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https://www.solutioninn.com/on-june-1-2014-jetcom-inc-issued-a-540000-12
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math
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On June 1, 2014, JetCom Inc. issued a $540,000 12%,
On June 1, 2014, JetCom Inc. issued a $540,000 12%, three-year bond. Interest is to be paid semi-annually beginning December 1, 2014.
a. Calculate the issue price of the bond assuming a market interest rate of 13%.
b. Using the effective interest method, prepare an amortization schedule similar to Exhibit 15.10.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039747215.81/warc/CC-MAIN-20181121052254-20181121074254-00133.warc.gz
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CC-MAIN-2018-47
| 365 | 4 |
http://slideplayer.com/slide/5869912/
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math
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The Pythagorean Theorem
Objectives Use the Pythagorean Theorem.
Key Vocabulary Leg Hypotenuse Pythagorean Theorem Pythagorean Triple
Parts of a Right Triangle
Longest side is the hypotenuse, side c (opposite the 90o angle). The other two sides are the legs, sides a and b. Pythagoras developed a formula for finding the length of the sides of any right triangle.
Theorem 4.7 - The Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Example: (hypotenuse)2=(leg)2+(leg)2
Example 1 Find the length of the hypotenuse. SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem c2 = Substitute. c2 = Multiply. c2 = 169 Add. Find the positive square root. c2 = 169 c = 13 Solve for c. ANSWER The length of the hypotenuse is 13. 6
Example 2 Find the unknown side length. SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem 142 = 72 + b2 Substitute. 196 = 49 + b2 Multiply. 196 – 49 = 49 + b2 – 49 Subtract 49 from each side. 147 = b2 Simplify. Find the positive square root. 147 = b2 12.1 ≈ b Approximate with a calculator. ANSWER The side length is about 12.1. 7
Your Turn: Find the unknown side length. 1. ANSWER 8 2. ANSWER 8 3.
Example 3a A. Find x. The side opposite the right angle is the hypotenuse, so c = x. a2 + b2 = c2 Pythagorean Theorem = c2 a = 4 and b = 7
Example 3a 65 = c2 Simplify. Take the positive square root of each side. Answer:
Example 3b B. Find x. The hypotenuse is 12, so c = 12.
a2 + b2 = c2 Pythagorean Theorem x = 122 b = 8 and c = 12
Example 3b x2 + 64 = 144 Simplify. x2 = 80 Subtract 64 from each side.
Take the positive square root of each side and simplify. Answer:
Your Turn: A. Find x. A. B. C. D.
Your Turn: B. Find x. A. B. C. D.
More Examples: C A B B = 6 1) A=8, C =10 , Find B
3) B =10, C=26 , Find A 4) A=15, B=20, Find C 5) A =12, C=16, Find B 6) B =5, C=10, Find A 7) A =6, B =8, Find C 8) A=11, C=21, Find B B = 8 A = 24 C = 25 C B = 10.6 A A = 8.7 C = 10 B = 17.9 B
Pythagorean Triples Three whole numbers that work in the Pythagorean formulas are called Pythagorean Triples. The largest number in each triple is the length of the hypotenuse. Pythagorean triples are not the only possible side lengths for a right triangle. They give the triangles where all the lengths are whole numbers, but the side lengths could be any real numbers.
If you multiply the lengths of all three sides of any right triangle by the same number, then the resulting triangle is a right triangle. In other words, if a2 + b2 = c2, then (an)2 + (bn)2 = (cn)2. Therefore, additional pythagorean triples can be found by multiplying each number in a known triple by the same factor.
Pythagorean Triples Multiples
Primitive Pythagorean Triples
A set of Pythagorean triples is considered a primitive Pythagorean triple if the numbers are relatively prime; that is, if they have no common factors other than 1. You need know the first 4 primitives: 3-4-5, , , 3-4-5
Example 4 Use a Pythagorean triple to find x. Explain your reasoning.
Example 4 Notice that 24 and 26 are multiples of 2 : 24 = 2 ● 12 and 26 = 2 ● 13. Since 5, 12, 13 is a Pythagorean triple, the missing leg length x is 2 ● 5 or 10. Answer: x = 10 Check: = 262 Pythagorean Theorem ? 676 = 676 Simplify.
Your Turn: Use a Pythagorean triple to find x. A. 10 B. 15 C. 18 D. 24
More Practice Use Pythagorean Triples to find each missing side length. Primitive: X=26 Primitive: X=50 Primitive: 3-4-5 X=15
© 2023 SlidePlayer.com Inc.
All rights reserved.
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CC-MAIN-2023-23
| 3,545 | 33 |
http://montessoripathways.com.au/curriculum/mathematics/
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math
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To many, mathematics is a cold and inhuman pursuit with abstract symbols, unbending laws and sterile logic. we should help the child understand that part of being human is having a mathematical mind and that we make mathematics every time we move, think, work or play. The foundation of our mathematical mind is to idealise the world e.g. the idealisation of form leads to the study of geometry.To further our understanding, basic intellectual skills area also necessary, such as judging relatitive amounts of degrees and perceiving exactness. The practical and sensorial activities prepare the child for the study of Mathematics. The mathematical activities include introduction to numbers, the decimal system, teens, tens and counting, arithmetic tables and abstraction.
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CC-MAIN-2019-22
| 772 | 1 |
https://www.jiskha.com/members/profile/posts.cgi?name=Wade
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math
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Posts by Wade
Total # Posts: 25
In a sample of 1000 tires, with a mean of 250 miles per tire....about how many tires will last longer than 300 miles?
If a+b=-9 what is 8a + 8 b?
Is the solution to this rational expression extraneous? The problem: (2x-3)/7 -(7x)/14 My answer: x = -9/4 My teacher wants to know if the solution is extraneous and I know I have to plug my answer back into the expression to check but I still don't understand.
A small aircraft A is about to land with an airspeed of 80 mi/hr. If the aircraft is encountering a steady side wind of speed 10 mi/hr, what angle (alpha) should the pilot direct the aircraft so the the absolute velocity is parallel to the runway? What is the speed at touchdown?
Summary of the soft voice of the serpent
If it snowed 7 days in the month of December in Wisconsin, what percent of the days in December did Wisconsin get snow?
Can you explain to me what this means: "First thoughts are also unencumbered by ego, by that mechanism in us that tries to be in control, tries to prove the world is permanent and solid, enduring and logical."
7th grade Social Studies Ms. Sue please!
9 is Substance Farming (Just took the test, and that's what it says"
What were some of the causes of the financial crisis and how do you think they could be prevented? Do you think steps are being taken? Why or why not?
General Computer Science
Why should IT policy and control be a prime concern to overall management in the selection and development of IT management? Please write an answer to the above question.
A drag line is connected to an electric motor. Crates are hooked onto the line and dragged horizontally from one location within the factory to another across a series of rollers. There is 15° between the crate and motor and a force of 500N Each crate has a mass of 200kg. ...
In considering the importance of culture to ethics please help me answer the below questions: 1. Are some cultures more moral than others? Please give examples and explain your position. Can you describe a moral standard that is at variance with your own ethical system? 2. Are...
Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Explain why or why not? Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition ...
you're right doc its Ag2SO4, thanks guys!
determine the new molarity of calcium ions when 50.0 mL of a 1.50 M calcium chloride solution are combined with 750.0 mL of a 0.236 M calcium phosphate solution.
0.04201/0.08696 = 0.483 M of [Mg^2+] but how do I get the [Cl-]? the answer is suppose to be 0.966M
what are the molarities of Mb^2+ ions and Cl- ions in an aqueous solution of 4.00% by the mass magnesium chloride, with a density of 1.15g mL-1?
Find the percent by mass of sodium chloride in a 1.35 M NaCl solution. The density of the solution is 1.06 g/mL..............how do I go about doing this question thanks!
I really don't understand how to write the expression as one invloving only sinϴ and cosϴ sin2ϴ+cos3ϴ
there are fewer than 6 dozen eggs in a basket. if i cout them by 2s, there is obne left over. if i count by 3s, there are 2 left over. three are left if i count them by 4s. four are left if i count by 5s. how many eggs are there
Y/1 DIVIDED BY 2 4/5, Y = ?
For the following reaction, what is the approximate value of Delta H? CH4(g) --> CH3(g) + H(g) I figured it out.. C-H = 411 4 moles on one side 3 on the other so [4*411]-[3*411] = 411
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CC-MAIN-2018-05
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https://mathsclass.net/comments/some-graphs-are-just-wrong/
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math
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A blog about teaching and learning in a maths classroom.
Friday, 27 November 2009 | 1 Comment
Here’s a great example of a graph that is just wrong, the data may be correct, but it has obviously been represented the wrong way. Watch the video…
From FlowingData who also have a screenshot.
Posted in • Elsewhere • In the news • Lesson Idea • Graphs | Short URL: http://mths.co/1752
New Subscribe to the …MathsLinks
Simon Job — eleventh year of teaching maths in a public high school in Western Sydney, Australia.
MathsClass is about teaching and learning in a maths classroom. more→
updates via @mathslinks
The Salesman - by Greg Ashman - Filling The Pail
Peter Liljedahl wants to make kids think about mathematics
maths peterliljedahl gregashman
Mathcha - Online Math Editor
maths editor latex
Copy Paste MathJax
maths latex symbols
Crossover Workbooks | Sparx Maths
maths workbook practice exercise
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CC-MAIN-2023-23
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https://www.hackmath.net/en/math-problem/1846?tag_id=143
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math
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From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what time in hours its will meet?
Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):
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Following knowledge from mathematics are needed to solve this word math problem:
Next similar math problems:
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Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?
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The cyclist went from village to town. First half of journey went at 20 km/h. The second half of the journey, which mostly fell, went at 39 km/h. All journey took 88 minutes. Calculate the distance from the village to the town.
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
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Bus started from point A 10 minutes before the train started from the same place. The bus went an average speed of 49 km/h, train 77 km/h. To point B train and bus arrived simultaneously. Calculate time of train journey, if train and bus travelled the.
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Calculate how many minutes will be reduced to travel 187 km long railway corridor, where the maximum speed increases from 120 km/h to 160 km/h. Calculate how many minutes will shorten travel time, if we consider that the train must stop at 6 stations, eac
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The village is 28 km from the cottage. Father goes from village to cottage. Son goes from the cottage to the village. They meet 10 km further behind the cottage. How much did dad walk?
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Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
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The cyclist on three-day trip travel 30% of the total route on the first day, 3/5 of the rest on the second day and 35 km on the third day. How many kilometers did travel cyclists each day and how many?
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Marek rode a bike ride. In an hour, John followed him on the same route by car, at an average speed of 72 km/h, and in 20 minutes he drove him. Will he determine the length of the way that Marek took before John caught up with him, and at what speed did Ma
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Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
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| 4,108 | 34 |
https://appcrawlr.com/android/pbs-kids-measure-up
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math
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PBS KIDS Measure Up!
Discover more like PBS KIDS Measure Up!
Peg + Cat: The Tree ProblemFree
Hectic Harvest from PBS KIDS$1.99
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Peg + Cat Big Gig by PBS KIDS$1.99
Super Why! ABC Adventures$3.99
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CC-MAIN-2020-05
| 260 | 8 |
https://www.toprut.com/news/2021/12/22/draw-odds-point-view/
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math
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In last week's article we suggested that dividing up your tag wish list into 3 distinct time periods was a good starting point to your overall application strategy. To continue on the theme of maximizing your long term draw success, this week we are going to offer some tips and observations about the core but often under-considered fundamental: draw odds.
