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https://sattakingtoday.com/mathsolver-819
|
math
|
Prealgebra homework help
There are a lot of Prealgebra homework help that are available online. We can solving math problem.
The Best Prealgebra homework help
Prealgebra homework help can help students to understand the material and improve their grades. Algebra can be a helpful tool for solving real-world problems. In many cases, algebraic equations can be used to model real-world situations. Once these equations are set up, they can be solved to find a solution that meets the given constraints. This process can be particularly useful when solving word problems. By taking the time to carefully read the problem and identify the relevant information, it is often possible to set up an equation that can be solved to find the desired answer. In some cases, multiple equations may need to be written and solved simultaneously. However, with a little practice, solving word problems using algebra can be a straightforward process.
A triple integral solver is a tool that can be used to solve integrals that have three variables. This tool can be used to find the volume of a certain object or region, as well as other properties such as surface area or moments. The triple integral solver is a powerful tool that can be used to solve a variety of problems.
This will help you stay organized and focused as you work through your problem. It also ensures that you don’t skip any steps along the way. When working with word problems, try to avoid unnecessary shortcuts. These could include using a calculator or making assumptions about the value of one variable based on another one. Instead, always make sure that you are solving for the right value in each case. Finally, remember that word problems should never be used as an opportunity to beat yourself up. They should instead be used as a chance to practice math skills that you already know. By doing this, you will not only improve your math skills but also build confidence in your abilities.
First, let's review the distributive property. The distributive property states that for any expression of the form a(b+c), we can write it as ab+ac. This is useful when solving expressions because it allows us to simplify the equation by breaking it down into smaller parts. For example, if we wanted to solve for x in the equation 4(x+3), we could first use the distributive property to rewrite it as 4x+12. Then, we could solve for x by isolating it on one side of the equation. In this case, we would subtract 12 from both sides of the equation, giving us 4x=12-12, or 4x=-12. Finally, we would divide both sides of the equation by 4 to solve for x, giving us x=-3. As you can see, the distributive property can be a helpful tool when solving expressions. Now let's look at an example of solving an expression with one unknown. Suppose we have the equation 3x+5=12. To solve for x, we would first move all of the terms containing x to one side of the equation and all of the other terms to the other side. In this case, we would subtract 5 from both sides and add 3 to both sides, giving us 3x=7. Finally, we would divide both sides by 3 to solve for x, giving us x=7/3 or x=2 1/3. As you can see, solving expressions can be fairly simple if you know how to use basic algebraic principles.
In addition, the website provides a forum for students to ask questions and receive help from other users. Whether you are looking for a way to improve your child's math skills or simply want to provide them with a fun and educational activity, web math is an excellent choice.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499801.40/warc/CC-MAIN-20230130034805-20230130064805-00691.warc.gz
|
CC-MAIN-2023-06
| 3,527 | 8 |
https://planetmath.org/sumsoftwosquares
|
math
|
sums of two squares
This was presented by Leonardo Fibonacci in 1225 (in Liber quadratorum), but was known also by Brahmagupta and already by Diophantus of Alexandria (III book of his Arithmetica).
The proof of the equation may utilize Gaussian integers as follows:
Note 1. The equation (1) is the special case
of Lagrange’s identity.
Note 2. Similarly as (1), one can derive the identity
Thus in most cases, we can get two different nontrivial sum forms (i.e. without a zero addend) for a given product of two sums of squares. For example, the product
attains the two forms and .
|Title||sums of two squares|
|Date of creation||2013-11-19 16:28:21|
|Last modified on||2013-11-19 16:28:21|
|Last modified by||pahio (2872)|
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243990584.33/warc/CC-MAIN-20210513080742-20210513110742-00594.warc.gz
|
CC-MAIN-2021-21
| 724 | 12 |
http://www.jetradar.co.nz/flights/Vilnius-VNO-to-Stockholm-STO/?dont_redirect_please=true&marker=direct
|
math
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Best airfares from Vilnius to StockholmJetradar compares airfares from Vilnius to Stockholm with hundreds of airlines (including Air China, Lufthansa, British Airways) and dozens of online travel agencies in one single place. We provide you with all the options to find the cheapest flights to Stockholm, you choose where to book. Also there you can find airlines special offers from Vilnius to Stockholm. The cheapest round-trip price found within the last week was NZ$50. The cheapest oneway price found within the last week was NZ$33.
Cheapest Flights from Vilnius to Stockholm
Airline One Way One Way / Round-Trip Round-Trip Air China NZ$4,477 Find Lufthansa NZ$199 NZ$299 British Airways NZ$518 NZ$447 Turkish Airlines NZ$179 NZ$333 KLM NZ$694 NZ$712
Airline One Way One Way / Round-Trip Round-Trip Air France NZ$1,128 Find Swiss International Air Lines NZ$1,138 Find Aeroflot NZ$533 NZ$268 Austrian Airlines NZ$293 NZ$369 Finnair NZ$226 NZ$233
Airline One Way One Way / Round-Trip Round-Trip Air Berlin NZ$1,476 NZ$3,589 Ryanair NZ$83 NZ$109 Scandinavian Airlines NZ$84 NZ$137 Norwegian Air NZ$134 NZ$86 Brussels Airlines NZ$289 NZ$294
Airline One Way One Way / Round-Trip Round-Trip Vueling NZ$435 NZ$518 LOT Polish Airlines NZ$112 NZ$181 Flybe NZ$230 NZ$237 Xiamen Airlines Find NZ$4,831 Norwegian Air International LTD. Find NZ$544
Flights from Vilnius to Stockholm
Travelling from Vilnius to Stockholm advices and facts
- The distance between Vilnius and Stockholm is 423 miles (or 681 kilometers).
- The shortest flight time is 1h 22m
- When you fly from Vilnius to Stockholm, don't forget about the time difference. The time in Stockholm is -1:00 from the Vilnius time. The current time in Stockholm is 22:52 and 23:52 in Vilnius. Check this again shortly before your flight.
- The currency exchange rate between Vilnius (VNO) and Stockholm (STO) is 1 LTL = 2.7263 SEK.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783396224.52/warc/CC-MAIN-20160624154956-00110-ip-10-164-35-72.ec2.internal.warc.gz
|
CC-MAIN-2016-26
| 1,881 | 12 |
https://www.kickaboutbisonfootball.com/forum/general-discussions/top-3-to-top-10-lists-which-are-best-greece-whatsapp-number-list
|
math
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The Hot Number Strategy simply states Greece WhatsApp Number List that the lottery numbers that have hit in the last 10 drawings must be somehow HOT numbers. HOT numbers being lottery numbers that you should play. Apparently, their recent activity makes them HOT. So Greece WhatsApp Number List they say. It is easy to see why many people fell for this pitch. But, the strategy begins to fall apart as soon as you ask some simple questions. The fallacy behind the Hot Number Strategy lies in the Greece WhatsApp Number List assumption. Do you see what the assumption is?
The assumption is that the best play list to use is the list of lottery numbers from the last 10 Greece WhatsApp Number List drawings. But, who says? Are we supposed to blindly accept that statement as truth? Where is the proof? A Healthy Lottery Strategy I can remember asking Greece WhatsApp Number List myself these very questions. And, asking these questions led directly to the critical question which was, 'If the winning numbers from the last 10 drawings aren't the best play list, then where do I find the best play Greece WhatsApp Number List list?'
As I worked the Greece WhatsApp Number List problem, I soon realized that a single lottery solution wouldn't be satisfactory. The solution had to be robust; one that would work for every lottery. The solution I was chasing also had to work for any size Greece WhatsApp Number List lottery, for 5 or 6 number lotteries and work over any period of the lotteries history. Basically, the solution needed to be universal. After many months of research and software development, a software program I created helped me find a solution. Lottery Cycles Surprisingly, the Hot Number Strategy is Greece WhatsApp Number List also a Cycle.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510520.98/warc/CC-MAIN-20230929154432-20230929184432-00696.warc.gz
|
CC-MAIN-2023-40
| 1,756 | 3 |
http://mathforum.org/kb/message.jspa?messageID=1956329
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math
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Developing computaion skills and learning number facts is a hot issue everywhere. I've found some success, both in terms of student achievement and administrative and parental support, for giving daily homework practice and weekly quizes using things like adding "combinations of 100". Here are some examples:
40 + 55 + 75 + 20 + 45 + 40 =
80 + 25 + 230 + 85 + 110 + 25 + 50 + 10 =
I give a few problems eaach night, with a small space to show how the kids "chunked" the numbers, then give a weekly quiz using the same or similar problems. This grew into the "mental math challenge" which was a class tournament. The kids loved this, and the parents were amazed that the kids could figure out the answers faster that they could using a calculator.
This type of calculation practice seems to me to be supportive of the philosophy of Investigations. I'd love to hear what other teachers have come up with. I hope this helps.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867254.84/warc/CC-MAIN-20180525235049-20180526015049-00351.warc.gz
|
CC-MAIN-2018-22
| 922 | 5 |
https://de.coursera.org/lecture/chemistry-1/2-04b-hydrogen-like-atom-of-flourine-xFFI9
|
math
|
As you read through this problem it seems kind of complicated, but I want to focus beginning with this information. This is giving us an equation. It tells us the amount of energy an electron has, if it's a hydrogen-like atom. Now, what do I mean hydrogen-like? To be hydrogen-like it needs to have only one electron in it. If it has only one electron in it, then we can use this equation. And this is the, similar to an equation we did see in our lecture, but it didn't have the Z term. Z is a nuclear charge. Now, if it's a hydrogen atom that's one. That's why we didn't see it. But let's look at this guy. This is florine. Florine has nine protons. So it's Z is equal to 9. So this could be how much energy as the number of protons in the nucleus increase. The amount of energy an electron is going to have as it is in its orbitals around that nucleus is going to increase as well. Okay, so let us consider having an electron, and this electron is sitting in the n equals 1. And it's only one electron and it's in its ground state. And let's determine the energy of that electron. Okay? And I want to put a little 1 here, saying the electron is sitting in the n equals 1 state. It is going to be negative Rydberg Constant, 2.18 times 10 to minus 18 joules. Z is going to be 9 squared. And, the electron is sitting in the one the first shell. So that's a 1 and that's squared. And when we multiply these values out. We're going to get the value of a negative 1.765 times 10 to the negative 16 joules. Oops, can't see that j. Now what does that mean? It's a negative number. Well the way the notation goes is the electron has been just removed from the atom. But it, it does not got any kinetic energy associated with, with it. It's just been pulled away and now it's no longer connected to the nucleus. That would be an energy of zero. And as it travels closer and closer to the nucleus, it gets a, a more and more negative number. Okay? So this electron is a negative value for it, is a negative 1.765 times 10 to the minus 16 joules. If I wanted to remove that electron from the nucleus, 'kay? That would be called its first ionization energy. Actually it wouldn't be its first ionization energy because I've already removed eight electrons. So this would be its ninth ionization energy. Removing it from there. I would have to supply exactly the amount of energy re, as that negative value is. So that is the ionization energy to remove the ninth electron from a Fluorine atom. So the negative number is associated with the electrons that are attached to or connected with an atom. And this is a value for the energy of the electron. But to remove it would require you to supply this much ema, energy in order to get it completely away from the nucleus. 'Kay. Now, we've got another one. Let's consider another scenario. So let's change colors for just a moment. Let's pick hm, how about a purple. Okay? Lets move this electron now into the n equals 4 state. Okay so we've promoted up, it is no longer sitting in the n equals 1. We now have an n equals 4. And we have an electron sitting right here. If we wanted to know the energy of that electron, we'd call n, with put a little 4 there. And would a negative 2.18 times 10 to the minus 18 Joules. This wouldn't change because that's the nuclear charge. What would change is I would be dividing it by 4 squared, okay? And when I do that, is again, it is a negative number. But it's a negative 1.655. No it's not, negative 1, when we multiply this out, negative 1.104 times 10 to the minus 17 joules. Now this is a less of a negative number. It's not quite as big a negative number as this. So it's sitting up here and it is a negative value, and if I wanted to figure out how much energy it required to remove that electron,. Okay, we would call it again it's the ninth electron but it's coming out of an excited state. So I would probably give it as 1.104 times 10 to the minus 17 joules. It's a positive value so we move it. So how much energy would it take to get it right disconnected from the atom. So now in red I know how much energy it takes to remove this electron. In purple, I know how much energy it takes to remove the electron from here. Now let's read what it's asking. What is the wavelength in nanometers of the emitted photon in a transition from the n equals 4 to the n equals 1 state? [NOISE]. Before we can determine the change in, or the wave length we need to know the energy of the photon. We need to know the change in energy of the electron. Let's use again, another color here. Let's, oops, what happened? Hm, let's choose [SOUND] on my screen. We're going to promote an electron up to the n equals 4 state and we're going to allow that to transition back down to the n equals 1 state. When it does that, it's going to emit a photon of light, mm 'kay? Now the energy of that photon of light will be equal to the change in energy of the electron. And that is going to be easily determined by subtracting red energy and purple energy. Okay? So change in energy is going to be 1.104 times 10 to the minus 17 minus 1.765 times 10 to the minus 16. And that's going to be equal to a negative 1.655, times 10 to the minus 16, and that's going to be the change in energy of the electron. We take the absolute value of that, that's what’s going to give us the energy of the photon. But what it wants to know is the wavelength of that light, of that photon. So the wavelength equals, and if we look back at previous problems that we've worked, I'll do it off to the side here. We know that E equals hc over lambda. So lambda equals hc over E. We can plug all of our values in. 6.626 times 10 to the minus 34 joules times seconds, times the speed of light, 3 times 10 to the 8 meters per second. Divided by that energy that we figured out for the energy of the photon, which is 1.655 times 10 to the minus 16 joules. Now that'll give it to me in meters, but it really wants it in nanometers. I'll go from meters to nanometers, 1 nanometer is 10 to the minus 9 meters and this will give me a value of 1.20 nanometers.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945182.12/warc/CC-MAIN-20230323163125-20230323193125-00172.warc.gz
|
CC-MAIN-2023-14
| 6,090 | 1 |
https://www.hackmath.net/en/math-problem/54641
|
math
|
Alisha needs 7 1/2 yards of fabric to make a quilt. She has one piece of fabric that is 1 1/2 yards and another piece of fabric that is 3 1/4 yards. How many more yards of fabric does she need to make a quilt?
Did you find an error or inaccuracy? Feel free to write us. Thank you!
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Joy has 3/4 yards of fabric. She cuts the fabric into pieces that are each 1/8 yard long. How many pieces of fabric does Joy have?
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A piece of bamboo is to 2 1/4 meter long. Jessie cuts 1 1/3 meter to be used for making some kites and another piece 3/4 meter long to be given to his friend. How long is the me remaining piece of bamboo?
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4 and 3/10 yards of red cloth. 3 and 1/10 yards of pink cloth and 9 and 2/10 yards of black cloth. How many meters of cloth did she buy in all?
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(a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to a mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate the follow
Alexandra made a rectangular quilt the measured 3 1/4. 2 3/4 feet in width. What is the area of the quilt in square feet? Write an equation to solve.
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Which of the following is equal to 4 and 2 over 3 divided by 3 and 1 over 2? A. 4 and 2 over 3 times 3 and 2 over 1 B. 14 over 3 times 2 over 7 C. 14 over 3 times 7 over 2 D. 42 over 3 times 2 over 31
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Jade was baking cupcakes for her class. She has 4 5/4 cups of flour. For one batch, she used 1 2/3 cups of flour. On another batch, she used 7/9 of a cup of flour. How much flour does Jade have left after making the two batches of cupcakes?
Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood. He uses 2 3/4 feet for the hull and 1 1/4 feet for a paddle. How much wood does he have left? Martin has feet of wood left.
Krishna bought 5 1/2 meters of ribbon from the market . She cut off a 2 3/4 m piece of ribbon from it and gave it to Sushima . What length of ribbon is left with her?
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Peter barman is making 8 gallons of Tropical trip punch. He has already poured in 1 3/4 gal of pineapple juice and 2 1/2 gal of orange juice. The only other ingredient us 7-Up. How much does 7-Up does Peter need?
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Hannah and Emily need to use 4 1/4 feet of ribbon to finish an art project. Hannah has 2 3/4 feet of ribbon and Emily has 1 3/4 feet of ribbon. How much ribbon will they have left over after they finish their art project?
- The pet
Ananya has a bunny. She bought 4 7/8 pounds of carrots. She fed her bunny 1 1/4 pounds of carrots the first week. She fed her bunny 5/6 pounds of carrots the second week. All together, how many pounds of carrots did she feed her bunny? 1. Draw a tape diag
Nelly’s mother also bought 3 1/3 pounds of strawberries to make strawberry smoothies. She estimates that she will need 1/9 of a pound of strawberries for each smoothie. How many smoothies can she make with the strawberries she bought?
Karina has 5 4/7 meters of cloth. She needs 3 1/6 meters of it in making a curtain for her window. How many meters of cloth were left to her after making the curtain?
- Simplify 7
Simplify. 7-1/3÷ 3-2/3 of 2+ 4-1/2÷ 2-1/4+ 1/2 solution and by step by step
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585183.47/warc/CC-MAIN-20211017210244-20211018000244-00133.warc.gz
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CC-MAIN-2021-43
| 3,944 | 34 |
https://us.vwr.com/cms/tech-article-fluid-fundamentals
|
math
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Fluids include liquids, gases, and mixtures of liquids, solids, and gases. For the purposes of this reference book, the terms fluid and liquid are both used to mean a pure liquid or a liquid mixed with gases or solids that acts essentially like a liquid in a pumping application.
Density or specific weight of a fluid is its weight per unit volume, often expressed in units of grams per cubic centimeter or pounds per cubic foot. The density of a fluid changes with temperature.
If weight is 36.36 kg (80 lb), density is 1.28 g/cm3 (80 lb/cu ft).
Specific gravity of a fluid is the ratio of its density to the density of water. Since it is a ratio, it has no units associated with it.
Specific gravity = 80 lb/62.4 lb or, Specific gravity = 1.282
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.22/warc/CC-MAIN-20230322082826-20230322112826-00782.warc.gz
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CC-MAIN-2023-14
| 746 | 5 |
http://www.softcns.com/top_software/mathematics-9-win_1.html
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math
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Best Sellers in Mathematics, For Win Pages: 1/2 Show: 24 Total: 41
A powerful statistical analysis, regression analysis and data mining tool
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Scientific/Financial/Geometry Calculator with Tape
Generate random numbers.
CalcSharp is .Net application that evaluates mathematical expressions.
Graph maker to create 2d, 2.5d and 3D function graphs and animations.
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Math tool for linear, nonlinear curve fitting and surface fitting.
Graphing, trend analysis and curve matching software.
Matrix calculator for matrix operation and matrix decomposition.
Fractal software to create Mandelbrot fractal, Julia fractal etc.
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697380733/warc/CC-MAIN-20130516094300-00022-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 1,662 | 29 |
http://xutermpaperttgq.dosshier.me/write-a-fraction-as-a-mixed-number.html
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math
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Video: converting decimals to mixed numbers we write 7 then, for our fraction, we look at how many spaces we have after the decimal point we have three. How to turn an improper fraction into a mixed number an improper fraction is a fraction with a larger top than bottom, like 5/2 mixed numbers are a whole number. Improper fraction to mixed number calculator converts given improper fraction to a mixed number (mixed fraction. Converting improper fractions to mixed fractions write down the whole number answer then write down any remainder above the denominator example. How to convert improper fractions into mixed numbers in math, improper fractions are fractions where the numerator (the top half) is a number that is bigger than or.
The concept of mixed numbers - free lesson to write a mixed number as a fraction just count the fractional parts count all the thirds you should get four thirds. How to change an improper fraction to a mixed number what is a fraction common fractions the number we write as 1 over 2. This is a fifth grade lesson about fractions and mixed numbers first, this lesson has some review exercises about mixed numbers then, we learn how to change mixed.
Note: mixed numbers and improper fractions can be positive or negative there a few simple steps to follow when writing a mixed number as an improper fraction. Write as a mixed number section 27 writing decimals as fractions 89 write the shaded part of the unit square as a decimal then write the decimal. Download video: rewriting improper fractions as mixed numbers write 7/4 as a mixed number so right now it's an improper fraction 7 is larger than 4.
Online calculator for converting mixed numbers to improper fractions this step-by-step online calculator will help you understand how to convert mixed numbers to. 1 sec 41 introduction to fractions and mixed numbers learning objectives: 1 identify the numerator and the denominator of a fraction 2 write a fraction to.
Calculator to convert mixed numbers to improper fractions, showing the work learn a three step method for changing mixed number fractions into improper fractions. To write an improper fraction as a whole number means to write the improper fraction as a mixed number. Convert mixed numbers and fractions to percents calculator to change mixed number to percentage converts to improper fractions then finds decimal and percent values.
Mixed numbers to fractions uses circle models to demonstrate how a number in mixed form can be renamed in fraction form the illustration below was made by mixed to. Improper fractions to mixed numbers, step by step, example for all free math videos visit. Mixed fractions (also called mixed numbers) 1 34 there are three types of fraction: mixed fractions or improper fractions write down the whole number answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514030.89/warc/CC-MAIN-20181021140037-20181021161537-00404.warc.gz
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CC-MAIN-2018-43
| 2,806 | 6 |
http://obarey.com/2V1Q913bm/tJ21221Dw/
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math
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Leaving about two to feat of walking space around a coffee table is generally a good rule of thumb. That ensures that you have plenty of room for the environment to flow naturally, while not isolating the piece in the center of a void.
In order to make a coffee table yourself, you will need some good coffee table plans. These can easily be found on many internet websites. Do be sure that you are getting plans from authorities on the matter of woodworking as this will ensure that you are getting good guidance.
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Once you decide to build your own coffee table the first thing you need to do find the plan that fits for your home. There are many places that you can find wooden table designs. You can find plans on the Internet. The nice thing about doing it that way is that you can find a large selection. In some cases you can even find videos of the exact table being built so you can get a good idea of how to do it. You can choose to get a book of designs, which gives you a greater variety, or just buy one plan at a time, depending on what works best for you.
The classic coffee table is a must for any home, and can describe an entire household with its style and level of distress. The recent fad of creating your own coffee table is one that really has resulted in a huge amount of blue prints for you to create your own. It’s as fun as it is different, and the options are incredible.
Whats Hot Today
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203326.34/warc/CC-MAIN-20190324043400-20190324065400-00384.warc.gz
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CC-MAIN-2019-13
| 1,861 | 6 |
https://www.hackmath.net/en/examples/7th-grade-(12y)?page_num=54
|
math
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Examples for 7th grade (seventh) - page 54
Jar with jam weighs 800 grams. Jam weighs three times as much as the empty glass. What is the weight of jam that is in the glass?
- Prism - eq triangle
Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
148 is the total number of employees. The conference was attended by 22 employees. How much is it in percent?
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16% of the unknown number is by 21 less than unknown number itself. Determine the natural unknown number.
Seven times of my age is 8 less than the largest two-digit number. How old I am?
Same number of tickets sold for 15 CZK, 20 CZK, 30 CZK and 40 CZK a total of CZK 13,230 on theatre performance. How many tickets were sold for this performance?
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Buses connections are started from bus stop on its regular circuit as follows: No. 27 bus every 27 minutes and No.18 every half hour. What time started this two bus lines run if the bus stop met at 10:15 am.?
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Plan has a scale of 1: 2500.Determine dimensions in centimeters which will have on plan field with a length of 310 meters and a width of 182.5 meters.
- Grass seeds
How many kg of grass seed is needed to be sowing a circular field with a diameter of 120 meters when the 1 m2 should be used 0.8 grams seeds?
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The ski club has 168 pupils and used lift with 60 seats, while students always follow the same sequence in filling seats. How many times while riding a ski lift skier sitting in the same seat as the first run?
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Mr. Happy planted 36.6 meters square gardens grass; It's a third of the garden more than half of the garden. What is square area of this garden?
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For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
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Determine the unknown number that is equal to a quarter of the fifth of number, which is by 152 more than unknown number.
- The percentages in practice
If every tenth apple on the tree is rotten it can be expressed by percentages: 10% of the apples on the tree is rotten. Tell percent using the following information: a. in June rained 6 days b, increase worker pay 500 euros to 50 euros c, grabbed 21 fro
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The first sales store passed the 1/3 and the second 2/5 of the total amount of goods.In third store passed the 2/3 rest of the goods. The remaining 40 kg of goods put into fourth store. How many kilograms of goods pass to a third store?
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Cat's school use a special numerical axis. The distance between the numbers 1 and 2 is 1 cm, the distance between the numbers 2 and 3 is 3 cm, between the numbers 3 and 4 is 5 cm and so on, the distance between the next pair of natural numbers is always in
- Type of triangle
How do I find the triangle type if the angle ratio is 2:3:7 ?
Four dwarfs would prepare firewood for Snow White in580 minutes. After an hour and a half they recruit friends so that finished preparing the wood for 280 minutes. How many dwarfs they recruited?
120 vehicles parking on the morning. Pasenger car is charged 20 CZK, 50 CZK per bus. The guard collected for parking 2640 CZK in total. How many cars and how many buses stood in the parking?
- Alarm clock
The old watchmaker has a special digital alarm in its collection that rings whenever the sum of digits of the alarm is equal to 21. Find out when the alarm clock will ring. What is their number? List all options ...
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https://blog.yacapaca.com/tag/analytics/page/3/
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math
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I threw this question into the 2014 Christmas quiz with no real expectation that anyone would get it. The (possibility of a) Technological Singularity is something every kid needs to grow up being aware of, so this was my contribution to building awareness.
But look! 40% got it! That is double the guess rate, so we can conclude that one student in 5 actually knew the answer.
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http://www.jstor.org/stable/2153965
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math
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A Global Lojasiewicz Inequality for Algebraic Varieties
Shanyu Ji, Janos Kollar and Bernard Shiffman
Transactions of the American Mathematical Society
Vol. 329, No. 2 (Feb., 1992), pp. 813-818
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2153965
Page Count: 6
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Let X be the locus of common zeros of polynomials f1, ..., fk in n complex variables. A global upper bound for the distance to X is given in the form of a Lojasiewicz inequality. The exponent in this inequality is bounded by dmin(n, k) where d = max(3, ° fi). The estimates are also valid over an algebraically closed field of any characteristic.
Transactions of the American Mathematical Society © 1992 American Mathematical Society
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https://wcedeportal.co.za/eresource/174566
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math
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Civil Technology Woodworking Gr. 10 T4 W4.
In this lesson, we will be covering various aspects of doors including:
• What is the purpose of doors?
