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https://www.jiskha.com/display.cgi?id=1267996666
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math
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posted by Dannie .
A solution is prepared by adding 50 mL of .050 M HCL to 150 mL of .10 M HNO3. Calculate the concentrations. I know I need to find the [H+] and [OH-] but im not sure how.
moles HNO3 = M x L = ??
M HNO3 = moles/total L.
moles HCl = M x L = xx
M HCl = moles/total L.
Another way, to me less complicated; however, it gets away from the defnitions of M = moles/L which is all the above. Just the definition. The other way is a dilution method.
(HNO3) = 0.1M x (150 mL/200 mL) = ?M
(HCl) = 0.05M x (50 mL/200 mL) = ?M
Try it both ways. You should get the same answer either way.
The balanced chemical equation for reaction of Ba(OH) and HCl is as follows:
Ba(OH) + 2HCl BaCl + 2H O
1 mole Ba(OH) produce 2 moles OH ions.
Number of moles of OH ion in solution = concentration of Ba(OH) x volume of Ba(OH)
= 0.1 mol L x 0.03 L x 2
= 0.006 mol
Number of moles of H ion in solution = Concentration of HCl x volume of HCl
= 0.05 mol L x 0.02 L
= 0.001 mol
Now after mixing 0.001 mol H will reacts with 0.001 mol OH .
Number of moles of OH left unreacted = 0.006 - 0.001
= 0.005 mol
Total volume of solution = 20 ml + 30 ml = 50 ml = 0.05 L
Concentration of OH ion in ánal solution = 0.005 mol / 0.05 L = 0.1 mol L .
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https://www.got-it.ai/solutions/excel-chat/excel-tutorial/averageif/google-sheets-2
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math
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The Google Sheets AVERAGEIF function returns the average of numbers that meet given criteria in a range. It is basically a combination of AVERAGE and IF functions and acts like an array formula to get the average of resulting array of numbers where a logical condition or criteria is TRUE.
The AVERAGEIF function in Google Sheets
For example, you have certain numbers, and you want to test a logical condition or criteria on those numbers, and then you need the average of those numbers where a logical condition is TRUE. So you can achieve this by using AVERAGEIF function in Google Sheets.
The syntax of the AVERAGEIF function in Google Sheets is;
AVERAGEIF(criteria_range, criterion, [average_range])
criteria_range – This is a range of values where you need to test logical condition or criteria.
Criterion – This is logical condition or criteria that you want to test on criteria_range. It can consist of a number or text or date or logical expression to test the condition.
average_range- This is a range of numeric values that you want to average. It is an optional argument, and if you do not supply this argument, the AVERAGEIF function takes criteria_range to calculate average.
Here you need to test the various criteria options to calculate the average of numbers that meet these criteria using the Google Sheets AVERAGEIF function.
AVERAGEIF for Number as criteria
You can use a number as criteria to calculate the average of those numbers that are equal to this criterion number. In this example, you want to calculate average marks of students in class 8th using Google Sheets AVERAGEIF function.
AVERAGEIF for Text as criteria
If you want to test a text value as criteria on criteria_range then you need to supply the criteria in double quotation marks (“”) in the criterion argument of the Google Sheets AVERAGEIF function. For example, you have data of quantity sold of various foods’ categories, and you need to calculate the average quantity sold of vegetables using AVERAGEIF function in Google Sheets.
AVERAGEIF for Date as criteria
The average can be calculated based on date as criteria using Google Sheets AVERAGEIF function. The date can be supplied directly or as a cell reference or as a date function like TODAY or DATE function in AVERAGEIF function in Google Sheets.
If you supply the date directly as criteria in the AVERAGEIF function, then you need to enter it in double quotation marks (“”), and if you enter it as cell reference or date function then it will be entered without double quotation marks, such as;
AVERAGEIF for Expression as criteria
Based on criteria expression you can calculate average of numbers in Google Sheets AVERAGEIF function. Like if you want to calculate average of numbers that are Greater Than (>) or Greater Than Equal to (>=) or Less Than (<) or Less Than Equal to (<=) or Not Equal to (<>) to a specified number, then these expressions must be supplied in double quotation marks in criterion argument, such as;
Greater Than ➔ “>10”
Greater Than Equal to ➔ “>=10”
Less Than ➔ “<10”
Less Than Equal to ➔ “<=10”
Not Equal to ➔ “<>10”
For example, you need to take the average of students’ marks that are Greater Than Equal to 80 then formula would be;
Still need some help with Excel formatting or have other questions about Excel? Connect with a live Excel expert here for some 1 on 1 help. Your first session is always free.
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| 3,436 | 25 |
https://www.microchip.com/forums/m1120636.aspx
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math
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I agree with PStechPaul that displaying the results after averaging, with more digits.
would be helpful in analyzing and understanding the noise present.
While + and - 1 digit is the theoretical limit of resolution for each single sample from a ADC conversion,
this isn't true for the averaged result.
The Averaged result will have better resolution than 1 LSB of the converter.
so displaying the result as Accumulator value divided by 20, is an excellent suggestion.
It may even be used in the user's calculation of final results.
This is actually the same technique that is used in high resolution 'Sigma/Delta' AD Converters
used in digital multimeters and other high resolution A/D converters, with 14 bit, 16 bit, 18 bit,
or even higher resolution.
For this to work, it is assumed that there is a little high frequency noise in the signal,
coresponding to about +/- 1 LSB of the AD converter,
and with a frequency higher than the sampling frequency of the ADC.
Some even apply dithering, that is adding a little high frequency noise to the signal to be measured.
However, neither Averaging nor Low Pass filter, in hardware or software, or high resolution ADC,
will help if there is Low frequency noise in the input signal,
that is if the noise have frequency lower than the period of averaging calculation.
In fact, in results displayed in message #7 and #12,
the variations come quite regularly:
47, 47, 48, 48, 49, 49, 49, 48, 47, 48, 48, 47, 47, 48, 49, 49
With one more decimal digit in printing of averaged values, as Paul suggest,
I suspect that it may be possible to plot a quite recognizable sine wave like curve.
I am not sure if the interval between printing values, is constant, or not.
What 'btbass' is suggesting in message #11 is another way of organizing calculation average value,
sometimes called a moving average or running average. See Wikipedia.
But it is average calculation anyway, with results similar to what the original poster is already doing.
Such a moving average is a way of organizing the calculation such that,
a updated average result value is available for each measurement value inserted.
It does however require a division to be performed for each measurement value added,
instead of one division at the end of a batch of measurements, as the OP. have been doing all the time.
The effort of doing divisions may be reduced, by using number of samples that is a power of 2.
e.g. 4 or 8 or 16 or 32 or 64 ... or 256 ... or 1024, ... , as suggested by pcbbc in message #4 above.
The compiler may, or may not recognice these numbers, and replace the division with shift operations.
Or it may be programmed with shift operator in the code.
Averaging with a number of samples = 256, may be made efficient by picking away a whole byte, instead of doing a long division.
It will however Not remove low frequency noise.
post edited by Mysil - 2019/12/09 06:49:54
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| 2,893 | 37 |
https://www.samudramanthan.co.in/mechanical_mcq/fluid_mechanics/2.php
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math
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2. What is the indicator diagram?
3. What are the purpose of taking indicator diagram?
4. What are the types of indicator diagram?
5. What is indicated power? How to calculate power?
6. Steps to take indicator diagram?
7. Purpose of Power diagram, Out-of-phase diagram, Compression diagram, Light spring diagram?
8. When indicator diagram is taken?
9. What are the necessary precaution to avoid indicator malfunction?
10. What are the steps to be taken when compression pressure is low?
Fluid Mechanics (Set 2)
Multiple Choice Questions
1. Steady flow occurs when
2. A flow is called super-sonic if the
3. In a forced vortex, the velocity of flow everywhere within the fluid is
4. The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where IG = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface, and x = Depth of centre of gravity of the immersed surface from the liquid surface)
5. Mach number is significant in
6. A fluid which obeys the Newton's law of viscosity is termed as
7. In order that flow takes place between two points in a pipeline, the differential pressure between these points must be more than
8. The error in discharge (dQ/Q) to the error in measurement of head (dH/H) over a triangular notch is given by
9. For similarity, in addition to models being geometrically similar to prototype, the following in both cases should also be equal
10. The value of coefficient of velocity for a sharp edged orifice __________ with the head of water.
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CC-MAIN-2022-49
| 1,585 | 21 |
https://www.wyzant.com/resources/answers/42661/physics_work_and_energy_question_please_check_my_answer
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math
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Bob A. answered 08/06/14
20 Years Making Science and Maths Understandable and Interesting!
For part A you have ignored the potential energy at the starting position of 1.5 m above ground.
Ui = mgh = (0.005kg) (9.81 m/s2) ((1.5 m) =
For part B finding the max position is needed as you do.
But not that way. You have U2 - v2 How can you subtract velocity from energy?
Since at the top vf = o we can take advantage of that and the fact that the up and down problems at symmetrical/mirror images with the falling velocity = initial velocity at the same height.
Δx = vf2 / 2a So you can see you were doing the correct maths with numbers but but not from the right formula.
Now for the second part of B
U = mgh that's right, but h is the 20.39 m + 1.5 meters ot less than less than
So for a) K = the 1 J , and U = mgh where h is 1.5 m - then total them.
and for b) K = 0 (zero v at top) and U is mgh with h = (20.39 m + 1.5 m)
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CC-MAIN-2023-14
| 922 | 12 |
https://hungryskinny.com/the-number-of-times-the-analog-wave-is-measured-each-second-when-digitizing-music-is-the/
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math
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The number of times the analog wave is measured each second when digitizing is called the sampling rate.
Checkout this video:
Analog waveforms are often digitized by sampling the amplitude of the wave at regular intervals. The rate at which these samples are taken is called the sampling rate, and is measured in samples per second, or hertz (Hz). The number of times that the analog wave is measured each second when digitizing will have an effect on the accuracy of the digital representation.
What is Analog Wave?
Analog wave is a type of wave that encodes information using the amplitude and frequency of the wave. It is often used in audio and telecommunication systems. The analog wave is measured by the number of times per second that the wave oscillates. This is called the sampling rate.
What is Digitizing?
The word “digitizing” simply means to convert an analog signal into a digital signal. Analog signals are the smooth, continuous signals produced by things like microphones and guitars. Digital signals are the on/off, square wave type signals used by computers. In order to convert an analog signal into a digital signal, the analog signal has to be sampled at a certain rate.
The Importance of Sampling Rate
In order to digitize an analog signal, it must be sampled at a certain rate. The rate at which the signal is sampled is important, as it determines the accuracy of the digital representation. Sampling too slowly will result in an inaccurate representation, while sampling too quickly will result in wasted resources. The Nyquist–Shannon theorem states that a signal can be perfectly reconstructed from a series of samples if the sampling rate is greater than twice the highest frequency present in the signal.
How to Digitize an Analog Wave?
Analog-to-digital conversion is the process of converting an analog signal, such as a sound wave or a light wave, into a digital signal. An analog signal is a continuous signal that can take on any values within a given range. A digital signal is a discontinuous signal that can take on only a finite number of discrete values.
To digitize an analog wave, the first thing that must be done is to determine the range of values that the analog signal can take on. The next step is to choose a suitable sampling interval. The interval must be small enough so that the sampled signal accurately represents the original signal, but it must also be large enough so that the number of samples taken is reasonably small.
Once the sampling interval has been chosen, the next step is to measure the value of the analog signal at each interval. These measurements are then converted into digital form, which can be stored in a computer or other digital device.
The Number of Times the Analog Wave Is Measured Each Second When Digitizing
Analog-to-digital converters (ADCs) are used in many electronic devices to convert continuous analog signals into discrete digital values. The ADC typically measures the amplitude of the input signal at regular intervals and encodes the results into a digital value. The sampling frequency is the number of times per second that the analog waveform is measured. For example, if the ADC is measuring a sinusoidal waveform with a frequency of 1 kHz (1000 Hz), and the sampling frequency is 10 kHz, then 100 samples will be taken each second.
The Significance of the Sampling Rate
The sampling rate is the number of times the analog wave is measured each second when digitizing. The purpose of a high sampling rate is to allow the reconstruction of the original analog signal with a minimum of error. For this reason, the sampling rate must be at least twice the highest frequency component in the original signal.
The human ear can hear frequencies up to about 20 kHz. To digitally store and reproduce this range of frequencies, a minimum sampling rate of 40 kHz is required. The Compact Disc (CD) uses a sampling rate of 44.1 kHz, which allows it to accurately reproduce frequencies up to 22.05 kHz, the highest frequency that most people can hear.
The Relationship Between Sampling Rate and Signal Quality
The sampling theorem is a fundamental result in the field of digital signal processing, which states that a signal can be completely recovered from its samples if the samples are taken at a rate greater than twice the highest frequency present in the signal. This result is known as the Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon.
The theorem is usually considered to be one of the most important results in the field of digital signal processing, as it provides a theoretical basis for the practice of digitizing continuous-time signals.
Why Is the Sampling Rate Important?
The sampling rate is the number of times the analog wave is measured each second when digitizing. It is important because it affects the quality of the digital signal. A lower sampling rate means that the digital signal will be more coarse, while a higher sampling rate means that the digital signal will be more fine.
To digitize an analog wave, you need to take a number of measurements each second. The more measurements you take, the more accurate your digitized wave will be. Here’s a quick rundown of how many measurements you should take:
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| 5,260 | 24 |
https://fr.slideserve.com/gilead/2005-1-28-seminar
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math
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2005/1/28 Seminar Student：Future Master CCY Advisor：Doctor Yung An Kao
Outlines • Introduction • Case Discussion • Simulation • Conclusion
Case Discussion(1) We have found that there is a large error in SFO estimation. WHY??? We take the following example to find out th- e problem. Environment: Trms, Ts=50; CFO=0.01; SFO=500Hz
Case Discussion(2) In this simulation, we used the 23th and 24th sub-carrier which have MAX signal energy. However, we would get a wrong estimation- 330 symbol.
Simulation Environment • SNR=20dB • 600 OFDM symbol, 1200 times • SFO=500; CFO=0.01 • No channel (each sub-carrier is equal energy) • We used the 26th and -26th sub-carrier in first figure. In second figure, we used the -26th and -25th sub-carrier.
Conclusion • We should use the sub-carriers that are not adjacent. • We could not only select the sub-carriers that have MAX signal power.
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CC-MAIN-2022-21
| 903 | 6 |
http://mathhelpforum.com/calculus/20760-derivatives-problem.html
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math
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For what values of x does the graph of:
F(X) = X^3 + 3X^2 + X + 3 have a horizontal tangent?
I don't know how to approach this but I got 0 as one of the values of X. I'm not really sure if there are other values.
If you have a graphing calculator like a TI-83 you can type in the equation for the derivative and then hit 2nd --> Calc to find the zeros. I'm guessing your teacher probably wants to see work and it doesn't hurt to practice by hand, but it's a good way to check your answers
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| 488 | 4 |
https://www.nagwa.com/en/videos/842138547687/
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math
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A line has a slope of negative three two and passes through the point five, zero. What is the equation of this line?
We have the slope and a point. Our first step will be using the point-slope form: 𝑦 minus 𝑦 one equals 𝑚 times 𝑥 minus 𝑥 one. Our point five, zero is our 𝑥 one, 𝑦 one. And the 𝑚 value is the slope, negative three-halves. We’ll plug this information in: 𝑦 minus zero equals negative three-halves times 𝑥 minus five. On the left, 𝑦 minus zero equals 𝑦, negative three-halves times 𝑥 equals negative three-halves 𝑥, and then negative three-halves times negative five equals positive 15 over two.
The equation we have now is in slope form. But we want to write the equation for this line in standard form. In standard form, the 𝑥 is positive and none of the coefficients are fractional. Not only that, the whole equation is set equal to zero. We have a negative 𝑥 that needs to be moved to the left side of the equation. So we add three-halves 𝑥 to the right and the left. Negative three-halves 𝑥 plus positive three-halves 𝑥 equals zero. Our new equation says three-halves 𝑥 plus 𝑦 equals 15 over two.
We want the right side to be equal to zero. So we subtract 15 over two from the right and the left. Positive 15 over two minus 15 over two equals zero. And the left side says three-halves 𝑥 plus 𝑦 minus 15 halves equals zero. Well let’s give ourselves a little bit more space. Remember, at the beginning I said that our 𝑥 needed to be positive and there could be no coefficients that are fractional. We can’t have these divided by two pieces.
To get rid of that we’ll multiply the whole equation by two. Two times three-halves 𝑥 equals three 𝑥. Two times 𝑦 equals two 𝑦. Two times negative 15 halves equals negative 15. And two times zero equals zero. The equation for this line is three 𝑥 plus two 𝑦 minus 15 equals zero.
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CC-MAIN-2020-45
| 1,936 | 5 |
http://mycrazylekkerlife.blogspot.com/2008/08/want-books.html
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math
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I decided to start a book exchange.
Here's how it will work:
You look through the books that I have available
You pick one you like
You let me know which one you like
You also let me know which books you have available to exchange
I pick a book I like
I send you a book
You send me a book
Go to my Michelle's Book Exchange page for all the details.
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CC-MAIN-2017-17
| 348 | 10 |
http://kingsitworld.forumotion.net/t415-eco402-assignment-no-1-solution
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math
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spring 2011 assignment solution
Question no 1:
a. Ali has certain amount of money and he has to spend on two goods apple
and strawberries. Suppose Ali completely prefers strawberries than apple.
How you will see this particular situation in the consumer equilibrium
b. Support your answer with the help of graph.
For the first question the answer is "corner solution.” As according to the corner solution ,if a consumer buys in extremes and buys all of the one category of good mean completely prefer one good over the other .In this situation the indifference curves are tangent to the horizontal and vertical exis.For the graph look in the lecture number 8 page no 50 in the topic of corner solution.
Question no 2:
Keeping in view the given data for the construction of roads from the year 2000
to year 2004, calculate the nominal price for the roads construction in each year.
Take year 2000 as base year where required.
For question number 2 the formula is given as follows
Nominal price = CPI (current year)/CPI (base year)*Real price.
Here is the solution for the first year. Solve others by similar formula.
Nominal Price for the year 2000 = 45.5/45.5*5550
Nominal Price for the year 2000= 5550
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| 1,204 | 16 |
http://stratfordnorthwestern.ca/mathlete-of-the-week-ethan-skinner/
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math
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Ethan Skinner is Northwestern’s Mathlete of the Week! He has a 93% this semester and has a great curiousity about math. He always ensures that he can master each assigned question. If he is stuck, he perseveres until he has an understanding of it!
Honorable Mention: Carla Rubio, Cathy Liang, and Owen Hahn
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CC-MAIN-2019-13
| 308 | 2 |
https://www.physicsforums.com/threads/equation-of-the-tangent-line-to-the-curve.182367/
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math
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Find an equation of the tangent line to the curve: 7*x*e^(x)+8 at (0,8)
Derivative I guess?
The Attempt at a Solution
I know you have to take the derivative of the equation given which I think is
7*x*e^(x) + 7*e^(x)
Then you plug it into slope intercept form: y-y=m(x-x)
I did this and got y-8=(7*e^(x)*(x+1))*x, but apparently that's not right...
What did I do wrong? Maybe i just typed it in wrong?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150129.50/warc/CC-MAIN-20210724032221-20210724062221-00105.warc.gz
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CC-MAIN-2021-31
| 400 | 8 |
http://ci.nii.ac.jp/naid/10004472787
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math
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オーバーパラメータモデルを用いた同定におけるパラメータ変換とバイアス補償最小2乗推定 Bias-Compensated Least-Squares Estimation and Parameter Transformation in Identification with Over-Parameterized
For the problem of estimating unknown parameters of the transfer function model from input and output (I/O) data contaminated by colored measurement noise, a three-step estimation procedure has been previously proposed to exploit the I/O correlation information with respect to the correlation time. This paper analyzes this procedure from the compatibility between the parameter transformation and the bias-compensated least-squares (BCLS) estimation used in the third step. The transformation is made from the over-parameterized model in the first and second steps to the final model with the true order in the final step, and is based on the minimization of the mean square error (MSE) between the outputs of the two models. The BCLS estimation is based on the minimization of MSE between the final model output and the process output. It is verified that the condition for compatibility, i.e. the equivalence of two minimizations, is a consequence of the two over-parameterized estimation equations in the first two steps, and that the over-parameterization assures an inclusive expansion of the I/O correlation information. Simulation results are presented to demonstrate the equivalence.
システム制御情報学会論文誌 13(2), 72-79, 2000-02-15
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CC-MAIN-2017-13
| 1,496 | 3 |
http://nrich.maths.org/public/leg.php?code=31&cl=2&cldcmpid=10328
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math
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In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This is an adding game for two players.
Who said that adding couldn't be fun?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
A game for 2 players. Practises subtraction or other maths
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Got It game for an adult and child. How can you play so that you know you will always win?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
This task follows on from Build it Up and takes the ideas into three dimensions!
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Investigate what happens when you add house numbers along a street
in different ways.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
You have 5 darts and your target score is 44. How many different
ways could you score 44?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049270513.22/warc/CC-MAIN-20160524002110-00233-ip-10-185-217-139.ec2.internal.warc.gz
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https://www.essays.se/essay/1b2974c1bd/
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math
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A Study of Momentum Effects on the Swedish Stock Market using Time Series Regression
Abstract: This study investigates if momentum effects can be found on the Swedish stock market by testing a cross-sectional momentum strategy on historical data. To explain the results mathematically, a second approach, involving time series regression for predicting future returns is introduced and thereby extends the cross-sectional theory. The result of the study shows that momentum effects through the cross-sectional strategy exist on the Swedish stock market. Although positive return is found, the time series regression do not give any significance for predicting future returns. Hence, there is a contradiction between the two approaches.
AT THIS PAGE YOU CAN DOWNLOAD THE WHOLE ESSAY. (follow the link to the next page)
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https://philosophy.stackexchange.com/questions/76918/a-distinction-between-knowledge-of-laws-of-physics-and-the-actual-laws
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math
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What exactly is a law of physics? Suppose, for an hypothetical example, that high-energy light travels ever-so-faster than low-energy light. Then it would turn out that in fact light does not always travel in the same speed in a vacuum, so that would be a false law. So, my question really is, does the term "law of physics" refer to our current knowledge, or to the actual laws, whatever they may be?
Science only gives explanations of what we observe, and how to predict future actions. They are not explanations of the 'thing' in itself. D'Arcy Wentworth Thompson says in his book On Growth and Form (p 288):
For as Newton said, to tell us that a thing "is endowed with an occult specific quality, By which it acts and produces manifest effects, is to tell us nothing; but to derive two or three general principles of motion [author's footnote] from phenomena would be a very great step in philosophy, though the causes of those principles were not yet discovered."
Footnote: This is the old philosophic axiom writ large; Ignorato motu, ignoratur natura, which again is but an adaption of Aristotle phrase [Greek] as equivalent to the "Efficient Cause". Fitzgerald holds that "all explanations consist in a description of underlying motions" (Scientific Writings, 1902, p 385); and Oliver Lodge remarked, "You can move Matter; it is the only thing you can do to it."
Science is not absolute. We adjust or find a better explanation or theory to describe interactions of matter and forces every day - no physical theories are absolute as none solve the question of the "Efficient Cause". The 'Efficient Cause' is the realm of philosophy not science.
Mathematics is the language of science, a language we use to understand the workings of the universe. The universe can be written in the language of mathematics, it explains how events in the universe seem to occur from our perspective. It does not explain what the universe is. In the book Quantum Physics and Ultimate Reality: Mystical Writings of Great Physicists by Michael Green, Wolfgang Pauli is quoted :
...a mathematical formula can never tell us what a thing is, but only how it behaves; it can only specify an object through its properties. And these are unlikely to coincide in toto with the properties of any single microscopic object of our everyday life.
[And Arthur Eddington:]
For example, we may admire the triumph of patience of the mathematician in predicting so closely the positions of the moon, but aesthetically the lunar theory is atrocious; it is obvious that the moon and the mathematician use different methods of finding the lunar orbit...But now we realise that science has nothing to say as to the intrinsic nature of the atom. The physical atom is, like everything else in physics, a schedule of pointer readings...
...matter is something that Mr. X knows. Let us see how it goes: This is the potential that was derived from the interval that was measured by the scale that was made from the matter that Mr. X knows. Next question: What is Mr. X? Well it happens that physics is not at all anxious to pursue the question: What is Mr. X? It is not disposed to admit that its elaborate structure of a physical universe is "The House that Mr. X built."...matter, in some indirect way, comes within the purview of Mr. X's mind is not a fact of any utility for a theoretical scheme of physics. We cannot embody it in a differential equation. It is ignored, and the physical properties of matter and other entities are expressed in their linkages in the cycle. And you can see how by the ingenious device of the cycle physics secures for itself a self-contained domain for study with no loose ends projecting into the unknown. All other physical definitions have the same kind of interlocking. Electrical force is defined as something which causes motion of an electric charge; an electric charge is something that exerts something that produces motion of something that exerts something that produces...ad infinitum.
Science and philosophy dwell in different realms, they are not opposed to each other or overlapping as some try to frame in arguments, they are complimentary. Science deals with matter and energy and their interaction or collocation. It explains how, never why. And both are as pointed out by D'Arcy Thompson only properties of three dimensional space; and as the others point out, only pointer readings as to how we interpret the universe and not 'the thing in itself' or 'Efficient Cause'.
The physicist and historian and philosopher of physics Pierre Duhem defines—in Aim & Structure of Physical Theory pt. 2, ch. 5 ("Physical Law"), p. 168—a physical law as
a symbolic relation whose application to concrete reality requires that a whole group of laws be known and accepted.
In that chapter, he shows that
- The Laws of Physics Are Symbolic Relations
- A Law of Physics Is, Properly Speaking, neither True nor False but Approximate
- Every Law of Physics Is Provisional and Relative because It Is Approximate
- Every Physical Law Is Provisional because It Is Symbolic
- The Laws of Physics Are More Detailed than the Laws of Common Sense
The Physical System of St. Thomas ch. 10 "Physical Laws" by G.M. Cornoldi, S.J., gives a broader definition:
Law is a rule and measure of operations and law must proceed from reason
cf. Summa Theologica I-II q. 90 "Of the essence of law"
Also: "3.3 How the laws of nature lie (or at least engage in mental reservation)" of Ed Feser's Aristotle’s Revenge: The Metaphysical Foundations of Physical and Biological Science
In practice, the term "law of physics" refers to things we already know to be wrong more often than not.
For instance, Newton's law of gravitation is wrong, it has been superseded by general relativity in terms of "correctness" for more than a hundred years now, yet no one has stopped calling Newton's law of gravitation a law, we still teach it in schools and textbooks, and it makes for reasonably decent simulations of solar systems in various computer games. That the Rayleigh-Jeans law cannot possibly be correct was pretty much known at the time it was conceived (see ultraviolet catastrophe). There are plenty of more examples.
Laws of physics, are not meant to be statements about some unchanging universal truths about the world. They are models, or the building blocks of models, enabling prediction and simulation of real-world systems to a reasonable precision. When you want to crank the precision up, or change the situation to something not well-modeled by the law you were using, you switch laws (e.g. Newtonian gravity -> General Relativity). Often there are competing descriptions of a physical situation in terms of different laws, and neither of them is "wrong" - they just look at different scales, at different things, with different accuracy. For instance, the strong nuclear force is "fundamentally" mediated by gluon particles, but in the context of atomic nuclei it is often useful to think of the residual nuclear force as being mediated by pions.
You can find some related discussion on the purpose of "wrong" laws on physics.SE, e.g. here.
Since it seems pertinent, I rush in with an observation by Stephen Jay Gould:
In science, “fact” can only mean “confirmed to such a degree that it would be perverse to withhold provisional assent.” ("Evolution as Fact and Theory", pp. 254–55)
I'm fond of that quote because every word counts, and because it makes clear that physicists are not after truth, but instead quantitative rules of thumb for dealing with the behaviour of the universe. The most useful such rules are those we have repeatedly tried to falsify by observation, but which have nevertheless proven reliable (either universally so, or in a well-defined set of limited circumstances).