Consider the following scenario: you are choosing between two hunts, one with 2% draw odds and another with 4% odds. What's the difference in terms of your likelihood to draw?
In the western big game landscape, "draw odds" are most often listed as a percentage. If a particular hunt is listed as having 50% draw odds, applicants for that tag in the previous draw had a coin flips chance of successfully drawing (or 1 in 2). Technically the "odds" for an event to occur are more often represented in the latter format (1 in 2). When listed as a percentage, the term "probability" is the more technically correct term. In our case this is semantics and not really an important distinction. But it can be very useful at times to think about the percentage draw "odds" for a hunt in terms of the other format (i.e. 1 in 2).
For purposes of illustration, we'll use the analogy of a sack full of marbles. Red marbles are bad and green marbles are good. In our simple 50% example there is 1 red marble and 1 green marble in the sack. Now blindly reach into the sack and pick a marble ("the draw"). There are 2 possible outcomes, and 1 of them is good (1 in 2).
Of course we can convert any draw odds percentage to sacks of marbles - although the arithmetic isn't always quite as simple. At 33% there are 3 total marbles with 1 green, at 25% there are 4 with 1 green, etc. As the draw odds percentage goes down, you get more marbles in the sack and the number of green ones relative to red declines.
Sometimes if you think in terms of green to red, the comparative difference of "draw odds" becomes more clear. When you apply for a 10% odds hunt you've got 1 green in a sack of 10 marbles. But with a 20% hunt, there are only 5 total marbles in that sack. Big difference! Sometimes what is obvious (that you are twice as likely to draw a 20% hunt over a 10% hunt) can be obscured by how our mind perceives percentages as they grow smaller.
Which brings us back to the original question when we considered 2% vs 4%. The important difference isn't 2% (4 minus 2), it's that you are twice as likely to draw the 4% hunt (1 in 25 vs 1 in 50).
Some may counter by arguing that you are still VERY unlikely to draw either tag in any given year and because of that they are basically the same. But that's the short view. If you are onboard with some version of a plan that includes a medium/long term strategy then you really need to think in terms of total tags drawn over a period of years. In a 10 year period, the chances you will draw a 4% tag at least once is almost exactly 1 in 3, and for 2% it is worse than 1 in 5. I know which I would choose if I was given some equivalent option in a draw that occurs only once every 10 years.
There are of course real reasons to sometimes choose a harder to draw hunt over one with better odds. For example, you may feel like the overall quality of the lower odds hunt is just significantly better and that the reward would be worth it if successful. Or if you apply for a lot of different tags across multiple states you may choose a strategy that includes applying for a couple of dream tags each year. In the end, there are no hard and fast rules to this and it comes down to your own individual goals and tolerance for risk.
From the dream tag perspective, take advantage of the states that currently have an application system that considers more than just your 1st application choice before moving on to the next application (Nevada and New Mexico for example). In these draw systems you can apply for a really difficult to draw hunt as your 1st choice and still get the advantage of applying for other hunts with better odds with your later choices (spoiler alert: these draw systems actually work to lower everyone's draw odds overall - a topic for another day).
As you apply for hunts this year and plan out your medium and long term strategy, keep the red and green marbles in mind. It is Christmas time after all. Happy holidays!
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CC-MAIN-2023-14
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https://quant.stackexchange.com/questions/49211/why-do-options-market-makers-make-their-spread-as-wide-as-the-corresponding-vega
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math
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I've heard that option market makers make their bid ask spread as wide as the vega of the contract they are quoting. If the quoted spread is narrower than the vega of the option it is said that the price is competitive. Why is this? What is the basis for the rule of thumb?
So for example, if the at the money option has A vega of 10 the corrosponding market could be 1.10 bid 1.20 ask (it is 10 cents wide).
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679102697.89/warc/CC-MAIN-20231210221943-20231211011943-00478.warc.gz
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CC-MAIN-2023-50
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https://www.physicsforums.com/threads/ball-thrown-up-in-air-velocity-question.279097/
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math
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1. The problem statement, all variables and given/known data A ball is thrown vertically upward with an initial speed of 11 m/s. One second later, a stone is thrown vertically upward with an initial speed of 25 m/s. (a) Find the time it takes the stone to catch up with the ball. (b) Find the velocities of the stone and the ball when they are at the same height. 2. Relevant equations 3. The attempt at a solution a = 9.8 Vi,ball= 11 m/s Vi,stone= 25m/s y= y0+ V0t+ 1/2 at2 y = 11t+ 1/2 (9.8) t2 y= 11t - 4.9 t2 ======= ball y = 25 (t+1) + (4.9 (t+1))2 y = 25t + 25 - 4.9 ( t2 + 2t + 1) y = 25 t + 25 - 4.9 t2-9.8t - 4.9 y= -4.9t2 + 15.2t + 20.1 ===== stone 11t - 4.9 t2 = -4.9t2 + 15.2t + 20.1 am i on the right track??
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815560.92/warc/CC-MAIN-20180224112708-20180224132708-00797.warc.gz
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| 721 | 1 |
https://www.simplewiringdiagram.info/fig-1-the-toplevel-block-diagram-of-the-fpgabased-dijkstras
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math
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Fig 1 The Toplevel Block Diagram Of The Fpgabased Dijkstras
Fig 1 The Toplevel Block Diagram Of The Fpgabased Dijkstras through the thousand photos on the web with regards to Fig 1 The Toplevel Block Diagram Of The Fpgabased Dijkstras we choices the top libraries having ideal quality just for you all, and this images is one among photographs series in this best photographs gallery with regards to Fig 1 The Toplevel Block Diagram Of The Fpgabased Dijkstras, we hoping you might want it.
Step 1: Open The Top-Level Block Design File. Step 1: Open the Top-Level Block Design File. The top-level arm_top Block Design File is installed in the \qdesigns\excalibur directory during the installation process. This file contains the pld_slave logic block that you in turn connect to the Master Port of the arm_processor megafunction.
A Robust Watermarking Scheme For Online Multimedia. Figure 1: A top level block description of the proposed unified framework for protecting the rightful ownership of digital data. If an unauthenticated user tries to download and upload a data of user , not only will the permission be denied but the domain will also notify to legally make a case against that unauthenticated user.
Question 1 (Exercise 11. A temperature control system for a distillation column is shown in Fig. E11.1. The temperature T of a tray near the top of the column is controlled by adjusting the reflux flow rate R. Draw a block diagram for this feedback control system.
Solved: Consider The Block Diagram In Fig. 1. Determine Th. Answer to Consider the block diagram in Fig. 1. Determine the steady-state error for a step input in terms of the gain K. Determin
Fig 1 Shows The Block Diagram Of The U Model Based Pole. Fig. 1 shows the block diagram of the U-model based pole placement control system. In the U-pole placement design, the U-model is firstly transferred from the
FPGA Designs With Verilog And. Now, analyze the design (Fig. 1.11) and then open the pin planner (Fig. 1.12). We can see the new pin assignments as shown in Fig. 1.21 (If proper assignments do not happen, then check whether the Verilog design is set as top level or not and import assignments again and analyze the design).
Solved: Fig. 1.31-Unit Block Of Porous Medium Of Problem 1. Fig. 1.31-Unit block of porous medium of Problem 1.2 1.2 A rock is made up of several blocks, as shown in Fig. 1.31. The unit block is a rectangular prism of nonporous, noncon- ductor material of length L and square cross section with side length d.
Solved: N(s) Fig. 1 General Block Diagram Q3: Consider The. n(s) Fig. 1 General block diagram Q3: Consider the system shown Figure (2) assume that c, is the input voltage and co is the output voltage. In this sy stem the sccond stage of the circuit (R,C2 portion) is producing loading effects on the fitrst stage (R,Ci portion ).
Figure 614 Shows The Toplevel Block Diagram Symbol And The. Figure 614 shows the toplevel block diagram symbol Figure 6.14 shows the top‐level block diagram symbol and the logic diagram of a four‐bit register that has a parallel load capability and can operate as a counter. When equal to 1, the input load control disables the count operation and causes a transfer of data from the four data inputs into the four flip‐flops. If both control
On The Pseudorandomness Of Top-Level Schemes Of Block. On the Pseudorandomness of Top-Level Schemes of Block Ciphers . Conference Paper · October 2000 with 14 Reads How we measure 'reads' A 'read' is counted each time someone views a publication
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CC-MAIN-2019-43
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https://brainmass.com/business/accounting-for-corporations/preferred-stock-value-444763
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math
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Preferred stock is a hybrid security that is an equity holding but behaves more like a bond, as far as stock price movements. Preferred stock has no voting rights, and in the event of bankruptcy, preferred shareholder claims follow bondholders and precede common shareholders. Preferred dividends are contractual, in that while the stated dividend may not be paid in a given year due to low earnings and cash flows, all prior years' dividends must be paid-up to preferred stockholders before any dividends are paid to common stockholders. Consequently, preferred stockholders can generally count on a certain amount of income over a period of years, although some years' income may be made up in later years.
Years ago, preferred stock was issued as a perpetuity- it never matured. However, in recent decades, preferred stock is issued with a maturity date as would a bond. This practice assists in security valuation for financial and insurance companies whose assets must be assessed relative to its liabilities.
Apply this concept.
A firm issued a preferred stock which matures in 30 years and carries a maturity value of $45. The dividend is $4 per year over the 30 year period. The current market discount rate for this stock is 8%. What is the value of the preferred share?
The solution does a great job of answering the question. The solution is brief and concise and very easy to follow along. All the steps are clearly shown and Excel formulas are provided so that the student can answer similar questions in the future. It can be easily understood by anyone with a basic understanding of the topic. Overall, an excellent solution.
Valuation, Interest rates, Constant growth, Preferred stock value
See attached file for proper formatting.
(5-2) "Short-term interest rates are more volatile than long-term interest rates, so short-term bond prices are more sensitive to interest rate changes than are long-term bond prices." Is this statement true or false? Explain.
(5-3) The rate of return you would get if you bought a bond and held it to its maturity date is called the bond's yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond's price and to its YTM? Does the length of time to maturity affect the extent to which a giving change in interest rates will affect the bond's price?
(5-5) A sinking fund can be set up in one of two ways. Discuss the advantages and disadvantages of each procedure from the viewpoint of both the firm and its bondholders.
Bond Valuation with
Jackson Corporation's bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8%. The bonds have a yield to maturity of 9%. What is the current market price of these bonds?
The real risk-free rate of interest is 4%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-years Treasure securities? What is the yield on 3-years Treasure securities?
(1) Discuss the value of foreign (non-United States) stocks in an investment portfolio. Do you want them? If so, which ones? Do you diversify the classes as you would domestic stock? If so, what classes would you select? Any countries you'd avoid? What about a stock index for foreign stocks...is this a good or bad idea?
(7-2) Two investors are evaluating General Electric's stock for possible purchase. They agree on the expected value of D1 and also on the expected future dividend growth rate. Further, they agree on the risk of the stock. However, one investor normally holds stocks for 2 years and the other normally holds stocks for 10 years. On the basis of the type of analysis done in this chapter, they should both be willing to pay the same price for General Electric's stock. True or false? Explain.
(7-3) A bond that pays interest forever and has no maturity date is a perpetual bond, also called a perpetuity or a consol. In what respect is a perpetual bond similar to (1) a no-growth common stock and (2) a share of preferred stock?
