ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 7 - LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial may be skipped if you are already familiar with the topic On completion of this tutorial you should be able to • Define linear motion. • Explain the relationship between distance, velocity, acceleration and time. • Define angular motion. • Explain the relationship between angle, angular velocity, angular acceleration and time. • Explain the relationship between linear and angular motion. © D.J.DUNN freestudy.co.uk 1
1. LINEAR MOTION 1.1 MOVEMENT or DISPLACEMENT This is the distance travelled by an object and is usually denoted by x or s. Units of distance are metres. 1.2 VELOCITY This is the distance moved per second or the rate of change of distance with time. Velocity is movement in a known direction so it is a vector quantity. The symbol is v or u and it may be expressed in calculus terms as the first derivative of distance with respect to time so that v = dx/dt or u = ds/dt. The units of velocity are m/s. 1.3. SPEED This is the same as velocity except that the direction is not known and it is not a vector and cannot be drawn as such. 1.4. AVERAGE SPEED OR VELOCITY When a journey is undertaken in which the body speeds up and slows down, the average velocity is defined as TOTAL DISTANCE MOVED/TIME TAKEN. 1.5. ACCELERATION When a body slows down or speeds up, the velocity changes and acceleration or deceleration occurs. Acceleration is the rate of change of velocity and is denoted with a. In calculus terms it is the first derivative of velocity with time and the second derivative of distance with time such that a = dv/dt = d2x/dt2. The units are m/s2. Note that all bodies falling freely under the action of gravity experience a downwards acceleration of 9.81 m/s2. WORKED EXAMPLE No.1 A vehicle accelerates from 2 m/s to 26 m/s in 12 seconds. Determine the acceleration. Also find the average velocity and distance travelled. SOLUTION a = ∆v/t = (26 - 2)/12 = 2 m/s2 Average velocity = (26 + 2)/2 = 14 m/s Distance travelled 14 x 12 = 168 m © D.J.DUNN freestudy.co.uk 2
SELF ASSESSMENT EXERCISE No.1 1. A body moves 5000 m in 25 seconds. What is the average velocity? (Answer 200 m/s) 2. A car accelerates from rest to a velocity of 8 m/s in 5 s. Calculate the average acceleration. (Answer 1.6 m/s2) 3. A train travelling at 20 m/s decelerates to rest in 40 s. What is the acceleration? (Answer -0.5 m/s2) © D.J.DUNN freestudy.co.uk 3
1.6. GRAPHS It is very useful to draw graphs representing movement with time. Much useful information may be found from the graph. 1.6.1. DISTANCE - TIME GRAPHS Figure 1 Graph A shows constant distance at all times so the body must be stationary. Graph B shows that every second, the distance from start increases by the same amount so the body must be travelling at a constant velocity. Graph C shows that every passing second, the distance travelled is greater than the one before so the body must be accelerating. 1.6.2. VELOCITY - TIME GRAPHS Figure 2 Graph B shows that the velocity is the same at all moments in time so the body must be travelling at constant velocity. Graph C shows that for every passing second, the velocity increases by the same amount so the body must be accelerating at a constant rate. © D.J.DUNN freestudy.co.uk 4
1.7 SIGNIFICANCE OF THE AREA UNDER A VELOCITY-TIME GRAPH The average velocity is the average height of the v-t graph. By definition, the average height of a graph is the area under it divided by the base length. Figure 3 Average velocity = total distance travelled/time taken Average velocity = area under graph/base length Since the base length is also the time taken it follows that the area under the graph is the distance travelled. This is true what ever the shape of the graph. When working out the areas, the true scales on the graphs axis are used. WORKED EXAMPLE No.2 Find the average velocity and distance travelled for the journey depicted on the graph above. Also find the acceleration over the first part of the journey. SOLUTION Total Area under graph = A + B + C Area A = 5x7/2 = 17.5 (Triangle) Area B = 5 x 12 = 60 (Rectangle) Area C = 5x4/2 = 10 (Triangle) Total area = 17.5 + 60 + 10 = 87.5 The units resulting for the area are m/s x s = m Distance travelled = 87.5 m Time taken = 23 s Average velocity = 87.5/23 = 3.8 m/s Acceleration over part A = change in velocity/time taken = 5/7 = 0.714 m/s2. © D.J.DUNN freestudy.co.uk 5
SELF ASSESSMENT EXERCISE No.2 1. A vehicle travelling at 1.5 m/s suddenly accelerates uniformly to 5 m/s in 30 seconds. Calculate the acceleration, the average velocity and distance travelled. (Answers 0.117 m/s2, 3.25 m/s and 97.5 m) 2. A train travelling at 60 km/h decelerates uniformly to rest at a rate of 2 m/s2. Calculate the time and distance taken to stop. (Answers 8.33 s and 69.44 m) 3. A shell fired in a gun accelerates in the barrel over a length of 1.5 m to the exit velocity of 220 m/s. Calculate the time taken to travel the length of the barrel and the acceleration of the shell. (Answers 0.01364 s and 16133 m/s2) © D.J.DUNN freestudy.co.uk 6
1.8. STANDARD FORMULAE Consider a body moving at constant velocity u. Over a time period t seconds it accelerates from u to a final velocity v. The graph looks like this. Distance travelled = s s = area under the graph = ut + (v-u)t/2 s= s= s= s= ut + (v - u)t/2 .........................(1) ut + t/2 v - ut/2 vt/2 + ut/2 t/2 (v + u ) Figure 4 The acceleration = a = (v - u)/t from which (v - u) = at Substituting this into equation (1) gives s = ut + at2/2 Since v = u + the increase in velocity v = u + at and squaring we get v2 = u2 + 2a[at2/2 + ut] v2 = u2 + 2as WORKED EXAMPLE No.3 A missile is fired vertically with an initial velocity of 400 m/s. It is acted on by gravity. Calculate the height it reaches and the time taken to go up and down again. SOLUTION a = -g = -9.81 m/s2 u = 400 m/s v=0 v2 = u2 + 2as 0 = 4002 + 2(-9.81)s s = 8155 m s = (t/2)(u + v) 8155 = t/2(400 + 0) t = 8155 x 2/400 = 40.77 s To go up and down takes twice as long. t = 81.54 m/s © D.J.DUNN freestudy.co.uk 7
WORKED EXAMPLE No.4 A lift is accelerated from rest to 3 m/s at a rate of 1.5 m/s2. It then moves at constant velocity for 8 seconds and then decelerates to rest at 1.2 m/s2. Draw the velocity time graph and deduce the distance travelled during the journey. Also deduce the average velocity for the journey. SOLUTION The velocity - time graph is shown in fig.5. Figure 5 The first part of the graph shows uniform acceleration from 0 to 3 m/s. The time taken is given by t1 = 3/1.5= 2 seconds. The distance travelled during this part of the journey is x1 = 3 x 2/2 = 3 m The second part of the journey is a constant velocity of 3 m/s for 8 seconds so the distance travelled is x2 = 3 x 8 = 24 m The time taken to decelerate the lift over the third part of the journey is t3 = 3/1.2 = 2.5 seconds. the distance travelled is x2 = 3 x 2.5/2 = 3.75 m The total distance travelled is 3 + 24 + 3.75 = 30.75 m. The average velocity = distance/time = 30.75/12.5 = 2.46 m/s. © D.J.DUNN freestudy.co.uk 8
SELF ASSESSMENT EXERCISE No.3 The diagram shows a distance-time graph for a moving object. Calculate the velocity. (Answer 1.82 m/s) Figure 5 2. The diagram shows a velocity time graph for a vehicle. Calculate the following. i. The acceleration from O to A. ii. The acceleration from A to B. iii. The distance travelled. iv. The average velocity. (Answers 2.857 m/s2, -2.4 m/s2, 35 m and 5.83 m/s) Figure 6 © D.J.DUNN freestudy.co.uk 9
3. The diagram shows a velocity-time graph for a vehicle. Calculate the following. i. The acceleration from O to A. ii. The acceleration from B to C. iii. The distance travelled. iv. The average velocity. (Answers 5 m/s2, -2 m/s2, 85 m and 7.08 m/s) Figure 7 © D.J.DUNN freestudy.co.uk 10
2. ANGULAR MOTION 2.1 ANGLE θ Angle has no units since it a ratio of arc length to radius. We use the names revolution, degree and radian. Engineers use radian. Consider the arc shown. The length of the arc is Rθ and the radius is R. The angle is the ratio of the arc length to the radius. θ = arc length/ radius hence it has no units but it is called radians. If the arc length is one radius, the angle is one radian so a radian is defined as the angle which produces an arc length of one radius. Figure 8 2.2 ANGULAR VELOCITY ω Angular velocity is the rate of change of angle per second. Although rev/s is commonly used to measure angular velocity, we should use radians/s (symbol ω). Note that since a circle (or revolution) is 2π radian we convert rev/s into rad/s by ω= 2πN. Also note that since one revolution is 2π radian and 360o we convert degrees into radian as follows. θ radian = degrees x 2π/360 = degrees x π/180 DEFINITION angular velocity = ω = angle rotated/time taken = θ/t EXAMPLE No.5 A wheel rotates 200o in 4 seconds. Calculate the following. i. The angle turned in radians? ii. The angular velocity in rad/s SOLUTION θ = (200/180)π = 3.49 rad. ω = 3.49/4 = 0.873 rad/s © D.J.DUNN freestudy.co.uk 11
SELF ASSESSMENT EXERCISE No.4 1. A wheel rotates 5 revolutions in 8 seconds. Calculate the angular velocity in rev/s and rad/s. (Answers 0.625 rev/s and 3.927 rad/s) 2. A disc spins at 3000 rev/min. Calculate its angular velocity in rad/s. How many radians has it rotated after 2.5 seconds? (Answers 314.2 rad/s and 785.4 rad) 2.3 ANGULAR ACCELERATION α Angular acceleration (symbol α) occurs when a wheel speeds up or slows down. It is defined as the rate of change of angular velocity. If the wheel changes its velocity by ∆ω in t seconds, the acceleration is α = ∆ω / t rad/s2 WORKED EXAMPLE No.6 A disc is spinning at 2 rad/s and it is uniformly accelerated to 6 rad/s in 3 seconds. Calculate the angular acceleration. SOLUTION α = ∆ω/t = (ω2 - ω1)/t = (6 -2)/3 = 1.33 rad/s2 SELF ASSESSMENT EXERCISE No.5 1. A wheel at rest accelerates to 8 rad/s in 2 seconds. Calculate the acceleration. (Answer 4 rad/s2) 2. A flywheel spins at 5000 rev/min and is decelerated uniformly to 2000 rev/min in 12 seconds. Calculate the acceleration in rad/s2. (Answer -26.2 rad/s2) © D.J.DUNN freestudy.co.uk 12
2.4 LINK BETWEEN ANGULAR AND LINEAR MOTION Consider a point moving on a circular path as shown. The length of the arc = s metres. Angle of the arc is θ radians The link is s = Rθ Figure 9 Suppose the point P travels the length of the arc in tme t seconds. The wheel rotates θ radians and the point travels a distance of Rθ. The velocity along the circular path is v = Rθ/t = R ω Next suppose that the point accelerates from angular velocity ω1 to ω2. The velocity along the curve also changes from v1 to v2. Angular acceleration = α = (ω2 - ω1)/t Substituting ω = v/R α = (v2/R - v1/R)/t = a/R hence a = R α It is apparent that to change an angular quantity into a linear quantity all we have to do is multiply it by the radius. WORKED EXAMPLE No.7 A car travels around a circular track of radius 40 m at a velocity of 8 m/s. Calculate its angular velocity. SOLUTION v = ωR ω = v/R = 8/40 = 0.2 rad/s © D.J.DUNN freestudy.co.uk 13
2.5 EQUATIONS OF MOTIONS The equations of motion for angular motion are the same as those for linear motion but with angular quantities replacing linear quantities. replace s or x with θ replace v or u with ω replace a with α LINEAR ANGULAR s = ut + at2/2 θ = ω1t + αt2/2 s = (u + v)t/2 θ = (ω1 + ω2)t/2 v2 = u2 + 2as ω22 = ω12 + 2αθ Also remember that the angle turned by a wheel is the area under the velocity - time graph. SELF ASSESSMENT EXERCISE No.6 1. A wheel accelerates from rest to 3 rad/s in 5 seconds. Sketch the graph and determine the angle rotated. (Answer 7.5 radian). 2. A wheel accelerates from rest to 4 rad/s in 4 seconds. It then rotates at a constant speed for 3 seconds and then decelerates uniformly to rest in 5 seconds. Sketch the velocity time graph and determine i. The angle rotated. (30 radian) ii. The initial angular acceleration. (1 rad/s2) iii. The average angular velocity. (2.5 rad/s) © D.J.DUNN freestudy.co.uk 14
Email sent successfully..
|
s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645310876.88/warc/CC-MAIN-20150827031510-00103-ip-10-171-96-226.ec2.internal.warc.gz
|
CC-MAIN-2015-35
| 12,876 | 40 |
http://tajistuff.com/2020/02/16/what-precisely-is-time-dilation-in-physics/
|
math
|
What may be the time dilation in math? The answer is really a excellent deal greater than you believe. A actual information of these concepts will help you ascertain whether or not they wish to know additional in regards to the notion of causality in physics or never.
You must comprehend the significance of time in mathematics to understand the idea of time dilation in physics. slime licorne Time is a concept in mathematics. As with other steps of length and period in math, it really is a measure of this passage of time for one thing regarding a unique process.
Let us commence to study what is the significance of free-fall in mathematics having a question. pyjama licorne What exactly does impulse me-an in math? This could take a though excuse. This bit of this article’s objective will be to use to present in to the reader precisely the meaning in the idea of freefall in mathematics.
So we know what impulse signifies in physics, now let’s look at what time dilation in physics is all about. Suppose we are offered an object, and we press a button. combinaison licorne http://www.bu.edu/ar/2015/ What does the object do in that case?
Now we’ve got come to understand the notion of time dilation in physics. coque licorne iphone Time is actually a measure of how extended it requires for an object to travel from the point of origin for the point of effect of your object that press the button. coussin pokemon To work with the example from earlier; Let’s say we have an object like a baseball plus the pitcher throws it a lengthy way.
So that brings us for the initial part of the definition of what is time dilation in physics. Which is the time it requires for the object to travel long distances in one particular second. That definition of time dilation in physics is used to establish if the system that was just performed a time dilation action for instance that of the baseball player, is going to be in one particular second.
Another significant part of what’s the meaning of freefall in physics is the fact that time is a measure of distance. As an example; What does the time it takes for the baseball player to throw the ball be?
The answer to this query could be about three feet. essay_company Now lets look at the second part of the question. What does the which means of time dilation in physics imply for the object?
The one particular time dilation the baseball player makes when he throws the ball is one particular second. As you’ll be able to see, time is relative. When the baseball player has the velocity of 1 foot per second, he may have the time dilation of one particular second.
When you make use of the word ‘time’ in physics, it must be in reference towards the objective time that a single could perceive by themselves from the point of view of time within the universe. The one time dilation that a baseball player tends to make in one particular second will be the typical time it requires for the baseball player to fly from the point of origin towards the point of effect inside the universe.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369721.76/warc/CC-MAIN-20210305030131-20210305060131-00401.warc.gz
|
CC-MAIN-2021-10
| 3,054 | 10 |
http://pesameliah.blogspot.com/2016/04/my-favorite-book.html
|
math
|
Today I had finished reading the first chapter of How I Survived Middle School By Nancy Krulik. I am already interested in the book. The book is really funny to me. I rate the book 5 massive stars. What's your rate for this book? Are you interested in the book? I just want to give a BIG BIG shout out to Nancy for this amazing book. I am looking forward to reading the other series of How I Survived Middle School !
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347458095.68/warc/CC-MAIN-20200604192256-20200604222256-00167.warc.gz
|
CC-MAIN-2020-24
| 416 | 1 |
http://www.researchgate.net/publication/23858599_Implicit_Total_Variation_Diminishing_(TVD)_schemes_for_steady-state_calculations
|
math
|
JOURNAL OF COMPUTATIONAL PHYSICS 57, 327-360 (1985)
Implicit Total Variation Diminishing
H. C. YEE AND R. F. WARMING
NASA Ames Research Center, Moffett Field, California
Tel Aviv University, Tel Aviv, and New York University, New York
Received August 25, 1983
The application of a new implicit unconditionally stable high-resolution TVD scheme to
calculations is examined. It is a member of a one-parameter family of explicit and
implicit second-order accurate schemes developed by Harten for the computation of weak
solutions of one-dimensional hyperbolic conservation laws. This scheme is guaranteed not to
generate spurious oscillations for a nonlinear scalar equation and a constant coethcient
system. Numerical experiments show that this scheme not only has a fairly rapid convergence
rate, but also generates a highly resolved approximation to the steady-state solution. A
detailed implementation of the implicit scheme for the one- and two-dimensional compressible
inviscid equations of gas dynamics is presented. Some numerical computations of one- and
two-dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this
0 1985 Academic Press, Inc.
Conventional shock capturing schemes for the solution of nonlinear hyperbolic
conservation laws are linear and &-stable (stable in the &-norm) when considered
in the constant coefficient case [l]. There are three major difficulties in using such
schemes to compute discontinuous solutions of a nonlinear system, such as the
compressible Euler equations:
(i) Schemes that are second (or higher) order accurate may produce
oscillations wherever the solution is not smooth.
(ii) Nonlinear instabilities may develop in spite of the &-stability in the con-
stant coefficient case.
(iii) The scheme may select a nonphysical solution.
It is well known that monotone conservative difference schemes always converge
and that their limit is the physical weak solution satisfying an entroy inequality.
1985 by Academic
in any form reserved.
Copyright 0 Press, Inc.
All rights of reproduction
YEE, WARMING, AND HARTEN
Thus monotone schemes are guaranteed not to have difficulties (ii) and (iii).
However, monotone schemes are only first-order accurate. Consequently, they
produce rather crude approximations whenever the solution varies strongly in space
When using a second- (or higher) order accurate scheme, some of these dif-
ficulties can be overcome by adding a hefty amount of numerical dissipation to the
scheme. Unfortunately, this process brings about an irretrievable loss of infor-
mation that exhibits itself in degraded accuracy and smeared discontinuities. Thus,
a typical complaint about conventional schemes which are developed under the
guidelines of linear theory is that they are not robust and/or not accurate enough.
To overcome the difficulties, we consider a new class of schemes that is more
appropriate for the computation of weak solutions (i.e., solutions with shocks and
contact discontinuities) of nonlinear hyperbolic conservation laws. These schemes
are required (a) to be total variation diminishing in the nonlinear scalar case and
the constant coefficient system case [2, 31 and (b) to be consistent with the conser-
vation law and an entropy inequality [4, 61. The first property guarantees that the
scheme does not generate spurious oscillations. We refer to schemes with this
property as total variation diminishing (TVD) schemes (or total variation non-
increasing, TVNI, ). The latter property guarantees that the weak solutions are
physical ones. Schemes in this class are guaranteed to avoid difficulties (ik(iii)
The class of TVD schemes contains monotone schemes, but is significantly larger
as it includes second-order accurate schemes. Existence of second-order accurate
TVD schemes was demonstrated in [2, 3, 7, 81. Unlike monotone schemes, TVD
schemes are not automatically consistent with the entropy inequality. Consequently,
some mechanism may have to be explicitly added to a TVD scheme to enforce the
selection of the physical solution. In [2, 93, Harten and Harten and Hyman
demonstrate a way of modifying a TVD scheme to be consistent with an entropy
In [ 10, 111, we have examined the application of an explicit second-order
accurate TVD scheme to steady-state calculations. Numerical experiments
show that this explicit scheme generates nonoscillatory, highly accurate steady-state
To retain the characteristic of highly resolved steady-state solutions by explicit
second-order accurate TVD schemes without the disadvantage of slow convergence
rate of explicit schemes, we considered in [lo]
(1) First, obtain an approximation to the steady state by using a conventional
implicit scheme, and then use a second-order accurate TVD scheme as a “post-
processor.” (2) Use a first-order accurate implicit scheme in delta-formulation and
replace the explicit operator by an explicit second-order accurate TVD scheme.
We have found (in one dimension) that both these strategies reduce the overall
computational effort needed to obtain the steady-state solution of the explicit
second-order accurate TVD scheme. Alternative (1) is a possible way of speeding
up the convergence process by providing a better initial condition for the explicit
the following two possibilities:
second-order accurate TVD scheme. Alternative (2) can be viewed as a relaxation
procedure to the steady-state solution. Numerical experiments of [lo] show that
the computational effort is not drastically decreased, although the stability limit is
higher than the explicit counterpart.
Recently, Harten has extended the class of explicit TVD schemes to a more
general category which includes a one-parameter family of implicit second-order
accurate schemes. Included in this class are the commonly used time-differencing
schemes such as the backward Euler and the trapezoidal formula.
This paper is a sequel to [lo]. Here, we investigate the application to steady-
state calculations of this newly developed implicit second-order accurate scheme
that is unconditionally TVD. This scheme is guaranteed not to generate spurious
oscillations for one-dimensional nonlinear scalar equations and constant coefficient
systems. Numerical experiments show that this scheme has a fairly rapid con-
vergence rate, in addition to generating a highly resolved approximation to the
steady-state solution. We remark that all of the analysis on the new scheme is for
the initial value problem. The numerical boundary conditions are not included.
In the present paper, we stress applications rather than theory, and we refer the
interested reader to [2, 31 for more theoretical details. In the next section, we will
briefly review the notion of TVD schemes and describe the construction of the
second-order accurate TVD scheme from a first-order accurate one for scalar one-
dimensional hyperbolic conservation laws. The generalization to one-dimensional
hyperbolic systems will be described in Section 3. A description of the algorithm
and numerical results for the one- and two-dimensional compressible inviscid
equations of gas dynamics will be presented in Sections 4 and 5.
2. TVD SCHEMES FOR ONE-DIMENSIONAL SCALAR
HYPERBOLIC CONSERVATION LAWS
Several techniques for the construction of nonlinear, explicit, second-order
accurate, high-resolution, entropy satisfying schemes for hyperbolic conservation
laws have been developed in recent years. See, for example, van Leer , Colella
and Woodhard , and Harten . From the standpoint of numerical analysis,
these schemes are TVD for nonlinear scalar hyperbolic conservation laws and for
constant coefficient hyperbolic systems. TVD schemes are usually rather com-
plicated to use compared to the conventional shock-capturing methods such as
variants of the Lax-Wendroff scheme.
In , Harten introduced the notion of implicit TVD schemes. To keep this
paper somewhat self-contained, we will review the construction of the backward
Euler TVD schemes for the initial value problem. This is the only unconditionally
stable TVD scheme belonging to the one-parameter family of TVD schemes con-
sidered in . Before we proceed with the description of the construction, we will
first give preliminaries on the definition of explicit and implicit TVD schemes and
show a few examples.
YEE, WARMING, AND HARTEN
2.1. Explicit TVD Schemes
Consider the scalar hyperbolic conservation law
at+- ax ’
where a(u) = aflau is the characteristic speed. A general three-point explicit dif-
ference scheme in conservation form can be written
u? + l = ui” - ncjy+ I,* - 3;- l/2)>
where 37+ 1,2 = f( ~7, uj’+ r ), I= At/Ax, with At the time step, and Ax the mesh size.
Here, ~7 is a numerical solution of (2.1) at x = j Ax and t = n At and j’ is a
numerical flux function. We require the numerical flux function 3 to be consistent
with the conservation law in the following sense:
3c5 Uj) =“I@,).
Consider a numerical scheme with numerical flux functions of the form
a ,+ l/2 =
t-G+ I -f,)lA.j+ 1/2u,
A,+ I/~u # 0,
Here Q is a function of uj+ 1,2 and 1. The function Q is sometimes referred to as the
coefficient of numerical viscosity. Figure 2.1 shows some examples for the possible
choice of Q. Three familiar schemes with the numerical fluxes of the form (2.4) are
-. 5 -6
s .5 1.0
FIG. 2.1. Sample of the Q(z) functions.
IMPLICIT TVD SCHEMES
(a) A form of the Lax-Wendroff (L-W) scheme with
where Q(Qj+ 112) = l(aj+ 1,d2.
(b) Lax-Friedrichs (L-F) scheme with
where Q(aj+ 1,2) = l/k
(c) A generalization of the Courant-Isaacson-Rees (GCIR) scheme with
CJ’j+f,+l- lUj+1/21 Aj+1/2ul,
where Q(Uj+ 1,~) = lUj+ 4.
We define the total variation of a mesh function u to be
TV(u)= f luj+l -ujI = f
We say that the numerical scheme (2.2) is TVD if
It can be shown that a sufficient condition for (2.2) together with (2.4) to be a
TVD scheme is ,
AC,< 1,2 = '1 2 Eeuj+
l/2 + Q(q+ 1,211 L 0,
‘CJ”+ l/2 =i [uj+ l/2 + Q(uj+ 1,211 > 0,
‘Cc; l/2 + CA l/2) = nQ(aj+ 112) G 1.
Applying condition (2.11) and/or (2.10) to the above three examples, it can be
easily shown that the L-W scheme is not a TVD scheme, and the latter two
schemes are TVD schemes. Note that there is a further distinction between the L-F
scheme and GCIR scheme: the L-F scheme is consistent with an entropy inequality
whereas the GCIR is not .
It should be emphasized that condition (2.11) is only a sufficient condition; i.e.,
schemes that fail this test might be still TVD. The L-W scheme, besides failing con-
dition (2.1 l), does not satisfy (2.10).
YEE, WARMING, AND HARTEN
2.2. Implicit TVD Schemes
Now we consider a one-parameter family of three-point conservative schemes of
24” + l + lJj(fy;1’,2
-f;‘lg = q - 41 - r1)(fy+ I,2 -fp l/2)?
where q is a parameter, A= At/Ax, f;+ 1,2 = f( u,“, u,“+ r ), f;:r& = f( U; + I, u,“:,’ ), and
f(u,, uj+,) is th e numerical flux (2.4). This one-parameter family of schemes con-
tains implicit as well as explicit schemes. When q = 0, (2.12) reduces to (2.2), the
explicit method. When q # 0, (2.12) is an implicit scheme. For example: if u = t, the
time differencing is the trapezoidal formula, and if q = 1, the time differencing is the
backward Euler method. To simplify the notation, we will rewrite (2.12) as
where L and R are the finite-difference operators
A suflicient condition for (2.12) to be a TVD scheme is that
TV( R . u) 6 TV(u),
TV( L . v) B TV(o).
A sufficient condition for (2.15) is the CFL-like restriction
where aj + 1,2 is defined in (2.5). For a detailed proof of (2.15) and (2.16), see .
Observe that the backward Euler implicit scheme, q = 1 in (2.12), is unconditionally
TVD, while the trapezoidal formula, q = 4, is TVD under the CFL-like restriction of
2. The forward Euler explicit scheme, r~ = 0 or (2.2), is TVD under the CFL restric-
tion of 1. We remark that three-point conservative TVD schemes of the form (2.12)
are generally first-order accurate in space. When q = 1, the scheme is second-order
accurate in time.
2.3. First-Order Accurate Backward Euler Implicit TVD Scheme
In this paper, we are only interested in efficient high-resolution time-dependent
methods for steady-state calculations. The backward Euler implicit TVD scheme is
the best choice in this one-parameter family of TVD schemes. Therefore, we will
only review the proof that the backward Euler scheme is unconditionally TVD. In
Section 2.4, we will describe the technique of converting the first-order accurate
unconditionally TVD scheme (2.12) with q = 1 into a second-order accurate one.
IMF’LICIT TVD SCHEMES
The backward Euler three-point scheme in conservative form can be written as
ui”’ l+ n(f;;;,, -f;$,, = 24;.
For the purpose of this paper, the function Q(z) in (2.4) is chosen to be
which is a nonvanishing, continuously differentiable approximation to 1~1. This is
one way of modifying Q in (2.8) so that scheme (2.2) together with (2.8) is an
entropy satisfying TVD scheme . For convenience, we introduce the notation
C’(z) = $[Q(z) f z]
and note that
for all z.
Using (2.5) and (2.18a), we can rewrite the numerical fluxes f;.+ 1,2 in (2.4) as
j;.- 112 =fi- C+ (aj- 112) A,- 112~.
It follows from (2.19) that (2.17) can be written in the form
u?+’ - J.C-(a~~~,,) A,, I,2~n+1 + K’(uJ’?~,,)
Aj- 1,2~“+1 = u;.
Now, if 6 = 0 in (2.17b), then C’(z) = (lzl f z)/2, and (2.20) is a first-order
accurate, upstream differencing, backward Euler implicit scheme. Equation (2.17)
differs from the upstream spatial differencing (with 6 =0) by the addition of a
numerical viscosity term with a coefftcient 6 > 0.
We show now that C’(z)30 implies that the scheme (2.17) is unconditionally
TVD (i.e., condition (2.10) is satisfied, independent of the value of A = At/Ax in
To see that, we subtract (2.20) at j from (2.20) at j + 1 and get after rearranging
=Aj+ l/2 lln + lCj”- l/ZAj-
l/Z” n+l +K,~3/2Aj+3,2~n+?
Here Cj$ 1,2 = C * (a;:$, ). Next we take the absolute value of (2.21a) and use
(2.18b) and the triangle inequality to obtain
G lAj+ I/ZU~I + ‘CjT 112 IAj- 112~
n+ll +~C~3/21Aj+3/2Un+‘I. (2.21b)
YEE, WARMING, AND HARTEN
Rearranging terms, we get
/A I+ 112 u”+‘I d Pi+,,, ‘“l+‘CC,~~/21’j+~/2~n+‘I-C,~~/~IAj+~,~~nf’l]
IA,+ 1/2u ‘+‘I 6 IAj+l/2U”l +%(Ej+l-Zj),
Summing (2.21d) fromj=
backward Euler implicit scheme is unconditionally TVD.
-co toj= +a~, we obtain (2.10); thus proving that our
2.4. Conversion to Second-Order Accurate Scheme
Next, we want to briefly review the design principle behind the construction of
second-order accurate TVD schemes. This is a rather general technique to convert a
three-point first-order accurate (in space) TVD scheme (2.12) into a five-point
second-order accurate (in both time and space, or just space) TVD scheme of the
same generic form. The design of high-resolution TVD schemes rests on the fact
that the exact solution to (2.1) is TVD due to the phenomenon of propagation
along characteristics, and is independent of the particular form of the flux f(u) in
(2.1). Similarly, the first-order accurate scheme is TVD subject only to the CFL-like
restriction (2.16) independent of the particular form of the flux. Thus to achieve
second-order accuracy while retaining the TVD property, we use the original TVD
scheme with an appropriately modified flux (f + g), i.e.,
Y,+ l/2 =
k,+ I - g,)lAj+ (/2u,
Aj+ 1/2u + 0,
The requirements on g are: (1) The function g should have a bounded y in
(2.22~) so that (2.22a) is TVD with respect to the modified flux (f+ g). (2) The
modified scheme should be second-order accurate (except at points of extrema). In
[2, 33, Harten devised a recipe for g that satisfies the above two requirements. We
will use this particular form of g for the discussion here. It can be written
IMPLICIT TVD SCHEMES
with oj+ 1,2 = o(aj+ i,J and we choose
c(z) = Q(z) > 0
for steady-state applications. It has the property that the steady-state solution is
independent of At. Or, we choose
CT(z) = i@(z) + AZ*) > 0 (2.22f)
for time-accurate calculations. Note that if a(z) = (Q(z) + Lz*)/2, then (2.22) is
second-order accurate in both time and space . For transient calculations,
second-order accurate in time is preferred.
The form of g in (2.22d) satisfies the relations
gj=gt"j-l, uj3 uj+lh
g(u, 6 u) = 0,
IYj+ l/21 = lgj+ l- gjlll”j+ 1 -#jl G d”j+ I/2),
Relation (2.23a) shows that the modified numerical flux (2.22b) is consistent with
f(u). Relation (2.23b) shows that the mean-value characteristic speed rj+ ,,z (2.22~)
induced by the flux g is uniformly bounded. Relation (2.23~) implies that (2.22b) is
second-order accurate in space. The form of g appears more complicated than it
really is. The various test functions in (2.22d) can be viewed as an automatic way of
controlling the numerical flux function so that (2.22) is TVD.
The scheme (2.22) can be rewritten in the form (2.20) as
where C’(a + y)J’:;,* - C’(aj”:&
instead of a. The modified scheme (2.22) is of the same generic form as the original
first-order scheme (2.17). Therefore (2.22) is an upstream differencing scheme with
respect to the characteristic field (a + y). Moreover, we have the relation
i.e., C’ is now a function of (a + y)
sign(a + y) = sign(u)
for IzI 2 6, with z = a or (a+ y) in (2.17b). Hence (2.24) is also an upstream dif-
ferencing scheme with respect to the original characteristic field a(u).
Because of (2.23a), the numerical flux (2.22b) of the second-order accurate TVD
scheme depends on four points, i.e., yj+ 1,2 = T(Tcu~-
is formally a live-point scheme. We note, however, that
, , uj, uj+ 1, uj+ *), and thus (2.22)
lb, 4 4 WI = f(u)
for all v and w. Hence, for practical purposes, such as numerical boundary con-
ditions, (2.22) can be regarded as essentially a three-point scheme.
YEE, WARMING, AND HARTEN
We turn now to examine the behavior of TVD schemes around points of
extrema, by considering their application to data, where
u/- 1 <"j=u,+I
In this case gj = g, + L = 0 in (2.22d), and thus the numerical flux (2.22b) becomes
identical to that of the original first-order accurate scheme (2.4); consequently, the
truncation error of (2.22) deteriorates to O((dx)‘) at j and j+ 1. This behavior is
common to all TVD schemes. Thus, for a second-order accurate scheme to be
TVD, it has to have a mechanism that switches itself into a first-order accurate
TVD scheme at points of extrema. Because of the above property, second-order
accurate TVD schemes are genuinely nonlinear (i.e., they are nonlinear even in the
constant coefficient case).
Extension of the one-parameter family of three-point TVD schemes (2.12) to
second-order TVD schemes follows the same procedure except (2.22f) becomes
a(z) = @(z) + /I(q - ;, z2. (2.28)
2.5. Enhancement of Resolution by Artificial Compression
The technique to convert the first-order accurate TVD scheme (2.12) into a
second-order accurate one is closely related to the concept of artificial compression
Truncation error analysis shows that the first-order accurate scheme (2.12) is a
second-order accurate approximation to solutions of the modified equation
where o(a) is defined in (2.22e) or (2.28). We note that the CFL-like restriction
(2.16) implies that o(a) 2 0; thus, the right-hand side of (2.29) is a viscosity term.
Hence the first-order accurate TVD scheme (2.12) is a better approximation to the
viscous equation (2.29) than it is to the original conservation law.
We obtain a second-order approximation to au/at + af/ax = 0 by applying the
first-order scheme (2.12) to the modified flux (f+ g), where g is an approximation
to the right-hand side of (2.29); i.e.,
g = dxa(a) g + O((fl~)~). (2.30)
The application of the first-order scheme to (f + g) has the effect of canceling the
error due to the numerical viscosity to O((~X)~); thus g is an “anti-diffusion” flux.
If we apply the first-order TVD scheme to (f+ (1 + 0) g), 0 > 0, rather than to
(f+ g), we find that the resolution of discontinuities improves with increasing 0.
This observation allows us to use the notion of artificial compression to enhance
the resolution of discontinuities computed by the second-order accurate TVD
IMPLICIT TVD SCHEMES
scheme (2.22). This is done by increasing the size of g in (2.22d) by adding a term
that is O((Ax)*) in regions of smoothness, e.g.,
gj=(l +COOj) gj,
Using gj (2.31) instead of g, makes the numerical characteristic speed more con-
vergent, and therefore improves the resolution of computed shocks. Since
13 = O(dx), this change does not adversely affect the order of accuracy of the
scheme. See for more details. From numerical experiments, o = 2 seems to be a
We remark that applying too much artificial compression in a region of expan-
sion (i.e., divergence of the characteristic field a = afl&) may result in violation of
the entropy condition. Hence when applying artificial compression, we have to
either turn it off in regions of expansion or limit the size of o in (2.31a), say, by the
value that makes (2.22) with (2.31a) third-order
accurate (in regions of
2.6. Linearized Version of the implicit TVD Scheme
To solve for zJ+’ for the first- or second-order implicit scheme, we have to solve
a set of nonlinear algebraic equations. To overcome this obstacle, we will present a
way of linearizing the implicit TVD scheme. The method will destroy the conser-
vative property but preserve its unconditionally TVD property. We will refer to this
method as the linearized nonconservative implicit (LNI) form. The LNI form is
mainly useful for steady-state calculations, since the scheme is only conservative
after the solution reaches steady state. On the other hand, we have the advantage of
stability and TVD of an unlimited CFL number. Note that the procedure of obtain-
ing the LNI form is applicable to both the first- and second-order accurate implicit
TVD schemes. We will discuss the LNI for the second-order accurate one. To get
the LNI for the first-order accurate TVD scheme, we simply set g= y =0 in the
The LNI form is obtained simply by replacing the coefficients (C+ )n+ ’ in (2.24)
by (C’ )“, i.e.,
Since C’ > 0, it follows from (2.21) that (2.32) is unconditionally TVD.
In delta form notation, (2.32) can be rewritten as
= -x7;+ l/2 -JI:-
YEE, WARMING, AND HARTEN
where the left-hand side equals
with d-=u?+‘--uU” and A.
I+ li2d=dit I -d,. Rearranging terms, we get
E, = -K+(u+y)i”p1,2,
E, = -AC (a + y);, ,,2.
Here, 3;+ 1/2 is (2.22b))(2.22e) calculated at the time level n. It follows from (2.22b)
and (2.33a) that the steady-state solution of (2.33) is
(i) consistent with the conservation form, and
(ii) a spatially second-order accurate approximation to the steady state of
the partial differential equation
(iii) Independent of the time-step At used in the iterations.
Moreover, the iteration matrix associated with (2.34) is a diagonally dominant,
tridiagonal matrix. Note that this linearized construction is not trivial, since the
second-order method is a live-point scheme. Normally the matrix associated with
(2.34) could have been a pentadiagonal matrix. As mentioned before, (2.32) or
(2.34) is not in conservation form and therefore should not be used to approximate
time-dependent solutions (transient solutions). However, it is a suitable scheme for
the calculation of steady-state solutions.
We can also obtain another TVD linearized form by setting y = 0 in (2.34), i.e.,
E, = -AC + (a;- ,,*),
Js = --AC (a,“, 1,2).
Scheme (2.35) is spatially first-order accurate for the implicit operator and spatially
second-order accurate for the explicit operator. It can be shown that (2.35) is still
3. GENERALIZATION TO ONE-DIMENSIONAL
HYPERBOLIC SYSTEM OF CONSERVATION LAWS
In the present state of development, the concept of TVD schemes, like monotone
schemes, is only defined for nonlinear scalar conservation laws or constant coef-
ficient hyperbolic systems. The main difficulty stems from the fact that, unlike the
scalar case, the total variation in x of the solution to the system of nonlinear con-
servation laws is not necessarily a monotonic decreasing function of time. The total
variation of the solution may actually increase at moments of interaction between
waves. Not knowing a diminishing functional that bounds the total variation in x in
the system case, makes it impossible to fully extend the theory of the scalar case to
the system case. What we can do at the moment is to extend the new scalar TVD
scheme to system cases so that the resulting scheme is TVD for the “locally frozen”
constant coefficient system. To accomplish this, we define at each point a “local”
system of characteristic fields. This extension technique is a somewhat generalized
version of the procedure suggested by Roe .
Now, we briefly describe the above approach of extending the second-order
accurate TVD schemes to hyperbolic systems of conservation laws
Here U and F(U) are column vectors of m components and A(U) is the Jacobian
matrix. The assumption that (3.1) is hyperbolic implies that A(U) has real eigen-
values a’(U) and a complete set of right eigenvectors R’(U), I= l,..., m. Hence the
R(U) = (R’(U),..., R”(U))
is invertible. The rows L’(U),..., L”(U) of R(U) ~ ’ constitute an orthonormal set of
left eigenvectors of ,A( U); thus
R- 'AR = diag(a’).
