Steve B (22.214.171.124)
|Posted on Friday, June 14, 2002 - 01:13 pm: ||
Before getting to the main subject of this posting, may I make a couple of comments based on my experiences on this web site over the last 16 months.
1) There is no point at all in posting wild theories regarding the Pyramids in Egypt without first making substantial efforts to prove what you're talking about. If it is just plain nonsense that you wish to post, post it elsewhere and allow the people who use this board for research purposes to communicate.
2) Egyptologists do themselves no favours at all by ridiculing those people who suspect that there is more to the Pyramids than meets the eye. If we do not learn from our history, then we are doomed to repeat it and part of our recent history is the following quote from the German scientist Albert Einstein "Imagination is more important than intelligence". This quote comes from the time before sound bites were important, and is a statement full of meaning.
Now on to my posting.....
I have spent the last 16 months following my own advice, and pulling my own scientific analysis of the Great Pyramid to pieces to see if it stands up to the test. The following algebraic equation may be of interest to anyone who is really interested in the subject of the pyramids
The distance from the block at the end of the lower southern shaft to the lateral dislocation in that shaft is
2 x Pyramid Base Length x SQR(f) / ( 5 x Pi )
where f is the ratio of the Earths equatorial and polar diametres
see : http://dgfi2.dgfi.badw-muenchen.de/geodis/REFS/grs80.html
f = 1.00336408986
Since the pyramid is a purely mathematical construction based on the exact shape of the Earth, any point or angle in the pyramid can be specified using similar mathematics (once you've worked it out of course, and that has taken me 16 months)
To prove the point, I can quite happily supply the mathematical formula to most parts of the Great Pyramid, and all angles of shafts and corridors.
and P.S. - before writing replies to this posting, have another read of points 1 & 2 above.
Erik Calero (126.96.36.199)
|Posted on Friday, June 14, 2002 - 03:32 pm: ||
Maybe I miss something, but according with Rudolf Gantenbrinck measurements of the Great Pyramid, the lenght of the lower southern shaft from the block to the lateral dislocation is about 57 mts.
From your formula :
or if "Pyramid Base Lenght" must be taken as pyramid base side lenght = 230 mts. then :
2(230)*sqrt(1.0033640896)/5*3.1416) = 29.3337
I think, there some wrong with the formula (maybe a 2 is surplus)
Steve B (188.8.131.52)
|Posted on Friday, June 14, 2002 - 05:07 pm: ||
Your maths is fine, the second of the two equations that you have worked out is the intended one, and the length is indeed 29.3337 m when based on a 230 metre base.
It is the total length of the shaft from the southern chamber that is the approx 57 mtrs that you quote.
Just an additional note -
For the precision in this monument we need to use exact details of lengths, and you would probably be better suited using 9068.8 inches (230.3475m) as the base length from the Petrie survey.
Look forward to hearing from you again
|Posted on Friday, June 14, 2002 - 05:08 pm: ||
"Since the pyramid is a purely mathematical construction based on the exact shape of the Earth. . ."
Is this not in violation of your point 1 or where is the proof that it is "based on the exact shape of the Earth. . ."?
Furthermore, assuming your calculations are right, what do you deduce from them? The simple fact that a distance between any two points in the GP matches a formula doesn't mean anything in itself.
Steve B (184.108.40.206)
|Posted on Friday, June 14, 2002 - 06:39 pm: ||
Another example: the height of the entrance passageway above the pavement floor is given by the following formula (shown as a fraction where the top line should be divided by the bottom)
4ep(p2f+4f2+16) - 8e.SQR( 32p2(f2+2)+4f(p4+64)+f3(p4-64) )
Work it out using the previously supplied value of f.
Steve B (220.127.116.11)
|Posted on Friday, June 14, 2002 - 06:47 pm: ||
I would agree with your second statement that
The simple fact that a distance between any two points in the GP matches a formula doesn't mean anything in itself.
However when all the points in the pyramid fit into the same mathematical model, it definately does mean something.
Steve B (18.104.22.168)
|Posted on Friday, June 14, 2002 - 06:51 pm: ||
The value of 'e' in the second equation is half of the pyramid's base length ie 9068.8 / 2 inches.
Erik Calero (22.214.171.124)
|Posted on Saturday, June 15, 2002 - 12:53 am: ||
Sorry for the misunderstanding, I was in the belief that the lateral dislocation was the change of angle at the shaft (from the horizontal).
After review the cyberdrawings at Gantenbrink's site, I have notice of the called "lateral dislocation" at the lower southern shaft.
From the measurements at this cyberdrawing the ending block is at about 59.45 mts. and the lateral dislocation is at about 30.25 mts., so the distance between this 2 points is :
d = 59.45 mts. - 30.25 mts. = 29.2 mts.
(very close with 29.378045 mts. from your formula)
Ok, What's next ?
P.S. Without a clear base mathematical model, from these formulas can be derived, I found them disassociated and very complex.
May you show this mathematical model to us?
Thanks in advance.
Steve B (126.96.36.199)
|Posted on Saturday, June 15, 2002 - 07:27 am: ||
The following evaluation programme will prove invaluable if you have Auto CAD and want to convert DWF to DWG formats
Once the original Gantenbrink drawing is converted over to CAD format, you will find that it needs scaling down on the CAD system by 1.23 ie 100 cm on the original drawing is shown by 123 units. (Don't ask me why, thats just how it was drawn/published).
From here one can use the measuring tools on autocad to get exact distances off the drawings.
The distance that we are talking about for the lower southern shaft is 29.287295 metres according to Mr Gantenbrink.
The difference between this measurement and the formula measurement is 9.075 cm, which I am currently assuming is the width of the end block of the shaft.
1) Notable by its absence on the Upuaut website is any reference to error in the measurements. ie one would expect angles and lengths to be followed by +/- factors.
2) The length of the pyramid base on the Upuaut drawing is 231.000813m,giving 9094.52 inches as the base length. I can find no reference to this figure in any survey ie Petrie gives this length as 9068.8, and can only conclude that the Upuaut drawing is not reliable on the detailed measure. If anyone can argue against this statement, then please do, as I find it hard to believe that the drawing contains errors.
Hope this clarifies this subject of the length, and, as to the question of the rest of the model. You are obviously adept at mathematics, and can see into this work. Since I can't see your profile on this board, could you send me an e-mail before we go any further?
|Posted on Sunday, June 16, 2002 - 04:12 am: ||
I have a few comments, if you don't mind.
1. You've tried your model on various points of the pyramid I suppose. What was the error margin? 1%? 5%? Does the deviation fluctuate?
I'm not a mathematician, but a consistent (percentual) error margin makes sense to me. If the deviation (between your model and reality) varies constantly, would that emply, they were sloppy architects?
2. You're obviously using the modern (9 digit?) value for PI. Do you have any knowledge on what value the Egyptians used? For your model to work, you'll of course need the original value.
I found this on the web:
The Babylonians found the first known value for Pi in around 2000BC. They used (25/8)
The Egyptians used Pi = 3 but improved this to (22 / 7). They also used (256/81).
3. I'll use my imagination and what I come up with is that (if your model is right) "f" could be ratio of volume of two bananas. Or the weight ration of Khufu before and after supper.
f = 1.00336408986
Furthermore, this number tells us, the difference between max. longditude and max. latitude is less than 0.34%. Noone without advanced technology is capable of measuring the earth to such precision ... unless you're saying, they had help from "outside".
Well, it's a neat idea. Spock and Cpt. Kirk came to earth, Spock helped out with the pyramids, Kirk fell in love with some Egyptian chick ... yeah, that's probably what happened.
Or maybe it was God after all? What's the difference ...
Graham Oaten (188.8.131.52)
|Posted on Sunday, June 16, 2002 - 05:37 am: ||
You are not alone in questioning the measurements of our good friend Gantenbrink. There are many more and if I can find my notes I'll post them shortly.
Steve B (184.108.40.206)
|Posted on Sunday, June 16, 2002 - 08:09 am: ||
Taking the last two lines of your posting first, may I politely suggest you re-read point 2 in the first of my postings. If you wish to start a trivial slanging match then perhaps this forum is not the appropriate place.
On your more serious points,
1) To analyse the accuracy of the mathematical model it would be appropriate to look at the surveying of the pyramid as a starting point.
Due to the 'plug blocks' in the ascending passageway, and the lengths of all the slopes inside the Great Pyramid, it can be deduced that the most accurately surveyed part of the GP is the entrance passageway. In comparision to the shaft angles, which have been measured by electronic tilt devices inside Gantenbrinks robots and averaged out , the surveying of the entrance is by far a more accurate and reliable measure. Since the outside of the Pyramid is largely destroyed, none of the estimates of angles of slope from here can provide any sort of reference data. So, the mathematical formulae will be best tested when compared against the angle of the entrance passage, and the deviation against this measure taken as the error margin in the calculations.
From the outstanding work of Sir William Petrie (chapter 7 section 36), the angle of this entrance passageway was measured as being 26º 31' 23" +/- 5", which by anyone's standards is a highly accurate measure. To translate this into more understandable terms, if you were to draw a two lines from Berlin to London both with a length of 920km and seperated by this error margin then, the distance between the two lines at the London end would be 22 metres. This is close to the accuracy of the guidance system of a modern missile, and is a particularly accurate measure.
So, what does the mathematics of the monument say about this angle? Well, the formula for the entrance passageway is the most difficult of all the angles on the pyramid to work out and is given by the formula (shown as a fraction top line / bottom)
giving a resultant angle of 26º 31' 26.00
However the mathematics is based on a starting formula which, to simplify the algebra, has an inherent error of 0.0002115% which is the actual accuracy of the mathematics that I am putting onto this board at present. (I am currently working on the more complex start formulas which have no error margin at all but are significantly more complicated to calculate.)
The angle of the entrance passage therefore from the algebra shown above is
26º 31' 26" +/- 0.2"
This error is the same for all of the formulae - angles and points, however the surveying errors on the monument vary dramatically, and so the difference between the mathematical model and the surveyed details does not remain constant.
2) I have copies of the Rhind and Moscow papirii on my hard drive, and have spent considerable time studying the mathematical knowledge of the Ancient Egyptians from these texts. It is quite obvious that the Ancient Egyptians didn't have the first idea about the value of pi. However, if you start looking at a problem by first assuming the answer then your study is doomed to failure. ie if you start analysing the construction of the GP by assuming that the architects were mathematically inept, then you will be biasing your study from the outset.
3) I agree that the value of 'f' could be arbitrary, and this is the very challenge that all scientific analysis is about. The trick is to prove beyond all reasonable doubt that the value of 'f' is not arbitrary, and with the GP this can be done. For example, you can accurately predict the positions of the Second and third Pyramids at Giza using this number, and the two pyramids at Zawiyet El-Aryan.
You are completely correct in your assumtion that you cannot know the value of 'f' without a substantial knowledge of modern science - in fact to be more precice you must have access to space and satellite radar techniques to measure the earth's shape to this accuracy, or at the worst radio telescope interferometry.
In conclusion Pope, you are going to have enormous problems with this work because, unlike previous stabs in the dark regarding the dubious origins of the Pyramids of Egypt, I can back up and prove beyond any doubt that it is impossible for these monuments to have been designed without knowledge of an extraordinarily advanced level.
I do not and would not question the work of the Egyptologists who have so carefully studied the subject over the centuries - I would be a fool to do so - and I happily accept the fact that the pyramids were built by the AE's (unless of course you guys are all wrong, which I seriously doubt). However I can prove that there is no way that they designed them.
Am I suggesting that they had help from the 'outside' ? - no.
I am telling you that they did and can prove it !
However, keep on questioning my mathematics, and the moment that you can show me an error in the thinking or working, I will happily back down and concede defeat.
Before replying please read again point 2 of my original posting otherwise this topic will draw to a premature close on this board.
|Posted on Sunday, June 16, 2002 - 06:51 pm: ||
Thank you for answering all my questions in such detail. As I said, I'm not the mathematician.
I wish you good luck!
Over and out.
Steve B (220.127.116.11)
|Posted on Sunday, June 16, 2002 - 07:37 pm: ||
Thanks for the civilised response and the good luck message. Nice to see that two people from opposite sides of the great divide can hold a sensible chat. If you ever wish to discuss the difference between God and star trek in more detail just get back to me.J
Erik Calero (18.104.22.168)
|Posted on Monday, June 17, 2002 - 02:11 pm: ||
I sent you two mails but they were returned to me.
It seems that your mail server have some troubles or it is in a failure state.
|Posted on Wednesday, June 19, 2002 - 11:05 am: ||
Hi Steve B,
If you care to visit: http://www.horatech.com
You may find what your looking for on the 231m bit
Monty J. Bowen.
Post Number: 9
Posted From: 22.214.171.124
|Posted on Tuesday, October 01, 2002 - 12:47 pm: ||
There hasn't been a posting here in ages but, I need to ask something.
Steve, could you please share the model from which all these formulae are derived? By e-mail if need be. A couple of isolated formulae are no use without the framework from which they are derived.
Thank you in advance.
Post Number: 510
Posted From: 126.96.36.199
|Posted on Tuesday, October 01, 2002 - 12:59 pm: ||
Please do this by e-mail thanks!