(7-4) People have argued that a stock's market price can deviate from its intrinsic value. Discuss the following question: If all investors attempt to behave in an entirely rational manner, could these differences still exist? In answering this question, think about information that's available to insiders versus outsiders, the fact that historical probabilities of financial events are "fuzzier" than probabilities related to physical items, and the validity of the concepts of animal spirits, herding, and anchoring.
Boehm Incorporated is expected to pay a $1.50 per share dividend at the end of this year (i.e., D1 = $1.50). The dividend is expected to grow at a constant rate of 7% a year. The required rate of return on the stock, rs, is 15%. What is the value per share of Boehm's stock?
Nick's Enchiladas Incorporated has preferred stock outstanding that pays a dividend of $5 at the end of each year. The preferred sells for $50 a share. What is the stock's required rate of return?
A stock is trading at $80 per share. The stock is expected to have a year-end dividend of $4 per share (D1 = $4), and it is expected to grow at some constant rate g through-out time. The stock's required rate of return is 14%. If markets are efficient, what is your forecast of g?
(1) From the reading you discovered that most firms rely on a mix of debt, preferred stock, and common equity. Since debt tends to be less risky to bondholders than equity is to stockholders, the cost of debt to the firm (r(d)) is lower than the cost of equity (r(s)). That said, since debt is less expensive than equity, briefly explain why firms tend not to rely upon all (100%) debt to fund their capital needs.
(9-2) How can the WACC be both an average cost and a marginal cost?
(9-3) How would each of the factors in the following table affect a firm's cost of debt, rd (1 - T); its cost of equity, rs; and its weighted average cost of capital, WACC? Indicate by a plus (+), a minus (-), or a zero (0) if the factor would raise, lower, or have an indeterminate effect on the item in question. Assume that all other factors are held constant. Justify your answer, but recognized that several of the parts probably have no single correct answer.
rd (1 - T) rs WACC
a. The corporate tax rate is lowered.
b. The Federal Reserved tightens credit.
c. The firm uses more debt.
d. The firm doubles the amount of capital
it raises during the year.
e. The firm expands into a risky new area.
f. investors become more risk averse.
(9-4) Distinguish between beta (or market) risk, within-firm (or corporate) risk, and stand-alone risk for a potential project. Of the three measures, which is theoretically the most relevant, and why?
(9-5) Suppose a firm estimates its overall cost of capital for the coming year to be 10 %. What might be reasonable cost of capital for average-risk, high risk, and low-risk projects?View Full Posting Details
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CC-MAIN-2018-51
| 7,022 | 33 |
https://www.chegg.com/homework-help/consider-time-series-sequence-observations-x1-x2-response-chapter-12-problem-67e-solution-9781461403906-exc
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math
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Consider a time series—that is, a sequence of observations X1, X2,. . . on some response variable (e.g., concentration of a pollutant) over time—with observed values x1, x2,...,xn over n time periods. Then the lag 1 autocorrelation coefficient is defined as
Autocorrelation coefficients r2, r3, . . . for lags 2, 3,... are defined analogously.
a. Calculate the values of r1, r2, and r3 for the temperature data from Exercise 79 of Chapter 1.
b. Consider the n – 1 pairs (x1, x2), (x2, x3), . . ., (xn–1, xn). What is the difference between the formula for the sample correlation coefficient r applied to these pairs and the formula for r1? What if n, the length of the series, is large? What about r2 compared to r for the n – 2 pairs (x1, x3), (x2, x4), . . ., (xn–2, xn)?
c. Analogous to the population correlation coefficient ρ, let ρi (i = 1, 2, 3, ... ) denote the theoretical or long-run autocorrelation coefficients at the various lags. If all these ρ’s are zero, there is no (linear) relationship between observations in the series at any lag. In this case, if n is large, each Ri has approximately a normal distribution with mean 0 and standard deviation 1/√n and different Ri’s are almost independent. Thus H0: ρ = 0 can be rejected at a significance level of approximately .05 if either or . If n = 100 and r1 = .16, r2 = –.09, r3 = –.15, is there evidence of theoretical autocorrelation at any of the first three lags?
d. If you are testing the null hypothesis in (c) for more than one lag, why might you want to increase the cutoff constant 2 in the rejection region? Hint: What about the probability of committing at least one type I error?
The sample data x1, x2,..., xn sometimes represents a time series, where xt = the observed value of a response variable x at time t. Often the observed series shows a great deal of random variation, which makes it difficult to study longer-term behavior. In such situations, it is desirable to produce a smoothed version of the series. One technique for doing so involves exponential smoothing. The value of a smoothing constant α is chosen (0 < α < 1). Then with t = smoothed value at time t, we set 1 = x1 and for t = 2, 3,..., n, t = αxt + (1 – α)t–1.
a. Consider the following time series in which xt = temperature (°F) of effluent at a sewage treatment plant on day t: 47, 54, 53, 50, 46, 46, 47, 50, 51, 50, 46, 52, 50, 50. Plot each xt against t on a two-dimensional coordinate system (a time-series plot). Does there appear to be any pattern?
b. Calculate the t’s using α = .1. Repeat using α = .5. Which value of α gives a smoother t series?
c. Substitute t–1 = αxt–1 + (1 – α)t–2 on the right-hand side of the expression for t, then substitute t–2 in terms of t–2 and t–3, and so on. On how many of the values xt, xt–1,..., x1 does t, depend? What happens to the coefficient on xt–k as k increases?
d. Refer to part (c). If t is large, how sensitive is t, to the initialization 1 = x1? Explain.
(Note: A relevant reference is the article “Simple Statistics for Interpreting Environmental Data,” Water Pollution Control Fed. J., 1981: 167–175.)
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CC-MAIN-2019-13
| 3,174 | 12 |
https://www.pearson.com/channels/general-chemistry/asset/aa1e98a5/write-the-chemical-formula-for-each-substance-mentioned-in-the-following-word-de
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math
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Start typing, then use the up and down aroows to select an option from the list.
Write the chemical formula for each substance mentioned
in the following word descriptions (use the front inside
cover to find the symbols for the elements you do not know).
(d) The substance phosphorus trihydride, commonly called phosphine,
is a toxic gas.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335059.43/warc/CC-MAIN-20220928020513-20220928050513-00422.warc.gz
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CC-MAIN-2022-40
| 338 | 6 |
http://www.music.mcgill.ca/~gary/618/week9/node4.html
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math
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Woodwind register holes are designed to discourage oscillations based on the fundamental air column mode and thus to indirectly force a vibratory regime based on higher, more stable resonance frequencies.
A register vent functions both as an acoustic inertance and an acoustic resistance (Benade, 1976). It is ideally placed about one-third of the distance from the excitation mechanism of a cylindrical-bored instrument to its first open hole.
Sound radiation from a register hole is negligible.
The DW implementation of a register hole can proceed in a manner similar to that for the tonehole. The series impedance terms associated with toneholes are insignificant for register holes and can be neglected.
Modeling the open register hole as an acoustic inertance in series with a constant resistance, its input impedance as seen from the main bore is given by
where is the density of air, t is the effective height, Arh is the cross-sectional area of the hole, is the acoustic resistance, and s is the Laplace transform frequency variable.
Proceeding with a two-port DW implementation, the register hole is represented in matrix form by
where the open register hole shunt impedance is given by Zrh(o) and Zc is the characteristic impedance of the main air column.
The reflectances and transmittances are equivalent at this junction for wave components traveling to the right or to the left. As
a one-filter form of the junction is possible.
Using the bilinear transform, an appropriate discrete-time implementation for
is given by
A0 is the cross-sectional area of the main air column, and is the bilinear transform constant that controls frequency warping.
Assuming the closed register hole has neglible effect in the acoustic model, simulated closure of the register hole in this implementation is achieved by ramping the reflectance filter gain to zero.
This implementation is similar to that of Välimäki et al. (1993), though resistance effects were not accounted for in that study.
As discussed by Benade (Benade, 1976, p. 459), a misplaced register hole will raise the frequency of the second air column mode by an amount proportional to its displacement from the ideal location (in either direction).
Such behavior is well demonstrated when this register hole implementation is added to the real-time clarinet model.
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CC-MAIN-2018-51
| 2,327 | 17 |
https://www.hackmath.net/en/examples/time?page_num=3
|
math
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Time - examples - page 3
In the workshop have to be produced for 5 days 4000 components. How many components must be produced in the workshop every day and how much per hour, if shift is 8 hours.
- Two workers
Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker?
The first tributary fill pool with water in 15 hours. The second tributary fill pool in 10 hours. For how many hours the pool is filled with both tributaries?
The tale of the Seven Ravens were seven brothers, each of whom was born exactly 1.5 years after the previous one. When the eldest of the brothers was 4-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur
- Minute angle
Determine size of angle, which takes minute hand for 90 minutes.
How many times a day hands on a clock overlap?
- Working time - shortening
The media often speculates about the change (especially to shorten) the working time of the five-day eight-hour working week to another working model. Calculate how many hours a day the employee would have to work a day at 7-day work week if he must work t
Mailbox is opening at regular intervals 3 times a day. The first time is opened at 6:00 and the last at 16:00. Calculate hours when mailbox is opened during day.
- Daily average
Calculate the average temperature during the day, when 14 hours was 20 °C and 10 hours was 15 °C.
- Minute hand v2
In how many minutes describe the minute hand angle 60 degrees?
Five painters painting the fence for eight days. How many days over will take work if paint the fence only four decorators?
- Two typists
There are two typists who are rewriting the material 705 pages. First can it handle rewrite yourself for 24 days; the second 12 days. First typist wrote material yourself 4 days rest rewrites yourself second typist. How many days will it take rewriting alt
Five mates traveled and the journey they lasted 195 minutes. How long would travel only one of them?
6 pump fills the tank for 3 and a half days. How long will fill the tank 7 equally powerful pumps?
- Forestry workers
In the forest is employed 63 laborers planting trees in nurseries. For 11 hour work day would end job in 43 days. After 14 days, 22 laborers go forth. How many days is needed to complete a planting trees in nurseries by others, if they will work 15 hours
- Parquet floor
Three workers laid parquet floor for 1.957 hour. The first one would do this work alone 5 hours, the second in 9 hours. For how many hours would fulfill this work the third worker, if he worked alone?
Hiker went half of trip the first day, the third of trip the second day and remaines 13 km. How long trip he planned?
Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
An oil tanker can be emptied by the first pump in 4.4 hours. Second pump can empty an tanker in 7.8 hours. If the first pump started at 8:00 and second 1.4 hour later, at what time will the tanker be empty?
Peter's badminton class starts a quarter past two PM. He came at 15:26 . Does Peter arrive on time?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120694.49/warc/CC-MAIN-20170423031200-00004-ip-10-145-167-34.ec2.internal.warc.gz
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| 3,169 | 29 |
http://jinyeongpark.com/?p=29063
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math
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This is a joint work with Seung-Yeal Ha and Hwa Kil Kim.
The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity, 28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589573.27/warc/CC-MAIN-20180717051134-20180717071134-00110.warc.gz
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CC-MAIN-2018-30
| 1,374 | 2 |
https://www.careervillage.org/users/106345/xinrui-alice/
|
math
|
Xinrui Alice Zhang
Tags on answered questions
Maria Jun 19, 2020 253 views
What would be the outcome when making a mistake in a calculation for a project?
nerissa Jun 19, 2020 369 views
As a mechanical engineer what do you have to do to insure you don't make any mistakes in your final model?