Truth we leave to the mathematicians, who are welcome to it.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817106.73/warc/CC-MAIN-20240416191221-20240416221221-00583.warc.gz
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CC-MAIN-2024-18
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https://bornholm-sommerhus.info/and-relationship/hookes-law-and-youngs-modulus-relationship.php
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math
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Hooke’s law | Description & Equation | bornholm-sommerhus.info
We know that the Young's modulus of an object is defined as the ratio We also know that Hooke's law, which can be applied to any linear. TAP 2: Hooke's law and the Young modulus. Purpose. The Young modulus tells you about what happens when a material is stretched – how stiff is it? are both interesting characters who have far more to them than this relationship. Young's modulus, numerical constant, named for the 18th-century English physician This is a specific form of Hooke's law of elasticity. stress-strain relation.
Is There A Relationship Between Young's Modulus And Spring Constant?
If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear. Otherwise if the typical stress one would apply is outside the linear range the material is said to be non-linear.
Steelcarbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear. However, this is not an absolute classification: For example, as the linear theory implies reversibilityit would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.
In solid mechanicsthe slope of the stress—strain curve at any point is called the tangent modulus. It can be experimentally determined from the slope of a stress—strain curve created during tensile tests conducted on a sample of the material. Directional materials[ edit ] Young's modulus is not always the same in all orientations of a material.
Most metals and ceramics, along with many other materials, are isotropicand their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional.
Elasticity: Young's modulus & Hooke's Law - SchoolWorkHelper
These materials then become anisotropicand Young's modulus will change depending on the direction of the force vector. Anisotropy can be seen in many composites as well. They are analytical approximations to realistic interatomic forces, but will illustrate how to relate atomic properties to macroscopic material properties. Consider the potential where A, B, n and m are constants that we shall discuss below.
Using 2 and rearranging: We can substitute this value into 1 to get the minimum value U r0. In a diatomic molecule, this value would give an estimate of the binding energy but, as it's more complicated for a crystal, we'll leave that calculation aside.
The sketch shows a simple model of a crystalline solid. In the horizontal x axis, the interatomic separation is r. In both perpendicular directions, the separation is y, as shown in this sketch. Young's modulus Y for a material is defined as the ratio of tensile stress to tensile strain.
However, the repulsive term is simply a convenient, differentiable function that gives a very strong repulsion. So, we have related Young's modulus to individual atomic forces and energies: To relate Hooke's law to Young's modulus in the experiment above, it would be necessary to consider bending of the wire. In bending, one side of an object is stretched and the other compressed.
This also requires considering the geometry of the spring. Although the length of the spring may change by many percent, nowhere is the steel compressed or stretched more than one percent. Polymers and entropic forces Many polymeric materials, such as rubber, have much lower values of Young's modulus than other solids. The stretching mechanism here is different, because to a large extent stretching straightens polymer molecules, rather than changing the average distance between them.
A completely straightened polymer molecule has only one possible configuration.
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| 4,016 | 14 |
https://www.salongeek.com/threads/part-time-study.182411/
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math
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I am interested in studying a part time nail technician course. However, I am unsure as to which course to choose. I have seen one with open study college which looks good but I am new to all this and am unsure to whether this will be a successful option for me. I need some advice please, is this a good course? If not, could you suggest one that is?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178365454.63/warc/CC-MAIN-20210303042832-20210303072832-00051.warc.gz
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CC-MAIN-2021-10
| 351 | 1 |
https://math.answers.com/Q/What_is_the_answer_to_a_math_problem_called_when_numbers_are_subtracted
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math
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Fractions and mixed numbers are numbers that can be added, multiplied, divided and subtracted. This is taught in math.
The same thing its just digits
The word increased in a math problem means you are adding to terms or numbers.
What do you do in a math problem if there are 2 median numbers?
A fact team is when 3 numbers are added and subtracted together. Another fact team is multiplying and dividing 3 numbers together.
the mean (in math) is the average of all the numbers in the problem
Add all of the numbers then divide them by how many numbers there are.
There a few numbers that can be added up to the sum of the numbers 22 and 400. This is a math problem.
The average is the sum of a set of numbers divided by the number of numbers in the set.
The number that occurs most often in a set of numbers.
you have to solve the problem
The st of counting numbers are called natural numbers. This is taught in math.
The symbols used for counting in math are called numbers, or numerals. They can be whole numbers, or fractions of parts of a number.
The quantity subtracted.
it means to have taken away from
Not if you're doing a math problem.
the average. all you have to do is is add all the numbers and then divide it by the number of numbers there are and that is your median.
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CC-MAIN-2021-43
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http://www.comp.hkbu.edu.hk/~icpr06/tutorials/Vehel.html
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math
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Wavelet-based Multifractal Methods in Image Processing
Jacques L¨¦vy V¨¦hel
Fractal and Multifractal analysis have made important progress in recent years. As a consequence they are being used in an increasing number of fields, including geophysics, finance, medicine, chemical engineering, telecommunications and more. Image processing has also strongly benefited from these recent advances. New methods have been proposed for segmentation, classification, denoising, compression, watermarking, interpolation ... In many cases, the algorithms are based on wavelet decompositions, which allow for efficient implementation.
We shall start this tutorial with an explanation of how this wealth of applications was made possible: We shall show how the focus has moved from fractal image processing to fractal processing of images. In other words, recent successes were possible because generic fractal tools have been applied to arbitrary images. Basically, this means that one uses global or local measures of regularity to analyze and process any kind of data. The most well known example of this point of view is probably fractal image compression (Fig. 1), where arbitrary images are modeled as attractors of iterated functions systems.
Figure 1: A (non fractal) image (left) and its fractally compressed version (right). Compression ratio 46:1.
Global Measures of Regularity
Global measures of regularity are typically used for applications such as classification and monitoring. The most well known measures of global regularity are fractal dimensions. We will focus on the regularization dimension. This dimension is specifically tailored for signal/image processing needs. It is a finer measure of global regularity than the classical box dimension, and may be estimated with better precision, with the help of the wavelet decomposition. A ¡°real life¡± application to automatic characterization enzymatic beet pulp degradation will be detailed.
Local Measures of Regularity
In contrast with global measure of regularity, local measures of regularity give an information specific to each pixel in the image. Powerful tools in this area are Holder exponents in their various versions. We will concentrate on the pointwise and local Holder exponents. We will show how to estimate these exponents on images, with the help of the wavelet decomposition. If time permits, we will present the basics of a new and very powerful local regularity characterization, called 2-microlocal analysis. As an application, we will present:
In some applications, most notably segmentation, the local regularity information is not sufficient. It must be supplemented with global information pertaining to the distribution of the Holder exponents. This is the aim of multifractal analysis. We shall give an easy introduction to the main multifractal spectra and explain their intuitive meaning in the field of image processing. Our application will be in edge detection (Fig. 3).
Figure 2: SAR image (left) and its local regularity based denoising (right).
Figure 3: Original image (left) and its multifractal based edge detection (right).
Each theoretical tool will be illustrated with
an example computed with FracLab, a free software toolbox
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CC-MAIN-2021-43
| 3,234 | 14 |
https://calhoun.nps.edu/handle/10945/14952
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math
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A deterministic analysis of limit cycle oscillations in recursive digital filters due to quantization
MetadataShow full item record
A deterministic analysis of the limit cycle oscillations which occur in fixed-point implementations of recursive digital filters due to roundoff and truncation quantization after multiplication operations, is performed. Amplitude bounds, based upon a correlated nonstochastic signal approach and Lyapunov's direct method, as well as an approximate expression for the frequency of zero-input limit cycles, are derived and tested for the two-pole filter. The limit cycles are represented on a successive value phase-plane diagram from which certain symmetry properties are derived. Similar results are developed for other second-order digital filter configurations, and the' parallel and cascade forms. The results are extended to include limit cycles under in-put signal conditions. A basic design relationship between the number of significant digits required for the realization of a filter algorithm with a desired signal-to-noise (limit cycle) ratio is stated.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711417.46/warc/CC-MAIN-20221209144722-20221209174722-00878.warc.gz
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CC-MAIN-2022-49
| 1,095 | 3 |
https://www.arxiv-vanity.com/papers/hep-ph/0605142/
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math
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It is important to provide guidance on whether CP violation may be measurable in top-quark production at the Large Hadron Collider. The present work extends an earlier analysis of the non-supersymmetric Two-Higgs-Doublet Model in this respect, by allowing a more general potential. Also, a more comprehensive study of theoretical and experimental constraints on the model is presented. Vacuum stability, unitarity, direct searches and electroweak precision measurements severely constrain the model. We explore, at low , the allowed regions in the multidimensional parameter space that give a viable physical model. This exploration is focused on the parameter space of the neutral sector rotation matrix, which is closely related to the Yukawa couplings of interest. In most of the remaining allowed regions, the model violates CP. We present a quantitative discussion of a particular CP-violating observable. This would be measurable in semileptonically decaying top and antitop quarks produced at the LHC, provided the number of available events is of the order of a million.
February 5, 2021
Consistency of the Two Higgs Doublet Model and
[4mm] CP violation in top production at the LHC
Abdul Wahab El Kaffas, Wafaa Khater, Odd Magne Ogreid and Per Osland
Department of Physics and Technology, University of Bergen, Postboks 7803,
N-5020 Bergen, Norway
Department of Physics, Birzeit University, Palestine
Bergen University College, Bergen, Norway
The Two-Higgs-Doublet Model (2HDM) is attractive as one of the simplest extensions of the Standard Model that admits additional CP violation [1, 2, 3]. This is an interesting possibility, given the unexplained baryon asymmetry of the Universe [4, 5], and the possibility of exploring relevant, new physics at the LHC . In particular, the model can lead to CP violation in production, a process which has received considerable theoretical attention [7, 8, 9], since it will become possible to severely constrain or even measure it.
CP violation can be induced in production at the one-loop level, by the exchange of neutral Higgs bosons which are not eigenstates under CP. This effect is only large enough to be of experimental interest if the neutral Higgs bosons are reasonably light, and have strong couplings to the top quarks.
Within the 2HDM (II), where the top quark gets its mass from coupling to the Higgs field (see sect. 3.5), the condition of having sizable couplings forces us to consider small values of . A first exploration of this limit was presented in . In that paper, the general conditions for measurability of CP violation in at the LHC were found to be satisfied in a certain region of the 2HDM parameter space. In addition to having small , in order to have a measurable signal with a realistic amount of data (of the order of a million events), it was found necessary that the lightest neutral Higgs boson be light, and that the spectrum not be approximately degenerate. In fact, it was found that in the most favourable observable considered, the effect would not reach the per mil level unless there is one and only one Higgs boson below the threshold, and that is at most of order unity. We here extend the analysis of to the more general case, allowing the most general quartic couplings in the potential.
At small , also certain Yukawa couplings to charged Higgs bosons are enhanced. Such couplings contribute to effects that are known experimentally to very high precision. In particular, at low the – oscillation data and the effective coupling, measured via [12, 13] severely constrain the model, whereas the data constrain it at low . Furthermore, the high-precision measurement of the and masses, as expressed via constrains the splitting of the Higgs mass spectrum. Unless there are cancellations, the charged Higgs boson can not be very much heavier than the lightest neutral one, and the lightest neutral one can not be far away from the mass scale of the and the . Also, the lightest one is constrained by the direct searches at LEP [16, 17]. We shall here study the interplay of these constraints, and estimate the amount of CP violation that may be measurable at the LHC in selected favorable regions of the remaining parameter space.
An important characteristic of the 2HDM (as opposed to the MSSM [18, 19, 20, 21, 22]) is the fact that, at the level of the mathematics, the masses of the neutral and the charged Higgs bosons are rather independent (see sect. 2). However, the experimental precision on (see sect. 4.3) forces the charged Higgs mass to be comparable in magnitude to the neutral Higgs masses. Another important difference is that whereas small values of are practically excluded in the MSSM , in the 2HDM, which has more free parameters, they are not.
For a recent comprehensive discussion of the experimental constraints on the 2HDM (though mostly restricted to the CP-conserving limit), see and . The latter study, which considers the CP-conserving limit, concludes that the model is practically excluded, with the muon anomalous moment being very constraining. However, the interpretation of the data is now considered less firm, and furthermore, that study focuses on large , and is thus less relevant for the present work.
We present in sect. 2 an overview of the 2HDM, with focus on the approach of ref. , and outline the present extensions. In sect. 3 we discuss the model in more detail, in particular the implications of stability and unitarity, and review the conditions for having CP violation. In sect. 4 we discuss various experimental constraints on the model, with particular attention to small values of . In sect. 5 we present an overview of allowed parameter regions, also restricted to small . In sect. 6 we discuss the implications of the model for a particular CP-violating observable involving the energies of positrons and electrons from the decays of and produced in gluon–gluon collisions at the LHC. Sect. 7 contains a summary and conclusions.
2 Review of the Two-Higgs-Doublet Model
The 2HDM may be seen as an unconstrained version of the Higgs sector of the MSSM. While at tree level the latter can be parametrized in terms of only two parameters, conventionally taken to be and , the 2HDM has much more freedom. In particular, the neutral and charged Higgs masses are rather independent.
Traditionally, the 2HDM is defined in terms of the potential. The parameters of the potential (quartic and quadratic couplings) determine the masses of the neutral and the charged Higgs bosons. Alternatively, and this is the approach followed here and in ref. , one can take masses and mixing angles as input, and determine parameters of the potential as derived quantities. This approach highlights the fact that the neutral and charged sectors are rather independent, as well as masses being physically more accessible than quartic couplings. However, some choices of input will lead to physically acceptable potentials, others will not. This way, the two sectors remain correlated.
In addition, the 2HDM neutral sector may or may not lead to CP violation, depending on the choice of potential. We shall here consider the so-called Model II, where -type quarks acquire masses from a Yukawa coupling to one Higgs doublet, , whereas the -type quarks couple to the other, . This structure is the same as in the MSSM.
2.1 The approach of ref.
The amount of CP violation that can be measured in production was related to the Higgs mass spectrum and other model parameters in . In that paper, the Higgs potential studied was parametrized as
Expanding the Higgs-doublet fields as
and choosing phases of such that and are both real , it is convenient to define orthogonal to the neutral Goldstone boson . In the basis , the resulting mass-squared matrix of the neutral sector, can then be diagonalized to physical states with masses , via a rotation matrix :
and parametrized as111In ref. , these angles were referred to as .
with , . The rotation angle is chosen such that in the limit of no CP violation (, ) then , where is the familiar mixing angle of the CP-even sector, and the additional provides the mapping , instead of being in the position of , as is used in the MSSM .
While the signs of and are fixed by our choice of taking the vacuum expectation values real and positive , the phase of has no physical consequence. One may therefore freely change the sign of one or more rows, e.g., let (see sect. 3.1.1).
Rather than describing the phenomenology in terms of the parameters of the potential (2.1), in the physical mass of the charged Higgs boson, as well as those of the two lightest neutral ones, were taken as input, together with the rotation matrix . Thus, the input can be summarized as
where and , with and .
This approach provides better control of the physical content of the model. In particular, the elements and of the rotation matrix must be non-zero in order to yield CP violation. For consistency, this requires and (as derived quantities) to be non-zero.
2.2 The general potential
For the potential, in this study, we take
The new terms proportional to and have to be carefully constrained, since this potential does not satisfy natural flavour conservation , even if each doublet is coupled only to up-type or only to down-type flavours.
The various coupling constants in the potential will of course depend on the choice of basis . Recently, there has been some focus on the importance of formulating physical observables in a basis-independent manner. Here, we shall adopt the so-called Model II for the Yukawa couplings. This will uniquely identify the basis in the space.
Minimizing the potential (2.7), we can rewrite it (modulo a constant) as
Here and in the following, we adopt the abbreviations
The mass-squared matrix of (2.4), corresponding to the neutral sector of the potential, is found to be
Here, compared with the potential (2.1), we have two more complex parameters, and (four new real parameters), but rather than those, we take as additional parameters , , and . Thus, the input will be
3 Model properties
We want to explore regions of parameter space where there is significant CP violation. In order to do that, we need to map out regions in the space where the model is consistent (figures are presented in sect. 5).
From eq. (2.4), it follows that
Here, it is evident that the signs of the rows of play no role.
we can solve for the ’s. In particular, it follows from (2.2) that
By exploiting certain symmetries of the rotation matrix , we can reduce the ranges of parameters that have to be explored.
3.1.1 Transformations of the rotation matrix
The rotation matrix is invariant under the following transformation;
which leaves its elements unchanged.
Actually, any one of these is a combination of the other two. For example, the transformation B3 is the combination of B1 and B2. Other transformations exist that will yield the same symmetries, but they will be combinations of one of these three transformations followed by the transformation A. In total we have 6 different transformations that yield symmetries of type B.
The third class of transformation we consider are those where two columns of change sign. These transformations are:
The transformation C3 is the combination of the transformations C1 and C2. Other transformations exist that will yield the same symmetries, but they will be combinations of one of these three transformations followed by the transformation A. In total we have 6 different transformation that yield symmetries of type C.
Under transformations of type A and B, the resulting mass-squared matrix will be invariant. We make use of this fact along with the symmetries A, B1 and B2 to reduce the parameter space under consideration to
Under transformations of type C, the mass-squared matrix will not be invariant, some of its non-diagonal elements will change sign while the rest are unaltered.
While a change of the sign of implies changes in the physical content of the model, a change of sign of and/or can be compensated for by adjusting the imaginary parts of , and . Thus, the most interesting transformation among the set (3.1.1) is C3.
The transformation is physically equivalent to C3 since transformations of type B leave the mass-squared matrix invariant:
When , it follows from (3) that a sign change of and can be compensated for by sign changes of and . These signs play no role in the discussion of stability (see Appendix A) and unitarity . We shall therefore, when discussing the case (sects. 5.1 and 5.2), make use of (3.9) to restrict the angular range from (3.7) to the smaller
When we need to consider the angular range as given in (3.7).
3.1.2 Inversion of
The Higgs sector is invariant under
This is just the symmetry between and , and will be violated by the introduction of Model II Yukawa couplings, which distinguish between the two Higgs doublets, i.e., between and .
3.2 CP violation
In general, with all three rotation-matrix angles non-zero, the model will violate CP. However, in certain limits, this is not the case. In order not to have CP violation, the mass-squared matrix must be block diagonal, i.e., one must require
Thus, CP conservation requires
One possible solution of (3.2) is that
The expressions (3.2) then vanish, by the orthogonality of . There are additional limits of no CP violation, as discussed below.
Expressed in terms of the angles of the rotation matrix, the above elements describing mixing of the CP-even and CP-odd parts of take the form
In the mass-non-degenerate case, they vanish (there is thus no CP violation) if either:
Note that for non-degenerate or partially degenerate masses, ordered such that (where no more than two of the masses are equal). Thus, there are no additional CP-conserving solutions for the vanishing of this factor. The cases of partial degeneracy, , and will be discussed in sect. 3.7.
It is thus natural to focus on the angles and . In particular, since is associated with CP-violation in the coupling (see sect. 3.5), we are interested in regions where is large.
3.3 Reference parameters
In order to search for parameters with “large” CP violation, we will assume is light, and that is not close to , as such degeneracy would cancel any CP violation.
For illustration, as a conservative default set of parameters, we take
Here, the lightest neutral Higgs boson can be accommodated by the negative LEP searches [16, 17] provided it does not couple too strongly to the , and the charged Higgs boson mass is compatible with the negative LEP and Fermilab searches as well as with the – oscillation, constraints (see sect. 4.1) and the analysis at low .
As a second set of parameters, we take
This set, which represents a light Higgs sector, is marginally in conflict with data (the combination of charged-Higgs mass and values violate the constraints by up to , see Table 2 in sect. 4.5), but is chosen for a more “optimistic” comparison, since it could give more CP violation due to a lower value of (which enhances the loop integrals).
3.4 Stability and unitarity
A necessary condition we must impose on the model, is that the potential is positive when and . This constraint, which is rather involved, is discussed in Appendix A. Two obvious conditions are that
In general, the additional stability constraint is that and cannot be “too large and negative”, and that , , cannot be “too large”.
Furthermore, we shall impose tree-level unitarity on the Higgs-Higgs-scattering sector, as formulated in [32, 30] (see also ref. ). This latter constraint is related to the perturbativity constraint (’s not allowed “too large”) adopted in ref. , but actually turns out to be numerically more severe.
3.5 Yukawa couplings
With the above notation, and adopting the so-called Model II for the Yukawa couplings, where the down-type and up-type quarks are coupled only to and , respectively, the couplings can be expressed (relative to the SM coupling) as
Likewise, we have for the charged Higgs bosons
With this Yukawa structure, the model is denoted as the 2HDM (II).
The product of the scalar and pseudoscalar couplings,
plays an important role in determining the amount of CP violation in the top-quark sector.
As was seen in ref. , unless the Higgs boson is resonant with the system, CP violation is largest for small Higgs masses. For a first orientation, we shall therefore focus on the contributions of the lightest Higgs boson, . (There will also be significant contributions from the two heavier Higgs bosons, as discussed in sect. 6.) For the lightest Higgs boson, the coupling (3.5) becomes
From (3.24), we see that low are required for having large CP violation in the top-quark sector. However, according to (3.5), for low the charged-Higgs Yukawa coupling is also enhanced. Thus, for low , the , [12, 13] and constraints force to be high. For a quantitative discussion, see sect. 4.1.
3.6 CP violation in the Yukawa sector
We shall in sect. 6 study CP violation in the process
focusing on the sub-process
where is some function of the neutral Higgs mass , in general determined by loop integrals.
When the three neutral Higgs bosons are light, they will all contribute to the CP-violating effects. In fact, in the limit of three mass-degenerate Higgs bosons, the model may still be consistent in the sense that solutions can be found in some regions of parameter space, but the CP violation will cancel, since [cf. eq. (3.23)]
due to the orthogonality of .
3.7 Degenerate limits
The set of free parameters (2.11) permits all three neutral Higgs masses to be degenerate. As discussed above, in this limit there is no CP violation, by orthogonality of the rotation matrix . However, in contrast to the case of studied in , the partial degeneracies are non-trivial and may lead to CP violation for certain choices of the angles :
In this limit, the elements of that induce CP violation, are
These both vanish, when the conditions (3.2) are satisfied, or else, when
By orthogonality, when the two lighter Higgs bosons are degenerate, the CP violation (3.27) in the top-quark sector is proportional to
Thus, even though the model violates CP in the limit , by for example having , the top-quark sector would not violate CP at the one-loop level unless .
In this limit, the elements of that induce CP violation are
We note that these both vanish for , meaning or . Thus, in the limit and , but arbitrary, the model does not violate CP, in agreement with the results of .
In this limit of the two heavier Higgs bosons being degenerate, the CP violation in the top-quark sector is proportional to222Whereas both these degenerate limits yield CP-violation in the -quark sector proportional to , the corresponding quantities in the -quark sector are proportional to .
In our parametrization, this is non-zero for
but with arbitrary.
In the more constrained model discussed in , the latter limits of only two masses being degenerate do not exist. In that case, with , a degeneracy of two masses forces the third one to have that same value.
4 Experimental model constraints at low
It is convenient to split the experimental constraints on the 2HDM into two categories. There are those involving only the charged Higgs boson, , and those also involving the neutral ones. The former, like the non-discovery of a charged Higgs boson, the constraint , and the – oscillations do not depend on the rotation matrix and the amount of CP violation. They are given by and its coupling to quarks, (3.5), i.e., on . On the other hand, constraints involving the neutral ones depend on the details of the couplings, i.e., they depend sensitively on the rotation matrix as well as on the neutral Higgs mass spectrum. We shall first review the constraints that depend only on the charged Higgs sector.
In subsections 4.2–4.5 we discuss constraints on the model that depend on the neutral sector. For the purpose of determining these constraints, one has to generalize some predictions for the CP-conserving case to the CP-violating case. Eqs. (4.3), (4.3), (4.3), (4.13) and (4.5) are the results of such generalizations. In the CP-conserving limit, , and these expressions simplify accordingly.
4.1 Constraints on the charged-Higgs sector
There are three important indirect constraints on the charged-Higgs sector: the – oscillations, and .
The mass splitting in the neutral mesons is sensitive to contributions from box diagrams with top quark and charged Higgs exchange [34, 35, 36, 37], involving the Yukawa couplings (3.5). Indeed, the diagrams with one or two exchanges give contributions proportional to or multiplied by functions of that for large behave like . These contributions to will constrain low values of , in particular at low values of .
While is known experimentally to considerable precision, , its theoretical understanding is more limited. The largest theoretical uncertainty is related to the parameter combination of the hadronic matrix element. This is only known to a precision of 10–15%. Thus, we cannot exclude models which give predictions for that deviate from the SM value by this order of magnitude, even if this deviation is large compared to the experimental precision.
In table 1 we show the contribution to that are due to the additional 2HDM fields, for the two parameter sets considered. It is clear that is incompatible with the experimental and theoretical constraints on , whereas the case is marginal.
As mentioned above, the constraints also force to be high, in particular for low . A recent analysis arrived at the bound . However, at the very low values of considered here, they are less severe than the and constraints. The experimental constraints on (see sect. 4.5) depend on the charged Higgs mass as well as on the neutral Higgs spectrum. However, this constraint is for low values of practically independent of the neutral spectrum.
4.2 Higgs non-discovery at LEP
One might think that both parameter Set A and Set B would be in conflict with the negative direct searches at LEP, because of the low values of . However, these bounds are marginally evaded by two facts which both dilute the experimental sensitivity. First, the coupling is suppressed by the square of the Higgs-vector-vector coupling, which relative to the Standard-Model coupling is
For large values of (which is of interest in order to maximise of (3.24)), will be rather small, and the second term in (4.1), proportional to , takes over. But this is suppressed by the factor . For some quantitative studies of this suppression, which can easily be by a factor of 2 or more, see Fig. 8 in . Secondly, the typical decay channel, , is suppressed by the square of the Yukawa coupling, Eq. (3.5). For small values of , this is approximately . In the limits of interest, both terms are small.
In the analysis of LEP data by DELPHI333There are such studies also by the other LEP collaborations (see, for example ), but limited to the CP-conserving case., a channel-specific dilution factor is defined by
where is the Standard Model cross section for a particular Higgs mass . In the 2HDM, for an decaying to or , the dilution is caused by the two effects discussed above: There is a reduced coupling to the boson [see (4.1)] and a modified (typically reduced) coupling to the (or ) [see (3.5)]. Thus, we take
and consider as excluded parameter sets those where this quantity exceeds the LEP bounds, roughly approximated as
The last term in (3.5), involving , is absent in the CP-conserving case. However, at small , it has little effect. Actually, similar results are obtained for both the and channels. Presumably, when these are combined, a more strict limit would be obtained.
It is instructive to consider this expression (4.3) and the corresponding constraints in three simple limits:
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CC-MAIN-2021-21
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https://www.stoodfarback.com/2013/05/06/cards.html
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math
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What is the chance of two cards with the same rank being next to each other if you draw
n cards from a 52-card deck?
(Hint: the chance becomes >50% when
n is 13)
Three cards in a row?
(Hint: the chance becomes >10% when
n is 47)
(Hint: if you go through four shuffled decks, one at a time, looking for four in a row, the chance is <1%. With 5 decks, the chance is >1%)
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CC-MAIN-2019-18
| 368 | 8 |
https://www.cross-x.com/tags/2nc/
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math
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Search the Community
Showing results for tags '2nc'.
Found 3 results
Okay, so I've been debating for quite a while and just recently, I both got on cross-x and the national circuit big-stick tournaments. I recently learned how to give a 1AR correctly (the 2AC + comparison - fluff; basically) and I've run into a large problem when reading: the 2NC, the 2AR, and especially the 2NR. I've lost many debates this season because I simply fail to contextualize arguments. My strategy is usually one-off case in the 2NC, which I either choose or the 1NR argument in the 2NR. I utilize a blocked out file with every answer imaginable which I then throw into a speech, separated into the Perm debate, link debate, impact debate, etc. This strategy used to work very well for me, before judges started wanting contextualization and refusing to flow things unless they fell down the flow with analysis. I read off a computer primarily, using my flows as an extra, and only read off of them for end-of-speech stuff (Ex. "They say TVA, I answered that above, it's impossible...") but I don't really use them for line-by-line. My blocks consisted of "blocky" overviews which I explained (sort of) later. The fact is, that this simply doesn't work in the 2NR. My question is, how do you as a negative debater, utilize the relationship between the flows and the computer, the line-by-line and pre-written blocks, to effectively give a speech in the 2NC and the 2NR. I know this varies greatly in terms of strategy and style, that's why I'm asking for a general understanding. Note: I already looked through the forums, not really sure where I could find this answered. Another Note: If you have any suggestions for practice speeches/ LBL drills as well, that would be cool.