Any lessons given to a child should start with various hands on activities to help him to understand the concept. And later the child can be helped to fill up the work sheets. Repeated works with the hands on activities help the child to get to know the concept better rather than filling down the worksheet as a one time process.
We give lots of hands on activities in all possible ways for our school children to help them to understand a concept better. I am sharing one such concept taught in our school today with the hands on activities that we gave.
Measurement is the concept, I am going to discuss today. We start giving the measurement of length lessons in montessori classroom. We set the tools for measuring length in a tray and give presentations on how to measure length with those tools and how should we interpret the measurement with the SI units.
The grade I children were also taught about the hand span, arm span and foot span. They did a project work to see how foot span of each people differ and so we need a standard measurement tools and units.
Grade children were also taught about measurement of weight and it’s SI units.
Measuring the weights of various objects exactly with the weight stones.
And measurement of liquids and SI units were also taught with various measuring tools with the scale in it. They also learnt how much 100 and 500 ml liquids are needed to fill a 1000ml bottle.
And that was our measurement lessons with hands on activities. Later the grade I children were taught about the conversion table as well.


1 edition of State Space and Input-Output Linear Systems found in the catalog.
|Statement||by David F. Delchamps|
|The Physical Object|
|Format||[electronic resource] /|
|Pagination||1 online resource (x, 425p. 12 illus.)|
|Number of Pages||425|
|ISBN 10||1461283647, 1461238161|
|ISBN 10||9781461283645, 9781461238164|
State Space Models In this section we study state space models of continuous-timelin-ear systems. The corresponding results for discrete-timesystems, obtained via duality with the continuous-timemodels, are given in Section The state space model of a continuous-time dynamic system can be derived either from the system model given in. A state-space model is a mathematical representation of a physical system as a set of input, output, and state variables related by first-order differential equations. The state variables define the values of the output variables. The ss model object can represent SISO or MIMO state-space models in continuous time or discrete time.
Fall /31 5–6 Creating State-Space Models • Most easily created from Nth order diﬀerential equations that describe the dynamics • This was the case done before. • Only issue is which set of states to use – there are many choices. The state space formulation of a set of differential equations is easier to solve with a digital computer. The state space formulation is applicable to both linear and non- linear systems. The state space formulation is applicable to multiple-input-multiple-output (MIMO) system. State Space Representation Example. Let’s use the following.
Minimal State-Space Realization in Linear System Theory: An Overview tter∗ Keywords: minimal realization, linear system theory, state space models Abstract We give a survey of the results in connection with the minimal state space realization problem for linear time-invariant systems. We start with a brief historical overview and a. by direct integration. The system state at any instant may be interpreted as a point in an n-dimensional state space, and the dynamic state response x(t) can be interpreted as a path or trajectory traced out in the state space. In vector notation the set of n equations in Eqs. (1) may be written: x˙ = f (x, u, t) Eq. (2).
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State Space and Input-Output Linear Systems on *FREE* shipping on qualifying offers. State Space and Input-Output Linear Systems5/5(1). State Space and Input-Output Linear Systems Softcover reprint of the original 1st ed. Edition byCited by: Reviewed in the United States on April 2, This book is a complete,contained and clear survey of Linear Systems theory from the point of view of an author jointly develops both linear systems theory and the analytical skills you need to master the style is clear always striving to elucidate the most difficult points and connecting the particular results in an organized and clear 5/5(1).
It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print.
State Space and Input-Output Linear Systems. Usually dispatched within 3 to 5 business days. It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of.
State Space And Input Output Linear Systems by Delchamps, David F. It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear.
numerous diagrams and graphs (especially input/output diagrams for transfer functions) are given so we "get" the underlying concepts.
Today we'd call these alogrithms, data structures, UML and parse control schematics, but they work regardless of nomenclature. The most common way of introducing state-space methods is via linear matrix algebra. ANALYSIS OF LINEAR SYSTEMS IN STATE SPACE FORM This course focuses on the state space approach to the analysis and design of control systems.
The idea of state of a system dates back to classical physics. Roughly speaking, the state of a system is that quantity which, together with knowledge of future inputs to the system, determine the future.
characterized by algebraic relationships derived from the state-space sys-tem description. Chapter 5 addresses the concept of minimality associated with state-space realizations of linear time-invariant systems.
Chapter 6 deals with system stability from both internal and external (input-output) viewpoints and relationships between them. To explicitly present the finding of the optimal PI tracker for the state-space representation with the input-output direct-feedthrough term and system disturbances in Section 3 (see (6)), instead.
State Space and Input-Output Linear Systems (Inglese) Copertina rigida – 18 dicembre di David F. Delchamps (Autore) › Visita la pagina di David F. Delchamps su Amazon. Scopri tutti i libri, leggi le informazioni sull'autore e molto altro.
Risultati di ricerca Author: David F. Delchamps. Schaum's Outline of Theory and Problems of State Space and Linear Systems | Donald M. Wiberg | download | B–OK. Download books for free. Find books. This book is a complete,contained and clear survey of Linear Systems theory from the point of view of an author jointly develops both linear systems theory and the analytical skills you need to master the style is clear always striving to elucidate the most difficult points and connecting the particular results in an organized and clear whole.5 stars!5/5.
Key Concept: Defining a State Space Representation. A n th order linear physical system can be represented using a state space approach as a single first order matrix differential equation. The first equation is called the state equation and it has a first order derivative of the state variable(s) on the left, and the state variable(s) and input(s), multiplied by matrices, on the right.
Linear system theory and design, by Chi-Tsong Chen input} output feedback systems. This has been. Fundamentals of Linear State Space Systems. Book. Jan ; John S.
Bay; View. Sontag clearly put much thought and eﬀort into this book, and it shows. The book succeeds in conveying the important basic ideas of mathematical control theory, with appropriate level and style, to seniors in mathematics.
References [Del88] D. Delchamps. State-Space and Input-Output Linear Systems. Springer-Verlag, New York, In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations.
State variables are variables whose values evolve through time in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables. The first and the second equations are known as state equation and output equation respectively.
The number of the state variables required is equal to the number of the storage elements present in the system. It is a vector, which contains the state variables as elements.
In the earlier chapters. State space and input-output linear systems. New York: Springer-Verlag, © (OCoLC) Online version: Delchamps, David F. State space and input-output linear systems.
New York: Springer-Verlag, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: David F Delchamps. This book originates from several editions of lecture notes that were used as teach-ing material for the course ‘Control Theory for Linear Systems’, given within the framework of the national Dutch graduate school of systems and control, in the pe-riod from to The aim of this course is to provide an extensive treatment.
TY - THES. T1 - Non linear system identification: a state -space approach. AU - Verdult, V. PY - /3/1. Y1 - /3/1. N2 - In this thesis, new system identication methods are presented for three particular types of nonlinear systems: linear parameter-varying state-space systems, bilinear state-space systems, and local linear state-space systems.In Chapter 7, we described state–space models of linear discrete time and how these models can be obtained from transfer functions or input–output differential equations.
We also obtained the solutions to continuous time and discrete-time state equations.Dual Spaces, Norms, and Inner Products --II State Space Linear Systems State Space Linear Systems: Formal Definitions and General Properties Realizations Eigenvectors, Eigenvalues, and Normal Modes The M + N Decomposition for Matrices Which are Not Semi-Simple