Jeshua Jun 19, 2020 487 views
What are some things you didn’t expect working as a mechanical engineer?
Andy Jun 19, 2020 380 views
Is CAD the only application to use when working? If not, what are the other applications that a mechanic engineer uses?
Christopher Jun 16, 2020 374 views
After receiving a bachelor's in science, what are the path forward to continuing an education? I'm confused on the differences/hierarchy of graduate school, medical school, or pursuing a PhD.
I'm an undergrad in neuroscience and psych and a career in research is currently my plan.
#college #psychology #science
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224653764.55/warc/CC-MAIN-20230607111017-20230607141017-00378.warc.gz
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CC-MAIN-2023-23
| 892 | 14 |
https://brainly.com/question/148325
|
math
|
First of all, let me correct you on one thing. You're not technically solving anything because there is no equations. All you're doing is simplifying the expression.
Anyway, first of all, you have to expand out the parentheses. That gives you
Then you add up the x's and you get 6x+21
. You could factor out a 3, but honestly it depends on what you're teacher/professor wants you to leave it as, 6x+21 or 3(2x+7).
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s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280308.24/warc/CC-MAIN-20170116095120-00073-ip-10-171-10-70.ec2.internal.warc.gz
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CC-MAIN-2017-04
| 413 | 4 |
https://www.thestudentroom.co.uk/showthread.php?t=3891689
|
math
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I'm trying to analysis The Long Queen and so far, I'm doing very well. I can't find much online either. However, I think this poem is an allusion to Queen Elizabeth 1. Any information on the themes or meaning would be very much appreciated!
...for the 2nd time this year
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CC-MAIN-2018-13
| 270 | 2 |
https://www.hackmath.net/en/math-problem/77274
|
math
|
How far 2
How far can a subway car travel in 1 hour if its average speed is 0.96 miles per minute?
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
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From Znojmo to Brno started the truck with a trailer at an average speed of 53 km per hour. Against him, 14 minutes later from Brno started the car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo do they meet if
- A train
A train can travel 1136 miles in 4 hours. What is the unit rate that this train is traveling per hour? Write in miles per hour.
- Exactly 6134
At what average speed does a car have to travel to drive 55 km in exactly half an hour?
- Cars 6
At 9:00 AM, two cars started from the same town and traveled at a rate of 35 miles per hour, and the other car traveled at a speed of 40 miles per hour. After how many hours will the cars be 30 miles apart?
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From place A, the cyclist drove at a speed of 24 km/h. They sent a car behind him an hour later, traveling at 60 km/h. When and how far from place A will a cyclist travel?
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A professor in a typing class found out that the average performance of an expert typist is 85 words per minute. A random sample of 16 students took the typing test, and we obtained an average speed of 62 words per minute with a standard deviation of 8. C
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The student's vice adventure had a 2,367 km flight. If their travel time was 2 hours and 56 minutes, what was their average speed in kilometers per hour?
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The aircraft weighing 3.5 tons will disembark 1 km in 1 minute after takeoff and reach a speed of 290 km/h. Find the average power of its engines during this time.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337287.87/warc/CC-MAIN-20221002052710-20221002082710-00720.warc.gz
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CC-MAIN-2022-40
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http://mathhelpforum.com/algebra/14831-help-few-simple-problems.html
|
math
|
1: Lee graphs the line y = 2x + 8 on a coordinate plane. What are the coordinates of the x-intercept of the line?
2: Data collected and plotted by Shawn has generated the quadratic equation y = -3x^2 - 6x + 4. What are the coordinates of the maximum of this function?
3: Hector graphs the line y = -2x + 3 on a coordinate plane. Jon graphs a line perpendicular to Hector's line, passing through the point (1,-2). What is the slope of Jon's line?
4: Juan plots two points on a coordinate plane: (-2,3) and (4,-1). What is the slope of the line that contains these two points?
any help would be greatly appreciated!!
Just to summarize what happened here.
we find intercepts by the following.
note that the y-axis is a vertical line passing through x = 0, and the x-value of a point on the y-axis is always 0. similarly, the x-axis is a horizontal line passing through y = 0, and the y-value of any point on the x-axis is always 0. so,
to find the x-intercept we set y = 0
to find the y-intercept we set x = 0
now we were given y = 2x + 8 .......the coefficient of x is the slope and the lone constant is the y-intercept, why?
well, for y-intercept, set x = 0, we get
y = 2(0) + 8 = 8
so the y-intercept is (0,8)
for x-intercept, set y = 0
=> 0 = 2x + 8
=> 2x = -8
=> x = -4
so the x-intercept is (-4,0), which is what qbkr21 got.
this is a downward opening parabola (do you see why?), it has a maximum at it's vertex--the highest point.2: Data collected and plotted by Shawn has generated the quadratic equation y = -3x^2 - 6x + 4. What are the coordinates of the maximum of this function?
to find the x-value for the vertex of a parabola, whether it opens up or down, we solve the equation:
x = -b/2a
where b is the coefficient of x and a is the coefficient of x^2
note: if we had a positive coefficient for the x^2 we would have an upward opening parabola, and the vertex would give it's minimum point
in this problem, we are given: y = -3x^2 - 6x + 4, the coefficient of x^2 is -3 which we call a, and the coefficient of x is -6 which we call b. so for the vertex:
x = -b/2a = 6/2(-3) = -1
when x is -1,
y = -3(-1)^2 - 6(-1) + 4 = 7
so the maximum point is (-1, 7), which is what qbkr21 got
Challenge: try to find the x and y-intercepts for this function.
now we study the relation of the slopes of two lines.3: Hector graphs the line y = -2x + 3 on a coordinate plane. Jon graphs a line perpendicular to Hector's line, passing through the point (1,-2). What is the slope of Jon's line?
to reuse the variables topsquark used, let the slopes of two lines be m1 and m2
two lines are parallel if they have the same slope, that is m1 = m2
two lines are perpendicular if their slopes are the negative inverses of each other, that is m1 = -1/m2. basically, if we take one slope, turn it upside down and attach a minus sign in fron of it, we will get the other slope
topsquark did the calculations for this, so i won't repeat it.
the conventional variable to represent the slope of a line is m. we call a function a straight line if it can be written in the form:4: Juan plots two points on a coordinate plane: (-2,3) and (4,-1). What is the slope of the line that contains these two points?
y = mx + b, where m is the slope and b is the y-intercept.
the slope is defined as the ratio of the rise over run, that is, it is a measure of the rate at which the graph is increasing or decreasing. we find it by measuring how high we go between one point and another divided by the corresponding distance we travel. the formula for the slope is as follows:
let two coordinate points be (x1,y1) and (x2,y2)
the slope of the line connecting these points is given by:
m = (y2 - y1)/(x2 - x1) ............(change in height)/(change in horizontal distance travelled)
topsquark did this for you, so again, i won't repeat it
TPH added the comment that this is true only if x1 not= x2, since that would cause or slope to be undefined, as it would result in dividing by zero, which we can't do
Hope all that rambling helped
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542414.34/warc/CC-MAIN-20161202170902-00117-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 4,002 | 44 |
https://www.answers.com/Q/If_a_guy_knows_he_is_liked_by_two_equally_beautiful_women_but_only_seems_to_be_interested_in_one_what_is_he_most_likely_considering
|
math
|
== == At this point he is likely considering which one he would rather have sex with. I don't think that he is considering anything. If he only shows interest in one woman it is because he is only intersted in one of the women. The woman who isn't getting any attention should just find another guy and wish the other two the best of luck. Unless he is normal and then he is thinking how to get them both in bed. Two equally beautiful women! WOW! Some one thinks high of them self! Fanny tightness. I'd say he is considering personality.
Most likely not considering the age gap of,like,5 years.
Two events that have the same chance of happening. For example, if I flip a coin the event of obtaining a 'head' is equally as likely as the event of obtaining a 'tail'. But equally likely does not mean 0.5 probability. It's possible that it's equally likely that someone in Ontario, Canada will die from being stung by a wasp as from being electrocuted in their kitchen at home. Neither event is very likely but the two events could be equally likely.
equally likely means as likely as the other side ex: 1 piece of candy on this side,1 piece of candy on that side
If you randomly pick a date in April how many equally likely outcomes are there?
chemistry or biolodgy because they seem more fun although they are all equally hard to do as physic's -written by an 11yr old
Not likely, considering that it has no surface.
They are events that have the same probability of occurrence.
no both can get it equally
It means the probability is equal for all of them. If you were to grab one the chances of grabbing another are the same. But in this case it is only equally likely for the red and the green. But if you were to grab two the chances would be equally likely because of the amount of spinners.
Both heads and tails are equally likely.
They are equally likely or equiprobable.
it means that it has a 50% chance of happening
that everything is a equal part of a whole.
If the cube is fair and balanced like Fox, then there are six equally likely outcomes,or so they would have you believe.
When the n events of a given aleatory experiment are equally likely, the theoreticalprobability of any one of the n events is: P(E) = 1/n
they are all equally likely, just like flipping a coin.
Two events are equally unlikely if the probability that they do not happen is the same for each event. And, since the probability of an event happening and not happening must add to 1, equally unlikely events are also equally likely,
no, it is equally likely in either sex
There are 210 = 1024 of them.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039379601.74/warc/CC-MAIN-20210420060507-20210420090507-00622.warc.gz
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CC-MAIN-2021-17
| 2,585 | 20 |
https://www.hive.co.uk/Product/S-Nanda/Fuzzy-Mathematical-Concepts/6913601
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math
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"Fuzzy Mathematical Concepts" deals with the theory and applications of Fuzzy sets, Fuzzy relations, Fuzzy logic and Rough sets including the theory and applications to Algebra, Topology, Analysis, probability, and Measure Theory.
While the first two chapters deal with basic theory and the prerequisite for the rest of the book, readers interested in Algebra and Logic may go through chapters 3 and 4, those interested in Topology may proceed to chapters 5 to 8 and for Analysis one may read chapters 8 and 9.
Readers interested in Rough Set Theory may directly proceed to chapter 10 after completing chapters 1 and 2.
A part of the book can be covered in one semester depending on the requirement and the whole book in two semesters.
- Format: Hardback
- Pages: 208 pages
- Publisher: Alpha Science International Ltd
- Publication Date: 23/03/2010
- Category: Fuzzy set theory
- ISBN: 9781842655801
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s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213540.33/warc/CC-MAIN-20180818095337-20180818115337-00337.warc.gz
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CC-MAIN-2018-34
| 900 | 10 |
http://aoessaygdhs.jayfindlingjfinnindustries.us/explain-the-difference-between-fixed-costs.html
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math
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For example rent expense, straight-line depreciation expense, etc fixed cost per unit decreases with increase in production following example explains this. An example should help explain the difference between fixed and variable costs let's take two costs that are common to most aviation. Cost reimbursement (cr) agreements are paid as costs are incurred and invoiced, typically monthly or quarterly one significant difference between fixed price.
1 what are fixed manufacturing overhead costs 2 calculate overhead cost 4 difference between operating expenses & overhead in a business, all costs. Fixed costs are costs which do not vary with the output level in other words, they do not change whether the firm increases or decreases output examples of. The relationship of direct & indirect costs with fixed & variable costs is a very crucial concept to understand for doing a real interpretation of. Learn what a fixed cost is, what a variable cost is, what total fixed costs are, and the difference between a fixed cost and total fixed costs.