• What materials do we use to construct doors?
• What alternate materials can we use to construct flush panel doors?
• What is the method of edging involved in the construction of doors?
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http://visitbulgaria.info/autozone-parts-diagram/
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Logician John Venn developed the Venn diagram in complement to Eulers concept. His diagram rules were more rigid than Eulers - each set must show its connection with all other sets within the union, even if no objects fall into this category. This is why Venn diagrams often only contain 2 or 3 sets, any more and the diagram can lose its symmetry and become overly complex. Venn made allowances for this by trading circles for ellipses and arcs, ensuring all connections are accounted for whilst maintaining the aesthetic of the diagram.
Usage for Venn diagrams has evolved somewhat since their inception. Both Euler and Venn diagrams were used to logically and visually frame a philosophical concept, taking phrases such as some of x is y, all of y is z and condensing that information into a diagram that can be summarized at a glance. They are used in, and indeed were formed as an extension of, set theory - a branch of mathematical logic that can describe objects relations through algebraic equation. Now the Venn diagram is so ubiquitous and well ingrained a concept that you can see its use far outside mathematical confines. The form is so recognizable that it can shown through mediums such as advertising or news broadcast and the meaning will immediately be understood. They are used extensively in teaching environments - their generic functionality can apply to any subject and focus on my facet of it. Whether creating a business presentation, collating marketing data, or just visualizing a strategic concept, the Venn diagram is a quick, functional, and effective way of exploring logical relationships within a context.
Euler diagrams are similar to Venn diagrams, in that both compare distinct sets using logical connections. Where they differ is that a Venn diagram is bound to show every possible intersection between sets, whether objects fall into that class or not; a Euler diagram only shows actually possible intersections within the given context. Sets can exist entirely within another, termed as a subset, or as a separate circle on the page without any connections - this is known as a disjoint. Furthering the example outlined previously, if a new set was introduced - birds - this would be shown as a circle entirely within the confines of the mammals set (but not overlapping sea life). A fourth set of trees would be a disjoint - a circle without any connections or intersections.
The structure of this humble diagram was formally developed by the mathematician John Venn, but its roots go back as far as the 13th Century, and includes many stages of evolution dictated by a number of noted logicians and philosophers. The earliest indications of similar diagram theory came from the writer Ramon Llull, whos initial work would later inspire the German polymath Leibnez. Leibnez was exploring early ideas regarding computational sciences and diagrammatic reasoning, using a style of diagram that would eventually be formalized by another famous mathematician. This was Leonhard Euler, the creator of the Euler diagram.
A Venn diagram, sometimes referred to as a set diagram, is a diagramming style used to show all the possible logical relations between a finite amount of sets. In mathematical terms, a set is a collection of distinct objects gathered together into a group, which can then itself be termed as a single object. Venn diagrams represent these objects on a page as circles or ellipses, and their placement in relation to each other describes the relationships between them. Commonly a Venn diagram will compare two sets with each other. In such a case, two circles will be used to represent the two sets, and they are placed on the page in such a way as that there is an overlap between them. This overlap, known as the intersection, represents the connection between sets - if for example the sets are mammals and sea life, then the intersection will be marine mammals, e.g. dolphins or whales. Each set is taken to contain every instance possible of its class; everything outside the union of sets (union is the term for the combined scope of all sets and intersections) is implicitly not any of those things - not a mammal, does not live underwater, etc.
Other Collections of Autozone Parts Diagram
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https://portalrecerca.uab.cat/en/publications/on-the-families-of-periodic-orbits-which-bifurcate-from-the-circu
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In this paper we deal with the circular Sitnikov problem as a subsystem of the three-dimensional circular restricted three-body problem. It has a first analytical part where by using elliptic functions we give the analytical expressions for the solutions of the circular Sitnikov problem and for the period function of its family of periodic orbits. We also analyze the qualitative and quantitative behavior of the period function. In the second numerical part, we study the linear stability of the family of periodic orbits of the Sitnikov problem, and of the families of periodic orbits of the three-dimensional circular restricted three-body problem which bifurcate from them; and we follow these bifurcated families until they end in families of periodic orbits of the planar circular restricted three-body problem. We compare our results with the previous ones of other authors on this problem. Finally, the characteristic curves of some bifurcated families obtained for the mass parameter close to 1/2 are also described. © 1994 Kluwer Academic Publishers.
- periodic orbits
- Sitnikov motions
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https://waqasghori.net/index.php/2022/05/19/gases/
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math
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Q.1. What is Boyle’s law of gases?
Ans. This law states, the volume of a given mass of a gas is inversely proportional to the pressure at constant temperature. Mathematics Boyle’s law can be expressed as:
V (When T and n are constant)
V = Or PV = K (When T and n are constant)
Where ‘k’ is proportionality constant. The value of k is different for the different amounts of the same gas.
Q.2. What are isotherms? What happens to the position s of isotherms when they are plotted at high temperature for a particular gas?
Ans. The curves obtained, when a graph is plotted between pressure and volume at constant temperature are called isotherms, ‘iso’ means same ‘therm’ means heat.
Isotherms go away from both the axes when they are plotted at high temperature for a particular gas, since the volume of the gas has increased at higher temperature.
Q.3. Why do we get a straight line when pressure exerted on a gas are plotted against inverse of volumes? This straight line changes its position in the graph by varying the temperature.
Ans. When the pressure exerted on a gas is plotted against I/V, we get a straight line because pressure and inverse of volume (I/V) are directly proportional to each other at constant temperature. This straight line changes its position by varying the temperature, because this straight line at higher temperature will be close to zero; which means when P is very close to zero, then the volume is so high that I/V is very close to zero;.
Q.4. The product of pressure and volume of a gas at constant temperature and number of moles is a constant quantity . why?
Ans. According to Boyle’s law, when the temperature and number of moles of a gas are constant, then the increase in pressure will decrease the volume in proportion to the increase, so that the product of pressure and volume remains constant (PV = K). by doubling the pressure the volume becomes half. Thus
P1V1 = P2V2 = P3V3 = K
Q.5. How will you explain that the value of the constant k in the equation PV depends upon (i) the temperature (ii) the quantity of a gas.
Ans. In Boyle’s law, the temperature and number of moles (quantity) of an ideal gas are kept constant, so that the value of the product PV remains constant. Now, if the temperature of the gas is increased, then the volume increase for the same quantity of the gas and thus the value of product PV increases.
When the quantity of gas is increased at the same temperature, then the volume of gas increases and thus the value of product PV increases. From these observations, it is clear that the value of the constant k in equation PV depends upon the temperature and the quantity of a gas.
Q.6. What is the Charles’s law? Which scale of temperature is used to verify V/T = K (P and n are constant)?
Ans. Charles’s law gives the relationship between gas volume and temperature. This law states, the volume of a given mass of a gas is directly proportional to the absolute temperature when the pressure is kept constant. Mathematically
V ∝ T Or V = kT (When P and n are constant)
Or = K (When P and n are constant)
Thus, doubling the absolute temperature, causes the gas volume of double. If the temperature is changed from T1 to T2, the volume changes from V1 to V2, then
The value of the constant, k, depends on the pressure and amount of the gas. Kelvin temperature scale is used to verify that V/T = K.
Q.7. What is absolute zero?
Ans. the hypothetical temperature, -273.16oC at which the volume of the gas would become zero is called absolute zero, and is taken as the zero point on the kelvin scale temperature. Of course, this temperature, -273.16 is never achieved because all gases liquefy or solidify before reaching this temperature. Thus real gases will liquefy or solidify while approaching absolute zero. For routine calculations, the value of absolute zero is taken as -273oC.
Q.8. A gas occupies 100dm3 at 283K. what will be its volume at -273oC at constant pressure?
Ans. All real gases liquefy or solidify before reaching this temperature, -273oC. it means that the gas is liquefied or solidified before reaching -273oC, so the volume of the gas cannot be predicted at -273oC at constant pressure.
Q.9. Justify that the volume of a given mass of a gas becomes theoretically zero at -273oC. or give the quantitative definition of Charles law.
Ans. The quantitative definition of Charles’s law is “ At constant temperature, the volume of a given mass of gas increase or decreases by 1/273 of its original volume at 0oC for every 1oC rise or fall In temperature” according to this definition, if the volume of the gas at 0oC is 273 cm3. Now if the temperature is decreased by 1oC, the volume of the gas decreases by x 273 cm3 or 1 cm3; the final volume is thus 273 cm3 – 1 cm3 = 272 cm3. At -273oC, the volume of the gas would become theoretically zero. The general equation to know the volumes of the gas at various temperature is
Vt = Vo (1 + )
When T = -273oC; then V -273oC = Vo (1 – ) = 0
Thus the volume of a give mass of a gas becomes theoretically zero at -273oC.
Q.10. What is Kelvin scale of temperature?
Ans. A scale of temperature at which -273.15oC, is taken as zero Kelvin is called Kelvin scale temperature. Zero on the Kelvin scale corresponds to -273oC. therefore K = 0oC + 273.15. the Kelvin scale, however, is the SI temperature scale and the SI unit of temperature is the Kelvin (K).
Q.11. Throw some light on the factor 1/273 in Charles’s law?
Ans. The factor 1/273 in Charles’s law shows that at constant pressure the volume of a given mass of a gas increases or decrease by 1/273 of its original volume at 0oC for every rise or fall in temperature respectively. The general equation to know the volumes of the gas at various temperatures is
Vt = Vo (1 + )
Where Vt is the volume of the gas at toC, Vo is the volume of the gas at 0oC and t is the temperature on the centigrade scales.
Q.12. Do you think that the volume of any quantity of a gas becomes zero at -273.16oC. is not against the law of conservation of mass? How do you deduce the idea of absolute zero from this information?
Ans. The volume occupied by a gas does not become zero at -273oC, because all the gases will liquefy before reaching this temperature -273oC. it is against the law of conservation of mass that the volume occupied by the gas becomes zero. This hypothetical temperature -273oC, at which the volume of a given mass of a gas becomes zero is called absolute zero.
Q.13. What is the general gas equation? Derive it?
Ans the equation which gives simultaneously the effect of changes of pressure and temperature on the volume of a given mass of a gas is known as the general gas equation or ideal gas equation. The general gas equation is derived by combining Boyle’s law, Charles’s law and Avogadro’s law.
According to Boyle’s law: V (when T and n are constant)
According to Charles’s law V T (when P and n are constant)
According to Avogadro’s law V n (at constant T and P)
If none of the variables are kept constant, then combining the above three relations, we get.
V Or V = R or PV = nRT
Where R is called the general gas constant and the equation, PV = nRT, is called general gas equation.
Q.14. How the value of the general gas constant ‘R’ can be derived with the help of Avogadro’s law?
Ans. According to Avogadro’s law, the volume of one mole of an ideal gas at STP (one atmospheric pressure and 273.16 K) is 22.414 dm3. Putting these values of P, T, V and n, in the general gas equation will give the value of R.
R = = = 0.0821 dm3 atm K-1 mol -1
Q.15. Calculate the value of R in SI units.
Ans. Using SI units of pressure and volume in the general gas equation, the value of R can Be calculated as follows. The SI units of pressure are Nm-2 and of volume is m3.
1 atm = 760 torr = 101325 Nm-2; V = 0.022414dm3 (1m3 = 1000 dm3)
T = 273.15 K; n = 1 mol
R = = = 8.3143 NmK-1 mole-1 = 8.3143 JK-1 mol-1
Note: 1Nm = 1J ; the units of R are expressed in energy K-1 mol-1. 1 erg = 10-7 Joule ; so R = 83.143 x 10-7 erg K-1 mol-1
Q.16. How will you calculate the density of an ideal gas from the general gas equation?
Ans. The density of an ideal gas can be calculated from the general gas equation by substitution the value of number of moles, n, terms of the mass, m, and the molar mass, M, of the gas.
PV = nRT = RT (n = )
Or PM = RT
PM = dRT (d = )
Or d =
Q.17. How the density of an ideal gas double by doubling the pressure or decreasing the temperature on Kevin scale by ½ ?
Ans. We Know that d=PM/RT
The density of an ideal gas is directly proportional to the pressure on the gas and is inversely proportional to the absolute temperature. Thus by doubling the pressure on the gas, the density becomes double. Similarly, when the temperature becomes one half, the density becomes double.
Q.18. How do you justify from general equation that increase in temperature or decrease of pressure decrease the density of the gas?
Ans. The equation for the density of a gas is d = PM/RT< which is derived from the general gas equation, PV = nRT . according to this equation, density is directly proportional to the pressure and is inversely proportional to the absolute temperature, therefore, increases of temperature of decrease of pressure decreases the density of the gas.
Q.19. What is Avogadro’s law of gases?
Ans. This law states, “equal volumes of all the ideal gases at the same temperature and pressure contain equal number of molecules”. Since equal number of moles of different ideal gases at the same temperature and pressure contain equal number of molecules, therefore, the number of moles on of any ideal gas is directly proportional to its volume, V. So
V ∝ n
One mole of an ideal gas at 273.16K and 1 atm pressure has a volume of 22.414dm3. One mole of a gas has Avogadro’s number of particles, so 22.414dm3 of various ideal gases will have Avogadro’s number of molecules, i.e. 6.02 x 1023.
Q.20. Do you think that 1 mole of H2 and 1 mole of NH3 at 0oC and one atm pressure will have Avogadro’s number of particles.
Ans. One mole of H2 of 0oC and atm pressure will have Avogadro’s number of particles, since H2 gas at 0oC and 1 atm pressure behaves like an ideal gas. Whereas, 1 mole of NH3 at 0oC and 1 atm pressure will not have Avogadro’s number of particles, because it does not behave like na ideal gas due to the presence of dipole interactions and hydrogen bonding among its molecules.
Q.21. Justify that 1cm3 of H2 an d1 cm3 of CH4 at STP will have same number of molecules. Although one molecule of CH4 is 8 times heavier than that of hydrogen.
Ans. According to Avogadro’s law, “Equal volumes of ideal gases at the same temperature and pressure contain equal number of molecules. Both H2 and CH4 is STP behave like ideal gases and both have equal volumes (1 Cm3 each), therefore, 1 cm3 of H2 and 1 cm3 of CH4 at STP will have same number of molecules. Although, one molecule of CH4 is 8 times heavier than that of H2 but this does not disturb the volume occupied, because molecules of the gases are widely separated from each other at because molecules of the gases are widely separated from each other at STP.
Q.22. State Dalton’s law of partial pressures. Gives its expression.
Ans. This law states, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of their individual partial pressure. Let Pt be the total pressure and P1, P2, P3, ……….. be the partial pressures of the gases in the mixture. Then
Pt = P1+ p2 + p3
Since each gas in the mixture behaves independently. So the general gas equation (PV = nRT) is applicable to the individual gases in the gaseous mixture. Let n1, n2, and n3 be the number of moles of each of the gas in the mixture and nt be the total number of gaseous mixture
(nt = n1 +n2+n3). Then
P1 = n1 ; p2 n2 ; p3 = n3
Pt = (n1 +n2+n3) = nt
We can relate the amount of a give gas in a mixture to its partial pressure by dividing the above equations.
The ratio n1/nt is called the mole ratio of gas 1, denoted Xt, then
Q.23. What is meant by partial pressure of gas?
Ans. The partial pressure of a gas in a mixture of gases is the pressure that it would exert on the walls of the container, if it were present all alone in the same volume under the same temperature.
Q.24. Explain that the process of respiration obeys the Dalton’s law of partial pressure.
Ans. The process of respiration depends upon the difference in partial pressures and is the application of Dalton’s law partial pressure. When human beings inhale air then oxygen moves into lungs as the partial pressure of oxygen in air (159 torr) is more than that of the partial pressure of oxygen in lungs (116 torr). CO2 produced during respiration moves out from the lungs into air, as the partial pressure of CO2 is more in the lungs than that in air. Thus, process of respiration obeys the Dalton’s law of partial pressure.
Q.25. Dalton’s law of partial pressures is only obeyed by those gases which do not have attractive forces among their molecules (ideal gases), explain it.
Ans. Gas pressure on a wall is due to molecules colliding with it . when a molecule about to collide with the wall, it is attracted away from the wall by attractive force of neighboring molecules (intermolecular forces). As a result, the pressure exerted by the gas would be less than that of an ideal gas. Therefore, gases having attractive forces among their molecules do not obey Dalton’s law of partial pressures, which is only obeyed by ideal gases.
Q.26. At higher altitudes, the pilots feel uncomfortable breathing. Why?
Ans. At higher altitudes, the pilots feel uncomfortable breathing because the partial pressure of oxygen in the unpressurizatoin cabin is low as compared to 159 torr, where one feels comfortable breathing.
Q.27. how will you calculate the partial pressure of dry gas which is collected over water?
Ans. When a gas is collected over water, it becomes moist. The pressure exerted by this moist gas is, therefore, sum of the partial pressures of the dry gas and that of water vapour. Mathematically,
Pmoist = ddry + P water vapour
Pmoist = ddry + aqueous tension
Pdry = Pmoist – aqueous tension
The partial pressure exerted by the water vapours is called aqueous tension.
Q.28. Differentiate between diffusion and effusion of gases?
Ans. The spontaneous mixing of the molecules of different gases by random motion and collisions to form homogeneous mixture is called gaseous diffusion. Th escape of gas molecules one by one without collisions through a pin hole in their container into an evacuated space is called effusion. The diffusion is the spread of one substance throughout a space or throughout second substances.
Q.29. What is Graham’s law of diffusion?
Ans. This law states that the rate of diffusion or effusion of a gas is inversely proportional to the spare root of its density at constant temperature and pressure.
Rate of diffusion (at constant T and P)
Rate of diffusion = or rate x = K
Let two gases 1 and 2, having rates of diffusion as r1 and r2 and densities as d1 and d2 respectively. Then according to Graham’s law of diffusion
r1 x = K
r2 x = K
Dividing the above two equations and rearranging
Since density of a given gas is directly proportional to its molecular mass. So, Graham’s law of diffusion can be written as
Where M1 and M2 are the molecular masses of gases:
Q.30. Lighter gases diffuse rapidly than heavier gases. Give reason.
Ans. Although the average kinetic energies of different gases are the same at the same temperature, but their molecular masses are different, so their velocities will also be different at the same temperature. The lighter gas molecules would have greater velocities and so they diffuse rapidly than heavier gas molecules.
Q.31. The rate of diffusion of NH3 is 1.5 times greater than HCl. Explain.
Ans. According to Graham’s law of diffusion, the rates of diffusion of gases are inversely proportional to the square roots of their molecular masses. The molecular mass of HCl is 36.5 amu and that of NH3 is 17 amu. Thus
This shows that the rate of diffusion of NH3 Is 1.5 times greater than HCl.
Q.32. What is kinetic equation for ideal gases?
Ans. R.J. Clausius deduced an expression for the pressure of an ideal gas from the basic assumptions of kinetic theory of gases in the form of an equation known as kinetic equation. According to kinetic molecular theory, the pressure of a gas is the result of collisions of molecules with the walls of the container. Due to these collisions, a force is exerted on the walls of the container. The force when divided by the area of the vessel gives force per unit area, which is called pressure. The kinetic equation is
Where P = pressure, V = volume, m = mass of one molecule of the gas, N = number of molecules of gas in the vessel and = mean square
Q.33. What is man square velocity .
Ans. It is the average of the squares of all the possible velocities of gas molecules. If there are n1 molecules with velocity c1, n2 molecules with velocity c2, and so on, then,
Here, n1 +n2 +n3 + ——— = N
Q.34. What is root mean square velocity, crms.
Ans. The root mean square velocity is defined as the under-root of the mean of the squares of the different velocities of all the N molecules of the gas.
The expression for the root mean square velocity deduced from the kinetic equation is
Crms = (M = molar mass of the gas)
Q.35. How will you derive Boyle’s law from kinetic gas equation?
Ans. According to the kinetic theory of gases, the kinetic energy of gas molecules is directly proportional to the absolute temperature of gas. Thus
T Or = kT (k is the proportionality constant)
According to the kinetic gas equation, PV
Multiplying the kinetic gas equation by , we get PV = ( ) =
But = kT
Hence PV = kT Or PV = kT
Since k is constant, so at constant temperature, PV is Constant, which is Boyle’s law.
Q.36. How will you derive Charles’s law from kinetic gas equation?
Ans. According to kinetic theory of gases, the kinetic energy of gas molecules, , is directly proportional to the absolute temperature of the gas. Thus
T Or = kT
We know. PV = , (kinetic equation)
Multiplying the kinetic equation by , we get ( ) = PV = kT (since = kT)
Or PV = kT Or V = T
Since k is constant, so at constant pressure, V T which is Charles’s law.
Q.37. Derive Avogadro’s law from kinetic theory of gas equation?
Ans. Consider equal volumes of two gases 1 and 2 under the same conditions of temperature and pressure, having molecules N1 and N2, masses m1 and m2 and mean square velocities respectively. Then the kinetic equation for two gases can be written as
PV = (Kinetic equation for gas 1)
PV = (Kinetic equation for gas 2)
Equalizing= PV = = PV = Or (1)
At the same temperature, the mean kinetic energies per molecule of both gases will be the same, so
= PV = Or (2)
Dividing equation (1) by Eq. (2) we get
N1 = N2
Thus equal volumes of all the gases at the same temperature and pressure contain equal number of molecules, which is Avogadro’s law.
Q.38. Derive Graham’s law of diffusion from kinetic theory of gases?
Ans. Applying the kinetic equation PV =
For 1 mole of an ideal gas, N = NA (Where NA is Avogadro’s number),
Hence PV = Or PV = (M = mNA = molecular mass of gas)
Or (Since = d, density of gas)
Since the root mean square velocity of the gas is directly proportional to the rate of diffusion of the gas. Thus r
At constant pressure, r , which is Graham’s law.
Q.39. Describe briefly the kinetic interpretation f temperature?
Ans. According to one fundamental postulate of kinetic theory, the absolute temperature of a gas is a measure of the average kinetic energy of its molecules. However, according to equation, Ek = 3RT/2NA, the kelvin (absolute) temperature of a gas is directly proportional to the average translational kinetic energy of its molecules. It means a change in temperature means change in the intensity of molecular motion. Thus at absolute zero of temperature the molecular motions cease. The absolute zero is unattainable, however, current attempts have resulted in temperature as low as 10-5K. in gases and liquids, absolute temperature is the measure of average translational kinetic energies of molecules, while in solids, it becomes a measure of vibrational kinetic energy.
Q.40. What two properties of gas molecules cause them to behave non-ideally?
Ans. The real (actual) volume of gas molecules and attractive forces between molecules cause gases to behave non-ideally.
Q.41. Under what conditions of temperature and pressures do gases usually behave non-ideally?
Ans. Non-ideal gas behaviors is observed at very high pressure and low temperatures.
Q.42. Give two causes for deviation of gases from ideality. Or what are faulty points in kinetic molecular theory of gases?
Ans. The deviation of real gases from ideality is due to the following two faulty assumptions.
- The actual volume of gas molecules is negligible as compared to the volume of the vessel.
- There are no forces of attraction among the molecules of a gas.
Real gas molecules, however, do have finite volumes, and they do attract one another.
Q.43. Why do real gases deviate from the ideal behavior at low temperature and pressure?
Ans. As the temperature of a gas is lowered, the average kinetic energy decreases and thus the attractive forces between the molecules become significant (dominant), and thus real gases deviate from the ideality at low temperature.
At high pressure, the gas molecules are pushed closer together and the volume of molecules themselves become significant relative to total volume occupied by the gas. So, collisions between molecules and attractive forces become significant. Thus at high pressure real gases deviate from ideal behaviors.
Q.44. Why gases do not settle?
Ans. According to the kinetic molecular theory of gases, the gas molecules are in a constant motion, they collide with one another and their collisions are perfectly elastic i.e. there is no gain or loss in energy during their collisions. Therefore, gases do not settle.
Q.45. Briefly describe the significance of the constants ‘a’ and ‘b’ in the van der Walls equation.
Ans. The van der walls constant ‘a’ is a measure of the intermolecular attractive forces. The van der Waals constant ‘b’ is a measure of actual volume occupied by a mole of gas molecules. The values of both ‘a’ and ‘b’ constants generally increase with an increase in mass of molecule and with an increase in the complexity of its structure. The units of ‘a’ is pressure (volume)2 mol-2, i.e., atm dm6 mol-2. Is SI units ‘a’ is expressed Nm-2 x (m3)2 mol-2 or Nm4mol-2, while b is a volume mol-1, i.e., dm3 mol-1.
Q.46. What is van der Waals equation of state?
Ans. Van der Waals recognized that for a real gas, the expression for an ideal gas, PV = nRT/V would have to be corrected for the two effects: the finite volume occupied by the gas molecules, and the attractive forces between the gas molecules. He introduced two constants ‘a’ and ‘b’ to make these corrections.
The volume is decreased by the factor nb, which accounts of the finite volume occupied by the gas molecules. The pressure is in turn decreased by the factor na/V2, which accounts for the attractive forces between the gas molecules. Correcting the pressure and volume terms in an ideal gas equation, we obtain van der Waals equation.
(P +n2a/V2 ) (V – nb) = nRT (Van der Waals equation)
Q.47. Pressure of NH3 gas at given conditions (say 20 atm pressure and room temperature) is less as calculated by van der Waals equation than that calculated by general gas equation. Explain.
Ans. NH3 is a polar molecule and attractive forces exist among its molecules. These attractive forces lessen the force with which the molecule hits the wall. As a result, the pressure is less than that of an ideal gas. Moreover. NH3 is a real gas, do have finite volume and , therefore, the less than the observed volume. Clearly, the ideal volume is less than the observed volume. Van der Waal’s introduced these two corrections in the ideal gas equation. Therefore, pressure of NH3 gas is less as calculated by van der Waal’s equation than that calculated by general gas equation.
Q.48. Water vapours do not behave ideally at 273K. explain.
Ans. Water vapours at 273oC have sufficient inter-molecular forces, because 273oC is below the critical temperature of H2O. therefore, water vapours do not behave ideally.
Q.49. SO2 is comparatively non-ideal at 273 K but behaves ideally at 327oC. Explain.
Ans. SO2 is non-ideal at 273K or 0oC, because this temperature is low and inter-molecular forces exist among SO2 molecules. While 327oC is very high temperature for SO2 gas and there are negligible intermolecular forces among gas molecules. Therefore, SO2 behaves ideally at 327oC.
Q.50. Gases deviate more from the ideal behavior at 0oC then at 100oC.