Only my partner was able to go to camp this year, so we decided to switch positions. Now I'm the 1a and I frankly don't know exactly how to be a 1a. What should I do specifically in the 1AR when rebutting? Is there a recommended order that I should follow? I usually put topicality on the top and follow that up with framework/K and other offcase (not in any specific order) and leave case at the end. 2NC--I know that's part of the neg block. What should the 2nc usually take? And then 2nr, do I go for 1-2 things? Thanks :3
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CC-MAIN-2020-05
| 2,285 | 5 |
https://rs.figshare.com/articles/dataset/Percentage_of_outliers_excluded_from_statistical_analysis_from_The_influence_of_aspect_ratio_and_stroke_pattern_on_force_generation_of_a_bat-inspired_membrane_wing/4233332/1
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math
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Percentage of outliers excluded from statistical analysis from The influence of aspect ratio and stroke pattern on force generation of a bat-inspired membrane wing
datasetposted on 15.11.2016 by Cosima Schunk, Sharon M. Swartz, Kenneth S. Breuer
Datasets usually provide raw data for analysis. This raw data often comes in spreadsheet form, but can be any collection of data, on which analysis can be performed.
Prior to statistical analysis the data of coefficients of lift and drag for down- and upstroke, respectively, versus velocity ratio for these four cases was grouped into 15 bins for the five different wings individually. In each bin, all data points with a force coefficient more than ± 1 standard deviation from the mean of the force coefficient in the respective bin were excluded from further analysis. The remaining data points per bin were averaged and subjected to an ANCOVA analysis.
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CC-MAIN-2020-40
| 903 | 4 |
http://mathcentral.uregina.ca/QQ/database/QQ.09.06/h/arul5.html
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math
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Please help me on this question..
Sequence 2, 7, 22,
after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit 33rd and tens digit of the 35 term?
Write a few more terms in the sequence, say the first 10 terms, and examine the tens digits.
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
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CC-MAIN-2023-06
| 418 | 5 |
http://www.shortopedia.com/I/N/Integral_equations
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math
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The electric field integral equation is a relationship that allows one to calculate the electric field intensity E generated by an electric current distribution J . ...more on Wikipedia about "Electric field integral equation"
In mathematics, the Fredholm integral equation introduced by Ivar Fredholm gives rises to a Fredholm operator. From the point of view of functional analysis it therefore has a well-understood abstract eigenvalue theory. In this case that is supported by a computational theory, including the Fredholm determinants. ...more on Wikipedia about "Fredholm integral equation"
In mathematics, Fredholm's theorem is a celebrated result of Ivar Fredholm on integral equations. ...more on Wikipedia about "Fredholm's theorem"
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Maxwell's equations. ...more on Wikipedia about "Integral equation"
In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind. ...more on Wikipedia about "Volterra integral equation"
This article is licensed under the GNU Free Documentation License.
It uses material from the Wikipedia . Direct links to the original articles are in the text.
If you use exact copy or modified of this article you should preserve above paragraph and put also : It uses material from the Shortopedia article about "Integral equations".
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CC-MAIN-2013-20
| 1,659 | 9 |
http://www.nctm.org/publications/article.aspx?id=18792
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math
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Calendar Problems - September 2004
September 2004, Volume 98, Issue 2, Page 104
This monthly set of Calendar Problems involves functions, problem solving, area, sequences, trig identities, and algebraic reasoning. Answers are also given. Calendar Problems is a regular department of Mathematics Teacher.
Sequences / Series
Problem Solving / Problem Posing
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| 355 | 5 |
https://www.whsmith.co.uk/products/interest-rates-and-coupon-bonds-in-quantum-finance/9780521889285
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math
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The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing on interest rates and coupon bonds, this book does not employ stochastic calculus - the bedrock of the present day mathematical finance - for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author's previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry.
Belal E. Baaquie is Professor of Physics in the Department of Physics at the National University of Singapore. He obtained his BS from Caltech and PhD from Cornell University. His specialization is in quantum field theory, and he has spent the last ten years applying quantum mathematics, and quantum field theory in particular, to quantitative finance. Professor Baaquie is an affiliated researcher with the Risk Management Institute, Singapore, and is a founding Editor of the International Journal of Theoretical and Applied Finance. His pioneering book Quantum Finance has created a new branch of research in theoretical and applied finance.
1. Synopsis; 2. Interest rates and coupon bonds; 3. Options and option theory; 4. Interest rate and coupon bond options; 5. Quantum field theory of bond forward interest rates; 6. Libor Market Model of interest rates; 7. Empirical analysis of forward interest rates; 8. Libor Market Model of interest rate options; 9. Numeraires for bond forward interest rates; 10. Empirical analysis of interest rate caps; 11. Coupon bond European and Asian options; 12. Empirical analysis of interest rate swaptions; 13. Correlation of coupon bond options; 14. Hedging interest rate options; 15. Interest rate Hamiltonian and option theory; 16. American options for coupon bonds and interest rates; 17. Hamiltonian derivation of coupon bond options; Appendixes; Glossaries; List of symbols; Reference; Index.
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| 2,460 | 3 |
https://newsbasis.com/what-is-budget-constraint-line/
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math
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What is budget constraint line?
In a budget constraint, the quantity of one good is measured on the horizontal axis and the quantity of the other good is measured on the vertical axis. The budget constraint shows the various combinations of the two goods that the consumer can afford.
How do you define a budget constraint?
Budget line is a graphical representation of all possible combinations of two goods which can be purchased with given income and prices, such that the cost of each of these combinations is equal to the money income of the consumer.
What is budget line in meaning?
Budget line definition The budget line is a graphical delineation of all possible combinations of the two commodities that can be bought with provided income and cost so that the price of each of these combinations is equivalent to the monetary earnings of the customer.
Why is budget a constraint?
Definition of Budget constraints A budget constraint occurs when a consumer is limited in consumption patterns by a certain income. When looking at the demand schedule we often consider effective demand. Effective demand is what people are actually able to spend given their limitations of income.
What is budget set and budget constraint?
A budget set represents those combinations of consumption bundles that are available to the consumer given his/her income level and at the existing market prices. On the other hand, budget constraint implies that the total amount spent on two goods together should be less than or equal to his/her given income level.
How do you write a budget constraint?
The Budget Constraint Formula This is where Y = income, PA = price of item A, and QA= quantity of item A consumed. PB = price of item B, while QB = quantity of item B consumed. Maria knows that her income to spend is $500, and what concerts and pizzas cost.
What is budget line example?
Example of Budget Line Suppose, a consumer has an income of Rs. 50, and it will be used to buy commodity X and Y. The required budget line is obtained by plotting the above budget against the following graph. In the graph, the X-axis represents commodity X, and Y-axis represents commodity Y.
Why is budget line negatively sloped?
Answer: The budget line is a negatively downward sloping line. The budget line is downward sloping because, in order to increase the consumption of one good, the consumption of the other good must be reduced, with constant M.
What is the significance of a budget line in economics?
A budget line shows the combinations of two products that a consumer can afford to buy with a given income – using all of their available budget.
What is budget constraint example?
A budget constraint is an economic term referring to the combined amount of items you can afford within the amount of income available to you. For example, if you are a sales professional with a $1,000 budget for promotional items, this sets the upper limit on the combined quantity of items you can purchase.
What is budget constraint slope?
Intuitively, the slope of the budget constraint represents how many of the goods on the y-axis the consumer must give up in order to be able to afford one more of the goods on the x-axis.
What is the budget constraint formula?
Thus, budget constraint is obtained by grouping the purchases such that the total cost equals the cash in hand. Hence, we can deduce a simple budget constraint formula as follows: P(G1) X Q(G1) + P(G2 + Q(G2) = I. P(G1) = Price of one good.
What is an example of a budget constraint?
Budget constraint is a concept from what is known as the consumer theory in economics, which shows how a consumer’s spending capacity is limited by his or her income or budget. For example, if a consumer has only $100 US Dollars (USD) to spend and he or she desires to buy some wine priced at $10 USD per bottle,…
What does it mean by budget constraints?
Budget Constraint Definition When consumers’ income limits their consumption behaviors , this is known as a budget constraint. In other words, it’s all of the many combinations of goods/services that consumers are able to purchase in light of their particular income as well as the current prices of these particular goods/services.
What is the slope of a budget constraint?
It also states that the slope of the budget constraint is the negative of the price of the good on the x-axis divided by the price of the good on the y-axis. (This is a bit odd since the slope is usually defined as the change in y divided by change in x, so be sure not to get it backward.)
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https://math.stackexchange.com/questions/2355276/2-problems-in-combinatorics
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math
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Teen kids are in the forest picking mushrooms. No one came home empty-handed, together they collected 54 mushrooms. Show that at least two children picked the same amount of mushrooms.
Paul has a rectangular patio which is covered with concrete slabs. Some of the plates in the form of 2x2, other form of 1x4.One of the plates has been broken, but as a possible replacement Paul only have a single plate of the other form. Can Paul replace the broken plate with the one he has, or possibly rearrange the tiles?
If two of them did not pick the same amount of mushrooms, then they must have at least collected 1,2,3...,10 mushrooms, with one mushroom coresponding to one child. But that gives a total of at least 55 mushrooms, a contradiction.
For the second one, it cannot be done. This is because, suppose that the 2×2 tile has been broken. Then replacing it with one of the 1×4 tiles changes the parity of the dimension across which the 1 width tile is placed. In that case, we cannot compensate for this by rearrangement. Likewise vice versa.
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http://mathcentral.uregina.ca/QQ/database/QQ.02.06/cathey1.html
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math
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Hi Cathey. You can use algebra to solve this problem.
Let M = the total number of marbles of all the children combined.
Then the first child has (1/2)M - 4 marbles.
The second child has (1/5)M + 6 marbles.
The third child has (1/3)( (1/2)M - 4) marbles.
The fourth child has ( (1/5)M + 6 ) - 1 marbles.
We can add up these totals in two ways. The simple way is just to
say that the total is M, as we decided in the beginning. The other
way is to add up each child's marble count. Since these two
quantities must be the same, they equal each other. So:
M = ( (1/2)M - 4 ) + ( (1/5)M + 6) + ( (1/3) ( ( 1/2) M - 4) ) + ((1/5)M + 6 ) - 1.
If you simplify this equation, you can "solve for M" and get the answer to your question.
Hope this helps,
Stephen La Rocque.
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http://www.sineofmadness.co.uk/ma101/ma101-19-the-chain-rule-one-variable/
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math
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Consider the function given by . We are used to wring such things as:
iii) . For example we would write for example.
Equally well, of course, it would be true to write .
The meaning of (i) and (ii) are mathematically precise. means the derived function and means the value of at x.
The meaning of can be more devious.
It can simply be taken as synonymous with . That is .
When such is the intention it would be indisputable that means .
But there are other more shady uses as we will see.
Now consider substituting in to define a function F defined as .
The chain rule says
where here means .
Note that F is not equal to f, but mathematicians frequently write the chain rule as,
Here does not mean which is after all .
To see the chain rule in a more precise and unambiguous form think of as defining a function g given by , then and we see the chain rule as saying
Of course the u here is an entirely dummy symbol.
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https://lepetiteprincesse.com/2022/04/18/what-to-do-if-vlookup-formula-is-not-working-in-excel/
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math
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In fact, the cells have been copied so that they are identical, except for the relative cell value they are supposed to reference. In other words, the lookup table is linked to the copied formulas. They said they had doubts about the Vlookup feature and didn`t know how to use it properly. Yes, the data comes from different sources 1 huge list of itenmumbers from an ERP (with all kinds of information in other columns) 1 huge list of article numbers from another source (with different information in other columns) I then use vlookup in Excel to combine the data into 1 sheet. – This happens either because the data you are looking for does not exist (see table below, where the numbers 1, 3 and 5 are not included in the second table. You will find that the “cash prize for riders at positions 1, 3 and 5 in the first table is “N/A” instead of the actual value), so the formula returns an “N/A” instead of the desired result. i) Make sure that if your table of tables has more than 65,000 rows, place everything between rows 65,0001 and 130,000 in a separate sheet, and then place everything from rows 130,001 to 195,000 in a separate sheet, etc., in increments of 65,000, because this is the maximum number of rows aligned by VLOOKUP. These are the top 7 reasons why VLOOKUP doesn`t work in Excel. Hopefully now the Excel VLOOKUP issue no longer works, but if not, use the automatic solution to fix the VLOOKUP error that doesn`t work in Excel. If you use an approximate matching formula (range_lookup argument set to TRUE or omitted), your virtual search formula can return the error #N/A in two cases: if the argument is col_index_num greater than the number of columns in the specified table, the search formulas return the #REF! Error. I have a search problem when I apply the search function to a cell that does not contain the actual data, but a formula is applied to get the value of two other cells, so that now the search cannot search for the cell where the formula was filled, but when I type the actual value into that cell, the search function works correctly, but if a formula is displayed, the search function for the correct values cannot work.
For example, look for a value 3 and look for it in a table, but if there are two columns that contain 1 in the first column and 2 in the second column and now in the third column, I use the formula to simply add them, so I summarize them and now the value is, which I get, 3 in the third column, but when I apply the search function to it. It displays #N/A as usual, but if I enter the value 3 in the third column directly instead of the formula, the search formula will work perfectly, so any solution will be useful. 2d) Use the formula “=int” as shown in the following screenshot – enter the formula “=int(” with an empty column, then the cell number you need to correct, in this case cell B2, then close the parentheses – the complete formula seems to look like your lookup_value is absolute, so it does not change, when you copy the formula. If there are additional spaces in the lookup column, there`s no easy way to avoid search errors #N/A. Instead of VLOOKUP, you can use a matrix formula with a combination of INDEX/MATCH and TRIM functions: – i) The SIMPLE method is to insert a column after your first reference column (so insert a column between cells B and C, then type the following formula in cell C2: you can solve almost any VLOOKUP problem that does not work, if you follow the techniques in this article. I only need the first 3 digits of the zip code, so I have = LEFT (M2.3) M is the customer`s zip code. My virtual search formula works when I manually add a 3-digit code in cell CF2 = VLOOKUP (CF2,Sheet2! A1:B921,2;false) if the cell contains cf2 =LEFT(M2,3), then I get #N/A The solution for this type of Excel VLOOKUP does not work to check where there are extra spaces and get rid of them. Additional spaces in the main table (lookup column) can cause the error, as can additional spaces in the lookup value.
This section provides an answer to this very important question about why VLookup doesn`t work. So, check out the 7 most common reasons why VLOOKUP is not working in Excel 2007/2010/2013/2016/2019. However, you should be careful because Excel assigns you a default argument, which in most cases prevents Excel VLOOKUP Search from working. So, if the argument col_index_num is less than 1, your Vlookup formula returns the #VALUE! Mistakes too. It`s hard to imagine a situation where someone wants to enter a number less than “1” to specify the column from which to return values. However, this argument can be returned by another Excel function nested in your virtual search formula. Hello – VLOOKUP works well for me, except to return only the first letter, that is, only return “J” instead of John. Any ideas? ii) Copy and paste your original VLOOKUP directly after the above, i.e. (VLOOKUP (A2, I:M, 5, FALSE) www.computergaga.com/tips/lookup_formulas/two_way_lookup_using_index_and_match.html Please indicate; what exactly am I missing here and how I can fix this problem I wondered why vlookup was not solved – I mean, it remained only literal, even after trying to solve it – for example “= VLOOKUP(E3, Sheet1!$A$2:$ B$2168,2,FALSE)”. I found out that the cell was locked – unlocking solved the problem.
If the VLOOKUP formula does not find a match, this error is displayed, which is “unavailable”. But it is still incorrect that the search value is not available. There can be several reasons why VLOOKUP returns this error. Make sure that the calculation in the formula bar is based on Automatic and not Manual. My VLOOKUP works if cell CF2 does not contain a formula. =VLOOKUP(CF2, Blatt2! A1:B921.2) my cell CF2 is =LEFT(M2,3). I want to look at a zip code, then take the 3-digit code (=LEFT(M2,3) and then vlookupene this 3-digit value to find shipping area 1-9 in my area.
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CC-MAIN-2023-40
| 5,936 | 4 |
http://www.pagalguy.com/@circleofmanias
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math
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1. case 1 ->
3W & 2M ->4C3*4C2=24 ways
Now three cases are possible ..
Now total possible cases are 5*4=20 (5 for President post and 4 for V.P)
But both cannot be male so we can have 2 cases where such thing happens (V-M1 & VP-M2 and vice versa)
So we have 18*24 here
2. case 2->
4M & 1 M->4 ways
And in each case we will have the required formation
So total 432+80=512
2. maximum 2 women is same as minimum 3 men
And also 1 women can hold the top two post . it means at least one M should be in top two . So it is the same as above and asking for Male so 512 again !
woman days required = 20*20
since man = 2woman =>a woman leaving and a man joining = net addition of 1 woman
trial and error shows n=14
=> work finishes on 15th Day.
QUANTEXPERT Quant Question of the Day (www.quantexpert.in)
If a train runs at 20 km/hr, it reaches its destination late by 10 min. But if it runs at 30 km/hr, it is late by 2 min. only. At some speed, it reaches on time. What is the time required if it reaches on time?
(a) 12 min (b) 8 min (c) 14 min (d) 15 min
Ram Singh deposits Rs.150 on the first of every month starting from 1st Jan1985, in the recurring deposit scheme of a bank which allows simple interest @ 6% p.a. on the sum standing to his credit at the end of each month. What is the amount, Mohan is entitled to on 31st Dec, 1985?
(a) Rs 1818 (b) Rs 1800 (c) Rs 1450 (d) Rs 1400
sir formula for number of non- integral solution is C(n+r-1 ,r ) or is it C (n+r-1,r-1)
in book i have seen first one i.e C(n+r-1,r) . Which is correct???
Since 3N is divisible by 3, we can say that (a1 + a2 + a3 + .. + a7) is divisible by 3.
=> N is divisible by 3
So, sum of digits of N should be a multiple of 3
Only option is 9, i.e., option (1)
NOTE:- Question says which of the following is possible. Although sum should be of form 3n and 9 satisfies that
Now say we had an overall average of 22 then the numbers are 1 to 43
So now the sum should be 64/3*41 which is not integer so the number must be in the form 3n+2
Hit & trial around 21 ...
41,38,35,32 ... or 44,47,50
1.Sum of 44 is 990
Now 64*3n/3 is always even so we need the sum to be odd possibility 50 ,38 & 41
lets check ...
So now it's impossible ...
36*64/3=768 (not possible)
possible so difference is 29 and the numbers are 14 & 15 so answer=210
from 0 to 9 pick any three numbers say 3 9 0 now u cn arrng thm in a>b>c way as 930
so if u pick any three nums from 0 to 9 we can have a num satisfyn the cndtn
=>10C3 = 120 ways
9C3 = 84 ways
total 204 ways
Question says,we need to have abc in increasing or decreasin order.In you cases you are taking all three digit no's.Isnt it ?
it says we have to arrange it in ascendin, descendin
so,10C3 is the number of ways to select 3 digits,
and as you know there is only one way in which these digits will be in ascendin or decending order rite ?
2*10C3 ways for both ascendin,descendin order. and there are cases when we have first digit as 0 a
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s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860117405.91/warc/CC-MAIN-20160428161517-00176-ip-10-239-7-51.ec2.internal.warc.gz
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CC-MAIN-2016-18
| 2,935 | 48 |
https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=500367
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math
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Dynamical modeling and analysis of epidemics / edited by Zhien Ma, Jia Li.Material type: TextPublisher: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., Copyright date: ©2009Description: 1 online resource (xiii, 498 pages) : illustrations (some color)Content type: text Media type: computer Carrier type: online resourceISBN: 9789812797506; 9812797505; 1282441663; 9781282441668; 9786612441660; 6612441666Subject(s): Epidemiology -- Mathematical models | Communicable diseases -- Mathematical models | Mathematical models | MEDICAL -- Health Risk Assessment | MEDICAL -- Epidemiology | Communicable diseases -- Mathematical models | Epidemiology -- Mathematical models | Mathematical models | Epidemiology & Epidemics | Public Health | Health & Biological Sciences | Disciplines and Occupations | Models, Biological | Communicable Diseases | Epidemiology | Public Health | Investigative Techniques | Models, Theoretical | Infections | Environment and Public Health | Medicine | Analytical, Diagnostic and Therapeutic Techniques and Equipment | Bacterial Infections and Mycoses | Health Occupations | Delivery of Health Care | Disease | Communicable Diseases -- epidemiology | Models, Statistical | Disease Outbreaks | Epidemiologic MethodsGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Dynamical modeling and analysis of epidemics.DDC classification: 614.4015118 LOC classification: RA652.2.M3 | D95 2009ebNLM classification: WA 950Online resources: Click here to access online
|Item type||Current library||Collection||Call number||Status||Date due||Barcode||Item holds|
Includes bibliographical references (pages 469-492) and index.
1. Basic knowledge and modeling on epidemic dynamics. 1.1. Introduction. 1.2. The fundamental forms of epidemic models. 1.3. Basic concepts of epidemiologic dynamics. 1.4. Epidemic models with various factors -- 2. Ordinary differential equations epidemic models. 2.1. Simple SIRS epidemic models with vital dynamics. 2.2. Epidemic models with latent period. 2.3. Epidemic models with immigration or dispersal. 2.4. Epidemic models with multiple groups. 2.5. Epidemic models with different populations. 2.6. Epidemic models with control and prevention. 2.7. Bifurcation. 2.8. Persistence of epidemic models -- 3. Modeling of epidemics with delays and spatial heterogeneity. 3.1. Model formulations. 3.2. Basic techniques for stability of delayed models. 3.3. An SIS epidemic model with vaccination. 3.4. An SIS epidemic model for vector-borne diseases. 3.5. Stability switches and ultimate stability. 3.6. An SEIRS epidemic model with two delays. 3.7. Quiescence of epidemics in a patch model. 3.8. Basic reproductive numbers in ODE models. 3.9. Basic reproductive numbers of models with delays. 3.10. Fisher waves in an epidemic model. 3.11. Propagation of HBV with spatial dependence -- 4. The epidemic models with impulsive effects. 4.1. Basic theory on impulsive differential equations. 4.2. SIR epidemic model with pulse vaccination. 4.3. SIRS epidemic model with pulse vaccination. 4.4. SIS epidemic model with pulse vaccination. 4.5. SEIR epidemic model with pulse vaccination. 4.6. SI epidemic model with birth pulse. 4.7. SIR epidemic model with constant recruitment and birth pulse. 4.8. SIR epidemic models with pulse birth and standard incidence. 4.9. SIR epidemic model with nonlinear birth pulses. 4.10. SI epidemic model with birth pulses -- 5. Structured epidemic models. 5.1. Stage-structured models. 5.2. Age-structured models. 5.3. Infection-age-structured models. 5.4. Discrete models -- 6. Applications of epidemic modeling. 6.1. SARS transmission models. 6.2. HIV transmission models. 6.3. TB transmission models -- Bibliography -- Index.
"This timely book covers the basic concepts of the dynamics of epidemic disease, presenting various kinds of models as well as typical research methods and results. It introduces the latest results in the current literature, especially those obtained by highly rated Chinese scholars. A lot of attention is paid to the qualitative analysis of models, the sheer variety of models, and the frontiers of mathematical epidemiology. The process and key steps in epidemiological modeling and prediction are highlighted, using transmission models of HIV/AIDS, SARS, and tuberculosis as application examples"--Provided by publisher.
Print version record.
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https://www.calculatorlibrary.com/blog/what-is-a-cas-calculator
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math
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WHAT IS A CAS CALCULATOR?
A CAS calculator, or computer algebra system calculator, is a tool used in mathematics to help solve problems. They can be used for a variety of purposes, including solving equations, graphing curves and performing complex calculations. There are many different types of CAS calculators available on the market today. In this article, we'll discuss what a CAS calculator is and what its benefits are!
About CAS calculators
CAS calculators are software programs that assist in the solution of mathematical problems using computer algebra systems. They do this by performing operations on algebraic expressions and equations. A CAS calculator can be used to solve equations, graph curves and perform complex calculations.
There are many different types of CAS calculators available on the market today. Some calculators include a computer algebra system (CAS), which allows them to generate symbolic solutions. These calculators can work with algebraic statements, such as factor, expand and simplify.
Algebra systems have been around for a long time. In 1987, the HP-28 was the first CAS in a calculator.
The Benefits Of Using A CAS Calculator
There are many benefits of using a CAS calculator. One benefit is that it can help you understand and solve problems more quickly. A CAS calculator can also help you check your work for errors. Additionally, using a CAS calculator can save you time when working on complex mathematical problems. Other benefits include
- Give exact answers without approximation: CAS calculators can give you the exact answer without any approximation.
- Create & save calculator documents: You can create and save your work in a CAS calculator. This is helpful if you want to go back and review your work or share it with someone else.
- Give symbolic results: Some CAS calculators can give you symbolic results. This means that the calculator will show you the steps it took to get the answer. This can be helpful if you want to see how the calculator arrived at the answer.
- Easy to use: CAS calculators are easy to use and understand. This makes them a great tool for students of all ages.
If you're looking for a tool to help you with your mathematics, then a CAS calculator may be the right choice for you!
Uses Of A CAS Calculator
A CAS calculator can be used for a variety of purposes, including solving equations, graphing curves and performing complex calculations.
One use of a CAS calculator is to solve equations. To do this, you'll enter the equation into the calculator and then press the "solve" button. The calculator will then generate a solution to the equation.
Another use of a CAS calculator is to graph curves. To do this, you'll enter the equation of the curve into the calculator and then press the "graph" button. The calculator will then generate a graph of the curve.
Performing Complex Calculations
A CAS calculator can also be used to perform complex calculations. To do this, you'll enter the calculation into the calculator and then press the "calculate" button. The calculator will then perform the calculation and give you the result.
CAS calculators are a powerful tool that can be used for a variety of purposes. If you're looking for a way to improve your mathematics skills, then a CAS calculator may be the right choice for you!
Difference Between CAS & Non-CAS Calculator
The term "CAS" stands for computer algebra system. When you buy calculators with CAS, you're getting an instrument that can solve equations and operate on factors, variables and other things. Simply said, these calculators can work out problems like x + y = 2x.
Non-CAS calculators, on the other hand, can not do these things. They are what we traditionally think of when it comes to a calculator. The four main arithmetic functions - addition, subtraction, multiplication and division - as well as a percent function and memory, are what you're limited to.
So if you need to work out problems that go beyond the basics, you need a CAS calculator. If all you need is something to help with your math homework, then any cheap calculator will do just fine.
CAS graphing calculators are more expensive than their non-CAS counterparts. This is because they offer more features and functionality. If you need a CAS calculator for school, then you may be able to get by with a cheaper version. However, if you need a CAS calculator for work or more advanced mathematics, then you'll need to invest in a higher-end model.
CAS calculators are also larger and heavier than non-CAS calculators. This is because they have more components and features. If you need a calculator that's easy to carry around, then a non-CAS calculator may be the better choice.
When deciding whether to buy a CAS or non-CAS calculator, you'll need to consider what you'll be using the calculator for. If you need a powerful tool for solving equations and performing complex calculations, then a CAS calculator is the right choice for you.
Best CAS Calculators
There are a few different CAS calculators on the market, so it can be difficult to know which one is the best for you. Here is a list of some of the best CAS calculators on the market:
- TI-89 Titanium CAS Graphing Calculator
- Casio fx-CP400
- HP Prime Graphing Calculator
- TI-Nspire CX CAS
Each of these calculators has its unique features and benefits. The TI-89 Titanium is one of the most popular CAS calculators on the market. It's a powerful calculator that can be used for a variety of purposes. The Texas Instruments TI calculators are some of the best known in the world.
The Casio fx-CP400 is a great choice for those who need a powerful calculator but don't want to spend a lot of money.
The HP Prime Graphing Calculator is a great choice for those who need a graphing calculator with CAS capabilities.
The TI-Nspire CX CAS is a great choice for those who need a powerful and user-friendly CAS calculator.
CAS calculators are a powerful tool that can be used for a variety of purposes. If you need a calculator that's easy to use and can perform complex calculations, then a CAS calculator is the right choice for you.