Find out how to differentiate between fixed cost, direct cost, indirect cost and several pmp exam questions focus on the difference between fixed cost, direct cost, i have written a detailed article on what is sunk cost and how to handle. In accounting, a distinction is often made between variable vs fixed costs variable costs change with activity or production volume. They are the same if a firm produces one unit of their product or one million units fixed costs typically include such things as the rent on the building in which the. By dennis caplan, university at albany (state university of new york) chapter 4: cost behavior chapter contents: - introduction - variable costs - fixed.
In economics, fixed costs, indirect costs or overheads are business expenses that are not in management accounting, fixed costs are defined as expenses that do not change as a function of the activity of a business, within the relevant period by definition, there are no fixed costs in the long run, because the long run is a. Learn what total costs are comprised of, what variable costs and fixed costs are, and the main difference between them. This article explains what fixed costs and variable costs a you can see a couple graphs that visually show you the difference between fixed and variable costs.
Fixed costs do not change with increases/decreases in units of production the table below summarizes the key difference between fixed and variable costs:. Fixed costs are those expenditures that do not change based on sales (or lack thereof. The average cost can be explained in two components: the average cost start declining as result of average fixed cost falls with velocity of. Let's have a look at the main differences between the two available models time and material vs fixed price contract – let's explain both and. Explain in outline what regression analysis is ○ explain the difference between direct and indirect costs ○ compare variable cost analysis with absorption cost.
Fixed cost is divided into two parts one is traceable fixed cost and other is difference between traceable cost and common fixed costs is explained here with. This article will explain the difference between the two costs related to food service, provide examples of both and educate the reader on proper. Variable product costs increase in total as more units of products are manufactured for example, a supervisor in the painting department would be a direct cost to the what is the difference between prime costs and conversion costs.
Fixed costs definition, a cost unvarying with a change in the volume of business ( distinguished from variable cost) see more. The difference between fixed and variable costs is that fixed costs do not change with activity volumes, while variable costs are closely linked to activity volumes. The main difference between fixed cost and variable cost is that fixed cost is cost that remains fixed throughout the production period.
Building an infrastructure for new brands or markets means adding to fixed costs no matter what the volume of sales achieved fixed costs are costs that do not. Answer to explain the difference between fixed cost, sunk cost, and variable cost give examples that illustrate their difference. In addition to variable costs, flexible budgeting also takes into the relationship formed between fixed and variable costs lies at the heart of the difference in net income gross profit vs contribution margin what is cvp. Costs they define fixed costs uniformly as the costs that are independent of the be false and to clarify the distinction between fixed costs and sunk costs we.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511642.47/warc/CC-MAIN-20181018022028-20181018043528-00076.warc.gz
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CC-MAIN-2018-43
| 4,682 | 8 |
https://fsmath.uni-bonn.de/studies/bachelor/bachelor.html
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math
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Bachelor of Science
You are interested in studying Mathematics, but can't imagine, how the first semester and studying at a university in general would be like?
With this page we want to share our experiences and give a few tips for a great start in your studies. You find detailed information in the "Ersti-Info".
Overview and links
We have collected some information for newcomers at the "Mathematisches Zentrum":
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570879.1/warc/CC-MAIN-20220808213349-20220809003349-00741.warc.gz
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CC-MAIN-2022-33
| 415 | 5 |
http://en.magomechaya.com/index.php/epub/a-first-course-in-computational-algebraic-geometry-aims-library-of-mathematical
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math
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By Professor Wolfram Decker, Professor Gerhard Pfister
A primary direction in Computational Algebraic Geometry is designed for younger scholars with a few historical past in algebra who desire to practice their first experiments in computational geometry. Originating from a direction taught on the African Institute for Mathematical Sciences, the e-book offers a compact presentation of the elemental idea, with specific emphasis on specific computational examples utilizing the freely on hand laptop algebra approach, Singular. Readers will speedy achieve the arrogance to start appearing their very own experiments.
Read or Download A First Course in Computational Algebraic Geometry PDF
Best algebraic geometry books
This variation has been referred to as ‘startlingly up-to-date’, and during this corrected moment printing you will be yes that it’s much more contemporaneous. It surveys from a unified standpoint either the trendy country and the traits of continuous improvement in quite a few branches of quantity concept. Illuminated via trouble-free difficulties, the primary rules of contemporary theories are laid naked.
From the studies of the 1st printing of this ebook, released as quantity 6 of the Encyclopaedia of Mathematical Sciences: ". .. My common effect is of a very great ebook, with a well-balanced bibliography, steered! "Medelingen van Het Wiskundig Genootschap, 1995". .. The authors supply the following an up-to-the-minute advisor to the subject and its major purposes, together with a couple of new effects.
This article presents an advent to ergodic idea appropriate for readers figuring out easy degree concept. The mathematical necessities are summarized in bankruptcy zero. it really is was hoping the reader may be able to take on study papers after interpreting the booklet. the 1st a part of the textual content is anxious with measure-preserving ameliorations of likelihood areas; recurrence homes, blending houses, the Birkhoff ergodic theorem, isomorphism and spectral isomorphism, and entropy conception are mentioned.
- Knotted Surfaces and Their Diagrams (Mathematical Surveys and Monographs)
- Arithmetic Algebraic Geometry
- Current Trends in Arithmetical Algebraic Geometry (Contemporary Mathematics)
- A Survey of the Hodge Conjecture (Crm Monograph Series)
Additional resources for A First Course in Computational Algebraic Geometry
Xn ] is a Gr¨ obner basis of Ik with respect to >lp on K[xk+1 , . . , xn ], for k = 0, . . , n − 1. 2 for details. 59 Let I ⊂ K[x1 , . . , xn ] be an ideal, let A = V(I) be its vanishing locus in An (K), let 0 ≤ k ≤ n − 1, and let πk : An (K) → An−k (K), (x1 , . . , xn ) → (xk+1 , . . , xn ), be projection onto the last n − k components. Then πk (A) = V(Ik ) ⊂ An−k (K). 5 on Buchberger’s algorithm and field extensions, the ideal generated by Ik in the polynomial ring K[xk+1 , . . , , xn ] is the first elimination ideal of the ideal generated by I in K[x1 , .
In particular, V(φ(I)) and, thus, V(I) are nonempty. 71 Let 0 = I K[x1 , . . , xn ] be an ideal. 69 at each stage, we may suppose after a lower triangular coordinate change 1 x1 .. . → xn ∗ 0 .. 1 x1 .. . xn that the coordinates are chosen such that each nonzero elimination ideal Ik−1 = I ∩ K[xk , . . , xn ], k = 1, . . , n, contains a monic 44 The Geometry–Algebra Dictionary polynomial of type (k) (k) fk = xdkk + c1 (xk+1 , . . , xn )xdkk −1 + . . + cdk (xk+1 , .
Hence, K[A] is naturally a K–algebra. Next, observe that each morphism ϕ : A → B of algebraic sets gives rise to a homomorphism ϕ∗ : K[B] → K[A], g → g ◦ ϕ, of K–algebras. Conversely, given any homomorphism φ : K[B] → K[A] of K–algebras, one can show that there is a unique polynomial map ϕ : A → B such that φ = ϕ∗ . Furthermore, defining the notion of an isomorphism as usual by requiring that there exists an inverse morphism, it turns out that ϕ : A → B is an isomorphism of algebraic sets iff ϕ∗ is an isomorphism of K–algebras.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571536.89/warc/CC-MAIN-20220811224716-20220812014716-00543.warc.gz
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CC-MAIN-2022-33
| 4,032 | 15 |
https://rockscarmedia.com/how-many-square-feet-cover-a-gallon-of-water/
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math
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How Many Square Feet Cover A Gallon Of Water
If you’ve ever wondered how much water covers an acre of land, or how many gallons fit in a square foot, now’s your chance to find out! In this article, we explore how to calculate the dimensions of various objects using simple formulas. We also provide examples and a worksheet so that you can easily figure out the answers for yourself.
How many square feet does a gallon of water take up?
A gallon of water is about 3.8 square feet.
How many gallons does it take to cover 1000 square feet?
Water covers a lot of ground. A gallon of water will cover around 3,500 square feet. That’s a lot of space!
To cover the same amount of space with liquid waste, it would take around 1,500 gallons of waste. That’s a lot of sewage!
It takes more water to cover the same amount of space as liquid waste because liquid waste is spread out over a large area. Water is concentrated in puddles and rivers, which makes it easy to clean up.
How many gallons is a 600 sq ft pool?
A sq ft pool covers an area of approximately 8.33 square feet. This is the approximate amount of water that is contained in a one gallon container.
How do I calculate the gallons in my pool?
If you are looking to calculate how many square feet cover a gallon of water, the following equation can be used:
3600 = gallons in pool
formula: 3600 = (area of pool ÷ 144) ÷ 100
How do I calculate tank capacity?
There’s no one right answer to this question – it depends on the size, type and shape of your tank, as well as the gallons of water it holds. But here’s a basic guide to help you get started:
– A 20-gallon tank holds about 3,000 gallons of water. So a gallon of water occupies about 3 square feet.
– A 40-gallon tank holds about 8,000 gallons of water. So a gallon of water occupies about 10 square feet.
How do you calculate the square footage of a water tank?
When calculating the square footage of a water tank, you need to take into account the dimensions of the tank and the surface area of the water. To do this, you need to know the dimensions of the tank and how many gallons it holds. Once you have this information, you can use simple math to figure out how many square feet are covered by each gallon of water.
How many square feet is a 5 gallon bucket?
If you were to fill a gallon bucket with water and measure the height, width, and depth of the bucket, you would find that it covers 3.785 square feet. That’s one cubic foot of water.
Now, imagine filling a bucket with water and measuring the same dimensions but doubling the amount of water. The bucket would now cover 8.34 cubic feet of water. That’s twice as much water as the first gallon bucket!
Similarly, if you filled a bucket with water and measured the height, width, and depth again but tripled the amount of water, the bucket would now cover 18.46 cubic feet of water. That’s three times as much water as the first gallon bucket!
How do I calculate gallons of water in my basement?
If you have a basement, you may be wondering how many square feet cover a gallon of water. To calculate this, first determine the total area of your basement. Next, multiply the total area by 1 gallon to get the number of gallons in a square foot.
When calculating how much water will cover in a gallon, it’s important to take into account the height and width of the container. For example, a gallon of water will cover a rectangle that is 8 inches long by 4 inches wide by 6 inches high.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712297295329.99/warc/CC-MAIN-20240425130216-20240425160216-00538.warc.gz
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CC-MAIN-2024-18
| 3,489 | 27 |
http://blog.sigma-systems.com/distinguish-between-price-elasticity-and-income-elasticity-of-demand.html
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math
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Distinguish between price elasticity and income elasticity of demand. Difference between Price Elasticity, Income Elasticity and Cross Price Elasticity 2022-12-11
Distinguish between price elasticity and income elasticity of demand Rating:
Price elasticity of demand is a measure of the responsiveness of the quantity demanded of a good or service to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. A good or service is said to be elastic if a small change in price results in a large change in quantity demanded, and inelastic if a large change in price is required to produce a significant change in quantity demanded.
Income elasticity of demand is a measure of the responsiveness of the quantity demanded of a good or service to a change in the income of the consumer. It is calculated as the percentage change in quantity demanded divided by the percentage change in income. A good or service is said to be income elastic if an increase in income leads to a proportionally larger increase in the quantity demanded, and income inelastic if the quantity demanded remains relatively unchanged despite an increase in income.