Ans. At 0oC (low temperature) the attractive forces between the gas molecules are significant (dominant) and thus gases become non-ideal. At 100oC (high temperature), the forces of attractions are negligible and thus they behave ideally.
Q.51. Hydrogen and He are ideal at room temperature but SO2 and Cl2 are non-ideal. How do you explain it?
Ans. H2 and He have very low boiling points which are far below the room temperature. So, the room temperature is very high for H2 and He. Moreover, the molecules of H2 and He have very small masses. Due to high temperature and small masses of H2 and He, the intermolecular attractions become negligible and they behave ideally while the boiling points of SO2 and Cl2 are close to room temperature and their molecular masses are relatively high. Thus sufficient attractive forces are present among their molecules; therefore, SO2 and Cl2 are non-ideal gases.
Q.52. what is Joule-Thomson effect? Joule Thomson effect is operative in the Linde’s method of liquefaction of air. How?
Ans. When a compressed gas is allowed to expand into a region of low temperature, it produces intense cooling and this phenomenon is called Joule-Thomson effect. In Linde’s method, the gas is compressed to about 200 atmosphere and this compressed gas is suddenly allowed to expand through and nozzle. The free expansion of the gas results in a fall in temperature. The process is repeated again and against until the gas is liquefied. So, in this way, Joule Thomson effect is operative in the Linde’s method of liquefaction of air.
Q.53. What is critical temperature of a gas? What is its importance for liquefaction of gases?
Ans. The temperature above which a gas cannot be liquefied, no matter how much pressure is applied is called critical temperature. In other words, the highest temperature at which a substance can exist as a liquid, is called its critical temperature. The critical temperature and the critical pressure provides us the information about the condition under which gases liquefy.
Q.54. What is Plasma state?
Ans. Plasma is often called the “fourth state of matter”. It occurs only in lightening discharges and in artificial devices like fluorescent lights, neon signs, etc. the lionized gas mixture, consisting of ions, electrons and neutral atoms is called plasma. Plasma is a distinct state of matter containing a sufficient number of electrical charged particles to affect its electrical and magnetic properties and behaviors.
Q.55. H2 diffuses through a porous plate at a rate of 500cm3 per minute at 0oC. What is the rate of diffusion of O2 through the same porous plate at 0oC?
Ans. Molar mass of H2 = 2 g mol-1 ; molar mass of O2 = 32 g mol-1
Q.56. why some amount of pressure should be added in the measured pressure of the non-ideal gas to get the ideal pressure of the gas?
Ans. In an ideal gas, there are no attractive forces between molecules and the molecular bombardment on the walls of vessel results in the ideal pressure, Pideal. However, in non-ideal gases there are forces of attraction between the molecules and become significant at higher pressures, the molecules will not strike the walls quite as hard on the average because each molecule will be slightly held back by the other nearby molecules. Thus the measured pressure P is slightly less than Pideal. So van der Waal needed a pressure correction, therefore lessened pressure is added in the measured pressure to get the ideal pressure : pi = P + P’
Q.57. What are the characteristics of plasma?
Ans. 1. The motions of the particles in the plasma generate fields and electric current from within plasma density of charged particles. This complex set of interactions makes plasma a unique, fascinating and complex state of matter.
- Although plasma includes electrons and ions and conducts electricity, it is microscopically neutral.
Q.58. Where plasma is found?
Ans. Entire universe is almost of plasma. Plasmas are found in every thing from the sun to quarks. It Is the stuff of stars. Our sun is a 1.5 million kilometer ball of plasma, heated by the nuclear fusion. On earth, it occurs in lightning bolts, flames, auroras and fluorescent lights.
Q.59. Why the excluded volume (effective volume) is less than molar volume of the gas?
Ans. Excluded volume ‘b” is the volume occupied by 1 mole of the real gas molecules in highly compressed state. But molar volume Vm is the actual volume of one mole of a gas molecules and is the measured container volume which is accessible to each molecule. In a real gas, however, the molecules do occupy some volume. Thus, the excluded volume is less than the molar volume of the gas.
Q.60. Why the volume correction is done by van der Waal.
Ans. The real gas molecules do have definite volume. This volume, however, is not negligible when the gas is subjected to high pressure. So van der Waals needed a correction in volume factor in order to make it applicable to the real gases. Thus, the volume available to gas molecules is the volume of the vessel minus the volume of gas molecules.
Vfree = Vvessel – b
The factor b is called the excluded volume which is constant and characteristic of a gas.
Q.61. a gas occupies 100dm3 at 283K. what will be its volume at -273oC at constant pressure?
Ans. V1 = 100 dm3 T1 = 283K
V2 = ? T2 = -273 + 273 = 0 K
Q.62. What is the density of CH4 (g) at 0oC and 1 atmospheric pressure.
Ans. T = 0oC + 273 k = 273 K ; P 1 atm
Molecular mass of gas ; M = 16 g mol-1
R = 0.0821 dm3atm K-1Mol-1
Q.63. the amount of pressure which is decreased due to force of attraction is given by a/V2 where ‘a’ is the van der Waal’s constant and V is the volume of vessel?
Ans. The pressure p’ is proportional to the number of moles of molecules, n, which are hitting the walls of the container. The total force of attraction on any molecules which is hitting a wall is proportional to the concentration of neighboring molecules, n/V , but the number of molecules hitting the wall per unit wall area is also proportional to the concentration, n/V. thus
P’ x or p’ Or
Where a is constant of proportionality and is called van der Waal’s constant if n = 1 mol of a gas, then
P’ Thus, Pi = P +
Q.64. How the various scales of thermometry can be interconverted?
Ans. There are three scales of thermometry; i.e., centigrade, Fahrenheit and absolute or Kelvin scale. These scales of thermometry can be interconverted as follows:
oC = (G – 32), F = (oC) + 32 and K = oC +273
Q.65. Greater the temperature of the gas, closer the straight line of P versus I/V to the pressure axis. Justify it.
Ans. The volume of the gas increases with the rise in temperature for the same number of moles at the same pressure. Thus inverse of volume, I/V decreases at the same pressure and so I/V will be close to zero when P is close to zero. Therefore, greater the temperature of the gas, closer the straight line of P versus I/V to the pressure axis.
Q.66. Give two uses of plasma?
Ans. 1. Plasma can be used to destroy bacteria.
2. Plasma can be used for cleaning and sterilization of food and operation theaters.
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https://chanceandnecessity.net/2020/12/23/when-masks-work-and-when-they-dont/
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math
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With billions wearing face coverings, the question we want answered is: How effective are they at reducing the probability of you becoming infected with COVID-19? This question is very hard to answer. We can split it up into two questions: If you wear a mask, how much does this reduce the dose of virus you breathe in? And how does the chance of you becoming infected decrease, when the dose of virus you breathe in is reduced? Colleagues and I have had a go at answering the first question — preprint here. Here I will just assume that mask wearing reduces the dose by a factor of one half. This does not mean that the probability that you will become infected is reduced by one half. It is not that simple, unfortunately.
Presumably the more virus you inhale, the more likely it is that you will become infected. But we have essentially no direct data on this. One model developed for TB (which spreads in a similar way to COVID-19) predicts that the probability of infection increases as one minus the exponential of the dose, this is the Wells-Riley model. But although we have no data for SARS-CoV-2, we do have some data for norovirus, and the results for transmission of the norovirus are not consistent with the Wells-Riley model – I looked at infection with norovirus in a previous post.
You can see the difference between the predictions of the Wells-Riley model and those you get by assuming a norovirus-like dependence on dose, in the plot at the top of the post. In this plot the x-axis scale measures the concentration of virus in the air you breathe. The scale and so the actual numbers are arbitrary but note that the x-scale is a log scale — the plot covers a huge range (it increases by a factor of ten million) of concentrations of virus in the air. The y-axis is the percentage reduction in probability of becoming infected, if wearing a mask reduces the viral dose by a factor of one half.
As the Wells-Riley model has an exponential dependence of infection probability on dose, the probability of infection goes from almost zero to almost 100% over about two decades in viral dose (from 101 to 103 above). Within those two decades, wearing a mask and so reducing the dose significantly reduces the probability of becoming infected — you can see the blue dashed curved is sharply peaked and reaches an almost 25% * reduction in probability of infection. But outside these two decades of dose, the prediction is that wearing a mask has little effect. If there is a lot of virus in the air, then even halving the dose is not enough to significantly reduce the chance of you becoming infected. And if there is very little virus, then you are unlikely to become infected, with or without a mask.
If infection is more norovirus-like, then the behaviour (orange curve) is different. The prediction is that masks never reduce the probability of infection by more than about 12% *, but that over a wide range of viral concentrations, mask wearing does reduce the probability of becoming infected. One interpretation of this is that if COVID-19 transmission is like that of norovirus, it may be that some of us are more resistant to COVID-19 infection than others. This means that the window of ambient dose over which a mask is of most benefit would be different for different people. This smears out the region of doses where masks benefit, resulting in smaller benefits but over larger ranges of conditions**.
The plot at the top is just speculative, we really need more data here. But maybe it is useful, it says one very obvious thing which is that wearing a mask when the air has very little virus achieves little – if you are alone on top of a mountain then you can take the mask off. The other thing it shows is a bit less obvious, and this is that as masks are not 100% effective filters, they cease to work at very high viral concentrations. If you are stuck for hours in a small poorly ventilated room with someone who is breathing out a lot of virus, then expecting a simple cloth or surgical mask to predict you, is too optimistic. There is a reason that medical staff on COVID-19 don’t just wear a simple surgical mask, but full PPE, and this is that they need to reduce the viral dose by a lot more than half.
* These numbers increase if wearing a mask reduces the dose by more than a factor of half, for example if it is factor of three quarters, they approximately double to approximately 50% and 20%.
** The distribution for the norovirus-like case effectively averages over many different people with different susceptibilities, which would be appropriate for you if you don’t whether you are more or less susceptible than average.
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https://www.physicsforums.com/threads/work-done-up-to-fracture.859829/
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math
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Good day everyone! i have a problem dealing with the fracture analysis. We all know that the work done per unit volume is equal to the area under the curve of stress-strain curve or we can express it in terms of integral form, and if we're looking at necking point stress can be express in this terms of stress = constant*(strain)^n where n is the work-hardening, but if we extend it up to fracture i don't know the expression for the stress and strain. So guys please help me figure out the work done up to fracture. Thank you!
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https://www.hackmath.net/en/math-problem/75524
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math
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Right rectangular prism
The right rectangular prism has a length of 3.2 feet, a width of 1.7 feet, and a height of 2.1 feet. What is its volume?
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https://www.hackmath.net/en/example/6926
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math
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Jana rose in the morning in the quarter to seven. She slept nine and a half hours. When did she go to sleep?
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https://www.stem.org.uk/resources/elibrary/resource/32831/fractions-mixed-numbers
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math
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Converting between mixed numbers and improper fractions – The explanation begins by showing the difference between a proper fraction, an improper fraction and a mixed number. Pictorial representations of the fractions are used to aid understanding of how a mixed number and an improper fraction represent the same value. The video continues with examples of converting mixed numbers to improper fractions and from an improper fraction to a mixed number.
Calculations with mixed numbers and fractions – This video covers addition, subtraction, multiplication and division of mixed numbers. Students should be comfortable with these operations and conversion between mixed numbers and improper fractions before moving on to this work. A number of examples are explained including multiplying a mixed number by a fraction, a mixed number divided by a mixed number, a mixed number added to a fraction, and a mixed number subtract a mixed number.
The videos are produced by MathsMaster.org
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https://elischolar.library.yale.edu/journal_of_marine_research/1418/
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math
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Two-dimensional analytic solutions are derived, as a function of depth and longitudinal distance, for the Eulerian and Lagrangian residual currents induced in narrow tidal channels of constant breadth, depth and rectangular cross-section by the nonlinear interactions of the first order tides. The turbulence is represented by several different vertically variable eddy viscosity models chosen to bracket the range of likely vertical variation....
Ianniello, John P.. 1977. "Tidally induced residual currents in estuaries of constant breadth and depth." Journal of Marine Research 35, (4). https://elischolar.library.yale.edu/journal_of_marine_research/1418
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https://www.hackmath.net/en/word-math-problems/system-of-equations?tag_id=148
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math
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System of equations + similarity of triangles - math problems
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Two similar triangles, one has a circumference of 100 cm, the second has sides successively 8 cm, 14 cm, 18 cm longer than the first. Find the lengths of its sides.
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When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
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One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
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Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lighth
Do you have a system of equations and looking for calculator system of linear equations? See also our trigonometric triangle calculator. System of equations - math problems. Similarity of triangles - math problems.
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https://www.math.lsu.edu/~madden/M4005s2006/04-03.htm
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math
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|Course Home Page >> log >> (Previous Class | Next Class)|
April 3, 2006
The imaginary number i, which has the property that ii = -1.
Complex numbers can be written in the form a + ib, where a and b are real numbers.
The complex numbers can be put into correspondence with points in the plane. Looking at them this way, adding a fixed complex constant b to an arbitraty complex number z is a translation:
T(z) = z + b (a translation).
Multiplying by a fixed complex constant m is a dilation together with a rotation about 0.
W(z) = mz (a rotation together with a dilation by a factor of |m| ).
In class, we did some experiments where we plotted collections of complex points, multiplied tham all by a fixed complex and looked at the resulting configuration.
The next class will include a more careful and rigorous treatment.
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https://www.hpacademy.com/forum/practical-diesel-tuning/show/l5p-horsepower-gain-to-percent-fuel
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Sale ends todayGet 30% off any course (excluding packages)
Ends in --- --- ---
Discussion and questions related to the course Practical Diesel Tuning
Any idea on percentage fuel vs. horsepower gains. Watching the practical examples seems Nick starts with 22-25%.
Any idea on what 20% fuel & boost will do on a L5P?
Also with diesel calibrations will roughly half of one value get you half the HP?
For example if 20% fuel & boost get say 100 rwhp will 10% gain approx 50 rwhp?
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https://mail.astarmathsandphysics.com/university-physics-notes/electricity-and-magnetism/1544-electric-displacement.html
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Dielectric may not be neutral even when unpolarised. If the dielectric carries a charge densityof free charges representing a net surplus or deficit of electrons in the atoms of the dielectric andis the charge density due to the polarizing effect of an electric field then the total charge density is given by
The macroscopic electric fieldis related to the total charge density, and in the presence of matter Gauss's Law becomes
We can rearrange this expression to giveIf we definethen this equation becomes
is a new vector field, called the electric displacement. Sincewe can write
The last equation is really Gauss's Law, apart from a constant factor, modified to include polarization charges. This can be further illustrated using the integral form of Gauss's Law:
which becomeson substituting (1).
has no clear meaning, but is useful because it makes many problems very easy to solve. It has the property that the normal component ofat a dielectric boundary is continuous, as illustrated in the diagram below.
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https://techcommunity.microsoft.com/t5/excel/how-to-change-a-date-format-back-to-a-decimal-in-excel/td-p/975817
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Nov 02 2019 06:58 PM
Nov 02 2019 06:58 PM
I opened an old excel spreadsheet populated with many data entries that were originally in a decimal format with 1 decimal place e.g 4.5 but I found that they have all been converted to a d-mmm date format. i.e. 4-May I have tried many of the different number formats available, but can't get close to the original format. For instance Number format changes 4-May to 41763.00. Any ideas?
Nov 03 2019 01:18 AM
I'm on a Mac and when I choose to format a date I can select the region "Alsatian (France)". It will show the decimal format as one of the standard options. If you don't have these you might try a custom format "d.m;@". I've attached some screen shots that show you what I mean.
Nov 03 2019 04:39 PM
Nov 19 2021 12:58 AM
It's that somebody sends you an excel file, let's say with mater data. On original computer, the data is in decimal values.
I receive it via email. I open it on my computer. And certain decimal values are ''automatically'' changed to arbitrary dates. Now, if I format it back to numbers, the numbers are not the same anymore.
e.g: 1.5 ---> May first (or June 5th, depends on the will of excel at that time), and then convert back to number, you get something like 412381.
1.5 =! 412381
That's the problem here.
Nov 19 2021 01:50 AM
The process has some things in common with unscrambling eggs!
Once you identify that Excel has misread the data input, you can take steps to reverse the process. The day and month can be separated using
and then treated as the integer and decimal parts of a number using the appropriate formula
= DAY(data)+MONTH(data)/10 or = DAY(data)+MONTH(data)/10^LEN(MONTH(data))
the later dealing with months Oct-Dec.
Another solution that could work given computer settings other than those that messed up the data in the first place would be
Nov 19 2021 05:21 AM - edited Nov 19 2021 05:22 AM
Thank you @Peter Bartholomew for your reply. This has actually worked. In some cases I needed to do some additional magic, but it would not have worked without your initial input.
Not to mention the burst of laughter brought on by your 'unscrambling eggs' comparison, which is the most precise way to describe this problem.
Thank you again!
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http://mathhelpforum.com/calculus/53092-area-bounded-curves.html
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Please do part(ii).My answer is 5.61% but the paper's answer is 5.31%.
Please check for me thanks...
Follow Math Help Forum on Facebook and Google+
I get 5.31%
Can tell me how u get? Like: what is your value for the shaded and unshaded area respectively, area of region OAPB, coords.of B AND Coords.of Q
I want to see where my workings and answer differ...
show me what you did ... maybe i can see your mistake.
Originally Posted by skeeter show me what you did ... maybe i can see your mistake. Please look at my qn 11 workings.Thanks
Thanks i found my mistake already..i forgot to add the unshaded area into the calculation of the area of the whole plot
View Tag Cloud
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https://dreammathematic.com/general-topology-mcqs-with-answers-in-pdf/
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There is general topology MCQs with answers for exam preparation. Dream Mathematic provides you with all types of basic questions on topology which is important for topology final term exams. Also, we are providing material for competitive exams of job tests. Most students want to get higher marks in competitive exam but he/she doesn’t have better study material for preparations. So, we start a series of topology Multiple choice questions with answers. Other following topology MCQs quizzes are; Quiz.1, Quiz.2, Quiz.3.
General Topology MCQs with Answers in PDF
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https://cris.vtt.fi/en/publications/measurement-of-the-smc-muon-beam-polarization-using-the-asymmetry
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A muon beam polarimeter was built for the SMC experiment at the CERN SPS, for beam energies of 100 and 190 GeV. The beam polarization is determined from the asymmetry in the elastic scattering off the polarized electrons of a ferromagnetic target whose magnetization is periodically reversed. At muon energies of 100 and 190 GeV the measured polarization is Pμ = -0.80±0.03 (stat.)±0.02 (syst.) and Pμ = -0.797±0.011 (stat.)±0.012 (syst.), respectively. These results agree with measurements of the beam polarization using a shape analysis of the decay positron energy spectrum.
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https://projecteuclid.org/euclid.tmna/1482289230
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math
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Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 48, Number 2 (2016), 567-595.
On the structure of the solution set of abstract inclusions with infinite delay in a Banach space
In this paper we study the topological structure of the solution set of abstract inclusions, not necessarily linear, with infinite delay on a Banach space defined axiomatically. By using the techniques of the theory of condensing maps and multivalued analysis tools, we prove that the solution set is a compact $R_\delta$-set. Our approach makes possible to give a unified scheme in the investigation of the structure of the solution set of certain classes of differential inclusions with infinite delay.
Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 567-595.
First available in Project Euclid: 21 December 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Guedda, Lahcene. On the structure of the solution set of abstract inclusions with infinite delay in a Banach space. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 567--595. doi:10.12775/TMNA.2016.060. https://projecteuclid.org/euclid.tmna/1482289230
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https://help.legalserver.org/home/other-modules/area-median-income-calculation
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math
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Area Median Income Calculation
Notes on Block Placement
The Admin > AMI page
In filling out the table, the columns indicate the household size. The values you enter should be the upper end of the range. For example, if the annual limit for a household of 1 is $16,000 to be under 30% of Area Median Income, then the first field should have $16,000 listed.
Case Data > AMI Category [Lookup] > AMI Category.
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https://www.letsrun.com/forum/flat_read.php?thread=7642750&id=7642927
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math
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When did she do that 100 meter? That is flying for middle to long distance runner.
Consider this.... wrote:
I know she has a doping history, but still, she ran a 11.58 100m and 14:45 5K.
Exactly my reaction.
11.58 is outlier time wrote:
I know she didn't run the 400 very often but it seems she should have been a lot faster than 56 if she could run 11.58.
Lying, disgusting cheat....
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https://www.physicsforums.com/threads/charged-ball-exiting-a-box.824008/
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math
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1. The problem statement, all variables and given/known data A small ball has mass 3.4x10^-8 kg and charge of 2.0x10^-5 C. It enters a box with initial speed 1.2x10^4 m/s. The point where the charge leaves the box is at a voltage 350kV higher than the entry point. Find the speed of the ball as it leaves the box. 2. Relevant equations ΔE = E - E0 ΔE = q(V) E = 1/2mv2 3. The attempt at a solution E = 1/2 (3.4x10-8)(1.2x104)2 = 2.448 J ΔE = (2.0x10-5)(350000)= 7 J 7J = E - 2.448J 9.448J = 1/2(3.4x10-8)v2 v = sqrt ((2(9.448))/(3.4x10-8) v = 23577 m/s Does this look right? Apparently the ball doesn't leave the box. But that doesn't make any sense to me.
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https://www.slideserve.com/deepak/modeling-simulation-and-control-of-a-real-system-robert-throne-electrical-and-computer-engineering-rose-hulman-instit
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Modeling, Simulation, and Control of a Real SystemRobert ThroneElectrical and Computer EngineeringRose-Hulman Institute of Technology
Introduction • Models of physical systems are widely used in undergraduate science and engineering education. • Students erroneously believe even simple models are exact.
Introduction • Obtained ECP Model 210a rectilinear mass, spring, damper systems for use in both system dynamics and controls systems labs. • Models for these systems are easy to develop and students have seen these types of models in a variety of courses.
Introduction(motor, rack and pinion, damper, and spring connecting to first cart)
Introduction We developed four groups of labs for the ECE introductory controls class for a one degree of freedom system: • Time domain system identification. • Frequency domain system identification. • Closed loop plant gain estimation. • Controller design based on the model.
Parameters to Identify In the transfer function model we need to determine • the gain • the damping ratio • the natural frequency
Time Domain System Identification • Log decrement analysis • Fitting the step response of a second order system to the measured step response
Frequency Domain System Identification • Determine steady state frequency response by exciting the system at different frequencies. • Compare to predicted frequency response. • Optimize transfer function model to best fit measured frequency response.
Closed Loop Plant Gain Estimation • We model the motor as a gain, , and assume it is part of the plant • We use a proportional controller with gain • The closed loop system is • The closed loop plant gain is then
Closed Loop Plant Gain Estimation • Input step of amplitude A • Steady state output • The closed loop plant gain is given by
Results with Controllers After identifying the system, I, PI, PD, and PID controllers were designed using Matlab’s sisotool to control the position of the mass (the first cart). Both predicted (model based) responses and actual (real system) responses are plotted on the same graph.
Conclusions Students learn: • Simple, commonly used models are not exact, but still very useful. • Simple models are a reasonable starting point for design. • Motors have limitations which must be incorporated into designs.
Conclusions We have extended these labs to include Model matching • ITAE • quadratic optimal • polynomial equation (Diophantine) 2 and 3 DOF state variable models
Acknowledgement This material is based upon work supported by the National Science Foundation under Grant No. 0310445
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http://torrebruna.eu/60872-data-analysis-and-interpretation-essay/
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math
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is a crucial observation. Further examining the data set in secondary analyses, to suggest new hypotheses for future study. The new date will be will be announced very soon and communicated to the affected students. Shes likely to regard literary flourishes as a waste of your energy and her time. Citation needed Methods of statistics may be used predicatively in performance art, as in a card trick based on a Markov process that only works some of the time, the occasion of which can be predicted using statistical methodology. 10 11 Mathematical statistics edit Main article: Mathematical statistics Mathematical statistics is the application of mathematics to statistics. XAT 2019 Exam Analysis 2019 will be published by m immediately after the XAT 2019 exam is over on January 6, 2019. In thesis manuscript writing both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed.
And, in most cases, it is far more than a couple of them. Statistics is a branch of mathematics dealing with the collection, organization, analysis, interpretation and presentation of data.
Statistical inference, however, moves in the opposite direction inductively inferring from samples to the parameters of a larger or total population. This is much harder than one may be willing to admit. The easiest format to use in writing this essay is the classic 5-paragraph style, and a simple, effective format will look something like this: Paragraph 1: Brief recap of argument and statement that the argument has merit but also contains multiple flaws. Statistics tools are necessary for the data analysis. Most studies only sample part of a population, so results don't fully represent the whole population. 29 Ways to avoid misuse of statistics include using proper diagrams and avoiding bias. For many, the assumption is that interactive visualization is only about wimp interfaces, direct manipulation, clicks, mouse overs, and such. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Therefore, you should be prepared for various assignments and be aware of different essay types and their peculiarities. How to Lie with secret river essays Statistics.
Describe academic interests essay
Boom essay writing scholarship
The annual uba foundation national essay competition
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https://gedanken451.wordpress.com/2008/09/05/curves-of-pursuit/
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I was delighted that the first applied maths assignment of the year I received was focussed on one of my key interests: algorithmic programming (despite it being a very simple task programmatically). The scenario is that a rabbit travels at a constant speed of 10m/s from the origin to (100, 0). There’s also a fox who starts at (0, 50) and runs with a speed of v directly towards where the rabbit is at any time.
The assignment was to use a mathematical model (which treats time as a discrete variable) and, by plotting points on graph paper, to find out the minimum speed of the fox to catch the rabbit before it gets to (100, 0); naturally this was job for Excel!
I’ve got the excel spreadsheet as an attachment, downloadable here. I’ve tried to explain everything in comments, but the formulae may need a bit of explaining here. If you go to the ‘Calculations’ tab, the first column is ‘t’ – the discrete time variable (time gets quantised into ticks like a computer game). The next two coumns are the rabbit’s x and y coords; it’s fairly easy to work out how that’s calculated. Columns E and F are the fox’s coords; at each tick it adds to the previous coord the ‘movement vector’ – how far the fox moves per tick in both x and y axes (in cartesian coordinates of course) per tick (columns J and K). For these, essentially, the fox has to move v units towards the rabbit at each tick. To do this, a program would draw an imaginary trajectory from the fox to the rabbit and get the fox to move v units along this line every tick; this is what I got Excel to simulate. This means I basically need to get a vector of magnitude v at every tick, and my task was to come up with a formula to work out this in cartesian coordinates. Let’s draw a diagram and revise some primary school maths:
Apologies if this seems patronising. Here, I’ve turned everything into similar (AAA similarity) right-angled triangles, the hypotenuse of the smaller one representing the path the fox runs in 1 tick, and that of the larger one representing the imaginary trajectory. The maths is painfully simple but some of my friends couldn’t work it out (Set 1 Maths at St Paul’s School…) so it’s included here for their benefit. The operator is supposed to be a dot (multiplication) even though it looks woefully like a minus sign. And now we’ve got our formula for the fox’s x and y increments per tick! Now it’s a simple matter of dragging formulae on Excel and we’ve got 257 rows of ticks.