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CC-MAIN-2023-40
| 6,125 | 38 |
http://hyfyditulahuco.ultimedescente.com/write-a-formula-for-a-column-in-excel-2328023280.html
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math
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Share on Facebook To help quickly add numbers, Excel displays a running sum of the currently selected cells in the status bar at the bottom of the window. You will have a result similar to this: In your newly created table, all of the columns are switched to rows. Transpose data in Excel using VBA macro To automate the conversion of rows to columns in Excel, you can use the following macro: In our formula, we supply the coordinates in the reverse order, and this is what actually does the trick!
J The range of cells in columns A through E and rows 10 through 20 A In the R1C1 style, Excel indicates the location of a cell with an "R" followed by a row number and a "C" followed by a column number.
Nothing dreadful at all, is it? Convert columns to rows using the Transpose tool Convert rows to columns in Excel using Paste Special Suppose you have dataset similar to what you see in the upper part of the graphics below.
Remember the position of the comma or calculate it again. So be careful to extend the SUM function to the top either by using the cursor or typing E2 where it says E3 to include the mortgage in the sum. How to transpose without zeros.
Click for day free trial! By default, new formulas use relative references. And this is exactly what we are going to do. The main benefit of using the TRANSPOSE function is that the rotated table retains the connection to the source table and whenever you change the source data, the transposed table will change accordingly.
Starting with OfficeExcel also includes a Quick Analysis tool that adds sums for multiple rows or columns in one click. How can two operators have the same precedence? My name is Chandoo. What does ROWS excel formula do? Find the position of the comma this shows where one word ends and the other begins.
Select the upper left cell of the destination range and click OK: The PI function returns the value of pi: Though, you can quickly restore it, as shown above. It is not well suited for rotating fully-functional Excel tables. Notice that you have to divide the interest rate by 12 since interest is calculated monthly.
Looking at the table above we see that exponents comes before multiplication. Image courtesy of Microsoft Open the "Formulas" tab and click the "AutoSum" icon to automatically create a formula that sums the current row or column.
Note, we have to subtract 1 from the length because FIND gives the position of the comma. Refers to the worksheet named Marketing 2. No one would want to waste their time on converting the same rows and columns over and over again, right?
Take the number of characters from Step 3 and subtract one to omit the comma and space. Start by creating a new worksheet.Before we write a few formulas, we need to create a function but before we can create a function, we first need to understand row and column notation.
Rows and Columns To understand how to write formulas and functions, you need to know about rows and columns. This article describes the formula syntax and usage of the COLUMN function in Microsoft Excel. Find links to more information about formatting columns in the See Also section.
Description. Returns the column number of the given cell reference. Overview of formulas in Excel In this course: Overview of of 16, columns) and refers to rows with numbers (1 through 1,). These letters and numbers are called row and column headings.
To refer to a cell, enter the column letter followed by the row number. such as clicking the AutoSum button to insert a formula that adds a.
Sometimes you may need to apply one same formula to an entire column or row in Excel, such as C1=A1*2, C2=A2*2,Cn=An*2. It will be quite tedious if you enter the formula in each cell one by one.
Dec 21, · Put the formula in cell then copy and paste (that formula) to the rest of the (required) cells in the column. If my comments have helped please Vote As Helpful. Thanks. The Excel COLUMN function returns the column number for a reference. For example, COLUMN(C5) returns 3, since C is the third column in the spreadsheet.
When no reference is provided, COLUMN returns the column number of the cell which contains the formula.Download
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http://lib.physcon.ru/doc?id=3c86fd08e374
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math
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Optimal control of hybrid systems with polynomial impulses
We address an optimal control problem for a measure driven hybrid dynamical system. The impulsive dynamics is due to the BV -relaxation (the compactification of the trajectory tube in the weak topology of the space BV of functions of bounded variation) of a dynamical system with polynomial dependence on a control variable in the right-hand side under the constraint on the norm of a control in the Lebesgue space Lp. The relaxed system is described by a certain measure differential equation. The hybrid feature is expressed in the presence of “nonstandard mixed constraints”. The latter term is used to name asymptotic constraints relating the state and the measure, and these conditions are formulated as constraints on one-sided limits of a solution to the measure differential equation. The main result is an equivalent transformation of the considered model to a usual optimal control problem. To this end we propose a special space-time transformation technique.
CYBERNETICS AND PHYSICS, Vol. 4, No. 1. 2015, 11-16.
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CC-MAIN-2024-10
| 1,086 | 3 |
http://ifhanneed.blogspot.com/2012/08/god-is-not-only-great.html
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math
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God is not only great! He is great in mathematician too. Why? Just look at the examples given below:
The Beauty of Mathematics and the Love of God! This is TOO cool!
Just the math part is good enough, the end is even better.
I bet you will NOT be able to read it without sending it on to at least one other person!
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CC-MAIN-2018-26
| 314 | 4 |
https://www.bbc.co.uk/bitesize/guides/z3ch2nb/revision/3
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math
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This is the most common question on exam papers, although the number of marks for each question may vary.
At its simplest, this type of question will ask you to remember a simple fact that you have been taught. This type of question is likely to be worth one mark, and will often start with 'Give...', 'State...' or 'Name..'. In some cases, a question may ask you to state two things, rather than just one, and will be worth 2 marks.
Other structured questions may be worth two or more marks. These will often start with a command word such as 'Describe...' or 'Explain...', and will require a more detailed answer:
More complex structured questions will be worth three or four marks. They include questions with complex descriptions and explanations, questions in which you need to compare and contrast two different things, or calculations with several stages.
The mark schemes given here may show answers as bullet points. This is to show clearly how a mark can be obtained. However, it is important that your answer is written in a logical, linked way. Examiners will not credit a key word if it is used out of context, or if your answer contradicts itself.
Questions courtesy of Eduqas.
Describe how an indicator could be used to find the exact volume of acid needed to neutralise 25 cm3 of sodium hydroxide solution. [3 marks]
Milk of magnesia is used to treat indigestion.
It contains magnesium hydroxide which reacts with excess hydrochloric acid in the stomach.
a) Complete the following word equation to show the products formed.
Magnesium hydroxide + hydrochloric acid → ______ + ______.
b) Another indigestion remedy contains calcium carbonate.
Name the gas produced when calcium carbonate reacts with hydrochloric acid and state how this gas can be identified. [2 marks]
a) Magnesium chloride + water
b) Carbon dioxide + turns limewater milky
Sulfuric acid is a strong acid
What is meant by a strong acid? [2 marks]
The acid is fully ionised/all the molecules are dissociated
This happens in aqueous solution/when dissolved in water
When sodium hydroxide reacts with sulfuric acid a solution of sodium sulfate is produced.
a) Give the formula of sodium sulfate. [1 mark]
b) Describe how crystals of sodium sulfate can be obtained from a solution of sodium sulfate. [2 marks]
a) Na2SO4
b) heat until half volume/remove some water
leave to form crystals
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CC-MAIN-2019-47
| 2,374 | 25 |
https://support.nag.com/numeric/nl/nagdoc_24/nagdoc_fl24/html/d02/d02ejf.html
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math
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D02EJF integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions, using a variable-order, variable-step method implementing the Backward Differentiation Formulae (BDF), until a user-specified function, if supplied, of the solution is zero, and returns the solution at points specified by you, if desired.
D02EJF advances the solution of a system of ordinary differential equations
from to using a variable-order, variable-step method implementing the BDF. The system is defined by FCN, which evaluates in terms of and (see Section 5). The initial values of must be given at .
The solution is returned via the OUTPUT at points specified by you, if desired: this solution is obtained by interpolation on solution values produced by the method. As the integration proceeds a check can be made on the user-specified function to determine an interval where it changes sign. The position of this sign change is then determined accurately by interpolation to the solution. It is assumed that is a continuous function of the variables, so that a solution of can be determined by searching for a change in sign in . The accuracy of the integration, the interpolation and, indirectly, of the determination of the position where , is controlled by the parameters TOL and RELABS. The Jacobian of the system may be supplied in PEDERV, if it is available.
Hall G and Watt J M (ed.) (1976) Modern Numerical Methods for Ordinary Differential Equations Clarendon Press, Oxford
1: X – REAL (KIND=nag_wp)Input/Output
On entry: the initial value of the independent variable .
On exit: if G is supplied by you, X contains the point where , unless anywhere on the range X to XEND, in which case, X will contain XEND. If G is not supplied X contains XEND, unless an error has occurred, when it contains the value of at the error.
2: XEND – REAL (KIND=nag_wp)Input
On entry: the final value of the independent variable. If , integration will proceed in the negative direction.
On entry: , the value of the independent variable.
2: Y() – REAL (KIND=nag_wp) arrayInput
On entry: , for , the value of the variable.
3: PW() – REAL (KIND=nag_wp) arrayOutput
On exit: must contain the value of
, for and .
PEDERV must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which D02EJF is called. Parameters denoted as Input must not be changed by this procedure.
If you do not wish to supply the Jacobian, the actual parameter PEDERVmust be the
dummy routine D02EJY. (D02EJY is included in the NAG Library.)
7: TOL – REAL (KIND=nag_wp)Input/Output
On entry: must be set to a positive tolerance for controlling the error in the integration. Hence TOL affects the determination of the position where , if G is supplied.
D02EJF has been designed so that, for most problems, a reduction in TOL leads to an approximately proportional reduction in the error in the solution. However, the actual relation between TOL and the accuracy achieved cannot be guaranteed. You are strongly recommended to call D02EJF with more than one value for TOL and to compare the results obtained to estimate their accuracy. In the absence of any prior knowledge, you might compare the results obtained by calling D02EJF with and if correct decimal digits are required in the solution.
On exit: normally unchanged. However if the range X to XEND is so short that a small change in TOL is unlikely to make any change in the computed solution, then, on return, TOL has its sign changed.
8: RELABS – CHARACTER(1)Input
On entry: the type of error control. At each step in the numerical solution an estimate of the local error, , is made. For the current step to be accepted the following condition must be satisfied:
where is a small machine-dependent number and is an estimate of the local error at , computed internally. If the appropriate condition is not satisfied, the step size is reduced and the solution is recomputed on the current step. If you wish to measure the error in the computed solution in terms of the number of correct decimal places, then RELABS should be set to 'A' on entry, whereas if the error requirement is in terms of the number of correct significant digits, then RELABS should be set to 'R'. If you prefer a mixed error test, then RELABS should be set to 'M', otherwise if you have no preference, RELABS should be set to the default 'D'. Note that in this case 'D' is taken to be 'R'.
, , or .
9: OUTPUT – SUBROUTINE, supplied by the NAG Library or the user.External Procedure
OUTPUT permits access to intermediate values of the computed solution (for example to print or plot them), at successive user-specified points. It is initially called by D02EJF with (the initial value of ). You must reset XSOL to the next point (between the current XSOL and XEND) where OUTPUT is to be called, and so on at each call to OUTPUT. If, after a call to OUTPUT, the reset point XSOL is beyond XEND, D02EJF will integrate to XEND with no further calls to OUTPUT; if a call to OUTPUT is required at the point , then XSOL must be given precisely the value XEND.
On entry: the dimension of the array W as declared in the (sub)program from which D02EJF is called.
13: IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to , . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value is recommended. If the output of error messages is undesirable, then the value is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is . When the value is used it is essential to test the value of IFAIL on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6 Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
With the given value of TOL, no further progress can be made across the integration range from the current point . (See Section 5 for a discussion of this error test.) The components contain the computed values of the solution at the current point . If you have supplied G, then no point at which changes sign has been located up to the point .
TOL is too small for D02EJF to take an initial step. X and retain their initial values.
XSOL lies behind X in the direction of integration, after the initial call to OUTPUT, if the OUTPUT option was selected.
A value of XSOL returned by the OUTPUT lies behind the last value of XSOL in the direction of integration, if the OUTPUT option was selected.
At no point in the range X to XEND did the function change sign, if G was supplied. It is assumed that has no solution.
A serious error has occurred in an internal call to the specified routine. Check all subroutine calls and array dimensions. Seek expert help.
A serious error has occurred in an internal call to an interpolation routine. Check all (sub)program calls and array dimensions. Seek expert help.
The accuracy of the computation of the solution vector Y may be controlled by varying the local error tolerance TOL. In general, a decrease in local error tolerance should lead to an increase in accuracy. You are advised to choose unless you have a good reason for a different choice. It is particularly appropriate if the solution decays.
If the problem is a root-finding one, then the accuracy of the root determined will depend strongly on and
, for . Large values for these quantities may imply large errors in the root.
8 Further Comments
If more than one root is required, then to determine the second and later roots D02EJF may be called again starting a short distance past the previously determined roots. Alternatively you may construct your own root-finding code using D02NBF (and other routines in sub-chapter D02M–N), C05AZF and D02XKF.
If it is easy to code, you should supply PEDERV. However, it is important to be aware that if PEDERV is coded incorrectly, a very inefficient integration may result and possibly even a failure to complete the integration (see ).
We illustrate the solution of five different problems. In each case the differential system is the well-known stiff Robertson problem.
with initial conditions , at . We solve each of the following problems with local error tolerances and .
To integrate to producing output at intervals of until a point is encountered where . The Jacobian is calculated numerically.
As (i) but with the Jacobian calculated analytically.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511424.48/warc/CC-MAIN-20231004220037-20231005010037-00099.warc.gz
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CC-MAIN-2023-40
| 8,668 | 54 |
https://fr.slideshare.net/alartindia14/harriet-marcus-is-concerned-about-the-financing-of-a-home-she-saw-a-pdf
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math
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Harriet Marcus is concerned about the financing of a home. She saw a small cottage that sells for $63,000. Assuming that she puts 20% down, what will be her monthly payment and the total cost of interest over the cost of the loan for each assumption? (Use the Table 15.1) Note: Do not round intermediate calculations. Round your answers to the nearest cent. e. What is the savings in interest cost between 6.25% and 7.25% ? Note: Round your answer to the nearest dollar amount. f. If Harriet uses 30 years instead of 25 for both 6.25% and 7.25%, what is the difference in interest? Note: Use 360 days a year. Round your answer to the nearest dollar amount..
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224654012.67/warc/CC-MAIN-20230607175304-20230607205304-00709.warc.gz
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CC-MAIN-2023-23
| 657 | 1 |
https://bumpercarfilms.com/qa/quick-answer-is-momentum-conserved-when-a-ball-bounces.html
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math
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- Why is energy lost when a ball bounces?
- Can a ball bounce forever?
- What happens when you double the mass?
- Why is momentum not conserved in a falling ball?
- Is energy conserved when a ball bounces?
- How do you know if linear momentum is conserved?
- Is momentum conserved in a closed system?
- How is momentum conserved when a ball bounces off a wall?
- How do you know if momentum is conserved?
- Why is momentum always conserved?
- What does it mean when momentum is conserved?
- Is momentum conserved when there is friction?
- Is momentum conserved when a ball falls?
- Is momentum always conserved?
- What happens to the energy when a ball bounces?
- What happens if momentum is not conserved?
- How do you know if momentum is conserved in an explosion?
Why is energy lost when a ball bounces?
Did you find that a single ball never bounced back to the height at which you released it, regardless of the ball you used.
During a collision, some of the ball’s energy is converted into heat.
As no energy is added to the ball, the ball bounces back with less kinetic energy and cannot reach quite the same height..
Can a ball bounce forever?
The law of conservation of energy implies that a bouncing ball will bounce forever. Of course, it does not. When you drop it on the floor, it changes some of its energy into other forms, such as heat, each time it hits the floor.
What happens when you double the mass?
If the net force on an object is doubled, its acceleration will double If the mass of an object is doubled, the acceleration will be halved . … Acceleration will be unchanged because although the mass is doubled, which will cut the acceleration in half, the fore is also doubled which will double the acceleration.
Why is momentum not conserved in a falling ball?
Consider a ball falling toward the earth because of the mutual attraction from the force of gravity. … The momentum of the ball is not conserved because an external force (gravity) is applied on it. The momentum of a system is conserved where there are no external forces on it.
Is energy conserved when a ball bounces?
Consider the energy. The total energy is constant between bounces if we neglect air friction. We have the kinetic energy of the ball and the potential energy due to gravity. At the top of the bounce, there is no kinetic energy so all the energy is potential.
How do you know if linear momentum is conserved?
The law of conservation of momentum says that the momentum of a closed system is constant in time (conserved). A closed (or isolated) system is defined to be one for which the mass remains constant, and the net external force is zero. The total momentum of a system is conserved only when the system is closed.
Is momentum conserved in a closed system?
1) Closed system – A closed system does not interact with its environment so there is no net external impulse. The total momentum of a closed system is conserved. That is, the total momentum of the system remains constant.
How is momentum conserved when a ball bounces off a wall?
Figure 52: A ball bouncing off a wall. Clearly, the momentum of the ball is changed by the collision with the wall, since the direction of the ball’s velocity is reversed. … It follows that the wall must exert a force on the ball, since force is the rate of change of momentum.
How do you know if momentum is conserved?
The total amount of momentum of the collection of objects in the system is the same before the collision as after the collision. … If momentum is conserved during the collision, then the sum of the dropped brick’s and loaded cart’s momentum after the collision should be the same as before the collision.
Why is momentum always conserved?
The conservation of momentum is simply a statement of Newton’s third law of motion. During a collision the forces on the colliding bodies are always equal and opposite at each instant. These forces cannot be anything but equal and opposite at each instant during collision. … Therefore the momentum is always conserved.
What does it mean when momentum is conserved?
Conservation of momentum, general law of physics according to which the quantity called momentum that characterizes motion never changes in an isolated collection of objects; that is, the total momentum of a system remains constant.
Is momentum conserved when there is friction?
Conservation of momentum applies when net force is zero. Total momentum of the system is zero before canonball is fired. … Now canonball is fired from the canon, and in frictionless cases, horizontal-axis momentum of the whole system would be preserved.
Is momentum conserved when a ball falls?
Linear momentum of a system remains conserved unless an external force acts on it. Since during free fall, a gravitational force acts on the body, it’s momentum will not remain conserved.
Is momentum always conserved?
Collisions. In collisions between two isolated objects Newton’s third law implies that momentum is always conserved. … In collisions between two isolated objects momentum is always conserved. Kinetic energy is only conserved in elastic collisions.
What happens to the energy when a ball bounces?
2. When the ball is falling towards the table, it has kinetic energy. … This elastic potential energy is why the ball is able to bounce, or rebound. After the ball rebounds, the elastic potential energy is transformed into kinetic energy, but it will never possess as much kinetic energy as during its original fall.
What happens if momentum is not conserved?
Momentum is not conserved if there is friction, gravity, or net force (net force just means the total amount of force). What it means is that if you act on an object, its momentum will change. This should be obvious, since you are adding to or taking away from the object’s velocity and therefore changing its momentum.
How do you know if momentum is conserved in an explosion?
Whether it is a collision or an explosion, if it occurs in an isolated system, then each object involved encounters the same impulse to cause the same momentum change. The impulse and momentum change on each object are equal in magnitude and opposite in direction. Thus, the total system momentum is conserved.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038078900.34/warc/CC-MAIN-20210414215842-20210415005842-00099.warc.gz
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CC-MAIN-2021-17
| 6,241 | 53 |
http://www.math.lsa.umich.edu/seminars/colloq/indexDETAIL.php?id=4034
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math
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|Date: Tuesday, December 06, 2016
Title: Geometric configurations of primes
Abstract: We'll explain how some particularly recalcitrant problems in number theory can be formulated geometrically. In particular the talk will explain how certain configurations of integers, "Lenstra-Hurwitz cliques" can be used to attack the class number one problem.
Speaker: Darren Long
Institution: UC Santa Barbara
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511872.19/warc/CC-MAIN-20181018130914-20181018152414-00182.warc.gz
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CC-MAIN-2018-43
| 398 | 5 |
https://magazineplush.com/what-is-the-best-way-to-study-math/
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math
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Despite its reputation, math isn’t as intimidating as you might think! It’s all about breaking down problems into manageable pieces and asking yourself the right questions. That’s why you need to find the best way to study math if you want to succeed in class and on your exam. Fortunately, there are several different strategies you can use to master any type of math problem, from geometry to algebra and beyond. Here are the most effective study math strategies for getting ahead in class.
Logarithm: Numerical Value of a Number
The numerical value of a number is raised to a given power. For example, 2 is a base-10 logarithm of 100 because 100 = 102. The base-10 logarithm of 1000 is 3 because 1000 = 103.
- Logarithms are commonly used in science and engineering to simplify multiplication and division calculations by hand. To find a base-10 logarithm, you can use an online calculator or lookup values in tables that list common logs (also called antilogs).
- However, it’s often easier just to remember that 10^x means x times 10. That is, 100^2 means 10*100 = 1000; therefore, 10^2 must be 2. If you want to find a base-10 logarithm without a calculator or table, you can use an iterative process by which you repeatedly multiply by 10 and then divide by 9 until your result gets closer and closer to 0.
5 Best Ways To Study Math
Are you looking for a new way to review those pesky arithmetic problems? Look no further. It’s no secret that studying math can be tough. But with these five tips, your calculator and calculator skills will be nothing but a distant memory.
1) Practice, practice, practice:
If you want to get better at arithmetic, you will have to put in some serious time. Fortunately, there are several fun ways that you can review basic math concepts. One great method is practising with a flashcard app on your phone or computer. Using one of these apps for just 15 minutes each day will help you memorize addition and subtraction facts—and even some multiplication and division concepts—in no time!
2) Pay attention to one concept at a time:
Trying to review too many concepts at once will only make it harder for you to remember everything. Instead, choose one topic that you’re struggling with and try to get it down cold. Once you feel confident about that concept, move on to another area of your weakness.
3) Use good old-fashioned paper and pencil:
The days of working with only a calculator are over. You need both hands free to write down numbers and equations, so it’s a good idea to bring a notebook and pencil with you wherever you go. Calculators aren’t allowed on many tests these days, so having an analogue backup will help you review any concepts that come up while you’re studying.
4) Read, read, read:
Math textbooks are great for reviewing basic concepts. You might want to consider purchasing a textbook specifically for review purposes. The more concepts you can commit to memory through practice and reading, the easier it will be for you to succeed on your tests.
5) Look for problem-solving strategies:
Practice problems from your textbook can help you remember concepts, but there’s no substitute for solving real-world problems. You should also consider looking for tips and tricks that will help you find solutions faster. Many students struggle with remembering how to solve specific types of problems, so a little extra reading about these issues can go a long way toward improving your score. For example, several common strategies can be used when trying to solve word problems in algebra or calculus.
Cuemath is an online math teaching platform that provides you with highly qualified and experienced teachers who will help you to grasp every concept of mathematics. It also provides you with various types of math puzzles and worksheets.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100523.4/warc/CC-MAIN-20231204020432-20231204050432-00216.warc.gz
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CC-MAIN-2023-50
| 3,822 | 18 |
https://news.surrey.police.uk/
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math
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News • Jan 16, 2019 11:21 GMT
We are still appealing for witnesses following four further arrests made early last Thursday morning (10th January), after disorder at a house party in Sheerwater last November left six people needing hospital treatment.
News • Jan 16, 2019 09:40 GMT
A 14-year-old boy from Kingston-upon-Thames has been remanded in custody following an assault on a group of teenage boys in Thames Ditton on Saturday evening (12 January).
News • Jan 15, 2019 16:02 GMT
We’re appealing for witnesses after an incident in Frimley where a man is alleged to have been driven at.
News • Jan 15, 2019 15:59 GMT
Residents of Little Street, Guildford should have a quieter start to the year after a three month partial closure order was granted on an address involved in drug-related activity and anti-social behaviour.
News • Jan 15, 2019 14:37 GMT
News • Jan 15, 2019 10:26 GMT
A man has been sentenced after a pursuit in Dorking led officers to find Class A drugs.
News • Jan 14, 2019 16:04 GMT
Three men have been sentenced following a series of burglaries across the south of England which resulted in a total of £60,000 worth of jewellery and other items being stolen, and caused damage amounting to over a total of £28,000 worth of damage.
About Surrey Police
Surrey Police's media relations office deals with enquiries from the media on all aspects of Surrey Police's work. They are contactable by phone on +44 (0)1483 632000. Outside office hours, please call Surrey Police on 101 and ask for the on-call press officer, available for urgent enquiries only.
These contact details are for use by journalists only. Members of the public who wish to contact Surrey Police should call 101.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658662.31/warc/CC-MAIN-20190117000104-20190117022104-00278.warc.gz
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CC-MAIN-2019-04
| 1,731 | 16 |
http://www.analyzemath.com/Trigonometry_2/Verify_identities.html
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math
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Verify Trigonometric Identities
How to verify trigonometric identities? Several examples with detailed solutions are presented. Since we will make use of the basic trigonometric identities, a list of these Trigonometric Identities
is available in this site.
No single method works for all identities. However following certain steps might help. To verify an identity, you may start by transforming the more complicated side into the other using basic identities. Or you may transform the two sides into one same expression.
Verify the identity cos x * tan x = sin x
Solution to Example 1:
- We start with the left side and transform it into sin x. Use the identity tan x = sin x / cos x in the left side.
cos x * tan x = cos x * (sin x / cos x) = sin x
Verify the identity cot x * sec x * sin x = 1
Solution to Example 2
- Use the identities cot x = cos x / sin x and sec x = 1/ cos x in the left side.
cot x * sec x * sin x = (cos x / sin x) * (1/ cos x) * sin x
- Simplify to obtain.
(cos x / sin x) * (1/ cos x) * sin x = 1
Verify the identity [ cot x - tan x ] / [sin x * cos] = csc2x - sec2x
Solution to Example 3
- We use the identities cot x = cos x / sin x and tan x = sin x / cos x to transform the left side as follows.
[ cot x - tan x ] / [sin x * cos] = [cos x / sin x - sin x / cos x] / [sin x * cos]
- Rewrite the upper part of the above with a common denominator .
= [cos 2x / sin x * cos x- sin 2x / cos x * sin x] / [sin x * cos]
= [cos 2x - sin 2x] / [sin x * cos]2 (expression 1)
- We now transform the right side using the identities csc x = 1 / sin x and sec x = 1 / cos x.
csc2x - sec2x = (1/sin x)2 - (1/cos x)<2
- We now rewrite the above expression with a common denominator
= [ cos2x - sin2x ] / [sin x * cos]2 (expression 2)
- We have transformed the left side to expression 1 and the right side to expression 2. These two expressions are equal. We have verified the given identity.
- Verify the identity sin x + cos x * cot x = csc x.
- Verify the identity [csc x / (1 + csc x) - csc x / (1 - csc x)] = 2*sec2x.
Trigonometric Identities and Their Applications
Trigonometric Formulas and Their Applications
Online Step by Step Calculus Calculators and SolversNew !
Factor Quadratic Expressions - Step by Step CalculatorNew !
Step by Step Calculator to Find Domain of a Function New !
Free Trigonometry Questions with Answers
Interactive HTML5 Math Web Apps for Mobile LearningNew !
Free Online Graph Plotter for All Devices
Home Page --
HTML5 Math Applets for Mobile Learning --
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Algebra Questions -- Math Worksheets
Free Compass Math tests Practice
Free Practice for SAT, ACT Math tests
Precalculus Tutorials --
Precalculus Questions and Problems
Precalculus Applets --
Equations, Systems and Inequalities
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Math Videos From Analyzemath
Updated: February 2015
Copyright © 2003 - 2015 - All rights reserved
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s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988930.94/warc/CC-MAIN-20150728002308-00051-ip-10-236-191-2.ec2.internal.warc.gz
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CC-MAIN-2015-32
| 3,055 | 58 |
https://www.coursehero.com/tutors-problems/Algebra/16549439-An-editorwants-to-publish-a-new-magazineBefore-being-approved-the-pu/
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math
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An editor wants to publish a new magazine. Before being approved, the publisher needs to make sure that it can profit with the production cost and staff.
Their accountant has given them a cost equation of y=0.55x+1875 and a revenue equation of y=0.8x .
Calculate and interpret the break-even point.
The break-even point tells us that the cost for producing___ magazines is $___.