There are several factors that can influence the elasticity of demand for a particular good or service. These include the availability of substitutes, the necessity of the good or service, and the proportion of income that is spent on the good or service.
For example, a luxury item such as a designer handbag may be highly elastic, as consumers may be willing to reduce their demand for the item if the price increases significantly. On the other hand, a necessity such as food may be inelastic, as consumers will continue to purchase it despite changes in price.
Income elasticity of demand can also vary significantly among different goods and services. Normal goods, which are those that are consumed more when income increases, are likely to have a positive income elasticity of demand. Inferior goods, on the other hand, are those that are consumed less when income increases and are likely to have a negative income elasticity of demand.
In conclusion, price elasticity of demand measures the responsiveness of quantity demanded to changes in price, while income elasticity of demand measures the responsiveness of quantity demanded to changes in income. Both measures are important in understanding consumer behavior and can be used to make informed decisions about pricing and marketing strategies.
Difference between Price Elasticity, Income Elasticity and Cross Price Elasticity
Prices can also be influenced by other factors influencing costs such as Comprehensively, the income effect looks at how rising or falling income effects demand for goods and services in the economy. So the quantity demanded of x 1 and x 2 remain un-effected. Theorem 1: In a two-commodity world both goods cannot be inferior simultaneously. Positive income elasticity of demand It refers to a condition in which demand for a commodity rises with a rise in consumer income and declines with a decline in consumer income. Both effects have demand as the central component but the difference is the isolated indirect variable affecting the direct variable which is demand. Income elasticity: Income elasticity of demand is defined as the responsiveness of demand to a change in income, while all other things remain unchanged. If real income increases, it will see an increase in demand.
Difference Between Elasticity of Demand and Price Elasticity of Demand
Cross price elasticity is measured as a ratio of the proportionate change in demand of good A to a proportionate change in price of good B. The convention is to ignore the negative sign and work with absolute values of e p. We are then much more concerned with the exploita- tion of human capacity which is also perfectly 'nat- ural' and the maintenance of a moving equilibrium in a progressive economy comes to depend more and more upon the effective organization and education of human capacity" p. What is the income elasticity of demand? Income elasticity refers to proportionate or percentage change in quantity demanded of a commodity due to the proportionate or percentage change in income. Key difference - price elasticity vs.
It is defined as the responsiveness of demand to a change in price, while other things remain unchanged. ADVERTISEMENTS: Elasticity of demand is of three types — price, income and cross. In expansions, demand for all types of goods and services is higher and therefore businesses charge more. Demand for a normal good grows with an increase in customer wages and vice versa, assuming other factors of demand are constant. Stigler, Trends in Employment in the Service Industries Princeton, N.
Income Elasticity of Demand: Definition, Formula, and Types
Therefore, none of the goods can be inferior. Consumer discretionary products such as premium cars, boats, and jewelry represent luxury products that tend to be very sensitive to changes in consumer income. Hence if demand is elastic at all points on the demand curve, every reduction in price must increase total expenditure. Also, It can be positive or negative depends upon the type of goods demanded whether normal or inferior. Elasticity of Demand vs Price Elasticity of Demand Similar in meaning to the expansion of a rubber band, elasticity of demand refers to how changes in X which can be anything such as price, income, etc.
The difference between price elasticity of demand and income elasticity of demand is that Select one: a. income elasticity measures the responsiveness of income to changes in supply while price elast
ADVERTISEMENTS: 4 The number of uses to which a commodity can be put. The article looked at 3 main types of demand elasticity that are similar because the increase or decrease in any of the 3 factors explained can either increase or decrease quantity demanded. A unit change an increase in price will lead to a 5 unit decrease in demand. In case of an inferior good IED is negative because an increase in m leads to a fall in demand. The point elasticity of demand is defined as the proportionate change in the quantity demanded resulting from a very small proportionate change in price. Inelastic products are usually necessities without acceptable substitutes.
Income Elasticity, Price Elasticity, and Cross Elasticity
When the price of a good with a close substitute, say cauliflower, increases, the demand for that particular product will likely shift to another vegetable, say broccoli. It is the ratio of the percentage change in quantity demanded to the percentage change in income of the consumer. Then they will react strongly to the price changes. Special Considerations: Understanding the Economy Income and prices are two variables followed by economists at large. The four main types of elasticity of demand are price elasticity of demand, cross elasticity of demand, income elasticity of demand, and advertising elasticity of demand. When an economy is expanding it usually comes with rising inflation due to increased demand.
Income Effect vs. Price Effect: What’s the Difference?
Conversely, complementary goods, like cell phones and chargers, have negative cross-price elasticity. The equations were fitted in both weighted 1958 state populations and unweighted form. ADVERTISEMENTS: The main determinants of income elasticity are: 1. A high value for e p implies that quantity is proportionately very responsive to price changes. Income elasticity of demand: Based on the calculation of the price elasticity coefficient of demand, products can be classified into the categories of inferior, luxury, normal, necessities, etc. Knowing this difference, you can distinguish between price elasticity and income elasticity of demand.
Difference between Price Elasticity and Income Elasticity
This form underlies the cardinal utility based demand theory of Alfred Marshall. His book, The Clash of Progress and Security, published in 1935, is perceptive and contains much that is relevant to the problems of Cohn Clark's writings on this point are better known, particularly his often- quoted conclusion, "We may well now turn to examine what much careful gen- eralization of available fact shows to be the most important concomitant of eco- nomic progress, namely, the movement of working population from agriculture to manufacture, and from manufacture to commerce and services. The results of this preliminary inquiry into a very complex econometric problem are consistent with the conclusions based on sector trends in output. Under Assumption II gross product in current dollars , real output in services rose 0 per cent per annum faster than in goods. The basic determinants of the elasticity of demand of a commodity with respect to its own price are: ADVERTISEMENTS: 1 The availability of substitutes; the demand for a commodity is more elastic if there are close substitutes for it.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945317.85/warc/CC-MAIN-20230325064253-20230325094253-00134.warc.gz
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CC-MAIN-2023-14
| 8,982 | 23 |
https://groupprops.subwiki.org/wiki/Algebraic_subgroup
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math
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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
WARNING: POTENTIAL TERMINOLOGICAL CONFUSION: Please don't confuse this with algebraic group
A subgroup of a group is termed an algebraic subgroup if it is an algebraic subset of the group, i.e., it is an intersection of finite unions of elementary algebraic subsets.
Relation with other properties
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348523564.99/warc/CC-MAIN-20200607044626-20200607074626-00485.warc.gz
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CC-MAIN-2020-24
| 517 | 4 |
http://www.bestcovery.com/texas-instruments-ti-89-titanium-graphing-calculator
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math
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Texas Instruments TI-89 Titanium Graphing Calculator
TI's Motorola 68000-based TI-89 provides a built-in computer algebra system akin to computer software such as Mathematica and Maple. It can simplify mathematical expressions and perform partial fraction decomposition, useful for some intermediate calculus classes. Basic algebra, systems of equations, limits, derivatives, and integrals are also possible and can be performed symbolically. It can plot most anything including 2D, parametric, polar, and differential equations. Unfortunately it is too powerful to be allowed on the ACT exam, although it works for the SAT and APCalc. It's a little more expensive than the others and if you're not past the ACT you probably don't need a calculator this advanced. The TI-89 does support USB for downloading programs.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986669057.0/warc/CC-MAIN-20191016163146-20191016190646-00122.warc.gz
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CC-MAIN-2019-43
| 816 | 2 |
http://fogyasztovedelem.info/date-of-maturity-calculator.html
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math
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Once you have that information, plug it into the formula PC 1-(1 1i)n i)M 1i)n where, P the bond price, C the coupon payment, i the yield to maturity rate, M the face value and n the total number of coupon payments.
2, use the formula: using this calculation, you arrive at an approximate yield to maturity.25 percent.
If you purchase the original bond at a price equal to the face value of the bond, then the yield to maturity is simply the nominal interest rate of the bond.
In order to accomplish this, Caesar inserted an additional 10 days to the Republican calendar, making the total number of days in a year 365.Bonds are usually issued in par values of 1,000.The YTM does not account for taxes or for purchasing or selling costs.In other words, this is the net dollar amount earned on the investment.In the above example, begin by taking the annual interest rate up by one point to 6 percent.The Republican calendar later used by Rome followed Greek calendars in its assumptions.5 days in a lunar cycle, and.5 synodic months in a solar year, which align every fourth year upon the addition of the intercalary months of January and February.Since this bond is priced at a discount, we know that the yield to maturity will be higher than the coupon rate.Number of years, months, weeks, and days between two dates.In other words, you could buy a newly issued 1,000 bond today at close to face value, but a month escort powertrac tractor 434 from now the bond might be selling for more or less than what you paid for.Home other Calculators date Calculator, the following are two date calculators.This is because this yield to maturity calculation is an estimate.What is Yield to Maturity?Bond Yield to Maturity Calculator Glossary of Terms Current price: The current (market) price of the bond.
This will give you a precise calculation of the yield to maturity.Enter it below and be sure to include your first name and a valid email address.B - Good, but needs slight improvement or an update.The par value (also referred to as the "face value is the amount the issuer (borrower) promises to pay at the end of the loan period.Check the validity of your calculation.12 Community Q A Search Add New Question Question How do I calculate current yield?Talk the annual interest rate up by one more point to 7 percent (or.5 percent on a semi-annual basis).
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s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525402.30/warc/CC-MAIN-20190717201828-20190717223828-00514.warc.gz
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CC-MAIN-2019-30
| 2,353 | 5 |
https://www.studyfull.com/question/40618/exam-2-stat-215-summer-2019-final
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math
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Name: _______________________________________ Stat 215 – Summer 2019 Final #1
Directions: Answer each question fully and to the best of your ability. Show all work and round answers to 4
1. Use the following dataset to find the following statistics.
x: 99, 136, 116, 175, 189, 2, 171, 24
A. Find the sample standard deviation.
B. Give an interpretation of your calculated standard deviation.
C. Find the skewness
D. Give an interpretation of skewness
E. What two features distinguish a histogram that follows the Normal Distribution?
F. Find the value of the median
G. Match each histogram to the boxplot that represents the same data set.
2. Suppose that one word is to be selected at random from the sentence The girl put on her lovely pink hat.
If X denotes the number of letters in the word that is selected. What is the value of E(X)? What is the
value of Var(X)?
3. Suppose that the measured voltage in a certain electric circuit has the normal distribution with mean 150
and variance 4. If three independent measurements of the voltage are made, what is the probability that
all three measurements will lie between 146 and 148?
4. Two different teaching procedures were used on two different groups of students. Each group contained
100 students of about the same ability. At the end of the term, an evaluating team assigned a letter grade
to each student. The results were tabulated as follows:
Group A B C D F Total
I 15 22 32 17 14 100
II 9 16 29 28 18 100
If we consider this data to be comprised of independent observations, test at the 5 percent significance
level the hypothesis that the two teaching procedures are equally effective.
5. The manager of a door-making company would like to estimate the amount of time it takes for a piece of
wood to be moved, cut, and packaged at two different plants. At Plant A, the manager observed 21
pieces that processed with an average time of 14.2 minutes and standard deviation of 2.6 minutes. At the
second plant, the manager observed 19 pieces with an average time of 13.1 minutes with a standard
deviation of 1.9 minutes.
a. Test whether there is a difference between mean process times of Plants A and B with an
assumed α = 0.1. State your conclusion properly with context.
b. What three assumptions are required to perform the above test?
c. Using the above information and α = 0.1 significance level, test to see if the plants have different
variability. State your conclusion properly with context.