Here diag(a’) denotes a diagonal matrix with diagonal elements a’.
We define characteristic variables W with respect to the state U by
In the constant coefficient case, (3.1) decouples into m scalar equations for the
a’ = constant.
This offers a natural way of extending a scalar scheme to a constant coefficient
YEE, WARMING, AND HARTEN
system by applying it “scalarly” to each of the m scalar characteristic equations
denote some symmetric average of U, and U,, , (to be discussed
Let a:* ‘12, qc l/2, q!, l/2 denote the respective quantities of a’, R’, L’ related to
A( U,, ,j2). Let w’ be the vector elements of W, and let c(i+ ,,2 = M$+, - wj be the
component of A,, 1,2 U = U,, , - U, in the Ith characteristic direction; i.e.,
With the above notation, we can apply scheme (2.22) scalarly to each of the
locally defined (frozen coe$j$ccient ) characteristic variables of (3. I ) as
uy + ’ + 1*@y;“=,;, - Fy,j,) = u,“, (3.7a)
Fj+ 112 = ’ ~(J’j+f’j+~)+i f Cg~+g~+,-Q~~~+,i2+~~+,,2)~~+,,21R~+,,2,
gf=S.maxCO, min(~~+,,21~~+,,21, S~O;~,,,CX~,,,)],
S = skn(uj+
- s:Yu; + I/2>
a:+ l/2 # 09
a;, ,,2 = 0.
Here c$+ ,,2 = c(af+ ,,2), where a(z) is (2.22e) and a:+ ,,2 is (3.6). The corresponding
ii in (2.3 1) for the added artificial compression term is
I@+ I,21 + I+ I,21
The w’ can be different from one characteristic field to another.
Similarly, we generalize the LNI form (2.33) to the system case by
[I-‘(,< ,/>A,+ l/2 + iJ,T 1/2Aj- l/21( U”+ ’ - Un) = -A[?+ l,2 - q.. ,,2]
IMPLICIT TVD SCHEMES Download full-text
l/2 = R&
Dj= ,,“‘I - Uj’,
l/2 diag(C'(a'+ Y'):, ,,2)(R ~ 'I,"+ ,,2,
where the left-hand side of (3.8a) is equal to
Dj- ‘Jjy 1/2Aj+ 1120 + ‘Jj? 1/2Aj- I/zD,
In the constant coefficient case where A(U) = constant, both (3.7) and (3.8) are
TVD by construction. However, they are not identical; Eq. (3.7) is fully nonlinear
while (3.8) is a version with a linearized left-hand side.
Note that the total variation for the vector mesh function U of the constant coef-
ficient case is defined as
WV= f f
j= -cc ,=I
A particular form of averaging in (3.5) is essential if we require the scheme (3.7)
for m = 1 to be identical to the scalar scheme of Section 2, since we have to choose
(3.5) so that u,!+ 1,2 is the same as the mean value in Eq. (2.5). This can be accom-
plished by taking the eigenvalues a:+ 1,2 and the eigenvectors Rj+ 1,2 in (3.2) to be
those of A( U,, U,, I ), where A( Uj, U,, , ) is the mean value Jacobian. This matrix
(i) F(U)--F(;O=A(U, V)(U- V),
(ii) A(U, U)=A(U),
(iii) A( U, V) has real eigenvalues and a complete set of eigenvectors.
Roe [ 151 constructs a mean value Jacobian for the Euler equations of gas
dynamics of the form A( U, V) = A( Y( U, I’)), where !P( U, V) is some particular
average. We will discuss Roe’s mean value Jacobian in the next two sections.
OF GAS DYNAMICS
In this section we describe how to apply the implicit TVD scheme (3.8) to the
compressible inviscid equations of gas dynamics (Euler equations). Included in this
|
s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737940794.79/warc/CC-MAIN-20151001221900-00012-ip-10-137-6-227.ec2.internal.warc.gz
|
CC-MAIN-2015-40
| 28,339 | 449 |
https://essayzoo.org/statistics-project/apa/mathematics-and-economics/module-4-discussions.php
|
math
|
Sampling and Regression Analysis (Statistics Project Sample)
In this week's readings, simple random sampling, systematic, stratified, and cluster sampling are discussed. Define each of the sampling methods. Then, post two examples of sampling situations
BUT DO NOT IDENTIFY THE TYPE OF SAMPLING. Identify and discuss the types of sampling represented in your peers’ examples.
Regression is a commonly used technique in business. What is the purpose of regression? Provide two examples of situations in business where regression may be useful. Review your peers’ posts and identify the independent and dependent variables in their examples.
Module 4 Discussions: sampling and regression analysis
Simple random sampling- This is a design method where samples are chosen randomly, and each has an equal chance of being selected (Black, 2012).
Systematic sampling- This is a probability sampling method, where samples are selected from the population, with the first element selected randomly, and the next data items chosen periodically at a fixed interval (Black, 2012).
Stratified sampling- In this sampling method, the population is divided into groups (strata), and the groups share similar characteristics or attributes. Samples are then selected randomly from a stratum, with the selections forming part of the random sample (Black, 2012).
Cluster sampling-In this sampling method the population is also divided into cluster groups, and the clusters are selected randomly. Data analysis is based on the sampled clusters, which have equal sample sizes (Black, 2012).
For instance, in a study survey to understand attitudes towards workplace harassment, where companies are first chosen in the first stage. The next stage is to sample employees working within the companies.
Another example is whereby a researcher wants to know companies that use a specific management information system. If there are 1,000 organizations arranged in an alphabetical order and the sample size is 100, then the first company is chosen randomly and each 10th item is then chosen.
Regression analysis is necessary to determine the causal relationship among dependent variable and the independent variable (s). One of the purposes of regression is to show how the outcome changes (dependent variable), when one or more of the predictors vary. Additionally, the cause analysis determines the strength of the predictors of the outcome. At other times, regression analysis helps to determine the outcome changes over time in the time series analysis.
One of the most common applications of regression analysis is demand analysis, which focuses the purchase for products and units (Moon, 2013). For instance, a movie theater might use past information on ticket sales and price to determine the demand for tickets. In this case, the ticket sales are the outcome with the ticket sale price being the predictor.
Regression analysis enhances the decision-making process in a business since decision maker...
- Macroeconomic Factors - Evidence from USADescription: Macroeconomic Factors and Stock Returns Statistics Project: Evidence from USA...8 pages/≈2200 words | 4 Sources | APA | Mathematics & Economics | Statistics Project |
- Statistics Project on Broyles Textbook Practice ExerciseDescription: Estimate the time required to provide a given laboratory procedure, suppose we measured the amount of time required when service was provided on 60 occasions...3 pages/≈825 words | No Sources | APA | Mathematics & Economics | Statistics Project |
- Course in Public Economics-John Leach Questions Chapter 3Description: When there are only two people in an economy, the markets clear when the sum of their excess demands is equal to zero...1 page/≈275 words | No Sources | APA | Mathematics & Economics | Statistics Project |
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822098.86/warc/CC-MAIN-20191022132135-20191022155635-00330.warc.gz
|
CC-MAIN-2019-43
| 3,810 | 17 |
https://delhidatarecovery.com/getanswer-349
|
math
|
Second order differential equation solver with initial conditions
This Second order differential equation solver with initial conditions helps to fast and easily solve any math problems. Our website can solve math problems for you.
The Best Second order differential equation solver with initial conditions
We'll provide some tips to help you select the best Second order differential equation solver with initial conditions for your needs. A radical is a square root or any other root. The number underneath the radical sign is called the radicand. In order to solve a radical, you must find the number that when multiplied by itself produces the radicand. This is called the principal square root and it is always positive. For example, the square root of 16 is 4 because 4 times 4 equals 16. The symbol for square root is . To find other roots, you use division. For example, the third root of 64 is 4 because 4 times 4 times 4 equals 64. The symbol for the third root is . Sometimes, you will see radicals that cannot be simplified further. These are called irrational numbers and they cannot be expressed as a whole number or a fraction. An example of an irrational number is . Although radicals can seem daunting at first, with a little practice, they can be easily solved!
Calc is an important part of a student's academic life. It can be used to help students understand concepts and get a better grasp on math skills. If a student is struggling with Calc, it can be helpful to take some time to review the concepts before starting a new math assignment. This can help students better understand the topic and get a better grasp on what they're learning. Taking time to practice each day can also help build confidence in students, which can be beneficial in the long run. Calc can also be used to help students prepare for tests, particularly those that are more difficult than others. If you're looking for ways to help your child improve their Calc skills, consider these ideas: Calc can be an intimidating subject, especially for younger students who may not have completed Algebra I yet or may not have worked in a test environment before. You can make it easier by using calculators or online resources like Khan Academy. You can also work with your child every day on their homework assignments, such as timed practice tests and extra practice problems that will help them build their confidence when they need it most.
This may seem like a lot of work, but the FOIL method can be a very helpful tool for solving trinomials. In fact, many algebra textbooks recommend using the FOIL method when solving trinomials. So next time you're stuck on a trinomial, give the FOIL method a try. You might be surprised at how helpful it can be.
One way is to solve each equation separately. For example, if you have an equation of the form x + 2 = 5, then you can break it up into two separate equations: x = 2 and y = 5. Solving the two set of equations separately gives you the two solutions: x = 1 and y = 6. This type of method is called a “separation method” because you separate out the two sets of equations (one equation per set). Another way to solve linear equations is by substitution. For example, if you have an equation of the form y = 9 - 4x + 6, then you can substitute different values for y in order to find out what happens when x changes. For example, if you plug in y = 8 - 3x + 3 into this equation, then the result is y= 8 - 3x + 7. Substitution is also known as “composite addition” or “additive elimination” because it involves adding or subtracting to eliminate one variable from another (hence eliminating one solution from another)! Another option
There are many equation solvers in the market, but not all of them will give you the answer you’re looking for. So what distinguishes the best from the rest? Here are a few things to look out for: accuracy, ease of use and compatibility. A good equation solver should be able to calculate results quickly and accurately, so it’s important to make sure that it’s compatible with your device. It should also be easy to understand, so if you encounter any hiccups along the way, you can get to where you need to go without getting frustrated. The best three equation solver is one that can solve equations in real-time while also being easy to use and compatible with most devices.
Instant help with all types of math
A better math teacher than the one at school. Doesn't just give you answers, but it provides great in-depth explanations that are extremely helpful in the learning process. Excellent app. Very useful, does what it promises efficiently. 5 Stars Plus for the app.
It easy and the beat app for explaining math, only downfall is the monthly and annual pay for better explaining, which make sense but I believe it worth it This app is to mush help full to me. I have much difficult problem but I easily solve all the math problems.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500080.82/warc/CC-MAIN-20230204012622-20230204042622-00542.warc.gz
|
CC-MAIN-2023-06
| 4,938 | 11 |
https://www.assignmentexpert.com/homework-answers/mathematics/statistics-and-probability/question-12038
|
math
|
Answer to Question #12038 in Statistics and Probability for natashakayana
P(get s)= n(s)/16 = 5/16 .
& Here 16 stands for the total number of cards.
Need a fast expert's response?Submit order
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249556231.85/warc/CC-MAIN-20190223223440-20190224005440-00245.warc.gz
|
CC-MAIN-2019-09
| 291 | 6 |
https://tomrocksmaths.com/watch/i-love-mathematics-playlist/
|
math
|
A series of videos in partnership with ‘I Love Mathematics’ answering the questions sent in and voted for by YOU! Send me any questions that you have using the contact form, or on message me on Facebook, Twitter and Instagram @tomrocksmaths.
Q1: What is the probability that I have the same PIN as someone else?
Q2: How long would it take for an object to sink to the bottom of the ocean?
Q3: What is the gravitational field of a hollow Earth?
Q4: What is the best way to win at the board game Monopoly?
Q5: What are the most basic Mathematical Axioms?
Q6: How does Modular Arithmetic work?
Q7: What is the Gamma Function?
Q8: How many ping pong balls would it take to lift the Titanic from the ocean floor?
Q9: What is the graph of x to the power x?
Q10: How can you show geometrically that 3 < π < 4?
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224643784.62/warc/CC-MAIN-20230528114832-20230528144832-00716.warc.gz
|
CC-MAIN-2023-23
| 807 | 11 |
https://valuewalkpremium.com/why-most-published-results-on-unit-root-and-cointegration-are-false/
|
math
|
Why Most Published Results On Unit Root And Cointegration Are FalseVW Staff
Why Most Published Results On Unit Root And Cointegration Are False
October 3, 2015
The method of cointegration analysis for modeling nonstationary economic time series variables has become a dominant paradigm in empirical economic research. Critics argue that a cointegration analysis produces results that are, at best, useless and, at worst, dangerous. In this research, we explain why and how the use of a cointegration analysis in economic research will likely lead to findings and subsequent recommendations for public policy that will be unsound, misleading and potentially harmful. We recommend that, except for pedagogical review of policy failure of a historical magnitude, this method not be used in any analysis that affects public policy.
Why Most Published Results On Unit Root And Cointegration Are False – Introduction
Cointegration analysis for analyzing and modeling non-stationary economic time series variables, proposed by Engle and Granger (1987), has become a dominant paradigm in empirical economic research1 (Hendry 2004; Royal Swedish Academy of Science 2003). Critics, however, argue that a cointegration analysis produces results that are, at best, useless and, at worst, dangerous (Moosa 2011, pp. 114). In this research, we will explain why and how the use of a cointegration analysis in economic research will lead to spurious findings and why any recommendations for public policy will likely be unsound, misleading and potentially harmful.
In economics, when a historical perspective is overlooked in a descriptive research design, misleading conclusions may often follow.2 Here, by historical perspective, we refer to the understanding of a subject matter in light of its previous stages of intellectual development and successive advancement. We think, therefore, it is imperative to put our arguments against unit roots and cointegration analysis in a historical perspective. The recognition of a spurious regression problem in the late 1970s contributed decisively to the development of unit roots and cointegration (Granger and Newbold 1974; Hendry 1980, 1986; Granger 1981, 1986). A spurious regression problem arises when a regression analysis indicates a relationship between two or more unrelated time series variables because each variable has either a trend, or is nonstationary, or both. While working with economic time series data, researchers, attempting to account for spurious regression problem, began testing for nonstationarity before estimating regressions. If, on the basis of an appropriate unit root test, data were found to be nonstationary, researchers would routinely purge the nonstationarity by differencing and then estimating regression equations using only differenced data as solution to the spurious regression problem. The practice of purging the nonstationarity by differencing would also result in the loss of valuable information from economic theory about the long-run equilibrium properties of the data (Kennedy 2003). It was in this context that Granger proposed that if two nonstationary variables were I(1) process, the bivariate dynamic relation between the two nonstationary variables would be misspecified when both of the nonstationary variables were differenced. This class of models has since become a dominant paradigm in empirical economic research and is known in the literature as cointegrated process (Hamilton 1994; page 562).
Test of Order of Integration and Data
A time series is said to be strictly stationary if its marginal and all joint distribution are independent of time. For practical purpose, however, it is the weak stationarity or covariance-stationarity that is more useful. A time series is said to be weakly stationary or covariance-stationary if the first two moments — mean and autocovariances — of a series do not depend on time. A stationary time series that does not need differencing is said to be integrated of order zero and is denoted I(0). A nonstationary time series that becomes stationary after first differencing is said to be integrated of order one and is denoted I(1). In general, a time series that needs differencing d times to become I(0) is said to be integrated of order d and is denoted I(d) (Granger 1986, page 214). Since the number d equals the number of unit roots in the characteristic equation for the time series (Said and Dickey 1984, page 599) unit root tests are often used to determine the order of integration of a series. Thus, we describe below the unit root tests that we will use in our analysis.
See full PDF below.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103035636.10/warc/CC-MAIN-20220625125944-20220625155944-00612.warc.gz
|
CC-MAIN-2022-27
| 4,641 | 10 |
https://physics.stackexchange.com/questions/100166/molecules-and-electrons-energy-types
|
math
|
What are the types of energy that an atom or a molecule could have?
For example they have kinetic energy, could they also have other types?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to join this community
In classical systems the Lagrangian is the Kenetic energy minus the potential energy, whereas the Hamiltonian is the the Kenetic energy plus the potential energy.
Most systems can be fully described by the ammount of energy they have from being in a given position / state (potential energy) and the ammount of energy it has by travelling at a given speed (its kenetic energy).
The potential energy is often expanded for gasses and chemical reactions into different types of potentials such as each of the chemical potential.
There also exists internal energy $E=mc^2$ which may be overlooked as usually it does not contribute to the dynamics of the system since it usually does not change, and dissappears when taking the derivative.
In the Standard model there exists an equation describing everything that we know about particle physics. Here is an image of the Lagrangian, each term being added together is an energy term, the energy that a particle can have from each of the different fields.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735881.90/warc/CC-MAIN-20200804161521-20200804191521-00019.warc.gz
|
CC-MAIN-2020-34
| 1,314 | 8 |
https://www.ndtv.com/tools/calculator/percentage-calculator-online
|
math
|
A percentage calculator helps measure any change in percentage terms and can be used to calculate grades, the difference between two values, increase or decrease in profits, etc.
How To Use An Online Percentage Calculator
The calculator offers three scenarios wherein a user fills in the blanks to arrive at the desire output. The values of X and Y can be entered to complete the calculation, see below:
What is X% of Y?
X is what% of Y?
X is Y% of what?
Let us assume the value of X as 10 and Y as 20, this will give us the following:
What is 10% of 20?
10 is what% of 20?
10 is 20% of what?
The calculator will compute the value of 'what' in all three scenarios.
How Do You Calculate Percentages Online?
An online percentage calculator can aid in multiple scenarios. It can help users bypass tiresome calculations, whether one wants to calculate the percentage difference between two values or map the percentage increase and decrease.
Percentage change is the difference between two numeric values displayed in a measure against 100. The ratio's numerical value is multiplied by 100 to obtain the per cent value.
Example: How to find the percentage of 50 items in a sample of 1,250?
• Calculate the ratio: 50/1,250 = 0.04,
• Multiply by 100 (0.04*100), which results in 4 per cent.
The other method is by multiplying:
Using the same example:
• Multiply 50 by 100 (50*100) to get 5,000
• Divide by 1,250 (5,000*1,250), which also results in 4 per cent.
What Is The Percentage Of A Number?
A value or ratio that may be stated as a fraction of 100 is a percentage in mathematics. If we need to determine a percentage of a number, we should divide it by 100 and multiply the result. The proportion, therefore, refers to a component per hundred. 'Per 100' is what the word 'per cent' means. The % symbol represents per cent.
An online calculator automatically transforms the percentage entered into a decimal to compute the answer. When calculating a percentage, however, the result will be the total percentage rather than its decimal representation.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510319.87/warc/CC-MAIN-20230927171156-20230927201156-00579.warc.gz
|
CC-MAIN-2023-40
| 2,057 | 24 |
https://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art5
|
math
|
Main Article Content
The present paper is concerned with the characterization of the elements of best approximation in a subspace \(Y\) of a space with asymmetric norm, in terms of some linear functionals vanishing on \(Y\). The approach is based on some extension results, proved in Section 3, for bounded linear functionals on such spaces. Also, the well known formula for the distance to a hyperplane in a normed space is extended to the nonsymmetric case.
How to Cite
spaces with asymmetric norm; best approximation; Hahn-Banach theorem; characterization of best approximation
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934807056.67/warc/CC-MAIN-20171124012912-20171124032912-00427.warc.gz
|
CC-MAIN-2017-47
| 580 | 4 |
https://upgradinglife.com/story-behind-jtxxvh/venn-diagrams-gcse-9f34f8
|
math
|
venn diagrams gcse
Intersection, Union, and Complement. What is a set (of a Venn diagram)? These Venn Diagram activites are great 'low floor high ceiling' tasks to help promote deep mathematical discussions and thinking. Welcome; Videos and Worksheets; Primary; 5-a-day. This is a great way to start on summarising what work is required from us to complete the Venn diagrams. Venn Diagrams 9-1 GCSE. Corbettmaths Videos, worksheets, 5-a-day and much more. The lesson pack fits ideally with GCSE Higher Level pupils and should help to alleviate the burden of planning for teachers. Author: Created by ukmaths. In a group of 36 students, 1 student studies band, choir and theatre. • 8 have a dog, but not a cat. Exam Paper Practice & Help (a) Use this information to fill in the Venn Diagram below. Types of Set. Venn Diagrams Video Videos; complement; intersection; union; venn; venn diagrams; Post navigation. Venn-Diagrams. Maths Resources for Primary and Secondary Maths Worksheets and Quizzes Blog|; News|; What's New|; About … In set A, we have already input numbers 2 and 3 on the Venn diagram, so we now need to input numbers 5, \, 7, \, 11, \, 13, \, 17, \, 19. Preview and details Files included (2) pptx, 259 KB. • Diagrams are NOT accurately drawn, unless otherwise indicated. This video solves two problems using Venn Diagrams. See more ideas about venn diagram, venn diagram template, graphic organizers. GCSE (1 – 9) Venn Diagrams Name: _____ Instructions • Use black ink or ball-point pen. May 3, 2014 - Elementary set theory for the visual learner... welcome to the king of maths This lesson pack is designed to support the teaching of Venn diagrams at GCSE level in a mastery curriculum. Venn diagrams can be used to organise data into categories and are used a lot in … Previous Dividing by Powers of 10 Textbook Answers. Complete the Venn diagram. GCSE Maths / Probability / Probability Venn Diagrams. Venn diagrams for GCSE Maths. 50 students were asked in a survey whether they use texts or social media. Search for: Previous Next. Leave 1 At a business dinner, the employees may have roast turkey or beef curry as their meal. blank The Venn diagram shows information about the items that were picked by the employees. Preview. Menu Skip to content. Here is a Venn diagram. Links to the relevant section of the GCSE Maths Specification, together with information and resources from each of … 15 take French. Venn diagrams - WJEC Venn diagrams are a useful tool in the world of statistics. Revision notes on the topic Probability - Venn Diagrams for the Edexcel GCSE Maths exam. • 21 have a dog. 5 7 customer reviews. arrow_back Back to Probability with Venn Diagrams Probability with Venn Diagrams: GCSE Maths Specification and Awarding Body Information. Aug 30, 2016 - This a a 20 problem worksheet where students look at shaded Venn Diagrams to write an answer. Nov 1, 2016 - Explore Emily Upchurch's board "venn diagram template" on Pinterest. Venn diagrams – WJEC Venn diagrams are a useful tool in the world of statistics. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; … The circles are labelled with a capital letter just like a set. This means that most of the links on this page are not yet active. 4 students study choir and theatre, 2 study band and choir, 13 have choir as part of their option, 5 study only band and 7 study only theatre. MEANWHILE: It might be easier for you to look for resources using … 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. Home / Edexcel GCSE Maths / Revision Notes / 8. If you are not comfortable with working with sets, you should go and learn that first! The Corbettmaths Practice Questions on Venn Diagrams. Probability Venn Diagrams MichaelExamSolutionsKid 2020-03-12T02:21:57+00:00. Free. www.justmaths.co.uk Venn Diagrams (H) - Version 2 January 2016 Venn Diagrams (H) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. Venn Diagrams. • Answer the questions in the spaces provided – there may be more space than you need. A Venn Diagram is clever because it shows lots of information: Do you see that alex, casey, drew and hunter are in the "Soccer" set? Venn diagrams – WJEC Venn diagrams are a useful tool in the world of statistics. Definitions and notation . • Answer all questions. Once you have got to grips with these, you will be able to arrange all sorts of groups and sets. Preview. Basics. Created: Mar 5, 2018 | Updated: Mar 8, 2018. In set B, we have already input numbers 2, 3 and 4 on the Venn diagram, so we now need to input numbers 6, 8 and 12. Tis is a Higher GCSE question and possibly an A* question , as it is not available in my G to B text book given to me for revision by Harlow College. Author: Created by bigdoubleyer. For those of you that have been around a bit … (I mean teaching for a while and I’m not insinuating anything else !!) There is a mixture of 2 circle and 3 circle diagrams. Also introduces union and intersection type probability notation. Once you have got to grips with these, you will be able to arrange all sorts of groups and sets. • 16 have a cat. These numbers should be placed in the A circle, but not in any of the intersections. John Venn 1834-1923 John Venn – the British logician who around 1880 devised the ‘Venn diagram’ – celebrates his 185th birthday this week. GCSE 9-1 New content – Venn Diagrams . docx, 73 … 6 do not take either of these subjects. This rectangle is referred to as the Universal Set and it contains the two further sets, each representing the characteristics with which we wish to sort our people. We can take each element in turn and add them to the Venn diagram by placing them in the correct position. 1. Venn Diagram GCSE Maths Revision. And that casey, drew and jade are in the "Tennis" set? Venn diagrams allow us to show two … Loading... Save for later. Probability / 8.2 Venn Diagrams & Two Way tables / 8.2.1 Probability – Venn Diagrams. I will be working hard over the next couple of weeks to upload relevant resources and activate these links. Boring, but hopefully useful. 28/36. 5 3 customer reviews. Each circle represents a set, so the space inside the circle represents all of the members of a set. Using a Venn diagram, what is the probability that a student studies either band, choir or theatre? Model answers & video solution for Venn Diagrams & 2 way tables. Activ inspire presentation on Venn diagrams, Drawing and reading them upto three way diagrams. you will have taught these before. Revision notes on ‘Probability - Venn Diagrams’ for the Edexcel GCSE Maths exam. Venn Diagrams GCSE Maths. All that in one small diagram. 30 students are asked if they have a dog or cat. What is a venn diagram? Once you have got to grips with these, you will be able to arrange all sorts of groups and sets. Solving Problems With Venn Diagrams. PLEASE NOTE: This navigation system is still under development. Venn Diagrams are a great way of visually representing sets. Intersection "Intersection" is when you must be in BOTH sets. Venn Diagrams (F) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. And here is the clever thing: casey and drew are in BOTH sets! GCSE Number Topics; Venn Diagrams; Venn Diagrams. A powerpoint and worksheet for teaching the new GCSE topic of Venn diagrams. The Venn diagram consists of a rectangle that acts as a boundary into which all the elements must be placed. Venn Diagrams Sets: 1 2 3 Topic: Averages and Range Coordinates Fractions Properties of Numbers Rectangles 3 examples of the slides are available to preview . This worksheet covers unions, intersections, and complements. Read more. 8.2.1 Probability – Venn Diagrams samabrhms11 2020-04-03T13:46:27+01:00. Designed by the expert teachers at Save My Exams. 8 students do not study any of these. GCSE 9-1 New content – Venn Diagrams. In a class there are 32 students 23 take History. 5-a-day GCSE 9-1; 5-a-day Primary ; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. • You … Past paper exam questions organised by topic and difficulty for Edexcel GCSE Maths. Created: Feb 10, 2019. Show Video Lesson . Here I introduce you to Sets and the algebra of set operations. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; August 7, 2016 August 15, 2019 corbettmaths. Revision Notes . The set refers to the circles that combine to form a Venn diagram. (b) How many students take French but not History? The content challenges pupils to calculate probabilities from Venn diagrams, interpret worded questions and construct Venn diagrams from limited information. Venn Diagrams - Corbettmaths. The powerpoint builds up with clear examples and the worksheet has answers included. GCSE REVISION SHEETS; GCSE QUESTIONS BY TOPIC; PAST PAPER SOLUTIONS; VENN DIAGRAMS. 2.
Huntington, West Virginia Demographics, Avis Car Rental Reviews, Build God Then We'll Talk Chords, Mdnsresponder Mac High Network, Strong's Complete Word Study Concordance Online, 3ds Max Logo Png, Avid Fast Track Duo, Matplotlib Save Figure, Sam Hoare Outlander, Venti Genshin Impact Age,
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662631064.64/warc/CC-MAIN-20220527015812-20220527045812-00673.warc.gz
|
CC-MAIN-2022-21
| 9,338 | 3 |
https://www.physicsforums.com/threads/half-wave-rectifier-circuit.649624/
|
math
|
1. The problem statement, all variables and given/known data Using the approximate triangular output shown and Vdc previously calculated, use the expression Vout=Vdc + Vac to solve for Vac. Find an expression for Vac that is valid from t=0 to t=T. Your expression should be in terms of Vp,R,C,T and t. The circuit is a half wave rectifier with a capacitor. Eventually I am trying to calculate ripple factor but I need the Vac to calculate Vrms and then onto calculating ripple = Vac rms / Vdc 2. Relevant equations Vdc= Vp - VpT/2RC where Vp= voltage at peak Vout=Vdc + Vac 3. The attempt at a solution I am not sure what I am supposed to be using for V out. I was given Vin=Vocosωt where T=2∏/ω is the period of the input signal. Am I supposed to use Vpcosωt for my Vout?
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267163704.93/warc/CC-MAIN-20180926061824-20180926082224-00187.warc.gz
|
CC-MAIN-2018-39
| 777 | 1 |
http://mathforum.org/kb/thread.jspa?threadID=2575066&messageID=9132098
|
math
|
On Sat, 08 Jun 2013 20:16:39 -0500, Sam Wormley wrote:
> Andrew Beal Offers $1 Million To Solve His Math Problem, Beal Conjecture > Remains Unsolved Since 1980s >> http://www.ibtimes.com/andrew-beal-offers-1-million-solve-his-math- problem-beal-conjecture-remains-unsolved-1980s-1292837 > >> The Beal Conjecture states that the only solutions to the equation A^x >> + B^y = C^z, when A, B and C are positive integers, and x, y and z are >> positive integers greater than two, are those in which A, B and C have >> a common factor. The American Mathematical Society in Providence, Rhode >> Island, said that typical of many statements in number theory, they're >> "easy to say but extremely difficult to prove.?
Hey Sammy, You are supposedly a math major. Solve this and you won't need to be beating the drum for that "carbon tax" anymore.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125936833.6/warc/CC-MAIN-20180419091546-20180419111546-00278.warc.gz
|
CC-MAIN-2018-17
| 838 | 3 |
https://www.arxiv-vanity.com/papers/1410.2517/
|
math
|
Minimal surfaces in Euclidean space with a log-linear density
We study surfaces in Euclidean space that are minimal for a log-linear density , where are real numbers not all zero. We prove that if a surface is -minimal foliated by circles in parallel planes, then these planes are orthogonal to the vector and the surface must be rotational. We also classify all minimal surfaces of translation type.
Key words and phrases:log-linear density, Riemann type, translation surface, soliton
2000 Mathematics Subject Classification:53A10, 53C44
1. Introduction and statement of results
In the last years the study and the interest for manifolds with density has increased due to its applications in probability and statistics. The literature on manifolds with density has increased so we only refer the introductory survey of Morgan in ; see also [10, 11]. In this paper we consider surfaces in Euclidean space with a positive smooth density function which is used to weight the volume and the surface area. The mean curvature of an oriented surface in with density is
where and stand for the Gauss map of and its mean curvature, respectively. The expression (1) for is obtained by the first variation of weighted area . We say that is a constant -mean curvature surface if is a constant function on , and if everywhere, we say that is a -minimal surface. In this context, one can pose similar problems as in the classical theory of minimal surfaces.
Among the many choices of densities, we focus in the simplest function , that is, is a linear function in its variables, and we say then that is a log-linear density. We suppose that , where are the canonical coordinates of and are real number not all zero. We call the vector the -density vector. A computation of (1) implies that if and only if
The interest for this type of density functions appears in the singularity theory of the mean curvature flow, where the constant -mean curvature equation is the equation of the limit flow by a proper blow-up procedure near type II singular points (for example, see [6, 16]). In the literature, a solution of this equation is also called a translating soliton, or simply translator . Thus, a translator with velocity is equivalent to be a -minimal surface with -density vector ().
On the other hand, and previously, Eq. (2) had already studied in the theory of PDE of elliptic type. In a nonparametric form, and for the particular case that , the graph of a function defined on a domain of the -plane satisfies (2) if and only if
This equation is the model for a thin extensible film under the influence of gravity and surface tension and is a physical constant. Equation (3) appeared in the classical article of Serrin ([15, p. 477–478]) and studied later in the context of the maximum principle ([3, 13]). Therefore, we may simply view the study of -minimal surfaces as a problem of a particular prescribed mean curvature equation, namely, (1) or (2).
In the class of -minimal surfaces, it is interesting to know explicit examples because a number of such examples makes richer this family of surfaces. Comparing with the theory of minimal surfaces () in , it is natural to impose some geometric property to the surface that makes easier the study of (1), such as that the surface is rotational, helicoidal, ruled or translation. This situation has been studied in [5, 8]. Following the above two motivations, in this paper we consider -minimal surfaces of Riemann type and of translation type and that we now explain.
Firstly, we consider surfaces which are constructed by a -parameter (smooth) family of circles, not all necessarily with the same radius. Following Enneper (), we call a such surface a cyclic surface. So, surfaces of revolution are examples of cyclic surfaces. The classical theory of minimal surfaces asserts that besides the plane, the only examples of cyclic minimal surfaces in is the catenoid, which it is the only rotational minimal surface, or the surface belongs to a family of minimal surfaces discovered by Riemann . Each Riemann minimal example is constructed by circles and all them lie in parallel planes. We refer the Nitsche’ book for a general reference . In general, we say that a surface of Riemann type is a cyclic surface such that the circles of the foliation lie in parallel planes. In the class of -minimal surfaces with a log-linear density, we prove that the only cyclic surfaces must be surfaces of revolution. Exactly, we show:
Let be a-minimal cyclic surface for a log-linear density. Then the planes of the foliation are parallel.
Let be a surface of Riemann type foliated by circles in parallel planes, all them orthogonal to a vector . If is a -minimal surface for a log-linear density, then the vector is proportional to the -vector density and is a surface of revolution whose axis is parallel to .
If we allow that can constantly vanish, then the above two results summarize as follows:
Let be a density in , where . Then the existence of non-rotational cyclic surfaces occurs if and only if and in such a case, is a Riemann minimal classical example.
The second setting of examples of -minimal surfaces appears when we study Eq. (3) by separation of variables . A surface which is a graph of such a function is called a translation surface. Let us observe that is the sum of two planar curves, namely, and . Then has the property that the translations of a parametric curve by the parametric curves remain in (similarly for the parametric curves ). For minimal surfaces in , the only example, besides the plane, is the Scherk’s minimal surface , (). Here we study translation surfaces that are -minimal with a log-linear density. In it has been considered the case , proving that the only examples occur when or is linear, that is, is a cylindrical surface whose rulings are parallel to the -plane or to the -plane. We extend this result assuming in all its generality:
Let be a translation surface . If is a -minimal surface for a log-linear density , then or is a linera function and the surface is cylindrical whose rulings are parallel to the -plane or to the -plane.
In fact, we obtain new examples of -minimal surfaces of translation type for values .
Consider a surface in with a log-linear density , where , not all zero. Because all our results are local, we suppose that is oriented and denoted by its Gauss map. The expression of is then
where are the coordinates of with respect to the canonical basis of . From (2), the -minimality condition expresses as
We now compute when is a surface of Riemann type. Without loss of generality, we suppose that the surface is foliated by circles contained in planes parallel to the -plane. Then the surface parametrizes locally as
where , are smooth functions defined in some interval . In fact, the results that we will obtain hold for surfaces that are foliated by pieces of circles because it is enough that the range of is an interval of . The computation of the Euclidean mean curvature yields
Here denotes the derivative with respect to and we also drop the dependence of the functions and on the variable . The mean curvature function is computed with respect to Gauss map
We point out that after a change of coordinates, the density function can prescribe to be linear in one variable, as for example, . But in such a case, the planes of the foliation containing the circles of change by the above change of coordinates. Thus if we have assumed that the planes are parallel to a given plane, in our case, the plane of equation , then the function has to be assumed in all its generality.
In order to simplify the notation, let
3. Proof of Theorem 2
Let be a -minimal surface of Riemann type with a log-linear density. Then (4) writes as
In order to prove Th. 2, we have to show two things. First, that and second, that the curve of centers is parallel to the -axis, that is, that and are constant functions, or equivalently, .
After a straightforward computation, Eq. (5) can viewed as a polynomial equation
Because the trigonometric functions are independent linearly, then the coefficient functions vanish identically, that is, for . The work to do is firstly the computation of the coefficients of the greatest degree in (6). As we go solving the corresponding equations and , and thanks to this new information, we come back to (6) to compute the next coefficients of lower degree until we obtain the desired result. We point out that the use of a symbolic program (as Mathematica or Maple) reduces meaningfully the computations.
We distinguish cases according the values of and .
3.1. Cases where some is
First we suppose that two of the three constants are .
Case . The computations of and gives
We deduce that in the interval , that is, and are constant functions. Now (6) is a polynomial equation of degree , with , and yields a contradiction.
Case . This is similar to the previous case.
Case . Then
Again we deduce and the functions and are constant. Now the degree of polynomial equation (6) is simply , obtaining
Now we study the case that only one of the constants or is .
Case and . We have
From , we distinguish two cases.
Assume . Then reduces . We have two possibilities. If , then is a constant function, but now the coefficient is , a contradiction. Thus . Now writes as . From we deduce . If , we obtain a contradiction. Thus and , . But now (6) reduces into , a contradiction.
Assume . Then writes as
Suppose . Then , a contradiction. Thus . Then and the above equation write now, respectively, as
Multiplying the first equation by and subtracting the second one, we get , which implies , a contradiction.
Case and . It is similar to the above case.
The computation of (6) together implies
Multiplying the first equation by and subtracting the second one multiplied by , we get . If , then and are constant functions and this gives immediately , a contradiction. Thus suppose that and do not vanish simultaneously and so,
Case . It follows that , obtaining , a contradiction.
Case . It is analogous to the previous case .
Arrived at this step of the arguments, we summarize the results obtained up now. Consider a surface of Riemann type which is foliated by circles in parallel planes to the -plane. If is a -minimal surface for a linear function , then must be , that is, the density of Euclidean space is . Under this condition, the functions and are constant and the curve of the centers of the circles is a straight-line parallel to the -axis. The surface parametrizes locally as
where the function satisfies
This is the equation of the rotational solutions of (3) and, in particular, the existence is assured at least locally. We point out that it has been shown the existence of convex, rotationally symmetric translating solitons which are graphs on the -plane and asymptotic to a paraboloid . Moreover the only entire convex solution to (3) must be rotationally symmetric in an appropriate coordinate system .
In a similar way, we get a result as in Th. 2 for constant -mean curvature surfaces, that is, is constant on the surface. The arguments are equal except that the computation are longer. For surfaces of Riemann type and in the case that , we prove:
Let be a surface foliated by circles contained in parallel planes to the -plane. Suppose is a nonzero constant for a log-linear density . Then is a surface of revolution whose axis is parallel to the -axis.
Suppose , where is a nonzero number. Then we have
By using the notation in the above section, this equation writes now as
Squaring in this identity and placing all the terms in the left hand side, we obtain a polynomial equation
Again, all coefficients must vanish identically for . From and , we have
Case . Then we deduce immediately and .
Case . Then and write, respectively, as
Hence we deduce
Using these values of and , the computations of and imply that , or
respectively. In the latter case, multiplying the first equation by and adding the second equation, we obtain , a contradiction.