I then added some extra stuff to allow changing of the time interval to smaller and smaller values for greater accuracy. The problem with this model is that when the fox catches the rabbit, it overshoots and the model has it turning back on itself back towards the rabbit; I exploited this as a detection method for when the fox catches the rabbit. Ultimately this is a fairly crap model, but it was pretty fun to write (and make fun of). The real reason why I blogged this was to share this: try setting the fox’s speed to numbers higher than 50 with a time interval of 1 – you get rather interesting results. Sheet 3 is just an additional sheet which shows the fox’s minimum speed to catch the rabbit at different time intervals which I shamefully worked out manually (should have used a macro) – part of the prep.
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https://wochenprogramm.mathematik.uni-freiburg.de/v.html?V=OS-DiffGeo&Semester=SS2020&l=en
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math
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Raum 404, Ernst-Zermelo-Str. 1|
Arpan Saha: Twists of quaternionic Kähler manifolds
virtual SR404 |
Ksenia Fedosova: On a stochastic version of transfer operators
For hyperbolic manifolds, there exists a straightforward connection between the spectral and the geometric data. More precisely, the lengths of its closed geodesics and the spectrum of its Laplace operator acting are connected by the Selberg trace formula, that can be considered a sibling of the Poisson summation formula. Selberg trace formula provides the information on the eigenvalues of the Laplace operator, however, completely ignoring its eigenfunctions.
There exists a method, originated from the classical statistical mechanics, that allows to obtain more information on the eigenfunctions. The method, called the transfer operator approach, involves a construction of a so-called transfer operator from a certain discretisation of the geodesic flow on the manifold. For a modular surface, this transfer operator is ultimately connected to a Gauss map. One can show that the 1-eigenfunctions of this operator correspond via a certain integral transform to the eigenfunctions of the Laplace operator. The integral transform mirrors the Eichler-Shimura-Manin isomorphism.
In this talk, we try to construct an analogue of the transfer operator, using the Brownian paths on the manifold instead of the geodesics. We obtain an operator, whose 1-eigenfunctions turn out to be the boundary forms of eigenfunctions of the Laplace operator.
Danu Thung: Symmetries of deformed c-map metrics and the HK/QK correspondence
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https://gmat.economist.com/support-faq/account-troubleshooting/when-will-i-be-able-see-my-progress-graph
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When will I be able to see my progress graph?
Your progress chart will appear after spending several hours in the course studying, at about 10% of course completion.
The progress tab represents how much time you have put into each section, and how much you have completed. It is usually proportional to the time you spend learning. For example. if you reached 50% progress in 40 hours, it is expected that you will take 80 hours in total to get near your maximum. Sometimes, the time isn't closely proportional to the progress percentage, such as with students who are having non-uniform difficulties in foundation topics vs. advanced technique/strategy topics. Therefore, a student could, for example, reach 50% progress in 60 hours, but take only 40 additional hours to get to 100%.
Overall, the performance chart shows the amount covered in time spent, and this informs you about how much more there is to do and what your pacing is like altogether.
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https://www.mail-archive.com/[email protected]/msg84344.html
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math
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I have a bunch of form variables that I need to process as integers. The problem is that some users are writing in values with commas - e.g. 100,000, and that isn't read as an integer. There's more than one variable so I don't want to have to do a string replace for each one. Is there a general way to curb this problem?
Thanks, Doug -- PHP General Mailing List (http://www.php.net/) To unsubscribe, visit: http://www.php.net/unsub.php
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https://www.coursehero.com/file/6734469/Physics-I-Lab-Manual-2011-22/
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EXPERIMENT 2.MEASUREMENT AND PRECISIONyour measured value asx0±δxwherex0is the average value from your measurements andδxis called the uncertainty and is half the deviation from the largest to smallest measuredvalues.Note that the number of significant figures you include in your results is limited by thenumber of significant figures in the least precise measurement in your data. Suppose youmeasured the circumference to bec= 508 mm (which has 3 significant figures) and youmeasured the diameter to bed= 148 mm (which also has 3 significant figures). Accordingto your calculator, the ratioc/dis equal to 3.432432432. This has 10 significant figures! Youmust round off this answer to three significant figures and writec/d=3.43.Numbers containing too many significant figures are wrong because they imply a precisionthat is not justified by your measurements! For the same reason quantities calculated frommeasured values that do not include the uncertainty are wrong. To reiterate, your final result
This is the end of the preview.
access the rest of the document.
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https://math.answers.com/Q/What_2_numbers_multiplied_by_each_other_total_15006
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The sum is the total when numbers are added together, the product is the total when they are multiplied.
The factor pairs of 104 are (104,1)(52,2)(26,4)(13,8) None of them differ by 10.
286 x 2 x 3 = 1716
It is: 25*75 = 1875
11 x 12 x 13 = 1716
Three distinct prime factors, eight total.
If the percentage and the total are both positive numbers, then there's no reason for the appearance of a negative sign.
The total area of a cube is the width multiplied by the base multiplied by the height. E.G A=W*B*H.
Work with the total sums of the numbers:The mean of eight numbers is 41, so the total of those eight numbers is 8 x 41 = 328The mean of two of those eight numbers is 29, so the total of those two numbers is 2 x 29 = 58So the total of the other six numbers must be the difference between these two totals, that is 328 - 58 = 270Thus the mean of these six numbers is their total divided by 6, namely 270 ÷ 6 = 45.
You have several choices:1 and 3782 and 1893 and 1266 and 637 and 549 and 4214 and 2718 and 21
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http://science.wikia.com/wiki/User_blog:Drakenkaul/When_we_divide_by_11
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Hello guys, it has been a long time... well, to be exact it has been 17 days or 408 hours or 24,480 minutes or 1,468,800 seconds.. some calculation, huh? I used a calculator! So I love to experiment with numbers and arithematics and all that thing. I mean I love math. I love playing with numbers and all that stuff. Due to this reason only I have been able to remember the Multiplication Table upto 25! So... in one of my previous blogs titled 'When we divide by 9' we observed a pattern in the series of division of natural numbers by 9. It was a very fascinating... Well this one's going to be more fascinating than that! So let's roll.
Dividing by 11
Now, if you are interested in the process of this problem then please keep a rough notebook and a pen/pencil with you to get an idea of the unimaginable result. SO here goes the series:-
and so on!
This pattern is continuous unlike the one when we divide by 9. You might have observed that this pattern is following the multiplication table of nine after the decimal point and the pattern recurs after a complete division happens (11 divided by 11).
Another way to learn the pattern
But there is another way to learn the pattern. All the digits follow the pattern of multiplication table of 9 (including the digits before decimal point). Let me elaborate- After a complete division step occurs, the product that we get in the future steps(till another complete division step occurs) is sum of the corresponding multiple of nine and the product of the previous complete-divison step. For example,
This is a complete-division step. Now, when we go further let's say I want to find the product of 13/11. What I will do is this:- The 13th multiple of 9 is 117. And the product of 11/11(most recent complete-division step) is 1. I will add them both and get 118. Now I will put a decimal point between the two 1s and get something like this : . Note that the overline above 18 represents the recurring decimal value. And this is the answer for 13/11. Easy huh!
Next in the Series
So I will be posting some more blogs in this series of 'When we divide by a #'. The next in the series are:-
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http://www.hotukdeals.com/deals/hp-w20-20-1-flat-panel-monitor-play-566333
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math
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The HP W20 20.1-inch Wide flat-panel monitor with integrated 2 watts per channel speakers delivers breath-taking viewing performance for video, photos and games and more thanks to impressive 1680 x 1050 resolution and 600:1 contrast. Its ultra-stylish, sleek design is the perfect design match for your HP PC and peripherals.
# Product Description: HP w20 - flat panel display - TFT - 20.1"
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# Diagonal Size: 20.1" - widescreen
# Max Resolution: 1680 x 1050 / 60 Hz
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# Power Consumption Operational: 55 Watt
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s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500550977093.96/warc/CC-MAIN-20170728183650-20170728203650-00045.warc.gz
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http://cressaynche.carolinadigital.us/t-test-statistical-thesis.html
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math
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The one sample t-test is a statistical procedure used to determine whether a sample of observations could have been generated by a process with a specific mean suppose you are interested in determining whether an assembly line produces laptop computers that weigh five pounds. Learn what a t-test is what assumptions are made when conducting a t-test and now refers to any test of a statistical hypothesis in which the statistic. Master thesis effects of major exports and imports on the balance of various statistical techniques at our disposal have. T-tests and one-way anova the statistical t-test procedure is used to determine a p-value that i'm working on my master's thesis and yesterday was crazy. Dissertation statistics help | statistical data analysis: our statistical consultants assist graduate students and professors.
Statistics research paper sample using one-sample t-test (for small sample) thesis writing term paper writing tips & examples. Hypothesis testing using z- and t-tests in hypothesis testing nowadays, we typically use statistical software to perform t-tests, and so we get a p-value. Statistical analysis in sensory evaluation insert statistical significance (ie t test p value that must be kept as controlled potential in my thesis.
What is statistics thesis all about topics for statistics thesis involves the applications of statistical techniques including t-test, anova (analysis of. 1 t-test statistics overview of statistical tests assumption: testing for normality the student’s t-distribution inference about one mean (one sample t-test. Z-test is a statistical test where normal distribution is applied and is basically used for dealing with problems relating to unlike the t-test for single.
Two-sample hypothesis testing is statistical analysis designed to test if test statistic or a t test one-sample test of a hypothesis for more. A statistical examination of two population means a two-sample t-test examines whether two samples are different and is commonly used when the variances of two.
Revised thesis on bir - download as word doc (doc / docx a t-test is a statistical test used to determine whether two population means are different when the. The t test is a comparison of the variance between the groups and the variance all about descriptive statistics for thesis different types of statistical tests.
Statistics iii: probability and statistical tests statistics iii: probability and statistical the appropriate statistical test is student's paired t-test. Paired t-test - usually used to determine before and t-test - a statistical test used to compare the return from the statistical tests reference guide to. An alternative framework for statistical hypothesis testing is to specify a set of statistical an example proved the optimality of the (student's) t-test.
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https://www.jiskha.com/display.cgi?id=1270499989
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math
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posted by Kelsey .
Objects with masses of 190 kg and a 490 kg are separated by 0.380 m.
(a) Find the net gravitational force exerted by these objects on a 57.0 kg object placed midway between them.
(b) At what position (other than infinitely remote ones) can the 57.0 kg object be placed so as to experience a net force of zero?
____ m from the 490 kg mass
I figured out the first part is 3.1E-5N
by using the G(m1*m2)/r^2 formula.
but I have no idea how to do it not knowing either distance.
I tried to set the equations equal to eachother and use different variables for both of the distances but the I don't think I can end up with a variable in the answer....
b. let x be one distance, and .380-x the other distance. Set the forces at these distances equal.
solve for x.
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https://thedesigningfairy.com/add-trendline-in-r/
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math
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You are watching: Add trendline in r
See more: Legia Warsaw Vs Real Madrid Vs Legia Warsaw Highlights, Real Madrid Vs Legia Warsaw 5
An international trend lines
One that the simplest approaches to identify trends is to fit a ordinary least squares regression design to the data. The version most world are familiar with is the direct model, yet you can include other polynomial terms for extra flexibility. In practice, protect against polynomials of levels larger than three since they are less stable.
ll.smooth = loess(xx~tt, span=0.75)ll.pred = predict(ll.smooth, se = TRUE)ll.df = data.frame(x=ll.smooth$x, fit=ll.pred$fit,lb = ll.pred$fit - (1.96 * ll.pred$se),ub = ll.pred$fit + (1.96 * ll.pred$se))ll.df = ll.df
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CC-MAIN-2022-27
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https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/how-to/gage-study/expanded-gage-r-r-study/interpret-the-results/key-results/
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math
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Step 1: Use the ANOVA table to identify significant factors and interactions
Use the ANOVA table to identify which sources of variability are significant. The ANOVA table includes the following terms in the Source column:
Part: The variation that is from the parts.
Operator: The variation that is from the operators.
Nested factors: The variation that is from nested factors. Two factors are nested when each level of one factor occurs with only one level of the other factor. For example, if two operators measure two different, but similar, sets of parts, parts are nested under operator, and is indicated by Part (Operator). In this case, if the average measurement of different parts by each operator varies greatly, then Part (Operator) will be a significant source of variability.
Interaction terms, such as Part*Operator: The variation that is from an interaction. For example, an interaction exists when an operator measures different parts differently.
Error or repeatability: The variation that is not explained by part, operator, or other terms in the model.
If the p-value for an interaction is 0.05 or higher, Minitab omits the interaction because it is not significant and generates a second ANOVA table without the insignificant interactions.
Step 2: Assess the variation for each source of measurement error
Use the variance components (VarComp) and %Contribution to assess the variation for each source of measurement error. The sources are as follows:
Total Gage R&R: The sum of the repeatability and the reproducibility variance components.
Repeatability: The variability in measurements when the same operator measures the same part multiple times.
Reproducibility: The variability in measurements when different operators measure the same part at the various conditions defined by the other factors in the model. The Reproducibility term can be divided further into Operator, Operator*Part, and other main effects and interaction effects.
Part-to-Part: The variability in measurements due to different parts. In addition to Part, other factors might be used to calculate part-to-part variation.
Ideally, very little of the variability should be due to repeatability and reproducibility. Differences between parts (Part-to-Part) should account for most of the variability.
Step 3: Examine the graphs for more information on the gage study
The gage R&R graphs provide information about the measurement system.
Components of variation graph
Shows whether the largest of component of variation is part-to-part variation.
In an acceptable measurement system, the largest component of variation is part-to-part variation.
R chart by operator
Shows whether any points fall above the upper control limit.
If the operators measure consistently, the points will fall within the control limits.
Xbar chart by operator
Shows whether most points fall beyond the control limits.
The parts that you choose for a gage R&R study should represent the typical part-to-part variability. Thus, you should expect more variation between part averages, and the graph should show that most points fall beyond the control limits.
Measurements by a single factor
Shows all measurements, arranged by one factor. This graph helps you visualize the differences between factor levels.
In addition to displaying measurements by part or by operator, an expanded gage R&R study also allows you to display graphs of measurements arranged by other factors.
Measurements by part graph
Shows whether multiple measurements for each part are close together.
Multiple measurements for each part that are close together indicate small variation between the measurements of the same part.
Measurements by operator graph
Shows whether differences between operators are small compared to the differences between parts.
A straight horizontal line across operators indicates that the mean measurements for each operator are similar. Ideally, the measurements for each operator vary an equal amount.
Shows the interaction between two factors. An interaction occurs when the effect of one factor is dependent upon a second factor. This plot is the graphical analog of the F-test for an interaction term in the ANOVA table.
In addition to displaying the interaction of operator by part, an expanded gage R&R study also allows you to display graphs of other interactions.
The operator*part interaction graph
Shows whether the lines that connect the measurements from each operator are similar or whether the lines cross each other.
Lines that are coincident indicate that the operators measure similarly. Lines that are not parallel or that cross indicate that an operator's ability to measure a part consistently depends on which part is being measured. A line that is consistently higher or lower than the others indicates that an operator adds bias to the measurement by consistently measuring high or low.
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https://www.ias.edu/sns/malda/public_lectures/EnglishLecture
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math
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Juan M. Maldacena: October 15, 2000 Lecture - English
Black Holes, Strings and Quantum Gravity
Institute for Advanced Study
School of Natural Sciences
Princeton, NJ 08540, USA
On leave from
Jefferson Laboratory of Physics
Cambridge, MA 02138, USA
Princeton Centennial Lecture, October 15, 2000
In this article we are going to describe some ideas about the most microscopic or most fundamental laws of physics. Before that we will review, in very general and oversimplified terms, the laws of physics as we understand them today. We will remark that there is an important logical inconsistency in these laws. There is a conflict between quantum mechanics and gravity. String theory was invented to solve this contradiction. We will explain what string theory is and how it describes some quantum aspects of black holes. This will be possible through a relationship between string theory and more conventional theories of particle physics.
Presently Known Physics
What are things made of?
When we ask ourselves what things are made of, we think of molecules, atoms, or elementary particles. Ordinary matter is made of molecules, which in turn contain atoms which in turn contain more elementary particles. An elementary particle is, by definition, a particle which is not made of some other particles. The particles which today we consider elementary might some day turn out to be made of some other more elementary particles. All we can say is that current experiments have not seen that they have any smaller constituents. Consider for example a piece of iron. It is made of atoms, these atoms consist of a nucleus and some number of electrons, 26 for the case of iron. The electrons are elementary, as far as we know now. The nucleus contains protons and neutrons, which in turn contain particles called "quarks" which are elementary. All these particles interact by emitting and absorbing other particles. The electromagnetic force, responsible for keeping atoms together, is due to the interchange of photons. The strong force, or nuclear force, is responsible for keeping the quarks together and keeping nucleus together. This force is due to the exchange of other particles called gluons. All of the ordinary matter we see is made of these particles.
In summary, we have a certain number of elementary particles, the ones mentioned explicitly above plus some other ones. They make all the matter we see, including the matter in distant galaxies, the matter making living organisms, etc.
In this picture of matter it is extremely important that the laws governing their motion are not the laws of classical physics, but the laws of quantum mechanics. From our classical intuition we would say an electron moving around the nucleus would be like a planet moving around the sun. In both cases there is an attractive force, the gravitational force in one case the electric force in the other. But a moving electron would emit electromagnetic waves, it would lose energy and after a fraction of second it would fall into the nucleus. What prevents the electron from falling in? Quantum mechanics is responsible for this. In quantum mechanics the energies of the system are quantized, this means that the electron can only have very definite energies. There is a minimum energy state and the electron cannot decay any further by emitting electromagnetic waves. In conclusion, quantum mechanics is crucial for the stability of matter. It is the reason we do not fall through the floor. In quantum mechanics particles do not have well defined positions and velocities. In fact, when the electron is in its low energy state we cannot say precisely where it is. It is more probable to find it near the nucleus than far away. So in quantum mechanics some things are a bit fuzzy, like the position of the electron. Quantum mechanics gives us a very precise way of characterizing and describing this fuzzyness.
Another important ingredient in the description of nature is the intimate relationship between space and time that results from the principle of "relativity." Relativity says that two observers which move at constant velocity relative to each other should see the laws of physics in the same way. They should also see light propagating at the same speed. This is possible only if time flows differently for each of the observers.
If someone is moving with respect to us at constant velocity we see his or her watch ticking more slowly. This is a small effect if we move at ordinary velocities, but it is a large effect if we move at velocities close to the speed of light. For example, there are particles that are unstable and decay after some time. In particle accelerators physicists can make these particles travel very fast, at speeds close to the speed of light, then they observe that these particles take much longer to decay. The clock is ticking more slowly for them.
Relativity implies that space and time are related. So it is convenient to think of them as a single entity, space-time. Our space-time has four dimensions. It has three spatial dimensions and one time dimension. Relativity also implies that information cannot travel faster than the speed of light.
The final ingredient in our understanding of nature is gravity. We have all heard about Newton's theory of gravity, which says massive bodies attract each other through gravitational forces. For this reason objects fall, the earth goes around the sun, etc.
In Newton's theory gravitational forces are instantaneous, so that if we were to move the sun now, we would feel the change in the gravitational force instantaneously here on the Earth. Relativity, on the other hand, says that no information can travel faster than light. So that if we move the sun, we could only feel any effect on the Earth after eight minutes, the time it takes the light to go from the sun to the Earth. Einstein realized that there was a contradiction between relativity and Newton's theory and he devised a way to solve it. His resolution to the problem involved a great conceptual jump. He proposed that space-time can be curved, it has some shape. This shape is determined by the matter distribution. Particles move along the trajectory that most closely resembles a straight line in this curved space-time. So the sun curves space-time and the Earth is moving along a trajectory that most closely resembles a straight line. An analogy is the following: The classical picture of space-time and particles moving in it is like a billiard table where billiard balls move, hit each other, etc. The balls move but the billiard table is totally rigid and does not move. Einstein's theory is analogous to replacing the billiard table by an elastic rubber sheet. The billiard balls deform the shape of the rubber sheet. If we have a very heavy billiard ball it will deform more the rubber sheet and if we throw another ball its trajectory will be determined by the shape of the rubber sheet. Interestingly, even if we do not have any balls the rubber sheet can oscillate and waves can propagate. Similarly in space-time there can be gravitational waves. These have been measured indirectly and some experiments are currently under way to see them directly.
In summary, space-time is dynamical, it can oscillate, it can move. Matter curves space-time and the motion of matter depends on the shape of space-time.
These are the laws of physics as we know them today, they explain most of what we see, including how we see. Biology and chemistry boil down to the interactions of these particles. Most of physics today is devoted to trying to approximate these laws,
developing methods to do calculations with them, experimentally observing how different configurations of particles behave, observing how matter is distributed in the universe, etc.
Both the theory of interacting quantum particles that we described above and the theory of gravity have been tested to a high degree of precision. You might be surprised then to learn that these laws are inconsistent!. Yes, they are mathematically, logically inconsistent. In practice this means that there are processes, or physical situations, that we cannot possibly explain using these laws. The problem comes from the fact that the theory of gravity is not consistent with quantum mechanics, which is a crucial component of our understanding of matter. Why does this contradiction never show up in the experiments we do? The reason is that quantum mechanics is important for small things and it is negligible for large things. On the other hand gravity is important for heavy things. Most objects that we deal with are either small and light, like atoms, elementary particles, etc, so that we can neglect gravity, or big and heavy, like us, planets, etc, so that we can neglect quantum mechanics.
So all experiments done to date only involve situations where one can neglect gravity or one can neglect quantum mechanics. If we had a small and heavy object we would need a new theory to describe it. A theory that manages to join together quantum mechanics and gravity, let's call it a theory of quantum gravity. The most important problem where something small and heavy arises is in the beginning of the universe. There is a big amount of evidence that the universe is expanding. So if we go back in time the universe would appear smaller and smaller until it is all concentrated in a very small region. The universe as a whole is certainly heavy, so we have a small and heavy object and therefore the effects of quantum gravity would be important. The question is how to describe this process, to explain what comes out of it, why the universe is as it is, etc. It is crucial to understand quantum gravity to understand this process. Quantum gravity is not yet understood well enough to tackle this problem.
There is another problem where quantum gravity is relevant and where a lot of progress has recently been made. The problem is to understand the quantum aspects of black holes. If we tried to make a small and heavy object by putting lots of matter is a small region, we would find that it collapses to a black hole. There is evidence that this actually does happen for very massive stars, which collapse under their own weight. When a black hole forms a small region of very high curvature develops where current theories would fail. This region, however, is surrounded by a horizon, which is a surface separating the interior from the exterior in such a way that something in the interior can never escape to the exterior. This horizon surface has some size. This size is about one mile for a black hole of the mass of a typical collapsing star. The horizon's presence implies that one would never see the region of strong curvature from the outside, and that whatever happens there will not leak out to the outside, according to Einstein's theory. Quantum mechanics on the other hand implies that some of the energy that fell into the black hole does actually leak out. The black hole emits radiation with a characteristic temperature. For astrophysical black holes this radiation is too weak to be detected, the temperature is too low. A black hole in empty space would gradually loose its mass due to this radiation. To first approximation this radiation seems to be unrelated to what fell into the black hole. But according to quantum mechanics the radiation should know about the objects that fell into the black hole. In the full quantum theory one should in principle be able to calculate what comes out from the black hole. Let us make an analogy. Suppose we had a star. If we knew all the quantum state of the star we would know all the properties of the radiation that comes out. In practice it is very difficult to know the quantum state of a system of many particles, let alone a star. In the case of the black hole, all the information about its quantum state seems to have fallen behind the horizon, so it seem that we cannot know it even in principle. The fact that quantum mechanics says that we need the information and that gravity says that we cannot have it, because it is behind the horizon, is called the "information paradox." We will see how quantum gravity resolves this paradox.
In summary, our current theories of physics are not consistent. Despite this we can use them for explaining almost everything except processes like the creation of the universe or some aspects of the evolution of black holes. For this need a better theory.
The Problem with Quantum Gravity
Before the 20th century we had just classical physics. In the beginning of the early 1900s relativity and quantum mechanics were discovered. During the rest of the century it was understood how to put together relativity and quantum mechanics into the modern theory of particle physics. In 1915 Einstein understood how to put together relativity and gravitation into the theory called "general relativity." We can think of classical physics as describing particles moving in a fixed space-time. Quantum physics describes fuzzy particles, particles that do not have well defined positions in a fixed space-time. General relativity describes particles moving in a moving space-time. The full theory of nature should incorporate both departures from classical physics, quantum mechanics and general relativity, this full theory is a theory of quantum gravity.
The earliest attempts in trying to put together Einstein's gravity together with quantum mechanics failed. The simplest calculational procedures that work in the case of particle physics give non-sensical infinite answers. In the 70's string theory was born. Though it started its life as an attempt to understand the strong force, it became clear that the theory was really describing gravity and that it could be used to solve the contradiction between quantum mechanics and gravity. It is really a theory under construction and we have not figured out all the rules that govern the theory, but we have figured out a great deal of them. It gives a unified description of all interactions. It can explain quantum aspects of black holes, and that is what we will focus on.
The way normal theories are quantized is to start with a simple configuration, in this case it could be a flat space-time, and then consider small deviations or small excitations around it. The small excitations of a flat, empty, space-time are gravitational waves. According to the rules of quantum mechanics the energy that these waves can carry are quantized. The wave carrying the minimum amount of energy, the quantum of energy, can be viewed as a particle. In the case of gravitational waves this particle is called a graviton. In normal quantum theories this particle would be point-like.