6. The distance between defects on a long wire is exponentially distributed with mean 14 mm.
a. What is the probability that the distance between two defects is greater than 17 mm?
b. Find the probability that the distance between two defects is between 11 and 20.
7. A consumer group is interested in estimating the proportion of packages of ground beef sold at a
particular store that have an actual fat content exceeding the fat content stated on the label. How many
packages of ground beef should be tested to estimate this proportion to within 0.03 with 98%
8. Let the number of chocolate chips in a chocolate chip cookie have a Poisson distribution. We want the
probability that a cookie of this type contains at least one chocolate chips to be greater than 0.99. Find
the smallest value of the mean that the distribution can take.
9. Do teachers find their work rewarding and satisfying? An article in Psychological Reports reported the
results of a survey of a random sample of 395 elementary teachers and 266 high school teachers. Of the
elementary school teachers, 224 said that they were very satisfied with their jobs, whereas 166 of the
high school teachers were very satisfied with their work.
a. Based on this data, is it reasonable to conclude that the proportion of very satisfied teachers is
different for elementary teachers than it is for high school teachers? Please state conclusion
properly with context.
b. Construct and interpret a 95% Confidence Interval in the context of the above scenario.
c. How do the results in Part a and b compare? Do the results contradict each other?
10. In a certain factory, machines I, II, and III are all producing springs of the same length. Machines I, II,
and III produce 1%, 5% and 3% defective springs, respectively. Of the total production of springs in the
factory, Machine I produces 26%, Machine II produces 32%, and Machine III produces 42%.
a. If one spring is selected at random from the total springs produced in a given day, what is the
probability that it is defective?
b. Given that the selected spring is defective, find the conditional probability that it was produced
by Machine II.
11. At a used-book sale, 100 books are adult books and 160 are children’s books. Seventy of the adult books
are nonfiction while 100 of the children’s books are fiction. Assume a book is selected at random, what
is the probability that the book is an adult book or a children’s nonfiction book?
12. A federal job placement director claims that the average starting salary for nurses is $66,500. A sample
of 10 nurses in Morgantown has a mean of $49,900 and a standard deviation of $5,000. Is there enough
evidence to determine if Morgantown nurses make a smaller salary than the national average at 𝛼 =
13. In a study of memory recall, 8 students from a large psychology class were selected at random and given
10 min to memorize a list of 20 nonsense words. Each was asked to list as many of the words as he or
she could remember both 1 hour and 24 hours later, as shown in the following table:
Subject 1 2 3 4 5 6 7 8
1 Hour 14 12 18 7 11 9 16 15
24 Hours 10 4 14 6 9 6 12 12
Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall
after 24 hours by more than 3? Use a level .01 test.
14. The probability distribution of x, the number of defective tires on a randomly selected automobile
checked at a certain inspection station, is given in the following table:
𝑥 0 1 2 3 4
𝑝(𝑥) 0.5423 0.1607 0.0546 0.0414 0.2010
a. Calculate the mean value of x.
b. Calculate the standard deviation of x
c. What is the probability that x exceeds its mean value?
15. Suppose that 85 percent of the students at WVU live in student housing and 15 percent of students at
WVU have alternative housing. If 1,776 students attending a career planning event represent a random
sample from the student population, what is probability that the number of students with alternative
housing will be fewer than 213?
16. Liam is a little boy who is about to have his first Tee-Ball practice. Unfortunately, Liam isn’t very good,
and the probability that he catches a ball is only 0.1. Let x be the number of tosses required until Liam
catches a ball.
a. What is the probability that it will take exactly two tosses for Liam to catch a ball?
b. What is the probability that more than three tosses will be required?
17. How is the power of the test related to the type II error?
18. How can the power of a test be increased?
19. What is considered a large sample?
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https://mediatorchrzanow.pl/nu2smj6t/beff24-calculate-velocity-of-falling-object-from-height
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Terminal velocity depends on atmospheric drag, the coefficient of drag for the object, the (instantaneous) velocity of the object, and the area presented to the airflow. If it takes 9.9 seconds for the object to hit the ground, its velocity is (1.01 s)*(9.8 m/s^2), or 9.9 m/s. Multiply feet per second by 0.68 to find the object's velocity in miles per hour. For example, if you’ve been given a time (usually in seconds), then the velocity of any falling object can be found with the equation v = g * t, where g is acceleration due to gravity. Calculate the maximum height. Required inputs are: the mass of the falling object/body, the drag coefficient and the projected area, as well as the air density and gravitational … The formula for finding average velocity is: A car starts at position x = 16 feet. It is a position function. For example, 483 ft^2/s^2 * 2 = 966 ft^2/s^2. As calculus is the mathematical study of rates of change, and velocity is the measure of the change in position of an object with respect to time, the two come in contact often. If you are at the surface of the earth the acceleration is g = 32.2 feet/sec 2 or 9.8 meter/sec 2.Integrating the acceleration once gives V = V o + g T where V o is the initial velocity, presumably zero, and T is the time of fall. Gravity will accelerate a falling object, increasing its velocity by 9.81 m/s (or or 32 ft/s) for every second it experiences free fall. What is the car’s average velocity? Setting h(t) = 0 gives: Step 3: Insert your answer from Step 2 into the function from Step 1: The velocity is 113.28 feet per second when the book hits the car, which is more than 100 feet per second. Ascertain the height from which the object fell. For example, if the velocity of the rock is calculated at a height of 8.10 m above the starting point (using the method from Example 1) when the initial velocity is 13.0 m/s straight up, a result of ±3.20 m/s is obtained. The car traveled from 16 feet to 134 feet (134 – 16 = 118). You know the function from Step 1. Example: at a straight jump from a ten meters tower, the jumper's center of gravity is about 11 meters above the water. If you are supplied an initial value, you can find the constant by setting time equal to 0. The sign of the function tells you the direction the object is traveling. d/dt 4t2 + 4t + 4 = 8t + 4 See: Integral Rules. Apart from the last formula, these formulas also assume that g negligibly varies with height during the fall (that is, … Take the square root of the previous result to calculate the velocity when the object hits the ground. In other words, you need to integrate the function. The total time taken by the object to reach earth is measured and entered in the speed of falling object calculator. If the mass is m = kg, then the kinetic energy just before impact is equal to K.E. Step 2: Solve the position function for zero (in other words, when the height is zero) to find out when the book will hit the car. The equation v = S/T gives you the average velocity of an object, given distance and time. It tells the speed of an object and the direction (e.g. Gravity accelerates you at 9.8 meters per second per second. If the object fell from 5 m, the equation would look like this: (2*5 m)/(9.8 m/s^2) =1.02 s^2. Male or Female ? In this example, we will use the time of 8 seconds. The Practically Cheating Calculus Handbook, The Practically Cheating Statistics Handbook, 2. Step 2: Perform integration on a(t). Your first 30 minutes with a Chegg tutor is free! Example problem: Frustrated with your calculus class, you throw your textbook out of your dorm window, which is 200 feet above your car in the parking lot. 1. Step One:Find the difference between the initial and final positions of the car. The general gravity equation for velocity with respect to time is: Since the initial velocity vi =0 for an object that is simply falling, the equation reduces to: where 1. vis the vertical velocity of the object in meters/second (m/s) or feet/second (ft/s) 2. g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2) 3. tis the time in seconds (s) that the object has fallen Velocity of a falling object as a function of time or displacement Example: Deflection of a Falling Object. This free fall calculator determines the velocity and the time of fall of a body falling to the Earth or another planet in a vertical direction if the height is known. a(t) = 10t + 5 The above equation can be used to calculate both impact force of a falling ojbect as well as impact force of a horizontally-moving object such as in a car crash or plane crash. If you are able to time how long it takes the object to fall, simply multiply that time by the acceleration due to gravity to find the final velocity. There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. It must also meet the requirements for being a function. These equations do not apply to objects dropped from very high up, because such objects will reach a terminal velocity before they hit the ground. Take the square root of the result to calculate the time it takes for the object … For example, v(t) = 2x2 + 9. Gravity will accelerate a falling object, increasing its velocity by 9.81 m/s (or or 32 ft/s) for every second it experiences free fall. The acceleration due to gravity is 32.2 ft/s^2 for English units, or 9.8 m/s^2 for SI units. Enter one value at height, time and speed, the other two values will be calculated. If we drop an object from height , the effect of the centrifugal force is already in the local value and local direction of .The Coriolis force is not included and it is proportional to velocity so it will not affect the direction of plumb bobs. Change in potential energy =mgh Once the object hits the beam which is pivoted at the centre and gets attached to it. So let's try it out with some numbers. Yes, there will be a dent! You can differentiate it (i.e. The calculator will determine the final velocity and total height the object was dropped from. Plot this against height on a new graph. with rectiliear motion), you can use the sign to tell you whether the object is speeding up or slowing down: Watch the video for an example of to use the function to find total distance traveled. (Y axis: velocity; X axis: height fallen.) If it were constant, it would not have the variable in it, and it would also have an acceleration of 0. She holds a Master of Science in agricultural engineering from Texas A&M University. Integration is a somewhat advanced calculus method, so be sure to take a look at the articles specifically detailing it (see: Integrals) if you are unfamiliar with it. The book will dent your car if it’s going more than 100 feet per second. Using the above for example: Multiply the height by the object's acceleration due to gravity. If you know the terminal velocity of an object, divide that number by the square root of 2*g to determine the maximum height for which these equations will be valid for that object. Consequently, the velocity of the falling object in the example is 27.2 feet per second. The calculator uses the standard formula from Newtonian physics to figure out how long before the falling object goes splat: The force of gravity, g = 9.8 m/s 2 How you do this depends on what type of function you have. These concepts are described as follows: 1. However, if you’ve been given a position function (e.g. In order to find the velocity of a particular falling object, just multiply time (t) by gravity (t). If you’re given a position equation like h(t) or s(t), you’ll need to differentiate that function in order to find the velocity of the falling object. But we know that our velocity is going to be downwards here, because that is our convention. Tip: A negative sign indicates the height is decreasing. Calculates the free fall distance and velocity without air resistance from the free fall time. Example question: Find the velocity for the following position function:x(t) = 4t2 + 4t + 4, Step 1: In order to get from the displacement to the velocity, you will take the derivative of the displacement with respect to time. No further calculations are required here. Terminal Velocity Calculator. What is it’s velocity? This is linear motion. The function v(t) is the derivative of the position function. If an object is dropped from height h = m, then the velocity just before impact is v = m/s. Ascertain the height from which the object fell. This gives you an object’s rate of change of position with respect to a reference frame (for example, an origin or starting point), and is a function of time. If an object is traveling in a straight line (i.e. The program will read the height in meters (m) from which user dropped the object. The car traveled east a total of 118 feet. for the height), then you need a little calculus to derive the answer. On the other hand, if you have a jerk function you’re going to want to work backwards. Question: Hello, I Am Trying To Use Python To Calculate The Terminal Velocity Of An Object Falling From A Height Of 3 Meters. Step 2: Solve for the derivative. An object in free fall experiences an acceleration of -9.8 m/s/s. Georgia State University; Energy as a Tool for Mechanics in Problem Solving; R. Nave, Western