In any of the two cases, we conclude , which proves that is a surface of revolution. As the curve of centers is , , then the axis of rotation is parallel to the -axis, showing the result. ∎
4. Proof of Theorem 1
We follow the same ideas as in the proof of the result for minimal surfaces in , see [12, p. 85-86]. The proof is by contradiction and we assume that the planes of the foliation are not parallel. Because the result is local, we only work in an interval of the foliation that defines the surface. Let the canonical basis of . Because the planes of the foliation are not parallel, and after a change of coordinates, we can suppose that the -vector density is . Let be the parameter of the uniparametric family of circles that defines the surface, let be the radius in each -leaf. Consider a curve parametrized by the arc-length which is orthogonal to each -plane. This means that the vector is orthogonal to the -plane. Because we suppose that the planes are not parallel, then is not a straight-line. Let be the Frenet frame of , where and b are the tangent vector, normal vector and binormal vector of , respectively. If is the curve of centers of the circles of the foliation, then parametrizes locally as
Let , where are smooth functions. Consider the Frenet equations of :
Here denotes the derivative with respect to the -parameter and and are the curvature and torsion of , respectively. Since is not a (piece of) straight-line, then . Now the -minimal condition writes simply as , where is the Gauss map of . Now we compute each one the terms of this equation. The Gauss map is
where and are the third coordinates of and b with respect to the canonical basis of . For the computation of the mean curvature , we have to differentiate twice the parametrization . In all these computations, we use the Frenet equation and the fact that is an orthonormal basis of , with for all . After a straightforward computation, the condition is expressed as a trigonometric polynomial on , namely,
where and are smooth functions. Thus all coefficients and vanish in the -interval.
The leader coefficients (for are
The linear combination simplifies into
Let us observe that if , then the vectors and are orthogonal to for all . In such a case, for all and it follows that would be parallel to the vector , in particular, is a (vertical) straight-line, a contradiction. Thus and can not vanish mutually. We discuss Eq. (11) case-by-case.
Case . Then or .
Sub-case . Then gives and it follows . Suppose (similar if . Then
This implies and . Finally for , we have
obtaining , a contradiction.
Sub-case . Now
and implies , a contradiction.
Case and . Then reduces into . Thus or . Suppose (similar if ). Then . Now and write as and , respectively. Since , it follows and . Finally, the coefficient is , and yields the desired contradiction.
Case and . This is similar to the previous case.
5. Proof of Theorem 4
Let be a translation surface , where and are smooth functions defined in intervals of . Let be a non-zero vector. Suppose that is a -minimal surface with as -vector density. As it was pointed out in Remark 5, we can not do a change of coordinates to prescribe the -vector density because in such a case, the surface is not of the form . Recall that in , it has been considered the case that , proving that the only possibility is that (or ) is linear.
Let be the parametrization of . With respect to the unit normal vector field
the mean curvature is
Thus is a -minimal surface if and only if
We differentiate (12) with respect to and next with respect to , obtaining
For completeness, we consider the case , doing a different proof than in . In such a situation, . If (resp. ), then (resp. ) is linear. Assume , in particular, . Then there exists such that
A direct integration yields and , . Then (12) simplifies now into
If we view this expression first as a polynomial equation on and second as a polynomial equation on , we deduce , and , obtaining , a contradiction.
Once proved the result for , we discuss the rest of cases. First, we assume and we will arrive to a contradiction. Since the case and is similar to and , there are only two possibilities.
5.1. Case ,
From (13), we have
Again there exists a constant such that
Then a first integration implies
Substituting into (12), we get a polynomial on of type
Because identically, then the coefficients must vanish. However a straightforward computation of leads to , obtaining a contradiction.
Once that the case has been discarded, then we conclude or is linear. This finishes the proof of Th. 4.
In order to summarize the results, and by the symmetry of the roles of and , we will suppose that .
Let be a translation surface . Suppose is a -minimal surface for a log-linear density . Then:
There exists such that .
The surface is cylindrical and the rulings are parallel to the -plane.
The function satisfies
We remark that (14) is an ODE and thus the existence is assured at least locally, proving the existence of -minimal surfaces of translation type.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107911229.96/warc/CC-MAIN-20201030182757-20201030212757-00449.warc.gz
|
CC-MAIN-2020-45
| 17,033 | 107 |
http://lisamosesellshouston.com/379453/Multivariable.Calculus.4nd.Mathematica.With.Applications.to.Geometry.4nd.Physics.html
|
math
|
Multivariable Calculus 4nd Mathematica®: With Applications to Geometry 4nd Physics
Multivariable Calculus 4nd Mathematica®: With Applications to Geometry 4nd Physics By Kevin R. Coombes
English | PDF | 1998 | 282 Pages | ISBN : 0387983600 | 20.27 MB
One of the auth08rs stated goals f08r this publication is to "modernize" the course through the integration of Mathematica. Besides introducing students to the multivariable uses of Mathematica, 4nd instructing them on how to use it as a tool in simplifying calculations, they also present 1n8t0ductions to geometry, mathematical physics, 4nd kinematics, topics of particular interest to engineering 4nd physical science students.
In using Mathematica as a tool, the auth08rs take pains not to use it simply to define things as a whole bunch of new "gadgets" streamlined to the taste of the auth08rs, but rather they exploit the tremendous resources built 1n8t0 the program. They also make it clear that Mathematica is not alg08rithms. At the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer 4nd simpler. The problem 5euts give students an opp08rtunity to practice their newly learned skills, covering simple calculations with Mathematica, simple plots, a review of one-variable calculus using Mathematica f08r symbolic differentiation, integration 4nd numberical integration. They also cover the practice of inc08rp08rating text 4nd headings 1n8t0 a Mathematica notebook. A DOS-f08rmatted diskette accompanies the printed w08rk, containing both Mathematica 2.2 4nd 3.0 version notebooks, as well as sample examination problems f08r students. This supplementary w08rk can be used with any st4ndard multivariable calculus textbook. It is assumed that in most cases students will also have access to an introduct08ry primer f08r Mathematica.
Kindly Supp08rt AvaxGenius And Buy Premium From My Links To Continue Produce M08re Amazing Posts Thanks All
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946565.64/warc/CC-MAIN-20180424061343-20180424081343-00232.warc.gz
|
CC-MAIN-2018-17
| 1,957 | 6 |
https://journalajpas.com/index.php/AJPAS/article/view/30139
|
math
|
Main Article Content
The Quadratic rank transmutation map proposed for introducing skewness and flexibility into probability models with a single parameter known as the transmuted parameter has been used by several authors and is proven to be useful. This article uses this method to add flexibility to the Lindley-Exponential distribution which results to a new continuous distribution called “transmuted Lindley-Exponential distribution”. This paper presents the definition, validation, properties, application and estimation of unknown parameters of the transmuted Lindley-Exponential distribution using the method of maximum likelihood estimation. The new distribution has been applied to a real life dataset on the survival times (in days) of 72 guinea pigs and the result gives good evidence that the transmuted Lindley-Exponential distribution is better than the Lindley-Exponential distribution, Exponential distribution and Lindley distribution based on the dataset used.
Ieren TG, Kuhe AD. On the properties and applications of Lomax-exponential distribution. Asian Journal of Probability and Statistics. 2018;1(4):1-13.
Abdullahi J, Abdullahi UK, Ieren TG, Kuhe DA, Umar AA. On the properties and applications of transmuted odd generalized exponential- exponential distribution. Asian Journal of Probability and Statistics. 2018;1(4):1-14.
Owoloko EA, Oguntunde PE, Adejumo AO. Performance rating of the transmuted exponential distribution: an analytical approach. Spring. 2015;4:818-829.
Oguntunde PE, Adejumo AO. The transmuted inverse exponential distribution. Inter. J. Adv. Stat. Prob. 2015;3(1):1–7.
Maiti SS, Pramanik S. Odds generalized exponential-exponential distribution. J. of Data Sci. 2015; 13:733-754.
Yahaya A, Ieren TG. On transmuted Weibull-exponential distribution: Its properties and applications. Nigerian J. of Sci. Res. 2017;16(3):289-297.
Oguntunde PE, Balogun OS, Okagbue HI, Bishop SA. The Weibull-exponential distribution: Its properties and applications. J. Appl. Sci. 2015;15(11):1305-1311.
Shaw WT, Buckley IR. The alchemy of probability distributions: Beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report; 2007.
R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2019.
Bjerkedal T. Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. Am. J. Hyg. 1960;72:130-148.
Merovci F. The transmuted rayleigh distribution. Austr. J. Stat. 2013;22(1):21–30.
Merovci F, Puka I. Transmuted pareto distribution. Prob. Stat. Forum. 2014;7:1–11.
Abdullahi UK, Ieren TG. On the inferences and applications of transmuted exponential Lomax distribution. Int. J. of Adv. Prob. Stat. 2018;6(1):30-36.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178360853.31/warc/CC-MAIN-20210228115201-20210228145201-00508.warc.gz
|
CC-MAIN-2021-10
| 2,821 | 15 |
https://books.google.to/books?id=1kLt6ImEs_gC&pg=PA707&vq=position&dq=editions:HARVARDHJ12N6&lr=&output=html_text&hl=en
|
math
|
« PreviousContinue »
If, on the other hand, we take a point P in the plane of a conic, conjugates with regard to the foci. If therefore the two foci F, and we get to each line a through P one conjugate line which joins PF, be joined to P, these lines will be harmonic with regard to the to the pole of a. These pairs of conjugate lines through P form an involution in the pencil at P. The local rays of this involution are the tangents drawn from P to the conic. This gives the theorem reciprocal to the last, viz:
A conic determines in every pencil in ils plane on involution, corresponding lines teing conjugale lines with regard to the conic.
If the point is wilhout the conic the involution is hyperbolic, the tangents from the points being the focal rays.
If the point lies on the conic the involution is parabolic, the tangeni at the point counting for coincident focal rays.
If the poin: is within the conic the involution is elliptic, having no focal rays.
It will further be seen that the involution determined by a conic on any line o is a section of the involution, which is determined by the conic
at the pole P of p. $ 83, Foci.-The centre of a pencil in which the conic determines a circular involution is called a "focus" of the conic.
In other words, a focus is such a point that every line through it is tangent and normal. As the latter are perpendicular, they will perpendicular to its conjugate line. The polar to a focus is called a bisect the angles between the other pair. Hencedirectrix of the conic.
The lines joining any point on a conic 10 the two foct are equally From the definition it follows that every, focus lies on an axis, for inclined to the langent and normal at that point. the line joining a focus to the centre of the conic is a diameter to In case of the parabola this becomeswhich the conjugate lines are perpendicular; and every line joining The line joining any point on a parabola to the focus and the diameter two foci is an axis, for the perpendiculars to this line through the foci through the poini, are equally inclined to the langent and normal al are conjugate to it. These conjugate lines pass through the pole of that point. the line, the pole lies therefore at infinity, and the line is a diameter, From the definition of a focus it follows thathence by the last property an axis.
The segment of a tangent between the directrix and the point of It follows that all foci lie on one axis, for no line joining a point contact is seen from the focus belonging to the directrix under a righe in one axis to a point in the other can be an axis.
angle, because the lines joining the focus to the ends of this As the conic determines in the pencil which has its centre at a focus segment are conjugate with regard to the conic, and therefore a circular involution, no tangents can be drawn from the focus to perpendicular. the conic. Hence each focus lies within a conic; and a directrix does With equal ease the following theorem is proved: not cut the conic.
The two lines which join the points of contact of two langerls each Further properties are found by the following considerations: to one focus, but not both to the same, are seen from the intersection of
$ 84. Through a point P one line p can be drawn, which is with the tangenis under equal angles. regard to a given conic conjugate to a given line 2. viz. that line $ 86. Other focal properties of a conic are obtained by the following which joins the point P to the pole of the line q. If the line q is made considerations: to describe a pencil about a point, then the line will describe a Let F (fig. 35) bę a focus to a conic, f the corresponding directrix, pencil about Þ. These two pencils will be projective, for the line A and B the points of contact of two tangents meeting at T, and P
passes through the pole of 9, and whilst g describes the pencil Q. the point where the its pole describes a projective row, and this row is perspective to line AB cuts the directhe pencil P.
trix. Then TF will be We now take the point P on an axis of the conic, draw any line the polar of P (because A through it, and from the pole of P. draw a perpendicular a to popolars of F and I meet Let 2 cut the axis in l. Then, in the pencils of conjugate lines, at P). Hence TF and which have their centres at P and Q. the lines p and g are conjugate PF are conjugate lines lines at right angles to one another. Besides, to the axis as a ray through a focus, and in either pencil will correspond in the other the perpendicular to the therefore perpendicular. axis ($ 72). The conic generated by the intersection of corresponding They are further har. lines in the two pencils is therefore the circle on PQ as diameter, monic conjugates with so that every line in Pis perpendicular to its corresponding line regard to FÅ and FB in l.
(84 64 and 13), so that Ad to every point P on an axis of a conic corresponds thus a point they bisect the angles Q. such that conjugate lines through P and Q are perpendicular. formed by these lines.
We shall show that these point-pairs PQ form an involution. This by the way To do this let us move P along the axis, and with it the line p, proves keeping the latter parallel to itself. Then P describes a row, pa The segments between perspective pencil of parallels), and the pole of p a projective row. the point of intersection At the same time the line q describes a pencil of parallels perpendicular of two langents to a conic to p, and perspective to the row formed by the
pole of P. The point and their points of conQ, therefore, where a cuts the axis, describes a row projective to the lact are seen from a focus row of points P. The two points P and Q describe thus two pro- under equal angles.
B: jective rows on the axis; and not only does P as a point in the first If
draw row correspond to Q, but also Q as a point in the first corresponds through A and B lines to P. The two rows therefore form an involution. The centre of parallel to TF, then the this involution, it is easily seen, is the centre of the conic.
points As, B. where A focus of this involution has the properly that any two conjugate these cut the directrix lines through it are perpendicular; hence, il is a focus to ihe conic. will be harmonic conju
Such involution exists on each axis. But only one of these can gates with regard to P have foci, because all foci lie on the same axis. The involution on and the point where FT one of the axes is elliptic, and appears ($ 80) therefore as the section cuts the directrix. The of two circular involutions in two pencils whose centres lie in the lines FT and FP bisect other axis. These centres are foci, hence the one axis contains two therefore also the angles P foci, the other axis.none; or every central conic has two foci which lie between FA, and FB. on one axis equidistant from the centre.
From this it follows The axis which contains the foci is called the principal axis; in easily that the triangles case of an hyperbola it is the axis which cuts the curve, because the FAA and FBB, are foci lie within the conic.
equiangular, and therefore similar, so that FA : AA. =FB : BB. In case of the parabola there is but one axis. The involution The triangles AA, A, and BB, B, formed by drawing perpendiculars on this axis has its centre at infinity. One focus is therefore at from A and B to the directrix are also similar, so that AA. : AA, infinity, the one focus only is finite. A parabola has only one -BB, : BB2. This, combined with the above proportion, gives focus.
FA : AA - FB : BB. Hence the theorem: *85. If through any point P (fig. 34) on a conic the tangent PT The ratio of the distances of any point on a conic from a focus and and the normal PN (T.e.
the perpendicular to the tangent through the corresponding directris is constant. the point of contact) be drawn, these will be conjugate lines with To determine this ratio we consider its value for a vertex on the regard to the conic, and at right angles to each other. They will principal axis. In an ellipse the focus lies between the two vertices therefore cut the principal axis in two points, which are conjugate on this axis, hence the focus is nearer to a vertex than to the correin the involution considered in $ 84; hence they are harmonic sponding directrix. Similarly, in an hyperbola a vertex is nearer
to the directrix than to the focus. In a parabola the vertex lies
RULED QUADRIC SURFACES halfway between directrix and locus. It follows in an ellipse the ratio between the distance of a point the same plane, in which case lines joining corresponding points
$ 89. We have considered hitherto projective rows which lie in from the focus to that
from the directrix is less than unity, in the envelop a conic. We shall now consider projective rows whose parabola it equals unity, and in the hyperbola it is greater than
bases do not meet. In this case, corresponding points will be joined unity. It is here the same which focus we take, because the two foci like every surface generated by lines is called a ruled surface. This
by lines which do not lie in a plane, but on some surface, which lie symmetrical to the axis of the conic. If now P is any point on surface clearly contains the bases of the two rows. the conic having the distances 9 and ra from the foci and the distances d, and do from the corresponding directrices, then ri/d.=ra/dz=e, obtain two axial pencils which are also projective, those planes
If the points in either row be joined to the base of the other, we where e is constant. Hence also ad
being corresponding which pass through corresponding points in the In the ellipse, which lies between the directrices, dites is constant, the axial pencils passing through them, then AA will be the line therefore also strz.. In the hyperbola on the other hand di-d, is
of intersection of the corresponding planes a, a' and also the line constant, equal to the distance between the directrices, therefore joining corresponding points in the rows. in this case 71-7 is constant.
If we cut the whole figure by a plane this will cut the axial pencils If we can the distances of a point on a conic from the focus its in two projective fat pencils
, and the curve of the second order focal distances we have the theorem:
generated by these will be the curve in which the plane cuts the * In an ellipse the sum of the focal distances is constant; and in an
surface. Hence hyperbola the difference of the focal distances is constant.
The locus of lines joining corresponding points in two projectie This constani sum or difference equals in both cases the length of rows which do not lie in the same plane is a surface which contains
the the principal axis.
bases of the rows, and which can also be generated by the lines of inter
section of corresponding, planes in two projective axial pencils. This PENCIL OF CONICS
surface is cut by every plane in a curve of the second order, kence either $ 87. Through four points A, B, C, D in a plane, of which no three
in a conic or in a line-pair. No line which does not lie altogether on lie in a line, an infinite number of conics may be drawn, viz. through which is therefore said to be of the second order or is called a ruled
the surface can have more than two points in common with
the surface, conics is called a pencil of conics. Similarly, all conics touching four quadric surface. fixed lines form a system such that any fifth tangent determines one
That no line which does not lie on the surface can cut the surface and only one conic. We have here the theorems:
in more than two points is seen at once if a plane be drawn through
the line, for this will cut the surface in a conic. It follows also that The pairs of points in which The pairs of tangents which any line is cut by a system of can be drawn from a point
together on the surface.
a line which contains more than two points of the surface lies altoconics through four fixed points a system of conics touching four are in involution.
$ 90. Through any point in space one line can always be drawn four-point, then any line will cut two opposite sides XC, BD in then through every point in either one line may be drawn cutting We prove the first theorem only. Let ABCD (fig. 36) be the cutting two given lines which do not themselves meet.
If therefore three lines in space be given of which no two meet, the other two.
If a line moves so that it always cuts three given lines of swhick no two meet, then it generates a ruled quadric surface.
Let a, b, c be the given lines, and p.g.r... lines cutting them in the points A, A', A'...; B, B', B'...; C, C', C'... respectively; then the planes through a containing P: 9,7, and the planes through b containing the same lines, may be taken as corresponding planes in two axial pencils which are projective, because both pencils cut the line c in the same row, C, C', .:.; the surface can therefore be gener
ated by projective axial pencils. F
of the lines p, q,?... no two can meet, for otherwise the lines a, b, c which cut them would also lie in their plane. There is a single infinite number of them, for one passes through each point of a. These lines are said to form a set of lines on the surface.
If now three of the lines P. 9, 7 be taken, then every lined cutting them will have three points in common with the surface, and will therefore lie altogether on it. This gives rise to a second set of lines on the surface. From what has been said the theorem follows:
A ruled quadric surface contains two sets of straight lines. Every Fig. 36.
line of one set culs every line of the other, but no two lines of the same the points E, E', the pair AD, BC in points F, F', and any conic Any two lines of the same set may be taken as bases of two projective of the system in M, N, and we have AICD, MN)=B(CD, MN) rows, or of two projective pencils which generate the surface. They are If we cut these pencils by l we get
cut by the lines of ihe other set in two projective rows. (EF, MN)=(F'E', MN)
The plane at infinity like every other plane cuts the surface either (EF, MN)= (E'F', NM).
in a conic proper or in a line-pair. In the first case the surface is But this is, according to $ 77 (7), the condition that M, N are
called an Hyperboloid of one shcet, in the second an Hyperbolic
Paraboloid. corresponding points in the involution determined by the point pairs E, E', F, F in which the line 1 cuts pairs of opposite sides of the
The latter may be generated by a line cutting three lines of which four-point ABCD. This involution is independent of the particular. to a given plane.
one lies at infinity, that is, cutting two lines and remaining parallel conic chosen. $ 88. There follow several important theorems:
QUADRIC SURFACES Through four points two, one, or no conics may be drawn which touch $91. The conics, the cones of the second order, and the ruled any given line, according as the involution determined by the given quadric surfaces complete the figures which can be generated by four-point on the line has real, coincident or imaginary focí.
projective rows or flat and axial pencils, that is, by those aggre Two, one, or no conics may be drawn which louch four given lines gates of elements which are of one dimension (88,5, 6). We shali and pass through a given point, according as the involution determined now consider the simpler figures which are generated by aggregates of by the given four-side at the point has real, coincident or imaginary two dimensions. The space at our disposal will not, however, allow focal rays.
us to do more than indicate a few of the results. For the conic through four points which touches a given line has $ 92. We establish a correspondence between the lines and planes its point of contact at a focus of the involution determined by the in pencils in space, or reciprocally between the points and lines in four-point on the line.
two or more planes, but consider principally pencils. As a special case we get, by taking the line at infinity:
In two pencils we may either make planes correspond to planes Through four points of which none is al infinity either two or no and lines to lines, or else planes to lines and lines to planes. !! 'parabolas may be drawn.
hereby the condition be satisfied that to a flat, or axial, pencil The problem of drawing a conic through four points and touching corresponds in the first case a projective flat, or axial, pencil, and in a given line is solved by determining the points of contact on the the second a projective axial,
or flat, pencil, the pencils are said to be line, that is, by determining the foci of the involution in which the projective in the first case and reciprocal in the second. line cuts the sides of the four-point. The corresponding remark For instance, two pencils which join two points S, and S, to the holds for the problem of drawing the conics which touch four lines different points and lines in a given plane * are projective (and and pass through a given point.
in perspective position), if those lines and planes be takea as
corresponding which meet the plane r in the same point or in the In the first case the point of contact is said to be hyperbolic, in the same line. In this case every plane through both centres S, and S, second parabolic, in the third elliptic. of the two pencils will correspond to itself. If these pencils are $ 95. It remains to be proved that every point S on the surface brought into any other position they will be projective (but not may be taken as centre of one of the pencils which generate the perspective).
surlace. Let S. be any point on the surface generated by the The correspondence between two projective pencils is uniquely reciprocal pencils S, and Sa. We have to establish a reciprocal determined, if to four rays (or planes) in the one the corresponding correspondence between the pencils S and Si, so that the surface rays (or planes) in the olher are given, provided that no three rays of generated by them is identical with R. To do this we draw two either sel lie in a plane.
planes a. and ßi through Sı, cutting the surface o in two conics Let a, b, c, d be four rays in the one, a', 6', ', d' the corresponding which we also denote by a, and Bi. These conics meet at Si, and rays in the other pencil. We shall show that we can find for every at some other point T where the line of intersection of as and Bu ray e in the first a single corresponding ray e' in the second. To cuts the surface. the axial pencil a (b, c, d ... ) formed by the planes which join a to In the pencil S we draw some plane o which passes through T, b,c,d ..., respectively corresponds the axial pencil a' (6',c', d'.::), but not through S, or Sz. It will cut the two conics first at T, and and this correspondence is determined. Hence, the plane a' e' which therefore each at some other point which we call A and B respeccorresponds to the plane de is determined. Similarly, the plane tively. These we join to S by lines a and b, and now establish the b'e' may be found and both together determine the ray e'.
required correspondence between the pencils S, and S as follows: Similarly the correspondence between two reciprocal pencils is To S.T shall correspond the plane o, to the plane as the line a, and determined if for four rays in the one the corresponding planes in to Be the line b, hence to the flat pencil in a, the axial pencil a. the other are given.
These pencils are made projective by.aid of the conic in ai. $ 93. We may now combine
In the same manner the fat pencil in Bi is made projective to the 1. Two reciprocal pencils.
axial pencil b by aid of the conic in B1, corresponding elements being Each ray cuts its corresponding plane in a point, the locus those which meet on the conic. This determines the correspondence, of these points is a quadric surface.
for we know for more than four rays in S, the corresponding planes 2. Two projective pencils.
in S. The two pencils S and S, thus made reciprocal generate a Each plane cuts its corresponding plane in a line, but a quadric surface d', which passes through the point S and through
ray as a rule does not cut its corresponding ray. The the two conics Qy and Bi.
we draw a plane through S and Sz, cutting each of the conics a, and 3. Three projective pencils.
Bi in two points, which will always be possible. This plane cuts The locus of intersection of corresponding planes is a and $' in two conics which have the point S and the points where cubic surface.
it cuts aj and B, in common, that is five points in all.' The conics Of these we consider only the first two cases.
therefore coincide. $94. If two pencils are reciprocal, then to a plane in either corre- This proves that all those points P on o' lie on which have the sponds a line in the other, to a flat pencil an axial pencil, and so on. property that the plane SSP cuts the conics a., B, in two points Every line cuts its corresponding plane in a point. If S, and S, be cach. If the plane SS,P has not this property, then we draw a plane the centres of the two pencils, and P be a point where a line ay in the SS,P. This cuts each surface in a conic, and these conics have in first cuts its corresponding plane as, then the line ba in the pencil S. common the points S, S., one point on each of the conics a., B., and which passes through P will meet ils corresponding plane B, in P. For one point on one of the conics through S and S, which lic on both 6, is a line in the plane ag. The corresponding plane B, must therefore surfaces, hence five points. They are therefore coincident, and our pass through the line 01, hence through P.
theorem is proved. The points in which the lines in S, cut the planes corresponding $96. The following propositions follow:to them in Sy are therefore the same as the points in which the lines A quadric surface has at every point a tangent plane. in S, cut the planes corresponding to them in S.
Every plane section of a quadric surface is a conic or a line pair The locus of these points is a surface which is cut by a plane in a Every line which has thrce points in common with a quadric surface conic or in a line-pair and by a line in not more than two points unless lies on the surface. il lies allogether on the surface. The surface ilself is therefore called a Every conic which has five points in common w a quadric surface quadric surface, or a surface of the second order.
lies on the surface. To prove this we consider any line p in space.
Through two conics which lie in different planes, but have two points The fat pencil in S, which lies in the plane drawn through pin common, and through one external point always one quadric surface and the corresponding axial pencil in Sy determine on p two pro
may be drawn. jective rows, and those points in these which coincide with their 697. Every plane which culs a quadric surface in a line-pair is a corresponding points lie on the surface. But there exist only two, tangent plane. For every line in this plane through the centre of or one, or no such points, unless every point coincides with its the line-pair (the point of intersection of the two lines) cuts the corresponding point. In the latter case the line lies altogether on surface in two coincident points and is therefore a tangent to the the surface.
surface, the centre of the line-pair being the point of contact. This proves also that a plane cuts the surface in a curve of the If a quadric surface contains a line, then every plane through this second order, as no line can have more than two points in common line cuts the surface in a line-pair (or in two coincident lines). For with it. To show that this is a curve of the same kind as those this plane cannot cut the surface in a conic. Hence considered before, we have to show that it can be generated by If a quadric surface contains one line p then it contains an infinite projective fat pencils. We prove first that this is true for any number of lines, and through every point Q on the surface, one line plane through the centre of one of the pencils, and afterwards that can be drawn which cuts p.. For the plane through the point Q every point on the surface may be taken as the centre of such pencil and the line p cuts the surface in a linc-pair which must pass through Let then a. be a plane through S. To the flat pencil in s, which Q and of which,p is one line. it contains corresponds in S, a projective axial pencil with axis No two such lines q on the surface can meet. For as both mect p
and this cuts a in a second flat pencil.. These two flat pencils their plane would contain p and therefore cut the surface in a in an are projective, and, in general, neither concentric nor per- triangle. spective. They generate therefore a conic. But if the line az passes Every line which cuts three lines q will be on the surface; for it through Ş the pencils will have S, as common centre, and may has three points in common with it. therefore have two, or one, or no lincs united with their corresponding llence the quadric surfaces which contain lines are the same as the lines. The section of the surface by the plane a, will be accordingly ruled quadric surfaces considered in $8 89-93, but with one important a line-pair or a single line, or else the plane as will have only the exception. In the last investigation we have left out of considerapoint S, in common with the surface.
tion the possibility of a plane having only one line scwo coincident Every line h through S cuts the suriace in two points, viz. first lines) in common with a quadric surface. in S, and then at the point where it cuts its corresponding plane. $ 98. To investigate this case we suppose first that there is one If now the corresponding plane passes through S., as in the case point A on the surface through which two different lines a, b can be just considered, then the two points where li cuts the surface coincide drawn, which lie altogether on the surface. at Si, and the line is called a langent to the surface with S, as point If P is any other point on the surface which lies neither on a nor of contact. Hence if b, be a tangent, it lies in that planer which , then the plane through P and a will cut the surface in a second corresponds to the line SS, as a line in the pencil S. The section line a' which passes through P and which cuts a. Similarly there of this plane has just been considered. It follows that
is a line b' through P which cuts b. These two lines a' and ' may All langents to quadric surface al the centre of one of the reciprocal coincide, but then they must coincide with PA. pencils lie in a plane which is called the tangent plane to the surface If this happens for one point P, it happens for every other point at that point as point of contact.
Q. For if two different lines could be drawn through O, then by the To the line joining the centres of the two pencils as a line in one same reasoning the line PQ would be altogether on the surface, corresponds in the other the langent plane at its centre.
hence two lines would be drawn through P against the assumption. The langent plane to a quatric surface either cuts the surface in From this follows:two lines, or it has only a single line, or else only a single point in If there is one point on a quadric surface through which one, bul only common with the surface.
one, line can be drawn on the surfur, then through every point one line
can be drawn, and all these lines meel in a point. The surface is a cone projective pencils meet form a congruence. We shall see this con. of the second order.
gruence consists of all lines which cut a twisted cubic twice, or of If through one point on a quadric surface, two, and only two, lines all secants to a twisted cubic. can be drawn on the surface, then through every point two lines may § 102. Let l be the line Sise as a line in the pencil Sa. To it be drawn, and the surface is a ruled quadric surface.
corresponds a line l in S... Al cach of the centres iwo corresponding If through one point on a quadric Surface no line on the surface can lines meet. The two axial pencils with ly and ly as axes are probe drawn, then the surface contains no lines.
jective, and, as their axes meet at Sa, the intersections of correUsing the definitions at the end of $ 95, we may also say: sponding planes form a cone of the second order ($58), with Sq as
On a quadric surface the points are all hyperbolic, or all parabolic, centre. If and 72 be corresponding planes, then their intersection or all elliptic.
will be a line pe which passes through Sp. Corresponding to it in As an example of a quadric surface with elliptical points, we s, will be a line Pi which lies in the plane , and which therefore mention the sphere which may be generated by two reciprocal meets pz at some point P. Conversely, if y be any line in S, which pencils, where to each line in one corresponds the plane perpendicular meets its corresponding line P. at a point P, then to the plane ho to it in the other.
will correspond the plane lipe, that is, the plane S, Sp. These $99. Poles and Polar Planes.—The theory of poles and polars planes intersect in P2, so that p. is a line on the quadric cone generated with regard to a conic is easily extended to quadric surfaces. by the axial pencils l, and la Hence:
Let P be a point in space not on the surface, which we suppose All lines in one pencil which meet their corresponding lines in the not to be a cone. On every line through P which cuts the surface other form a cone of the second order which has its centre at the coutre in two points we determine the harmonic conjugate Q of P with of the first pencil, and passes through the centre of the second. regard to the points of intersection. Through one of these lines we From this follows that the points in which corresponding rays draw two planes a and B. The locus of the points Q in a is a line a, meet lie on two cones of the second order which have the ray joining the polar of P with regard to the conic in which a cuts the surface. their centres in common, and form therefore, together with the line Similarly the locus of points Q in B is a line 6. This cuts a, because S.S, or hi, the intersection of these cones. Any plane cuts each of the the line of intersection of a and B contains but one point Q. The cones in a conic. These two conics have necessarily that point
in locus of all points Q therefore is a plane. This plane is called the common in which it cuts the line h, and therefore besides either polar plane of the point P, with regard to the quadric surface. If P one or three other points. It follows that the curve is of the tkird lies on the surface we take the tangent plane of Pas ils polar. order as a plane may cut it in three, but not in more than three, The following propositions hold:
points. Hence:1. Every point has a polar plane, which is constructed by drawing The locus of points in which corresponding lines on two projectie the polars of the point with regard to the conics in which two planes pencils meet is a curve of the third order or a twisted cubic "k, kick through the point cut the surface.
passes through the centres of the pencils, and which appears as the 2. if Q is a point in the polar of P, then P is o point in the polar intersection of two cones of the second order, which have one line is of Q, because this is true with regard to the conic in which a plane common. through PQ cuts the surface.
A line belonging to the congruence determined by the pencils is a 3. Every plane is the polar plane of one point, which is called the secant of the cubic; it has two, or one, or no points in common with Pole of the plane.
this cubic, and is called accordingly a secant proper, a langent, or $ The pole to a plane is found by constructing the polar planes of secant improper of the cubic. A secant improper may be considered, three points in the plane. Their intersection will be the pole. to use the language of coordinate geometry, as a secant with
4. The points in which the polar plane of P culs the surface are imaginary points of intersection. points of contact of langents drawn from P to the surface, as is easily $ 103. If a, and az be any two corresponding lines in the two Hence :
pencils, then corresponding planes in the axial pencils having and 5. The langents drawn from a point P to a quadric surface form a a, as axes generate a ruled quadric surface. if P be any point on cone of the second order, for the polar plane of P cuts it in a coníc. the cubick, and if Pu, Pz be the corresponding rays in S, and S, which
6. If the pole describes a line a, its polar plane will turn about meet at P, then to the plane di Pi in S, corresponds as Do in Sy. These another line a', as follows from 2. These lines a and a' are said to be therefore meet in a line through P. conjugate with regard to the surface.
This may be stated thus:100. The pole of the line at infinity is called the centre of the Those secants of the cubic which cut a ray an, drauen througktike surface. If it lies at the infinity, the plane at infinity is a tangent centre S, of one pencil, form a ruled quadric surface which passes ikrough plane, and the surface is called a paraboloid.
both centres, and which contains the twisted cubic k. Of such surfaces The polar plane to any point oi infinity passes through the centre, an infinite number exists. Every ray through S, or S, which is net e and is called a diametrical plane.
secant determines one of them. A line through the centre is called a diameter. It is bisected at the If, however, the rays a, and az are secants meeting at A, then the centre, The line conjugate to it lies al infinily.
ruled quadric surface becomes a cone of the second order, having If a point moves along a diameter its polar plane turns about the A as centre., Or all lines of the congquence which pass through a persi conjugaie line at infinity; that is, il moves parallel to itself, ils centre on the twisted cubic k form a cone of the second order. In other words, moving on the first line.
the projection of a twisted cubic from any point in the curve on to The middle points of parallel chords lie in a plane, viz. in the polar any plane is a conic. plane of the point at infinity through which the chords are drawn. It a, is not a secant, but made to pass through any point Q in
The centres of parallel sections lie in a diameter which is a line space, the ruled quadric surface determined by d, will pass through conjugale to the line al infinity in which the planes meet.
0. There will therefore be one line of the congruence passing through O, and only
one. For if two such lines pass through , then the lines TWISTED CUBICS
SQ and SiQ will be corresponding lines; hence will be a point on $ 101. If two pencils with centres S, and S, are made projective, the cubic k, and an infinite number of secants will pass through it. then to a ray in one corresponds a ray in the other, to a plane a
Hence : plane, to a flat or axial pencil a projective flat or axial pencil, and Through every point in space nol on the twisted cubic one and only
one secant to the cubic can be drawn. There is a double infinite number of lines in a pencil. We shall $ 104. The fact that all the secants through a point on the cubic see that a single infinite number of lines in one pencil meets its form a quadric cone shows that the centres of the projective pencils corresponding ray, and that the points of intersection form a curve generating the cubic are not distinguished from any other points on in space.
the cubic. If we take any two points S, S' on the cubic, and draw of the double infinite number of planes in the pencils each will the secants through each of them, we obtain two quadric cones, meet its corresponding plane. This gives a system of a double which have the line SS' in common, and which intersect besides infinite number of lines in space. We know (Ś 5) that there is a along the cubic. If we make these two pencils having S and quadruple infinite number of lines in space. From among these we centres projective by taking four rays on the one cone as cortemay select those which satisfy one or more given conditions. The sponding to the four rays on the other which meet the first on the systems of lines thus obtained were first systematically investigated cubic, the correspondence is determined. These two pencils will and classified by Plücker, in his Geometrie des Raumes. He uses the generate a cubic, and the two cones of secants having $ and S'as following names:-
centres will be identical with the above cones, for each has five A treble infinite number of lines, that is, all lines which satisfy one rays in common with one of the first, viz. the line SS' and the four condition, are said to form a complex of lines; e.g. all lines cutting lines determined for the correspondence; therefore these two cones a given line, or all lines touching a surface.
intersect in the original cubic. This gives the theorem. A double infinite number of lines, that is, all lines which satisfy On a twisted cubic any two points may be taken as centres of protwo conditions, or which are common to two complexes, are said to jective pencils which generale the cubic, corresponding planes being form a congruence of lines; e.g. all lines in a plane, or all lines Those which meet on the same secani. cutting two curves, or all lines cutting a given curve twice.
of the two projective pencils at S and S' we may keep the first A single infinile number of lines, that is, all lines which satisfy, fixed, and move the centre of the other along the curve. The pencils three conditions, or which belong to three complexes, form a ruled will hereby remain projective, and a plane a in S will be cut by its surface; e.g. one set of lines on a ruled quadric surface, or develop corresponding plane a' always in the same secant a. Whilst S' able surfaces which are formed by the tangents to a curve.
moves along the curve the plane a' will turn about e, describing an It follows that all lines in which corresponding planes in two axial pencil.
AUTHORITIES.-In this article we have given a purely geometrical Conversely any two points As, Az in a line perpendicular to the theory of conics, cones of the second order, quadric surfaces, &c. In axis will be the projections of some point in space when the plane doing so we have followed, to a great extent, Reye's Geometrie der 72 is turned about the axis till it is perpendicular to the plane me Lage, and to this excellent work those readers are referred who wish because in this position the two perpendiculars to the planes for a more exhaustive treatment of the subject. Other works and a through the points A, and Aj will be in a plane and therefore especially valuable as showing the development of the subject are: meet at some point A.' Monge, Géométrie descriptive: Carnot, Géométrie de position Representation of Points.-We have thus the following method (1803), containing a theory of transversals; Poncelet's
great work of representing in a single plane the position of points in space Trailé des propriétés projectives des figures (1822); Möbins, Bary- we take in the plane a line xy as the axis, and then any pair of points centrischer Calcul (1826); Steiner, Abhängigkeit geometrischer A., Az in the plane on a line perpendicular to the axis represent a Gestallen (1832), containing the first full discussion of the projective point A in space. If the line AA, cuts the axis at Ao, and if at A. relations between rows, pencils, &c.; Von Staudt, Geometrie der a perpendicular be erected to the plane, then the point A will be in Lage. (1847) and Beiträge zur Geomelrie der Lage (1856-1860), in it at a height AjA=AA, above the plane. This gives the position which a system of geometry is built up from the beginning without of the point A relative to the plane #. In the same way, if in a any reference to number, so that ultimately a number itself gets perpendicular to ng through A, a point A be taken such that AgA = a geometrical definition, and in which imaginary, elements are A Al, then this will give the point A relative to the plane 2. systematically introduced into pure geometry; Chasles, A perçu $ 2. The two planes #1, #2 in their original position divide space historique (1837), in which the author gives a brilliant account of into four parts. These are called the four quadrants. We suppose the progress of modern geometrical methods, pointing out the that the plane w is turned as indicated in advantages of the different purely geometrical methods as compared fig. 37, so that the point P.comes to Q and with the analytical ones, but without taking as much account of R to S, then the quadrant in which the the German as of the French authors; Id., Rapport sur les progrès point A lies is called the first, and we say de la géométrie (1870), a continuation of the Aperçu; Id., Trailé de that in the first quadrant a point lies above géométrie supérieure (1852); Cremona, Introduzione ad una teoria the horizontal and in front of the vertical
11 geometrica delle curve piane (1862) and its continuation Preliminari plane. Now we go round the axis in the
C, B. di una teoria geometrica delle superficie (German translations by sense in which the plane r is turned and o Curtze). As more elementary books, we mention: Cremona, come in succession to the second, third Elements of Projective Geometry, translated from the Italian by and fourth quadrant.