Breakeven point is (7500,6000) The... View the full answer
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s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256314.52/warc/CC-MAIN-20190521102417-20190521124417-00088.warc.gz
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CC-MAIN-2019-22
| 437 | 5 |
https://www.aging-us.com/figure/102841/f8
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math
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Figure 8. Kaplan-Meier analysis and Oncomine meta-analysis. (A) The overall survival analysis of CCL5. (B) The overall survival analysis of IFNG. (C) A meta-analysis of gene expression from Oncomine datasets. Colored squares represent the median of genes (relative to normal tissue) in five analyses. Red represents overexpression, blue represents low expression. This P value gives the average rank analysis.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657151761.87/warc/CC-MAIN-20200714212401-20200715002401-00010.warc.gz
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CC-MAIN-2020-29
| 409 | 1 |
https://studymoose.com/celestial-sphere-essay
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math
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Celestial Sphere Essay
Celestial Sphere:What we see, it contains the stars, planets, Sun, and Moon Celestial Equator- the imaginary line that divides the planet into Northern and Southern hemispheres. The celestial equator is a similar imaginary circle around the celestial sphere, also known as the visible universe. The celestial equator divides the visible universe in two, creating the Northern and Southern celestial hemispheres. This helps us locate celestial bodies. Ecliptics -an imaginary line on the sky that marks the annual path of the sun. It is the projection of Earth’s orbit onto the celestial sphere.
Besides define the path of the sun, the ecliptic marks the line along which eclipses occur, the moon and planets and asteroids wander, the Zodiac constellations live. The ecliptic is even the starting point for the celestial coordinate system used by astronomers to pinpoint the location of every star, nebula, and galaxy. Meridian-a great circle of the earth passing through the poles and any given point on the earth’s surface. The half of such a circle included between the poles. Astronomy. the great circle of the celestial sphere that passes through its poles and the observer’s zenith. A point or period of highest development,greatest prosperity,or the like. an of the path way sin the body along vital energy flows. Zenith-The point on the celestial sphere that is directly above the observer.
The upper region of the sky.The highest point above the observer’s horizon attained by a celestial body. Nadir-the point of the celestial spherethat is directly opposite the zenithand vertically downward from the observer Celestial Poles-Either of two diametrically opposite points at which the extensions of the earth’s axis intersect the celestial sphere. Either of the two points at which a northward or southward projection of the Earth’s axis intersects the celestial sphere. The north and south celestial poles are analogous to Earth’s geographic poles and are used in determining right ascension in the equatorial coordinate system. Depending on which hemisphere an observer is in, the stars and other celestial objects appear to revolve once around the north or south celestial pole every 24 hours, an effect produced by the rotation of the Earth on its axis.
Because of the precession of Earth’s axis, the celestial poles gradually shift position in the sky over a nearly 26,000-year cycle. Solstices-As the Earth travels around the Sun in its orbit, the north-south position (declination) of the Sun changes over the course of the year due to the changing orientation of the Earth’s tilted rotation axes with respect to the Sun. It is this change in the position of the sun that is responsible for seasons.
Solstices occur when Sun reaches maximum offsets from the equator projected on the sky . This offset corresponds to thetilt angle of Earth’s rotational axis with respect to its orbital plane, called the Earth’s obliquity.either of the two times a year when the sun is at its greatest distance from the celestial equator: about June 21, when the sun reaches its northernmost point on the celestial sphere, or about Dec. 22, when it reaches its southernmost point. Either of the two points in the ecliptic farthest from the equator.
•Equinoxes-Either of the two points on the celestial sphere where the ecliptic(the apparent path of the Sun) crosses the celestial equator. The point at which the Sun’s path crosses the celestial equator moving from south to north is called the vernal equinox. The vernal equinox marks the zero point in both the equatorial and ecliptic coordinate systems; horizontal angular distances are measured eastward from this point.
The vernal equinox is also known as the first point of Aries because when first devised some 2,000 years ago this point occurred at the beginning of Aries in the zodiac. The point at which the Sun’s path crosses the celestial equator moving from north to south is called the autumnal equinox. •Longitude-Lines of longitude, called meridians, run perpendicular to lines of latitude, and all pass through both poles. Each longitude line is part of a great circle. There is no obvious 0-degree point for longitude, as there is for latitude. Throughout history many different starting points have been used to measure longitude. By international agreement, the meridian line through Greenwich, England, is currently given the value of 0 degrees of longitude; this meridian is referred to as the Prime Meridian.
Longitude values are indicate the angular distance between the Prime Meridian and points east or west of it on the surface of the Earth. •Latitude-A line connecting all the points with the same latitude value is called a line of latitude. This term is usually used to refer to the lines that represent values in whole degrees. All lines of latitude are parallel to the Equator, and they are sometimes also referred to as parallels. Parallels are equally spaced. There are 90 degrees of latitude going north from the Equator, and the North Pole is at 90 degrees N. There are 90 degrees to the south of the Equator, and the South Pole is at 90 degrees S. When the directional designators are omitted, northern latitudes are given positive values and southern latitudes are given negative values.
•Right Ascension-The azimuthal angle at which the hour circleof a celestial object is located. The rotation axis taken as the direction of the celestial pole. Right ascension is usually measured in units of time (hours, minutes, and seconds), with one hour of time approximately equal to 15° of arc (360°/24 hours=15°/hour). •Declination-On the celestial sphere, the position of a celestial object north or south of the celestial equator. Declination is measured in degrees along a great circle drawn through the object being measured and the north and south celestial poles, with positive values north of the celestial equator and negative values south of it, so that the equator itself is 0° and the north and south celestial poles are +90° and -90° declination respectively the angular distance of a celestial body north or to the south of the celestial equator; expressed in degrees; used with right ascension to specify positions on the celestial sphere
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s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423716.66/warc/CC-MAIN-20170721042214-20170721062214-00328.warc.gz
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CC-MAIN-2017-30
| 6,295 | 10 |
http://www.slideshare.net/rkelch/12-using-scientific-method
|
math
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1-2 Using Scientific MethodPresentation Transcript
Warm -up Suppose you want to test which brand of floor cleaner is the best. What materials would you need? What procedure would you follow? How would you determine which cleaner produced the best results?
1-2 Scientific Method Describe the steps of the scientific method. Apply the steps of the scientific method to real world scenarios.
Scientific Method A series of steps that scientists use answer questions and solve problems A logical, organized way to solve problems.
Steps of Scientific Method State the problem – Ask questions Gather information Form a Hypothesis Perform experiment and collect data Analyze/Interpret data Draw a conclusion
Scientific Method SIX GREAT FARMERS PLANT ALL DAY
Six: State the Problem The scientist identifies the question or subject that he/she wishes to study Clear, specific & defined
Great: Gather Information The scientist researches the subject that he/she is studying. Places to do research: library, internet, encyclopedia, television, etc.
Farmers: Form Hypothesis Prediction about the outcome of an experiment Proposed answer to the question Usually has the words “If... Then” IF I eat too much, THENI will get sick
Plant: Perform Experiment Scientists develop a way to test their hypothesis Manipulated Variable: part of the experiment that can be changed or controlled Responding Variable: What is measured in the experiment Controlled Variable: part of the experiment that remain unchanged
All: Analyze Data Scientists compile data into charts and graphs This helps make sense of the information taken from the experiment
Day: Draw Conclusions Scientist decides whether the original hypothesis was correct. If the answer is “YES” then you are done If the answer is “NO” then a new hypothesis is made and you repeat the experiment
Law vs. Theory Law – a rule of nature
Answers the question “what?”
Examples: Law of Attraction and Repulsion, Law of Universal Gravitation Theory – An explanation based on repeated experimentation and observation.
Answers the question “why”
Examples: Theory of Evolution, Atomic Theory
Law vs. Theory Theories do not become laws!!! What doesn’t replace why! A theory represents everything currently known about a topic. Everything known supports the theory. If anything is discovered that disproves the theory, the theory is dismissed or adapted to suit the new information. A theory is “worth” much more than a “fact”!
Conclusion What is the purpose of the scientific method? How does a scientific law differ from a scientific theory?
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CC-MAIN-2014-10
| 2,602 | 19 |
https://www.hardmoneyhome.com/hard-money-loans/stanton-ca
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math
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Laverne finds a condo in the Southwest Anaheim neighborhood of Stanton, CA to remodel and sell. Since she doesn't have enough cash on-hand to acquire the $360,000 project outright, she takes out a hard money loan from Rolling Brook Funding. The loan-to-value (LTV) on the loan is 85%. This means Laverne will have to bring 15% of the purchase price to closing and the principle amount will be $306,000 on the loan. The note is interest-only, paid monthly, and is for 6 months at 9% interest with 1 points paid at closing.
In addition to paying the $3,060 origination fee, Laverne will also need to fund $54,000 of the purchase with her own money, or 15% of the purchase price. The lender will collect $2,295 in monthly interest payments from the borrower. This is computed by taking the total note amount of $306,000, multiplying that by the 9% interest rate, and then dividing that amount by 12. If Laverne sells the house for $540,000 after 6 months, she would then make a total profit of $163,170 after deducting the original principle of $306,000, the funds contributed at the close of $54,000, the origination points of $3,060, and the total interest payments of $13,770. This gross profit doesn't account for building costs.
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CC-MAIN-2023-14
| 1,230 | 2 |
https://www.coursehero.com/file/6773613/231E1F97/
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math
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-1-Stat 231 Exam IOctober 6, 1997Professor Vardeman1. The random variable the number of hours till failure of a WD disk drive\ œis described using an exponential distribution with mean 15,000 hours.(a) Evaluate the probability that a given drive lasts at least 20,000 hours.(b) A new computer network has 10 of these drives installed on computers in the network. Useyour answer to (a) and an assumption of independence of the 10 drive lifetimes and evaluate theprobability that at least 9 of these drives are failure-free through 20,000 hours. No need tosimplify. (If you could not do (a) use the incorrect value of .17.)(c) A WD warranty program pays customers for early failure of drives of this type according tothe following schedule:Failure in the first 10,000 hours produces a payment of $300Failure at hours (10,00020,000) produces a payment of $3002B B ÐÑB"!ß!!!Failure at hours with 20,000 produces no paymentBB Set up (but do not attempt to evaluate) an expression for the mean warranty payment under thisplan. (This is for an appropriate function .)E2Ð\Ñ2
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866511.32/warc/CC-MAIN-20180524151157-20180524171157-00448.warc.gz
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CC-MAIN-2018-22
| 1,155 | 3 |
http://www.zeierfamily.com/~rebecca/History%20of%20Pi.htm
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math
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Rebecca Zeier and Audrey Grammas
Math 388 – History of Math
History of Pi
Buffon’s Needle Experiment
Discovery of Pi
Students will have a cursory knowledge of the history of pi .
Students will obtain firsthand experience with Buffon’s Needle Experiment.
Students will make a connection with the calculation of pi .
Students will recognize the applications of p in everyday life.
Students will have access to technological resources demonstrating pi .
NCTM Curriculum Standards for grades 6-9
Standard #1: Problem solving
Standard #3: Reasoning
Standard #13: Measurement
Illinois Standards: (Goal 6)
Investigate, represent and solve problems using number facts, operations
and their properties, algorithms and relationships. Compute and estimate using
mental mathematics, paper-and-pencil methods, calculators and computers.
Rational: Students will have a deeper understanding of the mathematical function of p , it’s history and some of the great mathematicians working on p . Additionally, they will have an understanding of practical applications and the importance of its use in calculating circumference and diameter as used here and in astronomical configurations.
Computer for technology demonstration and projection capability, list of chronology of Pi, lengths of ribbon or string for circumference lab, round or cylindrical objects for measurement, measuring devise (ruler, tape measure etc.), chalk, blackboard (for recording findings), Homework for entire class, various applicable overheads.
Introduction to Pi: (Rebecca … 5 minutes)
A little known verse of the bible reads 'and he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. The same verse can be found in II Chronicles 4,2. It occurs in a list of specifications for the great temple of Solomon, built around 950 BC and it's interest here is that it gives pi = 3. With that, we will be discussing pi today.
Pi is an infinite decimal. Unlike numbers such as 3, 9.876, and 4.5, which have finitely many nonzero numbers to the right of the decimal place, pi has infinitely many numbers to the right of the decimal point. Although many mathematicians have tried to find it, no repeating pattern for pi has been discovered.
Brief History of Pi: (Audrey … 15 minutes)
Pi is a very old number. The earliest values of pi including the 'biblical' value of 3, were most certainly found by measurement. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3. The Egyptians calculated it to be approximately (4/3)^4 with equals 3.1604 and the Babylonians had an approximation of 3 1/8 which is about 3.125.
The earliest known reference to pi occurs in a Middle Kingdom papyrus scroll, written around 1650 BC by a scribe named Ahmes. He began the scroll with the words "The entrance into the knowledge of all existing things" and remarked in passing that he composed the scroll "in likeness to writings made of old." Toward the end of the scroll, which is composed of various mathematical problems and their solutions, the area of a circle is found using a rough sort of pi.
Around 200 BC, Archimedes of Syracuse found that pi is somewhere about 3.14. He wrote a book called "The Measurement of a Circle." In the book he states that Pi is a number between 3 10/71 and 3 1/7. He found this out by taking a polygon with 96 sides and inscribing a circle inside the polygon. That was Archimedes' concept of pi.
In the 1800's people sat down for years on end to find the values of pi to about 100 places. Imagine doing this by hand with no calculators. This has become a thing of the past, since the tedium that used to be done by hand is now done by computer.
This is of course just a brief history of how people studied pi … the study of pi has gone on for centuries upon centuries and if we covered it all, we'd probably bore you to death … so we'd like to give you this more detailed chronology of the history of pi for you to study at your own leisure.
Buffon's Needle Experiment: (Rebecca … 10 minutes)
One of the famous mathematicians we would like to point out to you on your chronology list is Compte De Buffon. Compete de Buffon was a French aristocrat with a courageous way of looking at the world. During the 18th Century most biological questions were answered by looking at biblical doctrine. Buffon rejected these ideas and dogmas and even went so far as to publish them in a book entitled "Historie Naturelle", which superceded the writings of Darwin by 100 years. He had some definite ideas about environment and organisms, which were in direct opposition to those ideas enforced by the church. In addition to his interest in nature, medicine and law, Buffon was a revolutionary thinker and because of this he was able to come up with an experiment known as the Buffon’s Needle Experiment which curiously proves the accuracy of Pi.
Buffon's needle experiment is one of the oldest problems in the field of geometrical probability. It was first stated in 1777. The idea is simple. Suppose you have a tabletop with a number of parallel lines drawn on it, which are equally spaced. Suppose you also have a pin or needle. If you drop the needle on the table, you will find that one of two things happen: 1) The needle crosses or touches one of the lines, or 2) the needle crosses no lines. The idea now is to keep dropping this needle over and over on the table, and to record the statistics. Namely, we want to keep track of both the total number of times that the needle is randomly dropped on the table, call that N, and the number of times that it crosses a line, call it C. The remarkable result is that if you keep dropping the needle, eventually you will find that the number 2N/C approaches the value of pi. Another way to look at it is that the probability is directly related to the value of pi.
We would like to show you three simulations to this experiment on the computer screen. The first simulation displays the idea of the number 2N/C approaching pi. This means that the more and more times we perform the experiment, the closer and closer the value gets to the value of pi. This is known as the limit. The second simulation shows the probability idea of the needle dropping. The third ….
Now isn't that interesting?
Discovering Pi: (Audrey and Rebecca … 20 minutes)
While many applications can be associated with pi, who knows the most common use of pi today? The most common use of pi is to calculate the circumference and area of a circle. In fact, by definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it. Believe us? Well let's test that out….
Learners will get into groups. In these groups, the learners will complete the Discovering Pi guide sheet (except for the Concluding Questions section). When each group has completed its worksheet, a member of each group will go to the board and add their answers to a chart on the board. After the data is on the board, the whole class will answer the Concluding Questions section together. See guide sheet for more information.
*** Another idea, which we included in our lesson, was to read the story of Sir Cumference and the Knight of Pi. We then followed up with practical applications and conclusions ***
Practical Applications of Pi: (Audrey)
We have demonstrated several different ways that we can prove Pi. We have even showed how we can use Pi to calculate circumference, diameter and radius of circles. We have some really important calculations that could not be done without the use of Pi.
A Greek philosopher named Eratosthenes used simple geometric reasoning to calculate the size of our planet in about 200 BC using a formulation including Pi. Using the formulation Erastosthenes was able to estimate the circumference of the Earth to within one percent accuracy using only simple geometry. The formula coupled with the angle at which the Sun passed overhead and the distance between Alexandria a city to the South of where he lived and his location allowed Erastothenes to do his detailed calculations.
Additionally Greek Astronomers Ptolemy, Aristotle a Greek Philosopher, were able to hypothesize the Geocentric model of our solar system and Isaac Newton, was able to create his laws of planetary motion reinforced later by Johannes Kepler in his laws of planetary motion and elliptic orbit in addition to escape speed.
Four thousand years ago, people discovered that the ratio of the circumference of a circle to its diameter was about 3. In nature people saw circles, great and small, and they realized that this ratio was an important tool.
This tool was used by the Babylonians and the Egyptians. Reference is made to the concept of pi in the bible. The Chinese found a value of pi that stood for one thousand years. One man felt the accomplishment of taking pi to 35 places was the most important achievement of his life, so much so, that he had it inscribed on his epitaph. With the help of computers, pi has been taken to over 6 billion places. People have been fascinated by pi, and irrational number, throughout history.
Please carefully follow the directions!
1. Get a circular cover and piece of ribbon.
2. Use the ribbon to measure the circumference of the circular object. With a pencil, make a mark on the ribbon to record the measurement of the circumference of the circular object. Using the ruler, measure the marked off length of the ribbon to the nearest centimeter. This is the circumference of your circular object. Record that measurement here:
Circumference of Object (C) = ______________
Diameter of Object (d) = ________________
C + d = _________________
C – d = _________________
C * d = _________________
C / d = _________________
We will answer these questions as a class, but record your answers since this sheet will be collected for a grade.
C + d C – d C * d C / d
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| 10,156 | 55 |
https://www.arxiv-vanity.com/papers/1307.7703/
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math
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Geometries via M-theory
We provide an M-theory geometric set-up to describe four-dimensional gauge theories. This is realized by a generalization of Hitchin’s equation. This framework encompasses a rich class of theories including superconformal and confining ones. We show how the spectral data of the generalized Hitchin’s system encode the infrared properties of the gauge theory in terms of curves. For deformations of theories in class , we show how the superpotential is encoded in an appropriate choice of boundary conditions at the marked points in different S-duality frames. We elucidate our approach in a number of cases – including Argyres-Douglas points, confining phases and gaugings of theories – and display new results for linear and generalized quivers.
8 \preprintSISSA 36/2013/MATE-FISI, CALT-68-2850
M-theory geometric description of supersymmetric gauge theories is a very powerful access key to the non-perturbative aspects of the formers and complements their perturbative Lagrangian description. In this context, a very powerful approach to four-dimensional gauge theories has been introduced in Witten:1997sc ; Gaiotto:2009we . In this paper we propose a general geometric set-up for four-dimensional gauge theories which naturally encompasses previous well known examples studied from the point of view of rotated M5-brane systems in Hori:1997ab ; Witten:1997ep ; Brandhuber:1997iy ; deBoer:1997ap .
The approach we follow consists in considering the six-dimensional theory compactified on a Riemann surface with marked points with a suitable topological twist. This is realized by wrapping an M5-brane bound system around , where is the base of a local Calabi-Yau (CY) threefold obtained as the total space of a rank 2 holomorphic vector bundle with normalized determinant over . For theories with superconformal invariance in the infrared, this set-up has been considered in Benini:2009mz ; Bah:2012dg . See also Maruyoshi:2009uk ; Bah:2011je ; Beem:2012yn ; Gadde:2013fma for relevant field theoretical arguments.
The dynamics of the M5-branes is determined by M2-branes suspended between them. These are particles in the spacetime and therefore are effectively open strings in ending on the holomorphic two-cycle . Therefore the dynamics of the M5-branes reduces to that of B-branes in and as such it is described by the appropriate dimensional reduction of the holomorphic Chern-Simons theory on . Its equations of motion give rise to a generalization of the Hitchin system with suitable singular boundary conditions at the marked points.
The spectral curve of this generalized Hitchin system describes the geometry of the M5-brane bound state as an -branched cover of . This is encoded in a specific overdetermined algebraic system that we study in detail. This system describes a rich class of theories including superconformal and confining ones, and contains the relevant infrared data of the four-dimensional gauge theory. We show how to obtain the generalized Konishi anomaly equation Cachazo:2002ry , the Dijkgraaf-Vafa curve Dijkgraaf:2002dh , the curves presented in Hori:1997ab ; Witten:1997ep , and the curve describing the gauge theory coupled to theories, related with Tachikawa:2011ea ; Maruyoshi:2013hja . In particular the factorization of both the Seiberg-Witten curve and the Dijkgraaf-Vafa curve is elucidated and worked out in new examples.
The above geometrical objects compute the vev of chiral ring observables. The moduli space of vacua of the theory is described by the moduli space of solutions of the generalized Hitchin system associated to it. A particularly important class of theories is the one obtained via turning on an breaking superpotential of adjoint chiral fields to theories. This sets the boundary conditions on the generalized Hitchin field and provides an obstruction in the Hitchin moduli space. Therefore the generalized system has a reduced moduli space corresponding to the lifting of the flat directions in the Coulomb branch of the theory, induced by the superpotential. Indeed, we see that in various examples the Coulomb moduli is completely fixed, leading to isolated vacua. The dual geometric set-up to the above case is described as arising via a complex structure rotation in the target space geometry, which connects the breaking potential to purely geometrical data.
We show how our set-up reproduces several known examples previously studied in the literature, namely super Yang-Mills (SYM) theory, supersymmetric QCD (SQCD) and theories as trial cases. The new results which are obtained concern the extension of the factorization condition of the Seiberg-Witten curve for linear and generalized quivers. We also discuss a subtle difference in the interpretation of the boundary conditions which has to be taken into account when considering gauge theories with group, rather than , via a shift of the boundary condition by the meson vevs.
The use of the generalized Hitchin system requires the introduction of a vector field on whose choice looks crucial in order to establish the S-duality frame of the underlying theory. For generalized quivers we show that the factorization condition is an easy consequence of the generalized Hitchin system and provides a simple recipe for computing the chiral condensates when combined with the appropriately chosen vector field. We exemplify the relation between the choice of the vector field and the S-duality frame for the corresponding gauge theory in the case of theory with .
This paper is organized as follows. In section 2 we consider the general geometric set-up generating four-dimensional gauge theories from M5-branes in the local CY curve. We discuss the generalized Hitchin system and its spectral curve data, and we focus on the theories obtained from ones via superpotential breaking. In section 3 we see how the framework provided in section 2 is applied to gauge theories. We show that the factorization condition which follows from the generalized Hitchin system is strong enough to determine the curves of various gauge theories. We also give some results for the gauge theory with gauge group. In section 4, we study the higher rank theories including SYM theory and the theories coupled to gauge groups. In section 5 the curve of linear quiver theory is obtained from the Konishi anomaly equations. We discuss the factorization condition of this theory in detail. Section 6 contains our final remarks and discusses some open issues. In appendix A we present some of our results by an alternative method making use of the type IIA branes picture.
2 Generalized Hitchin system
2.1 M-theory engineering
supersymmetric gauge theories in four dimensions can be engineered by considering the reduction of M5-branes on the CY geometry
where the M5-branes wrap , being an holomorphic two-cycle with genus and marked points in the CY threefold .
Let us concentrate on the geometry in the vicinity of the brane system and specify the CY threefold to be a local curve over 111Here and in the following we drop for simplicity the subscripts: ., namely , where is a rank two holomorphic vector bundle with the canonical line bundle on , to ensure supersymmetry by the usual CY condition.
The geometry of the M5-branes encodes the definition of the gauge theory and it is described by the following generalization of the Hitchin system
which should be supplemented by suitable boundary conditions at the marked points. Eqs. (1) are the Uhlenbeck-Yau equations in dimensionally reduced to the base . is a section in transforming in the adjoint representation of a given gauge bundle. The D-term equation is traded for the complexification of the gauge group and a stability assumption on the gauge bundle.
Notice that the BPS M5-branes, as seen from the internal CY geometry viewpoint, are B-branes of complex dimension one. The M2-branes stretching between them are particles in and open strings in with boundary on the B-branes. Indeed, the action functional generating the equations (1) is the dimensional reduction to of the holomorphic Chern-Simons theory on and reads
The geometry of the M5-brane bound state is described as an -branched cover of in the form of the spectral curve for the commuting pair . This can be easily written in components as follows. By specifying in components the generalized Hitchin equations (1) read
whose spectral curve is given by the overdetermined algebraic system
spanning an -sheeted cover of described by the simultaneous eigenvalues of and .
The set-up we just described is seemingly quite rich and can be used to define a wide class of supersymmetric gauge theories in four dimensions, whose moduli space of vacua is described by the moduli space of solutions of the generalized Hitchin’s system. In particular maximally confining vacua correspond to isolated solutions. An important subset of these theories is deformation of gauge theories in class by superpotential terms depending on the adjoint chiral fields. This subset includes the theories considered extensively in Douglas:1995nw ; Elitzur:1996gk ; Cachazo:2001jy ; Dijkgraaf:2002dh . We will mainly focus on this subset in this paper. Let us remark however that more general genuine theories can be described within our approach.
In order to see the theory as a deformation of an theory in class , one should rotate the target space complex structure as
In the following, for the sake of simplicity, we will restrict to the case in which is split in the sum of two line bundles, although more general cases can be considered. The rotation of the complex structure (5) can be encoded in a -dependent coordinate redefinition which has to be a canonical transformation to map (almost everywhere) the CY holomorphic top forms as
where and are generically different coordinates on , is a coordinate in the canonical bundle and in . The change of coordinates is then obtained from a generating potential valued in . For example one can have
The canonical transformation can be extended to the commuting pairs , where and are the components of the doublet in the rotated target space geometry.
As we will describe in the following subsection the pair subject to some precise boundary conditions describes breaking of theories in class . We remark that a non trivial constraint on the canonical transformation is that it produces the correct boundary conditions. This in general cannot be done and therefore in this setting this is the condition such that the initial theory can be seen as a deformation one. For example, the simplest canonical transformation is the coordinate rotation induced by meromorphic sections of , of and of
where and . This rotation has a non trivial effect on the behavior of the fields at the divisor dual to and can induce spurious singularities in the Hitchin field. In particular, if is positive we expect to have a genuine theory. For example for , if and , then one gets superconformal theories studied in Bah:2012dg .
In what follows we focus on the study of deformation of theories in class .
2.2 breaking of theories in class
gauge theories are obtained as particular cases of theories which are constrained in their spectrum and couplings. These constraints can be implemented in the M-theory engineering by imposing the existence of higher supersymmetry in the geometry, namely by requiring the -symmetry to get realized as a spacetime symmetry. In concrete we need the local CY geometry threefold to have a trivial fiber and therefore to be a local K3 manifold. This produces the familiar M-theory geometric background
where the local K3 geometry is uniquely determined by the holomorphic two-cycle to be the total space of its canonical bundle . More explicitly the holomorphic vector bundle is and .
The constraints on the M5-brane system should still be consistently enforced to guarantee the overall supersymmetry. The generalized Hitchin equations (3) now read
where is a -form on and is a scalar on both transforming in the adjoint representation of the gauge bundle.
The M5-brane system should occupy a point in the factor of the geometry and this can be enforced by setting to vanish the field reducing the extended Hitchin system (11) to the well known Hitchin equation
This should be supplemented by appropriate boundary conditions at the punctures describing the M5-brane asymptotic geometry. Notice the important fact that the above procedure of eliminating is independent on the boundary conditions imposed on .
The complete geometry is obtained by the Seiberg-Witten (SW) curve in the form of the spectral curve of the Hitchin system which follows directly from (4). By specifying and one gets
where is the fiber coordinate on the local K3 geometry around . Notice that in order to fix it is enough to set to zero its boundary values at the singularities, whenever the gauge bundle is irreducible.
In conclusion, by these two steps, namely the holonomy reduction of the target and the assignment of vanishing boundary conditions to at the punctures, we could enforce the -symmetry required to get an enhancement to an gauge theory.
Corresponding to the two steps above, we have therefore two seemingly different ways to break supersymmetry to within the family of theories which we are considering in this paper. One is by rotating the M5-branes in a direction orthogonal to the local K3 by fixing suitable boundary conditions, the other one is obtained by embedding the system in a more general local CY geometry and rotating the complex structure. Actually both these steps, in the perturbative regimes, should be equivalent to switch on an superpotential. Let us describe the two deformations in more detail.