In string theory we replace particles by strings. Strings are one dimensional objects. They are tiny loops. We can view them as microscopic rubber bands. These strings can oscillate. These strings can oscillate with no friction, as opposed to rubber bands. The string oscillation energies are quantized, as in any other quantum mechanical system. The string with the least possible oscillation energy is the graviton and it is massless since the minimum oscillation energy is zero. Massless particles always travel at the speed of light. This agrees with the fact that gravitational waves also move at the speed of light. Strings that have more oscillation energy are interpreted as massive particles. Different particles would be strings that oscillate in different ways. These strings can interact by splitting and joining interactions. So two strings can join to form a single string. These interactions lead to a consistent theory. There are precise mathematical formulas behind these words. The results of calculations using these formulas are sensible, i.e. we do not get infinite answers. At long distances we would see the strings as point-like objects. Since we have not yet seen experimentally any string inside known particles we conclude that the size of these vibrating strings should be smaller than the smallest distance we can probe with our current experiments, which is about 10-18 meters. There has been a lot of work understanding more precisely how strings can have properties similar to the properties today's elementary particles.
We said that black holes arise when we bring many particles together in a small region of space. Since particles are strings, we would say that black holes are a collection of strings all put together. The problem with this picture is that it is very hard to say how a large and strongly interacting collection of strings behaves. So despite that it has been known for a long time that strings describe quantum gravity, it was only recently that concrete calculations describing quantum aspects of black hole were done.
The progress in recent years was possible thanks to development of new ways of viewing string theory. We are going to describe now one such new description of string theory.
Imagine that you have some object, it could be a black hole, a normal star, a gravitational wave, or any other object, including just the vacuum. Then we surround it with an imaginary surface that is very far away from the object. Then we have two ways of describing what is happening inside. One is the traditional way that we were describing above, through strings, quantum gravity, etc. The second is to think that we have a theory of particles that move on the sphere that is far away. We will call this particle theory the "boundary theory." Then we can describe any object in the interior, including black holes, as excitations in the boundary theory. So we translated the problem of understanding black holes to the problem of understanding certain special configurations in the boundary theory. What is the advantage? First, we know that normal particle theories preserve information, then black holes should preserve information too. Second, in some cases it is possible to do concrete computations in the boundary theory which explain some of the quantum aspects of black holes.
This boundary theory is really an appropriate description for special space-times that have a natural boundaries. The simplest example is a negatively curved space-time with constant curvature. The simplest possible positively curved space that we can imagine is a sphere. If we add time we get the simplest positively curved space-time, it is called "de Sitter" after its discoverer. The simplest negatively curved one is called anti-de-Sitter. This space-time is static, it does not expand or contract (as opposed to the expanding space-time that describes our universe). That is has a boundary just means that there is a region far away where light can go and come back in finite time, so that it looks as if it has a boundary from which it is reflecting. The particle theory that lives at the boundary is a rather conventional particle theory, of the type we believe we understand, at least conceptually, fairly well. So one is replacing the complicated problem of quantizing gravity, by the problem of understanding a particular particle theory that lives at the boundary of space-time.
This description of the bulk physics in terms of theory at the boundary is analogous to the way a hologram works. A hologram is one of those pictures that looks three dimensional. A hologram is stored on a two dimensional photographic plate. Nevertheless, it manages to encode the full three dimensional information of the three dimensional object. Our boundary theory, which lives in the three dimensional boundary of space-time, encodes the full four dimensional information about an object in a four dimensional space-time.
Where are we? Where are we going?
Let us now summarize a bit the status of string theory. In the 70's string theory was discovered as a possible theory for the strong force. It was later realized that it can be used to describe quantum gravity. But for some time very few people worked on it. In the mid 80's some calculations showed that the theory passed very stringent mathematical consistency checks and that it was a viable theory for describing all interactions in a unified way. This sparked a great deal of interest and there was more activity in the field. Some physicists, however, thought that the ideas were too speculative and were not very enthusiastic about it. Princeton was then the most active center in this field. In the mid 90's many interesting results were found, it was understood that string theory was part of a bigger theory called M-theory which admitted many equivalent descriptions. All of known consistent quantum gravity theories were special limits of the same theory. This theory also contains other objects such as membranes. The understanding of these objects led to the theories we saw today about black holes.
At this point one of the major unresolved problems is to understand string theory, or M-theory, in space-times that describe cosmological situations, space-times that expand. Understanding these space-times would lead to a resolution of the big bang singularity and would explain how the universe started.
One of the lessons of the black hole problem is that it is useful to go to another description where space-time arises dynamically, as an approximation. The black hole singularity is similar in some respects to the big bang singularity. So understanding black holes better would probably lead to a better understanding of cosmology.
Let us end by drawing a comparison. Einstein saw that Newton's theory and relativity were inconsistent. It took him around ten years to come up with a consistent solution. It can be argued that his theory of general relativity was born out of trying to solve this contradiction and it did not have much experimental input. Later experiments were done that tested his theory in an impressive way. String theorists are playing a similar game. We are trying to solve a similar contradiction. We do not have experiments to guide us, unfortunately. However we hope that once we find a solution, that will be the right theory describing nature. The problem is more complex, it has taken more people, working for around 20 years to get us where we are now. A lot of progress has been made, but there is still a lot of work to do.
The research of J.M. was supported in part by DOE grant DE-FGO2-91ER40654, NSF grant PHY-9513835, the Sloan Foundation and the David and Lucile Packard Foundation.
A book explaining string theory to the general public is Brian Greene, "The Elegant Universe," W. W. Norton & Company, 1999.
Other articles about string theory are:
E. Witten, "Reflections on the Fate of Space-time," Physics Today, Vol. 49, No. 4, pages 24--30; April 1996.
E. Witten, "Duality, Space-time and Quantum Mechanics," Physics Today, Vol. 50, No. 5, pages 28--33; May 1997.
M. Duff, "The Theory Formerly Known as Strings," Scientific American, February 1998.
A web-site describing string theory is http://superstringtheory.com
More technical books describing string theory are:
Green, Schwarz and Witten, "Superstring Theory," Vol 1, 2, Cambridge University Press
Polchinski, "String Theory," Vol 1, 2, Cambridge University Press
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https://edustrings.com/mathematics/2372625.html
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math
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16 September, 16:44
Volume of a sphere with a radius of 10
16 September, 18:43
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» Volume of a sphere with a radius of 10
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CC-MAIN-2023-40
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http://jacm.acm.org/archive.cfm?id=2049697
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math
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enter search term and/or author name
In the setting of secure two-party computation, two mutually distrusting parties wish to compute some function of their inputs while preserving, to the extent possible, various security properties such as privacy, correctness, and more. One...
Truthful and Near-Optimal Mechanism Design via Linear Programming
Ron Lavi, Chaitanya Swamy
Article No.: 25
We give a general technique to obtain approximation mechanisms that are truthful in expectation. We show that for packing domains, any α-approximation algorithm that also bounds the integrality gap of the LP relaxation of the problem...
Compositional Shape Analysis by Means of Bi-Abduction
Cristiano Calcagno, Dino Distefano, Peter W. O’Hearn, Hongseok Yang
Article No.: 26
The accurate and efficient treatment of mutable data structures is one of the outstanding problem areas in automatic program verification and analysis. Shape analysis is a form of program analysis that attempts to infer descriptions of the data...
Randomized Shellsort: A Simple Data-Oblivious Sorting Algorithm
Michael T. Goodrich
Article No.: 27
In this article, we describe a randomized Shellsort algorithm. This algorithm is a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and succeeds in sorting any...
New Constructive Aspects of the Lovász Local Lemma
Bernhard Haeupler, Barna Saha, Aravind Srinivasan
Article No.: 28
The Lovász Local Lemma (LLL) is a powerful tool that gives sufficient conditions for avoiding all of a given set of “bad” events, with positive probability. A series of results have provided algorithms to efficiently construct...
This work considers the quantum interactive proof system model of computation, which is the (classical) interactive proof system model’s natural quantum computational analogue. An exact characterization of the expressive power of quantum...
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https://studysoup.com/tsg/math/457/numerical-analysis/chapter/21854/3-1
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math
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- 3.1.1: For the given functions /(a), let Aq = 0, A| = 0.6, and X2 = 0.9. C...
- 3.1.2: For the given functions/(a), let aq = 1,A| 1.25, and A2 = 1.6. Cons...
- 3.1.3: Use Theorem 3.3 to find an error bound for the approximations in Ex...
- 3.1.4: Use Theorem 3.3 to find an error bound for the approximations in Ex...
- 3.1.5: Use appropriate Lagrange interpolating polynomials of degrees one, ...
- 3.1.6: Use appropriate Lagrange interpolating polynomials of degrees one, ...
- 3.1.7: The data for Exercise 5 were generated using the following function...
- 3.1.8: The data for Exercise 6 were generated using the following function...
- 3.1.9: Let Pjix) be the interpolating polynomial forthe data (0, 0), (0.5,...
- 3.1.10: Let fix) = -fx x 2 and //(x) be the interpolation polynomial on xq ...
- 3.1.11: Use the following values and four-digit rounding arithmetic to cons...
- 3.1.12: Use the Lagrange interpolating polynomial of degree three or less a...
- 3.1.13: Construct the Lagrange interpolating polynomials for the following ...
- 3.1.14: Construct the Lagrange interpolating polynomials for the following ...
- 3.1.15: Let /(x) = e x , for 0 < x < 2. a. Approximate /(0.25) using linear...
- 3.1.16: Let f(x) e~x cosx, for 0 < x < I. a. Approximate /(0.25) using line...
- 3.1.17: Suppose you need to construct eight-decimal-place tables for the co...
- 3.1.18: In Exercise 24 of Section 1.1, a Maclaurin series was integrated to...
- 3.1.19: a. The introduction to this chapter included a table listing the po...
- 3.1.20: It is suspected that the high amounts of tannin in mature oak leave...
- 3.1.21: Show that max |g(x)| =/z2 /4, where g(x) = (x -/7z)(x - (y + 1)A).
- 3.1.22: Prove Taylor's Theorem 1.14 by following the procedure in the proof...
- 3.1.23: The Bernstein polynomial of degree n for / C[0, 1] is given by wher...
Solutions for Chapter 3.1: Interpolation and the Lagrange Polynomial
Full solutions for Numerical Analysis | 10th Edition
Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.
Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.
Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).
Dimension of vector space
dim(V) = number of vectors in any basis for V.
Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.
Eigenvalue A and eigenvector x.
Ax = AX with x#-O so det(A - AI) = o.
Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.
Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.
Jordan form 1 = M- 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.
Left inverse A+.
If A has full column rank n, then A+ = (AT A)-I AT has A+ A = In.
Length II x II.
Square root of x T x (Pythagoras in n dimensions).
Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).
Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.
Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.
Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.
Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.
Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn- 1 with P(Xi) = bi. Vij = (Xi)j-I and det V = product of (Xk - Xi) for k > i.
Stretch and shift the time axis to create Wjk(t) = woo(2j t - k).
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CC-MAIN-2020-45
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https://bialkeinsurance.com/ft-min-acd/b7286c-representative-fraction-scale-example
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math
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Map Scale: 1: Map Distance: Ground Distance Units: At a map scale of 1:100000, 1 millimeter on the map is equivalent to 1 kilometer on the ground. A representative fraction, or RF, shows the relationship between one of any unit on the map and one of the same unit on the ground. - Scale is a fraction, expressed in 3 ways: - Representative Fraction (RF), e.g. The proportion, or ratio, is also typically expressed in the form 1 … ), also known as scale ratios, relate the size … Verbal and RF scales do not. Representative fraction and scale bars from a United States Geological Survey (USGS) topographic map. Construct a graphical scale for representative fraction 1:50,000 in which distance is given in furlongs and miles. Example 2 If a 5 cm long line in the drawing represents 3 km length of a road, then in engineering scale it is written as 1 cm = 600 m and in graphical scale … The notes below highlight key points which are not explicitly stated on slides. The graphic scale is sometimes called the bar scale, and the representative fraction is the RF or the fractional scale. C. Representative Fraction (RF) or Natural Scale: 1:1,000,000 (this is the same as 1/1,000,000) The RF says that 1 of any measurement on the map equals 1 million of the same measurement on the original surface; for the example above 1-foot equals 1 million feet or 1 cm. carries no units (inches, centimeters, etc. This topographic map has an RF of 1:24,000, which means that one unit on the map represents 24,000 units on the ground. A verbal scale is inserted the same way as a representative fraction – click on Insert on the top bar menu and select Scale Text (figure 2). It is represented in ratio, which we call Representative Fraction. In representative fraction (RF), the scale on the map is expressed in the numerical fraction. The scale ratio is always written as one unit on the photo or map to the corresponding number of units on the ground. (no drawing work only, explaining their meanings.) The most common are: 1. If the scale is a representative fraction (and looks like 1/100,000), multiply the distance of the ruler by the denominator (100,000 in this case), which denotes distance in the ruler units. Scale bars are graphical representations of distance on a map. tells the size relationship between the map or model and the real earth.. For example, a map where one unit (centimeter, meter, inch, kilometer, etc.) Graphic scale remains accurate if a map is enlarged or reduced. Representative Fraction (R.F. scale is a ratio, or fraction, that expresses the mathematical relationship between MAP and LAND, such as 1 : 24,000. which means "1 map unit is equivalent to 24,000 land units." These are representative fraction, scale statement and graphic or bar scale. The actual printed map coordinates for the equirectangular cylindrical projection are Compared to the first two, it is the most abstract, but also the most versatile. Calculate ground distance given map scale and map distance. Scale can be stated in three ways. It can be written in three ways, the verbal scale, the graphic scale, and the representative fraction (RF) or fractional scale. Two of these different kinds of scale are shown on your map. Here such a scale means that one unit of measurment on the map is equal to 50000 of the same unit on the ground. RATIO or REPRESENTATIVE SCALE A ratio or representative fraction (RF) indicates how many units on the earth's surface is equal to one unit on the map. Such maps are called large scale because the representative fraction is relatively large. Other scale variations are sometimes used in addition to the standard forms. The units will be listed on the map, such as 1 inch or 1 centimeter. equals 1 million cm. Eg: 1: 50000 means 1 cm on the map is 50000 cms on actual ground. For example: The third type of scale is a representative fraction, or ratio scale. The representative fraction 1:100,000, for example, means that a section of road that measures 1 unit in length on a map stands for a section of road on the ground that is 100,000 units long. Its advantage is that it has universal application. A map scale can be printed in a variety of ways. By convention, the proportion is expressed as a "representative fraction" in which map distance (D m) is reduced to 1. Representative fraction (RF) or natural scale 1:1,000,000 (this is the same as 1/1,000,000) The RF says that 1 of any measurement on the map equals 1 million of the same measurement on the original surface; for the example above 1 foot equals 1 million feet or 1 cm. All but the first options are verbal scales – choose the one that will make the most sense to your map readers. It can be expressed as 1/100,000 or 1:100,000. The three ways of stating scale are the verbal scale, the graphic scale, and the representative fraction. Even people who live in foreign countries can find the distance on the map even if they are not familiar with the units of measurements of that country. The verbal scaleis a simple statement of the scale such as one inch equals one mile or 1" = 1 mile.The unit on the map should be appropriate to the dimensions of the map. This RF scale means that 1 unit on the map represents 50 000 of the same units on Earth's surface. Representative fraction. INTRODUCTION TO UNIT CONVERSION & SCALE PROBLEMS Representative Fraction (RF) When looking at a paper map, probably the most important thing to bear in mind is the map scale. Example sentences with "representative fraction", translation memory. C) A Representative Fraction Scale removes the units and shows the direct relationship between the two measurements. These formats are the representative fraction, the verbal statement, the graphic or bar scale, and the area scale. (It could also be shown as l/50 000, but this form is not as common.) Answer: For graphical scale, to know the length of the line we need to make following calculations. It may be expressed in various ways. At a map scale of 1:100000, 1 kilometer on the ground is equivalent to 1 millimeter on the map. Map scales are expressed in a variety of ways (RF, verbal, graphic). Representative fractions (R.F. Because an R.F. A simple ratio or fraction, known as the representative fraction. It can be used in all countries and also termed as International Scale. Representative Fraction (RF) - Fractional Scale - Ratio Scale: 1:50000 represents the map scale as a mathematical ratio or fraction, thus the name ratio scale or fractional scale. ), it means that the R.F. This type of description of a map's scale is called a representative fraction. REPRESENTATIVE FRACTION (R.F.) An RF is a ratio and is shown as follows: 1:50 000. The scale of a chart is the ratio of a given distance on the chart to the actual distance which it represents on the earth. 1:50,000 means 1 unit on map represents 50,000 units on ground. Converting Between Scale Types of Historic and Modern Maps, page 3 Converting Representative Fraction (RF)/Ratio Scale to Lexical Scale English and Metric Measures of Length to use:. This type of scale representation visually looks very similar to representative fraction (RF). However, representative fraction avoids the use of units in detailing the scale of a map. 2. 3. The advantage of this distinction between varying scale on the super map and a constant RF is that for the former we can analyse scale variation around a value of unity. 1:50000 can be shown as 1/50000 as well. Map scale is the proportion between a distance on a map and a corresponding distance on the ground: (D m / D g). The scale represents the ratio of a distance on the map to the actual distance on the ground. 3.2.1 Representative fraction. method called a universal method because of its usefulness on global scale. Graphic scale. SCALE Scale. 2. Topic: Example of Map Scale – Representative Fraction Fall 2020 Geog 104 1 Instructions: Online instruction provides challenges in delivering lecture material.The additional explanatory text below adapts lecture slides for online viewing. 1 inch (in) = 2.54 centimeters 1 centimeter (cm) = 0.39 inch 1 foot (ft) = 12 inches = 30.5 centimeters = 0.3 meter 1 yard (yd) = 36 inches = 3 feet = 91.44 centimeters = 0.9 meter For example, scale that has a RF of 1:100 means that every one unit on the map equals one hundred of the same units on the ground. This is preferable to the analysis of variations about fractions such as 1/10,000 or 1:10M (million). This fraction is called the representative fraction or simply "RF" in short. Representative Fraction. a representative fraction of the total sample that is to be analyzed in the individual laboratories. scales can be compared between different maps. The numerical scale of a map indicates the relationship of distance measured on a map and the corresponding distance on the ground. ... Representative Fraction (R.F.) 1:100,000 - Verbal Scale 'One cm represents one km' - Graphic Scale - a line labelled with the distance it represents. ): An R.F. For example, the graphic scale might show a scale marked of in 1 cm units but labels them each as 10 km, 20 km etc. The representative fraction (RF) is commonly stated as a ratio of two numbers separated by a colon. Verbal Scale Representative fraction scale (RF): Two other terms refer to the representative fraction scale - the fractional scale and the RF scale which is the scale ratio written in fractional form, 1/20,000. Most people chose this as the best definition of representative-fraction: (cartography) The scale o... See the dictionary meaning, pronunciation, and sentence examples. Statement of a scale describes in words the distance on the map, and it's equivalent distance on Earth's surface. This scale is usually written as a fraction and is called the representative fraction. ... EurLex-2. Representative Fraction The expression of map scale as a mathematical ratio. Verbal map scale: A map scale that expresses the relationship between distance on the map and distance on the ground in words; for example, "One inch equals 10 miles." on the illustration represents 1,000,000 of these same units on the actual surface of the Earth would have a representative fraction of 1/1,000,000 (fraction) or 1:1,000,000 (ratio). Correct answers: 1 question: Reading and using statement of scale, scale and scale shown by representative fraction method. The RF is always written with the map distance as … equals 1,000,000 cm. For example, a scale of one inch to a furlong (1:7920) ... To avoid confusion in the use of the word 'scale' this constant scale fraction is called the representative fraction (RF) of the printed map and it is to be identified with the ratio printed on the map. In this example, one centimeter on the map equals 100,000 centimeters (1 kilometer) on the earth. Representative fraction definition is - a map scale in which figures representing units (as centimeters, inches, or feet) are expressed in the form of the fraction 1/x (as 1/250,000) or of the ratio 1:x to indicate that one unit on the map represents x units (as 250,000 centimeters) on the earth's surface. For example, if we say that the scale of a map is 1 cm : 1 km, it would be understood by only that person who is familiar with the metric system of measurement.
Gloomhaven Enhancement Pdf, English Essay Titles, Principles Of Advertising Ethics, How To Draw Bacteria, True Lemon Cucumber, Best Quotes Pdf, Rick Steves Greek Islands, 8mm Vinyl Plank Flooring, Criterion Hotel, Trafalgar Menu,
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CC-MAIN-2021-25
| 11,512 | 2 |
https://www.mathmadeeasy.co/quadratic-equations
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math
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NATURE OF THE ROOTS OF A QUADRATIC EQUATION
What is the Discriminant of a Quadratic Equation? You will see how to calculate the discriminant and find the nature of the roots of the quadratic, depending on whether D > 0. D = 0 or D < 0. Different cases when D is a perfect square or not are also discussed.
PROBLEMS-NATURE OF THE ROOTS OF A QUADRATIC EQUATION
Presenting a few problems on nature of the roots of a quadratic equation. Given the nature of the roots, you will see how other parameters can be determined.
HOW TO FORM A QUADRATIC EQUATION GIVEN THE ROOTS
Given 2 roots of a quadratic equation, you will learn how to form the equation using a simple formula. 2 problems are solved here. A very profound concept.
SOLVING QUADRATIC INEQUALITIES
Learn how quadratic inequalities can be solved using the method of intervals. Note how this method works only if the coefficient of the highest degree term is non negative. This is extensively used in Calculus, Applications of Derivatives.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150266.65/warc/CC-MAIN-20210724125655-20210724155655-00103.warc.gz
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CC-MAIN-2021-31
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https://www.jiskha.com/members/profile/posts.cgi?name=KnowsNothing
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math
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Posts by KnowsNothing
Total # Posts: 10
The complete combustion of 1.00mL of octane increases the temperature of 250.00g of water by 22.7 degrees Celsius. The density of octane is 0.70g/mL. What is the efficiency of the octane in heating the water? I attempted this question and I have -400 something percent ...
Math (Adv. Functions)
Given that triangle ABC with sides a, b, and c, show that the area of the triangle is given by A = ((a^2)(sinB)(sinC))/((2sin(B+C)))
Is lead non-polar covalent, polar covalent, ionic, network, or metallic and why?
Determine a vector that is orthogonal to the vector e = [3, -1, 4]
A molecule has a glycerol backbone. The branches off of the three carbons are as follows: o-co-(ch2)14 - ch3 o-co-(ch2)12 - ch3 o-co-(ch2)16 - ch3 What is this compound called?
When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2. Determine the remainder when the polynomial is divided by (x-1)(x+2).
In a Milliken type experiment, two horizontal parallel plates are 1.0 cm apart. A sphere of mass 2.2 x 10^(-13) kg remains stationary when the potential difference between the plates is 350V with the upper plate is negative. How much excess or deficit of electrons does the ...
What is the difference between electric force, electric potential energy, electric field strength, electric potential, and electric potential difference?
THANK YOU. ;A;
A bullet with the mass of 45 g is fired into an 8.3 kg block of wood resting on a floor against a spring. This ideal spring (k = 76 N/m) has a maximum compression of 28 cm. What was the initial speed of the bullet?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886102891.30/warc/CC-MAIN-20170817032523-20170817052523-00577.warc.gz
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CC-MAIN-2017-34
| 1,651 | 13 |
https://vatcalculatorlive.co.uk/graphical-calculators/
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math
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Updated on February 23, 2024
Graphical Calculators: A Powerful Tool for Math and Science
Graphical calculators are handheld devices that have revolutionized the way students and professionals approach mathematics and science. These powerful tools allow users to visualize complex mathematical concepts, graph equations, and perform calculations with ease. In this article, we will explore the many benefits of graphical calculators and how they can help students excel in their studies.
What is a Graphical Calculator?
A graphical calculator is a portable electronic device that is specifically designed for solving complex mathematical problems. These calculators have advanced features such as graphing functions, solving equations, and performing statistical analysis. They are commonly used in high school and college-level math and science courses.
Benefits of Using a Graphical Calculator
There are numerous benefits to using a graphical calculator in your studies. Some of the key advantages include:
1. Graphing Functions
One of the most powerful features of a graphical calculator is its ability to graph functions. This allows users to visualize the relationship between different variables and understand complex mathematical concepts more easily. For example, students can graph trigonometric functions, exponential functions, and more with just a few keystrokes.
2. Solving Equations
Graphical calculators also make solving equations a breeze. Users can input an equation into the calculator, and it will provide the solution in a matter of seconds. This is especially helpful for solving systems of equations, quadratic equations, and other complex problems that would be time-consuming to solve by hand.
3. Performing Statistical Analysis
Graphical calculators are also ideal for performing statistical analysis. Users can input data into the calculator and quickly generate graphs, calculate averages, and perform hypothesis tests. This is particularly useful for students studying statistics or professionals working in the field of data analysis.
How to Choose the Right Graphical Calculator
There are several factors to consider when choosing a graphical calculator. Some of the key considerations include:
Consider the specific features that you need for your studies or work. Look for calculators that have graphing capabilities, solving equations, and statistical analysis tools to ensure that it meets your requirements.
2. Memory and Storage
Check the memory and storage capacity of the calculator. Make sure it has enough space to store equations, graphs, and other data that you may need for your calculations.
3. Design and User-Friendliness
Choose a graphical calculator that is easy to use and navigate. Look for calculators with intuitive interfaces, clear displays, and ergonomic designs that make it comfortable to use for long periods of time.
Graphical calculators are powerful tools that can help students and professionals excel in their math and science studies. With features such as graphing functions, solving equations, and performing statistical analysis, these devices make complex calculations easier and more accessible. When choosing a graphical calculator, consider factors such as features, memory and storage, and user-friendliness to ensure that it meets your specific needs. Invest in a high-quality graphical calculator today and take your math and science skills to the next level!
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CC-MAIN-2024-18
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https://nrich.maths.org/public/topic.php?code=104&cl=3&cldcmpid=653
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math
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Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
What is the same and what is different about these circle questions? What connections can you make?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Can you find triangles on a 9-point circle? Can you work out their angles?
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
This set of resources for teachers offers interactive environments which support work on properties of angles in circles at Key Stage 4.
Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.
Describe how to construct three circles which have areas in the ratio 1:2:3.
It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .
The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.
Can you find a relationship between the area of the crescents and the area of the triangle?
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .
A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?
A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?
An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
How much of the field can the animals graze?
Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
Keep constructing triangles in the incircle of the previous triangle. What happens?
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
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https://statanalytica.com/blog/discrete-mathematics/
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math
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There are several students who face issues related to the preparation of a discrete mathematics assignment because of the inadequate knowledge for the difference between continuous and discrete mathematics. Discrete mathematics is contrary to that of continuous math, as the following can deal with concepts that vary smoothly. How much be the complication of the assignment, one needs to prepare instant and good discrete math assignment. Various topics under discrete math involve focusing on executions, algorithms, and efficiencies. These can be done to improve the knowledge so that one can master the discrete maths’ skills and comfortably complete their assignment.