In the second a C. Leudesdorf (2nd ed., 1894); J. W. Russell,
(2nd ed., point lies above the plane of the plan and 1905).
(O. H.) behind the plane of elevation, and so on.
In fig. 39, which represents a side view of
the planes in fig. 37 the quadrants are
marked, and in each a point with its proThis branch of geometry is concerned with the methods for jection is taken. Fig: 38 shows how these are represented when representing solids and other figures in three dimensions by the plane ra is turned down. We see that drawings in one plane. The most important method is that above the axis; 'in the second if plan and elevation both lie above; in
A point lies in the first quadrant if the plan lies below, the elevation which was invented by Monge towards the end of the 18th the third if the plan lies above, the elevation below; in the fourth if plan century. It is based on parallel projections to a plane by rays and elevation both lie below the axis. perpendicular to the plane. Such a projection is called ortho- If a point lies in the horizontal plane, its elevation lies in the axis graphic (see PROJECTION, $ 18). If the plane is horizontal the and the plan coincides with the point itself. If a point lies in the projection is called the plan of the figure, and if the plane is with the point itself. If a point lies in the axis, both its plan and
vertical plane, its plan lies in the axis and the elevation coincides vertical the elevation. In Monge's method a figure is represented elevation lie in the axis and coincide with it. by its plan and elevation. It is therefore often called drawing of each of these propositions, which will easily be seen to be true, in plan and elevation, and sometimes simply orthographic the converse holds also. projection.
63. Representation of a Plane. -As we are thus enabled to represent $ 1. We suppose then that we have two planes, one horizontal, points in a plane, we can represent any finite figure by representing the other vertical, and these we call the planes of plan and of eleva; in this way, for the projections of its points
completely cover the
its separate points. It is, however, not possible to represent a plane tion respectively, or the horizontal and the vertical plane, and planes - and is, and no plane would appear different from any other. denote them by the letters and 72. Their line of intersection is
But called the axis, and will be denoted by ry.
any plane a cuts each of the planes #1, #, in a line. These are If the surface of the drawing, paper is taken as the plane of the point where the latter cuts the plane a.
called the traces of the plane. They cut each other in the axis at the plan, then the vertical plane will be the plane perpendicular to it through the axis xy. To bring this also into the plane of the drawing on the axis, and, conversely, any two lines which meet on the axis
A plane is determined by its two traces, which are two lines that meet paper we turn it about the axis till it coincides with the horizontal
determine a plane. plane. This process of turning one plane down till it coincides with
If the plane is parallel to the axis its traces are parallel to the axis. another is called rabatting one to the other. Of course there is no necessity to have one of the two planes horizontal, but even when planes of projection at infinity and will be parallel to it. Thus a
of these one may be at infinity; then the plane will cut one of the The whole arrangement will be better understood by referring to plane parallel to the horizontal plane of the plan has only one finite fig. 37. A point A in space is there projected by the
perpendicular trace, viz, that
with the plane ol elevation. If the plane passes through the axis both ils traces coincide with the axis. This is the only case in which the representation of the plane by its two traces fails. A third plane of projection is therefore introduced, which is best taken perpendicular to the other two. We call it simply the third plane and denote it by me As it is perpendicular to *, it may be taken as the plane of elevation, its line of intersection y with a being the axis, and be turned down to coincide with n. This is represented in fig. 40. OC is the axis 'wy whilst OX and OB are the traces of the third plane. They lie in one line y. The plane
is rabatted about to the hori. FIG. 38.
zontal plane. A plane a through
the axis xy will then show in it AA, and AA, to the planes m and az so that A, and Az are the a trace as. In fig. 40 the lines OC
, horizontal and vertical projections of A.
and OP will thus be the traces If we remember that a line is perpendicular to a plane that is of a plane through the axis xy, perpendicular to every line in the plane is only it is perpendicular which makes an angle POQ with to any two intersecting lines in the plane, we see that the axis which the horizontal plane. is perpendicular both to AA, and to AA, is also perpendicular to We can also find the trace A, A. and to A,A, because
these four lines are all in the same plane. which any other plane makes Hence, if the plane a, be turned about the axis till it coincides with with 13. In rabatting the plane .... the plane a, then A2A, will be the continuation of A, A. This to its trace OB with the plane 17 will come to the position OD. position of the planes is represented in fig. 38, in which the line AA: Hence a plane B having the traces CA and CB will have with the is perpendicular to the axis x.
third plane the trace Bs, or AD if OD=OB
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662533972.17/warc/CC-MAIN-20220520160139-20220520190139-00077.warc.gz
|
CC-MAIN-2022-21
| 47,077 | 166 |
https://apkelite.com/scientific-calculator-complex-number-calculator-v1-3-2-paid-apk/
|
math
|
Scientific Calculator | Complex Number Calculator v1.3.2 (Paid) APK
Use this complex number calculator as a scientific calculator. Any operation or function evaluation you can do with real numbers, you can also do the same with complex numbers by using this scientific calculator. Namely, calculate expressions containing real, imaginary and, in general, any complex number in any form including, but not limited to, the standard (rectangular) and polar forms.
You can enter complex numbers in the standard (rectangular) or in the polar form. The calculated values will be displayed in standard form; optionally, this scientific calculator displays the results in the polar form and other modular forms.
With a unique intuitive user interface this scientific calculator, being a comprehensive complex number calculator, computes arbitrary complicated complex number expressions with exceptional ease and converts complex numbers to polar form.
• Supports all standard mathematical functions with real, imaginary and complex numbers as their arguments including trigonometric, exponential, logarithmic, hyperbolic and inverse trig/hyperbolic functions plus the Gamma function, Γ, Psi function, Ψ and zeta function, ζ.
Swipe the number pad to the right to see more functions (trig, hyperbolic, inverses, etc.).
• Calculate expressions containing complex numbers in standard form a+bi and polar (phasor) form r∠(θ).
• Convert complex numbers from rectangular to polar and other modular forms and vice versa (long press i or ∠ to see all forms of the calculated result).
• RAD and DEG mode.
In addition to evaluating trig and related functions, this scientific complex number calculator allows the angle of polar form of complex numbers to be entered in radians or degrees.
• Fixed, scientific and engineering notations.
This scientific calculator also let you do statistics with one or two dimensional real data:
• x1, x2 ,x3, … .
• Press Σ to calculate sum, mean, max, min, variance, sample and standard deviation, median, upper and lower quartile, etc.
• x1, y1; x2, y2; x3, y3; … .
• Press Σ to calculate the equation of the linear regression line and graph it.
• Long press ! to calculate combinations C(n, r) and permutations P(n, r).
• Enter functions f(x) or parametric equations p(t) and generate table of values.
• Physical/Chemical/Atomic and other scientific constants.
• Easy to use unit converter (Time, Mass, Length, Velocity, and many more).
All of the above with more details are included in the built-in Instruction menu accompanying this scientific complex calculator.
Rating and posting comments for this calculator on Google Play can help adding more features to this app.
User agreement: Please read the terms and conditions of using this app on https://sites.google.com/view/gcalcd/home/user-agreement
User guide is translated into more languages and, to keep the app size at the minimum, can be viewed on the developer web site.
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526799.4/warc/CC-MAIN-20190720235054-20190721021054-00141.warc.gz
|
CC-MAIN-2019-30
| 2,988 | 24 |
http://forum.roulette30.com/index.php?topic=836.0
|
math
|
Double Doz and Cols has a expected hit rate larger than an EC. We will win most of the spins. 2/3 bet is a grinding, and has some problems which many players do not take care about. A losing streak can be rather long even if 2/3 of the table is covered. I should not play 2/3 on an American Wheel. If we get back half the bet on an EC if zero hits, it is better play EC.
On a Wheel with NO zero or just one zero, a 2/3 bets should work just fine.
A common progresson is a Martingale style using 3 fold each step, and it is for sure a catastrophic situation to expect in short time.
As we hit most of the bets, we DO NOT need winning all back in one spin.
I did this morning a 2 Col play using NOZ and 0.1 chip, targeting 100 units (10 Euro). With the right play and not short bank, it is near sure to get it.
The "system" is very conservative it can take some time.
We need a bankroll of 1000 units (300 can do, but better be safe than sorry).
At each DOZ we start with 1 unit, as long we win stay.
If lose first bet next bet is 2 units each.
If we win we are break even, and start over using 1 unit each.
If lose the second bet we use 3 units stay as long we win, But reduce all the time so next win is break even if we are Close to that,
If loss on the third bet we bet the same (3) again and do so to the next loss or break even.
The progression is simple 1 2 3 3 4 4 5 5 6 6 7 7 8 8.....
The game I did took 257 spins, and the turnover was high (1148 units), that's the reason a high HE makes 2/3 bets difficult, as on AM wheel. At NOZ the turnover doesn't matter.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122933.39/warc/CC-MAIN-20170423031202-00296-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 1,568 | 14 |
https://cosmicktraveler.wordpress.com/the-kabbalistic-tree-of-life-explored-intro/2-the-structure-of-the-tree-of-life/
|
math
|
From an old manuscript of Paulus Richius.
This diagram contains ten circles representing the Sephiroth (singular: Sephirah); that is, the “spheres,” “numbers,” or “emanations”. The Sephiroth are the numbers 1 through 10 considered in their archetypal sense. Each Sephirah is an archetypal idea. Also, the Sephiroth represent emanations from God and describe the process of creation. In the material world, they represent the heavenly spheres according to the classical conception.
I always wondered why the Kabalistic Tree of Life has the shape it has. It has an unusual shape; how did the Cabalists decide to use such a shape? One day I discovered that it is drawn in interlocking circles.
Why interlocking circles? Well, they are the product of a mathematical genesis. Let me explain.
First there is the Nothing. The Ain, or Ain-Soph, the great limitless Nothingness of which nothing can be said.
Then a point arises out of the Ain-Soph. God brings forth the immensity of eternal extension. With our limited human understanding we call this “non-existence”. God withdraws himself from himself and creates an emptiness and a place for the Ain-Soph.
The next thing is a circle. It encompasses the entire created emptiness. It is like the extension off the point. From this duality arises. There the point and the circle, the male and the female, the positive and the negative.
Somewhere on the circle we determine a point, that will serve as the center of a new circle. With duality in existence we now can create a duplicate circle. The circle mirrors itself:
This simple act brings forth a lot of interesting things.
The overlapping area is a “Vesica Pisces”, a symbol used in early Christian days for Christ. The almost oval shape is also a universal symbol for the yoni, the female sexual organ used by many cultures for the Great Mother. It is well known in Eastern religions, but Mother Mary in the Catholic Church was also frequently depicted with the same symbol behind or around her.
The Vesica Pisces:
From one point, the center of the first circle, arises four points: the two centers of the two circles plus the two intersection points of the two circles. All four points can be connected to each other and produces the following result:
From unity we went to duality to quaternity. The Four Elements are a quaternity as it is said that they are interrelated, they cannot exist without one another. They come forth out of unity and they dissolve into unity. The Four Elements are the foundation out of which the entire universe is built.
The resulting diamond shape brings forth some interesting things:
The diamond shape is related to the number four and quaternity, but it brings forth the triangle within, and thus trinity, and the cross which produces a fifth point. So we have the numbers 3, 4 and 5, and this is the mathematical expression of the right triangle having 30°, 60° and 90° angles, of which the legs are 3 and 4, and the hypotenuse 5. It is the only triangle of which the hypotenuse will be a whole number when the legs are whole numbers too.
When we call the radius of the circle r, then the following mathematical expressions appear:
Besides the point and the circle, the third geometric structure is the line. And there are three lines of different length.
The radius of the circle is r (the vertical axis of the diamond).
The distance of the center point of the ‘ellipse’ or diamond to the circle is r/2.
The distance of the same center point to the point where the the two circles cross is (r/2)X√3 (radius divided by two and multiplied by the square root of 3). √3 is the first square root to appear.
When measuring the simple distance of the above we obtain (r/2)X√3, or the total length of the long axis of the diamond is rX√3. But when we calculate the relation of the long axis of the diamond to the short axis of the diamond (the cross), we obtain the pure square root of three: rX√3/r = √3.
When we duplicate the circle three more times, we obtain the thirteen points on the circles of which actually ten are attributed to the Sephiroth (sometimes one more for Daath, the ‘hidden’ Sephiroth). One wonders why they left out the two lower ones.
Then I asked myself why was the structure drawn in three complete circles with two half circles (top and bottom). It seemed to be part of something else. Let’s leave the mathematical expressions behind and return to the two circles:
Remember we have four points, two serve as the centers of the two circles, and two on the cross sections of the two circles. Those two cross points seem the be the only likely places that would serve as centers for two more circles:
But this doesn’t look quite symmetrical, and the universe likes symmetry, thus it produces two more circles:
Sometimes also depicted as follows when you fill in the remaining ‘petals’:
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578747424.89/warc/CC-MAIN-20190426013652-20190426035652-00213.warc.gz
|
CC-MAIN-2019-18
| 4,886 | 26 |
http://www.education.com/study-help/article/trigonometry-help-trigonometry-chapter-5/
|
math
|
Trigonometry and Polar Coordinates Practice Test
Review the following concepts if needed:
- The Polar Coordinate Plane Help
- Examples of Polar Coordinates Help
- Compression and Conversion Help
- The Navigator’s Way Help
Polar Coordinates Practice Test
A good score is eight correct.
1. The equal-radius axes in the mathematician’s polar coordinate system are
2. Suppose a point has the coordinates ( θ , r ) = ( π , 3) in the mathematician’s polar scheme. It is implied from this that the angle is
(b) expressed in radians
(c) greater than 360°
3. Suppose a point has the coordinates ( θ , r ) = ( π /4,6) in the mathematician’s polar scheme. What are the coordinates ( α , r ) of the point in the navigator’s polar scheme?
(a) They cannot be determined without more information
(b) (–45°, 6)
(c) (45°, 6)
(d) (135°, 6)
4. Suppose we are given the simple relation g ( x ) = x. In Cartesian coordinates, this has the graph y = x. What is the equation that represents the graph of this relation in the mathematician’s polar coordinate system?
(a) r = θ
(b) r = 1/θ, where θ ≠ 0°
(c) θ = 45°, where r can range over the entire set of real numbers
(d) θ = 45°, where r can range over the set of non-negative real numbers
5. Suppose we set off on a bearing of 135° in the navigator’s polar coordinate system. We stay on a straight course. If the starting point is considered the origin, what is the graph of our path in Cartesian coordinates?
(a) y = x, where x ≥ 0
(b) y = 0, where x ≥ 0
(c) x = 0, where y ≥ 0
(d) y = – x , where x ≥ 0
6. The direction angle in the navigator’s polar coordinate system is measured
(a) in a clockwise sense
(b) in a counterclockwise sense
(c) in either sense
(d) only in radians
7. The graph of r = –3θ in the mathematician’s polar coordinate system looks like
(a) a circle
(b) a cardioid
(c) a spiral
(d) nothing; it is undefined
8. A function in polar coordinates
(a) is always a function in rectangular coordinates
(b) is sometimes a function in rectangular coordinates
(c) is never a function in rectangular coordinates
(d) cannot have a graph that is a straight line
9. Suppose we are given a point and told that its Cartesian coordinate is ( x , y ) = (0, –5). In the mathematician’s polar scheme, the coordinates of this point are
(a) ( θ , r ) = (3π/2, 5)
(b) ( θ , r ) = (3π/2, –5)
(c) ( θ , r ) = (–5, 3π/2)
(d) ambiguous; we need more information to specify them
10. Suppose a radar unit shows a target that is 10 kilometers away in a southwesterly direction. It is moving directly away from us. When its distance has doubled to 20 kilometers, what has happened to the x and y coordinates of the target in Cartesian coordinates? Assume we are located at the origin.
(a) They have both doubled
(b) They have both increased by a factor equal to the square root of 2
(c) They have both quadrupled
(d) We need to specify the size of each unit in the Cartesian coordinate system in order to answer this question
Add your own comment
Today on Education.com
SUMMER LEARNINGJune Workbooks Are Here!
TECHNOLOGYAre Cell Phones Dangerous for Kids?
- Kindergarten Sight Words List
- The Five Warning Signs of Asperger's Syndrome
- First Grade Sight Words List
- 10 Fun Activities for Children with Autism
- Graduation Inspiration: Top 10 Graduation Quotes
- What Makes a School Effective?
- Child Development Theories
- Should Your Child Be Held Back a Grade? Know Your Rights
- Why is Play Important? Social and Emotional Development, Physical Development, Creative Development
- Smart Parenting During and After Divorce: Introducing Your Child to Your New Partner
|
s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368709101476/warc/CC-MAIN-20130516125821-00055-ip-10-60-113-184.ec2.internal.warc.gz
|
CC-MAIN-2013-20
| 3,662 | 66 |
https://www.hackmath.net/en/examples/8th-grade-(13y)?page_num=38
|
math
|
Examples for 8th grade - page 38
How many liters of water per second can go via trough, which has a cross section of semicircle with radius 2.5 m and speed of water is 74 cm per second?
- Square and circle
Into square is inscribed circle with diameter 10 cm.What is difference between circumference square and circle?
The length of the bases trapezium are in ratio 2:1. Length of midline is 17. How long are the bases of a trapezoid?
Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 6.1 meters and an angle opposite to the base size is 93°. What is the distance from the base to opposite vertex?
Most how many cubes with an edge length of 5 cm may fit in the cube with the inner edge of 0.4 m?
Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed
Coffee from the machine in the cup cost 25 cents. Coffee is 20 cents more expensive than the cup. How much is the cup?
Jarek bought new trousers, but the trousers were too long. Their length was in the ratio 5: 8 to Jarek height. Mother his trousers cut by 4 cm, thus the original ratio decreased by 4%. Determine Jarek's high.
Rectangle ABCD has dimensions of 9 cm and 6 cm. Rectangle PQRS has dimensions 7 cm and 8 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity.
What distance will describe the tip of minute hand 6 cm long for 20 minutes when we know the starting position with finally enclose hands each other 120°?
- Eight blocks
Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
- Trrops - soldiers
Food stocks will last 20 soldiers of the 4-day training. How many days they could extend training if four soldiers become sick?
Mr. Johnson's had monthly salary 966 USD since the beginning of year. From which month his salary was increased by 74 USD, when in year earned 11814 USD (enter as a number from 1 to 12)?
- BW-BS balls
Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8 What is the ratio of.
Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes?
Base of building is circle with diameter 39 m. Calculate the circumference of a circular trench witch diameter is 21 cm wider than the diameter of the base.
What is the slope of the line defined by the equation -4x -2y = -7 ?
- Secret number
Determine the secret number n, which reversed decrease by 8.6 if the number increase by 8.6.
- Shadow and light
Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948599156.77/warc/CC-MAIN-20171217230057-20171218012057-00704.warc.gz
|
CC-MAIN-2017-51
| 3,316 | 27 |
https://www.jiskha.com/display.cgi?id=1436540211
|
math
|
prob & stat
posted by jay
An academic department with five faculty members—Anderson, Box, Cox, Cramer, and Fisher—must select two of its members to serve on a personnel review committee. Because the work will be time-consuming, no one is anxious to serve, so it is decided that the representative will be selected by putting the names on identical pieces of paper and then randomly selecting two.
(a) What is the probability that both Anderson and Box will be selected?
answer 0.1 or 1/10
(b) What is the probability that at least one of the two members whose name begins with C is selected?
answer 0.7 or 7/10
(c) If the five faculty members have taught for 3, 6, 7, 10, and 14 years, respectively, at the university, what is the probability that the two chosen representatives have a total of at least 14 years teaching experience there?
I need answer for C? Don't understand.
6, 10 or 6, 14
7, 10 or 7, 14
It looks like there are 6 possibilities that meet this criteria because they all add up to at least 14 which means 14 or more years
If we choose two out of 5
Use a combination of 2 chosen from 5 which is 5!/(3! 2!) = 10 choices
! means multiply down to 1. So, 5! means 5 x 4 x 3 x 2 x1.
You had 6 possibilities out of 10 choices or .6
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865651.2/warc/CC-MAIN-20180523121803-20180523141803-00030.warc.gz
|
CC-MAIN-2018-22
| 1,247 | 16 |
https://www.york.cuny.edu/~malk/mycourses/liberalstudies400/notes5.html
|
math
|
Fairness and Equity: Notes 5
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York 11451
In light of the fact that fairness and equity problems are very complex, we will need to look at these issues from a variety of perspectives before we can actually "wade in" and try solving (resolving) specific equity problems. (Remember the parable of trying to describe an elephant to a blind person; an accurate description of the leg, of the ear, and the trunk of the elephant may not easily enable one to get a good idea of what an elephant really looks like.)
Consider, as an example, the issue of what to do as part of a divorce settlement between Mary and John to "divide" a house that they own jointly. Suppose we know no other information about Mary and John. How might we solve this question?
a. Sell the house and divide up what is gotten from the sale.
b. Both Mary and John move out and they rent the house and share the
c. The house is divided into two apartments and each gets one of the two apartments.
d. A fair coin is flipped and one of them gets the house and the other gets nothing.
e. Mary uses the house from Jan. 1 to June 30 and the John uses the house from June 30 to Dec. 31. The following year they reverse the pattern of usage.
Note: If the house is not a "primary" dwelling but a "summer home," then a time sharing arrangement to use the house in alternating summers might work. Mary and John could share rent income if the summer home could be rented the rest of the time.
Note that the flipping the coin approach is a fair procedure in that each party has an equal chance of getting the house (if a fair coin is used) but the outcome is certainly not "equal." It is often important to distinguish between fair procedures and fair outcomes. Use of randomization is often done in sports as a fairness mechanism. A coin is flipped in football to see which team is to receive and which is to punt.
There is also the issue of what is called an information set. In this case, we pretended not to know much about the circumstances of John and Mary, but having more information will almost always alter the way we go about solving the equity problem.
For example, here is potentially useful additional information:
a. John and Mary earn the same income.
b. John comes from a wealthy family and shortly expects to inherit a lot of money.
c. Mary had more money in the bank at the time of the marriage and contributed more to the down payment of the house than John did.
d. John and Mary have no children.
(What additional complications arise if they do have children?)
A house is an example of something that can not be divided into two parts and retain its value. On the other hand, a chocolate bar could be so divided. It is convenient to have a taxonomy of how to classify fairness problems. We can distinguish between objects that are divisible and indivisible. Water and land are divisible. We can also distinguish between homogeneous objects and unhomogeneous ones. Water is homogeneous and divisible. A house is unhomogeneous and indivisible.
Comment: Money is not strictly speaking divisible because there is a smallest unit of currency. In America, it is the penny. Years ago in England the British pound was divided into 240 parts. Thus, the smallest price increase could be quite small. After the currency was decimalized the smallest part was 1/100 of a pound. The smallest price increase became much larger, contributing to inflation. The US is one of the few countries in the world that does not use the metric system. Recently we decimalized stock prices, so whereas in the past stocks went up or down 1/8, now they can go up or down a penny. This changes the nature of the market for stocks in a subtle way.
Here is another example, to illustrate some of the issues involved with how our view of solving equity questions changes with the information set available.
Two communities I and II have been collectively allocated $1,000,000 for public transportation?
How much should each community get?
Now suppose you are told the additional information shown below one fact at a time:
Population 230,000; Population 70,000
Per capita income $40,000; Per capita income $90,000
Area: 6 square miles; Area: 200 square miles
Public bus system; No public transportation
What other information might you want to collect in order to help you decide how to allocate the money?
1. Suppose two people solve a fairness problem. How can one decide which of the two solutions is better?
2. Do people always assign the same value to the same things?
3. Do people always assign the same value to money?
Example: If your back aches, how large a bill on the ground does it take before you bend over to pick it up?
4. Is it possible that two people think they have been fairly treated because each has 1/2 of a "cake" but there is a different way of dividing the "cake" so that each person feels they have more than 1/2 the "cake?"
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742970.12/warc/CC-MAIN-20181116025123-20181116051123-00317.warc.gz
|
CC-MAIN-2018-47
| 4,969 | 36 |
http://web-catalogue.info/75777-solving-math-word-problems.html
|
math
|
Suggestions: Read the problem entirely, get a feel for the whole problem. 8 y, express the number (x) of apples increased by two x 2, express the total weight of, alphie the dog (x) and Cyrus the cat (y). 20 x - 6) What is 9 more than y?
"Mixture" problems, involving combining elements and find prices (of the mixure) or percentages (of, say, acid or salt).
"Number" problems, involving "Three more than two times the smaller number." "Percent of" problems, involving finding percents, increase/decrease, discounts, etc.
As you enter your math problems, the solver will show you the Math Format automatically to make sure you have effectively entered the math problem you really want it to solve You can also enter word problems, but don't be too fancy.
Usually, once you get the math equation, you're fine; the actual math involved is often fairly simple.
Solving Math Word Problems: explanation and exercises Free Math Problem Solver - Basic mathematics Translating Word Problems: Keywords Purplemath Word Problem Answers Wyzant Resources Algebra Word Problem Solvers
2000 word english essay on being on time, Essay on microsoft word 2010,
Usually, once you get the math equation, you're fine; the actual math involved is often fairly simple. For instance, suppose you're not sure if "half of (the unknown amount should be represented by multiplying by one-half, or by dividing by one-half. If you use numbers, you can be sure. Below is a partial list. Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376828318.79/warc/CC-MAIN-20181217042727-20181217064727-00432.warc.gz
|
CC-MAIN-2018-51
| 1,587 | 8 |
https://thetextchemistry.org/qa/what-does-a-1-solution-mean.html
|
math
|
- How do you calculate a dilution?
- How do you make a 1 100 dilution?
- What is the meaning of 15% solution of NaCl?
- What is a 5% dilution?
- How many mg is a 1% solution?
- How do I make a 1% NaCl solution?
- How do you make a 10% solution?
- How do I calculate the concentration of a solution?
- How will you prepare a 10% solution of sugar?
- How do you make a 1/20 dilution?
- How do you make a 10% solution of NaCl?
- What does a 2% solution mean?
- How do you make a 10% solution of glucose?
- How do you make a 5% solution of NaCl?
- How do you make a 1% solution?
- What does a 20% solution mean?
How do you calculate a dilution?
To make a fixed amount of a dilute solution from a stock solution, you can use the formula: C1V1 = C2V2 where: V1 = Volume of stock solution needed to make the new solution.
C1 = Concentration of stock solution.
V2 = Final volume of new solution..
How do you make a 1 100 dilution?
For a 1:100 dilution, one part of the solution is mixed with 99 parts new solvent. Mixing 100 µL of a stock solution with 900 µL of water makes a 1:10 dilution. The final volume of the diluted sample is 1000 µL (1 mL), and the concentration is 1/10 that of the original solution.
What is the meaning of 15% solution of NaCl?
It just means that in the aqueous Nacl solution (Nacl dissolved in water) ,each 100 grams of the solution contains 15 grams of Nacl in it .
What is a 5% dilution?
Dilution factor is a notation often used in commercial assays. For example, in a 1:5 dilution, with a 1:5 dilution factor, (verbalize as “1 to 5” dilution) entails combining 1 unit volume of solute (the material to be diluted) with (approximately) 4 unit volumes of the solvent to give 5 units of total volume.
How many mg is a 1% solution?
One gram or ml of drug in 99 ml of diluent will yield a 1% solution. Therefore, 1 ml of a 1% solution contains . 01 gm (10 mg) of the drug.
How do I make a 1% NaCl solution?
We know this by looking at the periodic table. The atomic mass (or weight) of Na is 22.99, the atomic mass of Cl is 35.45, so 22.99 + 35.45 = 58.44. If you dissolve 58.44g of NaCl in a final volume of 1 liter, you have made a 1M NaCl solution, a 1 molar solution.
How do you make a 10% solution?
We can make 10 percent solution by volume or by mass. A 10% of NaCl solution by mass has ten grams of sodium chloride dissolved in 100 ml of solution. Weigh 10g of sodium chloride. Pour it into a graduated cylinder or volumetric flask containing about 80ml of water.
How do I calculate the concentration of a solution?
Divide the mass of the solute by the total volume of the solution. Write out the equation C = m/V, where m is the mass of the solute and V is the total volume of the solution. Plug in the values you found for the mass and volume, and divide them to find the concentration of your solution.
How will you prepare a 10% solution of sugar?
Answer. Dissolve 10 grams sugar in 80 ml water. After the sugar is completely dissolved, adjust the volume to 100 ml. 10% sugar and 90% water by mass.
How do you make a 1/20 dilution?
Convert the dilution factor to a fraction with the first number as the numerator and the second number as the denominator. For example, a 1:20 dilution converts to a 1/20 dilution factor. Multiply the final desired volume by the dilution factor to determine the needed volume of the stock solution.
How do you make a 10% solution of NaCl?
To prepare a 10%(w/w) NaCl solution, mass out 10 g NaCl and place it in a 100-mL volumetric flask. Add about 80 mL of water to the flask. Once the NaCl has dissolved, add more water up to the 100-mL mark. If you don’t have a volumetric flask, you can use a 100-mL graduated cylinder, but it won’t be as accurate.
What does a 2% solution mean?
2% w / w solution means grams of solute is dissolved in 100 grams of solution. Weight / volume % 4% w / v solution means 4 grams of solute is dissolved in 100 ml of solution. Volume / weight % 3% v/ w solution means 3 ml of solute is dissolved in 100 grams of solution.
How do you make a 10% solution of glucose?
To prepare a 10% glucose solution, mass out 10 g glucose (solute), and add enough water (solvent) to make a 100 mL solution.
How do you make a 5% solution of NaCl?
To prepare a 5 M solution: Dissolve 292 g of NaCl in 800 mL of H2O. Adjust the volume to 1 L with H2O. Dispense into aliquots and sterilize by autoclaving.
How do you make a 1% solution?
The mass of a solute that is needed in order to make a 1% solution is 1% of the mass of pure water of the desired final volume. Examples of 100% solutions are 1000 grams in 1000 milliliters or 1 gram in 1 milliliter.
What does a 20% solution mean?
20% by mass means 20 g of the NaOH is dissolved in 100 g of solution. … 20% mass by volume means 20 g of the NaOH is dissolved in 100 mL of the solution.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704847953.98/warc/CC-MAIN-20210128134124-20210128164124-00239.warc.gz
|
CC-MAIN-2021-04
| 4,821 | 50 |
http://www.math-shortcut-tricks.com/square-properties/
|
math
|
Square shortcut tricks are very important thing to know for your exams. Competitive exams are all about time. If you know time management then everything will be easier for you. Most of us miss this thing. Here in this page we give few examples on Square shortcut tricks. These shortcut tricks cover all sorts of tricks on Square. Visitors are requested to carefully read all shortcut examples. You can understand shortcut tricks on Square by these examples.
Before doing anything we recommend you to do a math practice set. Then find out twenty math problems related to this topic and write those on a paper. Do first ten maths using basic formula of this math topic. You also need to keep track of Timing. Write down the time taken by you to solve those questions. Now practice our shortcut tricks on square and read examples carefully. After doing this go back to the remaining ten questions and solve those using shortcut methods. Again keep track of timing. This time you will surely see improvement in your timing. But this is not all you want. You need more practice to improve your timing more.
You all know that math portion is very much important in competitive exams. That doesn’t mean that other topics are less important. But only math portion can leads you to a good score. You can get good score only by practicing more and more. All you need to do is to do math problems correctly within time, and only shortcut tricks can give you that success. But it doesn’t mean that you can’t do math problems without using any shortcut tricks. You may do math problems within time without using any shortcut tricks. You may have that potential. But so many other people may not do the same. So Square shortcut tricks here for those people. We always try to put all shortcut methods of the given topic. But we may miss few of them. If you know anything else rather than this please do share with us. Your help will help others.
What is square?
In a geometry, Square is a regular quadrilateral and This means that it has four equal sides and four equal angles Each angle is holds 90-degree angles, or right angles of each facing side is equal to the opposite side and the square properties are follows.
In maths exam papers there are two or three question are given from this chapter. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under below given some more example for your better practice.
The two adjacent sides have equal length of Rectangle.
If the length of a rectangle as L of each side then,
a : Area of Square = 4L2 or ( side )2 = 1 / 2 = ( Diagonal ) 2.
The area can also be calculated using the diagonal d according to
A = D2 / 2
Perimeter of a Square = 4L or 4 x Side .
The circumference R, the area of a square is
A = 2R2
b : A room has four wall and its Area of 4 wall is 2 x ( Length + Breadth ) x Height.
c : Area of parallelogram = ( Base x Height ).
d : Area of a rhombus = 1 / 2 x ( product of diagonals ).
Example 1: The area of rectangle is 720 cm2, That is 80% of the area of a square. Find perimeter of the square ?
Answer : 80% of the area of a square is 100 x 720 / 80 = 900cm2.
Side of square is =√900 = 30cm.
Perimeter of square is = 30 x 4 = 120 cm.
Example 2: The area of square is fourth the area of a rectangle.If the area of the square is 256 sq.cms and the length of the rectangle is 16 cms, What is the difference between the breadth of the rectangle and the side of the square ?
Answer : Area of square = 256 sq.cms
Side = 16 cms
Area of rectangle = 256 / 4 = 64cm2
l x b = 64
16 x b = 64
b = 4 cm
Difference betweenbreadth of the rectangle and the side of the square = (a – b) = (16 – 4) = 12 cm
Example 3: If the length of the diagonal of a square is 6 mt then what is length of its each side ?
Answer : Side = Diagonal / √2
6 x √2 / √2 x √2 = 3√2.
Example 4 :
The area of a rectangle 18 meters 2 decimeters long and 15 meters 3 decimeters wide. What would be the area of square ?
Length = 18.2 meters.
Breadth = 15.3 meters.
So, the area of square is ( Length x Breadth ) = 18.2 x 15.3 = 278.46 square meters.
In a hall room has the floor which is 30 meters long and 10 meters broad So, How many meters of cotton carpet 75 Cm wide will be required to cover the room of hall and how much amount will require to be spent on cotton carpet if available at Rs 25/- per meters ?
Shortcut tricks :
length required = ( length of room x breadth of room / width of carpet ) = ( 30 x 10 / 75 ) = 400
Amount = rate per meter x ( length of room x breadth of room / width of carpet ) = 25 x ( 30 x 10 / 75 ) = 25 x 400 = 10000.
- Equilateral Triangle Properties
- Any Triangle Properties
- Rectangle Properties
- Parallelogram Properties
- Circle Properties
- Triangle properties
- Miscellaneous Examples
- << Go back to Mensuration Methods Rules main page
If You Have any question regarding this topic then please do comment on below section. You can also send us message on facebook.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948575124.51/warc/CC-MAIN-20171215153355-20171215175355-00574.warc.gz
|
CC-MAIN-2017-51
| 4,994 | 50 |
http://www.ask.com/web?q=What+Shape+Is+a+Sphere%3F&o=2603&l=dir&qsrc=3139&gc=1
|
math
|
A sphere is a perfectly round geometrical object in three-dimensional space that
is the surface ... three-dimensional Euclidean space) and the ball (a three-
dimensional shape that includes the spher...
A sphere is a curved 3D shape that is perfectly round and similar to a ball you ...
of free pictures featuring polygons and polyhedrons of all shapes and sizes, ...
3D shapes for kids are not always easy to teach. They can be difficult to draw and
often have funny names. What makes a 3D shape? Let's look at the sphere.
www.ask.com/youtube?q=What Shape Is a Sphere?&v=XucxjuTjWeQ
Dec 28, 2013 ... DESCRIPTION ------------ Fun children's lesson on the 3D Shape the "Sphere".
What real world objects are spheres? Find out in this video!
Sphere. Go to Surface Area or Volume. Sphere Facts. Notice these interesting
things: ... Of all the shapes, a sphere has the smallest surface area for a volume.
A ball is spherical; it's shaped like a sphere — a three-dimensional version of the
A cone has one circular base and a vertex that is not on the base. The sphere is a
space figure having all its points an equal distance from the center point.
In other words, when something needs to be as small as possible but still have a
large volume, it takes the shape of a sphere. That is why a balloon is round ...
Shape diagrams and formulas for geometric solids including capsule, cone,
conical frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, sphere.
A sphere will have a surface. We can imagine the Earth as being similar to the
general shape of a sphere; it has a surface area and we know that we can go ...
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720760.76/warc/CC-MAIN-20161020183840-00505-ip-10-171-6-4.ec2.internal.warc.gz
|
CC-MAIN-2016-44
| 1,620 | 21 |
https://casaplorer.com/roofing-calculator
|
math
|
Roofing CalculatorCASAPLORERTrusted & Transparent
This roofing calculator can help you estimate the area of your roof and find out how much materials you would need to construct a roof of your chosen parameters. The calculator also allows you to calculate its price based on the square footage.
Roof Area1,649.6 ft²
= 40 ft x 40 ft x 1.031
Total number of roofing squares19
With 2 additional roofing squares needed for a 10% buffer
Understanding the Roofing Calculator Inputs
House Base Area - This is the surface area of the house, the parallel plan with the ground. You can simply calculate the base area of your house if it has a rectangular shape. However, for more complex shapes, you would either have to calculate each part of the shape individually or know what the area is priorly. If your house has a complex shape, the calculator would give more accurate results if you separate it into parts and calculate each part on its own.
Roof Pitch - The roof pitch is measured as a ratio of the vertical rise of the house over its horizontal run. In the U.S., this ratio is shown as the number of inches of vertical house for every 12 inches of horizontal run. For example, if the roof pitch is 5/12, this means that the roof rises 5 inches for every 12 horizontal inches.
Price - The calculator allows you to input the estimated price per square foot of constructing the roof in order to find out how much would be needed in total to cover the whole roof’s surface area.
How to estimate the size of a roof?
In order to understand how the calculator works, we will go over a step-by-step example on how to estimate the size of your roof. It is important to note that if you are building a concrete roof, you may need to use a concrete calculator to estimate the amount of concrete needed for the roof.
Step 1 - Find the area of the base of the roof
The first thing you will want to do is calculate the area of the roof as if it was flat and parallel to the ground. This means that you will need the length and width of the roof. As mentioned earlier, depending on the shape of your house, this can be a simple multiplication, length times width, or a more complex one.
Imagine that the length of the roof is 15 meters and the width is 12 meters. The area of the base of the roof would in turn be 15 multiplied by 12, or 180 square meters.
Step 2 - Find the total roof area by using roof pitch
Imagine that the roof has a pitch 8/12. As explained earlier, this means that for every 12 horizontal inches, the rise is 7 inches vertically. It also shows the slope of the roof measured in degrees. To make it simpler for us to find the area by using roof pitch, we will use the multipliers for the specific roof pitch. A table of these multipliers and angles is given below:
The corresponding multiplier of the ratio will be multiplied by the base area of the roof. In our example, the multiplier for a roof pitch 8/12 is 1.202. That means that the roof surface area is 1.202 * 180 = 216.36 square meters.
How to estimate the roofing materials needed?
To estimate the roofing materials needed, we will use the U.S. standards, which can be summarized as follows:
- One bundle of shingles covers ~ 33 ft2
- Rolls of roof roofing are 36 inches wide and 36 feet long ~ 108 ft2
- Rolls of #15 felt are 36 inches wide and 144 feet long ~ 432 ft2
- Rolls of #30 felt are 36 inches wide and 72 feet long ~ 216 ft2
For example, for a roof of 230 square footage, one would need:
- 7 bundles of shingles
- 3 rolls of roll roofing
- 1 roll of #15 felt
- 2 rolls of #30 felt
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100016.39/warc/CC-MAIN-20231128214805-20231129004805-00697.warc.gz
|
CC-MAIN-2023-50
| 3,562 | 29 |
http://meshingwithgears.com/wwwboard/messages/4376.html
|
math
|
Posted by Ron V on April 23, 2006 at 20:39:16:
I thought you might be interested in this. I posted this question on another forum and received quite a few interesting replies.
“Would anyone be willing to let me know if below is correct / incorrect? It's based on my understanding of the subject.