2.2.1 Breaking via M5-branes rotation
The first way of deformation corresponds to consider once more the extension of the Hitchin system
but now with non-vanishing boundary conditions on . As we noticed, if the field had vanishing boundary conditions at the punctures, then it vanishes everywhere. Changing the boundary conditions for at the punctures therefore corresponds to break to . The allowed boundary conditions for shall be given in terms of the field itself in order to automatically satisfy the equation . Henceforth the boundary conditions encode the supersymmetry breaking superpotential.
To write the boundary conditions we need to compare the and on the Riemann surface and this is obtained by introducing a (possibly singular) holomorphic vector field on . Let us denote this vector field by and consider then the system with boundary conditions at the punctures
where and are polynomials in . Let us notice that one of the boundary conditions in (12) can be set to zero, say , by the change of variables unless introduces spurious singularities by the vector field .
The rotated M5-brane is then described by the spectral curve of (11), namely by the curve in the space spanned by the overdetermined system
where and are the coordinates in and the fiber of respectively. As it will become evident in the following sections, the resulting system describes both the original Hitchin spectral curve at the singular point on the Coulomb branch which is not lifted by the deformation, and the curve describing the solution of the generalized Konishi anomaly equation in a unified way. The elementary, but crucial, observation we will use is that, once fixed by the boundary conditions, the algebraic system (13) is solved as an algebraic relation by the fields (Hamilton-Cayley theorem for the commuting pair).
In this framework the fixing of the Coulomb moduli to their vacuum values is due to the fact that the extended Hitchin system’s moduli space has a reduced dimension with respect to the Hitchin system itself because of the obstructions induced by the non-vanishing boundary conditions on . More precisely, the equations (13) describe a Kähler submanifold in the Hitchin moduli space obtained by specifying the Hitchin’s Hamiltonians to the condensates. Indeed, as we will show in section 3, the second equation of (13) can be identified for Lagrangian theories with the generalized Konishi anomaly equations encoding the chiral condensates.
2.2.2 Breaking via complex structure rotation
The second way to break supersymmetry down to corresponds to rotate the target space complex structure as
This can be implemented via a suitable canonical transformation, as discussed in the previous subsection as a coordinate redefinition preserving (almost everywhere) the CY holomorphic top form. The canonical transformation can be extended to the commuting pairs setting the equivalence between the descriptions in (11) and (1) if accompanied by the induced correspondence of the boundary conditions in the appropriate way.
The choice of the canonical transformation is indeed crucial in order to avoid a mismatch in the boundary conditions. In particular it is important to select adapted sections to match them. We will consider this issue in detail in the following examples.
2.3 M-theory curve and factorization condition
In the following sections we will mainly exploit the first description involving the Hitchin field. The curve is given by the generalized Hitchin system we discussed before, which includes the curve and a degree equation for the coordinate (the spectral curve for the field) which has the form
where are meromorphic functions on with poles at the punctures, since the coordinate lives in .
A curve exactly of the form written above, which encodes the matrix of gauge couplings, has been found recently for gauge theory coupled to theories Tachikawa:2011ea ; Maruyoshi:2013hja . It is thus natural to expect that what we need is precisely the generalization of these “ Seiberg-Witten curves”. We will indeed see that these curves emerge naturally for the class of theories considered in Tachikawa:2011ea ; Maruyoshi:2013hja , once we impose the correct boundary conditions at the punctures. Thus we refer to (15) as curve.
These two equations must then be supplemented by a third equation, which encodes the restrictions on the Coulomb branch coordinates of the underlying theory. From the perspective of the generalized system, this is encoded in the spectral equation for the product (the second equation in (13)). How can we understand it from the brane perspective? What we are trying to do is to construct softly broken theories obtained by compactifying the six-dimensional theory of type on . Indeed, the Seiberg-Witten (SW) curve associated to the underlying theory is an -sheeted covering of and the same should be required to hold in the present context if we want this picture to make sense. It is easy to see that this property is not satisfied for generic values of the parameters: for fixed the SW curve gives us possible solutions for , and the curve provides solutions for . This generically leads to possible pairs . We should then add to this system the condition that is fixed once we have chosen and (and of course is fixed once and are chosen), which reduces the solutions to possible pairs . Indeed, this is what the second equation in (13) implies. This simply translates into the requirement that is a rational function of and .
Introducing the vector field , we write the SW curve in terms of , where is the SW differential, as
where ’s are meromorphic functions. The factorization condition for a generic rank theory will be of the form
(of course an analogous equation holds with and interchanged) where and are polynomials in of degree , whose coefficients are meromorphic functions on (rational functions for theories on the sphere, elliptic functions for genus one theories and so on). We will see in section 5 that this leads directly to the well known factorization condition for SQCD.
3 curve in theory
In this section we consider four-dimensional gauge theories obtained from the theory in six dimensions (or compactification of two M5-branes). The gauge groups are always in this case. From the generalized Hitchin system viewpoint (the first description in section 2.2.1), we have two Hitchin fields and where the spectral curves can be put in the form, in terms of and ,
Nota that is identified with the coordinate appearing in the M-theoretic geometry if we choose in the theory with the Type IIA brane realization as we will see below. Since the Hitchin fields commute, they must be proportional to each other (which is true only for the case). This implies which gives us the condition or
Indeed, this condition can be obtained from the factorization condition in section 2.3. In this rank-one case the condition reads
Since the two solutions of (17) at fixed that we denote by (, ) and (, ) differ by a sign, we get
We can consider the analogous sequence of equalities for the inverse relation . Equating the leftmost and rightmost terms we find and . These in turn imply that is a square of a function222If some of the polynomials are zero, making these two equations trivial, it is easy to see that either or and this leads directly to the conclusion in any case. (18). Thus we refer to (18) as factorization condition below.
In this case we can turn on only mass terms for the adjoint chiral fields (quadratic superpotentials), so the ratio tends to a constant (possibly zero) at all the punctures. This is the boundary condition we have to impose for at the punctures. The value of the mass parameters for the adjoint fields in the various gauge groups (in a given weakly coupled limit) will be simply encoded in the difference between the values of at the punctures. Indeed, since is not constant, it has poles. To avoid singularities for away from the punctures, which indeed should not be there, the poles should be located at the zeroes of . In order for this to be possible, should have double zeroes. This is the way in which the restriction on the Coulomb branch coordinates appears in this description.
We will now show how one can use the above results to determine the curve for theory obtained by the mass deformation of the adjoint chiral field of gauge theory with fundamental hypermultiplets. These theories have a brane realization in Type IIA string theory. While the existence of the brane realization is not needed for our approach, it is helpful to identify each vacuum of theory with the brane configuration. Thus, we shortly review the Type IIA brane set-up Witten:1997sc ; Elitzur:1997fh ; Elitzur:1997hc ; Giveon:1998sr .
We consider D4-branes extended along directions and NS5-branes extended along directions. Two D4-branes stretched between two NS5-branes induce at the low energy four-dimensional SYM theory on the worldvolume. In the following we denote the NS5-branes as NS and NS below, as in figure 1. The addition of a D6-brane extended along directions between the NS5-branes in the -direction corresponds to the inclusion of a fundamental hypermultiplet. We always move this D6-brane to the left of NS- or the right of NS-brane, which produces the D4-branes stretched between the NS5- and D6-branes. Finally, in order to include the quadratic superpotential of the adjoint field we rotate one NS5-brane to -direction, where .
When , there is a Higgs branch in the corresponding theory. As in Argyres:1996eh , generically the Higgs branch is divided into the non-baryonic branches which are labeled by with and the baryonic branch. (The baryonic branch exists when .) These branches intersect with the Coulomb branch at the (non-)baryonic branch roots which are submanifolds in the Coulomb branch. On these submanifolds there are loci where mutually-local massless particles appear. We will see that these become vacua of theory after the mass deformation.
3.1.1 SYM theory
The M-theory curve of SYM theory (which is identified with the SW curve Seiberg:1994rs ) is
where and is the Coulomb moduli parameter. The SW differential is given by . The curve can be written as
as a double cover of the base sphere parametrized by . The quadratic differential has two irregular singularities of degree at and . Note that our choice of the vector field is and .
Let us rotate the NS-brane at . This means that the curve has the same behavior at as the SW curve and subleading at infinity (in order to avoid a global rotation of the brane system). In particular we require at . This requirement leads to the curve , where is a constant. In principle we can allow a constant term linear in but this can of course be eliminated by a redefinition of and . The curve is already in the form , so we can use (18)
The above expression can be the square of a rational function only if and . Indeed, these are the points where the curve degenerates. The curve is
implying that has a simple pole at where we have rotated the NS5-brane. This curve is sensitive only to the rotated puncture. The singularity of expresses that this puncture is obtained from the irregular puncture with degree . This agrees with the one obtained in appendix (130) following the method in Hori:1997ab .
The Dijkgraaf-Vafa curve follows from these: by substituting (24) into the SW curve with , we obtain the curve where . This is identified with the DV curve: is the gluino condensate. We can see that by the one-loop matching this is indeed the correct value where is the dynamical scale of the theory after integrating out the massive adjoint fields.
We next consider the case which is realized by the addition of a D6-brane. Here we put the D6-brane to the right of the NS-brane. The SW curve is
where is the mass parameter of the quark field. This leads to
Note that we have shifted such that the linear term disappears. Thus the quadratic differential has singularities of degree at and of degree at .
Rotating the NS-brane at as before the ansatz of the curve is , where and are constants. We then require
This equation imposes the constraint , so the numerator becomes of the form where , and implies that the denominator factorizes as . We thus find and is determined by the cubic equation . The Coulomb moduli is determined to be . We thus find three vacua. When the mass parameter is set to zero, the positions of the vacua in the Coulomb branch are symmetric, as expected. Finally the curve is given by
which agrees with (134). Note that the singularity of at the rotated puncture is a double pole, and is different from that of SYM case. This is because the rotated puncture is from the irregular one with degree .
(for instead of we have ) and check that these are the only points at which the discriminant vanishes (without setting ). At these points the curve degenerates to a sphere, corresponding to singularities of the Coulomb branch of theory which are not lifted by the deformation. In the massless case for example, the discriminant is , which precisely vanishes at the three points found above setting .
Since it is not trivial in this case, let us explain how one can extract the Dijkgraaf-Vafa curve. The easiest way is to use the factorization condition to write in terms of and , and then plug the result in the curve to get an equation in and only. This procedure works, provided we use the curve written in the parametrization as in (25) (and redefine accordingly). In the present case this is accomplished by the redefinitions
We then find
which is precisely the curve we were looking for. Without this redefinition we would have found a cubic equation in .
Let us consider gauge theory with . Note that there is Higgs branch in the corresponding theory: a non-baryonic branch and a baryonic branch. The latter exists only in the massless flavor case. There are three ways to construct this theory in Type IIA: the first is to place two D6-branes to the right of the NS-branes; the second is to put one D6 to the right of the NS and one D6 to the left of the NS; the third is to put two D6-branes to the left of the NS. Though the gauge theory and vacua obtained from these should be the same, the curve looks different. We will see these in the following.
The first realization
The SW curve is given by
This leads to
where we defined . It is easy to see that the quadratic differential has singularities of degree at and an irregular one at of degree . We refer to the former singularity of degree less than or equal to as regular. The SW differential is , thus the residues at regular punctures and are and respectively.
We will consider the rotation of the NS-brane as above. Let us set the mass parameter to be zero, namely for simplicity. The ansatz of the curve is . Therefore we require
One solution is , and . The curve is written as
At this locus of the Coulomb branch the SW curve degenerates. Thus this is the vacuum considered in Hori:1997ab , as reviewed in appendix A.1.3. Note that when we set , the curve is trivialized, signaling that the NS-brane is detached from the rest, as in figure 2. Indeed the baryonic branch of the massless theory intersects with the Coulomb branch at the locus obtained above. The detachment happens when the residue of the SW differential at vanishes. We will see the same phenomenon later in the with case.
The other solution is , and , where . The curve is written as
See (143) for comparison. This corresponds to the vacuum, namely the deformation at the root of the non-baryonic branch. Indeed, one can easily see from the curve that when we get , when we get , and when tends to two values . These are explained by the figure 2. In particular, the two values are interpreted as the positions of D4-branes in -direction at . Notice that the NS cannot detach from the rest because of the -rule.
As a consistency check, one can check that the discriminant of the curve (28) with and has simple zeros at and a double zero at . These are exactly the vacua we found above.
The second realization
Let us then consider the second realization. The SW curve is
We here consider the massless theory for simplicity. This leads to
There are two irregular punctures of degree at and .
We would like to rotate the brane at . From that the boundary condition at is and , the curve is of the following form . Thus the factorization condition is
There are two possibilities: one with the denominator factorized as , meaning , and the numerator factorized as , meaning and . In this case,
Note that the rhs of the curve is a square. The curve is identified with (146) (after the shift of ). Thus this solution of the factorization condition corresponds to the vacuum, and represents that the brane system is separated into two part as in figure 3.
The other possibility is and or . The latter corresponds to the previous solution after the shift of -coordinate, thus we do not consider this. The curve is calculated as
The third realization
The SW curve is in this case
Again we consider the massless case where
There are two regular punctures at and an irregular one at of degree .
Let us rotate the NS-brane at . The ansatz for the curve is . This is because the boundary condition at is and . Thus, we have
Solving the factorization condition leads to two solutions: the one with and corresponding to the vacuum
the one with and corresponding to the vacuum
By shifting -coordinate, we can see that these two curves agree with (148) and (149) respectively. See figure 4. The singularity of at is a simple pole and coincides with that of SYM case, since the rotated puncture is of degree .
Let us then turn to the case. There are two realizations of this theory in Type IIA: the first is to put two D6-branes to the right of the NS and one D6-brane to the left of the NS, the second is the opposite to the first case, as in figure 5. We will focus only on the second option below.
Note that there is a non-baryonic branch with in the corresponding theory. In the massless theory the root of the non-baryonic branch is the same as that of the baryonic branch.
The SW curve is given by
We will for simplicity consider the case and , where the curve can be rewritten as
In this parametrization the mass terms lead to a double pole at infinity. There is also the irregular singularity of degree at .
Rotating the puncture at , the curve is of the form: . We thus find the factorization condition
One solution corresponds to the fact that the denominator has the form . The constants and are determined by and . In terms of , we find . We thus get three vacua. The above factorization of the denominator in turn implies that . By considering the asymptotics at zero as before, we can fix . Note that in the massless case , , , . That is the curve is
The has a double pole at representing the behavior of the rotated puncture of degree . This is the same as that in subsection 3.1.2. Also the curve agrees with (157). Therefore this denotes the vacuum.
The other solution can be obtained by requiring the denominator to be a multiple of , which imposes the constraint . then reduces to . This can be the square of a rational function only if the numerator is a multiple of the denominator. Thus we obtain , and , namely the curve is
Notice that in the massless case the factorization condition and asymptotics at the NS5-branes do not allow to fix all the parameters in the curve. Once the mass parameters are turned on, this is no longer the case. This may corresponds to the vacuum as depicted in figure 5.
As a consistency check we can rewrite the curve (28) as and check that the discriminant has degree five in , a double zero at and other three simple zeros located precisely at the points described above. When is sent to infinity the vacuum at disappears and the other three are at , where is the third root of unity. This matches precisely the behavior of the theory with . Note that is precisely proportional to the cube of the dynamical scale of the theory with by the one-loop matching.
The SW curve of this theory is
where we have chosen the coefficients in such a way that the punctures are at and . All the punctures are regular. For simplicity we analyze the case and . We can write the SW curve as
With this choice of mass parameters the quadratic differential has simple poles at 1 and and double poles at zero and infinity whose coefficients are and . We can rotate either at or at . Let us consider the first option, so the curve has the form . The factorization condition is
Notice that and ’s are parameters and should not be tuned. The only parameter we can constrain is the coordinate on the Coulomb branch.
Requiring the denominator to be a square we find the two solutions . We are then forced to set . Imposing then at we find
The depends on which solution we choose for . Notice that diverges in the limit .
We can also require that the denominator is a multiple of . This implies then
This corresponds to detaching from the brane system the brane located at . This is signaled by the vanishing of the residue at of the quadratic differential of the SW curve.
There is another solution: . As in the previous solution, we now see that this corresponds to detaching the NS5-brane at . Since in this case the rotated brane is detached from the rest, the coordinate will be trivial except at . We thus expect the curve to develop two branches and become of the form . Indeed, this is precisely what we get if we multiply the curve written before by on both sides and then set . However, this solution will be consistent only if the residue of the pole at in the quadratic differential vanishes, which is true only for
This solution must be included whenever we can eliminate the corresponding pole in the differential with a suitable choice of point in the Coulomb branch. It is thus the structure of the curve which dictates when this solution is allowed. This phenomenon will occur in rank one theories with regular punctures and we have already encountered it in the study of the theory.
Rewriting the SW curve in the form
we can test as before our result checking that the above solutions are the only points in the Coulomb branch where the discriminant of the rhs vanishes. It turns out that it is a polynomial of degree six in , whose roots are precisely the four values found above. The last two solutions are actually double roots. With a more general choice of mass parameters they split. For large and only the first two solutions remain finite and correspond to the vacua of SYM (once we take into account the one-loop matching condition). The other four run away to infinity as all the matter fields become infinitely massive. In the massless limit all the vacua merge at , in agreement with the expectation that the theory flows to an IR fixed point in this limit Leigh:1995ep .
The S-dual frame
As we have just seen, the curve diverges when . To approach this limit the most natural procedure is to change S-duality frame and consider a description of the theory in which the gauge group becomes weakly coupled. More precisely what we want to do is to analyze the mass deformation of the dual theory. How can we do that in the present framework? Indeed the first step is to rewrite properly the SW curve. We can e.g. consider the reparametrization of the sphere that interchanges the punctures at leaving fixed by . This is accompanied by the redefinition . The resulting curve is
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https://math.answers.com/Q/What_is_four_over_thirty_two_equal_to
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math
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it equals eight
* * * * *
No, it does not!
Four over thirty two equals an eighth or one over eight!
what is a dry measure equal to four pecks or thirty two quarts?
Expressed in words, this is equal to thirty-one point two three four. how about thirty one and two hundred thirty four thousands!
Thirty-six times twelve comes out to equal four hundred and thirty-two.
no it is equal
The easiest way to do this question is not to think of it as multiplying by 0.2, but by multiplying it by two and then dividing it by ten. Thirty-two times two equals sixty-four, and sixty-four divided by ten equals six-point-four.
Expressed in words, this is equal to four million two hundred and thirty-eight thousand.
It is simply called a thirty-inch two-by-four.
no, its not one half is equal to a fractoin like two over four
It is: 4/32 times 100 = 12.5%
Four weeks with two days left over.
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http://www.solutioninn.com/prestigious-university-is-offering-a-new-admission-and-tuition-payment
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math
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Question: Prestigious University is offering a new admission and tuition payment
Prestigious University is offering a new admission and tuition payment plan for all alumni. On the birth of a child, parents can guarantee admission to Prestigious University if they pay the first year’s tuition. The university will pay an annual rate of return of 4.5% on the deposited tuition, and a full refund will be available if the child chooses another university. The tuition is $12,000 per year at Prestigious University and is frozen at that level for the next eighteen years. What would parents pay today if they just gave birth to a new baby and the child will attend college in eighteen years? How much is the required payment to secure admission for their child if the interest rate falls to 2.5%?
Answer to relevant QuestionsFill in the interest rate for the following tablea. Using the interest rate formula, r = (FV/PV)1/n – 1b. Using the time value of money keys or function from a calculator orspreadsheet.Fill in the number of periods for the following table.a. Using the waiting period formula, n = ln(FV/PV) / ln(1+r).b. Using the time value of money keys or function from a calculator orspreadsheet.In the chapter text, we dealt exclusively with a single lump sum, but often we may be looking at several lump-sum values simultaneously. Let’s consider the retirement plan of a couple. Currently, the couple has four ...If you increase the number of payments on an amortized loan, does the payment increase or decrease? Why or why not?Fill in the missing annuity in the following table for an ordinary annuitystream.
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https://www.jagranjosh.com/articles/wbjee-2016-solved-mathematics-question-paper-part-2-1476878611-1
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math
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WBJEE is state level engineering exam held in West Bengal. It also conducts state level engineering entrance examination. The Mathematics section of this paper contains 75 multiple choice questions. Only one of the four options is correct. There is also one-fourth negative marking for each incorrect response. Find WBJEE Solved Mathematics Question Paper 2016. This solved paper will help the students in their final level of preparation. It will help the students to understand the pattern and difficulty level of the examination. It has also been seen that sometimes questions are repeated in WBJEE Exam. The students must go through the complete paper in order to understand the examination pattern and the level of questions asked in the examination.
Detailed solution of each question has been provided so that students do not lose their precious time in searching solutions of these questions.
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http://slideplayer.com/slide/2464467/
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math
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Published byJoslyn Whitford
Modified over 4 years ago
7.RP.3b Day 4 first day Objective: I can find simple interest.
Journal Sarah estimated she would need 5 pillows but she actually used 8. What is her percent error?
Review Ted guessed he would spend $63 at the store but actually spent $89. What was his percent error?
Quiz Angelina estimated she would buy $56 worth of groceries but she actually spent $45. What was her percent error?
Grade Homework - Evens Pg 162 - #2: $98.5 Pg 163 - #2: $1,080.00 #6: Sport City Pg 164 - #10: In Class Pg 165 - #16: $26.80 #18: $4.90
Notes When you put money in the bank you earn interest. Interest is money you are paid when you invest or money you pay when you borrow from someone else.
Notes Principal is the amount you borrowed or invested. We use the letter “P” for principal. John borrowed $2000 to buy a car.
Notes The interest rate is the percent that you pay because you borrowed the money. John paid a 3% interest rate on his car. We use “r” for rate.
Notes Time is how long you borrowed or invested your money. Time is in years. John is going to make payments on his car for 4 years. We use “t” for time.
Notes John borrowed $2000 at a 3% interest rate for 4 years.
Notes Interest = principal * rate * time I = prt
Notes John borrowed $2000 at a 3% interest rate for 4 years. I = prt
Notes Mrs. Ramirez is investing $400 in a savings account at a simple interest rate of 2%. She plans on investing the money for 6 months. How much interest will she make?
Notes Arnold puts $580 into a savings account. The account pays 3% interest. How much will he earn in 5 years?
Notes Jenny puts $1,560 in a savings account. The account will pay 2.5% simple interest. How much interest will she earn in 3 years?
Notes Mrs. Hanover borrowed $1,400 at a rate of 5.5% per year. How much simple interest will she pay if it takes 8 months to repay the loan?
Notes Howard charged $425 to his credit card. If it has an interest rate of 9.9%, how much will he pay after one month?
Homework Lesson 8 Skills Practice
Rounding 3 Round to the nearest whole number 3.46
Cost of credit 18-2.
Simple Interest Lesson
HW # 70 - p. 306 & 307 # 6-18 even AND Warm up Simplify
Simple and Compound Interest
Simple Interest. is money added onto the original amount saved (earned) or borrowed (charged). Simple Interest.
Simple Interest I =Prt I = Interest P = Principle r = rate t = time
Simple Interest Day 2 Formula I = PRT.
Simple Interest Math 8. Simple Interest Can be interest gained (earned) or interest paid Interest paid- costs you money * loans * credit cards Interest.
Simple Interest SWBAT find simple interest ; find the total amount earned or due; find the rate of interest; find the time that principal is left on deposit.
Calculating Simple Interest
Simple Interest Essential Skill: Explicitly Assess Information and Draw Conclusions.
Simple Interest 7th Grade Math.
Simple Interest Formula I = PRT.
Warm Up 1. What is 35 increased by 8%? 37.8 Course More Applications of Percents.
Simple Interest 21.6 Vocabulary Principal = the original amount of money that is saved or borrowed. Simple interest = a fixed percent of the principal.
Pre-Algebra 8-7 More Applications of Percents Warm-up Pink handout #11-14 Turn in pink handout.
Notes 31 Simple Interest 6-6.
More Applications of Percents
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
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http://supermathman.com/vocabulary/p.html
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math
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Parallel lines Lines in the same plane that do not intersect.
planes Two or more planes
that will never intersect
quadrilateral with both pairs of
opposite sides parallel.
Percent A ratio
of a number to 100, shown by the symbol %.
Percent of change The
amount of change divided by the original amount.
number that results from taking a percent of another number.
square A number whose
square root is an integer.
The distance around a
An arrangement of a group of things in a particular order.
bisector The line
perpendicular to a line segment which divides the line segment into two
lines Two lines that
intersect to form four right angles.
The ratio of the circumference of a circle to its diameter
A picture graph
value The value of the
position of a digit in a numeral
A flat surface extending
infinitely in all directions.
figure A geometric figure
all of whose points are in one plane
The simplest figure in geometry, representing an exact
location. A point has no dimensions or
has only a position or location. The
idea of a point is represented by a dot and is usually named by a capital letter
A closed plane figure
made up of line segments.
figure formed of polygonal parts of planes.
A sum of terms involving
nonnegative integer powers of a variable.
The product of equal factors
The smallest unit of measure used when measuring an object
factorization Factoring a composite number into prime numbers
number A whole number greater than I that has only two whole number factors,
itself and .
An amount of money on which interest is paid.
A polyhedron that has two
parallel, congruent faces called bases. The
other faces are parallelograms.
The ratio of the number of
outcomes favoring an event to the total number of possible outcomes.
The answer to a multiplication problem
fraction A positive fraction whose numerator is less than its denominator,
or the opposite of such a fraction.
of one for division For each number, the quotient of the number divided by
one is the number.
for each number
of one for multiplication For each number, the product of the number and one
is the number.
for each number
of zero for addition For each number, the sum of the number and zero is the
of zero for multiplication For each number, the product of the number and
zero is zero. Or, f
An equation stating that
two ratios are equal.
A device used to measure
A polyhedron that has a
polygonal base and three or more triangular faces.
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https://en.m.wikisource.org/wiki/Page:EB1911_-_Volume_05.djvu/15
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consideration. The most convenient arrangement on the decimal system for purposes of calibration is to have the units, tens, hundreds, &c., arranged in groups of four adjusted in the proportion of the numbers 1, 2, 3, 4. The relative values of the weights in each group of four can then be determined by substitution independently of the others, and the total of each group of four, making ten times the unit of the group, can be compared with the smallest weight in the group above. This gives a sufficient number of equations to determine the errors of all the weights by the method of substitution in a very simple manner. A number of other equations can be obtained by combining the different groups in other ways, and the whole system of equations may then be solved by the method of least squares; but the equations so obtained are not all of equal value, and it may be doubted whether any real advantage is gained in many cases by the multiplication of comparisons, since it is not possible in this manner to eliminate constant errors or personal equation, which are generally aggravated by prolonging the observations. A common arrangement of the weights in each group on the decimal system is 5, 2, 1, 1, or 5, 2, 2, 1. These do not admit of the independent calibration of each group by substitution. The arrangement 5, 2, 1, 1, 1, or 5, 2, 2, 1, 1, permits independent calibration, but involves a larger number of weights and observations than the 1, 2, 3, 4, grouping. The arrangement of ten equal weights in each group, which is adopted in “dial” resistance-boxes, and in some forms of chemical balances where the weights are mechanically applied by turning a handle, presents great advantages in point of quickness of manipulation and ease of numeration, but the complete calibration of such an arrangement is tedious, and in the case of a resistance-box it is difficult to make the necessary connexions. In all cases where the same total can be made up in a variety of ways, it is necessary in accurate work to make sure that the same weights are always used for a given combination, or else to record the actual weights used on each occasion. In many investigations where time enters as one of the factors, this is a serious drawback, and it is better to avoid the more complicated arrangements. The accurate adjustment of a set of weights is so simple a matter that it is often possible to neglect the errors of a well-made set, and no calibration is of any value without the most scrupulous attention to details of manipulation, and particularly to the correction for the air displaced in comparing weights of different materials. Electrical resistances are much more difficult to adjust owing to the change of resistance with temperature, and the calibration of a resistance-box can seldom be neglected on account of the changes of resistance which are liable to occur after adjustment from imperfect annealing. It is also necessary to remember that the order of accuracy required, and the actual values of the smaller resistances, depend to some extent on the method of connexion, and that the box must be calibrated with due regard to the conditions under which it is to be used. Otherwise the method of procedure is much the same as in the case of a box of weights, but it is necessary to pay more attention to the constancy and uniformity of the temperature conditions of the observing-room.