Okay so HERES the Question.
The Movie Madness Video Store, newly-released videos rent for a Day. The store paid for a copy of Spider-man. If x Represents the number of times the video is rented in the first month, the expression 2x-18 gives the amount of money the store will make on this video.
A.Make a list of ordered pairs in which the x-cordinate represents the number of rentals in the first month And the y-cordanate represents the money made for 10, 15, 20, 25, or 30 rentals.
B. Then Graph the ordered pairs.
C. Show a table of the ordered pairs that result AS you evaluate the expression 2x-18 10, 15, 20, 25, 30, (show your work)
I have no idea what to do. so someone walk me through this completely or just answer it for me and then ill understand it.
Other Sites Movie Rental New Releases Site Online
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Tennis is a popular sport and the tennis ball is an important part of the tennis game. Always we need to play tennis balls to buy from a shop or Amazon and need to carry the ball. They always keep inside the limousine or pressure inside the tennis ball. But how many tennis balls can you fit into a limousine?
The answer is quite simple one tennis ball that fits into a limousine. Let’s check the more answer, Maybe I would say that, “I would first have to look up the average cubic feet of the inside of a limousine. Also, In a limousine, Only One Ball can fit. Because the limousine has only one ‘o’ we can fit the ball in ‘o’ not in the limousine.
How Big Is a Tennis Ball?
Table of Contents
First of all, we need to find out the volume of your tennis balls. Since the tennis ball is spherical in shape afterward the volume share is that: Check the best tennis balls that also you fit in your car.
- The volume of Shapre = 4/3πr3
There is various tennis brand in the market but which has different shape or length. Suppose a tennis ball is 2 inches in length, and the radius is half of the diameter. Besides, the radius should be 1 inch and 43 as a decimal and approximately 1.3 as 3 goes into 4 ounces.
Let’s calculate by applying the rules of the volume of the shape of the tennis ball.
- Volume = 4/3πr3
- Volume = 1.3*3*(1)3
- Volume = 3.9*(1)3
Finally, you got something to understand but we’re going deep. So now your question is how many tennis balls fit in a cubic meter? And the volume should be 3.9 cubic inches in size but the manufacturer takes the size 4 cubic inches.
How Many Tennis Balls Actually Fit in a Limo?
Now, you have got some idea to read above the tennis ball size. However, now we move to measure your tennis ball with a limo to find out how much tennis balls actually hold in your limo. Let’s read it.
In my experience, a limousine’s height and width look like same as your car. I measure it at 1.5 meters and 2 meters of it. Moreover, a limo is longer than a regular can, let’s convert them to applying the best way to the scientific method.
- Let’s figure out the formula
Volume = L W H
Volume = 800 80 60
Volume = 32000 60
Volume = 1500000 cubic inches
- Tennis Ball Size
10 meters in length = 800 inches
2 meters in width = 80 inches
1.5 meters in hight = 60 inches
Here, let’s input these keeping figures to apply the following formula in detail.
Volume = L x W x H (800 inches x 80 inches x 60 inches)
In the final analysis, the total volume is more than 15,00000 cubic inches and you dig out the volume using the same pattern. Otherwise, to get the total number of a tennis ball, you follow to use volume and cubic inch.
Further, let’s see the example; Your volume is 1500000 and 4 cubic. so let’s check the exact number; 15,00000/4 = 3.75. I hope that you can understand. At last, A 150000 volume limo easily fits 3 tennis balls, and dig out your exact tennis ball number to fit in your limo.
How Many Tennis Balls Will Fit In A Car?
What If you want to know the same question but for a car instead? Let’s go to calculate
So what is your car size 2m x 5m 1.5m (length x width x height) Please see the picture like that. We change the same figure, you can try your original size or figure.
- 6 meters in length = 240
- 3 meters in wide = 120
- 1.5 meters in heigh = 60
- Volume = Volume = L × W × H
- Volume = 240 × 120 × 60
- Volume = 28,800 × 60
- Volume = 1,728,000 cubic inches
Now, the vehicle parts and tires will take up almost half of the car volume. but the new volume would be 375,000 cubic inches.
From this example of the limo, there would be empty gaps between the shape and the tennis ball due. If they were to take ¼ of the space, you would be left with more car volume. It would be 280,000 for the final car volume.
Now, you can divide the volume of the car ( 280,000 by 4) which will amount to near 70,000. So the answer is how many balls can you fit in a car, it’s nearly 70,000 tennis balls that will be kept to fit inside the car.
How many tennis balls could you fit inside an airplane?
We know how to calculate, how many tennis balls can fit in a plane interview question? so it would arrive at around 650,000-700,000 tennis balls that you can fit inside an airplane or Boeing Beman.
How many tennis balls are in a cubic meter?
According to ITF (International Tennis Federation), A tennis ball must a diameter of 6.54-6.86 cm. And it would mean that tennis balls must be a volume of 8 cubic inches.
Sometimes it’s asked an interview question like that, how many tennis balls can you fit into a limousine. As you are ready for your job interview, you may be considering which questions the employer will ask you.
Frequently Ask Question
Q: How many tennis balls fit in a car?
A: It is confusing for everyone, but it depends on your volume and cubic. Frist fix your cubic then, your cubic is 3 and you have a lot of volumes. After you need to divide them, you will get the correct number. So the ball fit in a car is = volume/cubic
Q: What number of tennis balls can you fit into a sports car?
A: It nearly fits your sports car with around 1000 tennis balls. further, if it would 6 of those cubicles that could easier fit without any trouble. You must follow the formula that we show up in the earlier text.
Q: How many tennis balls fit in a 747?
A: The answer is 688,705 tennis balls. Also, you will travel with those tennis balls on Boeing. I think you get your answer.
I hope that all of the above discussion is easier to understand. That’s how many tennis balls hold in a limousine. So if you have any confusion please keep it in the comment box. If remove your confusion, you can try it yourself.