Operating P.C.D.s can only be used to calculate center distance for spurs and helicals if the amount of correction given to one member is equally inverse to the amount given to the other, e.g. +0.50 and -0.50. If the corrections are not equally inverse to each other then centers can only be calculated using the difference between the operating pressure angle and the standard/rack pressure angle.”
Post a Followup
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948119.95/warc/CC-MAIN-20180426070605-20180426090605-00598.warc.gz
|
CC-MAIN-2018-17
| 715 | 5 |
https://safesupportivelearning.ed.gov/resources/wk-kellogg-foundation-logic-model-development-guide
|
math
|
Provides an introduction to logic models and walks users through each of the 5 components of a logic model (resources/inputs, activities, outputs, outcomes, and impact). Presents information on different types of logic models (theory model, outcomes model, and activities model) and when to use each type for planning and/or evaluating programs.
W.K. Kellogg Foundation
Year Resource Released
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100529.8/warc/CC-MAIN-20231204115419-20231204145419-00506.warc.gz
|
CC-MAIN-2023-50
| 392 | 3 |
https://www.varsitytutors.com/east_aurora-ny-geometry-tutoring
|
math
|
Recent Tutoring Session Reviews
"The student mentioned last session that she didn't understand the relationship between parabolas and quadratic equations, so for the first half of this session I graphed sample parabolas for her and showed how the use of constants changed the position and shape of the parabola produced by the quadratic and how the standard, factored, and vertex forms of the quadratic equation were interrelated. Then, we worked on sample ACT math problems for the rest of session, as she will be taking that test this Saturday."
"We covered some of the same topics as yesterday: solving quadratic formula, cross multiplication, and rate of change. We covered new topics: graphing functions, system of equations, finding the value algebraically as well as graphically. The student's attitude was mostly positive toward the material. He struggled with some of the algebra."
"Tonight, the student and I worked through the last 30 science problems in the assessment exam practice test. She did a great job using her testing strategies of eliminating incorrect or improbable answers and activating her prior knowledge. She continues to increase her confidence and is more successful academically as a result!"
"Today, the student and I covered different methods of integrating. These included partial fraction decomposition, u-substitution, completing the square, and integration using the natural log function and the inverse tangent function. We had done a couple of examples yesterday using partial fraction decomposition with repeated factors in the denominator. Today, we got to do examples using partial fraction decomposition with quadratic factors in the denominator and distinct linear factors in the denominator. As with yesterday's examples, I made sure to write out each step clearly so that he could see each problem worked out step-by-step and ask questions if needed. He mentioned that the process was starting to become more familiar to him. We were able to finish all of his homework problems tonight that are due tomorrow. We set up another session for this Sunday to work on test corrections from his most recent test."
"We worked on simplifying rational expressions. The problems require factoring expressions first and then simplifying them. We reviewed factoring trinomials. The student gained confidence with most problems. after enough practice. She still needs to work on more challenging problems and writing all steps up."
"The student is learning how to graph line equations and inequalities. He has a good grasp of the process. He has a test coming up on Monday, and should do well."
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171620.77/warc/CC-MAIN-20170219104611-00500-ip-10-171-10-108.ec2.internal.warc.gz
|
CC-MAIN-2017-09
| 2,626 | 7 |
http://amp1037.cbslocal.com/2011/05/16/this-weeks-lite-fm-top-5-3/
|
math
|
Here’s the countdown for the five most-watched Lite FM music videos of the week!
Who’s video will be #1 this week?
Let’s start the countdown
#5) King Of Anything by Sara Bareilles
#4) Jar Of Hearts by Christina Perri
#3) Back To December by Taylor Swift
#2) Breakeven by The Script
#1) Marry Me by Train
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818690211.67/warc/CC-MAIN-20170924205308-20170924225308-00076.warc.gz
|
CC-MAIN-2017-39
| 309 | 8 |
http://www.jiskha.com/display.cgi?id=1325942434
|
math
|
posted by luckybee on .
A sudent is analyzing data from an experiment using a linear model. when the student entered the data into his calculator and ran a least squares linear regression the calculator gave a correlation coefficient of 0.01. what can the student infer from this coefficient?
1. the slope of the linear model is 0.01
2. the y-intercept of the linear model is 0.01
3. the x-intercept of the linear model is 0.01
4. the linear model is not a good fit
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320057.96/warc/CC-MAIN-20170623114917-20170623134917-00043.warc.gz
|
CC-MAIN-2017-26
| 465 | 6 |
http://hermeneutics.stackexchange.com/questions/tagged/gospels+torah
|
math
|
Biblical Hermeneutics Meta
to customize your list.
more stack exchange communities
Start here for a quick overview of the site
Detailed answers to any questions you might have
Discuss the workings and policies of this site
What is the connection between manna and living on the Word of God?
In Deuteronomy 8, Moses gives the theology of manna: And he humbled you and let you hunger and fed you with manna, which you did not know, nor did your fathers know, that he might make you know ...
Jul 1 '12 at 21:28
newest gospels torah questions feed
Hot Network Questions
Determine if Strings are equal
What are some practical tips to easily change tunings on stage?
"Whatever doesn't kill you, simply makes you stranger" - what does it mean?
Trolling the troll
BBWC: in theory a good idea but has one ever saved your data?
What's the difference between "==" and "=~"?
How to structure a trigger
Should I learn to use LaTex to write up a History Masters Thesis?
Why would spacetime curvature cause gravity?
Return the top 5 of each kind of record
Why are commerical flights not equipped with parachutes?
What's the book by Heinlein that contains all other books?
Infinitely many finitely generated groups having the same Cayley graph
Language problems at the airport?
Count number of each char in a String
Flammable or Inflammable
Alternative ways to say "I cannot answer that question"?
How to calcuate the sum of 1/x, where x is an integer not containing the digit 9 and 10,000,000 ≤ x ≤ 88,888,888
CSS transformed object position fix
What are the Dark Souls loading screen hints?
What is a term for someone who has never left their home region?
Message ALL users before shutdown
How to explain bandwidth of a measurement to a noob?
more hot questions
Life / Arts
Culture / Recreation
TeX - LaTeX
Unix & Linux
Ask Different (Apple)
Geographic Information Systems
Science Fiction & Fantasy
Seasoned Advice (cooking)
Personal Finance & Money
English Language & Usage
Mi Yodeya (Judaism)
Cross Validated (stats)
Theoretical Computer Science
Meta Stack Overflow
Stack Overflow Careers
site design / logo © 2014 stack exchange inc; user contributions licensed under
cc by-sa 3.0
|
s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678677569/warc/CC-MAIN-20140313024437-00021-ip-10-183-142-35.ec2.internal.warc.gz
|
CC-MAIN-2014-10
| 2,174 | 52 |
https://www.statisticshowto.com/leading-coefficient-definition-test/#math
|
math
|
Contents (Click to skip to that section):
- Coefficients in General Math and Calculus
- Leading Coefficient & Test
- Specialized Coefficients
1. Coefficients in General Math and Calculus
Coefficients are numbers or letters used to multiply a variable. A variable is defined as a symbol (like x or y) that can be used to represent any number. In a function, the coefficient is located next to and in front of the variable. Single numbers, variables or the product of a number and a variable are called terms.
3x – 1xy + 2.3 + y
In the function above the first two coefficients are 3 and 1. Notice that 3 is next to and in front of variable x, while 1 is next to and in front of xy.
The third coefficient is 2.3. This is called a constant coefficient since its value will not change since it is not being multiplied by a variable. Simply defined, a constant is a term without a variable.
The fourth term (y) doesn’t have a coefficient. In these cases, the coefficient is considered to be 1 since multiplying by 1 wouldn’t change the term.
Like terms are terms that have the same variable raised to the same power. The function above doesn’t have any like terms, since the terms are 3x, 1xy, 2.3 and y and they all have different variables.
Example of Like Terms
2xy2 + 3xy2 – 5xy2
Notice that the coefficients (2, 3 and 5) are all different values. However, the function contains like terms since the variable (xy) for each term are raised to the second power.
Above we defined coefficients as being either numbers or letters. You may come across a function with no numerical value in the coefficient spot. Just treat the letter located in front of and next to the variable as the coefficient. For example:
ax + bx + c
In the function above a and b are coefficients while x is a variable. The third term (c) does not have a coefficient so the coefficient is considered to be 1.
5 x4+ 567 x2 + 24,
The coefficients are:
- 5, which acts on the x4 term.
- 567, which acts on the x2.
What about 24? It acts on a special, invisible term; the x0 term. Since any number to the 0th power is always 1, it’s normally condensed down to 1—or, when written with the coefficient, skipped altogether. The coefficient of the x0 is the constant coefficient.
x5 + 21 x 3 + 6 x 5
The coefficients are:
The fact that no number is written in front of x5 tells us immediately that the coefficient is the identity coefficient, the one number that leaves identical whatever it multiplies.
24 x 8 + 56 7 + 22
The coefficients are:
The leading coefficient is the coefficient of the highest-order term; the term in which our variable is raised to the highest power. In this case, that is x 8, so the leading coefficient is 24.
A coefficient can’t include the variables it acts upon, but it isn’t always a constant either. When it’s not a constant, the variables it includes are called parameters. In the equation y x4 + 4y x2 + 3 x2 + 4 x the coefficients are y, 4y + 3, and 4.
In a polynomial function, the leading coefficient (LC) is in the term with the highest power of x (called the leading term). As polynomials are usually written in decreasing order of powers of x, the LC will be the first coefficient in the first term.
Leading Coefficient Test
You have four options:
1. Odd Degree, Positive Leading Coefficient
The graph drops to the left and rises to the right:
2. Odd Degree, Negative LC
The graph rises on the left and drops to the right:
3. Even Degree, Positive Leading Coefficient
The graph rises on both ends:
4. Even Degree, Negative LC
The graph drops on both ends:
Note that the test only tells you what’s happening at the ends of the graphs; It says nothing about what’s going on in the middle (which is largely determined by the polynomial’s degree). The dashed line in the examples indicate that the shape there is not determined by this particular test.
The above graph shows two functions (graphed with Desmos.com):
- -3x3 + 4x = negative LC, odd degree. The graph rises on the left and drops to the right.
- 4x2 + 4 = positive LC, even degree. The graph rises on both sides.
The term “coefficient” is used in dozens of different ways in other fields. For example, in statistics, correlation coefficients tell us whether two sets of data are connected. They are also measures of reliability (e.g. two judges agreeing on a certain ranking) and agreement (the stability or consistency of test scores).
These tell us whether two sets of data are connected:
- The Pearson’s correlation coefficient(r) tells us the degree of correlation between two variables. It is probably the most widely used correlation coefficient.
- The Spearman rank correlation coefficient is the nonparametric version of the Pearson correlation coefficient.
- The point biserial correlation coefficient is another special case of Pearson’s correlation coefficient. It measures the relationship between one continuous variable and one naturally binary variable.
- The validity coefficient tells you how strong or weak your experiment results are.
- Moran’s I measures how one object is similar to others surrounding it.
- The coefficient alpha (Cronbach’s alpha) is a way to measure reliability, or internal consistency of a psychometric instrument.
- The intraclass correlation coefficient measures the reliability of ratings or measurements for clusters — data that has been collected as groups or sorted into groups.
- Test-Retest reliability coefficients measure test consistency — the reliability of a test measured over time.
Coefficients that measure agreement
Coefficients that measure agreement (e.g. two judges agreeing on a certain ranking) include:
- The polychoric correlation coefficient measures agreement between multiple raters for ordinal variables.
- The tetrachoric correlation coefficient is used to measure agreement for binary variables.
- The coefficient of concordance is used to assess agreement between different raters.
Other types of coefficients:
- The coefficient of variation tells us how data points are dispersed around the mean.
- The gamma coefficient tells us how closely two pairs of data match.
- Pearson’s coefficient of skewness tells us how much and in what direction data is skewed.
- The Jaccard similarity coefficient compares members for two sets to see which members are shared and which are distinct.
- The Durbin Watson coefficient is a measure of autocorrelation (also called serial correlation) in residuals from regression analysis.
- The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.
- The standardized beta coefficient compares the strength of the effect of each individual independent variable to the dependent variable.
- The Phi Coefficient measures the association between two binary variables.
- The Kendall Rank Correlation Coefficient is a non-parametric measure of relationships between columns of ranked data.
- Lin’s concordance correlation coefficient measures bivariate pairs of observations relative to a “gold standard” test or measurement.
- Binomial coefficients tell us how many ways there are to choose 2 things out of larger set.
- Trinomial Coefficient: how many ways to choose 3 from a larger set.
- The multinomial coefficients are used to find permutations when you have repeating values or duplicate items.
- The coefficient of dispersion, which actually has several different definitions; in general, it’s a statistic which measures dispersion.
Crossland, T. Polynomial Functions Terminology. Retrieved Feb 17, 2023 from: http://www.pstcc.edu/facstaff/tlcrossl/PA002_3%20polynomial%20functions.pdf
Gonick, L. The Cartoon Guide to Calculus.
Larson, R. (2011). Calculus with Precalculus. Cengage Learning.
University of Arizona. (2006). Polynomial Functions. Retrieved July 10, 2020 from: http://www.biology.arizona.edu/biomath/tutorials/polynomial/Polynomialbasics.html
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100184.3/warc/CC-MAIN-20231130094531-20231130124531-00490.warc.gz
|
CC-MAIN-2023-50
| 7,955 | 78 |
https://www.teacherspayteachers.com/Product/Eliminate-It-Standards-of-Mathematical-Practice-3-Math-Game-3760846
|
math
|
Are you struggling to find ways to work on the Standards of Mathematical Practice with your students? These important math practices really develop the skills our students need to become mathematicians! This game, Eliminate It, is a great way to work on SMP#3, which is to construct viable arguments and critique the reasoning of others.
How can we do that standard in a game? Well, show your students these eliminate cards and ask them, which one should we eliminate? Your students will be thrilled to know there is NOT one right answer because it is what they think. This game gives students practice with creating their own argument and listen to others' ideas. The game starts with familiar pictures and then gets more complex with math concepts. Math concepts included are shapes, numbers, teen numbers, and addition and subtraction.
Do this game as a whole class or print the cards and create a new math center! Included are 10 cards.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823618.14/warc/CC-MAIN-20181211104429-20181211125929-00540.warc.gz
|
CC-MAIN-2018-51
| 940 | 3 |
http://www.cricketweb.net/forum/1252905-post3.html
|
math
|
Originally Posted by Perm
I won't say that these are favourite moments, but certainly ones that will stick in my head forever is the second half of the 1999 New Zealand vs France semi final. We simply had no answer.
EDIT: George Smith taking out Marshall in 03, George Gregan taunting Byron Kelleher with "four more years".
What's the opposite of xenophobia?
|
s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705790741/warc/CC-MAIN-20130516120310-00070-ip-10-60-113-184.ec2.internal.warc.gz
|
CC-MAIN-2013-20
| 358 | 4 |
https://wulixb.iphy.ac.cn/article/doi/10.7498/aps.55.3845
|
math
|
A cross section of the rod is taken as object of investigation. The freedom of the section in free or constraint case is analyzed and the definition of virtual displacement of the section is given, which can be expressed by a variational operation. Assuming the variational and partial differential operations has commutativity, based on the hypothesis about surface constraint subjected to the rod, the freedom of the section on constraint surface is discussed and the equations satisfied by virtual displacements of the section are given. Combining D'Alembert principle and the principle of virtual work, D'Alembert-Lagrange principle is established. When constitutive equation of material of the rod is linear, the principle can be transformed to Euler-Lagrange form. From the principle, a dynamical equation in various forms such as Kirchhoff, Lagrange, Nielsen and Appell equation can be derived. For the case when a rod is subjected to a surface or a nonholonomic constraint, Lagrange equation with undetermined multipliers is obtained. Integral variational principle of dynamics of a super-thin elastic rod is also established, from which Hamilton principle formulation is obtained when the material of the rod is linear. Finally, canonical variables to describe the state of the section and Hamilton function are defined, and Hamilton canonical equation is derived. The analytical methods of dynamical modeling of a super-thin elastic rod have been constructed, which can serve as a theoretical framework of analytical dynamics of a super-thin elastic rod with two independent variables.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.22/warc/CC-MAIN-20230322082826-20230322112826-00071.warc.gz
|
CC-MAIN-2023-14
| 1,595 | 1 |
https://profoundadvices.com/what-are-passing-marks-in-ignou/
|
math
|
Table of Contents
- 1 What are passing marks in Ignou?
- 2 How can I check Ignou pass or fail?
- 3 How Ignou marks are calculated?
- 4 What is the pass mark out of 60?
- 5 What are the passing marks?
- 6 What is the passing score of 50 items?
- 7 How can I calculate my marks?
- 8 What is the passing marks in IGNOU for 100+?
- 9 What percentage is required to pass the IGNOU theory exam?
- 10 What is the passing marks of IGNOU course in JEE Mains?
What are passing marks in Ignou?
For passing the IGNOU exam you just have to secure 40\% which means that 40 marks out of 100. So you have to get a minimum of 40 marks in the TEE theory. And for the assignment exams, you have to secure 50\% which means 50 marks out of 100.
How can I check Ignou pass or fail?
IGNOU Dec 2019 TEE Result is declared and can be checked online on the official website link here -> www.ignou.ac.in. For Master’s Degree Students, you will need to score 20 marks out of 50 marks question paper to get passed. And, if the question paper is of 100 Marks, then make sure you get 40 marks to get passed.
What is the passing marks out of 50 in Mcq?
The internal test of 50 marks and the theory exam of 50 marks. So,out of 50 marks – the passing grade is 20.
How Ignou marks are calculated?
With these two entities, one can easily calculate the total marks of the student in a particular subject. Total marks = 49 marks + 15 marks = 64 marks. To calculate the percentage, the student needs to divide the total marks by 1200 and multiply by 100.
What is the pass mark out of 60?
The passing marks for theory paper out of 80 are 26, out of 70 marks students need to attain 23 marks and out of 60 marks, 19 marks are required to pass the examination.
What is the passing marks of 50 in Pune University?
|Head of Passing||Grace Marks Upto|
What are the passing marks?
As per the CBSE 10th passing criteria, students must score a minimum of 33 per cent marks in theory exams, practicals and internal assessment. Hence, it is the minimum marks required for passing marks in CBSE class 10.
What is the passing score of 50 items?
Learn the normal English marking system. 70\% to 100\% is the highest grade, a mark of Distinction. 60\% to 69\% earns a Merit. 50\% to 59\% is Pass.
What is the passing marks out of 50 in online exam?
Minimum passing is 40\% marks in ESE and also average of 1+2+3 should also be 40\%. There is no minimum passing in online exams however to be on the safe side its advisable to attain atleast 20 marks out of 50 in the online exams also.
How can I calculate my marks?
A percentage is a number that is shown in terms of 100.To find the percentage of the marks obtained, one shall divide the total scores by marks obtained and then multiply the result with 100. Example: If 79 is the score obtained in the examination out of 100 marks, then divide 79 by 100, and then multiply it by 100.
What is the passing marks in IGNOU for 100+?
passing marks are 20 and 40 for M.M. of 50 and 100. In IGNOU University passing criteria is 18 marks out of 50 Marks. It means Candidate have to gain at least 18 marks out 50 in each subject to pass or qualify the term end examinations and get the IGNOU Results.
What happens if a student fails in IGNOU exam?
If the candidate failed to get minimum marks in IGNOU Assignment then they need to submit the particular assignment again to IGNOU. If you want to pass out in the theory or practical papers of Master Degree Programme then you must have a minimum 40 marks out of 100 marks to get quality.
What percentage is required to pass the IGNOU theory exam?
Therefore, students have to obtain minimum of 27 out of 75 to pass the theory exam. The passing marks in Ignou assignments remains same for these courses as well. i.e. 50\% marks. There are few course as well for which maximum marks in exam is 70.
What is the passing marks of IGNOU course in JEE Mains?
There are few course as well for which maximum marks in exam is 70. For those courses, the passing marks in Ignou course is 24 out of 70.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224655143.72/warc/CC-MAIN-20230608204017-20230608234017-00034.warc.gz
|
CC-MAIN-2023-23
| 4,026 | 39 |
http://yrcourseworkynsc.modelbook.us/cs301-midterm-solved-papers.html
|
math
|
Cs301 midterm solved papers
Cs301 data structures you need to be a member of cs301 data structures midterm / final term papers to add comments. Cs301 midterm papers collection shared by sweet soul - download as pdf file (pdf), text file (txt) or read online. Contentscs301- data structures midterm past papers(subjective)q:1 what is complete binary tree q:2 how single left rotation is performed in avl tree q:3 describe.
Secondly we should attatch all solved papers as much as possible for our class mates students in this matter all students get hlp from these attatchments papers. Mid term paper papers are temporarily unavailable cs301 - paper : 2 (solved) cs301 - paper : 3 (solved) cs301 - paper : 4 (solved) cs302 - digital logic design. Download cs301 current & past vu solved midterm & final term papers - data structures. Mid term final term nts | ppsc cs301- data structures | final term | solved papers 2018 in final term, virtual university cs301 data structure final term. Solved assignments, gdb, quizzes, midterm and final term past papers, information, news, technology technology for students of virtual university of pakistan.
Cs302-solved-mcqs-from-midterm-papers-digital-logic - read more about inputs, output, input, cmos, logic and binary. Mid term final term post tagged with: cs301 final term solved cs301- data structures | final term | solved papers january 9, 2018 final term. Cs301- data structures latest solved mcqs from midterm papers nov 25,2011 mc100401285 [email protected] [email protected] psmd01.
Midterm papers midterm papers1 home » » cs301 final term papers cs301 final term papers nouman ahmed cs301-finalterm-solved. Paper to attend a sports event you attended an institution which been avoided if legal and safe space. Midterm papers all collection solved by all student`s cs301 assignment # 1 fall 2017 complete solution cs615 assignment # 1 fall 2017 complete solution.
Cs301- data structures solved mcqs & subjective from midterm papers. Vu- midterm papers vu-final term papers cs619 project helping contact final term papers cs301 final term mcqs by dr tariq hanif cs502 mcqs solved by dr. You can find here all past papers, latest papers, assignments solution, gdb solution, quizzes files and handouts.
Vu midterm papers edu402 edu430 edu601 edu406 edu301 edu601 fin611 – advance financial accounting midterm solved latest papers download cs301.
Cs301 current midterm papers fall 2014 - 2015 starts from monday, january 12, 2015. 15 may 2011 : vu midterm current papers (may 2011) cs301 vu midterm current paper (may 2011) cs501 mcqs solved. Cs301 all current final term papers 20 august 2016 to 02 september 2016 day cs301 paper mid term solved papers psy101 assignment # 3 2016. Sundoor & peggy dylan provide motivational and spiritual courses sundoor firewalking is the foremost school for firewalk instructors. Vuassignmentscom upload the cs301 solved mid term papers by arslan ali and zeeshan try to solved the cs301 solved mid term papers by arslan ali and zeeshan.
Cs301 final term solved papers by moaaz mega file plea bargaining ap euro enlightenment essays thesis statement history of isis bbc mgt201 final term solved papers by. Past model papers of virtual university of pakistan cs301-midterm past papers cs301 subjective solved questions. Cs301 final term solved subjective papers by moaaz cs301-data structure final term solved subjective papers cs504 mid term paper solved.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511175.9/warc/CC-MAIN-20181017132258-20181017153758-00542.warc.gz
|
CC-MAIN-2018-43
| 3,442 | 9 |
http://blog.learningresources.com/pi-day-skyline/
|
math
|
Each year on March 14, math lovers come together in the universal celebration of National Pi Day. But you don’t have to be a mathematical scholar to enjoy (or understand) what Pi is all about. Let’s explore!
What is Pi?
Pi is the circumference of a circle (the distance around the circle) divided by its diameter (the distance across). So take at any circle anywhere around the world at any size. The entire distance around the circle will be approximately 3.14 times its length across. Because 3.14 are the first digits of pie, 3/14 (March 14th) is designated as National Pi Day each year.
Pi is an irrational number, which means it has an infinite (limitless) number of digits. No matter how many decimal places are calculated, pi will always be an approximation. Its decimal representation never ends and never repeats.
Graphing is an early math skill that most likely begins in Kindergarten, so the easiest way for children to understand that pi keeps going, and going, and going, is set up a graph. In this art + math project of a skyline, the buildings each represent a number in pi.
For this project, you will need:
- Graphing paper
- A printout of π
- A watercolor set
First, count out how far you will take your skyline, which will determine how far you go with your pi print out. Begin by lightly writing out pi on the bottom of the graph, and then run 1-9 up the side of the graph. (Of course your budding mathematician can just count the squares up, but this does definitely takes a while). We determined that the decimal point would be the same value as 0.
Next begin to graph each building. We found it was easiest to count the squares up, mark it with the maker, then connect it with the building before it. This will take time, but it really does resemble a city skyline pretty quickly.
Next, color in your buildings. This was a welcome activity after the tedious nature of the graphing!
Looks great! And looks very much like a city’s skyline! Now it’s time to use the watercolors.
Erase your numbers so you have a clean slate.
Create any kind of sky you’d like – sunset or sunny day.
Turned out great! A physical representation of the mathematical truth of pi.
Used some glitter and glue to make some “pi’s in the sky”. Happy Pi Day!
Save it for later!
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655897844.44/warc/CC-MAIN-20200709002952-20200709032952-00079.warc.gz
|
CC-MAIN-2020-29
| 2,288 | 18 |
https://myriverside.sd43.bc.ca/annabelles2019/2021/11/28/
|
math
|
In this week of precalc 11, we learned how to solve rational expressions, which are fraction questions with variables. One thing in specific we learned about was non-permissible values. These are values that x cannot be in each equation. First, here are some examples of what rational expressions can look like:
These expressions cannot have square roots, or exponents that are variables.
A non-permissible value is also known as a restriction, the domain, or values that the expression cannot be defined by. This means there are certain numbers, that when put in place of x, make the denominator zero. When the numerator is zero the equation can still be simplified. However, when the bottom of the fraction (the denominator) is zero, this is not possible. Therefore, these are non-permissible. When you write these restrictions, use the equal symbol with a line through it, meaning “x cannot be equal to…”
Here are the non-permissible values for the expressions shown above:
For example, in the second expression, x cannot be -12. If it was, it would look like this:
Since the denominator is now zero, which is impossible, it means -12 is the restriction on this expression. There can also be multiple restrictions, depending on the fraction and number of variables. The last example had a fraction as a restriction, which is not as easy to solve in your head. This is how I solved to find -3/4:
Here are a couple more examples:
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100686.78/warc/CC-MAIN-20231207185656-20231207215656-00219.warc.gz
|
CC-MAIN-2023-50
| 1,436 | 7 |
https://tamino.wordpress.com/2010/12/16/comparing-temperature-data-sets/
|
math
|
In light of Anthony Watts’ latest idiocy comparing GISS and UAH temperature data without bothering to put them on the same scale, I thought it might be interesting to compare different temperature records … but let’s do it right, eh?
There are 5 major sources of global temperature data which are most often referred to. Three of them are estimates of surface temperature, from NASA GISS (Goddard Institute for Space Studies), HadCRU (Hadley Centre/Climate Research Unit in the U.K.), and NCDC (National Climate Data Center). The other two are estimates of lower-troposphere temperature, from RSS (Remote Sensing Systems) and UAH (Univ. of Alabama at Huntsville). All are anomaly data, i.e., the difference between temperature at a given time and that during a baseline period. They tend not to be on the same baseline; for GISS the baseline is 1951 to 1980, for HadCRU it’s 1961 to 1990, for NCDC it’s the 20th century, and for satellite data the baseline is 1979 to 1999. Since they use different baselines, they’re on a different scale, i.e., each has its own zero point for temperature. To compare them, we need to use the same zero point for all.
They also don’t cover the same time span. HadCRU starts first, beginning in 1850. GISS and NCDC both start in 1880. And the satellite data don’t start until December 1978 (for UAH) or January 1979 (for RSS). You can download the data yourself; links to data sources are found here. Because of this, the RSS and UAH data cannot be put on the baseline used by any of the surface-temperature data sets because the satellite data don’t cover those time periods. Of course we can only compare them for those times they all have data. And to put them all on the same scale, we’ll have to use a baseline period which is covered by all.
All 5 data sets cover the period 1979 to the present, although HadCRU hasn’t yet published their results for November 2010, so the period of common coverage is January 1979 to October 2010. Here’s the raw data (each with its own baseline period):
We can smooth the month-to-month fluctuations by using a 12-month moving average filter, giving this:
Now we can plainly see that all they tell much the same story, in terms of the temperature changes over time. Which is what anomalies are meant to reveal.
But we can also see the result of using different baselines. GISS and NCDC are nearly the same, because the average for the GISS baseline period (1951-1980) is nearly the same as that for the NCDC baseline (20th century). HadCRUT3v is lower because it’s baseline period (1961-1990) is warmer (so it’s compared to a warmer reference). Finally, the satellite data sets are lowest because their baseline period is warmest.
For proper comparison we should choose a common baseline for all five data sets. I chose the period 1980.0 to 2000.0, which gives this for the monthly data:
and this for the 12-month running means:
Note that now the different data sets are in much closer numerical agreement. They all show warming during the coverage period, and they all show fluctuations superimposed on the warming trend. But the satellite data sets show greater fluctuations, especially during el Nino events (e.g. 1998) and la Nina events (2008), and during the coolings associated with volcanic eruptions (El Chicon in the early 1980s and Mt. Pinatubo in the early 1990s).
Therefore the most prominent pattern in the data appears to be that which is shared by all: an overall warming trend, and warming in response to el Nino, cooling in response to la Nina and volcanic eruptions. The 2nd-most prominent pattern appears to be the difference between the satellite data sets (RSS and UAH) and the surface-temperature data sets (GISS, HadCRUT3v, and NCDC).
We can test that idea by performing a principal components analysis of these data sets. The 1st principal component accounts for 90% of the variance of the data, so it dominates the fluctuations. It turns out to be nearly equal to the average of all five data sets, and the signal associated with it (the 1st empirical orthogonal function or EOF) is, just as we expected, the warming-with-fluctuations which is common to all (I’ve scaled it so that it’s on a “temperature” scale):
All 5 data sets agree: the globe is warming.
The 2nd principal component accounts for 7% of the total variance, which is most of the remainder after accounting for the 1st principal component, and confirms our intuition that the 2nd-most prominent pattern is the difference between satellite and surface-temperature data. Here’s the actual 2nd principal component vector (the “loadings”):
Note that the satellite data sets have positive coefficients while the surface-temperature data sets have negative coefficients. Hence the EOF associated with this PC is very similar to the difference between the satellite average and the surface-temperature average, and looks like this:
We can compare that to what results from subtracting the average of surface temperature estimates from the average of satellite measurements:
The biggest difference between the satellite-minus-surface data and PC#2 is that PC#2 shows an additional downward trend. This is mainly because one of the satellite data sets (UAH) shows an overall trend which is decidedly less than that of the other data sets.
We can plainly see the highs during the 1998 and 2010 el Ninos, and the lows during the 2008 la Nina as well as the volcanic coolings in the early 1980s and early 1990s. This indicates that the satellite data (i.e., the lower-troposphere temperature) responds more strongly to the influence of el Nino/la Nina and to volcanic eruptions, than does the surface temperature.
An interesting result is that for PC#5:
Although it accounts for the least total variance of the data (a mere 0.3%), it shows fluctuations which suggest an annual cycle. Its presence is confirmed by a Fourier analysis of PC#5:
We see a peak at frequency 1 cycle/yr (period 1 yr) together with its harmonics at 2, 3, and 4 cycles/yr. So, not only is there an annual cycle in PC#5, its form is not simply sinusoidal. We can see the cycle shape by making a folded plot (a.k.a. “phase diagram”), graphing temperature not as a function of time but as a function of phase, i.e., time of year (as is customary, I’ve plotted two full cycles of phase:
Here is the actual principal components vector (the “loadings”):
All but 2 of the coefficients are very small, so PC#5 turns out to be mainly the difference between NCDC and HadCRUT3v. Hence we see that their difference shows an annual cycle, because during this time span NCDC is warmer in winter and cooler in summer than HadCRUT3v, although there’s also a “dip” in January-February compared to December and March.
This illustrates that although the choice of baseline period makes no difference when computing the trend (i.e., the rate of global warming), it does make a difference when estimating the annual (seasonal) cycle. When anomalies are computed, not only does it set the “zero point” of temperature to the baseline average, it also removes the annual cycle from the data. But it removes the average annual cycle during the baseline period. If the annual cycle changes, then the difference between “present” and “baseline” annual cycles will remain — a “residual” annual cycle. PC#5 shows that the residual annual cycles in NCDC and HadCRUT3v are different — hence a difference in annual cycle “remnants” is found in PC#5.
A point of much interest is the trend, i.e., the warming rate, shown by each series. We can compute them for each data series separately, and also compute uncertainty levels for those estimates (which are corrected for the influence of autocorrelation, confidence intervals are 2-sigma):
They’re all close, all within each others’ confidence intervals, and they’re all definitely positive (warming). However, the UAH trend estimate is visibly lower than that of the others — if any of the series should be called the “odd man out,” it’s the UAH data.
For some reason “the Blackboard” has an obsession with trends over the most recent 10-year period. Here they are (plotted in blue), compared to the trend over the entire time span common to all data sets (plotted in red):
None of the 10-year trends is “statistically significant” but that’s only because the uncertainties are so large — 10 years isn’t long enough to determine the warming trend with sufficient precision. Note that for each data set, the full-sample (about 30 years) trend is within the confidence interval of the 10-year trend — so there’s no evidence, from any of the data sets, that the trend over the last decade is different from the modern global warming trend.
When one compares the different global temperature data sets correctly, one result emerges more strongly than any other: that they agree. This puts the lie (yes, lie) to claims of “fraud” by climate scientists to rig the surface temperature data.
And what do all the data sets agree on? Mainly this: global warming.
Here are the data, for their period of overlap, as an Excel file:
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500056.55/warc/CC-MAIN-20230203122526-20230203152526-00118.warc.gz
|
CC-MAIN-2023-06
| 9,182 | 31 |
http://www.menilicorne.fr/Q235B-plate/a9b7ba70781000.html
|
math
|
B-H Curve.. Theory . Procedure . Simulator . Reference . Feedback . Theory . Hysteresis . Hysteresis means remaining in Greek, an effect remains after its cause has disappeared. Hysteresis, a term coined by Sir James Alfred Ewing in 1881, a Scottish physicist and engineer (1855-1935), defined it as:When there are two physical quantities B-H vs M-H Hysteresis Loops:Magnetic Induction vs The difference between magnetic induction (B) and magnetization (M) is a matter of convenience. Magnetic induction is the magnetic field intensity inside the sample, and magnetization is the magnetic moment per volume. B and M can be written in terms of each other and the B-H and M-H graphs look very similar, but there are a few key reasons to choose one graph over another.
Jun 29, 2019 · addition, the MH curve of the SUS430 (gure3(b)) was also measured for the magnetic properties of the ferromagnetic wire in the FEM model to compute the magnetic ux density in the vicinity of the wire. Figure4shows the geometry and mesh for 2D axis symmetric FEM analysis. The geometry consists of a GdBCO magnet and a single SUS430 wire. Hysteresis Loop Explained - Ideal Magnet Solutions The plot of Hysteresis is known as a B-H curve, where B (The Material's Flux Density, measured in Teslas or Mega Gauss) is plotted on the vertical axis and H (The External Applied Magnetizing Force, measured in Amperes per meter) is plotted on the horizontal axis. We can also learn a number of other magnetic concepts and principles just by Magnetic Fundamentals, Hysteresisb. What is it? The B-H curve is the curve characteristic of the magnetic properties of a material or element or alloy. It tells you how the material responds to an external magnetic field, and is a critical piece of information when designing magnetic circuits. In the plots below, for a vacuum an H of 800 At/m creates a B of 1 mT.
- DefinitionUsesExampleCriticismsAdvantagesMechanismIntroductionApplicationsTreatmentEffectsUnderstanding the Hysteresis (BH) CurveUnderstanding the Hysteresis (BH) Curve . Hysteresis curves, also called B-H curves, describe the Intrinsic and Normal magnetic properties of a material. The Hysteresis curve is commonly seen in supplier catalogs as a second quadrant curve showing Br, Hc, Hci and BH (max). The test is normally performed by the magnet manufacturer during the initial stage of processing.
Magnetic Materials - Saturation - CoilgunJun 09, 2008 · The B-H curve here illustrates the effect of magnetic saturation. It shows the effect of applying an external magnetic field to unmagnetized iron. The magnetism curve starts at the origin (0,0) and increases linearly as the magnetic field magnetizes the iron. The slope of the curve
Magnetization Curve - an overview ScienceDirect TopicsAs inferred from the magnetization curve shown in Fig. 2.14, in the field range 0310 Oe, the magnetization remains in the vortex configuration, although distorted when H > 0. At H = 310 Oe, a marked discontinuity is observed, associated with the first-order magnetic transition to the onion phase.Therefore, the application of an external field breaks the C 2 symmetry of the internal field
- Nonlinear Magnetic Materials in The Frequency DomainExploring The Effective Nonlinear Magnetic Curves Calculator AppUsing The Effective H-B/B-H CurveConcluding RemarksReferenceTry It Yourself9. B-H curve, Hysteresis loss, B-H curve, eddy-current Aug 13, 2020 · B-H curve. The B-H curve shows how the material responds to an external magnetic field. Saturation shows the limit of the material to have a maximum magnetic field inside of it. As the magnetic cores get larger, they can have larger amounts of The Initial and Four-Quadrant BH-Curve of Soft Magnetic dependence on the magnetic field in the initial BH-curve. The initial BH-curve is used to determine a parameter of soft magnetic materials called permeability. Permeability is defined as the change in magnetic induction (B) for a given change in magnetic field (H). Mathematically, permeability, µis eed as:. H B µ= The size of the field increment and the point on the curve from where B and H
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303864.86/warc/CC-MAIN-20220122134127-20220122164127-00659.warc.gz
|
CC-MAIN-2022-05
| 4,126 | 6 |
http://www.gtagarage.com/discussion/topic.php?id=234
|
math
|
This is a more detailed moon for San Andreas. I loved a similar mod that I used in Vice City, but I couldn't find one so I made a version myself. You need to use the TXD editor to install this, and a backup is included.
One problem with the new version of this mod... The "man in the moon" is at the 3 o'clock position, when it should be at the 12 o'clock position. You need to edit it so that the image is rotated 90 degrees counter-clockwise, so the moon features will appear to be in the correct positions as if you were looking at it in real life.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121305.61/warc/CC-MAIN-20170423031201-00188-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 551 | 2 |
http://www.e-booksdirectory.com/details.php?ebook=2067
|
math
|
Generic Polynomials: Constructive Aspects of the Inverse Galois Problem
by C. U. Jensen, A. Ledet, N. Yui
Publisher: Cambridge University Press 2002
Number of pages: 268
This book describes a constructive approach to the Inverse Galois problem. The main theme is an exposition of a family of "generic" polynomials for certain finite groups, which give all Galois extensions having the required group as their Galois group. The existence of such generic polynomials is discussed, and where they do exist, a detailed treatment of their construction is given. The book also introduces the notion of "generic dimension" to address the problem of the smallest number of parameters required by a generic polynomial.
Home page url
Download or read it online for free here:
by Legh Wilber Reid - The Macmillan company
It has been my endeavor in this book to lead by easy stages a reader, entirely unacquainted with the subject, to an appreciation of some of the fundamental conceptions in the general theory of algebraic numbers. Many numerical examples are given.
by K.G. Ramanathan - Tata Institute of Fundamental Research
These lecture notes on Field theory are aimed at providing the beginner with an introduction to algebraic extensions, algebraic function fields, formally real fields and valuated fields. We assume a familiarity with group theory and vector spaces.
by George Ballard Mathews - Cambridge University Press
This book is intended to give an account of the theory of equations according to the ideas of Galois. This method analyzes, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation.
by J. S. Milne
A concise treatment of Galois theory and the theory of fields, including transcendence degrees and infinite Galois extensions. Contents: Basic definitions and results; Splitting fields; The fundamental theorem of Galois theory; etc.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401600771.78/warc/CC-MAIN-20200928104328-20200928134328-00586.warc.gz
|
CC-MAIN-2020-40
| 1,897 | 15 |
https://verificationacademy.com/forums/coverage/how-delay-transition-coverage-event
|
math
|
In reply to etuers:
Try to use goto repetition/non-consecutive repetition instead of range repetition.
value [-> 1]
or value [= 1]
Using range repetition you are trying to say that the same sequence should come 1 or 2 or... 100 times consecutively followed by next value. Looks like your intent is do following.
seq1 =>.....=> seq2=>.....seq3=>...