Method of Equal Steps.—In calibrating a continuous scale divided into a number of divisions of equal length, such as a metre scale divided in millimetres, or a thermometer tube divided in degrees of temperature, or an electrical slide-wire, it is usual to proceed by a method of equal steps. The simplest method is that known as the method of Gay Lussac in the calibration of mercurial thermometers or tubes of small bore. It is essentially a method of substitution employing a column of mercury of constant volume as the gauge for comparing the capacities of different parts of the tube. A precisely similar method, employing a pair of microscopes at a fixed distance apart as a standard of length, is applicable to the calibration of a divided scale. The interval to be calibrated is divided into a whole number of equal steps or sections, the points of division at which the corrections are to be determined are called points of calibration.
Calibration of a Mercury Thermometer.—To facilitate description, we will take the case of a fine-bore tube, such as that of a thermometer, to be calibrated with a thread of mercury. The bore of such a tube will generally vary considerably even in the best standard instruments, the tubes of which have been specially drawn and selected. The correction for inequality of bore may amount to a quarter or half a degree, and is seldom less than a tenth. In ordinary chemical thermometers it is usual to make allowance for variations of bore in graduating the scale, but such instruments present discontinuities of division, and cannot be used for accurate work, in which a finely-divided scale of equal parts is essential. The calibration of a mercury thermometer intended for work of precision is best effected after it has been sealed. A thread of mercury of the desired length is separated from the column. The exact adjustment of the length of the thread requires a little manipulation. The thermometer is inverted and tapped to make the mercury run down to the top of the tube, thus collecting a trace of residual gas at the end of the bulb. By quickly reversing the thermometer the bubble passes to the neck of the bulb. If the instrument is again inverted and tapped, the thread will probably break off at the neck of the bulb, which should be previously cooled or warmed so as to obtain in this manner, if possible, a thread of the desired length. If the thread so obtained is too long or not accurate enough, it is removed to the other end of the tube, and the bulb further warmed till the mercury reaches some easily recognized division. At this point the broken thread is rejoined to the mercury column from the bulb, and a microscopic bubble of gas is condensed which generally suffices to determine the subsequent breaking of the mercury column at the same point of the tube. The bulb is then allowed to cool till the length of the thread above the point of separation is equal to the desired length, when a slight tap suffices to separate the thread. This method is difficult to work with short threads owing to deficient inertia, especially if the tube is very perfectly evacuated. A thread can always be separated by local heating with a small flame, but this is dangerous to the thermometer, it is difficult to adjust the thread exactly to the required length, and the mercury does not run easily past a point of the tube which has been locally heated in this manner.
Having separated a thread of the required length, the thermometer is mounted in a horizontal position on a suitable support, preferably with a screw adjustment in the direction of its length. By tilting or tapping the instrument the thread is brought into position corresponding to the steps of the calibration successively, and its length in each position is carefully observed with a pair of reading microscopes fixed at a suitable distance apart. Assuming that the temperature remains constant, the variations of length of the thread are inversely as the variations of cross-section of the tube. If the length of the thread is very nearly equal to one step, and if the tube is nearly uniform, the average of the observed lengths of the thread, taking all the steps throughout the interval, is equal to the length which the thread should have occupied in each position had the bore been uniform throughout and all the divisions equal. The error of each step is therefore found by subtracting the average length from the observed length in each position. Assuming that the ends of the interval itself are correct, the correction to be applied at any point of calibration to reduce the readings to a uniform tube and scale, is found by taking the sum of the errors of the steps up to the point considered with the sign reversed.
|No. of Step.||1||2||3||4||5||6||7||8||9||10|
|Ends of thread.||+.010||−.016||−.020||−.031||+.016||+.008||+.013||+.017||+.004||−.088|
|Error of step.||–17.6||–22.6||–6.6||+1.4||+16.4||+7.4||–9.6||+9.4||+6.4||+15.4|
In the preceding example of the method an interval of ten degrees is taken, divided into ten steps of 1° each. The distances of the ends of the thread from the nearest degree divisions are estimated by the aid of micrometers to the thousandth of a degree. The error of any one of these readings probably does not exceed half a thousandth, but they are given to the nearest thousandth only. The excess length of the thread in each position over the corresponding degree is obtained by subtracting the second reading from the first. Taking the average of the numbers in this line, the mean excess-length is −10.4 thousandths. The error of each step is found by subtracting this mean from each of the numbers in the previous line. Finally, the corrections at each degree are obtained by adding up the errors of the steps and changing the sign. The errors and corrections are given in thousandths of 1°.
Complete Calibration.—The simple method of Gay Lussac does very well for short intervals when the number of steps is not excessive, but it would not be satisfactory for a large range owing to the accumulation of small errors of estimation, and the variation of the personal equation. The observer might, for instance, consistently over-estimate the length of the thread in one half of the tube, and under-estimate it in the other. The errors near the middle of the range would probably be large. It is evident that the correction at the middle point of the interval could be much more accurately determined by using a thread equal to half the length of the interval. To minimize the effect of these errors of estimation, it is usual to employ threads of different lengths in calibrating the same interval, and to divide up the fundamental interval of the thermometer into a number of subsidiary sections for the purpose of calibration, each of these sections being treated as a step in the calibration of the fundamental interval. The most symmetrical method of calibrating a section, called by C. E. Guillaume a “Complete Calibration,” is to use threads of all possible lengths which are
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https://online.visual-paradigm.com/spreadsheet-editor/calculator/finance/gross-margin-calculator/
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math
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Gross Margin Calculator
Gross margin is the difference between revenue and cost of goods sold (COGS) divided by revenue. Gross margin is often expressed as a percentage. In other words, it is the sales revenue a company retains after incurring the direct costs associated with producing the goods it sells, and the services it provides.
Gross Margin Formula
Generally, Gross Margin is calculated as the selling price of an item, less the cost of goods sold (e.g. production or acquisition costs, not including indirect fixed costs like office expenses, rent, or administrative costs).
Gross profit margin = [ ( Revenue - Cost of goods sold ) / Revenue ] x 100
GOGS (Cost of Goods Sold) = Row Materials cost, Direct labor cost and Factory Rental expense (and etc.)
- Revenue = $500,
- Cost of goods sold = $200 and
- Revenue = $200
Gross margin (%) = [ ( $500 – $200 ) / $200 ] = 60% gross margin
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https://www.ambertheeducator.com/post/but-first-what-do-we-know-about-the-answer
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I apologize for the oversight. Here's the revised version without changing your words:
This simple question has made a huge difference in my classroom. It's like those seven words "What do we know about the answer?" helped my students realize how they should be thinking when solving a problem.
I always tell my students "Practice like a Mathematician using (some Mathematical Practice)." In this particular case, especially MP. 7 and MP. 8. I always tell them to ask themselves "Does My Answer Make Sense?" Many of my students listened, but some did not. In group collaboration or discourse AFTER solving problems, students would catch their mistake and agree that their answer "didn't make sense."
While reading the book "Beyond Invert and Multiply" prior to students solving a problem, they asked the students to think about what they knew about the answer. I knew I needed to apply that ASAP. At the time, I was building my students' conceptual understanding of fractions before our actual fraction lessons. I asked them what do we know about the answer in more of a scaling fractions way while adding fractions with unlike denominators. I loved the result.
Sooo...I decided to ask my students "What do we know about the answer?" after they completed their "Find Three Ways" and had gotten different answers with various strategies. I was so amazed at some things that they said. I also demonstrated how to be more specific about things I would know about the answer.
For example, in the problem 34 x 38 students would say:
1. I know my answer will have a 2 in the ones place because 8 x 4 = 32.
2. I know my answer will be more than 900 because 30 x 30 = 900.
One thing a few of my students would say is:
I know my answer will have a 9 in the highest place because 3 x 3 is 9. At that moment, I let students discourse about why starting in the front (highest place) might not be the best way to get to know something about the answer in multiplication or addition problems. They discussed how 4 x 8 equals 32, so the three tens needed to be bundled and added to the tens column.
This practice was so helpful; I actually turned it into a discourse routine. Getting students to apply their knowledge before actually working their problems was exactly what my students needed. I have personally seen so much improvement in my students just by simply asking the question "What do we know about the answer?"
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https://www.projecteuclid.org/euclid.ejp/1485831704
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math
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Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 8, 37 pp.
Uniform in time interacting particle approximations for nonlinear equations of Patlak-Keller-Segel type
We study a system of interacting diffusions that models chemotaxis of biological cells or microorganisms (referred to as particles) in a chemical field that is dynamically modified through the collective contributions from the particles. Such systems of reinforced diffusions have been widely studied and their hydrodynamic limits that are nonlinear non-local partial differential equations are usually referred to as Patlak-Keller-Segel (PKS) equations.
Solutions of the classical PKS equation may blow up in finite time and much of the PDE literature has been focused on understanding this blow-up phenomenon. In this work we study a modified form of the PKS equation that is natural for applications and for which global existence and uniqueness of solutions are easily seen to hold. Our focus here is instead on the study of the long time behavior through certain interacting particle systems.
Under the so-called “quasi-stationary hypothesis” on the chemical field, the limit PDE reduces to a parabolic-elliptic system that is closely related to granular media equations whose time asymptotic properties have been extensively studied probabilistically through certain Lyapunov functions [17, 4, 9]. The modified PKS equation studied in the current work is a parabolic-parabolic system for which analogous Lyapunov function constructions are not available. A key challenge in the analysis is that the associated interacting particle system is not a Markov process as the interaction term depends on the whole history of the empirical measure.
We establish, under suitable conditions, uniform in time convergence of the empirical measure of particle states to the solution of the PDE. We also provide uniform in time exponential concentration bounds for rate of the above convergence under additional integrability conditions. Finally, we introduce an Euler discretization scheme for the simulation of the interacting particle system and give error bounds that show that the scheme converges uniformly in time and in the size of the particle system as the discretization parameter approaches zero.
Electron. J. Probab., Volume 22 (2017), paper no. 8, 37 pp.
Received: 24 July 2016
Accepted: 8 January 2017
First available in Project Euclid: 31 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60H30: Applications of stochastic analysis (to PDE, etc.) 60H35: Computational methods for stochastic equations [See also 65C30] 60K40: Other physical applications of random processes 60F05: Central limit and other weak theorems
weakly interacting particle systems uniform propagation of chaos McKean-Vlasov equations kinetic equations chemotaxis reinforced diffusions Patlak-Keller-Segel equations granular media equations uniform exponential concentration bounds long time behavior uniform in time Euler approximations
Budhiraja, Amarjit; Fan, Wai-Tong Louis. Uniform in time interacting particle approximations for nonlinear equations of Patlak-Keller-Segel type. Electron. J. Probab. 22 (2017), paper no. 8, 37 pp. doi:10.1214/17-EJP25. https://projecteuclid.org/euclid.ejp/1485831704
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http://www.wjcl.com/article/officials-us-army-soldier-from-south-carolina-dies-in-iraq/939314
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FORT DRUM, N.Y. - The U.S. Army says a soldier from South Carolina has died during a non-combat incident at a military facility in Iraq. \n \n\t \n \n\tA spokeswoman for the Army says 19-year-old Pvt. Christopher Castaneda died Thursday at the Al Asad Air Base in Iraq. \n \n\t \n \n\tSpokeswoman Kathleen Young said in a statement Friday that Castaneda died in a "non-combat related incident," but provided no further details. The Army did not immediately respond to a request for additional information. \n \n\t \n \n\tOfficials said Castaneda was from Fripp Island, South Carolina. He was an infantryman who joined the Army in January. \n \n\t \n \n\tHe was stationed at Fort Drum in New York before his troop deployed to Iraq in August. \n \n\t \n \n\tThe Army says he has been posthumously awarded the Army Achievement Medal.
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https://www.dr.library.brocku.ca/handle/10464/2881/browse?type=subject&value=Particle+swarm+optimization
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Browsing M.Sc. Computer Science by Subject "Particle swarm optimization"
Now showing items 1-1 of 1
Characterizing Dynamic Optimization Benchmarks for the Comparison of Multi-Modal Tracking Algorithms Population-based metaheuristics, such as particle swarm optimization (PSO), have been employed to solve many real-world optimization problems. Although it is of- ten sufficient to find a single solution to these problems, ...
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https://community.bt.com/
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Search the community.....
If someone has provided an answer to your question or resolved the problem you had, please mark that post as the solution. This way, other customers who may have the same question will be able to find the answer. Find out more here, Accepted Solutions
BTCare Community Newsletter Issue 17 is now available
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https://www.taylorfrancis.com/chapters/mono/10.4324/9781351288965-17/statistical-inference-travis-hirschi?context=ubx&refId=4b0b6fa7-b743-4740-b188-f367d42145b7
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The idea of statistical significance is meaningless unless some random phenomenon is involved. In many instances in delinquency research, however, there is no obvious source of randomness. William W. Wattenberg and James Balistrieri justify their use of chi-square tests with the statement that these tests "establish the degree of statistical reliability with which the null hypothesis could be rejected." Some statisticians would extend the logic of drawing a sample from a finite, existing population to assuming that a sample drawn has come by a random process from an infinite hypothetical universe. Properly conducted, the replications are vital in the task of inductive inference, the formulation and testing of general propositions from particular sets of data. The use of statistical tests of signficance was considered justified as 1952 is a sample of years and San Diego a sample of cities which might have been used.
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https://downloads.zdnet.com/product/20417-75448096/
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Natty Scientific Calculator is an original scientific calculator. Using an advance mathematical parser (JEP), it is able to calculate mathematical equations very accurately. What makes this calculator different is its simplicity. It is much easier to use than its competitors and any input can immediately be converted to a graph.
Natty Scientific Calculator features:
Scientific and engineering calculations.
Complex numbers can be inserted and stored (e.g. (radians&angle) OR (real+imaginary)).
Easy store and recall.
Definite Integration function (e.g. I(1,5,sin(x)+2))
Differentiation function (e.g. D(3,cos(x^2)))
y(x) graphing function.
polar graphing function.
parametric graphing function.
||Free to try
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https://link.springer.com/chapter/10.1007/978-1-4684-6694-2_7
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Evolution of Grouping Patterns
In Chapter 2, I argued that primate societies should be viewed as multilayered sets of coalitions based on relationships that differ in intensity, character and function. The most obvious and perhaps important respect in which these clusters of relationships differ from each other is, of course, their spatial localisation and temporal stability. Traditionally, observers have always recognised that animals of many species spend much of their time in the physical company of conspecifics rather than wandering alone. In this chapter, I shall concentrate mainly on the evolution of group-living.
KeywordsGroup Size Predation Risk Habitat Quality Capuchin Monkey Large Group Size
Unable to display preview. Download preview PDF.
- 1.Note that exactly the same set of curves will result if groups form for reasons of resource defence: the point is only that some factor promotes the formation of large groups because lifetime reproductive output is greater in large groups. Several candidate principles can fill this role. Thus, although the interpretation of the curves will differ, the shape will remain substantially the same. I prefer predation as the explanation because the weight of evidence favours this hypothesis. Note also that we could not use the results of this analysis to test the predation-defence hypothesis, since both the resource-defence and the predation-defence hypotheses would yield the same results.Google Scholar
- 2.For graphical convenience, I have represented the optimum group size as lying at the intersection of the relevant cost and predation graphs. In fact, with graphs of these particular shapes, the optimum will generally lie slightly to the right of their intersection, but this will not make any difference to the conclusions we draw.Google Scholar
- 3.Because of the paucity of data in the outer arms, a curvilinear regression is heavily biased by the mass of data in the mid-range and so generates a nearly linear relationship between group size and rainfall. The slope of this relationship is not, however, significant: linear regression set by least squares gives a slope of b = −0.012 (r2 = 0.039, t29 = −0.643, p > 0.30 2-tailed). But this clearly ignores a very significant negative relationship over the mid-section within the range 500–1200 mm rainfall: slope b= −0.089 (r2 = 0.435, t21= −3.793, p < 0.01 2-tailed). An N-shaped curve of this kind is often the product of an interaction between two different curves: in this case, these could be an inverted-U-shaped curve and a positively increasing exponential curve, each reflecting the influence of a different environmental variable.Google Scholar
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https://brainmass.com/chemistry/chemical-measures-of-environmental-indicators/sedimentation-tank-bod-580920
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A town in Virginia has a population of 50,000 people. The average flow for each person is 100 gpd. If the design were to use a detention time of 6 hours, and a recirculation rate of 0.5, WAS concentration of 9,000 mg/l, an F/M Ratio of 0.4, and a reactor loading rate of 30 lbs of BOD / 1000 cu.ft. Assume the BOD concentration is 0.25 lbs/c/day and the sedimentation basin has a removal rate of 40% BOD reduction.
Question #1: BOD Load to the AST Tank
Question #2: Volume of the AST Tank in cubic feet
Question #3: Recirculation Flow Rate in MGD
Question #4 Sludge Age in hours
(See attached file for diagram)© BrainMass Inc. brainmass.com October 10, 2019, 7:25 am ad1c9bdddf
This solution offers guidelines on how to solve some numerical problems on waste water treatment, by showing the steps.
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https://vebewot.vetconnexx.com/rewriting-as-a-mixed-number-33237fx.html
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The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions. Mixed Numbers Calculator also referred to as Mixed Fractions: This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists.
So this is going to be equal to-- the easiest way I do it is you say, well, you divide 4 it 7. Let me do this in another color. And then what is our remainder? So you see that 4 goes into 7 one time, so you have one whole here, and then how much do you have left over? Well, you have 3 left over, and that comes from right over there.
That is the remainder when you divide 4 into 7. Now, it might seem a little bit like voodoo what I just did. But why does that make sense?
Why does that actually makes sense?
Copy and then paste it. Now I have 3 one-fourths. Now, I have 4 one-fourths. Now this is a whole, right? I have 4 one-fourths.
This is a whole. So let me start on another whole. So now I have 5. Now I have 6 one-fourths, and now I have 7 one-fourths. Now, what does this look like? I just kind of drew it for you. Now, what does this represent?
So let me write it this way. Hopefully that makes sense and hopefully you understand why it connects. Because you say, well, how many wholes do you have? So the number of wholes, or you can imagine, the number of whole pies. And then how many pieces do we have left over? So we have one whole pie and three pieces, which are each a fourth left over.How Disney's Coco movie helped one mom cope with the loss of her dad.
First, we will practice rewriting mixed numbers as improper fractions, and vice versa. To turn a mixed number into an improper fraction, you multiply the whole number by the denominator, then add the numerator.
Rules for Converting a Mixed Number to an Improper Fraction. 1. Multiply the denominator times the whole number and then add the numerator. This is the new numerator.
2. Write this number over the existing denominator. 3.
This is your new improper fraction. Fractions: Rewriting as Mixed Numbers. Home > Printable Resources > Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
Mixed numbers calculator to add, subtract, multiply and divide mixed numbers (mixed fractions), fractions and integers. Do math with mixed numbers and mixed fractions such as 1 1/2 or 3 5/8.
Gordon Training International This year we commemorate the th birthday of our Founder, Dr. Thomas Gordon (March 11, August 26, ).
He was .
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https://ecstasyshots.wordpress.com/tag/waves/
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But how do we, sitting on earth know how rapidly a planet like Mercury which is around 48 million miles away is rotating ?
This is a very interesting example of Doppler effect.
Radio waves are shot from the earth towards the surface of mercury, one side of the planet will be red shifted (since it is moving away from you) and the other will be blue shifted (since it is moving towards you).
By measuring this apparent change in frequency, we can find out how rapidly mercury is rotating.
Using this method we have found out that the rotation period of mercury is approximately 58.6 days.
Whenever you see physicists talking about light, you might have noticed they prefer to use wavelength of the light rather than it’s frequency.
This is not a slip of the tongue and there is a very simple reason to it.
It is convenient to measure the wavelength of light experimentally rather than its frequency.
Take the violet light of wavelength 400nm. If we calculate it’s frequency, it turns out to be:
Why is this a problem?
Can’t we measure 7.5 x 10^14 Hz directly ?* There is a theorem by Nyquist in signal processing which states that:
minimum rate at which a signal can be sampled without introducing
errors, is twice the highest frequency present in the signal.
This means that if you want to measure the frequency of light accurately then you need to be sampling at 2*(7.5 x 10^14) Hz in order to measure it and this is incredibly hard to achieve this instrumentally!
On the other hand, here is how easy it is to measure the wavelength of the light:
Measure the angle(theta) between the highest intensity (zero order) and say the ‘nth’ order. (see diagram above).
Use the following formula for the wavelength : **
where, d – distance between the slits (will be provided by manufacturer of diffraction slit), n – order of the slit, theta- from measurement.
And voila, you have the wavelength of the light. That’s how simple it is to get the wavelength of a source light. Since speed of light is a constant, the frequency of light is found out from the following relation:
In addition to this, you can also derive the energy of a photon using the relation:
And so on and so forth. All of these following from a simple diffraction experiment! That’s why calculating the wavelength of light is so crucial.
I saw someone working out with Battle Ropes the other day and this wonderful pattern emerged was absolutely fascinating. Of course, the waveforms are not purely sinusoidal but it helps us to understand why you see such patterns
Ripple tank experiments are probably one of the best ways to understand wave phenomenon. In this post lets explore the Interference phenomenon that leads to the distinct patterns formed in the Double Slit experiment.
When the two sources are in perfect sync ( there is no time delay between the two occurrences )
When the sources are not in perfect sync. ( there is a time delay between the two occurrences )
Pulse 1 : in phase , Pulse 2: out of phase ( Notice how the resultant pattern is a combination of the previous two patterns )
Pulse 1 and 2 – in phase ( Establishing Symmetry )
Pretty cool eh ?
I hope this post provided you with the intuition on how these interference patterns are formed.
The same analogy can be extended for higher/lower wavelengths as well.
Now, by using Capacitors and Inductors Hertz was able to alter the frequency of oscillation of this spark between the gap. These are known as L-C oscillations. ( Click here to know more on how they work )
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=34&t=16221
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2 posts • Page 1 of 1
Right now we have been talking about atomic orbitals, s, p, d, etc. In a couple chapters we will begin talking about molecular orbitals, which are just combinations of atomic orbitals. In a molecule you can have two (or more) different molecular orbitals with the same energy (degenerate). When each of the two orbitals are occupied by only one electron, you then have a diradical. You cannot pair them since they have the same spin (can't have electrons with all the same quantum numbers) and are in different orbitals to begin with. Similarly, we can think of Hund's rule where we singly occupy atomic orbitals rather than doubly occupying them as we fill them because we have to consider electron-electron repulsion.
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https://www.physicsforums.com/threads/two-charges-and-electric-field.791312/
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Two charged particles are located on the x axis. The first is a charge +Q at x= -a. The second is an unknown charge located at x= +3a. The net electric field these charges produce at the origin has a magnitude of 2kQ/a^2. Explain how many values are possible for the unknown charge and find the possible values.
The Attempt at a Solution
I got the right answer, I'm just not sure if my thinking is right, because I kind of ignored the way the electric is facing. First of all I assumed q is negative and got 2kQ/a^2=kQ/a^2-k1/9a^2 based on the attraction of q to Q. That turns out to be q=-9Q. Then I did the same thing for when q is positive and got 2Qk/a^2=qk/9a^2 - kQ/a^2, again based on the attraction of q and Q. That turns out to q=27Q, which are the right answer. Is this a valid way of doing it or am I thinking of it wrong?
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https://brainmass.com/physics/velocity-time-graphs/velocity-vs-time-and-acceleration-vs-time-205859
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math
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Need help with this problem on position and velocity. I'm given a graph of velocity vs. time, how do I draw the acceleration vs. time from these graph?(question 2) And then I am given acceleration vs. time and need to draw velocity vs. time from these graph (question 3). Please see attachment.© BrainMass Inc. brainmass.com December 24, 2021, 7:38 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
Let's start by defining the key terms:
• velocity is the rate at which an object changes its position
• acceleration is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.
Looking at the definitions you can see that velocity and acceleration are related and it is this connectivity which will allow you to develop graphs of acceleration vs time using velocity vs time graphs and vice versa. To think more about this connection consider a car moving with a constant velocity of +10 m/s. Even though the car is moving it is not accelerating. A car moving with a constant velocity has an acceleration of 0 m/s^2. Now consider a car moving with a changing velocity. A car with a changing velocity will have an acceleration.
Now let's think about what the graphs are telling us. To start with velocity vs time: the shape of a velocity versus time graph reveals pertinent information about an object's acceleration. A line sloping up from left to right tells us that the car has a positive velocity (is getting faster) and since the velocity is changing the object has an acceleration. If the velocity vs time line is horizontal then velocity is constant or not changing - and if velocity is not changing then acceleration is zero. If velocity is negative (slowing) the velocity vs time graph will have a line sloping down from left to right and acceleration will be negative. Acceleration is directly related to the slope of the line on the velocity vs time scale. To calculate acceleration from velocity find the slope of the line. To find slope divide rise (vertical difference) by run (horizontal difference).
Lets go through your first graph as an example:
There are four different sections to consider in this graph -
1) A positive velocity (+slope)
2) A constant velocity (horizontal line)
3) A negative velocity (-slope)
4) Another positive velocity (+slope)
For each change in velocity you need to calculate an acceleration by calculating the slope.
1) The first 1 second of the graph is a positive slope. In that second the velocity changes from 0 m/s to 0.5 m/s. To calculate slope use this equation: velocity time 2 - velocity time 1/time 2 - time 1 or in this case 0.5 - 0/1-0 (0.5 minus zero divided by one minus zero - * do the subtraction and then the division). So the slope is 0.5 and the acceleration is 0.5 m/s^2 (meters per second squared).
2) For the next second, time 1 second to 2 seconds, the line is horizontal which means a slope of zero and an acceleration of zero (or no acceleration)
3) For the next two seconds (time 2 sec to 4 sec) velocity changes from 0.5 m/s to -1m/s. So slope equals -1 - 0.5/4-2 which equals -0.75 m/s^2.
4) For the last two seconds (time 4 sec. to 6 secs.) velocity changes from 0 m/s to 1 m/s. So slope equals 1-0/6-4 or 0.5 m/s^2.
*Note that acceleration vs time graphs only have straight horizontal or vertical lines not diagonal.
To convert an acceleration vs time graph to a velocity vs time graph you need to examine the lines on the acceleration graph as they tell us the slope to draw on the velocity graph.
Let's look at your first acceleration graph as example.
In this graph there are five different rates of acceleration.
1) Time 0 to time 2 seconds, acceleration is zero so the velocity slope will be zero and velocity will be constant. Since your instructions say that velocity at time zero is 0 m/s then this velocity is maintained. Time 0 to time 2 velocity is 0 m/s.
2) Time 2 to time 3 seconds, acceleration is 1 m/s^2. So the velocity graph will have a positively line with slope 1. Remember slope is velocity 2 - velocity 1/time 2-time 1. To figure out velocity you need to do a bit of algebra (or just think about it as these values are rather simple). Plugging in the values we know 1 m/s^2 = v2-0/1, now solve for v2. v2 equals 1. So your line should be a diagonal from 0m/s at time 2 to 1 m/s at time 3.
3) Time 3 to time 4 seconds, acceleration is 0.5; velocity slope will be positive 0.5.
4) Time 4 to time 5 seconds, acceleration and velocity slope will be -0.5
5) Time 5 to time 6 seconds acceleration and velocity slope will be zero.
You may also find this website helpful: http://www.glenbrook.k12.il.us/gbssci/Phys/Class/1DKin/U1L4b.html© BrainMass Inc. brainmass.com December 24, 2021, 7:38 pm ad1c9bdddf>
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| 4,776 | 28 |
https://amp.doubtnut.com/question-answer/factorise-i-a4-b4-ii-p4-81-iii-x4-y-z4-iv-x4-x-z4-v-a2-2a2b2-b4-5252
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math
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Apne doubts clear karein ab Whatsapp (8 400 400 400) par bhi. Try it now.
Click Question to Get Free Answers
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Question From class 8 Chapter FACTORISATION
Latest Blog Post
Introduction of Factorisation
Factors of a monomial
Common factors of two or more monomials
Greatest common factor (gcf) or highest common factor (hcf) The greatest common factors of given monomials is the common factor having a greatest coefficient and highest power of the variables.