This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.
My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.
You can find my Algebra 1 (year long class) INB posts here:
And my Algebra 2 INB posts here:
I am starting Algebra 1 again from the beginning as a semester class, so you can find my revised posts for that here:
Our fifth standard for Algebra 2 is F.IF.7c:
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Ignore the proficiency log side of the index file – I decided about two days into this unit that I HATED the way I had set this up and wanted a new one, which I am now using successfully, so you’ll see more about that in my next posts! Also ignore the fact that skill 3 has been pasted in in the picture above – I realized we needed that skill to say something totally different from what it originally read after we had already put them in our notebooks. The change is in the uploaded files, though 🙂
Skill 1: I can name a polynomial based on its degree and number of terms
I got the naming polynomials chart from Sarah Carter here and I really like it. It’s to the point and does its job! I had a total mind blank moment when I was filling my copy out, as you can see in the picture, because I forgot about degree 0. I did not have this mind blank during class, thankfully! We also use a Frayer model as she does in that post to talk about the definition of a polynomial.
I throw in adding and subtracting polynomials here because it is actually an Algebra 1 standard, but I find that my Algebra 2 students need a refresher on combining like terms and putting polynomials into standard form before we start working with graphs and other manipulations of polynomials in our next few units. This also let us get some practice naming the resulting polynomials!
Skill 2: I can graph a polynomial function with technology and identify its key features
On the outside of this you see definitions of what each of these key features is – where do we look for them? My students already know where to find the intercepts, but the extrema and end behavior are new ideas to them. When you open up the flaps, you see instructions on how to find each one using a TI – 83 plus graphing calculator, which is what we have a class set of. I need to find some better way to phrase the instructions on how to place the “left bound” and “right bound” when finding the x-intercepts and the extrema. I have some ideas from working with my students when we were practicing, but this is a tricky thing to communicate without individually showing each student!
Then I put two practice polynomials in the center, one with the graph given so they could make sure it looked okay before finding the key features, and one with just the equation. These two examples took us an entire 47 minute class period to discuss and get through together, so I’m glad I only put 2!
Skill 3: I can match a polynomial function to its graph and identify its increasing/decreasing intervals
I decided to separate increasing and decreasing intervals from the other key features because the other four that students have to be able to find (extrema, x-intercepts, y-intercept, and end behavior) all essentially involve looking in one single place on a graph. The increasing and decreasing are intervals, so they’re a bit different. I’m really glad I separated these this year because my students understood all of the key features a lot better than last year’s Algebra 2, when I tried to do all of those at the same time.
The inside of this needs to be edited to align more with our assessments. The main skill needed in our assessments is to be able to identify the minimum degree of the polynomial by visually inspecting the graph. I will change this page next year to just include that skill, because any other matching can be done by just graphing the equation in a calculator and matching the image that results.
I threw in two more examples that asked to find all possible key features, which gave us some good practice as a class manipulating the calculators and how to list each feature.
Skill 4: I can write a polynomial function based on its graph
My students LOVED doing this. I was so surprised, but they kept asking me if we could do more practice with this skill because they just wanted more of this! That made it really fun to teach. I like the structure I used for these notes as well, I think it was really clear to students.
After we did these for practice, they played Match My Polynomial on Desmos, which they loved and was good practice with immediate feedback!
Skill 5: I can write a polynomial function based on a list of its key features
This essentially is a preview of a skill we will go deeper into about two standards from now. It leads somewhat naturally from the previous skill and our sequence guide suggests that we include it here, but it is also included in that other standard in the future. I think that I plan to just let it be in that other standard the next time I teach this and conclude this unit after skill 4, since this unit is so focused on the graphs of polynomials and this skill doesn’t particularly fit there.
You can find the files I created for this unit here, in Publisher and PDF versions. Any files that were not my own are linked within this post 🙂


Each year the Mathematical Grammar School (Belgrade, Serbia) organizes an international computer science, mathematics, and physics competition for the best high school students from all over Europe. The best mathematicians from 15 countries participated, and GDi Belgrade, under the initiative ‘GDi for Education, Science and Innovation’, were delighted to have the opportunity to support the competition and provide awards to the winning students in these subjects.
Congratulations this year go to:
Laura from Romania (Informatics)
Mihail from Russia (Physics)
Strahinja from Serbia (Mathematics)
The Mathematical Grammar School (MGS) is a unique school in Serbia, specialised for students talented in mathematics, physics and computer science, aged 13-18. The school is of national importance and its students have thus far won over 150 medals in the World Olympiad.
The presentation of prizes this year took place in the National Assembly of Serbia, with the participation of the Secretary of the Ministry of Telecommunications, (representing the competition main sponsor).
For GDi, it was a real pleasure to help young future computer scientists and mathematicians from all over Europe.
For more information about the competition see HERE


Encourage your Group to be patient, listen and work as a team with this challenging counting game.
Ask your Scouts to stand in a circle facing each other.
Their aim is to take it in turns to count from 1 to 10 and back down to 1.
Anybody can say a number, but if a number is said by more than one person, the Group will have to start again from 1.
Your Scouts will need to listen to each other and really concentrate to be successful.


Current Research Projects of Edwin Langmann
I am working on several projects in quantum field theory which at the borderline
between mathematical physics, high energy physics and solid state physics.
Below I give a more specific description of some of my recent results.
(1) The geometry of quantum fields.
Despite of our extensive knowledge on quantum field theory (QFT) we are
still lacking a complete conceptual and mathematical understanding of it.
Noncommutative geometry (NCG) is a powerful mathematical framework promising
a deeper understanding of central issues such as regularization and renormalization.
We have been interested in gauge theories and associated anomalies where
the noncommutative nature of quantum systems and the geometric nature of
gauge fields can be united into a coherent picture. Our aim is not only
a better understanding of QFT but also to obtain novel results in noncommutative
geometry which are interesting on their own right. In recent work we have
found QFT models motivated by NCG and which are exactly solvable [1,2,3].
I also found variants of these models which describe 2D correlated
fermions which can be solved exactly [4,5]
- these recent results are connecting my research in NCG to my other two
projects described below.
Collaborators: J. Mickelsson, R. Szabo, K. Zarembo
quantum field theory
(2) Exact results on quantum many-body systems.
This project is on an interesting class of integrable quantum systems and
their relation to anyons, the fractional quantum Hall effect, and gauge
theories. Exploiting these relations I recently found a novel algorithm
to solve the general elliptic case by using a second quantization of this
I now am working on getting more explicit explicit formulas on the solution
of this model. We have also recently found and solved a novel type of exactly
solvable system with local momentum dependent interactions [8,9].
Collaborators: Cornelius Paufler, Martin Hallnäs, Harald
quantum Hall effect
(3) Computation methods for correlated fermion models.
In this project we combine analytic and numeric methods to develop new
computation tools for strongly correlated fermion systems such as the two
dimensional Hubbard model. Recently I found a class of exactly solvable
models describing correlated fermions in 2D. They can be obtained by a
truncation from the 2D Hubbard model which generalizes mean field theory
by taking into account a particular type of spatial correlations [4,5].
Collaborators: M. Wallin
correlated fermion systems
My research is funded by:
VR (The Swedish Research Council)
Göran Gustafssons Foundation


Spark Global Limited reports:
If you are an active day trader, you probably realize that Fibonacci retractions and extensions are the most important and useful tools in all price activity.
Day traders and technical analysts can use Fibonacci level analysis to identify entry levels, target profit taking, and determine stop loss levels.
In this guide, we will explain exactly how to plot Fibonacci levels so that you can better decide when to enter and exit trades.
What are Fibonacci numbers and ratios?
The Fibonacci sequence, sometimes called the Golden ratio, is a string of numbers in which each number is the sum of the first two.
For string 0,1,1,2,3,5,8,13,21,34,55, for example, if we add 0 + 1, we get 1. If I add 1 plus 1, I get 2. If we add 1 plus 2, we get 3, and so on and so on.
The resulting sequence is called the Fibonacci sequence, and each number in the sequence is called the Fibonacci sequence. The Fibonacci ratio is then calculated by divisor over the sequence. These calculations give the ratios used in the Fibonacci levels below.
0, 0.236, 0.382, 0.5, 0.618, 0.786, 1, 1.618, 2.618
These ratios are translated into percentages – 23.6%, 38.2%, 61.8%, 78.6% and so on – and then applied to charts in an attempt to identify potential levels of hidden support or resistance in the market.
The Fibonacci sequence was discovered by the Italian mathematician Pisa Leonardo in 1202 when he was considering a practical problem involving the growth of a rabbit population based on idealized assumptions.
This order governs many aspects of life; From the creation of flowers, to the formation of waves, to the proportions of human bodies. It also provides traders and technical analysts with the information they need to develop resistance and support levels that can be used in a risk management framework.
You can use the Fibonacci level on your own or in combination with other trading methods.
The Fibonacci sequence was used to form other theories, such as Elliott wave principle and Dow theory. You can also use other technical analysis tools to use the Fibonacci ratio.
How to calculate the Fibonacci callback level
One of the most common technical analysis tools derived from the Fibonacci gold ratio is the Fibonacci correction level.
The Fibonacci ratio of 61.8% and The Fibonacci ratio of 32.8% are calculated by subtracting the recent high from the recent low and targeting the upcoming rally. Most of these points can be calculated using graphing software.
As the S&P 500 chart above shows, Fibonacci retractions often act like magnets, creating a self-fulfilling prophecy.
As you can see from the chart, the realization that the coronavirus pandemic was about to hit the US economy triggered a rapid bear market that began in February and bottomed out in March. Prices fell from around 3400 to 2200 before rebounding to a 38.2% retracement level.
If we multiply the drop point by 38.2% and add that number to the low (2200), we get the Fibonacci retracement level of 38.2%, or 2647. The index starts to consolidate at this point.
After the consolidation period, prices retested the 38.2% retracement level and broke through the next level, the 50% retracement level. The merger was short-lived. The S&P 500 then began testing the 61.8% retracement and consolidated around that area.
When you draw the Fibonacci retracement line, you will measure the peak to trough of your target’s movement. Then multiply the difference between high and low by 61.8% and 38.2%.
If you measure a drop, these results are added to the low values; If you measure the rise, these results are subtracted from the high values. When prices rebound, these levels will serve as target support for your corrections or resistance levels.


DEPARTMENT OF MATHEMATICS
The department of Mathematics was carved out of science department in September 2012 by the school management. This must have been as a result of the fact that the department can now stand on its own considering the staff strength and the performance of students in the subject [mathematics].
The subject available in the department are Mathematics for all the students and Further mathematics for senior school only.
The department has seven  competent and experienced staff. In terms of academic excellence student performance in the school cannot be underrated.
Since the department of Mathematics came into existence, students; performance has always been excellent over the years, both in internal and external examinations [JSCE and SSCE].
The department of Mathematics [subject room] is equipped to an enviable standards; with overhead projector interactive board and other instructional materials that aid effective teaching – learning process.
Students in the department are given one-on-one attention for better performance. This students-centred teaching / learning techniques have resulted in some of the achievements recorded in the department.
So far, they include
– Gold medal in 2016 National Mathematics Competition
– Gold medal in 2016 American Mathematics Competition
– 5th Best [Nigeria] in 2017 National Mathematics Competition
– Best overall in Nigeria 2018 National Mathematics Competition
– Best in Additional Mathematics in 2018 IGCSE
– Our Generation Foundation Mathematics Competition
[Best in Sagamu L.G.A and Best ten  in Ogun State
More are still in the pipeline because God is our source of strength and knowledge in the department.