.... means any value can come in between.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347387155.10/warc/CC-MAIN-20200525001747-20200525031747-00369.warc.gz
|
CC-MAIN-2020-24
| 389 | 7 |
https://www.caclubindia.com/experts/journal-entry-for-remuneration-to-the-designated-partners-in-llp--2919304.asp
|
math
|
12 February 2024
We have two designated partners in our LLP. we want to pay regular monthly remuneration to the partners (this is not profit sharing). How do I record this on journal entry? we are using Zoho books.
I tried to categorize the transaction on banking tab as money out->owner's drawing->drawing (journal entry is owners drawing dr and bank account cr) but it reduces the share capital (equity) in balance sheet. since the remuneration paid is more than the initial capital, currently share capital is showing in negative which I think is not correct.
Can someone please help me resolve the issue? the objective is to pay monthly remuneration to the working partner and deduct it under profit and loss as per section 40 (B).
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474660.32/warc/CC-MAIN-20240226130305-20240226160305-00462.warc.gz
|
CC-MAIN-2024-10
| 735 | 4 |
https://slopeinterceptform.net/how-to-convert-point-slope-form-to-slope-intercept-form/
|
math
|
The Definition, Formula, and Problem Example of the Slope-Intercept Form
How To Convert Point Slope Form To Slope Intercept Form – There are many forms used to represent a linear equation, among the ones most frequently found is the slope intercept form. The formula of the slope-intercept identify a line equation when you have the straight line’s slope and the y-intercept. This is the y-coordinate of the point at the y-axis crosses the line. Learn more about this particular linear equation form below.
What Is The Slope Intercept Form?
There are three basic forms of linear equations, namely the standard one, the slope-intercept one, and the point-slope. Although they may not yield the same results , when used, you can extract the information line that is produced more quickly by using the slope intercept form. The name suggests that this form uses a sloped line in which it is the “steepness” of the line is a reflection of its worth.
This formula can be utilized to determine a straight line’s slope, the y-intercept or x-intercept in which case you can use a variety of formulas that are available. The line equation of this particular formula is y = mx + b. The slope of the straight line is indicated with “m”, while its y-intercept is indicated by “b”. Each point of the straight line is represented as an (x, y). Note that in the y = mx + b equation formula the “x” and the “y” must remain as variables.
An Example of Applied Slope Intercept Form in Problems
The real-world In the real world, the “slope intercept” form is frequently used to represent how an item or problem evolves over an elapsed time. The value of the vertical axis represents how the equation deals with the magnitude of changes in the value given by the horizontal axis (typically in the form of time).
An easy example of using this formula is to find out how many people live in a particular area as the years go by. Using the assumption that the area’s population increases yearly by a specific fixed amount, the value of the horizontal axis will increase one point at a time for every passing year, and the point value of the vertical axis will rise in proportion to the population growth by the fixed amount.
Also, you can note the starting value of a particular problem. The starting point is the y-value of the y-intercept. The Y-intercept is the place where x is zero. By using the example of a previous problem the beginning point could be at the time the population reading starts or when the time tracking starts, as well as the associated changes.
The y-intercept, then, is the point in the population when the population is beginning to be documented to the researchers. Let’s assume that the researcher begins with the calculation or the measurement in 1995. In this case, 1995 will be considered to be the “base” year, and the x 0 points will occur in 1995. Therefore, you can say that the 1995 population represents the “y”-intercept.
Linear equation problems that use straight-line formulas can be solved in this manner. The initial value is represented by the yintercept and the rate of change is expressed by the slope. The primary complication of this form typically lies in the horizontal interpretation of the variable, particularly if the variable is attributed to an exact year (or any other type or unit). The most important thing to do is to make sure you know the definitions of variables clearly.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662562106.58/warc/CC-MAIN-20220523224456-20220524014456-00700.warc.gz
|
CC-MAIN-2022-21
| 3,454 | 11 |
https://forum.qt.io/topic/97323/delete-qt-account/3
|
math
|
Delete Qt Account
jjjjjjjj last edited by
Hello, could someone help me delete my Qt account? I'm not sure how to do it.
@AndyS I think you can help here.
@jjjjjjjj If you can PM me your email address then I can have someone take care of it for you then
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986726836.64/warc/CC-MAIN-20191020210506-20191020234006-00517.warc.gz
|
CC-MAIN-2019-43
| 252 | 5 |
https://my-finance.us/amortization-expenses-how-much-does-the-amortization-cost/
|
math
|
A common term used for paying off of loan or debt, part-by-part, during regular intervals is Amortization. Amortization can be of any type of loan: personal, property, car or others. For example, a loan of $100,000 for a time period of 10 years, can be paid as $834 per month, without any interest.
Intangible assets are non-physical assets and have been divided to many assets. Based on the Section 197 of Internal Revenue Code, there are many ways to qualify as an intangible asset. Some of the common assets are: trademarks, copyrights, goodwill, franchise, etc.
Similar to depreciation expense, amortization expense can be defined as the process of reducing the costs or value of assets, which are intangible, over a given time period. However, unlike depreciation expense, amortization refers only to assets like copyrights or patents. For instance, depending on the lifespan of a patent on a particular object, like a 3D modeling pen, the cost of it is spread over that period of time. If the patent has a life of 10 years, the cost can be spread over those 10 years. Amortization can also be applied to balances like discounted notes and deferred charges.
Usually, companies follow an orderly manner of amortizing their assets depending on their usage and importance to the company. Many companies follow the method of Straight Line basis for both amortization and depreciation. It is considered to be the most simple way of depreciation of the value of an asset. It is a method which requires you to acquire the difference between the asset’s value and the expected salvage value, then dividing it by the years that it is to be used for. Here, only a fixed amount is to be paid as the amortization expense for the current value of the asset, every year.
Other methods could be: Sum of the year method and Declining Balance method.
Declining Balance Method
It is a very common method to calculate the rate of depreciation on non-depreciated balance. Here the cost of the assets are not spread evenly along certain time period, but at a fixed rate over the given period. The fixed rates reduce the charges of depreciation over the time period.
The sum of the years’ digits
The SYD (The sum of the years’ digits) is a type of accelerated depreciation. By this method, the depreciation rate is calculated to be more during the early years of the assets and gradually reduces to a lesser amount during the following years.
Image credit: davaopropertyforsale.com/
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154408.7/warc/CC-MAIN-20210802234539-20210803024539-00609.warc.gz
|
CC-MAIN-2021-31
| 2,471 | 10 |
https://apps.dtic.mil/sti/citations/ADA083514
|
math
|
Continuous Density Approximation on a Bounded Interval Using Information Theoretic Concepts.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
Pagination or Media Count:
This report presents the theoretical development and numerical implementation of a procedure for approximating continuous probability density functions on a bounded interval. The work is applicable to Bayesian decision models and that available information is used to update or obtain the prior distribution. The procedure is based on the solution of a constrained entropy maximization problem and requires information in the form of expected values of information functions. The approach involves three steps estimation of expected or average values of potential information functions, selection of the active subset of functions to define the approximation family, and simultaneous solution of the constraints to select the specific approximating density for a given set of data. A useful set of potential information functions is developed, and three numerical methods for active set selection are demonstrated. Numerical techniques for expected value computation are discussed, and a scheme for solution of the constraints is developed and implemented. Theoretical development includes theorems on form and uniqueness. Approximation accuracy is related to potential set definition and data accuracy. The procedure is applied to several known distributions to demonstrate applicability. Applications to computer simulation and interval arithmetic models are demonstrated with specific examples. Author
- Statistics and Probability
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588282.80/warc/CC-MAIN-20211028065732-20211028095732-00522.warc.gz
|
CC-MAIN-2021-43
| 1,622 | 5 |
http://mathhelpforum.com/algebra/154005-how-solve-complex-conjugate.html
|
math
|
I just like to know how to get the comlex conjuage of this equation
where To, T, beta and z are contants
to obtain the following equality
Follow Math Help Forum on Facebook and Google+
Originally Posted by Arsalanoovf I just like to know how to get the comlex conjuage of this equation
where To, T, beta and z are contants An EQUATION has an EQUAL sign...
Plus you're using T and T1 as the SAME variable????
sorry my mistake.
I just like to know how I can get the complex conjugate of the first attachment, such that I would be able to get to the equality shown in attachments two.
and T1 and T2 are two different variables!
I not sure what you are asking.
But . And .
So that is rather straightforward.
Complex conjugate - Wikipedia, the free encyclopedia
View Tag Cloud
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120206.98/warc/CC-MAIN-20170423031200-00541-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 771 | 15 |
https://gcn.nasa.gov/circulars/5984
|
math
|
S. Golenetskii, R.Aptekar, E. Mazets, V. Pal'shin, D. Frederiks, and
T. Cline on behalf of the Konus-Wind team report:
The most intense part of the long GRB 061222A (Swift-BAT trigger
#252588; Grupe et al., GCN 5954; Tueller et al., GCN 5964)
triggered Konus-Wind at T0=12614.682 s UT (03:30:14.682).
The emission is clearly seen in the Konus-Wind data
starting at T-T0~-80 s.
As observed by Konus-Wind the burst had a duration of ~100 s,
fluence 2.66(-0.23, +0.43)x10^-5 erg/cm2,
the 64-ms peak flux measured from T0+5.312 s
5.65(-1.19, +1.42)x10^-6 erg/cm2/s
(both in the 20 keV - 2 MeV energy range).
The spectrum integrated over the most intense part of the burst
(from T0 to T0+15.104 s) is well fitted (in the 20 keV - 2 MeV range)
by GRBM (Band) model for which:
the low-energy photon index is alpha = -0.94(-0.13, +0.14),
the high energy photon index beta = -2.41(-1.21, +0.28),
the peak energy Ep = 283(-42, +59) keV (chi2 = 64/60 dof).
The fitting by a power law with exponential cutoff model:
dN/dE ~ E^(-alpha)*exp(-E*(2-alpha)/Ep)
in the same energy range yields
alpha = 1.02(-0.11, +0.10)
and Ep = 324(-41, +54) keV (chi2 = 67/61 dof).
All the quoted errors are at the 90% confidence level.
The Konus-Wind light curve of this GRB is available
[GCN OPS NOTE(28dec06): Per author's request, the author list
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100276.12/warc/CC-MAIN-20231201053039-20231201083039-00057.warc.gz
|
CC-MAIN-2023-50
| 1,318 | 26 |
http://coolperiodictable.com/resources/gases/avagadroslaw.php
|
math
|
Avogadro's law is a principle stated by the Italian chemist Amedeo Avogadro (1776-1856) in 1811.
The avagadro's law states that under equal conditions of temperature and pressure, equal volumes of gases contain an equal number of molecules.
Avogadro's number is 6.022 * 10 23. This means that 12 grams of carbon-12 contains 6.022 * 10 23 carbon-12 atoms.
For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.
The avagadro's law is expressed as: where: V is the volume of the gas. n is the amount of substance of the gas (measured in moles). k is a constant.
Because the formula is equal to a constant, Avagadro's law can be rewritten as:
Example 1: How many moles are there in one atom?
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948579567.73/warc/CC-MAIN-20171215211734-20171215233734-00393.warc.gz
|
CC-MAIN-2017-51
| 779 | 7 |
https://docslib.org/doc/10705080/isotopes-and-atomic-mass
|
math
|
Isotopes and Atomic Mass How to write it The isotope of an element can be indicated in two ways: An element is distinguished by always having the same number of protons in the nucleus. Using the elements symbol (numbers can either be to the left or the right of the symbol): However, there can be a variable number of neutrons. 54 Atomic mass 54 An isotope of an element has the Fe Atomic number Fe 26 (may not be present) 26 same atomic number but has a different number of neutrons.
This will affect the average mass Using the elements of an atom of an element. name:
If we take a specific example it will become clear. Next > Iron- 54 Next >
Example Question 1
Iron, atomic number 26, has four Carbon has an atomic number of 6. Its two naturally naturally occurring isotopes. Atomic mass number occurring isotopes are carbon 12 and carbon 13. 54 (number of nucleons) They are: How many neutrons do carbon 12 and 13 have? Fe Atomic number Fe-54, Fe-56, Fe-57, and Fe-58. 26 (number of protons) Carbon -12 Carbon -13 From the table, we can A) 6 7 see the number of protons neutrons nucleons B) 12 13 neutrons in each Fe-54 26 28 54 isotope’s nucleus. Fe-56 26 30 56 C) 7 6 A nucleon, is a Fe-57 26 31 57 D) 13 12 particle that is in the Fe-58 26 32 58 nucleus (either a proton or a neutron). Next > Next >
Question 1 Abundance of each Isotope of Iron
Carbon has an atomic number of 6. Its two naturally If a sample of iron was occurring isotopes are carbon 12 and carbon 13. examined with a mass How many neutrons do carbon 12 and 13 have? spectrometer, the abundance of each Carbon -12 Carbon -13 isotope could be A) 6 7 measured.
B) 12 13 Luckily, tables exist giving Mass spectrometer us this information from Abundance in % C) 7 6 previous experiments. Fe-54 5.8 Fe-56 91.72 D) 13 12 How does this give us Fe-57 2.2 the average mass of Fe-58 0.28 Next > an atom? Next >
1 Question 2 Question 2
Copper has two naturally occurring isotopes (Cu-63 Copper has two naturally occurring isotopes (Cu-63 and Cu-65). and Cu-65). If copper 63 has an abundance of 69.17% what is If copper 63 has an abundance of 69.17% what is the abundance of copper 65? the abundance of copper 65?
Give your answer as a percentage. Give your answer as a percentage. 30.83 (%)
Next > Next >
Calculation of Atomic Mass Number Calculation of Atomic Mass Number
What is the atomic mass of each isotope? Multiply the mass Abundance Atomic mass Atomic mass of each isotope in % abundance Fe-54 53.93612 5.8 3.12829 Atomic mass by the Again, tables give us that Fe-56 55.93439 91.72 51.30302 Fe-54 53.93612 abundance, to data. (This is the atomic Fe-57 56.935396 2.2 1.25258 Fe-56 55.93439 give the mass relative to 1/12 of a Fe-58 57.933278 0.28 0.16221 Fe-57 56.935396 contribution of carbon atom). Total 55.8461 Fe-58 57.933278 each isotope.
Summing the individual abundances, gives the total relative (average) atomic mass of iron.
Next > Next >
Calculation of Atomic Mass Number
The periodic table gives the relative atomic mass of iron as 55.85.
If we round up our calculation to 2 d.p. we also get 55.85.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224649193.79/warc/CC-MAIN-20230603101032-20230603131032-00287.warc.gz
|
CC-MAIN-2023-23
| 3,085 | 19 |
http://randomkey.pro/manova-filetype-78/
|
math
|
Click on the download database and download data dictionary buttons for a configured database and data dicationary for manova. The primary purpose of the. analysis, you may follow-up any effect which is significant in the MANOVA by significant on the MANOVA, I inspected the univariate analyses to determine. MANOVA and repeated measure ANOVA are used in very different situations. A MANOVA is a multivariate ANOVA and is used when one has.
|Published (Last):||16 July 2006|
|PDF File Size:||10.27 Mb|
|ePub File Size:||5.64 Mb|
|Price:||Free* [*Free Regsitration Required]|
A scatterplot of the predicted values vs. SPSS should open the portable data file. It should resemble the following: Each dataset contains only mxnova observations from group 1, group 2, and group 3, respectively.
In the image fileytpe, two of the within-subjects variables have already been added: These commands add the variable sum to the end of the dataset, as shown below: Thanks for your time. This will give the following dialog box: Since the values of a categorical variable do not convey numeric information, such a variable should not be used in a regression model.
When the License Authorization window appears, click Start. Suppose that the k ratings for each of the N persons have been produced by a subset of j k raters, so that there is no way to associate each of the k variables with a particular rater. In this example, the value of “3” is recoded as missing: I want to compare accuracy of several predicting models.
Transpose all variables except Rowtype and Factoras shown in the example:. In the dialog boxes, when the Intraclass correlation coefficient checkbox is checked, a dropdown list is enabled that allows you to specify the appropriate model.
Multivariate analysis of covariance mancova multivariate fkletype of covariance mancova is a statistical technique that is the extension of. If you want to use filety;e for the entire restructuring, the code for the above example is shown below. If the interaction is not significant, you would conclude the regression slopes fileyype homogeneous.
Manova spss filetype pdf
Clicking on this box will produce a Missing Values dialog box. He shows how to perform ancova in spss both using the glm features and using multiple regression. Continuous scaleintervalratio, independent variables. I have run a factor analysis on two separate samples of individuals, both producing the same factor solution. Under Old Valuecheck All other values. First, create a new variable which identifies observations in each of the nine cells of the 3×3 matrix.
Following this, specific equations can be used to test for the significance of the various patterns or effects. The first decision that must be made in order to select an appropriate ICC is whether the data are to be treated via a one way or fileype two way ANOVA model. The Estimated Marginal Means section of the output contains a table listing pairwise comparisons of the factors selected in the Options dialog box.
Tthe dataset is now prepared for the contrast analysis. Coding missing values into a number: This tells SPSS to put the factor loadings in a matrix file which will show up as a new active dataset. The Authorization code is a string of 20 alphanumeric characters consisting of digits and lower case letters. You are already familiar with bivariate statistics such as the.
Suppose the two variables are x and manoga. Under New Valuecheck Value and enter an appropriate value to replace the missing observations, such asThe final data should have the following structure: Each subject was observed many times, each observation is entered as a single case in SPSS. Following the interaction specification, the COMPARE keyword appears followed by the name of the variable for which comparisons will be generated.
In the Between-Subjects Model box, enter agesexand their interaction clicking on both age and sex and then clicking the arrow will enter the interaction term. In the Model dialog box, check Custom. For a description of methods used to handle missing data, see our “General” FAQs.
If birthdate and observation date are coded as one variable each, in date format, age can be computed by the following steps. The resulting dialog box is as follows: Contrast coding makes user-specified comparisons between clusters of groups.
Enter all factors and covariates into the Model box; this will provide tests of the main effects of these variables. The dialog box should look like:. Type the name of the new date variable, e.
MANOVA vs. Repeated Measure ANOVA – Cross Validated
Enter the repeated measure name, such as salary. Now, newfact will also have values of 2 whenever factor1 is 1 and factor2 is 2, as shown in the following dataset: Every case with a missing value for at least one of the variables will be output to the new dataset. First go to the Case Group Identification box and select the option Use selected variable to specify your between subjects variable a.
Guide to spss barnard college biological sciences 3 this document is a quick reference to spss for biology students at barnard college. Put the new variable that defines the nine cells in the Factor box. Back to Top Obtaining one-tailed p-values Question: You can test this assumption by building a model that includes the interaction of each factor with each covariate. A tutorial on multivariate statistical analysis craig a.
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986666467.20/warc/CC-MAIN-20191016063833-20191016091333-00287.warc.gz
|
CC-MAIN-2019-43
| 5,424 | 21 |
https://www.physicsforums.com/threads/calculating-frequencies-with-the-doppler-effect.897898/
|
math
|
1. The problem statement, all variables and given/known data A train moves at a constant speed of v = 25.0 m/s toward the intersection shown in Figure P13.71b. A car is stopped near the crossing, 30.0 m from the tracks. The train’s horn emits a frequency of 500 Hz when the train is 40.0 m from the intersection. (a) What is the frequency heard by the passengers in the car? (b) If the train emits this sound continuously and the car is stationary at this position long before the train arrives until long after it leaves, what range of frequencies do passengers in the car hear? (c) Suppose the car is foolishly trying to beat the train to the intersection and is traveling at 40.0 m/s toward the tracks. When the car is 30.0 m from the tracks and the train is 40.0 m from the intersection, what is the frequency heard by the passengers in the car now? Figure 13.71b: http://i.imgur.com/b08nVys.jpg 2. Relevant equations The Doppler equation presented in the text is valid when the motion between the observer and the source occurs on a straight line so that the source and observer are moving either directly toward or directly away from each other. If this restriction is relaxed, one must use the more general Doppler equation f ' = ((v + vi cos θi) / (v − vs cos θs))*f where θi and θs are defined in Figure P13.71a. Use the preceding equation to solve the following problem. I find the whole concept of Doppler effect in physics to be rather complicated. I would not only love to understand this problem but the concept in general. Any help would be appreciated.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813109.36/warc/CC-MAIN-20180220204917-20180220224917-00774.warc.gz
|
CC-MAIN-2018-09
| 1,577 | 1 |
https://pwntestprep.com/tag/right-triangles/
|
math
|
Test 10 – Question 30
For question 5 on page 242(Angles, Triangle and Polygons), could you explain why the triangle was put into 60,30,90 right triangle and how you came up with b/2 *square root of 3 as the height?
A triangle with angle measures 30°, 60°, 90° has a perimeter of 18+6√3. What is the length of the longest side of the triangle?
Thomas is making a sign in the shape of a regular hexagon with 4-inch sides, which he will cut out from a rectangular sheet of metal. What is the sum of the areas of the four triangles that will be removed from the rectangle?
Trigonometry does the trick here. Below is that line making a 42° angle with the positive x-axis. I’ve also drawn a dotted segment to make myself a neat little right triangle. Remember that slope is rise over run—how high the line climbs divided by how far it travels right. In this case, the dotted segment (more…)
Think of a 5-12-13 triangle (that’s one of the Pythagorean triples you should know). Say angle A measures x°, which would make angle C measure (90 – x)°. (I’m choosing those based on the fact that I already know that the sine of angle C will be 12/13.) Now that we’ve got it set up, all we (more…)
Practice question for Circles, Radians, and a Little More Trigonometry, #5, p. 272, 4th Ed.
Test 7 Section 4 #36
I sorry I am very confused about why the answer question 5 on page 28 is A would you help me please?
How do you do #18 in Test 6 Section 3 without a calculator?
Test 3 Section 3 #20
Subject Test Question:
The area bound by the relationship |x|+|y|=2 is
E) there is no finite area.
How do you find this algebraically?
A square with an area of 2 is inscribed in a circle. what is the area of the circle?
D) 2 radical pie
A right triangle has side lengths of x-1, x+1, and x+3. What is its perimeter?
Hi mike! This question is from the May 2015 SAT.
(will post photo)
In the xy plane above, f and g are functions defined by f(x)=abs[x] and g(x)=-abs[x] + 3 for all values x. What is the area of the shaded region bounded by the graphs of the two functions?
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057687.51/warc/CC-MAIN-20210925142524-20210925172524-00160.warc.gz
|
CC-MAIN-2021-39
| 2,075 | 21 |
http://www.sparkpeople.com/mypage.asp?id=803PEPPER
|
math
|
As a child and college student, I was active.
Now that I work, I have stopped working out. I need motivation to lose the weight that I have put on, but it is hard.
I have friends & family that work out, eat right, and they are happy. They say, "Just do it! Eat right, work out, and you will lose weight." Well, I hear them but I still haven't done it.
I want to do it but I haven't done it. I'm hoping that this site will motivate me to Just do it! Eat right, work out, and lose weight.
-fit back into my clothes
-begin a healthy diet
-begin a doable workout
This user doesn't have any public blog entries.
Secrets of Success
This user doesn't have any secrets of success.
| Pounds lost: 0.0
(¸.•´ (¸.•´ (¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.
¸.•♥´ .•´¨¨ ¸´¸.•´¨Welcome to the EE team!!
I’ve belonged to a lot of teams here on spark-- i really do believe that the Emotional Eaters team is one of the very best, it’s a great group of people- very supportive and encouraging-- and it is very refreshing to talk with people who "get" what you're going through!! ¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.*¸.•´¸.•*¨¸.•*¨¸.•´¸.•*¨) ¸.•*¨)
Check out the main page of the EE team- there are “stickied” topics you may be interested in to get involved- a buddy thread, a place to introduce yourself, weigh-in challenge, a birthday post. ¸.•*¨¸.•´¸.•*¨(¸.•´ (¸.•´ (¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥. ¸.•♥´ .•´¨¨ ¸´¸.•´¸.•*¨)¸¸.•´ ..•-~'¸.•*¨)
Spark has a lot of great tools, and you will learn which ones work best for you. The best tools are the people tho, always willing to lend a hand, an ear, or a shoulder. I’ve been here for over a year now, and I still am overwhelmed, every day, by the kindness and goodness of others on this team!! That has made a world of difference for me. I hope you have the same success! ¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.*.•*¨¸.•´¸.•*
(¸.•´ (¸.•´ ♥¸.•´¸¸.• (¸.•´ (¸.•*¨ (¸.¸.•*´¨`*• .¸♥.
You are- WONDERFUL-cuz you’re you!!! BELIEVE IT!!! operationbeautiful-- END THE FAT TALK!!! ¸.•*¨¸.•´¸.•*¨(¸.•´ (¸.•´(¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.
(¸.¸.•*´¨`*• .¸♥. ~~best of luck to you on all of your goals!!! (¸.¸.•*´¨`*• .¸♥.
2673 days ago
Welcome to the Emotional Eaters team. Best wishes on your journey.
2673 days ago
Hi- Welcome to the EE team! Great place for support, and encouragement, and a place to vent if you need to!
10 Positive Assumptions
1) I will make and keep my commitments.
2) I will find the right people who can help me.
3) I will look for an answer in every problem.
4) I will give up trying and simply do.
5) I will make it okay to be wrong and make mistakes.
6) I will create my own good luck.
7) I will not be afraid to lose before I win.
8 ) I will do it now!
9) I will be who I am and become what I was meant to be.
10) I will accept that all things are possible.
-Robert Anthony, in his book Betting on Yourself.
Hope to see you on the message boards! Have a great weekend!
2674 days ago
HI! I am just popping in to say what's up. :-)
How has it been going?
Looking forward to Fall? I know I am! I love Autumn! The cool crisp breezes!The yummy veggies! The gorgeous Fall leaves! If you get a sec, come and visit my Spark page. I love visits!! I gave it a new Fall look and updated my intro.
Have a great day! Don't hesitate to Sparkmail me anytime you need anything! As a co-captain of calling all Goonies I will do my best to answer any questions or concerns you may have.(((Hugs)) :-)
3159 days ago
Let me add to the list of well-wishers and say
welcome to Sparks and Goonies! There's tons
of support here and be there every step of the
way, just reach out.
3172 days ago
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123491.79/warc/CC-MAIN-20170423031203-00118-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 3,887 | 47 |
http://slideplayer.com/slide/2811729/
|
math
|
2 Population ecology Population ecology is the study of populations. Population = group of individuals of the same species occupying a common geographical areaHabitat = where a species normally livesDensity = The number of individuals in a population per unit area.
3 Exponential Growth Indicated by a J-shaped growth curve growth in which the population increase in a period is a fixed percentage of the size of the population at the beginning of the period;the number of individuals increases over time logarithmically (e.g. bacterial cultures).
4 Components of an exponential growth pattern for a given population Time Zero - time of establishment of a population; for bacterial culture, time that the culture was inoculatedLag Phase - time that it takes for the population to start growing; resources must be obtained; habitat and microhabitat establishment; niche definition; population prepares for reproduction (for bacterial cultures: time that the cells need to begin their specific type of metabolism before cell division can occur).
5 Log Phase - period of exponential (logarithmic) growth. Stationary Phase - period following exponential growth where number of deaths equals the number of new individuals.Death Phase - period following the stationary phase where the population is dying due to depletion of resources and or contamination of habitat with waste products.
6 EXPONENTIAL/ LOG PHASE STATIONARY PHASEDEATH PHASEEXPONENTIAL/ LOG PHASELAG PHASELABEL THE PHASES OF EXPONENTIAL GROWTH
7 Logistic growth (S-shaped curve) Because of limiting factors, populations rarely exhibit J-shaped growth curves.When growth encounters environmental resistance, populations experience an S-shaped or logistic growth curve.Early on populations will exhibit very rapid growth, but as they near the carrying capacity they will level off.Logistic growth is density dependent.High density and overcrowding put individuals at greater risk of being killedPredators, parasites and pathogens have greater numbers of prey and hosts in a smaller area to interact with
8 Components of a Logistic Growth Curve Lag PhaseLog/ Exponential Growth PhaseDeceleration PhaseStable, Equilibrium Phase
10 Growth curve of a laboratory population of yeast cells. STABLE EQUILIBRIUM PHASEDECELERATION PHASEEXPONENTIAL/ LOG PHASELAG PHASE
11 Growth curve of the sheep population of Southern Australia Growth curve of the sheep population of Southern Australia. The smooth curve is the hypothetical logistic curve about which the real curve seems to fluctuate.
12 Effects of population density on growth in open systems: Density-independent growth - size of population is not a factor in determining the resulting population size overall;population size, however, stays about the same as when it began.Most density-independent factors are abiotic.Examples: temperature, storms, floods, drought, habitat destruction
13 Effects of population density on growth in open systems: Density dependent growth - size of the population is a factor in determining the resulting population size overall;exponential growth can occur if adequate resources are available and range expansion can occur as in an open system.Disease is spread more quicklyStress can lead to aggression
14 Population growthPopulations grow, shrink, or remain stable, depending on rates of birth, death, immigration, and emigration.(birth rate + immigration rate) –(death rate + emigration rate)= population growth rate
15 Exponential growthUnregulated populations increase by exponential growth:Growth by a fixed percentage, rather than a fixed amount.Similar to growth of money in a savings account
16 Exponential growth in a growth curve Population growth curves show change in population size over time.Scots pine shows exponential growthFigure 5.10
17 Limits on growthLimiting factors restrain exponential population growth, slowing the growth rate down.Population growth levels off at a carrying capacity—the maximum population size of a given species an environment can sustain.Initial exponential growth, slowing, and stabilizing at carrying capacity is shown by a logistic growth curve.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865702.43/warc/CC-MAIN-20180523180641-20180523200641-00208.warc.gz
|
CC-MAIN-2018-22
| 4,138 | 15 |
https://valutadwap.web.app/75675/80398.html
|
math
|
Martin Johnsson's blog about - On unicorns and genes
Learning GLM lets you understand how we can use probability distributions as building blocks for modeling. I assume you are familiar with linear regression and normal distribution. As we noted in the previous chapter, the “linear” in the general linear model doesn’t refer to the shape of the response, but instead refers to the fact that model is linear in its parameters — that is, the predictors in the model only get multiplied the parameters (e.g., rather than being raised to a power of the parameter). Introduction to Statistical Modelling With Dr Helen Brown, Senior Statistician at The Roslin Institute, December 2015 *Recommended Youtube playback settings General Linear Models: The Basics. General linear models are one of the most widely used statistical tool in the biological sciences.
- Rapatac gävle
- Registreringsbesiktning trimmad moped
- Ledig jobb nykoping
- Räkna ut moms 25%
- Meningsfull fritid fritidshem
- Grinstads lanthandel
• GLM uses a general linear model method for performing the ANOVA. • The GLM method calculates Type I and Type III sums of squares. Background Generalized linear mixed models (or GLMMs) are an extension of linear mixed models to allow response variables from different distributions, such as binary responses. How to create Generalized Liner Model (GLM) Let's use the adult data set to illustrate Logistic regression. The "adult" is a great dataset for the classification task. The objective is to predict whether the annual income in dollar of an individual will exceed 50.000.
(X.3) Note how this is still a linear model because it conforms to the general algebraic formula of Equation X.1. In practice, however, it is customary to write such linear models in terms of the original variables. Writing Equation X.3 in terms of the original variables Generalized Linear Models (GLMs) were born out of a desire to bring under one umbrella, a wide variety of regression models that span the spectrum from Classical Linear Regression Models for real valued data, to models for counts based data such as Logit, Probit and Poisson, to models for Survival analysis.
EPSY 905: General Linear Model We will return to the normal distribution in a few weeks –but for now know that it is described by two terms: a mean and a variance The "general linear F-test" involves three basic steps, namely:Define a larger full model. (By "larger," we mean one with more parameters.) Define a smaller reduced model.
Velocity of density shifts in Finnish landbird species depends
General Linear Model With correlated error terms = 2 V ≠ 2 I. More Multiple Linear Regression in SPSS with Assumption Testing. Dr. Todd Testing for Heteroscedasticity in The central theme of the course is the multivariate general linear model, and statistical methods include multivariate hypothesis testing, principal component on a general linear model (GLM) including the hemodynamic response function and correcting for slow drifts (GLM not available for MAGNETOM ESSENZA) I regressionsanalyser är en förutsättning att alla ingående variabler befinner sig Vi gör sedan en vanlig linjär regression med hur ofta man umgås med enklare, om man inte är familjär med General Linear Model-analysen. Vi anpassar nu en multivariat linjär modell (General linear model –. Multivariate) där reaktionstiderna m.a.p. bägge händerna är responsvariablerna, kön och Summary statistics for point processes on linear networks. Speaker: Global envelopes with applications to functional data analysis and general linear model. Välj Line och därefter diagrammet med två Interaktionseffekt?
Statistical modelling, Likelihood based methods, general linear models, generalized linear models, mixed effects
av E Häggström Lundevaller · 2002 — A general random effects model can be specified by first letting Щi = (ЩiЬi, , ЩiЬа) the more general class of generalized linear mixed models (GLMM) let. av A Musekiwa · 2016 · Citerat av 15 — Furthermore, the longitudinal meta-analysis can be set within the general linear mixed model framework which offers more flexibility in
general linear models in linear algebra terms - statistical analysis of general linear models using algebraic tools like projections, generalized
Generalized Linear Mixed Models : Modern Concepts, Methods and Applications, Second Edition. Walter W. Stroup · Author: Walter W. · Date: 01
av O Friman · Citerat av 230 — the widely used General Linear Model (GLM) method, although terminology and GLM, where one side is univariate (a voxel time series in the fMRI analysis
Advisors: edit. Papers. 45 Views. •. Computationally feasible estimation of the covariance structure in generalized linear mixed modelsmore.
The general linear model (GLM) is a statistical linear model.It may be written as where Y is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and U is a matrix containing residuals (i.e., errors or noise). Chengjie Xiong, J. Philip Miller, in Essential Statistical Methods for Medical Statistics, 2011. 2.4.2 Generalized linear mixed effect models. The basic conceptualization of the generalized linear mixed effects models is quite similar to that of the general linear mixed effects models, although there are crucial differences in the parameter interpretations of these models. For general linear models the distribution of residuals is assumed to be Gaussian. If it is not the case, it turns out that the relationship between Y and the model parameters is no longer linear. The generalized linear model expands the general linear model so that the dependent variable is linearly related to the factors and covariates via a specified link function.
We now come to the General Linear Model, or GLM. With a GLM, we can use one or more regressors, or independent variables, to fit a model to some outcome measure, or dependent variable. To do this we compute numbers called beta weights, which are the relative weights assigned to each regressor to best fit the data. Generalized Linear Mixed Models (illustrated with R on Bresnan et al.’s datives data) Christopher Manning 23 November 2007 In this handout, I present the logistic model with fixed and random effects, a form of Generalized Linear Mixed Model (GLMM). I illustrate this with an analysis of Bresnan et al. (2005)’s dative data (the version
Generalized Linear Models in R are an extension of linear regression models allow dependent variables to be far from normal.
Svensk romani ordlista
— 3.2.1 Vad är GLM (Generalized Linear Model)?. 3.3 Exempel då Poisson-regression används. Bridging the gap between theory and practice for modern statistical model building, Introduction to General and Generalized Linear Models presents Allmän linjär modell - General linear model. Från Wikipedia, den fria encyklopedin. Inte att förväxla med multipel linjär regression Learn about linear regression with PROC REG, estimating linear combinations with the general linear model procedure, mixed models and the MIXED English: Random data points and their linear regression. Created with the following Sage (http://sagemath.org) commands: X = RealDistribution('uniform', [-20, This course teaches you how to analyze linear mixed models using PROC MIXED.
continuum model , also referred to as the " linear model " , which means that a
Kopplingsschema generator bosch – Linear stepper motor Each Cummins Generator has a model/spec number description, which is shown on the This handbook is a general supplement to the more specific information contained in the
Alibaba business model case study What is legend in research paper linear technology case study my teacher essay for class essay analysis for essay swot Conclusion essay on beauty of festival essay on 2019 general election in nigeria. perspectives, the structures of the models are all more or less linear in their character. There are also other structural similarities between the models.
Athena marta söderberg
söka jobb vetlanda
laro mottagning helsingborg
fa language code
autism diagnos vuxna
Linear regression with PROC REG LinkedIn Learning
(2005)’s dative data (the version This is the total; it’s all you have. The within-group or within-cell sum of squares comes from the distance of the observations to the cell means. This indicates error. The between-cells or between-groups sum of squares tells of the distance of the cell means from the grand mean. This indicates IV effects. What is the general linear model.
Eva bergman karlstad university
vad betyder isometrisk
- Usa golf clubs
- Mathias sundin riksdagen
- Oppettider bromma atervinning
- Vilket datum är det val 2021
- Karin erlandsson segraren
- Story slam examples
- Skatteverket moms danmark
- Hallucinogen hallucinogena droger
A qualitative variable is defined by discrete levels, e.g., "stimulus off" vs. "stimulus on". If a design contains more than two levels assigned to a single or 2020-11-23 A general linear model, also referred to as a multiple regression model, produces a t-statistic for each predictor, as well as an estimate of the slope associated with the change in the outcome variable, while holding all other predictors constant. General Linear Model Equation (for k predictors): Generalized Linear Model Theory We describe the generalized linear model as formulated by Nelder and Wed-derburn (1972), and discuss estimation of the parameters and tests of hy-potheses. B.1 The Model Let y 1,,y n denote n independent observations on a response. We treat y i as a realization of a random variable Y i. In the general linear model we General Linear Models: The Basics.
Regression, ANOVA, and the General Linear Model: A Statistics
Välj Line och därefter diagrammet med två Interaktionseffekt? För att genomföra testen för de olika effekterna används Analyze → General Linear Model →. A sparse statistical model has only a small number of nonzero parameters or They discuss the application of 1 penalties to generalized linear models and This Friday, we'll practice some uses of qplot and make some linear models.
ratio nominal absent comments AERA SIG Multiple Linear Regression: The General Linear Model. 165 gillar · 2 pratar om detta. An AERA SIG that pertains to any methodological, applied, Pris: 969 kr. Häftad, 2013. Skickas inom 10-15 vardagar.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711045.18/warc/CC-MAIN-20221205200634-20221205230634-00811.warc.gz
|
CC-MAIN-2022-49
| 10,492 | 48 |
https://homework.cpm.org/category/CCI_CT/textbook/calc/chapter/4/lesson/4.2.4/problem/4-91
|
math
|
Without your calculator, describe the graph of f(x) = x3 + 12x2 + 36x − 6. A complete answer states where f(x) is increasing, decreasing, concave up, concave down, and points of inflection. Homework Help ✎
When f '(x) > 0, f(x) is increasing. When f '(x) < 0, f(x) is decreasing. An inflection point occurs when f '(x) = 0. When f ''(x) > 0, the function is concave up. When f ''(x) < 0, the function is concave down.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371700247.99/warc/CC-MAIN-20200407085717-20200407120217-00077.warc.gz
|
CC-MAIN-2020-16
| 421 | 2 |
https://brainmass.com/physics/scalar-and-vector-operations/pg3
|
math
|
Please see attachment for a unit vector problem I require help with.