Factorization of algebraic expressions when a common monomial factor occurs in each term
Factorizations of algebraic expressions when a binomial is a common factor
Grouping of the terms of an algebraic expression may lead to its factorization.
Factorize each of the following expressions : (i)
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| 798 | 13 |
https://divxturka.com/2022/05/15/abstract-algebra-with-applications-in-two-volumes-rings-and-fields/
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math
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Abstract Algebra with Applications – In Two Volumes-Rings and Fields | 4.18 MB
English | 569 Pages
Title: Noncommutative Structures in Mathematics and Physics (NATO Science Series II: Mathematics, Physics and Chemistry, Volume 22) (NATO Science Series II: Mathematics, Physics and Chemistry, 22)
Author: Steven Duplij
A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.
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| 1,028 | 5 |
https://forum.aquaveo.com/tags/reverse%20direction/
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math
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Search the Community
Showing results for tags 'reverse direction'.
I have got three basic question: The angle in the angle of the nodestring in the status windows is measured from which axes? East an ccw does not fit and there is no descrition in the SMS manual...or I am not able to find it. The second question: the direction of the nodestring maybe reversed, but actually it is just reversing the arrows at both sides of the nodestring. The angle is not changed. But reversing the direction of creation, both angle and arrows are turned. In my understanding that would be actually reversing the direction. The last question: What function may the arrows
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CC-MAIN-2021-21
| 656 | 3 |
http://perplexus.info/show.php?pid=6044&cid=40454
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math
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You start a rumor by telling it to n people and each of them tells it to another n-1 people. If each of these people, in turn, tells the rumor to another n-2 people, and so forth with no person hearing the rumor from more than one source, find a closed-form expression (in terms of n) for the total number of people that have been told the rumor.
(In reply to computer aided solution (spoiler)
Sloane A007526 gives the equation as
a(n) = n(a(n-1)+1)
Posted by Dej Mar
on 2008-04-25 23:33:23
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| 490 | 6 |
https://thedisciplinedinvestor.com/blog/2012/06/10/europe-risk-not-as-bad-as-expected/
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math
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During the height of the EuroCrisis last year, the spreads and overall risk conditions in Europe were pronounced. However, after the LTRO and the backdoor bailout from the FED, that all changed.
Even with yields rising and worry about the overall EuroZone, it appears as though the liquidity risk has subsided somewhat. Hard to believe.
While there is still a great deal of apprehension, the fact remains that the money that was pushed into the system has provided some relief.
Below are the key metrics we look at. Who knows what are the real numbers if we did not have the $$$$$$$$$ pumped in…
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| 597 | 4 |
https://homework.zookal.com/questions-and-answers/a-package-of-mass-m-is-released-from-rest-at-595083165
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math
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Question: a package of mass m is released from rest at...
A package of mass m is released from rest at a warehouse loading dock and slides down the h = 2.4 m- high, frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2m, from the bottom of the chute.
Express your answer to two significant figures and include the appropriate units
A) Suppose the packages stick together. What is their common speed after the collision?
B) Suppose the collision between the packages is perfectly elastic. To what height does the package of mass m rebound?
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CC-MAIN-2021-25
| 626 | 5 |
https://vietlienminh.com/qa/quick-answer-is-college-algebra-hard.html
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math
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What is the hardest class in college
It shouldn’t surprise you that organic chemistry takes the No.
1 spot as the hardest college course.
This course is often referred to as the “pre-med killer” because it actually has caused many pre-med majors to switch their major..
Is college algebra harder than precalculus
Precalculus is not a topic itself, but a set of topics that you should know before taking Calculus. … However, college Algebra is much more complex than this basic algebra in precalculus. Generally, you enter college with the notion that algebra is related to the manipulation and solution of equations.
Is college hard or easy
In summary, college classes are definitely harder than high school classes: the topics are more complicated, the learning is more fast-paced, and the expectations for self-teaching are much higher. HOWEVER, college classes are not necessarily harder to do well in.
What is the most hated subject
mathA quarter of students (25.1%) said that they liked math, which ranked ahead of physical education and arts and crafts. On the other hand, math was also the most disliked subject at 24.0%, followed by Japanese and physical education.
What math comes after college algebra
Trigonometry, analytic geometry and pre-calculus.
Is college algebra easy
College Algebra, like any lower division math course is extremely easy… when you understand it. At this level there is no “easy” and there is no “hard”. There is math that you know (easy) and math that you have yet to learn (hard).
What is the easiest math class in college
The easiest would be Contemporary Mathematics. This is usually a survey class taken by students not majoring in any science. The hardest is usually thought to be Calculus I. This is the full on, trigonometry based calculus course intended for science and engineering majors.
Is college algebra harder than high school algebra
Yes. College classes move faster than high school classes, regardless of the content. However, if you did well in high school algebra, you probably can test out of at least 1 year of college algebra. “College Algebra” is also refered to as Algebra 2 in high schools.
Is Statistics harder than algebra 2
a fundamental course in statistics, then, generally, statistics is more difficult. … Algebra concepts are much easier to grasp, Stats concepts are harder to grasp but the work itself at an INTRO level stat class will be easier as most of it is just memorizing a bunch of formulas and plugging them in.
Is college math harder than high school
“College math” is a very vague term. I had been teaching a lot of “college algebra” classes at several local universities as adjuncts, and those typically are not harder high school (or even easier than some high-caliber high school). It’s sad but it’s true. … “College math” is a very vague term.
What is algebra 2 called in college
Algebra II, or intermediate algebra, has a prerequisite of Algebra I. Historically, intermediate algebra has been a high school level course, the minimum math requirement to enter the California State University.
Is it OK to get Bs in college
Getting straight A’s in college may look good on paper, but getting B’s while taking the time for professional and personal growth is just as valuable. While a 4.0 GPA may help achieve your career goals, employers will consider a number of factors, including character and experience with internships and activities.
Which is the most toughest subject in the world
Toughest Courses in the World ExplainedEngineering. Considered one of the toughest courses in the world, engineering students are required to have tactical skills, analytical skills, critical thinking, and problem-solving abilities. … Chartered Accountancy. … Medicine. … Pharmacy. … Architecture. … Law. … Psychology. … Aeronautics.More items…•
What high school math is equivalent to college algebra
In the US it is what they used to call Advanced Algebra, and Trigonometry. The latest I knew of name-wise was Algebra-Trigonometry combined. These are normally taught after algebra and geometry in the US. Is anything past algebra 1 really needed if you’re not working in a math field?
What level of math is college algebra
Entry-level college algebra courses help prepare students for upper-level math, science, business, computer and engineering classes.
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| 4,395 | 32 |
https://www.wyzant.com/resources/answers/281415/write_a_plan_to_prove_that_the_midpoins_of_the_sides_of_a_rhombus_determine_a_rectangle_using_coordinate_geometry
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math
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Write a plan to prove that the midpoins of the sides of a rhombus determine a rectangle using coordinate geometry.
Full Question: The coordinates for a rhombus are given (2a, 0), (0, 2b), (-2a, 0), (0,-2b). Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Be sure to include the formulas.
Image Description: The image looks like a rhombus. The very top vertex ( (0,2b), the left vertex ( (-2a, 0) ), the bottom vertex ( (0,-2b, the right vertex ( (2a,0) ). There are four more vertexs on the figure. (-a,-b) is in the middle of (-2a, 0), (a,-b) is in the middle of (0,-2b) and (2a,0), (a, b) is in the middle of (0,2b) and (2a,0), and finally (-a,b) is in the middle of (0,2b) and (-2a,0)
I'm not really good with proofs, so I don't really know where to even start. So if someone could please help me answer this and go into detail so I understand what I'm doing, that would be awesome! Thank you to whoever helps.
If you need any more details about the image, please let me know
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| 1,046 | 5 |
https://www.mathselab.com/logical-reasoning-math-puzzles/
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math
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In a game of eight players lasting for 90 minutes, four reserves alternate equally with each player. This means that all players, including the reserves, are on the pitch for exactly the same length of time. For how long is each player on the pitch?
A. 60 minutes
B. 90 minutes
C. 65 minutes
D. 55 minutes
Total time for 8 players = 80 x 90 = 720 minutes.
However, as 12 people (8 + 4) are on the pitch for an equal length of time,
they are each on the pitch for 60 minutes (720 ÷ 12)
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https://www.cravencountryjamboree.com/lifehacks/what-is-the-critical-value-of-q-at-the-95-confidence-level/
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math
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What is the critical value of Q at the 95% confidence level?
|Critical Values for the Rejection of Quotient Q|
|Number of Observations||90% Confidence||95% Confidence|
How do you calculate q exp?
Answer: The corresponding Qexp value is: Qexp = (6.18 – 4.85) / (6.69 – 4.85) = 0.722. Qexp is greater than Qcrit value (=0.710, at CL:95% for N=5). Therefore we can reject 4.85 and being certain that the probability (p) of erroneous rejection of the null hypothesis (type 1 error) is less than 0.05.
Is Q test absolute value?
The test statistic, Qexp, is the defined as the absolute value of the ratio of the gap to range. When Qexp exceeds a critical value, we remove the suspect value from our data set. You should exercise caution when using a significance test for outliers because there is a chance you will reject a valid result.
Why Q test is important?
The Q test is designed to evaluate whether a questionable data point should be retained or discarded. In general, this test can be thought of as a comparison of the difference between the questionable number and the closest value in the set to the range of all numbers.
What is Q critical value?
For a sample size of 7 and an alpha level of 5%, the critical value is 0.568. Step 4: Compare the Q statistic from Step 2 with the Q critical value in Step 3. If the Q statistic is greater than the Q critical value, the point is an outlier. Qcritical value = 0.568.
What is the Q value for a 90% confidence for a data set with 4 data points?
|Number of values:||3||4|
What is the Q critical value?
Qcritical value = 0.568.
How does Q test work?
The basis of the Q-test is to compare the difference between the suspected outlier’s value and the value of the result nearest to it (the gap) to the difference between the suspected outlier’s value and the value of the result furthest from it the range).
What is the F test used for?
ANOVA uses the F-test to determine whether the variability between group means is larger than the variability of the observations within the groups. If that ratio is sufficiently large, you can conclude that not all the means are equal.
What is Tukey’s Q?
Tukey’s range test, also known as Tukey’s test, Tukey method, Tukey’s honest significance test, or Tukey’s HSD (honestly significant difference) test, is a single-step multiple comparison procedure and statistical test. It can be used to find means that are significantly different from each other.
How do you find the deviation from the mean?
Steps to Calculate the Mean Deviation:
- Calculate the mean, median or mode of the series.
- Calculate the deviations from the Mean, median or mode and ignore the minus signs.
- Multiply the deviations with the frequency.
- Sum up all the deviations.
- Apply the formula.
What is the critical value for a 95% confidence interval?
In the TV-watching survey, there are more than 30 observations and the data follow an approximately normal distribution (bell curve), so we can use the z -distribution for our test statistics. For a two-tailed 95% confidence interval, the alpha value is 0.025, and the corresponding critical value is 1.96.
What is the critical value for Dixon’s Q test?
Let’s consider the following sample consisting of 5 observations: First, we sort it in ascending order: 0.002, 0.135, 0.142, 0.153, 0.175 Now, we look up the critical value for n=5 for a confidence level 95% in the Q-table =≥ 0.71
What should be the confidence level of a statistical test?
Your desired confidence level is usually one minus the alpha ( a ) value you used in your statistical test: So if you use an alpha value of p < 0.05 for statistical significance, then your confidence level would be 1 − 0.05 = 0.95, or 95%.
Which is not an outlier in the Q test?
However, at 95% confidence, Q = 0.455 < 0.466 = Qtable 0.167 is not considered an outlier. McBane notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r10 or Q version that is intended to eliminate a single outlier.
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https://class10notes.perfect24u.com/sindh-class-10-physics-notes-cha-11-heat/
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math
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The best top free and high-quality pdf download notes for Sindh and Karachi chapter 11 heat MCQs, short long question answers, and numerical problems.
Physics Notes Cha 11 Heat Pdf Download for Sindh board
Describe in detail the construction and working of Celsius and Fahrenheit scales of temperature.
There are basically three temperature scales which are Celsius, Fernand and Kelvin. Kelvin is used as a SI scale temperature. Temperature Celsius and Fernand scales are described below:
In) Celsius scale of temperature:
The temperature on this scale is measured in relation to a standard temperature which is called the “triple point” of water which is orbitally 273.16 kg (note: here defined as KLVIN). As a seriousness, this temperature is taken as 273K. At this temperature, all three states can be involved in the water equation (which is ice, water and water vapour). This temperature Celsius scale is called zero 0 ° C. Here stands for ° C degree Celsius. This is the low fixed point of the thermometer. The upper fixed point of this scale is the temperature of the steam at a pressure in an atmosphere which will be 100 ° C. The interval between these points is divided into 100 equal parts. Each part measures 1 ° C.
ii) Fernate scale of temperature:
The lower fixed point on this scale is the triple point of water (or the melting point of ice at a vapour pressure) which is marked as 32 ° F. The upper fixed point is the temperature of the water vapour or boiling point under pressure in an atmosphere. This temperature is marked as 212 ° F. The interval between these points is divided into 180 equal parts. Each part measures 1 ° F.
What are gas laws?
The laws which explain the behaviour of gases are called gas laws. There are following gas laws.
i) Boyle’s Law
ii) Charles’s Law
Read more: Physics Notes Cha 10 Properties Of Matter
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| 1,864 | 13 |
https://qualityessayheroes.com/economics-582/
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math
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is it correct?
Which of the following is NOTlikely to be an example of a product with an inelastic demand?
I chose Water. is it correct?
When the price of a pair of shoes is $80, 10 pairs are demanded. When the price of the pair of shoes is $60, 20 pairs are demanded. Using the initial value, the price elasticity of demand is ________ starting at a price of $80 and ________ starting at a price of $60.
I chose 3;2 is it correct?
Assume Sarah is a CPA who earns $85,000 a year and her favorite entertainment magazine costs her $15 a year. For her, the price elasticity of demand for the magazine is likely to be
None of these
I chose None of these. is it correct?
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| 665 | 8 |
https://www.borgia.com/geometry.html
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math
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2 semesters, 1 credit
Open to sophomores and juniors
Prerequisites: Minimum grade of C in 410 Algebra I and/or teacher approval
In Geometry, students will learn how geometric shapes relate to our world. They will develop logic and reasoning skills through writing two-column proofs. Students will study various topics such as congruent triangles, properties of parallel lines, polygons, similar triangles, Pythagorean theorem, right triangle trigonometry, transformations, and circles. A TI-84 graphing calculator is required for this class.
By the completion of this course, students will be able to…
- Correctly use the symbols, definitions, properties, postulates, and theorems of geometry in proofs and application problems.
- Write proofs based on valid assumptions and deductive logic using definitions, properties, postulates, and theorems.
- Apply the geometric concepts of congruence, similarity, parallelism, and equality to application problems.
- Demonstrate their understanding of the attributes of polygons and solids by correctly calculating areas, perimeters, surface areas, and volumes.
- Apply their knowledge of ratios to relationships among the parts of a triangle, specifically sine, cosine, and tangent.
- Create geometric diagrams, including triangles, parallel lines cut by a transversal, polygons, and circles.
- Find the sine, cosine, and tangent of an angle.
By the completion of this course, students will know…
- Basic defined and undefined terms such as distance, angles, congruent segments, congruent angles, types of triangles, conditional statements, postulates, and theorems
- The purpose of a two column proof and how to write one
- The principles of parallel lines and planes, perpendicular lines, skew lines, angles formed by two lines cut by a transversal, sum of angles in a triangle, exterior angle of triangle properties, types of polygons, and the sum of interior and exterior angles of polygons
- The principles of congruent triangles, medians, triangle centers, altitudes, angle, and segment bisectors in triangles
- The structure of parallelograms, rectangles, rhombuses, squares, trapezoids, and triangles
- The purpose of ratios, proportions and similar polygons as well as applications involving similar triangles
- Properties of right triangles, special right triangles, basic trigonometric ratios, and applications involving angles of elevation and depression
- Circle vocabulary and properties of angles and arcs in a circle
This course last updated on January 27, 2021, by the Math Department.
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| 2,549 | 22 |
https://www.downshireps.co.uk/5-min-crafts/
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math
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Let’s Get Creative!
While out walking make use of the array of natural products there are around to create some wonderful pieces of artwork!
Let’s make a measuring stick.
Find a straight stick and using a ruler measure 1cm lines along the stick. Colour each centimeter a different colour. Then see how many different natural objects you can measure.
What object is the longest? Which one is the shortest?
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| 408 | 5 |
https://www.jotform.com/answers/324755-Can-t-add-country-code-to-phone-number
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math
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- FHHFormsAsked on January 28, 2014 at 05:32 PM
When I click on the preferences for the phone number field I have added to my form and try to add the option for country code, the change will not save. When accessing the preferences from the icon next to the element almost no changes will save for that element. The only way that I have been able to change preferences to elements is from the top menu for preferences of the element. The problem here is that the country code option does not appear in the top menu.
- JotForm SupportTitusNAnswered on January 28, 2014 at 06:41 PM
Thank you for contacting us.
I checked your form:
Please check the form again, have the changes been effected?
When you experience this, try logging out then loggin back in, and attempt the changes again.
The browser caches some changes which may not be delivered to the form when saved.
Please let us know if this helped.
- FHHFormsAnswered on January 29, 2014 at 02:08 AM
This change has taken, thank you.
I do have some issue with the input on the phone number element. When I use the predefined triple box format for the phone number "country code" "area code" "Phone number" the fields are not properly formatted to limit characters entered into each field. A user could enter their whole number in any one of the boxes.
- JotForm Supportardy0689Answered on January 29, 2014 at 04:42 AM
Hello, you may use the "Input Mask" option and define the "Mask Value" to set the digit limit for your form users using # symbol.
In the example below, the structure is set to 3 digit for Country, 3 digit for Area and 4 Digit for phone number. However, this will merge the 3 separate textboxes into a single textbox.
Please let us know if you require further assistance. Thank you
- FHHFormsAnswered on January 29, 2014 at 12:20 PMArdy0689,
Thanx for the help. The fact that this would merge into one box is fine.
Can you respond back to me with what the input mask should look like for
international numbers. For US numbers I would simply have the following
(###)###-#### for international numbers what would this look like
(###)(###)###-####. I quess what I am saying is that I am not familiar with
the structure of international phone numbers.
- JotForm SupportTitusNAnswered on January 29, 2014 at 01:41 PM
The rules are quite simple: Use @ symbol to mask letters inputs, # for numbers and * for both.
So all your suggestions are correct as they are. :-)
Be sure to add some guidance text so that your form users would not be confused. Use the properties button to add the sub-label as shown above.
Does this help? Let us know
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864558.8/warc/CC-MAIN-20180521220041-20180522000041-00244.warc.gz
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CC-MAIN-2018-22
| 2,602 | 28 |
https://virtualnerd.com/texas-digits/tx-digits-grade-6/integers-and-rational-numbers
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math
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In this tutorial you'll see how you can think of absolute value in a very intuitive way. Let us know if you have any questions about it!
There are lots of different kind of numbers that you should know about, and that includes rational numbers. Check out the tutorial!
The real world has all sorts of math clues! See how to use math to represent real world situations by watching this tutorial:
You may know how to calculate the absolute value of a number, but what are you really finding? This tutorial uses a real world example to help you gain a better understanding of absolute value.
Plotting points on the coordinate plane is the foundation of graphing equations! But before you can graph equations, you should be very familiar with the coordinate plane. In this tutorial, you'll see how to identify the ordered pair of a point on the coordinate plane. Plus, see how to figure out which quadrant the point is in!
Plotting points on the coordinate plane is the foundation for graphing equations! Check out this tutorial to get some practice plotting points and identifying which quadrant each point is in.
Trying to figure out if a negative number is larger than another can be a little tricky. To make things easier, you could use a number line! This tutorial shows you how to use a number line to compare two negative numbers and determine which is larger.
A number line is a way we can visually represent numbers. This tutorial gives you a great introduction to the number line and shows you how to graph numbers on the number line in order to compare them. Check it out!
Ordering numbers from least to greatest? Are the numbers in different forms? To make comparing easier, convert all the numbers to decimals. Then, plot those decimals on a number line and compare them! This tutorial shows you how!
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817438.43/warc/CC-MAIN-20240419141145-20240419171145-00787.warc.gz
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CC-MAIN-2024-18
| 1,809 | 9 |
https://duniatechnos.me/education/what-is-a-whole-fraction.php
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math
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Fractions were invented long before decimal numbers, as a way of showing portions less First, multiply the whole number by the denominator of the fraction . See how each example is made up of a whole number and a proper fraction together? That is why it is called a mixed fraction (or mixed number). How is fraction as a part of a whole? We know, a fraction means a part. So, fraction is the part of a whole object. Thus, a fraction is the part of a collection or.
convert fraction to whole number
An improper fraction can also be written as a mixed number. Mixed numbers contain both a whole number and a proper fraction. Examples of mixed numbers . Since a whole number can be rewritten as itself divided by 1, normal fraction multiplication. Introduction to Fractions. What is a fraction? A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how.
The fractions above are similar since each one has a denominator of 4. Look at the Each of these fractions is an improper fraction, equal to one whole (1). We begin with a definition of what fractions are. A fraction simply tells us how many parts of a whole we have. You can recognize a fraction by the slash that is . Whole numbers are non-negative numbers that haven't been broken into smaller parts. Fractions express division from a whole number into.
Yes. But not any fraction. 5/8, for example, is if you write out its decimal expansion. However, if the denominator (number on the bottom of. A mixed number is a combination of a whole number and a fraction. For example, if you have two whole apples and one half apple, you could describe this as 2. There are two ways to add whole numbers and fractions. You can either express them as mixed numbers or as improper fractions.
The top number is the Numerator, it is the number of parts you have. The bottom number is the Denominator, it is the number of parts the whole is divided into. The denomination is the number of equal parts that would be required to make up the whole. In the fraction ¼, four parts make up the whole, and we have one of . Solution. Step 1. Multiply the denominator by the whole number 9 × 3 = Step 2. Add the answer from Step 1 to the numerator 27 + 5 = Step 3. When dividing a whole number by a fraction, you are finding how many groups of the fraction you can fit in the whole. The standard way of. One of mans earliest needs was the development of a system for counting; that is, describing the number of objects in a group. What is a Fraction? A fraction is a part of a whole number. Free online Mathematics lessons and tests. Glossary of Mathematics terms. Also, we will learn here to perform operations like multiplying, dividing, adding and subtracting fractions. Read the whole article to clear the concepts for this. How to compare fractions that have equal denominators. How do we change an improper fraction to a mixed number or a whole number? How do we change . Fraction Types: Proper Fractions, Improper Fractions, Mixed Fractions. Play the Practice Game 5 denominator says how many equal parts in the whole object. Product of a Unit Fraction and a Whole Number - A tutorial to learn maths in simple and easy steps along with word problems, worksheets, quizes and their.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145708.59/warc/CC-MAIN-20200222150029-20200222180029-00543.warc.gz
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CC-MAIN-2020-10
| 3,275 | 6 |
http://mathhelpforum.com/algebra/164340-rational-numbers-print.html
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math
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So yesterday, on math class, I solved a difficult task (a quadratic polynomial).
I solved it correctly, but at one point teacher asked me something I couldn't explain.
The task says: "The biggest value of the quadratic polynomial is 3/2
and one of its zeros is √3 - 1.
Determine the polynomial if it's coefficients are rational numbers."
The first zero was √3 - 1, and I knew the other one had to be -√3 - 1.
(I know it had to be its conjugate).
Teacher said that these are NOT complex numbers - so i can't conjugate anything.
Your teacher is wrong!
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122720.81/warc/CC-MAIN-20170423031202-00237-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 555 | 9 |
https://projecteuclid.org/journals/journal-of-the-mathematical-society-of-japan/volume-64/issue-1/Gromov-hyperbolicity-of-Denjoy-domains-with-hyperbolic-and-quasihyperbolic-metrics/10.2969/jmsj/06410247.full
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math
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We derive explicit and simple conditions which in many cases allow one to decide, whether or not a Denjoy domain endowed with the Poincaré or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. As a corollary, the main theorem allows us to deduce the non-hyperbolicity of any periodic Denjoy domain.
"Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics." J. Math. Soc. Japan 64 (1) 247 - 261, January, 2012. https://doi.org/10.2969/jmsj/06410247
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335190.45/warc/CC-MAIN-20220928082743-20220928112743-00267.warc.gz
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CC-MAIN-2022-40
| 534 | 2 |
https://ideas.repec.org/p/mpr/mprres/ed0498975f9b467b9858ee06560a447e.html
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math
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Why Have Divorce Rates Fallen? The Role of Women's Age at Marriage
Explores the extent to which the rise in age at marriage can explain the rapid decrease in divorce rates for cohorts marrying from 1980 to 2004.
Paper provided by Mathematica Policy Research in its series Mathematica Policy Research Reports with number ed0498975f9b467b9858ee06560a447e.
|Date of creation:||20 Dec 2011|
|Contact details of provider:|| Postal: Mathematica Policy Research P.O. Box 2393 Princeton, NJ 08543-2393 Attn: Communications|
Fax: (609) 799-0005
Web page: http://www.mathematica-mpr.com/
More information through EDIRC
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s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948519776.34/warc/CC-MAIN-20171212212152-20171212232152-00555.warc.gz
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CC-MAIN-2017-51
| 608 | 8 |
https://www.coursehero.com/file/p261h8t/Question-6-Go-to-the-grid-on-page-3-Put-a-dot-representing-a-data-point-at-the/
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math
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25%(4)1 out of 4 people found this document helpful
This preview shows page 5 out of 5 pages.
Question 6Go to the grid on page 3. Put a dot (representing a data point) at the intersection of 100% rock (x-axis) and 3.0 g/cm3(y-axis) to indicatea moon that is 100% rock. Likewise, put a dot at the intersection of 0% rock (x-axis) and 0.9 g/cm3to indicate a moon that is 100% ice.Plot the other points from the data table. Failure to plot ALL the points will result in points taken off. Draw a straight line from (0,0.9)and (100,3.0). USE A RULER. (Lines drawn without a ruler will result in loss of points.)Question 7Using the GRAPH on page 3, estimate the value of “% Rock” (the 4thand last column of table 1 on page 2). Write in the value of amoon’s percentage of rock (based on its density) in this table. To repeat: this value of each moon’s percentage of rock is read from thegraph. Note that a moon cannot be more than 100% rock (or ice).Question 9Beginning at the bottomof page 3 and continuing onto page 4 is a discussion of how to compare determining a moon’s percentage ofrock by two methods: graphical and algebraic. The moon chosen for the exercise is Callisto. From table 1 (top of page 2), you knowCallisto’s density—1.8 g/cm3—and have determined its percentage of rock (from the graph). Now, to determine Callisto’s percentageof rock algebraically, you use the first equation found just after the graph on page 3. However, this equation has two variables, whichmakes itawkward to work with. At the top of page 4, we have an equation with just one variable: “x.” But the equation given needssimplification. That is what you are to do in part (a): show the two steps needed to simplify the equation by writing them in the box. Inpart (b), youare going to solve the equation to determine Callisto’s percentage of rock. On the left side of the equation, you haveDmoon,which is 1.8 (you know that the moon is Callisto, and its density is found in table 1). The right side of the equation is the simplifiedversion worked out in part (a). Solve the equation for “x.” That will bethe percentage of rock of Callisto. Write that value into the blankspace for part (c). In part (d) compare the Callisto’s density determined graphically with the value just determined algebraically. Justplug the two numbers (graphical value and algebraic value) into the formula at the bottom of page 4 and calculate the answer.
We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00612.warc.gz
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CC-MAIN-2022-21
| 2,554 | 5 |
https://www.careervillage.org/users/104806/tiffany/
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math
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Tags on answered questions
I would like to know how many years are studying this career because I like it. #nurse
I am a wildly curious person about life as we all are but I think that one of the things that I am lacking is that I have no passion and that I don't have an interest. I also feel that I lack a strong foundation and I have no foundation when it comes to anything and I am not good at anything....
If you graduate college with a bsn do you still have to go to nursing school or can you take the nlcex
This is my question that I have please answer it #nurse
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710813.48/warc/CC-MAIN-20221201121601-20221201151601-00213.warc.gz
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CC-MAIN-2022-49
| 569 | 5 |
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