Test administrator guides
The NAA has created a number of free training resources for national curriculum test administrators.
Correctly administering the national curriculum tests in English, mathematics and science is an important task. The downloadable videos and guides below have been created to help school or local authority staff organise and administer the tests.
- Key stage 2 (PDF 333KB)
- Key stage 3 English (PDF 249KB)
- Key stage 3 mathematics and science (PDF 282KB)
- Year 7 progress tests (PDF 232KB)


P4/5 were very lucky to receive a presentation and workshop focusing on Growth Mindset. We learned about ‘the power of yet’ and how to change negative thoughts into positive ones. Instead of saying “We can’t do that!” we should say “We can’t do that yet!”
In Maths we have been learning about different units of measure. We have looked at Length and Area and last week focussed on Weight. We had a great time using scales and weights to compete some challenges! This week we will be moving on to Volume.
Miss McFadyen and Primary 4/5


If you are looking for the answer of how to whatsapp plus, you’ve got the right page. We have approximately 10 FAQ regarding how to whatsapp plus. Read it below.
IDENTIFY THE STEPS IN ADDING INTEGERS, THEN SHOW 4 EXAMPLES
Ask: IDENTIFY THE STEPS IN ADDING INTEGERS, THEN SHOW 4 EXAMPLES ON HOW TO ADD INTEGERS ( + plus +, + plus -, – plus + and – plus -)
Positive or (+) negative or(-)
Positive plus Positive =Positive
Positive plus negative = depende kung saan yung mas malaking number
negative plus Positive = depende din kung saan yung mas malaking number
negative plus negative = negative
Examples lang po ito;
(+5)+(+5) = +10
Sanaa po makatulong
how to find the factor of xsquared plus 5x plus
Ask: how to find the factor of xsquared plus 5x plus 6
x squared equals to 1
ano ang masamang epekto ng WhatsApp
Ask: ano ang masamang epekto ng WhatsApp
Yung sumikat na mo mo challenge noon
pag kakaroon ng mga kaibigan na masama
1 plus 1 is how much 20 plus 20 then
Ask: 1 plus 1 is how much 20 plus 20 then add 50
whatsapp is the function
Ask: whatsapp is the function
Whatsapp Is The Function Of What?
lol meaning in whatsapp
Ask: lol meaning in whatsapp
WhatsApp is a free mobile messaging application, massively used for international messaging and voice calls.
pa brainliest plss
In computer terms whatsapp?
Ask: In computer terms whatsapp?
WhatsApp Messenger is a cross-platform mobile messaging app which allows you to exchange messages without having to pay for SMS. Because WhatsApp Messenger uses the same internet data plan that you use for email and web browsing, there is no cost to message and stay in touch with your friends.
HOW MANY IS 1 PLUS 7 PLUS 8?
Ask: HOW MANY IS 1 PLUS 7 PLUS 8?
16 is the right answer
1 + 7 + 8 = 16
pag gamit ng skype,Viber o whatsapp?
Ask: pag gamit ng skype,Viber o whatsapp?
para san po ba Yan?
how to solve a positive plus positive plus negative ysing
Ask: how to solve a positive plus positive plus negative ysing number line?
Not only you can get the answer of how to whatsapp plus, you could also find the answers of lol meaning in, IDENTIFY THE STEPS, how to find, 1 plus 1, and HOW MANY IS.


Publications and preprints
My papers on DBLP.
(No, I don’t have a paper titled “#P”! This is some sort of parsing error; the actual title is “Quantum Invariants of 3-manifolds and NP vs #P.”)
Grants held as Principal Investigator
Quantum-Secure Cryptography and Fine-Grained Quantum Query Complexity (NSF; 2018-2021)
Quantum algorithms for algebra and discrete optimization (ARO; 2019-2022).
Practical Quantum Protocols (AFOSR; 2020-2023)
CV [pdf] (updated July 2020.)


Improving Teacher Quality
English Language Development Professional InstituteGrant Number: 02-301 Grant Award: $996,878 Duration of Project: Friday, August 05, 2005 - Wednesday, September 30, 2009 Project Subject Areas: Math and Science Grade Band: 9-12
Institutes of Higher Education:
- California State University, Bakersfield
Local Education Agencies:
- Delano Joint Union High, Delano
- Bakersfield College, Bakersfield
- California State University, Bakersfield, Bakersfield, School of Education
- California State University, Bakersfield, Bakersfield, School of Math and Sciences
Number of teachers/principals/highly qualified paraprofessionals participating in the project:0
Goals:The project goals are to improve the knowledge of principals, teachers and other school staff in the core subjects of Math and Science, with an emphasis on academic language and literacy.
- Using a research-based professional development model over a three year period of time, stakeholders will be able to increase student achievement on the CAHSEE, the CST, and Delano High School District benchmark exams. This will be accomplished through a collaborative effort between the CSUB School of Education, the School of Natural Sciences and Mathematics and the Delano Joint Union High School District.
- The school will improve student achievement as well-researched instructional strategies are implemented by the teachers through modeling and coaching by project staff.
Activities:Math and Science secondary school teams (with an administrator) will attend a five-day intensive summer training with four follow-up sessions which will address topics such as: literacy and academic language instruction with effective assessment techniques (especially in the core content areas); working with learners from diverse backgrounds; sheltered language instructional techniques; and a review of CA state adopted content specified standards. This institute will be conducted by professors from the CSUB Math and Science departments and School of Education. Participants will be expected to produce a school plan which will depict how strategies will be implemented at their school site. They will also be expected to produce and edit a ˇ§best practiceˇ¨ video which highlights an instructional strategy learned at the summer institute and which will serve as a reflective piece for the participant. Follow-up sessions conducted throughout the year will emphasize instructional strategy implementation. Participants will be paid stipends to attend the professional development sessions.
- Increased achievement on the CAHSSE
- Increased achievement on the CST (Math and Science)
- Increased use of instructional strategies which promote the use of Academic Language in Math and Science classrooms
Contacts:Project: Dr. Debra Cook-Hirai, email@example.com
Project: Dr. Emilio Garza, firstname.lastname@example.org
Institute of Higher Education: Efrain Rodriguez , email@example.com


Let’s look at an example of going long, using EUR/USD as our currency pair;
Consider the following scenario; there is a considerable amount of market tension concerning upcoming US GDP figures, as well worry that an upcoming election will see gains for a party traditionally hostile to big business.
As a result, you decide that the Euro looks likely to strengthen against the dollar and so you go long on EUR/USD, which is currently trading at bid/ask rate of 1.6764/1.6770. You decide that you’re going to take full advantage of the leverage opportunities available to you; you ‘buy’ €10,000 at that rate of 1.6770, at a leverage scale of 200:1.
The following equation determines how much your initial deposit needs to be;
(Amount I want to buy times counter currency exchange rate/leverage scale)
So, (10,000 times 1.6770/200), which equals €83.85. This is the amount required in the initial deposit. Let’s say events play out as you expected, with the result being that the Euro does strengthen against the dollar. The bid/ask rate is now 1.6811/1.6817 and you decide to close out the trade at this point, ‘selling’ your €10,000 at a price of 1.6811
Having bought at 1.6770, I sold at 1.6811, which is a rise of 41 percentage points.
(Level I sold at – Level I bought at) times Amount I bought
So, (1.6811-1.6770) times 10,000 = $41
However, let’s say the markets went the other way to my trade and the dollar strengthened against the Euro. When the bid/ask rate hits 1.6720/1.6726 I decide to cut my losses and sell all €10,000. My losses would be worked out as follows;
(Level I bought at - Level I sold at) times Amount I bought
So, (1.6770-1.6720) times 10,000 = $50


MEME Coin Cryptocurrency Strategy
If it's trending on Twitter and it's cheap, Buy it!
MEME Coin Cryptocurrency Investment Strategy
If it's trending on Twitter and it's cheap, less than $0.00001 of a dollar and new...
Source ... Coin98 Analytics on Twitter … @Coin98Analytics
Follow the MEME Coin Cryptocurrency Investment Strategy to Wealth.
F. the Utility
F. the Team
F. the Website
F. whether it's a security
F. ... Everything and just EXECUTE ...
Just F'ing Buy it and Dump it when you get a 1000x return and F'ing do it again and again and again.
At this buy price ... $0.00001 ... you can buy 1 MILLION coins for $10 bucks.
At 1000x return ... the coin will be worth 1 F'ing Penny.
Hmmmmm, 1000x is ???
If you bought $10 bucks worth at $0.00001 and sell when it's $0.01, you now have made $10,000 Dollars.
Hell, sell half. Make $5,000 and HODL until it's at $1.00.
You will make (500,000 times $1.00) = Half a Million Dollars.
1000x = 100,000 PERCENT RETURN.