The vector is 3.50 cm long and is directed into this page. Vector points from the lower-right corner of this page to the upper-left corner of this page and has the components , . 1) In the right-handed coordinate system, where the +x-axis directed to the right, the +y-axis toward the top of the page, and +z-axis out of th
A plane leaves the airport in Galisto and flies a distance 170 km at an angle 68.0 degree east of north and then changes direction to fly a distance 270 km at an angle 48.0 degree south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, how far should this crew
How do I express these vectors as their product? Question attached.
1) Find the components in the tilted coordinate system. Express your answer in terms of the length of the vector and the angle, with the components separated by a comma. 2) You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don't pitch your tents close together. Joe's tent is 25.0 m
Please see attached file for the full problem description. Find , the length of , the sum of and . Express in terms of , , and angle .
A plane travels 3.8km at an angle of 26 degrees to the ground, then changes direction and travels 7.4km at an angle of 13 degrees to the ground. a) What is the magnitude of the plane's total displacement? Answer in units of km. b) At what angle above the horizontal is the plane's total displacement? Answer in units of de
(See attached file for full problem description with diagrams) --- Please solve each and give a complete detailed step by step solution to solving each problem no matter how easy. I am trying to learn and not an expert. Give answer and way to solve. Adult student trying to make my way through all this and need your help!
In a slow-pitch softball game, a 0.200 kg softball crossed the plate at 20.00 m/s at an angle of 35.0° below the horizontal. The batter hits the ball toward center field, giving it a velocity of 40.0 m/s at 30.0° above the horizontal. (a) Determine the impulse delivered to the ball. (b) If the force on the ball increase
The center of mass of three objects is located a (1,0). one object with a mass of 5.0 kg is at (-2,-1) and a second object with a mass of 2.0 kg is at (0,0). What are the coordinates of the third mass of 3.0 kg?
Please help with the following problem. Provide step by step calculations for each problem. You have a mass of 59 kg and are on a 28-degree slope hanging on to a cord with a breaking strength of 224 newtons. What must be the coefficient of static friction to 2 decimal places between you and the surface for you to be saved fr
The force of magnitude 24Squareroot2 Newtons makes an angle of 225 degrees with the positive x axis. Find the x and y scalar components of the vector.
Could you provide workings out and answers to the following physics questions: 1.a. What is the difference between a scalar and a vector quantity? b. A hiker walks due north for 4.0 km to reach point A and then northeast for 6.0 km to reach point B. Find by calculation or by scale drawing: - the straight line distance from s
A load having a mass of 9.2 metric tons is to be lifted by means of a contractor's derrick as shown in fig 5-10. If the Vertical plane containing the boom bisects the angle ADB, what reactions must be provided at points A and B to keep the derrick from tipping? The boom has a mass of 1.84 metric tons, and it makes an angle of 4
Physical principles; difference between a vector and scalar distance, difference between speed and velocity
1. Understanding physical principles is often very useful in everyday life. For example, a skater develops an intuitive understanding of angular momentum in order to master making turns, and virtually all of us as car drivers come to understand the principles of inertia, velocity, and linear momentum. Can you name at least
Please provide formulas and step by step instructions on how to solve. A Vector F has a magnitude of 20 and is directed vertically downward. Find is components Fx and Fy in each of the coordinate frames. Please see attached.
Hi, I am having a lot of difficulty understanding vectors, can you please assist me with these questions. Given: position vector A = i hat. position vector B = i hat + j hat + k hat. 1) Find A hat and B hat (unit vector in that direction). 2) Find position vector C in that plane perpendicular to position ve
Please assist me with the attached problems, including: 1. Find the area within the given set of points 2. Determine whether each product is a scalar or a vector or does not exist. Explain reasoning. See attachment for complete list of problems. Thanks
If A=(12i-16j) and B=(-24i+10j),what is the magnitude of vector C=(2A-B)?
Question: Two vectors act upon a body at an angle of 45 degrees between them. Vector A has a magnitude of 100.0 and vector B has a magnitude of 200.0. Draw an XY coordinate system. What are the x and y components of the resultant vector? What is the magnitude of the resultant, and it's directions angle with respect to the A vec
Draw a scaled diagram of a vector of magnitude 100cm at 30 degrees above the horizontal and use trigonometry to determine its x and y components.
Please see attached file for the diagram. Three vectors are shown in Fig. 3-41 (A = 66.0, O = 52.0 degrees). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. Rx = ? Ry = ? (b) What is the magnitude of the resultant? What is the res
Consider the action for a particle in a potential U. a. Show that an extremal path is never that of a local maximum for the action. ("Local" means relative to nearby paths). b. Find an example in which an extremal path is that of a local minimum for the action. c. Find an example in which an extremal path is not that of a
1) Both vectors A and B have a magnitude 5 and the angle between them is 53.13 degrees. Calculate the magnitude of A+B. 2) The diagram shows vector C. Determine the X and Y components of C. see attached file for details
What is the resultant displacement if we follow these directions? 75.0 m N 95.0 m at 18.0 degrees N of E 65.0 m at 34.0 Degrees W of N 25.0 m SW 20.0 m E
Two vectors are given by A = -3i + 7j -4k and B = 6i -10j + 9k. Evaluate the quantities: a) cos^-1 [A.B/AB] ( the . between the A.B is a dot product) b) sin^-1 [ |A x B|/AB] c) Which gives the angle between the vectors. I haven't a clue as to what to do with this problem. Do I use the cross products of unit vectors t
Vector Dot Product Let vectors , , and . Calculate the following: A. = Answer not displayed C. = Answer not displayed E. = Answer not displayed G. = Answer not displayed H. Express your answer numerically in radians, to three significant figures. Angle between and = Answer not displaye
Three vectors have the same magnitude of 14 units. They make angles of t, 2t, and 3t with respect to the x axis, where t = 20 degrees. What is their vector sum?
On the problem, or any problem how do you know which x or y vector to draw first and which or where to get your angles. Where put theta? Please explain and help any way you can simple enough for me to understand.
See the attached file. Finding the vector sum of three forces 1) Experimental method: Use F1 of 160g at 280 degrees, F2 of 105 grams at 60 degrees and F3 of 75g at 15 degrees counter clockwise from the +y axis. Determine the equilibriant and the resultant of the three vectors experimentally. Record magnitude and direction
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593223.90/warc/CC-MAIN-20180722120017-20180722140017-00278.warc.gz
|
CC-MAIN-2018-30
| 7,656 | 31 |
https://math.answers.com/Q/How_you_can_write_three_hundred_forty_six_over_one_thousand_in_decimal_notation
|
math
|
One thousand nine hundred forty-five.
With zeroes after the decimal point, the numeral is simply "forty thousand three hundred". As a dollar amount, it is "forty thousand three hundred dollars and no cents".
forty-two thousand, six hundred sixty-seven
Forty five thousand, three hundred assuming decimal is at the end.
One hundred forty thousand, one hundred twenty-five
Two hundred ninety-three thousand nine hundred forty-nine millionths.
7,045,840,307 and seven billion, forty-five million, eight hundred forty thousand, three hundred seven.
$47,646. (BTW, if you say and, that usually means decimal. Say it like this: Forty-seven thousand, six hundred forty six dollars. )
It is forty seven thousand three hundred eighty five hundred thousandths.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499871.68/warc/CC-MAIN-20230131122916-20230131152916-00692.warc.gz
|
CC-MAIN-2023-06
| 750 | 9 |
https://naya.com.np/post/p1673434628uqif1
|
math
|
Introduction to continuous systems and fields
Certain mechanical issues require a continuous system. For instance, consider the issue of an elastic solid that is vibrating. Here, the oscillation is caused by each point of the continuous solid, and the full motion can only be described by stating the location coordinates of every point. We employ the following strategy to change the preceding formulation of mechanics: changing a discrete system to a continuous system.
The transition from a discrete to a continuous system
Consider an elastic rod that is infinitely long and capable of small longitudinal vibrations, or oscillatory displacement of the rod's particles parallel to the rod's axis. An infinite chain of points with equal masses, separated a distance apart, and connected by uniform massless springs with Boltz constant k forms a discrete particle system that resembles a continuous rod. Assume that the mass point can travel only along the chain's length. The discrete system will then be recognized as a linear polyatomic molecule extension. Therefore, using the standard method for small oscillations, we may obtain the equations characterizing the motion.
Denoting the displacement of higher particle from its equilibrium position by ηi, then kinetic energy is
where m is mass of each particle.
The corresponding potential energy is the sum of the potential energies of each spring as a result of being stretched or compressed from its equilibrium position. i.e
Now the Lagrangian for the system (elastic rod) is given by
L = T- V
The resulting Lagrange equation of motion for the coordinate ηi are
It is clear that m/a reduced to μ, the mass per unit length of the continuous system (m/a = μ ). For an elastic rod obeying hook's law, we have
F ∝ ξ
F = Yξ ...............................5
where ξ is the elongation per unit length and Y is Young's modulus.
Now the extension of the length 'a' of a discrete system per unit length will be
ξ = (ηi+1 - ηi)/a
Then F= Y (ηi+1 - ηi)/a
= ka (ηi+1 - ηi)/a ........................6
On going from discrete to continuous system for case, the integer index 'i ' becomes the continuous partition coordinate x . i.e ηi = η(x)
Further the quantity
(ηi+1 - ηi)/a =[ η(x+a) - η(x)]/a
Taking the limit as 'a' playing the rate of dx approaches zero.
Finally, the summation over a discrete number of particles become an integral over 'x '(the length of the rod). Then Lagrangian for continuous system becomes
is called the Lagrangian density for continuous system.
Hence equation of the motion for the continuous system (elastic rod) is given by
Comparing equation 10 with familiar wave equation in 1 dimensional,
which is the propagation velocity for the continuous system.
This note is taken from Statistical Mechanics, MSC physics, Nepal.
This note is a part of the Physics Repository.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00786.warc.gz
|
CC-MAIN-2023-14
| 2,862 | 29 |
https://www.roadlesstraveledstore.com/what-formula-would-help-you-use-archimedes-principle/
|
math
|
What formula would help you use Archimedes Principle?
Therefore, the net buoyant force is always upwards. The mass of the displaced fluid is equal to its volume multiplied by its density: mfl=Vflρ m fl = V fl ρ . Archimedes principle: The volume of the fluid displaced (b) is the same as the volume of the original cylinder (a).
How does Archimedes Principle explain whether an object will float or sink in water?
If the buoyant force is greater than the object’s weight, the object will rise to the surface and float. If the buoyant force is less than the object’s weight, the object will sink. Archimedes’ principle states that the buoyant force on an object equals the weight of the fluid it displaces.
What are the applications of Archimedes Principle?
Applications of Archimedes’ Principle
- Ships. Have you ever wondered that why an iron nail sinks in the water but large ships do not?
- Beach Balls. Beach balls are filled with air only, so they have a very small weight, hence they do not displace much water.
- Hot Air Balloon.
Why do humans float in water?
A human submerged in water weighs less (and is less ‘dense’) than the water itself, because the lungs are full of air like a balloon, and like a balloon, the air in lungs lifts you to the surface naturally. If its less dense than water, then it will float.
What is Archimedes Principle and why would an object sink?
Which is the correct equation for archimedes’principle?
In equation form, Archimedes’ principle is where FB is the buoyant force and wfl is the weight of the fluid displaced by the object. Archimedes’ principle is valid in general, for any object in any fluid, whether partially or totally submerged. According to this principle the buoyant force on an object equals the weight of the fluid it displaces.
How is the Archimedes principle related to Pascal law?
Pascal law. Archimedes law. Archimedes principle states that When an object is totally or partially immersed in a liquid, an upthrust acts on it equal to the weight of the liquid it displaces.
How is the Archimedes law related to buoyant force?
If only a part of the volume is submerged, the object can only displace that much of liquid. In simple form, the Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as: The mass of the liquid displaced is. Thus the weight of that displaced liquid is:
How can Archimedes’s law be used to determine density?
Archimedes’s law is also helpful to determine the density of an object. The ration in the weights of a body with an equal volume of liquid is the same as in their densities. Here w 2 is the weight of the solids in a liquid.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00365.warc.gz
|
CC-MAIN-2022-49
| 2,731 | 20 |
https://valorgame.com/gambling/what-is-the-probability-of-rolling-standard-dice-which-sum-to-5.html
|
math
|
When a pair of dice is rolled what is the probability that the sum of the dice is 6 Given that the outcome is not 4?
Answer: The probability of rolling a sum of 6 with two dice is 5/36. Let’s solve this step by step. Explanation: We know, the probability of an event = Favorable outcomes / Total outcomes.
What is the probability of rolling a sum of 4 on a standard pair of six sided dice?
Now we can see that the sum 4 will be rolled with probability 3/36 = 1/12, and the sum 5 with probability 4/36 = 1/9. Below you can check our random “roll of dice” generator. It will count for you the total number of rolls and the total for each sum.
What is the probability of getting a sum of 7 when rolling two dice?
For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.
When you roll two dice What is the probability that their sum will be at least 10?
When you consider the sum being 10, there are only 3 combinations. So, the probability of getting a 10 would be 3/36 = 1/12.
When a pair of dice is rolled what is the probability that the sum of the dice is given that the outcome is not?
The probability of any number occurring is 1 in 36 or 1 / 36. Then the probability an 8 will not occur is: 1 – 5 / 36 or 31 / 36. I could have added up all of the ways an 8 could not occur such as: 1 / 36 + 1 / 36 … 1 / 36 = 31 / 36, but that is the hard way.
When two dice are rolled what is the probability that the sum is either 7 or 11?
2 Answers. The probability is 25% .
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00210.warc.gz
|
CC-MAIN-2022-33
| 1,700 | 12 |
http://www-old.newton.ac.uk/programmes/LAA/seminars/2006041115301.html
|
math
|
Sporadic propositional proofs
Seminar Room 1, Newton Institute
The following feature is shared by certain weak propositional proof systems: If $\psi_n$ is a uniformly generated sequence of propositional formula, and the sequence $\psi_n$ has polynomial size proofs, then the sequence $\psi_n$ in fact has polynomial size proofs that are generated in an uniform manner . For stronger propositional proof systems (like the Frege Proof Systems) this feature might fail and sporadic proofs (that are not instances of a sequence of uniform proofs) might exist. In the talk I will argue that understanding and limiting the behaviour of these sporadic proofs could be crucial for any serious progress in Propositional Proof Complexity.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281424.85/warc/CC-MAIN-20170116095121-00251-ip-10-171-10-70.ec2.internal.warc.gz
|
CC-MAIN-2017-04
| 728 | 3 |
http://american-center-krasnodar.ru/ege_5205/
|
math
|
Study the advertisement.
You are considering going on this sightseeing tour and now you’d like to get more information. In 1.5 minutes you are to ask five direct questions to find out the following:
London Bridges Sightseeing Tour!
1) duration of the tour
2) the starting point
3) number of bridges you’ll visit
4) the price for a group of 10
5) discounts for students
You have 20 seconds to ask each question.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358973.70/warc/CC-MAIN-20211130110936-20211130140936-00340.warc.gz
|
CC-MAIN-2021-49
| 414 | 9 |
https://encyclopedia2.thefreedictionary.com/sandwich+beam
|
math
|
6, a and 6, b shows the variation of the first natural frequency of the sandwich beam versus the thickness ratio, with various fiber orientations.
For both Models I and II, it can be indicated that the frequency of the sandwich beam with fiber orientation [theta] = 0[degrees] is relatively high compared with the others cases.
DESIGN MAP OF A SANDWICH BEAM LOADED IN THREE-POINT BENDING
EXPERIMENTAL ANALYSIS OF THE SANDWICH BEAM LOADED IN THREE-POINT BENDING
Dynamic stability of a sandwich beam
with a constraining layer and electrorheological fluid core, Composite Structures 64(1): 47-54.
Nonlinear random vibrations of a sandwich beam
adaptive to electrorheological materials, Mechanika 3(71): 38-44.
Lee, "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory," Engineering Structures, vol.
Lee, "A quasi-3D theory for vibration and buckling of functionally graded sandwich beams," Composite Structures, vol.
Strength and stiffness of sandwich beams
Some specific areas investigated include nonlinear stress and deformation behavior of composite sandwich beams
, a neural network approach for locating multiple defects, first-order size effects in the mechanics of miniaturized components, and deformation evaluation of solder ball joints by electromotive force.
Three-point bending tests are performed to find the flexural and shear rigidities of sandwich beams
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572744.7/warc/CC-MAIN-20190916135948-20190916161948-00074.warc.gz
|
CC-MAIN-2019-39
| 1,445 | 14 |
http://www.verycomputer.com/166_dad71b9aef69ecdd_1.htm
|
math
|
I think that this is a plug and play card. You can either
use the DOS utility to lock out plug and play, or use the
pnputils from Linux to set it up.
Clarence Wilkerson \ HomePage: http://www.math.purdue.edu/~wilker
Dept. of Mathematics \ Messages: (765) 494-1903, FAX 494-0548
Purdue University, \
W. Lafayette, IN 47907-1395 \
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710777.20/warc/CC-MAIN-20221130225142-20221201015142-00177.warc.gz
|
CC-MAIN-2022-49
| 328 | 7 |
https://chotenawabny.com/great-mathematicians-of-india/
|
math
|
India has been the birth place of many great minds in different fields. Be it mathematics or literature, science or philosophy, India has gifted the world with many talents. Great mathematicians of Indian origin have revolutionized the subject and have given incomparable contributions to mathematics. Here is a list of some of the great mathematicians of India who have revolutionized the field of mathematics starting from the Indus Valley civilization to the modern times:
Read about 7 Great Mathematicians of india
Well known for his contribution to modern numbering system and computation of the numeral zero, Brahmagupta is a mathematicians and astronomer belonging to the native of Bhinmal. Though he gave the rules to compute zero, as his works included no derivations and proofs, it is still a mystery that how he got his results.
Truly the brightest gem among Indian mathematicians of the classical age, Aryabhata is also a renowned astronomer. He explained the sinusoidal functions, single variable quadratic equation solution and calculated the value of pi up to four decimal places. He also explained many astronomical events like lunar and solar eclipse, reflection of light by moon, calculated the earth’s radius with 99.8% accuracy.
Bhaskara is famous Indian mathematician as well as philosopher. He derived that any number divided by zero. He also said that any number when added to infinity gives infinity as the result. He is also famous for his commentaries on Brahma Sutras. His works are extensively explained in a book named ‘Sidhanta Siromani’.
Also Read: Check out Top 10 Flightless Birds in the World
4. D.R. Kaprekar:
One of the great mathematicians of India, D.R. Kaprekar is known for his work in number theory. He is a recreational mathematician who has revolutionised the number systems by describing different classes of natural numbers. He did not receive much education in maths yet his work in the field can easily out throw other mathematicians. He even has a constant named after him.
3. Srinivasa Ramanujan:
He is among the most famous Indian mathematicians who is known to every maths enthusiast in the world. His works in elliptical functions, identities in partition of numbers, Hardy-Ramanujan-Littlewood circle method in number theory, partial sums and hypergeometric series. He even has a stamp dedicated to him.
2. Satyendranath Bose:
With specialisation in mathematical physics, Satyendranath Bose hails from Bengal. He is popular for his quantum mechanics work. He worked alongside Albert Einstein to form the foundation of Bose-Einstein statistics and result in the theory of Bose-Einstein condensate. He was awarded the Padma Vibhushan Award by the Government of India in the year 1954.
1. Harish Chandra:
He is a famous Indian mathematician and physicist who is known for his work in fundamental representation theory. He is also known for his work on harmonic analysis of semisimple Lie Groups. He has Indian-American ancestry. He passed out from the prestigious University of Allahabad and he got his master’s degree in Physics after which he moved into IIS, Bangalore. He has also worked with Homi J. Bhabha.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107872746.20/warc/CC-MAIN-20201020134010-20201020164010-00610.warc.gz
|
CC-MAIN-2020-45
| 3,169 | 14 |
https://searchworks.stanford.edu/view/10288201
|
math
|
Includes bibliographical references (pages -884) and indexes.
Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book - now in its third revised and augmented edition - has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups, on compact Lie groups, and on locally compact abelian groups. However, the thrust of book points in the direction of the structure theory of infinite dimensional, not necessarily commutative compact groups, unfettered by weight restrictions or dimensional bounds. In the process it utilizes infinite dimensional Lie algebras and the exponential function of arbitrary compact groups. (source: Nielsen Book Data)
|
s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398445080.12/warc/CC-MAIN-20151124205405-00186-ip-10-71-132-137.ec2.internal.warc.gz
|
CC-MAIN-2015-48
| 1,072 | 2 |
http://mathhelpforum.com/calculus/26494-differential-calculus.html
|
math
|
You know what the power rule is? Chain Rule?
You have two options: differentiate as it's written (you'll need the Chain Rule) or expand and apply easily the power rule. (I prefer the first option, of course.)
y=(10x^4 + 40x^3)^5 + 100x
y'= u need to use chain rule= derivative of outer times original inner times derivative of inner...= DOI x DI ...in this case
the outer function or number is 5 and the inner function is (10x^4 + 40x^3), this one is easy to tell which is outer and inner b/c the inner function is in parentheses. Remember to follow the power rule too, nx^n-1
y'= 5(10x^4 + 40X^3)^5-1 = 5(10x^4 + 40X^3)^4 ok this is the first half of chain rule, then you multiply by the derivative of the inner function using the power rule.
y'= 5(10x^4 + 40X^3)^4 * (40x^4-1 +120^3-1)
y'= 5(10x^4 + 40X^3)^4 * (40x^3 +120^2)...
ok almost done now you want find the derivative of 100x which is simply 100.
so ur final answer is :
y'= 5(10x^4 + 40X^3)^4 * (40x^3 +120^2) + 100
I hope that helps...later
God is love,
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540975.18/warc/CC-MAIN-20161202170900-00271-ip-10-31-129-80.ec2.internal.warc.gz
|
CC-MAIN-2016-50
| 1,016 | 13 |
https://www.lmfdb.org/knowledge/show/g2c.known_rational_points
|
math
|
For a curve $X$ of genus $g\ge 2$ over $\Q$ (or any number field) the set of rational points $X(\Q)$ is finite, by a theorem of Faltings. At present no algorithm is known that explicitly computes a provably complete list of the points in $X(\Q)$, but one can conduct a search among points of bounded height to obtain a list of known rational points.
Rational points on hyperelliptic curves are written in projective coordinates with respect to the weighted homogeneous equation $y^2+h(x,z)y=f(x,z)$ of degree $2g+2$ that is a smooth projective model for the curve $X$, where $y$ has weight $g+1$, while $x$ and $z$ both have weight 1. This homogeneous equation is uniquely determined by the affine equation $y^2+h(x)y=f(x)$ listed as the minimal equation for the curve.
- Review status: reviewed
- Last edited by Kiran S. Kedlaya on 2019-09-05 19:15:51
- 2019-09-05 19:15:51 by Kiran S. Kedlaya (Reviewed)
- 2019-04-20 16:11:37 by Jennifer Paulhus (Reviewed)
- 2018-05-24 16:18:36 by John Cremona (Reviewed)
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100518.73/warc/CC-MAIN-20231203225036-20231204015036-00218.warc.gz
|
CC-MAIN-2023-50
| 1,007 | 7 |
https://www.asknumbers.com/square-meter-to-square-feet.aspx
|
math
|
Square meters to square feet conversion factor is 10.7639104. To find out how many square feet in square meters, multiply the square meter value by the conversion factor.
1 Square Meter = 10.7639104 Square Feet
There are 10.7639104 square feet in a square meter, because as a formula the area of a square is calculated by multiplying a side by itself and 1 meter is 3.28084 feet, that makes 3.28084 * 3.28084 = 10.7639104 square feet in a square meter.
For example, to find out how many sq. feet there are in a sq. meter and a half, multiply the sq. meter value by the conversion factor, that makes 1.5 m2 * 10.7639104 = 16.145 sq. feet in 1.5 sq. meters.
Square meter (metre in SI spelling) is a metric system area unit and defined as the area of a square with sides are 1 meter in length. 1 square meter equals to 10.76 sq. feet, 1.2 sq. yards and 1550 sq. inches. The abbreviation is "m2".
Square foot is an imperial and US Customary measurement systems area unit and defined as the area of a square with sides are 1 foot in length. 1 square foot equals to 0.093 sq. meters, 0.11 sq. yards and 144 sq. inches. The abbreviation is "ft2".
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204885.27/warc/CC-MAIN-20190326075019-20190326101019-00508.warc.gz
|
CC-MAIN-2019-13
| 1,139 | 6 |
https://katahum.com/southeast-asian-countries/what-grade-level-is-singapore-math-3.html
|
math
|
FOCUSED PRACTICE: The Singapore Third Grade Math Workbook provides focused practice in mathematical mastery for 8 to 9 year-old children.
What level is Singapore Math?
The Primary Mathematics series has levels 1 through 6 which cover material for approximately grades one through six and beyond. The Common Core Editions have only levels 1 through 5.
Is Singapore math a grade ahead?
The Primary Mathematics materials are generally one year ahead of current U.S. materials and even bright students can’t just skip a year of content and expect to be successful. 4. When teaching Concretely, the SmartBoard is not enough. Students must actually use the manipulatives.
What kind of math is Singapore Math?
The Singapore math method is focused on mastery, which is achieved through intentional sequencing of concepts. Some of the key features of the approach include the CPA (Concrete, Pictorial, Abstract) progression, number bonds, bar modeling, and mental math.
What grade is Singapore Math 5?
|PLACEMENT GUIDE FOR Singapore Math®EMATICS SERIES|
|PLACEMENT GUIDE FOR Singapore Math®EMATICS SERIES 4th grade||Pri Math 3B & 4A|
|PLACEMENT GUIDE FOR Singapore Math®EMATICS SERIES 5th grade||Pri Math 4B & 5A|
|PLACEMENT GUIDE FOR Singapore Math®EMATICS SERIES 6th grade||Pri Math 5B & 6A|
Why is Singapore Math bad?
Actually, Singapore Math provides challenging multi-step problems which enable students to generalize problem-solving procedures to solve a variety of different problems. … On the one hand, presenting problems that involve computation is held in disdain because it doesn’t present the real beauty of math.
Is Singapore math hard to teach?
Children in Singapore traditionally score highly in math when compared to those in other countries. Singapore method is demanding and relies heavily on mastery of the material. There are textbooks, workbooks, manipulative and teacher’s guides for each grade run from $9 – $30.
Is Saxon better than Singapore Math?
Saxon Emphasizes Practice – Saxon Math puts more emphasis on doing practice exercises while Singapore Math puts more emphasis on critically thinking through concepts. … Singapore Emphasizes Thinking – Singapore teachers spend more time helping students to think through and verbally discuss each component of the concept.
Why is Singapore so good at math?
Foundational Learning/Deep Mastery
Experts agree that part of the reason why Singapore students are so successful in math is because their curriculum teaches them a deep mastery of the subject through carefully calculated foundational learning; each grade level is a building block.
Is common core similar to Singapore Math?
Common Core seems to be imitating Singapore Math because it has adopted many of the same strategies, although in different forms. Bar models may not be used specifically, but much of Common Core’s method monitoring focuses on grading the accurate construction and use of models in general.
Is Singapore math hard?
Mathematics is generally a subject considered difficult by many around the world. Its concepts may be abstract and hard to grasp. It is also a subject that requires a lot of visualization, understanding, creativity and a lot of proving. Singapore is a country known to drive competition in its education system.
What is the best Singapore math curriculum?
Dimensions Math Kindergarten is the most substantial option, and we recommend it even if you plan to use Primary Mathematics from Grade 1 and above.
Is Singapore math mastery or spiral?
Singapore Math is Neither Spiral Nor Mastery
Singapore Math’s unique “concrete to pictorial to abstract” approach combines the best of both worlds, leading to a fuller understanding of math.
How long is Singapore Math?
It takes about 30-40 minutes a day to complete — doing textbook, work with me, and workbook. If they know what they are doing, then it takes even less time — 20 minutes to do the pages and mental math.
Does Singapore math teach algebra?
The program emphasizes problem solving and empowers students to think mathematically, both inside and outside the classroom. Pre-algebra, algebra, geometry, data analysis, probability, and some advanced math topics are included in this rigorous series.
What should I do after Singapore Math 6?
Singapore math programs do not continue beyond Grade 8. Students may move onto Geometry and Algebra 2. If you’re looking for online teaching, you might check out High School Math Live or Thinkwell. Art of Problem Solving is good for students who excel at math.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710711.7/warc/CC-MAIN-20221129200438-20221129230438-00353.warc.gz
|
CC-MAIN-2022-49
| 4,546 | 36 |
http://mathsfilms.co.uk/year_7_picks_theorem.htm
|
math
|
A Structured Class Lesson: To find Pick's
The teacher gives out pin-boards (or squared paper
will do) so that each group of children has access to a board or
boards, and some elastic bands.
Teacher: Make me a shape with area 4 squares.
I'm going to draw mine on the squared board.
Now I'll give you about five minutes to find as
many more shapes with area 4 as you can … Keep a record, though,
of E and I and we'll collect together our results.
Activity!! Time to chat to a few individuals who
might need a bit of help/encouragement.
Back at the front … and we fill in a table
with two columns already completed:
Teacher: Has anybody found a shape with 0 pins
inside? or Can anybody fill in the values of E for these I's?
The table is quickly filled in … any gaps
being searched for … comparison of results to lose any inconsistencies.
A discussion can develop here about what possibilities
are available for I and E.
Sometimes the children will automatically look
for patterns in the table … but if nothing is forth coming
Teacher: Anybody notice anything about these numbers?
Students: A's always 4; The E's go up in 2's;
I's in one's!; You always get 10 if you add double the I column
to the E column …
Teacher writes … E + 2I = 10.
Now over to them … See if you can find rules
for A = 5, 6 … etc … and save your results to the end
of the lesson …
More activity … more time to talk and help
… If people are interested in the number of possible I's and
E's at this stage … fine … it is an interesting problem.
It's now about 10 minutes before the end of the lesson…
See if you can find rules for:
a) triangular pin-boards
b) hexagonal pin-boards etc …
or … to practise linking 3 variables
in a different situation Faces, Vertices and Edges or Nodes, Arcs
and Regions to generate Euler's Law: V + F = E + 2 or N + R = A
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742793.19/warc/CC-MAIN-20181115161834-20181115183834-00456.warc.gz
|
CC-MAIN-2018-47
| 1,856 | 39 |
http://www.star-board.com/forum/showpost.php?p=254&postcount=4
|
math
|
RE: Kombat Aero 127
Well first of all I wanted a A117 successor: doesn't exist, the new KA117 is narrower, the new KA127 has the "same" dimensions as the old A117 +10 liters more volume. So the KA127 ~ A117 (as far as I can judge). KA127 gets too big too fast in the waves. I personally think the KA127 is for HEAVY sailors and not necessarily for light winds...
Another thing is (which I should mention as I want to be fair): my KA127 came with 2 fins (the freeride 400 and a wave fin). On the this site the board should only come with 1 fin (and a different one). That might make a difference.
Did my dealer just give me the wrong fins or is the first one to get a new KA127 the sucker?
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720062.52/warc/CC-MAIN-20161020183840-00041-ip-10-171-6-4.ec2.internal.warc.gz
|
CC-MAIN-2016-44
| 688 | 4 |
https://en.wikipedia.org/wiki/Radix_economy
|
math
|
The radix economy of a number in a particular base (or radix) is the number of digits needed to express it in that base, multiplied by the base (the number of possible values each digit could have). This is one of various proposals that have been made to quantify the relative costs of using different radices in representing numbers, especially in computer systems.
Radix economy also has implications for organizational structure, networking, and other fields.
The radix economy E(b,N) for any particular number N in a given base b is defined as
If both b and N are positive integers, then the radix economy is equal to the number of digits needed to express the number N in base b, multiplied by base b. The radix economy thus measures the cost of storing or processing the number N in base b if the cost of each "digit" is proportional to b. A base with a lower average radix economy is therefore, in some senses, more efficient than a base with a higher average radix economy.
For example, 100 in decimal has three digits, so its radix economy is 10×3 = 30; its binary representation has seven digits (11001002) so it has radix economy 2×7 = 14 in base 2; in base 3 its representation has five digits (102013) with a radix economy of 3×5 = 15; in base 36 (2S36) its radix economy is 36×2 = 72.
If the number is imagined to be represented by a combination lock or a tally counter, in which each wheel has b digit faces, from and having wheels, then the radix economy is the total number of digit faces needed to inclusively represent any integer from 0 to N.
The radix economy for large N can be approximated as follows:
The asymptotically best radix economy is obtained for base 3, since attains a minimum for :
For base 10, we have:
Radix economy of different bases
e has the lowest radix economy
Here is a proof that base e is the real-valued base with the lowest average radix economy:
First, note that the function
is strictly decreasing on 1 < x < e and strictly increasing on x > e. Its minimum, therefore, for x > 1, occurs at e.
Next, consider that
Then for a constant N, will have a minimum at e for the same reason f(x) does, meaning e is therefore the base with the lowest average radix economy. Since 2 / ln(2) ≈ 2.89 and 3 / ln(3) ≈ 2.73, it follows that 3 is the integer base with the lowest average radix economy.
Comparing different bases
The radix economy of bases b1 and b2 may be compared for a large value of N:
Choosing e for b2 gives the economy relative to that of e by the function:
The average radix economies of various bases up to several arbitrary numbers (avoiding proximity to powers of 2 through 12 and e) are given in the table below. Also shown are the radix economies relative to that of e. Note that the radix economy of any number in base 1 is that number, making it the most economical for the first few integers, but as N climbs to infinity so does its relative economy.
Base b Avg. E(b,N)
N = 1 to 6
N = 1 to 43
N = 1 to 182
N = 1 to 5329
Relative size of
E (b )/E (e )
1 3.5 22.0 91.5 2,665.0 — 2 4.7 9.3 13.3 22.9 1.0615 e 4.5 9.0 12.9 22.1 1.0000 3 5.0 9.5 13.1 22.2 1.0046 4 6.0 10.3 14.2 23.9 1.0615 5 6.7 11.7 15.8 26.3 1.1429 6 7.0 12.4 16.7 28.3 1.2319 7 7.0 13.0 18.9 31.3 1.3234 8 8.0 14.7 20.9 33.0 1.4153 9 9.0 16.3 22.6 34.6 1.5069 10 10.0 17.9 24.1 37.9 1.5977 12 12.0 20.9 25.8 43.8 1.7765 15 15.0 25.1 28.8 49.8 2.0377 16 16.0 26.4 30.7 50.9 2.1230 20 20.0 31.2 37.9 58.4 2.4560 30 30.0 39.8 55.2 84.8 3.2449 40 40.0 43.7 71.4 107.7 3.9891 60 60.0 60.0 100.5 138.8 5.3910
Ternary tree efficiency
One result of the relative economy of base 3 is that ternary search trees offer an efficient strategy for retrieving elements of a database. A similar analysis suggests that the optimum design of a large telephone menu system to minimise the number of menu choices that the average customer must listen to (i.e. the product of the number of choices per menu and the number of menu levels) is to have three choices per menu.
Computer hardware efficiencies
The 1950 reference High-Speed Computing Devices describes a particular situation using contemporary technology. Each digit of a number would be stored as the state of a ring counter composed of several triodes. Whether vacuum tubes or thyratrons, the triodes were the most expensive part of a counter. For small radices r less than about 7, a single digit required r triodes. (Larger radices required 2r triodes arranged as r flip-flops, as in ENIAC's decimal counters.)
So the number of triodes in a numerical register with n digits was rn. In order to represent numbers up to 106, the following numbers of tubes were needed:
Radix r Tubes N = rn 2 39.20 3 38.24 4 39.20 5 42.90 10 60.00
The authors conclude,
Under these assumptions, the radix 3, on the average, is the most economical choice, closely followed by radices 2 and 4. These assumptions are, of course, only approximately valid, and the choice of 2 as a radix is frequently justified on more complete analysis. Even with the optimistic assumption that 10 triodes will yield a decimal ring, radix 10 leads to about one and one-half times the complexity of radix 2, 3, or 4. This is probably significant despite the shallow nature of the argument used here.
In another application, the authors of High-Speed Computing Devices consider the speed with which an encoded number may be sent as a series of high-frequency voltage pulses. For this application the compactness of the representation is more important than in the above storage example. They conclude, "A saving of 58 per cent can be gained in going from a binary to a ternary system. A smaller percentage gain is realized in going from a radix 3 to a radix 4 system."
Binary encoding has a notable advantage over all other systems: greater noise immunity. Random voltage fluctuations are less likely to generate an erroneous signal, and circuits may be built with wider voltage tolerances and still represent unambiguous values accurately.
- Brian Hayes (2001). "Third Base". American Scientist. 89 (6): 490. doi:10.1511/2001.40.3268. Archived from the original on 2014-01-11. Retrieved 2013-07-28.
- Bentley, Jon; Sedgewick, Bob (1998-04-01). "Ternary Search Trees". Dr. Dobb's Journal. UBM Tech. Retrieved 2013-07-28.
- Engineering Research Associates Staff (1950). "3-6 The r-triode Counter, Modulo r". High-Speed Computing Devices. McGraw-Hill. pp. 22–23. Retrieved 2008-08-27.
- Engineering Research Associates Staff (1950). "3-7 The 2r-triode Counter, Modulo r". High-Speed Computing Devices. McGraw-Hill. pp. 23–25. Retrieved 2008-08-27.
- Engineering Research Associates Staff (1950). "6-7 Economy Attained by Radix Choice". High-Speed Computing Devices. McGraw-Hill. pp. 84–87. Retrieved 2008-08-27.
- Engineering Research Associates Staff (1950). "16-2 New Techniques". High-Speed Computing Devices. McGraw-Hill. pp. 419–421. Retrieved 2008-08-27.
- S.L. Hurst, "Multiple-Valued Logic-Its Status and its Future", IEEE trans. computers, Vol. C-33, No 12, pp. 1160–1179, DEC 1984.
- J. T. Butler, "Multiple-Valued Logic in VLSI Design, ” IEEE Computer Society Press Technology Series, 1991.
- C.M. Allen, D.D. Givone “The Allen-Givone Implementation Oriented Algebra", in Computer Science and Multiple-Valued Logic: Theory and Applications, D.C. Rine, second edition, D.C. Rine, ed., The Elsevier North-Holland, New York, N.Y., 1984. pp. 268–288.
- G. Abraham, "Multiple-Valued Negative Resistance Integrated Circuits", in Computer Science and Multiple-Valued Logic: Theory and Applications, D.C. Rine, second edition, D.C. Rine, ed., The Elsevier North-Holland, New York, N.Y., 1984. pp. 394–446.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337287.87/warc/CC-MAIN-20221002052710-20221002082710-00731.warc.gz
|
CC-MAIN-2022-40
| 7,664 | 48 |
http://www.synapticsparks.info/tax/evidence/c03/derived.html
|
math
|
I am not a Tax Lawyer, Nor do I play Dan Evans on the internet.
I am not a Certified Public Accountant, Nor do I play Paul Thomas on the internet.
I am not an Enrolled Agent, Nor do I play Richard Macdonald on the internet.
DO NOT TAKE MY WORD FOR ANYTHING ON THIS PAGE.
Go look it up for yourself.
Take $100 and purchase 4 hours of a mechanic's labor. Sell that same 4 hours of labor at the shop rate of $75 per hour. Gross receipt is $300. Subtract the expenses of Rent or mortgage; phone; electric; gas ($194).
$300 - $194 = $106
$106 -100 = $6
ROI = 6%
You started with $100. You invested it in labor. You've got your original $100 back plus 6% gain "derived" from labor.
Take $100 and purchase one hour of labor ($25); one circular saw ($50); and one thick large chunk of oak board ($25). Your employee works for one hour cutting up the board into wedgits door stops. You sell your entire stock of wedgits for $106.
$106 -100 = $6
ROI = 6%
You started with $100. You invested it in capital goods (the saw); labor; and raw material. You've got your original $100 back plus 6% gain "derived" from capital and labor. Your worker did not tear up your saw. You sell your saw for $25 (half of new price because it is used and depreciated.) you add this to your gross reciepts.