What is mathematics/maths?
Table of Contents
Math is a discipline that includes the study of quantity, shapes, and arrangements. It is the basic foundation of each one’s daily life, such as in sports, engineering while driving the bus/car on the road, and much more. Maths lies in all aspects of daily routine.
There are two types of math which are discussed below
It deals with the real numbers or continuous number lines. It is described by the point that within any two numbers, there is nearly always an infinite numbers’ set. For instance, a function of continuous math can be outlined in a constant curve without dividing the line anywhere.
It includes distant values that are between the two given points, which are countable numbers. For instance, if one has a finite number set, then the function defines as an ordered pairs’ list that has several objects, and it can be presented as an overall list of these defined pairs.
Topics that include in the discrete mathematics
Though it does not have a definite number of the branches, still, there are following topics that are always considered as discrete mathematics in the study. Almost all students need to make the discrete math assignment based on these following topics:
- Mathematical logic.
- Counting theory.
- Recurrence relation and mathematical induction.
- Relation, Set, and Functions.
- Group theory.
- Graph theory.
- Boolean Algebra.
Why one needs to study the discrete math
It is essential for college-level maths and beyond that too
Discrete mathematics comprises abstract algebra and calculus, which are the core subjects of maths at the undergraduate level. Therefore, it is necessary that students must learn this before taking admissions to the colleges. So that they can easily study this subject in college and after college studies.
Discrete math uses for computing
The modern computer science’s mathematics is entirely based upon discrete mathematics, particularly with graph theory and combinatorics. It implies that if one wants to learn the basic algorithms for the computer programming language, they require to have a solid background in this mathematical subject. Even though, at various universities, an undergraduate course with discrete mathematics is mandatory to pursue a degree in computer science subjects.
Discrete math deals with “real world” mathematics
Several students have complained that subjects such as geometry, algebra, trigonometry, and other maths branches do not have any use for them. Therefore, if they feel these subjects as boring, but in contrast, discrete math, especially probability and counting, grant the students to explore non-trivial problems of the “real world” quickly and effectively. It might be challenging for them, and besides this, it is very interesting too.
Discrete math involves in content at middle and high school to increase knowledge
Renowned American math competitions (at high school level) and math competitions like MATHCOUNTS (at middle school level) feature the questions of discrete math as an essential portion of the contents. Other harder level of the competitions like AIME, the level of discrete math is even larger. Therefore, students who do not have any ideas about discrete mathematics may work against them in these kinds of contents. There is a coach of MATHCOUNTS who tells that he spends almost 50% of his practice time with the students for covering probability and counting topics, as both are the important topics of discrete math in MATHCOUNTS contest.
Discrete math increase knowledge of mathematical proof and reasoning techniques
Algebra deals with the series of algorithms and formulas, and students need to memorize them (for instance, solving the linear equation with substitution methods, the quadratic formula, and much more), whereas geometry deals with the series of definitions, its theorem, then finally of exercises, which are done with the rote (for instance, “Two-column proof”). So, we can say that it is undoubtedly the subject of being taught with effective material so that it helps you to develop creative mathematical thinking. Besides this, discrete helps the students to think creatively and flexibly, which leads to thinking out of the box. Discrete math deals with various formulas that need to memorize, instead, masters with the fundamental concepts.
Discrete math is “fun”
There are some students who find geometry, calculus, and algebra uninspiring and dull. But this is in some cases. But a study shows that various students whose favorite topics are “number theory” or “combinatorics”, but the same students define their least favorite topics are related to geometry. Therefore, it can be concluded that discrete math has more fun than that of geometry or algebra.
How to deal with your discrete mathematics assignment effectively
During a class
Attend regular math classes that help you with discrete math assignments by providing the course notes and relevant materials. As the classes can not be repeated; therefore, you need to attend them regularly. Ask your teachers questions related to discrete math and practice them. After the class, review your class notes and rework on them to have the command on them. If you still face any difficulty with your assignment, then you can take your teachers’ help to solve them.
Outside of class before the material would be covered within the class
At the beginning of the exercises, you might face issues while your teacher assigns you a discrete math assignment. Therefore, it becomes necessary to understand the problems; for this, you can read the notes of the exercises, understand definitions. Make the effective notes of definitions understand properties, formulas, and theorems. Keep in mind that one does not spend more than 20 minutes on a single exercise. When one comes to study materials, one needs to believe that it helps you to solve the exercises, make relevant notes, and try the exercise. Besides this, take participation in an online quiz of each unit.
Outside of class after the material would be covered within the class
Work on the section in which you find the most difficult and if one is not able to progress in that section, make you can take your teachers’ help to make the relevant notes. Always keep reread the notes and practice them so that you can easily make a discrete mathemati assignment effectively. Reread lectures and exercises note and cover all the study material that you have given during the classes as you know that after completing the syllabus, the teacher can take your test or exams to know what you have learned during the classes. Therefore, you need to revise the notes that you have made during the class and practice them several times to get perfect in these problems.
Other tips for dealing with discrete mathematics assignment
Study at the same place
When you study in the same place, you get familiar with it, which helps you to get comfortable so that you can write your discrete math assignment easily.
Distraction like smartphones, t.v. noise might cause a problem to focus on your study. This might also be the reason for low grades in your discrete math assignment because discrete math needs high concentration to understand its definitions, theorems, and other things.
Schedule your study
Discrete math is one of the complicated subjects of mathematics; therefore, it is necessary to schedule your study with at least 90 minutes that involve 10 minutes breaks. Structure it with proper planning about what you have to study in these 90 minute periods and complete your discrete math assignment within this duration.
Avoid passive study
When you are studying notes, try to take your own written notes, conclusions, grouped topics in a meaningful manner, write the questions related to your readings, and practice exercises that you have involved in your notes.
Make weekly plans
Because of the complexity of the mathematics, it is necessary that one should divide the units in a small portion. This will help you to solve the problem more effectively. This can do it by studying each unit for at least 3 days each week outside of the classroom.
Prefer a group study with your classmates or with the people who love discrete mathematics. Work thoroughly with them, and this helps you to make your discrete math assignments too. Besides this, keep in mind that your intensive study and initial reading must be done alone as you are the only one who can understand your own problems and analysis where you stuck while solving the problems.
Avoid dehydration and hunger (like junk food)
Keep yourself hydrated, and do not eat snacks too much as it leads to laziness while studying. Try to include bananas, power bars, raisins, and other healthy snacks in your diet. Exercise regularly to remain active.
Manage your break time
f you need a break for lunch or dinner between your study, then manage it for at least 30 minutes. Other breaks must be of 10 minutes, also ensure that when you take the break, it should be a complete break.
NOTE: Adequate food and sleep are mandatory to remain healthy and to keep your brain work properly. Besides all this, try to include some extra in your life and your schedule such as sport, other activities. One requires to plan “playtime” to enjoy life outside of the classes.
This blog has provided all the relevant information about how to deal with your discrete math assignment effectively. This post involves the definition of mathematics, its types, topics that include discrete mathematics, why one needs to study discrete math, and methods to deal with discrete math with tips. Follow all these methods to learn discrete math effectively. Make sure that you should test yourself with online test series so that you can work on your mistakes to score good grades in academics.
If you still face any difficulty related to your discrete math assignment, then avail of our services for trigonometry assignment help. Our trigonometry homework experts can provide you high-quality content within deadlines. We are accessible 24*7, and all your assignments are available at a reasonable price. This will let anyone afford our services from around the globe.
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https://www.fxstreet.com/education/using-the-options-profit-loss-graph-201805300655
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math
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The next few articles will be about using the Option P/L Graph. This is a tool built into every option trading platform. Most option traders know it is there, but not all fully understand its use or its importance.
Today’s examples will be the simplest possible ones. We’ll progress from these to more sophisticated ones in future articles.
The example today depicts a trade on a particular option: called a Call option, at a strike price of $273 on shares of the exchange-traded fund SPY.
SPY was trading around $273. The price of the 273 call, expiring in a few days on June 15, 2018 was $325 per option contract at the time. So, $325 would be the amount paid by any option buyer to the option seller in this trade. Assume that to begin with, neither the buyer nor the seller of the call had any position in the shares of SPY itself – the option position alone is the entire position for each of them.
Below are two graphs of the trade. The first graph represents the profit or loss on the trade that would be experienced by the option buyer, if the position was held until expiration. The second graph represents the profit or loss experienced by the seller of that same option. Everything but the essentials has been removed from the graphs.
The horizontal axis is labeled Underlying Price. On option P/L graphs we read stock price from left to right, rather than from bottom to top.
The vertical axis is labelled Theo Value P/L (Theoretical Value Profit or Loss).
The blue line on each graph relates the profit or loss on the trade at a particular date, in this case the expiration date of 06/15/18, to any given price of the stock at that time.
Note what is similar about the two graphs. On each one, there is a horizontal section of the blue P/L line. Looking at the blue line from left to right, it is flat from the left side of the graph up to the point where Underlying Price equals 273.
Now look at the value on the left-hand scale next to the horizontal blue lines.
On the first graph (the buyer’s), the value is a little below -$300. To be precise, it is at -$325. What this means in practical terms is that, if at expiration of the call the value of the stock is below the $273 strike price, then the call will be worthless; and because the call buyer originally paid $325 for the call and he now receives nothing, his P/L would be a loss of the full purchase price of $325.
Now look at the second graph. The value on the P/L axis at the horizontal line section is a little above +$300. To be precise, once again, it is at +$325. This means the same thing that it did for the call buyer, but in reverse: if the stock is at any price below the $273 strike at expiration, then the 273 call will be worthless. This is the best case for the call seller. He will have been paid $325 for something that subsequently became worthless. He does not need to take any action to terminate the trade. The option expires and he has a clear profit equal to the $325 that he originally received.
So, in any case where the stock on expiration day is below $273, then the score is Option buyer $-325, Option Seller +$325.
Now look to the right side of that $273 Underlying Price, first on the buyer’s graph. In particular, find $276 on the Underlying Price scale. Look up the dotted vertical line at 276 until you locate the intersection with the blue line. Now look left from that point to see at what position that intersection is on the left scale. You’ll find that it is a little below zero. To be exact, it is at -$25.
Think about the value of the call if SPY were to be at $276 at expiration. In that case, the 273 call would not be worthless. It would then be the right to buy 100 shares at a $3.00 discount per share ($276 market price less $273 strike price). This discount to market value would be the intrinsic value of the call in that case. (At expiration, every option is worth exactly its intrinsic value). The call buyer at that time could recover the $300 intrinsic value in one of two ways. He could either sell the call for $300; or he could exercise the call and then sell the stock for a $300 profit. Same result either way. In either case, he would have salvaged $300 of his original call purchase price of $325, and so would have a $25 net loss. Hence the value shown on the Theoretical P//L scale of $-25.
Now do the same for the second (seller’s) graph. Notice that at an Underlying price of $276, the value for Theo Value P/L is a little above zero. It is at +$25 to be exact.
Since with the stock at $276, the intrinsic value of the call is ($276 – $273) X 100 = $300 (same as in the buyer’s case), the call seller must now pay $300 to terminate the trade. Once again, this can happen in one of two ways. First, if the call seller does nothing, the option will be exercised. All in-the-money options are automatically exercised at expiration. In that case he will be forced to buy the shares at their market value of $276, so that he can meet his obligation to deliver the stock in exchange for $273 in cash. He loses $3 per share ($276 market price paid, less $273 received upon exercise), times 100 shares, for a total of $300 out of pocket.
Alternatively, the call seller could just buy back the call for its $300 market value just before expiration, which would also negate his obligation to deliver the stock. Either way, he is out of pocket by $300.
Since the call seller originally received $325 for the call, and he must now pay $300 of that back to extract himself from the trade, he has a net profit of $325 – $300 = $25.
So, in the case where the stock ends up at $276 at expiration, the score is Call Seller +$25, Call Buyer -$25.
If you follow the same process at a higher Underlying Price, say, 279, you’ll find that the score is Call Seller -$275, Call Buyer +$275.
In fact, no matter what the price of the stock might be at the point in time depicted by the blue line (expiration), whatever the call buyer’s profit or loss is, the call seller’s is equal and opposite.
In graphic terms, imagine a horizontal line at the zero P/L level, drawn from left to right across each graph. Now imagine the chart being rotated top-to-bottom around that horizontal line. After the rotation, the graph is now that of the other player. The buyer’s graph becomes the seller’s, or vice-versa. This is proof that this option trade (and every option trade) is a zero-sum game, with one player’s gain exactly equaling the other’s loss. Their positions are mirror images of each other, with the edge of the mirror on the zero P/L line.
If you are interested in options, take the time to study and understand these two graphs. Make sure these points are clear:
A situation where an option is worthless is the best case for the seller, because the seller keeps the whole amount originally received for the option as clear profit. This shows on a P/L graph as a horizontal line at a positive P/L value equal to the credit received.
That is also the worst case for the buyer, who loses everything he paid. On his graph, this appears as a horizontal line at a negative value, equal to the debit paid.
If the option is not worthless at expiration, then the buyer can recover some of what he paid, or maybe more than he paid. Whatever he realizes from the option in that case in effect comes out of the pocket of the option seller. There is no limit on how much this could be. The option buyer’s potential profit is unlimited; his P/L graph extends upward off the chart. The same is true in reverse for the seller, showing that his maximum loss is unlimited.
So far, in this example we have only looked at the situation as it would exist at one particular moment in time – the moment of expiration. In future articles we will see how the P/L graphs portray the situation at different future times.
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CC-MAIN-2020-29
| 7,846 | 28 |
https://www.theinternet.io/articles/ask-ai/136q24q73q12-solve-for-q/
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math
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Ask AI on The InternetAsk Another Question Browse Other Questions
First, let's eliminate the fractions and distribute the 1/3 to both terms within the parentheses: (1/3)*(6q - 2) = 3*(4q - 7/3q - 1/2) 2q - 2/3 = 12q - 7 - 3/2 Now, let's clear the fractions by finding the least common denominator (LCD) which is 6: 6(2q - 2/3) = 6(12q - 7 - 3/2) Now, distribute the 6 on both sides of the equation: 12q - 4 = 72q - 42 - 9 Next, let's move all the terms with the variable 'q' to the right side and constant terms to the left side: -4 + 42 + 9 = 72q - 12q Combine the like terms: 47 = 60q Now, to find the value of 'q', simply divide both sides by 60: q = 47 / 60 Since both 47 and 60 are prime, we cannot simplify this fraction further: q = 47/60
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CC-MAIN-2023-23
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https://www.coursehero.com/file/6381202/3cEstimatingPopulationSizeDi/
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math
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Unformatted text preview: Exercise 3C Estimating Population Size & Distribution
Parts of this lab adapted from General Ecology Labs, Dr. Chris Brown, Tennessee Technological University and Ecology on
Campus, Dr. Robert Kingsolver, Bellarmine University. Introduction
One of the goals of population ecologists is to explain patterns of species distribution and
abundance. In today’s lab we will learn some methods for estimating population size and for
determining the distribution of organisms.
Measuring Abundance: Quadrats
One of the first questions an ecologist asks about a population is, "How many individuals are
here?" This question is trickier than it appears. First, defining an individual is easier for some
organisms than others. In Canada geese, a "head count" of geese captured on the ground during
their summer molt gives a clear indication of adult numbers, but should eggs be counted as
members of the population or not? In plants, reproduction may occur sexually by seed, or
asexually by offshoots that can remain connected to the parent plant. This reproductive strategy,
called clonal reproduction, makes it difficult to say where one individual stops and the next one
Once the individual is defined, ecologists working with stationary organisms such as trees or
corals can use spatial samples, called quadrats, to estimate the number of individuals in a larger
area. Quadrats are small plots, of uniform shape and size, placed in randomly selected sites for
sampling purposes. By counting the number of individuals within each sampling plot, we can see
how the density of individuals changes from one part of the habitat to another. The word "quadrat"
implies a rectangular shape, like a "quad" bounded by four campus buildings. Any shape will work,
however, as long as quadrats are all alike and sized appropriately for the species under
investigation. For creatures as small as barnacles, an ecologist may construct a sampling frame a
few centimeters across, and simply drop it repeatedly along the rocky shore, counting numbers of
individuals within the quadrat frame each time. For larger organisms such as trees, global
positioning equipment and survey stakes may be needed to create quadrats of appropriate scale.
The number of individuals counted within each quadrat is recorded and averaged. The mean ( x )
of all those quadrat counts yields the population density, expressed in numbers of individuals
per quadrat area (barnacles per square meter, for example, or pine trees per hectare).
Population size can then be estimated using the formula:
N = (A/a) * n where: N = the estimated total population size
A = the total study area
a = the area of the quadrat
n = the number of organisms per quadrat Note: this formula can be used with one quardat or an average of all the quadrats as long as the
area (a) matches the number of organisms/quadrat (n).
Biology 6C 73 An alternative approach is to measure ecological density, expressed in numbers of individuals
per resource unit (numbers of ticks per deer, for example, or numbers of maggots per apple).
Members of a population constantly interact with physical features of their environment, one
another, and other species in the community. Distinctive spatial patterns, describing the
distribution of individuals within their habitat, result from these interactions. Movements, family
groupings, and differential survival create spatial patterns that vary from one population to
another. A population can also change the way it is scattered through space as seasons or
conditions change. As an example, monarch butterflies spread out to feed and reproduce during
the summer, but congregate in dense assemblies during fall migration and winter dormancy. The
physical arrangement of organisms is of interest to ecologists because it provides evidence of
interactions that have occurred in the past, and because it can significantly affect the population's
fate in the future. Analyzing spatial distributions can reveal a lot more about the organism's natural
history than we could ever know from estimates of population size alone. Since it is often impossible to map the location of every individual, ecologists measure features of
spatial pattern that are of particular biological interest. One such feature is the dispersion of the
population. D ispersion refers to the evenness of the population's distribution through space.
(Dispersion should not be confused with dispersal, which describes movement rather than
pattern.) A completely uniform distribution has maximal dispersion, a randomly scattered
population has intermediate dispersion, and an aggregated population with clumps of individuals
surrounded by empty space has minimal dispersion (Figure 3.1). Figure 3.1 Three types of spatial distribution. Individuals spread evenly through
the environment are highly dispersed, individuals clumped together exhibit low
dispersion. How can we measure dispersion in populations? A typical approach again involves quadrat
sampling. By counting the number of individuals within each sampling plot, we can see how the
density of individuals changes from one part of the habitat to another. To get a measure of
dispersion in our population, we need to know how much variation exists among the samples. In
other words, how much do the numbers of individuals per sampling unit vary from one sample to
the next? The sample variance (s2) gives us a good measure of the evenness of our distribution. 74 Exercise 3.C. Estimating Population Size & Distribution Consider our three hypothetical populations, now sampled with randomly placed quadrats (Figure
3.2). Notice that the more aggregated the distribution, the greater the variance among quadrat
counts. To standardize our measurements for different populations, we can divide the variance by
the mean number of individuals per quadrat. This gives us a reliable way to measure aggregation.
Statisticians have demonstrated that the variance/mean ratio,
x , yields a value close to 1 in a
randomly dispersed population, because in samples from a random distribution the variance is
equal to the mean. Any ratio significantly greater than 1 indicates aggregation, and a ratio less
than 1 indicates a trend toward uniformity. We could therefore call the variance/mean ratio an
index of aggregation, because it is positively related to the "clumping" of individuals in the
population. The variance/mean ratio is also called an index of dispersion, even though
dispersion is inversely related to
x . It is good to remember: a high value of
x means high
aggregation, but low dispersion. Bear in mind that the size of the sampling frame can significantly influence the results of this kind
of analysis. A population may be clumped at one scale of measurement, but uniform at another.
For example, ant colonies represent dense aggregations of insects, but the colonies themselves
can be uniformly distributed in space. Whether we consider the distribution of ants to be patchy or
uniform depends on the scale of our investigation. Figure 3.3 illustrates a population that would be
considered uniformly distributed if sampled with large quadrats, but aggregated if sampled with
smaller quadrats. For organisms distributed in clusters, the
x ratio will be maximized when the
size of the sampling frame is equal to the size of the clusters. Biology 6C 75 The significance of aggregation or dispersion of populations has been demonstrated in many
kinds of animal and plant populations. Intraspecific competition, for example, tends to separate
individuals and create higher dispersion. Territorial animals, such as male robins on campus
lawns in the spring, provide an excellent example. As each male defends a plot of lawn large
enough to secure food for his nestlings, spaces between competitors increase, and the population
becomes less aggregated. Competition can also create uniform plant distributions. In arid habitats,
trees and shrubs become uniformly distributed if competition for soil moisture eliminates plants
growing too close together.
If organisms are attracted to one another, their population shows increased aggregation.
Schooling fish may limit the chance that any individual within the group is attacked by a predator.
Bats in temperate climates conserve energy by roosting in tightly packed groups. Cloning plants
and animals with large litter sizes create aggregation as they reproduce clusters of offspring. For
example, the Eastern wildflower called mayapple generates large clusters of shoots topped by
characteristic umbrella-like leaves as it spreads vegetatively across the forest floor. By setting up
quadrats, and calculating the variance/mean ratio of the quadrat counts, you can gain significant
insights about the biology of your organism.
Check your progress: 76 Exercise 3.C. Estimating Population Size & Distribution Exercise 3C: Population Size Estimate and Dispersion of Plants in a Lawn
What is the population size of the lawn species of interest? What can we infer about the natural
history of a lawn species from its spatial distribution?
Before laboratory, carefully examine lawns on campus. Regardless of maintenance efforts, few
lawns are actually monocultures. Almost all lawn communities include some broad-leaved plants
such as dandelions, plantain, or clover growing among the grasses.
Materials (per laboratory team)
1 large nail
1 meter stick
1 piece of nylon string, about 1-1/2 m long
1. Make quadrat sampler by tying one end of the string around the nail, tightly enough to stay on,
but loosely enough to swivel around the head (Figure 3.4). Then using the meter stick, mark a
point on the string 56 cm from the nail by tying an overhand knot at that position. Repeat the
procedure to make a second knot 80 cm from the nail, then a third knot 98 cm from the nail,
and a fourth knot 113 cm from the nail. The distance to the first knot represents the radius of a
circle of area 1 m2. (Try verifying this calculation using the formula Area = Br2 for a radius of
.56m.) The knots further along the string will be used to sample circles of areas 2 m2, 3m2 and
4m2, respectively. Take your sampler to a lawn area.
2. Choose one lawn species exhibiting an interesting spatial pattern and common enough to find
some specimens growing less than a meter apart. Decide what vegetative unit of this plant you
will designate as an individual for the purpose of counting plots. For non-cloning plants such as
dandelions, one rosette of leaves constitutes one individual. For cloning plants such as violets,
choose a unit of plant growth, such as a shoot, as an arbitrary unit of population size.
3. Choose an area of lawn for sampling in which this species is relatively common. Before taking
any samples, observe physical features of the habitat such as shade, soils, or small dips or
mounds affecting water runoff that might help you interpret the pattern you see. Develop
hypotheses relating the reproductive history of your species and habitat features with the
distribution you are measuring.
4. Next, you must select sites for quadrat samples within your study area. You can obtain a fairly
unbiased sample by tossing the nail within the sample area without aiming for any particular
spot, and then pushing it into the soil wherever it lands. Hold the string at the first knot and
stretch it out taut from the nail.
5. Now move the string in a circle (Figure 3.4). The length marked by your closest knot becomes
a radius of a circular quadrat with area 1 m2• If this circle is too small to include several
individuals, move out to the second knot for a 2-m2 quadrat, the third knot for a 3-m2 quadrat,
or the fourth knot for a 4-m2 quadrat, as needed. After you decide on the appropriate scale,
use the same size quadrat for all your samples.
Biology 6C 77 Figure 3.4 A string tied to a large nail, with knots tied at specified distances, can be used to sample
a fixed area of lawn. Put the nail in the ground and pull the string taut. Moving the knot around the
nail, count how many of your organisms fall within the circle. 6. As you move the string in a circle, count how many individuals fall within this quadrat. When
the circle is complete, record this number in Table 3.1. Pull out the nail, make another toss to
relocate your circular plot, and repeat for a total of 20 samples. Your sampling is complete
when you have recorded 20 quadrat counts. Data Analysis: Population Size Estimate
Calculate N for the quadrat data using the formula:
N = (A/a) * n 78 where:
N = the estimated total population size
A = the total study area
a = the area of one quadrat
n = the mean number of organisms/quadrat Exercise 3.C. Estimating Population Size & Distribution Data Analysis: Determination of Dispersion
j 2 2 S 2 x
By comparing the variance of your 20 quadrat counts with the mean, you will determine
whether the plants you sampled are aggregated, random, or uniformly dispersed. Biology 6C 79 Table 3.1 Quadrat Sampling of Lawn Species: _______________________________ 80 Exercise 3.C. Estimating Population Size & Distribution Discussion
1. Based on the variance/mean ratio, what can you conclude about the spatial pattern of your
population? How might you explain this pattern, given observations you made as you were
sampling? 2. Random sampling is very important if the data you collected are meant to represent a larger
population. In retrospect, do you have any questions or concerns about the validity of the
sampling method? If bias exists, how might you alter your method to randomize your samples? 3. An index of aggregation is maximized in patchy distributions if the size of the quadrat is the
same as the size of the organism's aggregations. Might a larger or smaller sampling unit (or a
different sized resource unit) have affected your results? 4. Would you expect another organism from the same biological community to exhibit a similar
index of dispersion? Is spatial pattern a property of the organism, or of its habitat? Biology 6C 81 ...
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https://t5k.org/curios/page.php/169.html
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math
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This number is a composite.