We are delighted to extend an exclusive invitation to join us at the Propeller Club Port of Istanbul’s esteemed monthly luncheon. This month, we have the honor of welcoming the illustrious Prof. Dr. Ali Nesin, who will share his profound insights on “The Philosophy of Mathematics,” shedding light on the deeper implications and the foundational questions that mathematical concepts evoke.
Prof. Dr. Ali Nesin, a paragon in both mathematics and education, is celebrated for his pioneering efforts to demystify the most intricate mathematical ideas. As the founder of the Nesin Mathematics Village, he has imparted his life’s work to cultivating an appreciation for mathematics, guiding students and aficionados to probe the philosophical aspects that underpin mathematical thought.
This distinguished gathering is scheduled for Thursday, March 28th, at the Grand Hyatt Hotel. It promises to be an extraordinary chance to network and engage in profound dialogues on the philosophical undercurrents that drive mathematical innovation and inquiry.
As a luminary and advocate for accessible education, Professor Nesin’s contribution transcends teaching, reaching into the realm of philosophical inquiry. His dedication to the Nesin Mathematics Village and beyond has touched many lives through a pedagogical philosophy that champions critical thinking and a quest for fundamental understanding. The upcoming discussion will not only highlight the critical role of philosophy in mathematics but will also inspire and inform our approaches to complex problem-solving in various fields.
In line with our tradition of inclusivity and support for burgeoning scholars, we encourage you to invite dedicated students, particularly those benefiting from educational programs, to join us as your guests. In collaboration with the Association of Türk Üniversiteli Kadınlar Derneği, we are prepared to support the participation of a meritorious female student, providing her with an expansive educational opportunity.
Agenda: • 12:00 PM:
Networking • 12:30 PM:
Luncheon • 14:30 PM: Closing Remarks
Event Details: • Venue: Grand Hyatt Hotel • Participation Fee: 1200 TL per person
RSVP: Please confirm your attendance with the club’s secretariat by the latest March 25, 2024
Photography Consent: Attendance implies consent to be photographed, with images potentially used as per the Personal Data Protection Law (KVKK).
Do not forgo this chance to converse with Prof. Dr. Ali Nesin and delve into the intriguing world of mathematical philosophy. Please respond promptly to confirm your presence. We eagerly await hosting you for an afternoon of stimulating conversation, networking, and exquisite cuisine.
Yaprak Özer President 2023-2025
Propeller Club Port of Istanbul


In the question above, you are asked to calculate Gibb’s Free Energy for the Haber Process. The Haber Process is a process of manufacturing ammonia in a factory. The raw materials are nitrogen and hydrogen. Nitrogen is obtained by burning hydrogen in air. Hydrogen is obtained by reacting methane with steam. Haber Process combines nitrogen and hydrogen to create ammonia. Ammonia is used widely in household cleaners and other applications such as fertilizers, explosives and dyes.
Steps for calculating Gibb’s Free Energy
The equation N2 + 3H2 = 2NH3 tells you there are 3 moles of hydrogen and 2 moles of ammonia.
You will apply the moles to your calculations below.
1. Sum up the entropies of reactants
- The ΔTS are given in J/K•mol (joules per kelvin per mole). Multiply by the number of moles to obtain the total change in entropy.ΔTS (Nitrogen) + ΔTS (3 moles of Hydrogen) =
192 + 3 x ( 131 ) = 585 J/K
2. Calculate the entropy for ammonia
ΔTS (2 moles of Ammonia) =
2 x 193 = 386 J/K
3. Calculate the entropy change of the whole process
ΔTS (reactants) – ΔTS (product) =
585 – 386 = -199 J/K
4. Apply Gibb’s Equation
ΔG = ΔH(system) – TΔS(system)
= – 92 – (-0.199 x 298) = – 32.7 kJ
(nb. The value -0.199 kJK-1 mol-1 is the entropy per Kelvin temperature. You multiply it by 298 to get the entropy at 298 Kelvin temperature. )
(nb. the the TΔS is converted from joules to kilojoules)
(nb. ΔH is given in the question. You don’t need to work it out.)


- Psychology Home Page
- Undergraduate Programs: Psychology
- Undergraduate Programs:
Human Resources Management
- Graduate Programs
- Research Groups/Labs/Centres
- Early Childhood Education Centre (ECEC)
- Centre for Mental Health Research (CMHR)
- Faculty of Arts
Mathieu Le Corre
My research program aims to characterize the nature of the conceptual building blocks of knowledge of the natural numbers and of the interface between knowledge of numbers and linguistic structure. Examples of basic questions that flow from this general paradigm are:
Are the earliest forms of knowledge of the natural numbers based on concepts similar to the ones used in mathematical theories of the foundations of numbers (e.g., sets, quantifiers, variables, recursion) or does the acquisition of these concepts involve a protracted reorganization of children’s thinking?
How much arithmetic is naturally encoded in language? For example, why do multiple languages from diverse language families use multiplication to create complex number words (e.g., “seven hundred”)? Is it because the concepts required for multiplication are innate? How difficult is it for children to learn that some combinations of number words mean that one number multiplies the other (e.g., that “seven hundred” means seven times one hundred)?
Different languages encode numerical information differently. For example, Chinese, unlike most languages, does not encode the difference between singular and plural. Does this affect the acquisition of concepts and words for the natural numbers?


Tuesday, November 15, 2016
9:45 a.m. and 12 noon
Math matters! Filled with exciting props, this interactive program will add fun, subtract boredom, multiply test scores and keep the audience's undivided attention. This program will help students hone their skills in: Measurement, Patterns, Money, Probability, Percentages, Operations, Place value, Fractions and Number Relations.
All tickets $7
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He was a clever guy who lived in Egypt around 240BC.
To him it was obvious that the sun was a long way away, therefore, he assumed that when its ray hit us, they’d be parallel. Well, so close to parallel that it wouldn’t affect his calculations.
He lived in Alexandria, a port town where the Nile reached the Mediterranean.
Watching the sun and its shadows as it move throughout the day, he realised that for this to happen the world had to be round.
He also noticed that at midday in the summer, the sun’s rays were nearly vertical. In fact, he calculated the angle of the rays, well, when I say that, they didn’t actually have angles of degrees in those days. What he did was use an ancient unit of measurement, which was basically a circle very similar to today’s sun dial.
Having worked out the angle, then, this is the mad bit, he sent a man to walk 800 miles down the river Nile to Syene!
When he got there, at the same time of the day, his man worked out the angle, and then he walked all the way back. You see the man had to walk it to give Eratosthenes an accurate figure of the distance, which was essential for his calculations. They didn’t have Google Maps then!
With this data being the angles and the distance between them, he was able to calculate the speed the sun was moving around the earth and then naturally the actual size of the earth.
Would you believe he nearly got it right? He wasn’t perfect, he was just a little out, however, when you think about it this has to be some achievement, as this was over 2,000 years ago.
To learn how he actually did it go to https://www.wikiwand.com/simple/Eratosthenes
Using the information he had gathered he even worked out the world was on a tilt!
This leads to the obvious question. Could a maths class of children work out the circumference of the world using his information?
Of course, you really need to take a measurement at home, then on holiday, as long as it is on the same meridian.
That could be an expensive school trip!


This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.


The 2014 National Curriculum for Maths aims to ensure that all children:
- are fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
- are able to reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems systematically by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions
At St Joseph’s, these skills are embedded within Maths lessons and developed consistently over time. We are committed to ensuring that children are able to recognise the importance of Maths in the wider world and that they are also able to use their mathematical skills and knowledge confidently in their lives in a range of different contexts. We want all children to enjoy Mathematics and to experience success in the subject, with the ability to reason mathematically. We are committed to developing children’s curiosity about the subject, as well as an appreciation of the beauty and power of Mathematics.
The Mastery Approach
Mastery of mathematics is something that we want all pupils to acquire throughout their school lives and beyond. To achieve this, we include aspects of fluency, reasoning and problem solving in mathematics lessons and aim for pupils to gain a deep understanding of mathematical concepts.
What is a Maths Mastery Approach?
- Depth before breath – a rigorous and systematic programme that is developed to ensure every child can achieve excellence.
- It provides a deep understanding of the subject through a Concrete, Pictorial and Abstract approach.
- Mastery – when a concept or skill can be applied over time in a multiple of ways and to an unfamiliar setting
- A child’s mind-set is more important than prior attainment.
Our Vision for Maths alongside the Maths Mastery Approach
- Sets High expectations for every child and makes learning accessible for all
- Puts Number sense and place value
- Encourages the use of pictures and a range of representations to understand new concepts
- Puts real-life problem solving at the centre of our learning
- Is rich in the use of mathematical language and pupil discussion at all ages
- Challenges individuals through increased depth, rather than acceleration of content
- Shows that every child is a mathematician!
What can you do at home to support?
- Role model a positive attitude towards maths (even if you don’t particularly enjoy the subject!) It can be very easy to say ‘I’m not a maths person’ but the way maths is taught has changed vastly over the last few years, making it more interactive, enjoyable and in a way that supports children’s understanding, like through the use of pictures. So try to share that positive, growth mindset with your child!
- Have a look at your child’s year group curriculum and see what concepts they will be studying. The teachers will add things to the Google Classroom pages to support the learning
- Point out where maths is seen in everyday life – this helps to give children a context and show why we are learning these things, not just as one off maths lessons. Can you spot any shapes, count amounts of money, tell the time, cut food into fractions, use multiplication to count groups of objects… the possibilities are endless!
- Engage in homework – classes are given homework which reflects the work completed in school so any work completed at home is really beneficial in supporting and cementing the children learning. Always let the teacher know if you require any support with this – we are aware some of the taught methods are very different to how adults might have been taught in school!
- Practice, practice, practice! Any practice that a child can do at home, particularly of key facts like knowing number bonds and their times tables are key in every year group to support their learning as they move through the school and learn to apply this in different ways.
Our Mathematics Curriculum
At St Joseph’s, we use Timestables Rockstars to support our learning and recall of key times tables facts. It has had great success so far with those who have used it regularly.
By the time your child reaches the end of Year 4, the National Curriculum specifies that they should be able to recall the multiplication tables up to and including 12x12. From June 2020, the children in Year 4 are required to take an online Multiplication Tables Check where they will be asked 25 questions and be expected to answer each one in under 6 seconds. So it’s really important that every child knows these facts and can recall them quickly!
For year groups 2 - 6, each child has a log in for TTR and their teacher should have set their 'Garage' mode to the times table(s) they are working on. If you have any issues with logging onto TTR, please speak with your child's class teacher and they will be happy to help you.