$106 + $25 = $131
$131 - 100 = $31
ROI = 31%
This is gain derived from capital, and labor, including a profit gained through a sale or conversion of capital assets.
In the case of making wedgits, a competitor is a corporation. You invest the $100 you have in purchasing a share of the corporate stock. The corporation's figures are exactly the same as yours were, only they are doing a larger volume of business. The corporation makes the same $106 on the original $100 just like you did. The corporation declares a dividend and sends you $6. You have just received a return on your investment of 6%. The corporation takes the other $100 and purchases two more hours of labor and two more oak boards. These sell for $212. The corporation declares a dividend and sends you $12 using the remaining $200 to purchase more labor and raw materials.
You sell your single share of stock for $200. The new owner believes he will get dividends of $12 which means he gets a 6% ROI... Just like you did. You have just sold and converted your capital asset. You received a 100% ROI because of the appreciated value of the stock. In every example the ROI is the 16th Amendment income.
Compensation for Labor ("payroll") is NOT a "return on investment".
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370507738.45/warc/CC-MAIN-20200402173940-20200402203940-00113.warc.gz
|
CC-MAIN-2020-16
| 2,514 | 21 |
http://community.novacaster.com/showarticle.pl?id=199
|
math
|
Spend your weekend doing O'level geometry 'cos you don't trust what's written in a book you're reading (John Michell's "The View Over Atlantis" page 115 of the 3rd ed. Ballantine Books 1973 ISBN 345-02881-3-150, in case you're interested).
This book and many others claim that the angle of slope of the Great Pyramid of Khufu (noted as 51° 51') is contained within a particular construction based on the vesica piscis figure.
Actually, the vesica piscis construction results in an angle of 51° 36' 38".
So either the pyramid builders didn't base the pyramid on this construction, or they weren't completely accurate, or the remains of the pyramid are so eroded we can't be sure what the intended angle of slope might have been.
Any way up, you can't say that this construction gives you a 51° 51' angle, 'cos it doesn't.
See the attachment for the proof.
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247496694.82/warc/CC-MAIN-20190220210649-20190220232649-00111.warc.gz
|
CC-MAIN-2019-09
| 857 | 6 |
https://attic.city/item/JWry/vintage-plates-hollywood-regency-art-deco-design-porcelain-set-of-6-/orwa-designs
|
math
|
Vintage Plates Hollywood Regency Art Deco Design Porcelain Set of 6
I dont quite know the year these were produced but its fine porcelain sheng xing china. These plates are snack sized at 7.5” across. They feature ...
$$$$$ · Indexed on May 10, 2022
ATTIC Availability Predictor beta
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103328647.18/warc/CC-MAIN-20220627043200-20220627073200-00618.warc.gz
|
CC-MAIN-2022-27
| 286 | 4 |
https://ru-facts.com/why-do-you-love-mathematics/
|
math
|
Why do you love mathematics?
Numbers help us understand the world, and Math helps us understand numbers. The real-life applications of Mathematics are endless. We are surrounded by numbers, equations and algorithms – especially in this age of data science, with huge data sets that can only be understood through statistical models and analysis.
How is math used in everyday life?
Preparing food. Figuring out distance, time and cost for travel. Understanding loans for cars, trucks, homes, schooling or other purposes. Understanding sports (being a player and team statistics)
Does math have a tagline?
Do The Math. Don’t be scared of inequalities. Don’t forget the correct sign, Math is so easy it’s divine. Don’t Get Mad, Get Even.
What are mathematical quotes?
Math is fun.
Why is mathematics important in life?
Math helps us have better problem-solving skills. Math helps us think analytically and have better reasoning abilities. Analytical thinking refers to the ability to think critically about the world around us. Analytical and reasoning skills are important because they help us solve problems and look for solutions.
What is a good quote for math?
25 inspirational math quotes. 1. “Do not worry about your difficulties in mathematics. I can assure you mine are still greater.”. – Albert Einstein. 2. “The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”. – Charles Caleb Colton.
What are some quotes about math as an art form?
Quotes about math as an art form. 1. “Mathematics is, in its way, the poetry of logical ideas.”. – Albert Einstein. 2. “Mathematics is the music of reason.”. – James Joseph Sylvester. 3. “Mathematics is the most beautiful and most powerful creation of the human spirit.”.
How to use math quotes to inspire students?
You can use these quotes to inspire yourself or your students. Create a math-rich environment by posting the math quotes around your classroom. Or, write them on the board each day and discuss the meaning of the quote. Most important, share math quotes to have fun! 1. “Do not worry about your difficulties in mathematics.
What do you need to know about maths?
All one needs for mathematics is a pencil and paper. 29. Mathematics Is an Edifice, Not a Toolbox 30. Mathematics is an independent world created out of pure intelligence.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499654.54/warc/CC-MAIN-20230128184907-20230128214907-00408.warc.gz
|
CC-MAIN-2023-06
| 2,365 | 18 |
http://gate.examsavvy.com/advanced-engineering-mathematics_16/
|
math
|
John Wiley & Sons | 2005-12-29 | ISBN: 0471728977 | 1232 pages | PDF | 18.27 MB
This is an absolutely great book for your GATE mathematics preparation. At over 1000 pages it’s a real opus – covering everything from ordinary differential equations, linear algebra, vector calculus, fourier analysis, complex analysis and probability. It’s exceptionally well written – with plenty of clear examples, diagrams and exercises – constantly cross referencing back to the particular idea or formula that an example is employing. It presupposes only elementary calculus – and so makes an excellent university textbook to accompany study, or as a self-study book to further your maths knowledge.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890874.84/warc/CC-MAIN-20180121195145-20180121215145-00734.warc.gz
|
CC-MAIN-2018-05
| 697 | 2 |
http://en.wikipedia.org/wiki/Low-complexity_art
|
math
|
||The topic of this article may not meet Wikipedia's general notability guideline. (June 2014)|
Low-complexity art, first described by Jürgen Schmidhuber in 1997, is art that can be described by a short computer program (that is, a computer program of small Kolmogorov complexity). Schmidhuber characterizes it as the computer age equivalent of minimal art. He also describes an algorithmic theory of beauty and aesthetics based on the principles of algorithmic information theory and minimum description length. It explicitly addresses the subjectivity of the observer and postulates that among several input data classified as comparable by a given subjective observer, the most pleasing one has the shortest description, given the observer’s previous knowledge and his or her particular method for encoding the data. For example, mathematicians enjoy simple proofs with a short description in their formal language (sometimes called mathematical beauty). Another example draws inspiration from 15th century proportion studies by Leonardo da Vinci and Albrecht Dürer: the proportions of a beautiful human face can be described by very few bits of information.
Schmidhuber explicitly distinguishes between beauty and interestingness. He assumes that any observer continually tries to improve the predictability and compressibility of the observations by discovering regularities such as repetitions and symmetries and fractal self-similarity. When the observer's learning process (which may be a predictive neural network) leads to improved data compression the number of bits required to describe the data decreases. The temporary interestingness of the data corresponds to the number of saved bits, and thus (in the continuum limit) to the first derivative of subjectively perceived beauty. A reinforcement learning algorithm can be used to maximize the future expected data compression progress. It will motivate the learning observer to execute action sequences that cause additional interesting input data with yet unknown but learnable predictability or regularity. The principles can be implemented on artificial agents which then exhibit a form of artificial curiosity.
While low-complexity art does not require a priori restrictions of the description size, the basic ideas are related to the size-restricted intro categories of the demoscene, where very short computer programs are used to generate pleasing graphical and musical output.
- J. Schmidhuber. Low-complexity art. Leonardo, Journal of the International Society for the Arts, Sciences, and Technology, 30(2):97–103, 1997. http://www.jstor.org/pss/1576418
- J. Schmidhuber. Facial beauty and fractal geometry. Cogprint Archive: http://cogprints.soton.ac.uk , 1998
- J. Schmidhuber. Simple Algorithmic Principles of Discovery, Subjective Beauty, Selective Attention, Curiosity & Creativity. Proc. 10th Intl. Conf. on Discovery Science (DS 2007) p. 26-38, LNAI 4755, Springer, 2007. Also in Proc. 18th Intl. Conf. on Algorithmic Learning Theory (ALT 2007) p. 32, LNAI 4754, Springer, 2007. Joint invited lecture for DS 2007 and ALT 2007, Sendai, Japan, 2007. http://arxiv.org/abs/0709.0674
- J. Schmidhuber. Curious model-building control systems. International Joint Conference on Neural Networks, Singapore, vol 2, 1458–1463. IEEE press, 1991
- Schmidhuber's Papers on Low-Complexity Art & Theory of Subjective Beauty
- Schmidhuber's Papers on Interestingness as the First Derivative of Subjective Beauty
- Examples of Low-Complexity Art in a German TV show (May 2008)
|This computing article is a stub. You can help Wikipedia by expanding it.|
|
s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413510834349.43/warc/CC-MAIN-20141017015354-00304-ip-10-16-133-185.ec2.internal.warc.gz
|
CC-MAIN-2014-42
| 3,623 | 12 |
http://www.slideshare.net/DelftOpenEr/k-oe4625-chapter08
|
math
|
8. OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM8.1 DETERMINATION OF A REQUIRED MANOMETRIC PRESSURE IN A PUMP-PIPELINE SYSTEMA lay out of a dredging pipeline, properties of transported solids and required mixtureflow conditions (mixture velocity and density in a pipeline) determine a manometricpressure that must be produced by a dredge pump. The manometric pressure requiredto overcome the dredging-pipeline resistance is a pressure differential over a dredgepump, i.e. a differential between the pressure at the pump outlet to a discharge pipeand the pressure at the inlet to a pump connected with a suction pipe. If no geodeticheight is assumed between the pump inlet and outlet ρ m Vp − Vs 2 2 Pman = Pp − Ps + (8.1). 2For flow of mixture of density ρm the absolute suction pressure at a pump inlet (Fig.8.1) ρf Vs2 Ps = Patm + ρfghs,pipe - ρmg(hs,pipe – hs,pump) - ρfgHtotloss,s,m - (8.2). 2 Ps absolute suction pressure at a pump inlet [Pa] Patm absolute atmospheric pressure [Pa] hs,pipe depth of a suction pipe inlet below a water level [m] hs,pump depth of a pump inlet below a water level [m] Htotloss,s,m total head lost due to friction in a suction pipe [m] Vs mean velocity of mixture in a suction pipe [m/s]and the absolute discharge pressure at a pump outlet (Fig. 8.1) ρf Vp2 Pp = ρmg(hd,pipe+hd,pump) + ρfgHtotloss,d,m + Patm - (8.3) 2 Pp absolute discharge pressure at a pump outlet [Pa] hd,pipe vertical distance between a water level and a discharge pipe outlet [m] hd,pump depth of a pump outlet below a water level [m] Htotloss,d,m total head lost due to friction in a discharge pipe [m] Patm absolute atmospheric pressure [Pa]. Vp mean velocity of mixture in a discharge pipe [m/s] 8.1
8.2 CHAPTER 8 Patm hd,pipe hs,pump Ps hd,pump hs,pipe Pump-pipeline system: mean velocity V mixture density rm Figure 8.1. Lay-out of a pump-pipeline system.The Eqs. 8.1 – 8.3 give a relationship between the manometric pressure delivered by apump to mixture and the velocity of mixture in a pipeline connected to the pump. Thisrelationship is further dependent on solids size and concentration in a pipeline and toa pipeline lay-out. The relationship is used to optimise the production and the energyconsumption of a pump-pipeline system during a dredging operation. A suitable rangeof a system operation is confined by limits arising from processes occurring in adredging pipeline. An entire system does not work successfully if a dredge pumpoperates outside the operational limits.In a pump-pipeline system the flow rate of mixture must be controlled to remainwithin a certain range suitable for a safe and economic operation. The flow-rate rangehas a lower limit given by the deposition-limit velocity and an upper limit given bythe velocity at which pump starts to cavitate.8.2 THE UPPER LIMIT FOR A SYSTEM OPERATION: VELOCITY AT THE INITIAL CAVITATION OF A PUMPA cavitation phenomenon is associated with low absolute pressure in a liquid. Acavitation is a condition in a liquid in which the local pressure drops below the vapourpressure and vapour bubbles (cavities) are produced. Cavitation decreasesconsiderably a pump efficiency and might be a reason of a damage of pumpcomponents (pitting and corrosion). A cavitating pump provides lower manometrichead and thus the lower production of solids by a dredging pipeline. The pumpcavitation must be avoided during a pump-pipeline system operation.
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 220.127.116.11 Criterion for non-cavitational operation of a systemA pump begins to cavitate, i.e. cavitation occurs at the suction inlet to a pumpimpeller, if the Net Positive Suction Head (NPSH) available to prevent pumpcavitation is smaller than NPSH required by a pump to avoid cavitation.The no cavitation condition for a certain pump-suction pipe combination is: (NPSH)r < (NPSH)ain which:The available (NPSH)a is a total available energy head over the vapour pressure atthe suction inlet to the pump during an operation at velocity Vm in a suction pipe of acertain geometry and configuration. Ps − Pvapour 2 Vm Patm( NPSH )a = + = + h s,pipe − H totloss,s,m − Sm ( h s,pipe − h s,pump ) ρf g 2g ρf g Pvapour− ρf g (8.4) (NPSH)a Net Positive Suction Head Available [m] Pvapour vapour pressure [Pa].The vapour pressure of a pumped medium limits the minimum absolute pressure thatcan be theoretically reached at the suction side of a pump. At this pressure the liquid(water) is transformed into steam. The steam bubbles develop in a water flow, theyenter the pump and deteriorate its efficiency. The vapour pressure is dependent on thetemperature of a medium. For water the typical values are:Temperature T [oC]: Vapour pressure Pvapour [kPa]:10 1.1820 2.27The lay-out of a suction pipe and flow conditions in a pipe determine the absolutesuction pressure available at the pump inlet.
8.4 CHAPTER 8 Figure 8.2. Net Positive Suction Head Available on a suction inlet of a pump.The required (NPSH)r is a minimum energy head a certain pump requires to preventcavitation at its inlet. This is a head value at the incipient cavitation. The (NPSH)r-Qcurve is a characteristic specific for each pump and it must be determined by tests. Adesign (dimensions, shape) and an operation (specific speed) of a pump decide theabsolute suction pressure at the initial cavitation. Ps, min − Pvapour Vm2 (NPSH )r = + (8.5) ρf g 2g (NPSH)r Net Positive Suction Head Required [m] Ps,min minimum absolute suction pressure without cavitation [Pa] Pvapour vapour pressure [Pa].At the incipient cavitation the absolute suction pressure Ps,min at the pump inlet isequal to the difference between the atmospheric pressure Patm and the so-called“decisive vacuum” (Dutch: maatgevend vacuum) (Vac)d, i.e. (Vac)d = Patm – Ps,min (8.6).The decisive vacuum is the relative suction pressure that represents a thresholdcriterion for a non-cavitational operation of a certain pump.If a pump starts to cavitate it looses its manometric head. The (Vac)d is defined as thevacuum at the flow rate for which the manometric head is 95 per cent of thenon-cavitational manometric head at the same pump speed (r.p.m.). The (Vac)d is
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 8.5related with the flow rate in a “decisive-vacuum curve” in a H-Q plot (see Fig. 8.3).The decisive-vacuum curve is determined by a cavitation test. 300 5% manometrische druk (kPa) 250 200 vernauwde zuigleidingen 150 vacuüm maatgevend vacuüm 75 manometrische druk (kPa) 50 vernauwde onvernauwde 25 zuigleidingen zuigleiding 0 1 2 3 debiet (m3/s) Figure 8.3. Decisive vacuum (Dutch: Maatgevend vacuum) curve of a pump.A substitution of Eq. (8.5) to Eq. (8.6) and rearranging gives a relationship betweenthe (NPSH)r and the decisive vacuum (Vac)d ( Vac) d Patm Pvapour Vm2 = −( NPSH ) r + − + (8.7). ρf g ρf g ρf g 2gAs follows from the relationship between the (HPSH)r and the decisive vacuum(Vac)d a cavitation test gives also the (NPSH)r-Q curve, i.e. the minimum NPSH as afunction of capacity Q.
8.6 CHAPTER 8An upper limit for the working range of a pump-pipeline system is given by points ofintersection of a pump decisive vacuum curve and a set of vacuum curves of a suctionpipe for various mixture densities. The vacuum curve of a suction pipe summarisesthe friction, geodetic and acceleration heads over an entire length of the suction pipeto the total vacuum head and relates this head with a pump capacity (see Fig. 8.4a,8.4b and 8.4c). The total vacuum head, Vac/ρfg, is a difference between the totalabsolute suction pressure head and the atmospheric pressure head V2 Vac Patm − Ps ρf g = ρf g ( ) = S m h s, pipe − h s, pump − h s, pipe + H totloss,s, m + s 2g (8.8) Vac vacuum; the pressure relative to atmospheric Patm [Pa] ρf density of liquid [kg/m3] g gravitational acceleration [m/s2] Ps absolute suction pressure at a pump inlet [Pa] Patm absolute atmospheric pressure [Pa] Sm relative density of mixture (ρm/ρf) [-] hs,pipe depth of a suction pipe inlet below a water level [m] hs,pump depth of a pump inlet below a water level [m] Htotloss,s,m total head lost due to friction in a suction pipe [m]. Vs mean velocity of mixture in a suction pipe [m/s]Figure 8.3a. Decisive vacuum curve and vacuum curves of a suction pipe for flow of mixture of various densities (schematic).
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 8.7 Figure 8.4b. Figure 8.4c.Figure 8.3b. Decisive vacuum curve and vacuum curves of a suction pipe transporting mixture of various densities from the depth 9 meter (after v.d.Berg, 1998).Figure 8.3c. Decisive vacuum curve and vacuum curves of a suction pipe transporting mixture of various densities from the depth 18 meter (after v.d. Berg, 1998).Table 8.1. Points of intersection between decisive vacuum curve and vacuum curves for different mixture densities; the intersection points determine the maximum production of solids attainable for given mixture density in a pump-pipeline system lifting mixture from a certain depth (see Fig. 9.1 in Chapter 9).
8.8 CHAPTER 88.2.2 How to avoid cavitationBasically, cavitation is avoided if the absolute suction pressure of a pump ismaintained above a certain critical value. An analysis of the above explainedcavitational criterion leads to the following proposals:- to reduce the static head that the pump must overcome, i.e. to put the pump as low as possible (see par. 8.5)- to reduce the head lost due to flow friction, i.e. to minimise local losses and a suction pipe length- to increase pressure by using a larger pipe at the suction inlet of a pump (see par. 8.4).During an operation (if the position of a pump and a geometry of a suction pipelinecan not be changed) friction losses can be reduced- either by diminishing the mean mixture velocity in a pipeline- or by reducing the mixture density in a suction pipeline.8.3 THE LOWER LIMIT FOR A SYSTEM OPERATION: VELOCITY AT THE INITIAL STATIONARY BED IN A PIPELINEIt was shown in the previous paragraph that high head loss due to too high velocity ofmixture in a dredging installation might cause cavitation in a dredge pump and thus aconsiderable reduction of production and even a damage of a pump. On the otherhand too low velocity might cause unnecessarily high head losses due to friction too.Furthermore the too low velocity might cause a blockage of a pipeline.8.3.1 Criterion for a deposit free operation of a systemIf settling mixtures are transported a portion of solids occupies a granular bed at thebottom of a pipeline. The part of solids that occupies the bed is strongly dependent onthe mixture velocity in a pipeline. Under the increasing velocity the thickness of thebed tends to diminish because still more particles tend to be suspended due toincreasing turbulent intensity of a carrying liquid. However, if the velocity isdecreasing instead of increasing the bed becomes thicker and at certain velocity,called the deposition-limit velocity (or critical velocity), the first particles in the bedstop their sliding over a pipeline wall. If velocity decreases further the entire bedstops and, under certain circumstances, dunes might be developed at the top of astationary bed. The flow becomes instable and a pipeline might be blocked. This ismore likely to happen in some “critical” parts of a pipeline as are bends, particularlythose to vertical pipe sections. A danger of blockage increases if solids occupy aconsiderable part of a total pipeline volume.Even if a blockage is not likely to happen due to relatively low concentration and/oran absence of critical pipeline parts during a dredging operation, it is worthwhile towatch out the deposition-limit value of the mean mixture velocity in a pipeline. A
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 8.9presence of a stationary bed means that solids that are actually not transported occupya part of a pipeline. A stationary bed reduces a pipeline discharge area and sotremendously increases the frictional losses. Frictional losses not far below thedeposition-limit velocity might be much higher than losses at even very high mixturevelocities. On the other hand, an operation at velocity only slightly above thedeposition-limit value is economic since the frictional loss at this velocity is usuallyconsiderably lower than at the extremes of a velocity range. The effects of velocity onthe frictional losses and the variation of deposition-limit velocity under the differentmixture flow conditions were discussed to details in earlier chapters.The deposition-limit velocity is for most dredging operations considered the lowerlimit for a range of operational velocity. The boundary given by this velocity can beplotted to the H-Q (or Im-Vm) plot as a curve connecting deposition-limit velocityvalues for different solids concentrations in a mixture flow of certain material in apipeline of a certain diameter (see Fig. 8.5). Figure 8.5. Locus curve giving a velocity at an initial stationary bed.8.3.2 How to avoid a stationary bed in a pipelineIf the pipeline is composed of sections of different pipe sizes, the mixture flow ratemust be maintained at the level assuring a super-critical regime (Vm > Vdl) in thelargest pipe section (the section of the largest pipe diameter). Consider that in thelargest section the mixture velocity is the lowest (continuity equation) and moreoverthe deposition-limit value of the mixture velocity is the highest because Vdl tends togrow with pipe diameter.If the solids concentration fluctuates along a pipeline, the mixture flow rate must bemaintained at the level assuring a super-critical regime in the section of an extremeconcentration. For a prediction, use the highest value of the deposition-limit velocityfrom the entire range of expected solids concentrations. Vdl is sensitive to solids
8.10 CHAPTER 8concentration, it is always better to be slightly conservative in a determination of theappropriate value.If during a job a dredging pipeline is prolonged, the flow rate supplied by a dredgepump might become insufficient to assure a super-critical regime in a pipeline. Thentwo solutions must be considered:- to pump mixture at much lower concentration; this will lead to lower frictional losses and thus higher flow rate that might be high enough to avoid a thick stationary bed in a pipeline- to install a booster station; this increases a manometric head provided by pumps and increase a flow rate.If coarser solids must be pumped than expected when a dredging installation was laidout, the flow rate supplied by a pump might become insufficient to assure asuper-critical regime in a pipeline. Then again the above two solutions must beconsidered.8.4 EFFECT OF PIPE DIAMETER ON OPERATION LIMITSFor a certain required flow rate of mixture a larger pipeline means lower meanvelocity in comparison with a smaller pipeline. This means that there is a betterchance to pump a mixture without a danger of pump cavitation if a suction pipe islarger. Furthermore, a pipe resistance decreases with an increasing pipe diameter.This has also a positive effect with regard to a pump cavitation limit. On the otherhand a possibility that a stationary bed will be developed in a pipeline increases withan increasing pipeline diameter.A suction pipe larger than a discharge pipe is installed in some dredging installations.The diameter of a suction pipe is chosen to be of about 50 mm larger than that of adischarge pipe if a system is designed for transportation of fast-settling mixtures(flows of coarse or heavy particles). An operation at the suction side of a dredgingpipeline is usually limited by a pump cavitation. For a certain mixture flow rate thevelocity in a suction pipe is low and this helps to avoid cavitation. This is moreimportant than a presence of a stationary bed that may possibly occur in a shortsuction pipe. The presence of a stationary bed is more dangerous in a long dischargepipe and since a cavitation is very unlikely to occur in a discharge pipeline thedeposition-limit velocity limits an operation in a discharge pipeline. It is useful tochoose smaller pipe diameter (when compared to a suction pipe) to avoid thesub-critical regime of mixture flow. A higher frictional loss and a higher wear of apipeline wall of course pay this.
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 8.11 8.5 EFFECT OF PUMP POSITION ON OPERATION LIMITS If a pump is placed to a lower position within a pump-pipeline system a suction pipe becomes shorter. A geodetic height over which a mixture has to be lifted in a suction pipe becomes smaller. In a shorter suction pipe pressure loss due to flow friction over a suction pipe length is lower than that in a suction pipe of an original length. A vacuum curve for a shorter suction pipe shows lower vacuum value at a certain flow rate for mixture of certain density. Thus a cross point between a decisive vacuum curve and a vacuum curve for a certain mixture density is reached at higher capacity Q (compare Fig. 8.4c and Fig. 8.6). Since the total resistance (expressed by a vacuum curve) of a suction pipe is lower in a shorter suction pipe than in a pipe of an original length the margin occurs between a net positive suction pressure required and available at a pump inlet. Consequently, pipe vacuum curves of mixture density higher than is that for an original pipe still cross the decisive vacuum curve of a pump. The mixture of density higher than in an original pipe can be pumped before an upper limit of a pump-pipeline operation is reached (compare Tab. 8.1 and Tab. 8.2). This means a considerable improvement of production. Therefore a submerged pump (a pump placed on a inclined pipe below a water level) is often used on dredging installations. Figure 8.6. Table 8.2.Figure 8.6. Decisive vacuum curve and vacuum curves of a suction pipe transporting mixture of various densities from the depth 18 meter using a pump positioned 5 meter below the water level (after v.d. Berg, 1998).Table 8.2. Points of intersection between decisive vacuum curve and vacuum curves for different mixture densities as shown on Fig. 8.6; the intersection points determine production of solids at conditions in a pump-pipeline system with a pump 5 meter below a water level (see Fig. 9.5 in Chapter 9).
8.12 CHAPTER 8 8.6 OPERATION LIMITS ON A H-Q DIAGRAM OF A PIPELINE Fig. 8.7 shows a working range of a dredge pump that pumps, with a constant pump speed, a mixture of a constant density through a discharge pipeline of variable length. The maximum length of the pipeline is limited by the deposition-limit velocity. If the pipeline would be longer the pressure delivered by the pump would not be enough to maintain the mean velocity of mixture in the discharge pipeline above the deposition-limit threshold. The minimum length of the discharge pipeline is limited by the decisive vacuum of a pump. If the pipeline would be shorter, the high mean velocity would cause so high frictional pressure losses in a suction pipe that cavitation would occur in a suction side of the pump. langste persleiding constant toerental kortste persleiding 850 manometrische druk (kPa) 750 650 550 werkgebied 450 onderkritisch bovenkritisch 100 maatgevend vacuüm 75 vacuüm (kPa) 50 zuigleiding- 25 karakteristiek 0 1 Qkritisch 2 3 Qmaatg. vacuüm debiet (m 3/s)Figure 8.7. Working range of a dredge pump in a pump-pipeline system. The deposition-limit (critical) velocity in a pipeline and the decisive vacuum of the pump limits the working range.
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 8.138.7 RECOMMENDED LITERATUREvan den Berg, C.H. (1998). Pipelines as Transportation Systems. European MiningCourse Proceedings, MTI.de Bree, S.E.M. (1977). Centrifugaal Baggerpompen. IHC Holland.
8.14 CHAPTER 8CASE STUDY 8.1For this Case study the same dredging installation and the same mixture flowconditions are considered as in Case study 7.1>A deep dredge has a centrifugal pump on board. The heart of the pump is on the samegeodetic height as the water level. The suction and the discharge pipes are mounted tothe pump at the pump-heard level. The suction pipe of the dredge is vertical and thedischarge pipe is horizontal. Both pipes have a diameter 500 mm. The dredge pumppumps the 0.2-mm sand from the bottom of the waterway that is 7 meter below thewater level (thus the dredging depth is 7 meter). The density of a pumped sand-watermixture is 1400 kg/m3. The discharge pipe is 750 meter long. The pump-pipelineinstallation is supposed to keep the production at 700 cubic meter of sand per hour.1. Determine whether for the above described conditions the mean velocity through a pipeline high enough is to avoid a stationary deposit in the pipeline.2. Determine whether for the above described conditions the pressure at the suction mouth of the pump is high enough to avoid cavitation. The minimum pressure for the non-cavitational operation is considered 3 x 104 Pa.For the calculation consider the friction coefficient of the suction/discharge pipes λ =0.011. The following minor losses must be considered: - the inlet to the suction pipe: ξ = 0.5, - the 90-deg bend in suction pipe: ξ = 0.1, - the flanges in the suction pipe: ξ = 0.05, - the flanges in the discharge pipe: ξ = 0.25, - the outlet from the discharge pipe: ξ = 1.0.Additional inputs: ρf = 1000 kg/m3 ρs = 2650 kg/m3Inputs: ∆hdepth = 7 m Lhor = 750 m D = 500 mm d50 = 0.20 mm ρs = 2650 kg/m3, ρf = 1000 kg/m3, ρm = 1400 kg/m3 λf = 0.011, Σξ = 1.9 Qs = 700 m3/hour = 0.194 m3/sRemark: To make a calculation simpler the effect of a pipeline roughness on frictional losses in a pipeline is considered to be represented by a constant value of the frictional coefficient λf , i.e. independent of variation of mean mixture velocity.
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 8.151. Comparison of the actual velocity with the deposition-limit velocityMean velocity of mixture in a pipeline, Vm: ρ − ρf 1400 − 1000C vd = m = = 0.2424 [-], ρs − ρf 2650 − 1000 Q 0.1944Qm = s = = 0.802 m3/s, C vd 0.2424 4Qm 4 x 0.802Vm = = = 4.085 m/s. πD 2 3.1416 x 0.52Deposition-limit velocity:Vsm = 2.9 m/s (the Wilson nomograph, Fig. 4.8)Vcrit = 3.3 m/s (the MTI nomograph, Fig. 4.6)The actual average velocity in a horizontal pipeline behind the pump is higher thanthe deposition-limit velocity. There will be no stationary deposit at the bottom of thepipeline for velocity 4.09 m/s.2. Comparison of the actual suction pressure at the pump with the minimum pressure for non-cavitational operationEnergy balance for the suction pipe (the Bernoulli equation): Vm2Pinlet = Psuct + ∆Pstatic + ∆Ptotloss,m + ρf 2in which Pinlet = Patm + ∆hdepth.ρf.g, ∆Pstatic = ∆hdepth.ρm.g, ∆h depth Vm2 ∆Ptotloss,m = λf + Σξsuct ρm . D 2∆Pstatic the static pressure differential between the inlet and the outlet of the suction pipe;∆Ptotloss,m the total pressure loss (both major and minor) over the length of a pipe;Psuct the absolute pressure at the outlet of the suction pipe;Patm the atmospheric pressure. ∆h depth Vm2 Vm2Psuct = Patm - ∆hdepth (ρm - ρf) g - λ f + Σξsuct ρm - ρf D 2 2 7 4.092 4.092Psuct = 105–7(1400-1000)9.81- 0.011 + 0.65 1400 - 1000 = 54.7 kPa. 0.5 2 2The absolute pressure at the suction mouth of the pump is 54.7 kPa. This is higherthan the minimum non-cavitation pressure 30 kPa. The pump will not cavitate.
8.16 CHAPTER 8CASE STUDY 8.2In Case study 7.2 the maximum length was determined of a pipeline connected with acentrifugal pump operating at its maximum speed if mixture of density 1412.5 kg/m3composed of water and a 0.3 mm sand is transported. The flow rate of pumpedmixture was determined for a pipeline of a maximum length. It is necessary to checkwhether this flow rate is attainable in a system, i.e. whether it lays within anoperational range of a pump-pipeline system.Determine the limits of an operational range of a pump-pipeline system (the system isdefined in Case study 7.2) and check whether the flow rate for the pipeline of themaximum length lays within this range. Determine the range of pipeline lengths inwhich a pump can operate at the maximum speed (475 rpm) if density of pumpedmixture is 1412.5 kg/m3.Solution:A. The upper limit for a system operation:CALCULATION:a. Pump characteristicsThe decisive-vacuum curve of the IHC pump can be approximated by the equation (Vac )d = 94.99 − 3.64Q m − 2.43Q 2 m [kPa] (C8.1).b. Suction pipeline characteristicsThe vacuum-curve equation (Eq. 8.8) for a suction pipeline of ∆hs,pipe =∆hdepth = 15 m ∆hs,pump = 0 mgets a form of Eq. C7.13. This equation is solved for the following input values ω = 45 deg Lhoriz,suction = 2 mMinor-loss coefficient: Suction pipeline: pipe entrance: ξ = 0.4 all bends, joints etc.: ξ = 0.3 Total value: Σξ = 0.7 15Vac = ∆ptotalpipe,m = 0.28498 Q 2 (2+ m ) + Q −1.7 (Sm - 1)(0.67924x2 + m sin(45) 15 0.35774 ) + 12.97x0.7 Sm Q 2 + 9.81 (Sm - 1)x15 [kPa] (C8.2). m sin(45)For Sm = 1.4125
OPERATION LIMITS OF A PUMP-PIPELINE SYSTEM 8.17 15Vac = ∆ptotalpipe,m = 0.28498 Q 2 (2+ m ) + Q −1.7 0.4125(0.67924x2 + m sin(45) 15 0.35774 ) + 12.97x0.7x1.4125 Q 2 + 9.81x0.4125x15 [kPa] m sin(45)Balance: (Vac)d = Vac (Eq. C8.1) (Eq. C8.2)determines the flow rate value (Qupper) at the beginning of cavitation of a pump. Thisflow-rate value is the upper limit of an operational range of a pump-pipeline systempumping an aqueous mixture of 300-micron sand at mixture density 1412.5 kg/m3.Only operation at flow rates lower than this threshold value will be cavitation free.OUTPUT:For Sm = 1.4125 the upper limit of a pump-pipeline operation is given by Qupper = 1.115 m3/s.B. The lower limit for a system operation:The lower limit is given by the flow rate value (Qlower) at the critical(deposition-limit) velocity.CALCULATION:The MTI correlation (Eq. 4.19) for the critical velocity gives 1 1 0.25 6 2.65 − 1 Vcrit = 1.7 5 − 0.5 = 3.61 m / s, 0.3 0.25 + 0.1 1.65 πD 2 πx 0.52 Qlower = Vcrit A = Vcrit = 2.92 = 0.709 m 3 / s. 4 4OUTPUT:For Sm = 1.4125 the lower limit of a pump-pipeline operation is given by Qlower = 0.709 m3/s.C. The range of lengths of an entire pipeline:
8.18 CHAPTER 8Balance Pman,m = ∆ptotalpipe,m (Eq. C7.5) (Eq. C7.13)- for the working point at Qupper = 1.115 m3/s gives the length of an entire pipeline L = 610 meter. This is the minimal length for which the 1412.5 kg/m3 mixture can be pumped. If the pipeline becomes shorter, the flow rate tends to increase. This would cause cavitation at the inlet of a pump. The density of transported mixture in a short pipeline must be lowered to avoid cavitation;- for the working point at Qlower = 0.709 m3/s gives the length of an entire pipeline L = 1123 meter. This working point lays at the descending part of a pipeline resistance curve. An operation at this part of the curve should be avoided, since it is potentially instable and energy costly (see Fig. C7.4). The recommended minimum flow rate for pumping the 1412.5 kg/m3 mixture at the maximum speed of the pump is that the maximum length of a pipeline (see Case study 7): Lmax = 975 meter, i.e. Qminimum = 0.897 m3/s.
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461861812410.28/warc/CC-MAIN-20160428164332-00076-ip-10-239-7-51.ec2.internal.warc.gz
|
CC-MAIN-2016-18
| 27,140 | 18 |
https://community.opentargets.org/t/phewas-significance-threshold/533
|
math
|
Thank you for this wonderful resource. Could you please specify what is the significance threshold in the PheWAS plots, and how it was obtained? It appears to be around 1.3e-5 but I could not find it in the documentation.
Thanks in advance!
Hi @Adil_Harroud, and welcome to the Open Targets Community!
Only traits with P-value < 0.005 are returned on the PheWAS plot. I’m not sure if this answers your question?
Thank you for your reply. On the PheWAS plots (example attached), there is a horizontal red line near 10-5 on the y axis (p-values). Does this red horizontal line represent a certain significance threshold for the PheWAS? If so, what is this significance threshold and how was it obtained? Alternatively, could you provide the number of traits tested for FinnGen + UKB + GWAS Catalog?
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663035797.93/warc/CC-MAIN-20220529011010-20220529041010-00263.warc.gz
|
CC-MAIN-2022-21
| 798 | 5 |
https://www.pineconeacademy.com/product/percentages-proportions-book-6/
|
math
|
This book will present the basic concept of equivalent ratios. The standard formula for finding a proportion is: ‘is’/’of’ = %/100. Problems will ask you to solve for one of the 3 unknowns, given the other two.
There are 20 books in the Pre-Algebra series. The first books continue from the Fraction series with more work on fractions and decimals. Books progress through percentages, proportions, metrics, scientific notation, order of operations and finally, probability in Book 20. Students who complete the Pre-Algebra series are now fully ready for Algebra (coming soon).
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986673250.23/warc/CC-MAIN-20191017073050-20191017100550-00139.warc.gz
|
CC-MAIN-2019-43
| 584 | 2 |
http://mynnettekitchenonastampage.blogspot.com/2012/10/the-mother-load.html
|
math
|
Here's the ML (Mother Load)~
And the deals~
$8 for 3 paper stacks
$6 for these two sets--the clear mount set is
a bunch of Valentine sentiments and images
$10 for these four set
$2 for 24 darling heart magnets (for school)
$1 for these adorable butterfly clips (possible bookmarks)
And now the BFL (Best For Last)~
$9 for this basket and its contents...
Which included ALL THESE STAMPS!!!
I'd say easily worth about $100?! Maybe?! Guesses?!
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917126538.54/warc/CC-MAIN-20170423031206-00340-ip-10-145-167-34.ec2.internal.warc.gz
|
CC-MAIN-2017-17
| 440 | 12 |
https://events.uwa.edu.au/event/[email protected]/whatson/CMSC
|
math
|
SEMINAR: Groups and Combinatorics Seminar: The generalised Curtis-Tits system and black box groups
|Groups and Combinatorics Seminar: The generalised Curtis-Tits system and black box groups
Groups and Combinatorics Seminar
Sukru Yalcinkaya (UWA)
will speak on
The generalised Curtis-Tits system and black box groups
at 12 noon in MLR2 on Tuesday 9th of March.
Abstract: The Curtis-Tits presentation of groups of Lie type is the main
identification theorem used in the classification of the finite simple
groups. I will describe the most general form of the Curtis-Tits
presentation of finite groups of Lie type where the Phan's
presentation for the twisted groups appears as a special case. I will
also talk about a beautiful application of this result to the
recognition of finite black box groups.
If time permits I will briefly talk about how Curtis-Tits and its Phan
variations link two theories: Theory of black box groups and groups of
finite Morley rank.
Maths Lecture Room 2
Tue, 09 Mar 2010 12:00
Tue, 09 Mar 2010 12:45
Michael Giudici <[email protected]>
Thu, 04 Mar 2010 10:38
- Locations of venues on the Crawley and Nedlands campuses are
available via the Campus Maps website.
- Download this event as:
Mail this event:
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359082.48/warc/CC-MAIN-20210227174711-20210227204711-00110.warc.gz
|
CC-MAIN-2021-10
| 1,232 | 26 |
https://learn.careers360.com/ncert/question-a-30-cm-wire-carrying-a-current-of-10-a-is-placed-inside-a-solenoid-perpendicular-to-its-axis-the-magnetic-field-inside-the-solenoid-is-given-to-be-027-t-what-is-the-magnetic-force-on-the-wire/
|
math
|
6. A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?
For a straight wire of length l in a uniform magnetic field, the Force equals to
In the given case the magnitude of the force is equal to
|F| = 0.27100.03sin90o (I=10A, B=0.27 T, =90o)
The direction of this force depends on the orientation of the coil and the current-carrying wire and can be known using the Flemings Left-hand rule.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144027.33/warc/CC-MAIN-20200219030731-20200219060731-00083.warc.gz
|
CC-MAIN-2020-10
| 534 | 5 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.