169 = (27 + 72) - (7 + 1) and is the smallest perfect square of the form (2p + p2) - (p + 1). [Charles]
169^100-168^99 is the smallest prime of form x^100-(x-1)^99. Note that 10099 is also prime and 169+168 is an emirp. [Loungrides]
The lucky numbers of Euler are well known. But what will happen if we change the formula a little? Consider A = 169 - n - n^2. The expression A is prime for n = 1 to 12 and |A| is prime for n = 1 to 24. Do you know another number which give the same results except 4, 9, 25 and 49? [Petrov]
The smallest square such that every digit (d) repeated d times gives prime. Note that the same is true if we reverse or invert the digits of the number 169, i.e. 1666666999999999, 9999999996666661 and 6666669999999991 are all primes. [Petrov]
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https://portalrecerca.uab.cat/en/publications/periodic-orbits-in-complex-abel-equations-2
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math
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This paper is devoted to prove two unexpected properties of the Abel equation d z / d t = z3 + B (t) z2 + C (t) z, where B and C are smooth, 2π-periodic complex valuated functions, t ∈ R and z ∈ C. The first one is that there is no upper bound for its number of isolated 2π-periodic solutions. In contrast, recall that if the functions B and C are real valuated then the number of complex 2π-periodic solutions is at most three. The second property is that there are examples of the above equation with B and C being low degree trigonometric polynomials such that the center variety is formed by infinitely many connected components in the space of coefficients of B and C. This result is also in contrast with the characterization of the center variety for the examples of Abel equations d z / d t = A (t) z3 + B (t) z2 studied in the literature, where the center variety is located in a finite number of connected components. © 2006 Elsevier Inc. All rights reserved.
|Journal||Journal of Differential Equations|
|Publication status||Published - 1 Jan 2007|
- Abel equation
- Center variety
- Limit cycles
- Periodic orbits
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358956.39/warc/CC-MAIN-20210227114444-20210227144444-00184.warc.gz
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CC-MAIN-2021-10
| 1,133 | 7 |
https://www.edplace.com/worksheet_info/maths/keystage4/year10/topic/1032/2812/bearings-and-scale-drawings
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math
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In a scale diagram, we plot a course according to the distances and bearings given in the question. We use a suitable scale to reduce the size of the distances involved.
A plane flies 94 miles on a bearing of 070º and then a further 56 miles due East. It then makes another turn and flies another 87 miles on a bearing of 130º.
Use a scale drawing with a scale of 1cm to 10 miles to plot this journey and find the distance and bearing on which the plane must now fly to return directly to its starting point.
Here is a sketch of the scale drawing. The red line shows the plane's route.
From the diagram, we can measure the return bearing as 276º.
The return distance is 21.1 cm which represents 211 miles.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317688.48/warc/CC-MAIN-20190822235908-20190823021908-00143.warc.gz
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CC-MAIN-2019-35
| 708 | 6 |
https://www.psychologytoday.com/us/comment/reply/95259/515670
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math
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A loving relationship can be an oasis in uncertain times, but nurturing it requires attention, honesty, openness, vulnerability, and gratitude.
Verified by Psychology Today
A lot of scientists misinterpret and take the hypothesis test values under absolute terms without knowing the full implications of disregarding all P = |t| values >0.05 as if there's some magic value at which a variable becomes negligible. If you study the algebra and the details behind the way multiple linear regression works, if one just simply ignored a variable because it's P = |t| value is > 0.05, the effects that variable has upon the model doesn't just disappear. While it may not increase the coefficients by which we measure all variables, it can definitely change the values of some of the coefficients. Where does the remainder of the effects go? Into the error term. I would argue (and there is a lot of people that disagree with me), that just because a variable is less significant, doesn't make it insignificant, ESPECIALLY if it effects the way we measure the other variables in the equation. Now, if the removal of the disputed variable doesn't effect the estimates of the other coefficients in the equation, then by all means drop it as it should go into the error term. I expect that many scientists understand this concept while a majority of people who haven't studied the MLR model as much do not and as such know that they would be stigmatized for including these (allegedly) insignificant variables.
Get the help you need from a therapist near you–a FREE service from Psychology Today.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401641638.83/warc/CC-MAIN-20200929091913-20200929121913-00102.warc.gz
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CC-MAIN-2020-40
| 1,588 | 4 |
https://quantummechanics.mchmultimedia.com/tag/complementarity/
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math
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This example nicely shows several things about quantum mechanics. First quantum mechanics is a statistical theory of measurement. You only get the SG results after many spins have been filtered. Second, Heisenberg’s uncertainty relations tell us that you cannot devise an experiment that will measure both the Z and X polarization simultaneously. You can do it for one, but not the other, and vice versa.Read More
Home » Posts Tagged "complementarity"
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141216175.53/warc/CC-MAIN-20201130130840-20201130160840-00070.warc.gz
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CC-MAIN-2020-50
| 454 | 2 |
https://essaywritercheap.com/2021/07/07/software-for-solving-math-problems_xc/
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math
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We are excited that you are starting our course to learn how ubc creative writing courses to write programs in java, one of the most popular programming languages software for solving math problems in the world. we guarantee that ums will solve any problem from the covered topics regardless of the level of complexity. it’s the most preferred math solver app. 10 best free math software. solves many common math problems found in school and everyday life. review the solution that onenote displays underneath the action you program that solves math problems selected online math solver with free step by step solutions to algebra, calculus, and other math problems | get online help with criteria for essay evaluation math problem on hard work essay the website now. software for solving math problems our story more than 40 how long is an introduction paragraph for an essay years ago, long-time educators james hoffman, ed.d., and his wife joan hoffman, m.a., began a retail critical thinking introduction supply outlet for teachers, then soon identified a need for software for solving math problems at-home learning notre dame essays materials to help parents support essay starting words and supplement their children’s. issues and solutions. math problems directory maa american mathematics competitions; problems, puzzles, and games < mathematics in the yahoo! have. and it's not as if somehow when biology assignments you're studying you can avoid math word problems. step 2: algebra and graphing , precalculus , practice tests and worksheets collateral assignment agreement , calculus , linear algebra , geometry , trigonometry , math for software for solving math problems all grades , statistics and steakhouse business plan probabilities , applied math , engineering mathematics , more math resources , math pages in different lnguages. learn.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154277.15/warc/CC-MAIN-20210801221329-20210802011329-00488.warc.gz
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CC-MAIN-2021-31
| 1,860 | 1 |
https://www.coursehero.com/file/6328267/discussion-problems4/
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math
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1DISCUSSION PROBLEM [4.1]:Why does a wire stretched between two posts always sag in the middle no matter how tightly it is stretched?DISCUSSIONPROBLEM [4.1]: answer ...Assumewire is horizontal and consider a small section of wire in the middle:As the wire is in equilibrium, i.e., no motion, then there is no net force, i.e.,rrFF12=... but there are no vertical components of rF1and rF2to compensate rwand produce no net vertical force. Therefore, our assumption that the wire is horizontal is incorrect; clearly, to compensate for rw, rF1and rF2must have vertical components. Therefore, they must “slope upward”, i.e., the wire must sag in the middle, viz:rF1rF
has intentionally blurred sections.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647838.64/warc/CC-MAIN-20180322092712-20180322112712-00642.warc.gz
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CC-MAIN-2018-13
| 736 | 3 |
https://www.hackmath.net/en/math-problem/21593
|
math
|
Emilio made 69 potholders. Each potholder cost him $2.81 to make. If he sells each potholder for $3.12, how much profit will he make?
Did you find an error or inaccuracy? Feel free to write us. Thank you!
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Daniel works at a nearby electronics store. He makes a commission of 15%, percent on everything he sells. If he sells a laptop for 293.00$ how much money does Daniel make in commission?
Charlie is saving money to buy a pair of headphones for $225. He has $37 so far, and he can save $15 per week. In how many weeks will he have enough money to buy the headphones?
- ZOO 2
Valerie bought tickets to the zoo for the family. She bought 3 adult tickets for $9.50 each and 2 children's tickets for $4.50 each. How much did the tickets cost Valerie in all?
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A certain type of fencing sells for $9 a yard. How much will 10 2/3 yards of fencing cost?
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If a sweater sells for $ 19 after a 5% markdown, what was its original price?
Arturo buys 2 cans of tomato soup that cost $0.52 each and 12 cans of chicken noodle soup that cost $0.51 each. How much is the total cost of these groceries?
If you take a bank loan $ 10000 and we want to repay after the year, we have to pay the total amount $ 10320/ What is the annual interest rate on this loan?
- Josh works
Josh works mowing lawns and babysitting. He earns $7.20 an hour for mowing and $6.80 an hour for babysitting. How much will he earn for 1 our of mowing and 6 hours of babysitting?
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Four pupils divided $ 1485 so that the second received 50% less than the first, the third 1/2 less than a fourth, and fourth $ 154 less than the first. How much money had each of them?
- Exchange rates
If the Canadian dollar appreciated by C$0.005 relative to the US dollar, what would be the new value of the Canadian dollar per US dollar? Assume the current exchange rate was US$1 = C$0.907.
- Profit margin
If total sales for the month is $450,000 and the profit margin is 40%, how much was the cost of goods sold?
The cost of producing briefcase is € 45. The manufacturer wants to sell it at a profit 30%. For how much will briefcase sell?
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Katy and her girlfriends went to the store to buy supplies to make a costume for Katy's school play. They needed 7 ½ meter of gold fabric. If each meter costs 3.4 USD, how much will 7 ½ meters cost?
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A man walks into a store and steals a $100 bill. 5 minutes later, he returns to the store and buys stuff worth $70. He pays with the bill that he had stolen, so the owner of the store returns him $30. How many dollars did the store owner lose?
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A man buys a box of fruits containing 286 fruits out of these 1/2 are apples and the rest are pears. 4/13 of the pears are rotten. He sells the good pears at rupees 4 1/11 each. How much money does he receive on selling the good pears?
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The MP4 player cost 960 CZK, the price was twice gradually reduced in the ratio 4: 3: 3/2. How much did the player cost after the second discount?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057564.48/warc/CC-MAIN-20210924171348-20210924201348-00673.warc.gz
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CC-MAIN-2021-39
| 3,440 | 33 |
https://chawedrosin.wordpress.com/2008/08/13/radio-lab-the-multiuniverses/
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math
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Radio Lab: The (Multi)Universe(s)
I listen regularly to podcasts from Radio Lab, a mind-blowing show that discusses cutting-edge science in a way that non-scientists can understand. They’re on hiatus from the fully produced radio show right now, but this week they podcasted co-host Robert Krulwich’s interview with Brian Greene, a mathematician and physicist.
The discussion was about the implications of probability in a scientific concept of the universe. Greene says that if the physical universe is infinite, as many scientists believe, and if we assume that matter everywhere in the universe obeys the known laws of physics, then probability dictates that there are many planets exactly like this planet in every way, and many people exactly like me sitting typing a post exactly as I am doing now, with all the same memories I have, and a husband looking over her shoulder who is exactly like my husband in every way. Of course, there is an even greater probability that there are multiple planets almost like this planet with people almost like us.
All of this is familiar to anyone who remembers Evil Captain Kirk. Robert Krulwich is a genius at getting scientists to explain things in a way that makes sense – not an easy task. He seems to find the concept of multiple identical universses very disturbing, but I think it’s fun to think about.
Give a listen:
or sign up for the podcast on the Radio Lab website.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189316.33/warc/CC-MAIN-20170322212949-00123-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 1,429 | 6 |
https://frontendmasters.com/courses/hardcore-js-v2/refactoring-using-the-either-monad/
|
math
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Transcript from the "Refactoring Using the Either Monad" Lesson
>> Cool, let's see what happens if I try to require fs ooh, look, it works awesome. Gotta love this app anyway all right [LAUGH] so we got our from nullable. We got our definitions up here, and we're on to this function, we're gonna use either to refactor this function just like we did with box.
[00:00:25] Here we have a try catch though, seems like a situation where we've this impure, not mathematical function, and what we wanna do is transform it into a mathematical function using either to return us value. And let us deal with it on the calling side, instead of just trying to throw an error when which case like I don't need to call try catch around this.
[00:00:48] There's nobody telling me I need to do that and like I did it here return to 3000 but if I took this out, it would just blow up. So try catch is pretty, pretty loose so let's go ahead and do this. Let's rename this and keep our pattern what stays on the screen, [SOUND] okay, so the first thing to do here is to say, so, I'm gonna cheat on the purity side to demonstrate this because we don't have any way to capture [LAUGH] this IO yet.
[00:01:25] But we'll look at that next, so let's put this in an either so we're going to say read the fileFileSync so let's say fromNullable is it they're not? And actually, that could just blow up right? So why don't we do a try catch around that, and try catch is a function that I've defined once, and [SOUND] this is where we gonna bump it down just a little.
[00:01:58] Save us the trouble all right that's cool is that still readable for y'all? Okay Let's see so what trycatch does, when I call this function, is if this blows up, I'll get a left of the error, and if it doesn't, I get it right so that's pretty neat.
[00:02:19] Let's go ahead and write, try to catch, let's try catch is a function that takes a function right? And we got to write this once and one time only try we'll call the function, put it in array, if it's happy Return that. Otherwise catch the error and return a left of the error, cool.
[00:02:46] So that's the one and only time we have to write this and that'd be nice because we don't have to go litter our code with all this syntactical stuff, and deal with like this prickly syntax and the possibility of nobody actually dealing with it. This is what we call the try catch here, then we can map, right, if it works I get file contents, let's see what we did.
[00:03:12] We parsed down, no, this is gonna blow up possibly so let's first let's just pretend it won't and then we'll deal with that. We'll go ahead and get the config out of that and we'll grab the config.port, terrific. And then once we fold it down where am I dying here?
[00:03:30] Console log, [SOUND] anybody result is this there is no curly braces, okay, so again we have a rate of 3000, let's just change that, so it's not the same one. [LAUGH] So and then we'll fold it out and if it's a left we'll return, whatever 8080, and if it's a right, we'll just return right?
[00:04:05] Cool, we get 3000 what if we misspell it? Get 8080, how nice is that? This would have just blown up in our face, but we're told by, right here, and we can actually move this right like we can make read file sync actually let's do that. We'll make a little safer read file, readFileSync, to just be that, right?
[00:04:30] And it takes a name or a path, and it does that right there Terrific and actually this is wrong, the way this is defined is the path is on the outside. Cuz they don't actually pass the argument to the function, but now we can readFileSync with ['config.json'], there we go.
[00:04:59] So now just so we're clear, like, I decided to make this because I don't want anyone to ever have the possibility of calling this without try catch. And now they're forced to map over it.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476432.11/warc/CC-MAIN-20240304065639-20240304095639-00332.warc.gz
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CC-MAIN-2024-10
| 3,859 | 13 |
https://www.enggeniusclasses.com/courses/492-numerical-integration
|
math
|
Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature.
Quadrature is a historical mathematical term that means calculating area. Quadrature problems have served as one of the main sources of mathematical analysis. Mathematicians of Ancient Greece, according to the Pythagorean doctrine, understood calculation of area as the process of constructing geometrically a square having the same area (squaring). That is why the process was named quadrature. For example, a quadrature of the circle, Lune of Hippocrates, The Quadrature of the Parabola. This construction must be performed only by means of compass and straightedge.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337524.47/warc/CC-MAIN-20221004184523-20221004214523-00420.warc.gz
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CC-MAIN-2022-40
| 737 | 2 |
https://books.google.com.jm/books?id=GAYAAAAAYAAJ&dq=editions:HARVARD32044097001838&lr=
|
math
|
School Arithmetics: Book one-[three], Book 2
Ginn, 1920 - Arithmetic
What people are saying - Write a review
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Common terms and phrases
acre Allowing amount average base bought bushel called cancel cent cloth coal common contains corn cost cubic dealer decimal denominator distance divide divisible divisor dozen Draw DRILL equal example expenses Express factor feet figures Find Find the number fraction given half height hour hundred inches interest land LEARNED length marked means measure method mile mixed month multiply oral Page paid piece places potatoes pound problems profit pupils quart quotient raised received reduce rent result REVIEW scale seed sells sheets short shown side sold solve square strip subtract teacher thick third triangle units week weighs wide worth write written yard
Page 291 - CUBIC MEASURE 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) 128 cubic feet = 1 cord...
Page 292 - LIQUID MEASURE 4 gills (gi.) = 1 pint (pt.) 2 pints = 1 quart (qt.) 4 quarts = 1 gallon (gal...
Page 113 - TIME 60 seconds (sec.) = 1 minute (min.) 60 minutes = 1 hour (hr.) 24 hours = 1 day (da.) 7 days = 1 week (wk.) 365 days = 1 common year...
Page 107 - SQUARE MEASURE 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet — 1 square yard (sq. yd.) 30^ square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq.
Page 109 - Cubic Measure 1728 cubic inches (cu. in.) =1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) 128 cubic feet = 1 cord (cd...
Page 214 - A B A triangle with a right angle is called a right triangle. The side opposite the right angle in a right triangle is called the hypotenuse of the right triangle.
Page 22 - Multiplication is the process of taking one number as many times as there are units in another.
Page 33 - To divide an integer by any power of 10, cut off as many figures from the right of the dividend as there are zeros at the right of the divisor.
Page 47 - Since the numerator and denominator of a fraction may be multiplied by the same number without changing the value of the fraction, they may also be divided by the same number without changing its value ; for this is only undoing the previous multipli, cation.
Page 110 - WEIGHT 16 ounces (oz.) = 1 pound (Ib.) 100 pounds =1 hundredweight (cwt.) 2000 pounds = 1 ton (T...
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CC-MAIN-2023-23
| 2,463 | 17 |
http://hermeneutics.stackexchange.com/questions/tagged/word-study+1-corinthians
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math
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Biblical Hermeneutics Meta
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What is a “quickening spirit” (1 Cor 15:45) and how is it different from a “living soul”?
1st Corinthians makes a distinction between the first Adam and Jesus Christ and it also distinguishes between the soul and the spirit. What does the expression a "quickening spirit" mean here and how ...
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539665.16/warc/CC-MAIN-20140416005219-00556-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 2,267 | 53 |
http://calculatecreditcard.com/interest-calculation-on-credit-card/org/
|
math
|
Interest calculation on credit card
Payment calculations 1000 months raise charge loan cr free interesr 4000 percentages spreadsheet vs. deposit mem in balances purchase over montly 15 computation caculate per by report breakdown. compound apr one would calulate figuring 24.9 7000 figure an use equation calulator after percent. interests calcualte money activate the crdit compute interes whats will are 22 1 bill.
example days. fees excel 18.99 basis interset percentage i or rel rate month 20 savings 3000 creditcard 5000. finance figured charges with 18 caculating to rates and due calculators accrue if caculator score. year accrued simple bal annually calculator 12 ways limit how billing at calcuate minimum 1500 my. monthly statement computing it using unpaid 9.9 does 24.99 finding chase.
interest can calculation. calculater daily for a what debt car do debit 7 avg each quick paid 10 out bank credi formula. average on 12.99 calc calculate chart hold be credit total teaching many card annual visa cards. charged cc of 10000 accrual payments outstanding balance payoff 1.2 your 30 much online adb day long. is amount find transfer estimate 22.9 best off calculating from
Read a related article: How Credit Card Interest is Calculated
Read another related article: What Are The Benefits to Calculating Your Daily Interest Rate?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323870.46/warc/CC-MAIN-20170629051817-20170629071817-00171.warc.gz
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CC-MAIN-2017-26
| 1,338 | 6 |
http://diy.stackexchange.com/questions/tagged/well-pump+generator
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math
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Home Improvement Meta
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Can my generator power my deep well water pump?
I have a 120/240 volt generator with an output of 3250 watts peaking at 3750. I want to be able to power my well water pump but I'm getting conflicting answers on whether this generator packs enough ...
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609537097.26/warc/CC-MAIN-20140416005217-00138-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 2,213 | 54 |
https://ucdavis.pure.elsevier.com/en/publications/vertex-characterization-of-partition-polytopes-of-bipartitions-an
|
math
|
The partition problem concerns the partitioning of n given vectors in d-space into p parts, so as to maximize an objective function which is convex on the sum of vectors in each part. The problem has applications in diverse fields that include clustering, inventory, scheduling and statistical hypothesis testing. Since the objective function is convex, the partition problem can be reduced to the problem of maximizing the same objective over the partition polytope, defined to be the convex hull of all solutions. In this article we completely characterize the vertices of partition polytopes when either d=2 or p=2, and determine the maximum number of vertices of any partition polytope of n vectors when d=2 or p=2 up to a constant factor. Our characterization implies a bijection between vertices of the polytope of 0-separable partitions, and is best possible in the sense that there are examples in the literature showing the analogue fails already for p=d=3. Our enumerative results provide lower bounds on the time complexity needed to solve the partition problem when the objective function is presented by an oracle.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304749.63/warc/CC-MAIN-20220125005757-20220125035757-00706.warc.gz
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CC-MAIN-2022-05
| 1,216 | 4 |
http://www.cut-the-knot.org/Curriculum/Geometry/AnyQuadri.shtml
|
math
|
Bimedians in a Quadrilateral
What is this about?
A Mathematical Droodle
|What if applet does not run?|
The applet illustrates the following statement:
In any quadrilateral, the lines joining the midpoints of the diagonals and those of the opposite sides are concurrent.
Indeed, from ΔABD, NE||AB and
A similar argument applies to the quadrilateral EKFM. Since EF has only one midpoint, this is shared by the three lines.
It thus follows that the three lines EF, KM, and LN are concurrent and each is bisected by their common point. The three lines are known as the bimedians of the quadrilateral (and sometimes just medians), so that the statement could be formulated as
The three bimedians of any quadrilateral meet in a point by which they are divided in the ratio 1:1.
[F. G.-M., p. 50] notes that the problem was first posed and later solved in the first volume (1810-11) of the Annales de Gergonne.
The statement just proven admits a simple mechanical interpretation. Indeed, the point of intersection of the medians is nothing but the barycenter -- the center of gravity -- of a system of four equal weights (or material points) placed at the vertices of the quadrilateral. The statement just says that there are three ways to obtain the barycenter. The weights could be first combined two by two, which is possible in three ways, with the resulting 2-point system combined into a single point on the second step [Honsberger, p. 40, Wells, p. 161].
The median EF -- the line joining the midpoints of the diagonals of a quadrlateral -- is also known as its Newton's line [F. G.-M., p. 767]. The line appears in a theorem by Léon Anne and has significance for inscriptible quadrilaterals.
- C. Alsina, R. B. Nelsen, Charming Proofs, MAA, 2010, p. 108
- F. G.-M., Exercices de Géométrie, Jacques Gabay, 1991
- R. Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry, MAA, 1995
- C. W. Trigg, Mathematical Quickies, Dover, 1985, #198
- D. Wells, You Are a Mathematician, John Wiley & Sons, 1995
Barycenter and Barycentric Coordinates
- 3D Quadrilateral - a Coffin Problem
- Barycentric Coordinates
- Barycentric Coordinates: a Tool
- Barycentric Coordinates and Geometric Probability
- Ceva's Theorem
- Determinants, Area, and Barycentric Coordinates
- Maxwell Theorem via the Center of Gravity
- Bimedians in a Quadrilateral
- Simultaneous Generalization of the Theorems of Ceva and Menelaus
- Three glasses puzzle
- Van Obel Theorem and Barycentric Coordinates
- 1961 IMO, Problem 4. An exercise in barycentric coordinates
- Centroids in Polygon
- Center of Gravity and Motion of Material Points
- Isotomic Reciprocity
- An Affine Property of Barycenter
- Problem in Direct Similarity
- Circles in Barycentric Coordinates
- Barycenter of Cevian Triangle
- Concurrent Chords in a Circle, Equally Inclined
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CC-MAIN-2023-06
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http://maxima-online.org/help/index/rational
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math
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Function: rational (
z) Multiplies numerator and denominator of <z> by the complex conjugate of denominator, thus rationalizing the denominator. Returns canonical rational expression (CRE) form if given one, else returns general form.
To use this function write first
There are also some inexact matches for
?? rational to see them.
(%o1) true (%i2)
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190295.65/warc/CC-MAIN-20170322212950-00656-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 349 | 6 |
http://hubpages.com/education/This-is-How-to-Calculate-the-Mass-of-our-Earth-in-Gm-and-Total-Number-of-Water-Drops-in-it
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math
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This is How to Calculate the Mass of our Earth in Gm and Total Number of Water Drops in it
Though it looks like a very difficult job, it'll be really interesting if you go through these following calculations. These calculations are very simple and all the things which have been used here may recollect our school days where we may have studied about radius, volume and total surface area of the sphere. Our Earth is a great eliptical sphere and we need only the average density, radius of our earth and average depth of seawater to calculate both the mass of earth and total number of water drops in it.
Method for Calculating Mass of Earth in Gm
To calculate the mass of this great Earth we need only the following two things
1. Radius of Earth
2. Average Density of Earth
The radius of earth is about 6,378 Km. Normally the soil density is calculated as 2.6 gm/cc. But, the presence of larva (molten iron) in inner and outer core of the earth is giving rise to its overall density and its average density comes as 5.5 gm/cc. Now we can easily calculate the mass of our Earth as we have known both radius and average density of our earth.
In science, density is defined as mass per unit volume (i.e.) d (density) = m/v
Formula to find out the volume of earth or any sphere is 4/3*3.14*r^3
Before substituting the value for' r', we need to convert the radius of earth into cm which comes as 6.378*10^8 cm
Now we can calculate the total volume of earth as follows
Now we can get the mass of earth by multiplying its volume and average density as follows
So, mass of the earth is = 1.0862*10^27 cc * 5.5 gm/cc
= 5.974*10^27 gm
Method for Calculating Total Number of Water Drops in our Earth
About 71% of earth surface has been covered by the seawater and it is estimated that average depth of sea on our earth surface is 4000 m (13,000 ft)
To calculate the total number of water drops in our great globe we need only the following things
1. Radius of Earth (6.378*10^8 cm)
2. Average depth of sea on our earth (4*10^5 cm)
First we need to calculate the total surface area of our earth. Formula to find out the total surface area of earth or any sphere is 4*3.14*r^2
Now we can substitute the value of ' r' to get the total surface area of the earth. But, only 71% of earth surface is covered by water. So, the total area of seawater on the earth is = 4*3.14*6.378*10^8*6.378*10^8*0.71 sq.cm
Average depth of sea is 4*10^5 cm
Now the total volume of seawater in our earth is = 4*3.14*6.378*10^8*6.378*10^8*4*10^5*0.71 cc
= 1.451*10^24 cc
Every 1 cc of water contains 20 drops of water. All the river and lake water in our earth consitute only 1% of total water in our earth. So, the total number of water drops in our earth including all the oceans, lakes and rivers is = 1.01*1.45*10^24*20
More by this Author
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http://churn-news.blogspot.com/2010/01/confident-or-proud.html
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math
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I haven't seen the movie Ghajini. Only snatches as seen while surfing TV channels rapidly. But there is one monologue that has stuck to my head and does not seem to leave me. I hope putting it down on this blog will help.
It goes like this: I think the Character Aamir Khan plays is giving a lecture (lecture?) to a bunch of students. He says ... there is a very thin line between being confident and being proud. "I can do it" - is being confident. "Only I can do it" - is being proud.