New Customers only. Up to £100 in Bet Credits. Sign up, deposit £5 or more to your account and bet365 will match your qualifying deposit in Bet Credits when you place qualifying bets to the same value and they are settled. Min odds/bet and payment method exclusions apply. Returns exclude Bet Credits stake. T&Cs, time limits & exclusions apply.
Odds are simply a measure of probability. They represent the most likely outcome of a particular event.
Below is how bookmakers display their odds:
Fractional odds are the traditional way of showing odds in the UK. They show the total to be paid out for a successful bet in relation to the stake.
Betting £1 at Odds of 5/1 would return £6. You win £5 plus your stake of £1.
Be careful you are looking at the fraction correctly because:-
Betting £1 at Odds of 1/5 would return £1.20. You win 20p plus your stake of £1.
Decimal odds are more common in Europe. They show an outcome equivalent to the decimal value of the fractional odds plus one.
5/1 would be Decimal 6.
Betting £1 on Decimal 6 would return £6.
1/5 would be Decimal 1.2.
Betting £1 on Decimal 6 would return £1.20.
American Odds are also known as Moneyline or US Odds. The figure quoted will be either positive or negative.
If they are shown with a + sign it means how much you would win on a £100 stake.
If they are shown with a - sign it means how much you would have to stake to win £100.
5/1 (Decimal 6) would be +500.
Betting £1 on US +500 would return £6.
1/5 (Decimal 1.2) would be -500
Betting £1 on Us -500 would return £1.20
Article written by Michael Flynn.


Kindergarten students have been learning about two dimensional shapes in math. They read a book called Mouse Shapes by Ellen Stoll Walsh, and they saw how shapes could be manipulated to make pictures. Then students in Mrs. Manibusan's kindergarten class used two dimensional shapes found in the computer program Kidspiration 3 to create pictures of their own. Students added a sentence about their picture.
Mrs. Manibusan printed her students' work. When she showed me the pictures, I asked her to choose two or three for me to feature on this tech blog. Instead, Mrs. Manibusan sent me the whole stack of pictures with a note that said, "Please choose your favorite ones . . . I love them all." Take a look at the slideshow below, and you will see why it was too hard to choose just a few. That's why I published ALL of them!


Cardboard Adding Machine
Here's something for the junior readers. Before people had computers, children used to play with, and invent, all kinds of games. Once I made an adding machine out of a cornflakes packet. The idea comes from a BBC children's television program called Blue Peter. Below you will find instructions on how to make one.
What you will need:
- 1 box (for example: use an empty cornflakes packet)
- 9 toothpicks (you could also use something like tent pegs)
- 36 drop down cards
First you will need to make the drop down cards. Each card must have two peg support holes and seven escape slits cut into it, as shown in picture below. In the picture, the peg support holes appear at positions: 2 and 7. Two plus seven equals nine, so you need to write the answer 9 in centre of the card. You will have to work out the support hole positions and the correct answers for each individual card. The holes and slits must be positioned accurately or they won't line up properly. The easiest way to do this is to use a template.
Drop Down Card
The next thing to do is make the adding machine. Cut out a rectangular area from the front of the box, as shown in the picture on the right. This will be the card dispenser. Next you need to make nine peg holes in both the front and in the back of the box. Make sure that the peg holes are positioned accurately, so that they will line up with the holes in the drop down cards. Then, on the front of the box, number the holes 1 to 9.
Once you have made all the parts, you can assemble your adding machine. To do this: you need to line up the all cards and position them inside the box. The cards need to be supported by the pegs, by placing them through the holes. Now the adding machine is ready to be used. To add two numbers together, just remove two pegs. The answer should drop down into the card dispenser below.
You could vary the design by using more or less numbers. The one I made only used the numbers from 1 to 6. You could also create a different machine by using a different set of cards.


Joined: 05 Jan 2007
| Posted: Sun Apr 22, 2007 7:17 am Post subject: lat/lon projection methods
|I was recently asked by a 214th member if there was a way of determining the Latitude and Longitude of an unknown steerpoint, when given the bearing and distance FROM a known steerpoint.
For instance, using the Recon function you have determined the Latitude and Longitude of a target point. For example, the end of a runway you have tasked an OCA strike against. However, you want to begin your ingress to the target steerpoint some distance from it. You have also determined the heading you want to ingress on. In this case, the runways magnetic heading.
A simple diagram should help explain...
X---180 degs.---36 _________________18
Since you know the lat/lon of the target point, for example between the VASI lights, and you know the reciprocal of the ingress heading (180 in the example above) as well as the ingress distance, you can calculate the Latitude and Longitude of X, the unknown steerpoint.
In this way you can place a steerpoint there! Upon reaching that steerpoint you turn to the ingress heading and you should be lined up with the runway.
This is beneficial, especially when at low altitude and you don't want to fly up in order to acquire the correct ingress heading visually. In this case, the runway itself.
There are several ways of performing this calculation depending on how precise you need to be. However, since the Earth is not a perfect sphere the math can be daunting for some as it requires a sound understanding of Trigonometry. Specifically, Spherical Trigonometry, etc. But fear not, there are easier ways. After all, if I can do it, it can't be too hard, right?
In Falcon 4 and/or Allied Force one can assume the Earth is flat and therefore, given the relatively short distances involved, we can use a "Flat Earth" model to perform the calculations. See, I keep it simple.
Here are several ways you can perform the calculation and determine the Latitude and Longitude of X as depicted above:
The manual method for you geeks out there...
lat2 = lat1 + cos(hdg) * dist * (360/40000)
lon2 = lon1 + sin(hdg) * dist * (360/40000) / cos(lat1)
Note: you will need to convert the lat/lon values into the units required by your calculators trigonometry functions. For example: convert degrees to radians.
Again, this formula is based on a "flat Earth" model and assumes the lines of longitude are parallel to one another. It isn't perfect, but it's simpler than performing great circle calculations which are not needed for our purposes in Falcon 4 or Allied Force. Why not you ask? Because the distances involved are too short to be affected by the Earth's curvature. Assuming Falcon 4 even models it.
If you have a handheld GPS unit with a waypoint projection feature you can use it, as it will do precisely what is needed. Refer to your units instruction manual.
Method 3. No calculator wristwatch needed.
(Is cheating and if I catch anyone using it!...)
Use a small program called GeoCalc. It can be found here:
- Click on the Projection tab
- Set distance unit to Nautical Miles
- Select the Rhumb Line option button
Here's an example:
Enter the following exactly as shown. You must use this format so you'll need to convert from the Falcon 4 or Allied Force lat/lon as displayed on the recon screen or in the DED to this one.
Point = 71 45 23 N 67 45 23 E
Distance = 10
Bearing = 145
Result = N 71 37.192, E 68 03.640
Compare with the other methods shown above.


[MLB-WIRELESS] GPS Co-ordinates
nodegxt at yahoo.com.au
Tue Oct 10 05:28:39 EST 2006
LAT Decimal = Dg+(mn/60)+(sec/3600)
LON Decimal = Dg+(mn/60)+(sec/3600)
whats so hard about that?
Daryl Knight wrote:
>>Or just do it on paper!!!!!
>How about putting the formula on the web page with the node creation/edit
>page with the gps co-ordinates? You're right its easy peasy, but only if you
>know, or remember from High School, to long ago... how many minutes and
>seconds there are :)
>Melbwireless mailing list
>Melbwireless at wireless.org.au
More information about the Melbwireless


Welcome to Mrs. Fish's school web page!
I am very excited to be a part of the Falcon Nation!!!!
This is my 20th year teaching! My husband is the Assistant Principal & Athletic Director for Constantine High School. We have been married for 21 years and have two amazing sons. Tony is a Senior (Class of 2022) and Joel is a Freshman (Class of 2025). It is an honor to be a member of the Falcon Family!
I teach 8th grade math, Algebra 1, 7th grade Adv. Math, and 6th grade Adv. Math!
Below, I have attached the syllabus for each of my classes.


The Veritas Homeschoolers Math Team earned first place in the 2018 state MATHCOUNTS competition, just ahead of Arizona College Prep and Basis Chandler. Veritas member Karen Culley won first place in the individual competition after a head-to-head countdown speed round. The Veritas Coach, homeschool high school student Michael Gintz, traveled with Karen and three other Arizona students to Washington, D.C. May 12-15, 2018 to compete in the national MATHCOUNTS competition.
The Veritas math team was also first place at the 2018 Chandler-Gilbert Community College Excellence in Mathematics Competition and has earned multiple trophies in Math League.
Pictured: Coach Michael Gintz, Team members Nathaniel Teo, Annalise Baniecki, Adriana Baniecki, State Champion Karen Culley, Peter Culley


Example 2: Breaking the Ancient Numbering Systems – A Tease
Some believe that I broke the ancient numbering systems. They believe that I have created a bridge between physics and mathematics. If anyone should think this is a joke, consider the mathematical conundrum, “The Squaring of the Circle”. The sales letter for either Gicle’e or Oil Painting is here: > http://www.cosmicsleuth.com/oil-painting/ . This was done to prove a
point, not because I like being an artist. It includes the geometric construct and proof, validated by an MS ME MIT PE.
The skinny follows based on the Rhind Papyrus value of Pi*:
- Circle.Area = 256/81* x 144 x 144 = 65536
- Square.Area = 256 x 256 = 65536
- Circle.Area = Square.Area = 65536
- The Circle is squared.
- A full proof and graphic is available with a purchase.


Frequently Asked Questions#
Q: What is the Hybrid Symbolic-Numeric Framework in ANDES?
A: It is a modeling and simulation framework that uses symbolic computation for descriptive modeling and code generation for fast numerical simulation. The goal of the framework is to reduce the programming efforts associated with implementing complex models and automate the research workflow of modeling, simulation, and documentation.
The framework reduces the modeling efforts from two aspects: (1) allowing modeling by typing in equations, and (2) allowing modeling using modularized control blocks and discontinuous components. One only needs to describe the model using equations and blocks without having to write the numerical code to implement the computation. The framework automatically generate symbolic expressions, computes partial derivatives, and generates vectorized numerical code.
Q: Where to find the line admittance matrix?
A: ANDES does not build line admittance matrix for computing line power injections. Instead, line power injections are computed as vectors on the two line terminal. This approach generalizes line as a power injection model.
Q: Without admittance matrix, how to switch out lines?
A: Lines can be switched out and in by using
See the example in
One does not need to manually trigger a Jacobian matrix rebuild
Toggle automatically triggers it using the new
Reference of the existing model#
Q: Is there any further reference of the existing model?
A: Most of them can be found online, such as ESIG and PowerWorld.


Worshipping God. Learning to excel in reading, writing, math and social sciences.
Course of Study
5 Year old Kindergarten (K-5):
- Reinforcement of letters and their sounds
- Intensive study of blending special sounds
- Reading short stories (Phonetic approach to reading)
- Motor skills continue to develop as they write each day
- Basic math concepts (simple adding and subtracting)
- Bible: The students will actively participate in a Bible story each day and memorize scripture passages throughout the year.


- You go to a party. There are 3 drinks, 2 sandwiches, and 4 kinds of candy. How many combinations of all three are possible?
- You have the sides of a rectangular prism flattened out. How many faces and how many total cubic inches are there?
- You have a carpet and a runner of certain dimensions. Is the rug 3 square feet more than the runner?
These test questions or for 4th graders, do they seem like they might be over their heads? I’m not qualified to say what’s good for a 4th grader and what’s not but this seems like they are bit complicated. I even had a hard time understanding exactly what the questions are asking on the first few read through.
Albuquerque schools are in a dismal state. I;m glad to see the school district trying to improve things but this might be a bit more than the kids are ready for right now.
Click through to see if I answered them correctly.
Let’s see if I answered these questions correctly?
- 3x2x4 = 24
- This question was confusing to me. But it says a flattened rectangular prism. So at one point it was 3 dimensional which mean it has 6 faces. But since it’s flattened out it has no cu inches, otherwise they would have to give some size information.
- I have no freaking idea.


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Kara Dawson from School District #71 teacher in Courtenay has been awarded a Prime Minister’s Award for Teaching Excellence in STEM, Certificate of Achievement.
The Prime Minister’s Awards for Teaching Excellence in STEM honour outstanding Science, Technology, Engineering, and Mathematics (STEM) teachers at the elementary or secondary school level who keep students engaged in STEM learning and who help develop the culture of innovation that Canada needs today, and in the future.
Ms. Dawson is a district leader in technology education and brings cutting-edge technology to elementary schools in her area, introducing tools to support students who struggle in the traditional classroom and supporting educators so they can integrate STEM into their teaching.
A complete bio of Ms. Dawson is available at: https://www.ic.gc.ca/eic/site/
The Prime Minister’s Awards, offered at the Certificate of Excellence (national) and Certificate of Achievement (regional) levels, carry cash prizes of $5,000 and $1,000 respectively. Each recipient receives a letter and a certificate signed by the Prime Minister.


Discussion in 'MSC Clan' started by Haite, Apr 18, 2001.
How small 1 x 10^negative infinite?
The answer is "10^negative infinite" since "1 x" effectively cancels itself out of the expression. The answer to the expression "10^negative infinite" is not definable. Since the value of the exponent cannot be defined as either odd or even then the answer to the above expression could be either positive or negative. The answer cannot be less than |1| or else you would never get a value above 1. In fact, with an answer of less than |1| you would ultimately approach a zero value but never reach it. With an answer of exactly |1| the end result could be 1 or -1 depending on whether the exponent was originally odd or even which cannot be determined. So the answer would have to be greater than |1|, but if it was anything greater than |1| than that wouldn't work either because you would ultimately pass up the value of 10 by infinite fold. For these reasons the above expression is undefined.
I think I got my logic right on this. I was using absolute value signs everywhere since the answer could be a +/- answer depending on the value of the exponent. Am I right on this?
Right on the cancelling out, and I guess you were right on your logic, although you weren't addressing my question. I was trying to express my figure in scientific notation, 1 x 10^-infinite, and the above quote is exactly what it is. It almost approaches a zero value, but never reaches because of the infinite regress. Now back to my original question, try to imagine this in physical terms, can you do it?
Some right, some wrong. The sign of the exponent has nothing to do with the sign of the final product. You are confusing it with the sign of the base, which is 10 in this case. If the 10 were negative, then it would matter whether the exponent was odd or even. You are right when you say the 1 is irrelevant, since anything multiplied by 1 equals itself. A negative exponent simply means you place the exponential term in the denominator.
The answer is 10^negative infinity, which is the same as 1 divided by 10^positive infinity. 10^positive infinity is just infinity. A number divided by infinity is, by definition, equal to zero.
So, in the end, the answer is zero.
Stop assailing my question with postulates and corrolaries, let me try and rephrase. I don't think my unit can be expressed mathematically, however I'll try verbally. Think of 0.1, then divide this by 10, and that by 10, ad infinitum. Can you imagine this physically? Now vote people!
I suppose in a philosophical context you could say this. It is technically true. For simplicity, though, mathematicians just define 1 divided by infinity to be zero, and they are correct in a very real sense. A number approaching infinite smallness will behave like zero, mathematically speaking.
If you've had some pre-calculus, you've done limits. This is the same as the limit of the function 1/x, as x approaches infinity. The answer is zero.
And to address your philosophical question: The human brain, which is finite, cannot conceive of infinity in any sense other than an abstract concept. This is true not only for infinite largeness, but infinite smallness as well.
(Sometimes I even amaze myself.)
DON'T MAKE ME LOCK DOWN THIS THREAD!!!!
oowwwwww...that yelling made my brain hurt I've been up since 5:00am
Now another philosophical question, cow's a guy, but that defies the definition of a cow. Please enlighten me.
The answer is 0. Because the exponent is infinity, you must take the limit to evaluate it. limit of 1/10^infinity is 0
come on guys, this is an easy one.
the answer is cream cheese.
I like cream chips
No, I believe the answer is cheddar. It is the more logical conclusion!
well, I was having a bagel at the time. Cheddar on a bagel before 10am is, well, kind of nasty.
thus, the answer remains cream cheese
what about butter?
Acctually I can't make out any difference between cheese and butter. But I know ice cream.
The world "bagel" is often used as a synonym for zero, therefore zero = bagel.
1/infinity is also equal to zero.
So, by the transitive property of mathematics, 1/infinity = bagel
Cream cheese is the only thing that belongs on a bagel before 10 AM.
Thus, as Oni has pointed out, the answer is cream cheese. (At least before 10 AM).
Hey what about
I know that my calculator can't do it... it's probably a pizza with mozza on it.
Ah, grasshopper, but what is the true value of Bagel^Cream cheese?
bagel= 0 so bagel^n = 0 always.
Ah, but cream cheese is not a number! Back to the salt mines for you, slaggard! <whack!>
Butter is the milk solids seperated out from the whey and churned. Cheese is milk with a coagulant added, like rennet.
Separate names with a comma.


In the 20th century, Ansel Adams can be considered as one of the best photographers and we have Elliot McGucken to just prove why it is that way. When he was going through the public work as showcased by Adams, he saw that all his art work was done by taking into consideration the golden ratio, which was aesthetic by itself and it also showcases how nature is in harmony with the golden ratio, if looked at from the right angle.
He kept the golden ratio intact across all the photos he has captured, be it either with consciousness or not. He actually intrigues the viewer and it also showcases the mathematical intellect of Adams. He could achieve it by taking into consideration the golden harmonies and being in sync with nature.
You can observe the golden spiral across all of his works and once you realize how hard it is, it is truly mesmerizing. You can also take a closer look at how the golden ratio is being followed. McGucken has also published a free book on Kindle to make more people aware regarding Adams’ work.