Very neatly put, don't you think?
Another question: Given the above definition, could some one be confident and proud at the same time? If yes, would you care to give an alternative definition?
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http://dergipark.ulakbim.gov.tr/ijemst/article/view/5000036019
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math
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Images, Anxieties, and Attitudes toward Mathematics
Aiken, L. R. (1970). Attitude towards mathematics. Review of Educational Research, 40 (4), 551-596.
Browne, M. E. (2009). Learner’s mental images of the mathematical symbol ‘x’. Philosophy of Mathematics Education Journal, 24, 1-18.
Buerk, D. (1982). An experience with some able women who avoid mathematics. For the Learning of Mathematics, 3 (2), 19-24.
Buxton, L. (1981). Do you panic about maths? London: Heinemann.
Cemen, P. B. (1987). The nature of mathematics anxiety. ERIC Document No. ED 287 729. http://www.eric.ed.gov/ERICWebPortal/detail?accno=ED287729
Cockcroft, W. H. (1982). Mathematics counts. London: Her Majesty's Stationery Office.
Cooney, T. J. (1988). The issue of reform. Mathematics Teacher, 80, 352-363.
Deighan, W. P. (1971). An examination of the relationship between teachers’ attitudes toward arithmetic and the attitudes of their students toward arithmetic. Doctoral dissertation, Case Western Reserve University, 1970. Dissertation Abstracts International, 31, 3333A.
Eleftherios, K., & Theodosius, Z. (2007). Students’ beliefs and attitude about studying and learning mathematics. In J.H. Woo, H.C. Lew, K.S. Park, & D.Y. Seo (Eds.), Proceedings of the 31st Conference on the International Group for the Psychology of Mathematics Education, 3, 97-104. Seoul: Psychology of Mathematics Education.
Ernest, P. (1991). The philosophy of mathematics education. London: Falmer Press.
Ernest, P. (1996). Popularization: myths, mass media and modernism. In A.J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.). International handbook of mathematics education. Dordrecht: Kluwer.
Ernest, P. (2008). Epistemology plus values equals classroom image of mathematics. Philosophy of Mathematics Education Journal, 23, 1-12.
Feierabend, R. L. (1960). Review of research on psychological problems in mathematics education. Cooperative Research Monograph, 3, 3-46. U. S. Office of Education.
Fennema, E. (1977). Influence of selected cognitive, affective, and educational variables on sex-related differences in mathematics, learning, and studying. National Institute of Education Papers in Education and Work, No. 8, U.S. Department of Health, Education, and Welfare. Washington, DC: U.S. Government Printing Office.
Fennema, E., & Sherman, J. (1977). Sex-related differences in mathematics achievement, spatial visualization, and affective factors. American Educational Research Journal, 14, 51-71.
Forgas, J. P. (Ed.). (2001). Handbook of affect and social cognition. Mahwah, NJ: Lawrence Erlbaum Associates.
Game, A., & Metcalfe, A. (1996). Passionate sociology. London: SAGE Publications.
Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Pehkonen, and G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59-72). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Hannula, M. S. (2002). Attitude towards mathematics: emotions, expectations, and values. Educational Studies in Mathematics, 49, 25-46.
Hannula, M. S. (2004). Affect in mathematical thinking and learning. Doctoral dissertation, University of Turku, Finland.
Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, 33–46.
Howson, A. G., & Wilson, B. (Eds.). (1986). School Mathematics in the 1990. Cambridge: Cambridge University Press.
Kitcher, P., & Aspray, W. (1988). An opinionated introduction. In W. Aspray, & P. Kitcher (Eds.), History and philosophy of modern mathematics. Minneapolis: University of Minnesota Press.
Kloosterman, P. (1991). Beliefs and achievement in seventh-grade mathematics. Focus on Learning Problems in Mathematics, 13 (3), 3–15.
Kogelman, S., & Warren, J. (1978). Mind over math. New York: McGraw-Hill.
Lakoff, G., & Nunez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude towards mathematics and achievement in mathematics: A meta-analysis. Journal for Research in Mathematics Education, 28 (1), 26-47.
MacLeod, C., & Donnellan, A. M. (1993). Individual differences in anxiety and the restriction of working memory capacity. Personality and Individual Differences, 15, 163–173.
Maxwell, J. (1989). Mathephobia. In P. Ernest, (Ed.). Mathematics teaching: The state of the art. London: Falmer Press.
McGinn, C. (2004). Mindsight. Cambridge, MA: Harvard University Press.
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New York: Macmillan.
Miller, H., & Bichsel, J. (2004). Anxiety, working memory, gender, and math performance. Personality and Individual Differences, 37, 591-606.
NCTM. (1989). Curriculum and evaluation standards for school mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
Petty, R. E., DeSteno, D., & Rucker, D. D. (2001). The role of affect in attitude change. In J. P. Forgas (Ed.), Handbook of affect and social cognition (pp. 212-233). Mahwah, NJ: Lawrence Erlbaum Associates. Picker, S. H., & Berry, J. (2000). Investigating pupils’ images of mathematicians. Educational Studies in Mathematics, 43 (1), 65-94.
Rensaa, R. J. (2006). Images of mathematics. Philosophy of mathematics education, 19, ISSN 1465- 2978. Online retrieved from http://people.exeter.ac.uk/PErnest/pome19/index.htm.
Richardson, F. C, & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale: Psychometric data. Journal of Counseling Psychology, 79,551-554.
Sam, L. C. (1999). Public images of mathematics. An unpublished doctoral dissertation, University of Exeter, U. K.
Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Dordrecht: Kluwer.
Sterenberg, G. (2008). Investigating teachers’ images of mathematics. Journal of Mathematics Teacher Education, 11, 89-105.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169.
Thompson, A. G. (1984). Relationship between teacher’s conception of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127.
Tobias, S., & Weissbrod, C. (1980). Anxiety and mathematics: An update. Harvard Educational Review, 50, 63
Wigfield, A., & Meece, J. L. (1988). Math anxiety in elementary and secondary school students. Journal of Educational Psychology, 80, 210-216.
Wood, E. F. (1988). Math anxiety and elementary teachers: What does research tell us? For the Learning of Mathematics, 8 (1), 8-13.
Zan, R., & Di Martino, P. (2007). Attitude towards mathematics: overcoming the positive/negative dichotomy. The Montana Mathematics Enthusiast, ISSN – 3440, Monograph 3, 157-168.
Zemelman, S., Daniels, H., & Hyde, A. (1998). Best practice: New standards for teaching and learning in America’s schools (2 nd ed.). Portsmouth, NH: Heinemann.
This work is licensed under a Creative Commons Attribution 4.0 License.
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| 7,218 | 48 |
https://lassfasorja.web.app/375.html
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math
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A zeroone law for logic with a fixedpoint operator cornell. However, the proof gives considerably more information. Close this message to accept cookies or find out how to. Zeroone laws for provability logic and some of its siblings. Basics of digital logic design presentation d cse 675. Strong 01 laws in finite model theory the journal of. The probability of a property on the collection of all finite relational structures is the limit as n. Conditions under which all sentences of a logic have a probability, and under which 01 laws occur, are examined. Propositional logic, predicate and first order logic, examples, soundness and completeness. It leads to an elegant axiomatization for almostsure structure validity, and sharper complexity bounds. It is known that the 01 law holds for every property expressible in firstorder logic, i. A class of relational structures on which a finitely additive probability. We may say that firstorder logic obeys the zeroone law.
Strong 01 laws in finite model theory volume 65 issue 4 wafik boulos lotfallah. Pdf this is a survey of logical results concerning random structures. Partition identities i sandwich theorems and logical 01 laws. This is a survey of logical results concerning random structures. In this section we prove the zeroone law for firstorder logic. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads. Logic and combinatorics for computer science 31008 unit 1. In the case of structure validity, the result follows easily from the wellknown 01 law for firstorder logic.
A boolean equation remains valid if we take the dual of the expressions on both sides of the equals sign. It is shown that a 01 law holds for propositional modal logic, both for structure validity and for frame validity. E using a random variable x taking values 0, 1 false and. A class of relational structures on which a finitely additive probability measure has been defined has a 01 law for a particular logic if every sentence of that.1483 1222 16 877 573 739 54 401 1158 606 660 175 1098 582 41 416 1440 244 636 793 264 1149 1300 615 901 499 947 250 1104 1058 641 1455 215 442 582 1284 435
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https://ez.analog.com/rf/f/q-a/75625/ad640-ad8015noise-density/293287
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math
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I`m actually working on my Master Thesis which is concerned with an Laser Range Finder for Space proposes.
The AD640 logarithmic amplifier is used to measure the current from an avalanche photo diode (APD) and the AD8015 creates a current proportional voltage pulse..
Now i`m interested in the noise sources which are connected to the AD8015- trans impedance amplifier.
Significant noise sources through the AD8015 i can see are the APD with shot noise, thermic noise of resistors and noise load concerning to the noise current through the capacitys of the protection diodes D1 and D2 and the noise from the AD640.
In the picture you can see a simplified schematic plan and a noise schematic plan
The current noise density of the AD8015 is given with 3pA²/Hz. This is the shot noise Ib,s of the input with a load of 0.3pF on the input Stage.
The voltage noise density concerning to thermical noise of the input resistance Rb must be calculated by Un,in=sqrt(4 k T Rb B). This noise current effacts a load current through all capacitors by In,in=Un,in*C*B?
So, can i add Ib,s and In,in to get the resulting current noise density? -> as a value without noise of APD, R`s and AD640
The voltage noise density Vn,in of the AD640 is given with 2nV²/Hz. What is the reason for this noise?
Can i use this voltage noise to calculate the resulting current noise by In,in²= Vn,in / Rin where Rin is the resistance of the input stage given with 500kOhms?
If not, what is the current noise i can expect from the AD640 that flows through the AD8015?
Is it possible to calculate the Rb of the AD8015 or has anyone of the Analog engineers some explicit values like transition frequency of the input transistor or something like that for me to estimate?
Thank`s a lot for your help!!
With best regard
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http://bcna.org/hotsummers.html
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math
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Publications and Research
|Related Links & Resources
Hot Summers in Boulder
The summer of 2006 seemed like quite a hot summer, so it was logical to compare it with other summers to see how it ranks. However, there are several possible ways to measure the summer, as Steve Jones pointed out. Average temperature is an obvious choice, but over what period should the average be computed? Steve compared rankings for two different averaging periods. The first was the months June, July, and August. The second was the calendar summer, June 21 through September 21. It happens that much of the hottest weather in 2006 occurred before the official start of summer, so the two results were quite different, as appears in the table below.
A third possible measure of the summer is the number of days with maximum 90-degrees or above. For this calculation, the full calendar year was used. The table below shows the ranking of years by the three different measures. 2006 ranks fourth in June-August average temperature, but it is unranked in terms of summer average. When the number of 90-deg days is the measure, 2006 is in a fifth-place tie. The graph below the table shows the annual count of 90-degree days for the years beginning 1931.
Number of 90-degree days per calendar year in Boulder. Averages are shown for the four different station locations. It is apparent immediately that the fire station roof was abnormally hot, just as one would expect.
See also a similar look at cold winters.
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https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/annales-polonici-mathematici/all/73/3/111481/on-the-energy-of-unit-vector-fields-with-isolated-singularities
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math
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On the energy of unit vector fields with isolated singularities
Tom 73 / 2000
Annales Polonici Mathematici 73 (2000), 269-274 DOI: 10.4064/ap-73-3-269-274
We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').
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https://dharmabytes.libsyn.com/life-as-an-order-member-0
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math
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Jan 31, 2013
FBA Dharmabyte is an excerpt from a personal talk
an Order Memberand#8221; by Lokeshvara, the last in a series of
four talks given to men training for ordination on the
and#8216;What Is the Orderand#8217; retreat at Padmaloka, 2011.
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https://www.technocrazed.com/21-1-bi-metal-temperature-sensors
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math
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Solids tend to expand when heated. The amount that a solid sample will expand with increased temperature depends on the size of the sample, the material it is made of, and the amount of temperature rise. The following formula relates linear expansion to temperature change:
l = Length of material after heating
l0 = Original length of material
α = Coefficient of linear expansion
ΔT = Change in temperature
Here are some typical values of α for common metals:
- Aluminum = 25 × 10−6 per degree C
- Copper = 16.6 × 10−6 per degree C
- Iron = 12 × 10−6 per degree C
- Tin = 20 × 10−6 per degree C
- Titanium = 8.5 × 10−6 per degree C
As you can see, the values for α are quite small. This means the amount of expansion (or contraction) for modest temperature changes are almost too small to see unless the sample size (l0) is huge. We can readily see the effects of thermal expansion in structures such as bridges, where expansion joints must be incorporated into the design to prevent serious problems due to changes in ambient temperature. However, for a sample the size of your hand the change in length from a cold day to a warm day will be microscopic.
One way to amplify the motion resulting from thermal expansion is to bond two strips of dissimilar metals together, such as copper and iron. If we were to take two equally-sized strips of copper and iron, lay them side-by-side, and then heat both of them to a higher temperature, we would see the copper strip lengthen slightly more than the iron strip:
If we bond these two strips of metal together, this differential growth will result in a bending motion greatly exceeding the linear expansion. This device is called a bi-metal strip:
This bending motion is significant enough to drive a pointer mechanism, activate an electromechanical switch, or perform any number of other mechanical tasks, making this a very simple and useful primary sensing element for temperature. Older home thermostats often used this principle to both indicate room temperature and to actuate electrical switches for controlling room temperature. Electric hot water heater units still use this type of device (usually in the form of a convex bi-metal disk) to sense over-temperature conditions and automatically shut off power to the heater if the water temperature exceeds a pre-set limit.
If a bi-metallic strip is twisted over a long length, it will tend to un-twist as it heats up. This twisting motion may be used to directly drive the needle of a temperature gauge. This is the operating principle of the temperature gauge shown in the following photograph:
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https://sentence.yourdictionary.com/equipotential
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math
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Equipotential Sentence Examples
The presence, however, of apparatus or observers upsets the conditions, while above uneven ground or near a tree or a building the equipotential surfaces cease to be horizontal.
If the shape of the equipotential surfaces near it is influenced by trees, shrubs or grass, their influence will vary throughout the year.
Above the level plain of absolutely smooth surface, devoid of houses or vegetation, the equipotential surfaces under normal conditions would be strictly horizontal, and if we could determine the potential at one metre above the ground we should have a definite measure of the potential gradient at the earth's surface.
In an ordinary climate a building seems to be practically at the earth's potential; near its walls the equipotential surfaces are highly inclined, and near the ridges they may lie very close together.
This only means that the equipotential surfaces are crowded together, just as they are near the ridge of a house.Advertisement
Bearing this in mind, one can readily imagine how close together the equipotential surfaces must lie near the summit of a high sharp mountain peak.
If the current is interrupted or alternating, and if a telephone receiver has its terminals connected to a separate metallic circuit joined by earth plates at two other places to the earth, not on the same equipotential surface of the first circuit, sounds will be heard in the telephone due to a current passing through it.
Canal system of flow lines of current through the sea, and these might be detected by any other ships furnished with two plates dipping into the sea at stem and stern, and connected by a wire having a telephone in its circuit, provided that the two plates were not placed on the same equipotential surface of the original current flow lines.
If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn = F, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.
The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles.Advertisement
The potential due to a single pole of strength m at the distance r from the pole is V = m/ r, (7) the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii.
The potential due to a thin magnet at a point whose distance from the two poles respectively is r and r' is V =m(l/r=l/r') (8) When V is constant, this equation represents an equipotential surface.
The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis.
Hall Efect.-If an electric current is passed along a strip of thin metal, and the two points at opposite ends of an equipotential line are connected with a galvanometer, its needle will of course not be deflected.
These surfaces are called "equipotential" or "level surfaces," and we may so locate them that the potential difference between two adjacent surfaces is one unit of potential; that is, it requires one absolute unit of work (I erg) to move a small body charged with one unit of electricity from one surface to the next.Advertisement
The surface of a charged conductor is an equipotential surface, because when the electric charge is in equilibrium there is no tendency for electricity to move from one part to the other.
We may describe, through all the points in an electric field which have the same potential, surfaces called equipotential surfaces, and these will be everywhere perpendicular or orthogonal to the lines of electric force.
Then the charge at A together with the induced surface charge on the plate makes a certain field of electric force on the left of the plate PO, which is a zero equipotential surface.
Let us assume the field divided up into tubes of electric force as already explained, and these cut normally by equipotential surfaces.
Hence the equipotential surfaces cannot cut each other.Advertisement
Suppose that we have any distribution of electricity at rest over conductors, and that we know the potential at all points and consequently the level or equipotential surfaces.
Take any equipotential surface enclosing the whole of the electricity, and suppose this to become an actual sheet of metal connected to the earth.
Therefore, whatever may be the distribution of electric force produced by the charges inside taken alone, it can be exactly imitated for all space outside the metal surface if we suppose the inside charge removed and a distribution of electricity of the same sign made over the metal surface such that its density follows the law Q = - (1 /47r)dU/dn (27), where dUldn is the electric force at that point on the closed equipotential surface considered, due to the original charge alone.
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CC-MAIN-2023-23
| 5,032 | 24 |
http://www.fullgk.com/?cat=24
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math
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Home » APTITUDE
Category Archives: APTITUDE
If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192 m2. What is the area of the original rectangle ?
(a) 184 m2
(b) 196 m2
(c) 198 m2
(d) 200 m2
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
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| 482 | 9 |
https://www.physicsforums.com/threads/work-emptying-a-bowl.161761/
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math
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A hemispherical bowl with radius 8-inches is filled with punch (weighing .04 pound/in^3) to within 2-inches of the top. How much work is done emptying the bowl if the contents are pumped just high enough to get over the rim?
The Attempt at a Solution
Work = Force(weight)* displacement.
i said displacement was "x"
and for the weight:
r = sqrt(64- x^2)
weight = (.04) (pi * r^2)dx
and so, work to lift weight at a given "x"
so i get total work is
integration from 2 to 8 of
(.04pi)(x)(64 - x^2)dx
Is this the right way to approach this problem?
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CC-MAIN-2022-33
| 544 | 12 |
https://www.hackmath.net/en/math-problem/15363
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math
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Try to estimate the weight of the water in an aquarium 50cm long 30cm wide, when poured to a height of 25cm. Calculates the weight of the aquarium's water.
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CC-MAIN-2020-16
| 3,031 | 34 |
http://www.merriam-webster.com/concise/differential%20operator
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math
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In mathematics, any combination of derivatives applied to a function. It takes the form of a polynomial of derivatives, such as D2 D2 D2, where D2 is a second derivative and the subscripts indicate partial derivatives. Special differential operators include the gradient, divergence, curl, and Laplace operator (see Laplace's equation). Differential operators provide a generalized way to look at differentiation as a whole, as well as a framework for discussion of the theory of differential equations.
This entry comes from Encyclopædia Britannica Concise.For the full entry on differential operator, visit Britannica.com.
What made you look up differential operator? Please tell us what you were reading, watching or discussing that led you here.
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https://www.enotes.com/homework-help/find-volume-374000
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math
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Find the volume An ornament is carved from a rectangular block of wood which has a square base and a height of 24 cm. The ornament consists of two identical spheres and two identical cubes. The diameter of each sphere is equal to the length of the side of each cube. The ornament has the same width as the original block. Find the volume of the ornament.
You should come up with the following substitution for the length of the side of square such that:
`l = x`
You need to evaluate the volume of rectangular block of wood such that:
`V = 24x^2`
The ornament is formed from two spheres and two...
(The entire section contains 117 words.)
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| 672 | 8 |
http://www.mywordsolution.com/question/if-no-extra-work-is-done-after-initial-milling/918947
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math
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Q1) Sonimad Sawmill produces two lumber products from joint milling process. Two products developed are mine support braces (MSBs) and unseasoned commercial building lumber (CBL). Standard production run incurs joint costs of $300,000 and results in 60,000 units of MSB and 90,000 units of CBL. Each unprocessed unit of MSB sells for $2 per unit and each unprocessed unit of CBL sells for $4 per unit.
If CBL is processed further at cost of $200,000, it can be sold at $10 per unit but 10,000 units are unavoidably lost (with no discernible value). MSB units can be coated with preservative at cost of= $100,000 per production run and then sold for $3.50 each.
a) If no extra work is done after initial milling process, compute cost of CBL by using physical quantities to assign the joint cost.
b) If no extra work is done after initial milling process, compute cost of MSB using relative sales value to assign joint cost.
c) Must MSB and CBL be processed further or sold immediately after initial milling?
d) Given your decision in (c), make a schedule calculating completed cost assigned to each unit of MSB and CBL as charged to finished goods inventory. Utilize net realizable value for allocating joint costs.
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http://vixra.org/abs/1202.0066
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math
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Authors: Stephen Crowley
The Riemann zeta function at integer arguments can be written as an infinite sum of certain hypergeometric functions and more generally the same can be done with polylogarithms, for which several zeta functions are a special case. An analytic continuation formula for these hypergeometric functions exists and is used to derive some infinite sums which allow the zeta function at integer arguments n to be written as a weighted infinite sum of hypergeometric functions at n − 1. The form might be considered to be a shift operator for the Riemann zeta function which leads to the curious values ζF(0) = I_0(2) − 1 and ζF(1) = Ei(1) − γ which involve a Bessel function of the first kind and an exponential integral respectively and differ from the values ζ(0) = −1/2 and ζ(1) = ∞ given by the usual method of continuation. Interpreting these “hypergeometrically continued” values of the zeta constants in terms of reciprocal common factor probability we have ζF(0)^-1 ~ 78.15% and ζF(1)^-1 ~ 75.88% which contrasts with the standard known values for sensible cases like ζ(2)^-1 ~ 60.79% and ζ(3)^-1 ~ 83.19%. The combinatorial definitions of the Stirling numbers of the second kind, and the 2-restricted Stirling numbers of the second kind are recalled because they appear in the differential equatlon satisfied by the hypergeometric representation of the polylogarithm. The notion of fractal strings is related to the (chaotic) Gauss map of the unit interval which arises in the study of continued fractions, and another chaotic map is also introduced called the “Harmonic sawtooth” whose Mellin transform is the (appropritately scaled) Riemann zeta function. These maps are within the family of what might be called “deterministic chaos”. Some number theoretic definitions are also recalled.
Comments: 25 Pages.
Unique-IP document downloads: 691 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
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| 2,597 | 7 |
https://www.dummies.com/education/math/pre-calculus/how-to-use-the-foil-method-to-factor-a-trinomial/
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math
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How to Use the FOIL Method to Factor a Trinomial
For polynomials with a nonprime leading coefficient and constant term, you can use a procedure called the FOIL method of factoring (sometimes called the British Method). The FOIL Method always works for factoring trinomials and is a very helpful tool if you can’t wrap your brain around guess-and-check. When the FOIL method fails, you know for certain the given quadratic is prime.
The FOIL method of factoring calls for you to follow the steps required to FOIL binomials, only backward. Remember that when you FOIL, you multiply the first, outside, inside, and last terms together. Then you combine any like terms, which usually come from the multiplication of the outside and inside terms.
For example, to factor x2 + 3x – 10, follow these steps:
Check for the Greatest Common Factor (GCF) first.
The expression x2 + 3x – 10 doesn’t have a GCF when you break it down and look at it. The breakdown looks like this:
No factors are common to all terms, so the expression has no GCF. You get to move on to the next step.
Multiply the quadratic term and the constant term.
Be careful of the signs when you do this step. In this example, the quadratic term is 1x2 and the constant is –10, hence
Write down all the factors of the result that result in pairs in which each term in each pair has an x.
The pairs factors of –10x2 in which each term contains an x are –1x and 10x, 1x and –10x, –2x and 5x, and 2x and –5x.
From this list, find the pair that adds to produce the coefficient of the linear term.
You want the pair whose sum is +3x. For this problem, the answer is –2x and 5x because
and –2x + 5x = 3x.
Break up the linear term into two terms, using the numbers from Step 4 as the coefficients.
Written out, you now have x2 – 2x + 5x – 10.
Life is easier in the long run if you always arrange the linear term with the smallest coefficient first. That’s why we put the –2x in front of the +5x.
Group the four terms into two sets of two.
Always put a plus sign between the two sets: (x2 – 2x) + (5x – 10).
Find the GCF for each set and factor it out.
What do the first two terms have in common? An x. If you factor out the x, you have x(x – 2). Now, look at the second two terms. They share a 5. If you factor out the 5, you have 5(x – 2). The polynomial is now written as x(x – 2) + 5(x – 2).
Find the GCF of the two new terms.
As you can see, (x – 2) appears in both terms, so it’s a GCF. Factor out the GCF from both terms (it’s always the expression inside the parentheses) to the front and leave the remaining terms inside the parentheses. Thus x(x – 2) + 5(x – 2) becomes (x – 2)(x + 5). The (x + 5) is the leftover after factoring out the GCF of (x-2).
Sometimes the sign has to change in Step 6 in order to correctly factor out the GCF. But if you don’t start off with a plus sign between the two sets, you may lose a negative sign you need to factor all the way. For example, in factoring x2 – 13x + 36, you end up in Step 5 with the following polynomial: x2 – 9x – 4x + 36. When you group the terms, you get (x2 – 9x) + (–4x + 36). Factor out the x in the first set and the 4 in the second set to get x(x – 9) + 4(–x + 9). Notice that the second set is the exact opposite of the first one? In order for you to move to the next step, the sets have to match exactly. To fix this, change the +4 in the middle to –4 and get x(x – 9) – 4(x – 9). Now that they match, you can factor again.
Even when an expression has a leading coefficient besides 1, the FOIL method still works. The monkey wrench comes only if in Step 2 you can’t find any factors that add to give you the linear coefficient. In this case, the expression is prime. For example, in 2x2 + 13x + 4, when you multiply the quadratic term of 2x2 and the constant of 4, you get 8x2. However, no factors of 8x2 also add to be 13x, so 2x2 + 13x + 4 is prime.
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https://space.stackexchange.com/questions/51406/what-is-the-increase-in-drag-by-adding-a-space-station-module
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math
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Imagine a cylindrical space station module, orbiting at an arbitrary height - the same as the ISS say.
Another identity cylindrical module docks on the end. Real station cross section hasn't changed - the same surface area is pointing in the direction of travel.
How does this effect the total drag caused by the atmosphere? If zero impact, what if we add a third? A fourth? A fifth?
At what point would we materially change the drag experienced?
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| 446 | 4 |
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