Kentucky University; Falling Object Problems; David Neal; 2008. This is to say that the velocity of a free-falling object is changing by 9.8 m/s every second. The function enables you to find instantaneous change as well as average change. In order to find the velocity … The following formula is used to calculate an impact velocity. Tip: The velocity is not constant over time, so t makes an appearance. Velocity of a Falling Object Using Calculus, https://www.calculushowto.com/problem-solving/velocity-of-a-falling-object/. Multiply the height by 2, and divide the result by the object's acceleration due to gravity. Final Velocity of freely falling body from height h, when it reaches ground calculator uses Velocity on reaching ground=sqrt(2*Acceleration Due To Gravity*Height) to calculate the Velocity on reaching ground, The Final Velocity of freely falling body from height h, when it reaches ground is the speed just before touching the ground. v = Sqrt ( 2 * g * h ) Where v is the impact velocity (m/s) g is the acceleration due to gravity (9.8 m/s^2) h is the height of the object (m) Impact Velocity Definition The more, the heavier and more compact the falling object is. Determine the imperial solution by multiplying the time in free fall by 32 ft/s^2. Take the square root of the result to calculate the time it takes for the object to drop. If an object is merel… Calculate free fall velocity of an object Write a program that determines the speed or velocity of an object is traveling when it hits the ground. Hint:The given equation is not for the velocity of a falling object. When the projectile reaches the maximum height, it stops moving up and starts falling. Multiply the result by 2. If an object of mass m= kg is dropped from height h = m, then the velocity just before impact is The object undergo two kinds of forces they are, gravitational force and aerodynamic force. Copyright 2021 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. The average velocity that the car traveled was 14.75 feet-per-second eastward. Impact Force from Falling Object Even though the application of conservation of energy to a falling object allows us to predict its impact velocity and kinetic energy, we cannot predict its impact force without knowing how far it travels after impact. , which is of course equal to K.E total of 118 feet expert the... 118 ) jerk function you ’ ve been given a position function velocity and total the... Going to calculate velocity of falling object from height to work backwards this calculator well you need one more,..., we will use the program will read the height equation for time if! Motion that will be of value when using the free fall experiences an acceleration of -9.8 m/s/s any. Falling object depends calculate velocity of falling object from height what information you ’ ve been given a position (... Speed as it travels mass is m = kg, then you need to integrate the function final and... They are, gravitational force and aerodynamic force on various websites, focusing primarily on topics about science, and. Rights Reserved Enter one value at height, it would not have the variable in it and. Are a few conceptual characteristics of free fall motion of gravity: -9.81 m/s2 ( 32 ft/s.... S say you were given a position function to get the velocity of an object is by. Function v ( t ) = 2x2 + 9 integral and again come to the solution Leaf Ltd.! Will dent your car if it were constant, it would also an. Other words, you may not be able to measure it accurately we will use time... The constant by setting time equal to K.E calculator by the object 's acceleration due gravity... Example would hit the ground, the velocity just before impact is v 32... All Rights Reserved and again come to the solution forces they are, gravitational force and aerodynamic force in to. J, which is of course equal to 0 this calculator and Rule derivative! Fitness and outdoor activities change as well as average change t + gT 2 /2 velocity solve! Study, you need a little calculus to derive the answer tutor is free a height h with. Time ( t ) ( 2d/g ) and V=sqrt ( 2dg ) given distance and velocity, solve the function..., for example, let ’ s say you were given a position function 2! Other two values will be calculated or not, the Practically Cheating calculus Handbook, 2 of... Use of calculus one: find the constant by setting time equal to its initial potential energy =mgh the. How to do this, see: velocity of a function is 2 16. More gives d = v o t + gT 2 /2 what type of function you have jerk. Is different from the free fall motion that will be of value when using the free fall motion if isn! Experiences an acceleration of -9.8 m/s/s for any freely falling object using calculus, https: //www.calculushowto.com/problem-solving/velocity-of-a-falling-object/ was from! Which is pivoted at the centre and gets attached to it root of 966 ft^2/s^2 find change!, 483 ft^2/s^2 with this calculator not constant over time calculate velocity of falling object from height if it were constant, it stops moving and... In other words, you may not be able to measure it accurately calculate the time 8. Of velocities acquired by a freely falling object to drop hit the ground traveling 31.1. Come to the solution try it out with some numbers fitness and outdoor activities Leaf Media. Starts at position x = 16 feet to 134 feet ( 134 – 16 = ). A car starts at position x = 16 feet to 134 feet east of its initial potential energy force! Not, the velocity of a falling object ft/s^2 to get the function! First, differentiate the position function to get the velocity of a human object. The values into the formula and solve time equal to its initial position read the height 2! Feet-Per-Second eastward in miles per hour Plug the values into the calculator will determine the final velocity total... Just before impact is equal to 0 how you solve for a object. 0 you get t = sqrt ( 2d/g ) and V=sqrt ( 2dg ) derivative ) get. It were constant, it would not have the variable in it and. Force ( a.k.a would hit the ground traveling at 31.1 ft/s, so t makes an appearance object 1... The ground denoted as v ( t ) change in potential energy of object. Is defined in terms of the previous result to calculate an impact velocity the. The resulting average impact force ) by multiplying the resulting average impact force two... Earth is measured and entered in the question we have a jerk you... Direction ( e.g of science in agricultural engineering from Texas a & m University just before impact equal! The values into the formula for the height by 2, and calculate velocity of falling object from height the result to calculate height cliffs... M = calculate velocity of falling object from height, then the kinetic energy just before impact is equal to initial! Approximate maximum impact force ( a.k.a use the Power Rule, and then solve height... Resulting average impact force by two so we want to work backwards an. On topics about science, fitness and outdoor activities solutions to your questions from an in! Traveled for 8 seconds the car Enter one value at height, time and gravitational constant entered can step-by-step... 'S try it out with some numbers Power Rule, and performing calculus operations becomes necessary before is... Cheating calculus Handbook, 2 being a function, solve the velocity is: where.! 8 seconds the car is 134 feet east of its initial position energy... Measured and entered in the question we have a falling object under gravity miles per hour distance and. Constant, it stops moving up and starts falling -9.8 m/s/s feet per second 14.75 feet-per-second.! Function ( e.g ), then the kinetic energy just before impact is equal to 0 in miles per.... Different from the free fall motion that will be calculated Stuck trying to Actually calculate the it. Form a flower-like design try it out with some numbers and Rule for derivative of constants have Far. Ft * 32.2 ft/s^2 for English units, or 9.8 m/s^2 for SI units initial position takes to that. Trying to calculate the time it takes to travel that distance or not, value. Topics about science, fitness and outdoor activities: //www.calculushowto.com/problem-solving/velocity-of-a-falling-object/ we know that the velocity of functions... For an example, v ( t ) = 8t + 4 v ( t ) multiplying! In order to find the function enables you to find the difference between the distance traveled and direction... Or 9.8 m/s^2 for SI units impact is v = 32 ft/s^2 * 0.850 = 27.2 ft/s height object. Elapsed time, and Rule for derivative of the result to calculate impact... = 118 ) total height the object 's acceleration due to gravity book will dent your car it. That distance a Chegg tutor is free multiply feet per second height ' the field (... With this calculator a new column of data representing the square root longer in freefall step-by-step solutions to your from. Final positions of the velocity equation distance and velocity without air resistance from free... Sure we get the velocity of the falling object free-falling object is = m, calculate velocity of falling object from height. V o t + gT 2 /2 the end of 1 second and 2 seconds is.. From the velocity just before impact is v = S/T gives you the average velocity is defined in of... Leaf Group Ltd. / Leaf Group Ltd. / Leaf Group Media, Rights... V o t + gT 2 /2 team of skydivers jumps from a plane and hands. Mass is m = kg, then you need one more fact, the Practically Cheating Statistics,! Also have an acceleration of 0 may not be able to measure it accurately is 134 feet of. The end of 1 second and 2 seconds is _____, see: velocity of an object is traveling a... 2 /2 a car starts at position x = 16 feet to feet... Per second various websites, focusing primarily on topics about science, fitness and outdoor.! Chegg tutor is free it were constant, and divide the result to calculate an impact.... ( t ) is the derivative of constants was 14.75 feet-per-second eastward jerk function you ’ ve been given position., if you drop an object, just multiply time ( t ) by multiplying the resulting average impact (. The form 'velocity is proportional to the square root of the result calculate. When the graph of a free-falling object is of free fall velocity calculator the... To derive the answer by 9.8 m/s every second traveled east a total of 118 feet impact velocity form! We know that the velocity equation you probably came across in algebra Plug the into! Example would hit the ground, the velocity of simple functions can be done the. ), then you need to integrate the function v ( t ) multiply (... To want to work backwards velocity … the following formula is used to the... At the end of 1 second and 2 seconds is _____ integrating once more gives d v. Example is 27.2 feet per second so let 's try it out with some numbers = 0 you get =... Used to calculate the amount of elapsed time, so the object 's acceleration due to.! Value, you would multiply 15 ft * 32.2 ft/s^2 for English units, or 9.8 m/s^2 SI... Falling into the formula can easily be extended to calculate the time and speed, the other two values be. Heavier and more compact the falling object using a differential equation Cheating Handbook... Outdoor activities 16 ) t2-1 = -32t would not have the variable in,!
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The standard is equal to approximately 5.5 cm. Determine the internal cylinder radius. It's the internal radius of the cardboard part, around 2 cm. Find out what's the height of the cylinder, for us it's 9 cm. Tadaaam! The volume of a hollow cylinder is equal to 742.2 cm 3. Calculate the volume or height of a partially filled cylinder or cylindrical tank. Cylinder Volume Calculator in Feet and Inches. How to find out the volume of a cylinder. Work out the volume of a cylinder using feet and inches. Calculate volume of cylinders or tanks. Results in either cubic feet, cubic inches, UK gallons or US gallons. Cylinder Volume Formula. Volume of a cylinder = pi x radius squared x height Mar 14, 2013 · GCSE Grade C question to calculate the volume of a cylinder with a radius of 3cm and a height of 4cm. I hope this is useful and please do add a comment below - thanks. Calculate the volume or height of a partially filled cylinder or cylindrical tank.
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Let V = C0[0, 1] and for f and g in V, consider the mapping f, g = 1 0 x f (x)g(x)dx. Does this define a valid inner product on V? Show why or why not.
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Textbook: Differential Equations
Author: Stephen W. Goode
This textbook survival guide was created for the textbook: Differential Equations, edition: 4. The full step-by-step solution to problem: 16 from chapter: 5.1 was answered by , our top Math solution expert on 03/13/18, 06:45PM. Since the solution to 16 from 5.1 chapter was answered, more than 231 students have viewed the full step-by-step answer. The answer to “Let V = C0[0, 1] and for f and g in V, consider the mapping f, g = 1 0 x f (x)g(x)dx. Does this define a valid inner product on V? Show why or why not.” is broken down into a number of easy to follow steps, and 37 words. Differential Equations was written by and is associated to the ISBN: 9780321964670. This full solution covers the following key subjects: . This expansive textbook survival guide covers 91 chapters, and 2967 solutions.
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http://www.expertsmind.com/questions/positive-amount-of-capital-30145078.aspx
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math
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A paint manufacturing company has a manufacter function Q = K+ √L. For this manufacter function MPK = 1 and MPL = 1=(2√L). The rm faces a price of labor w that equivalent $1 per unit and a price of capital services r that equivalent $50 per unit.
a. Show that the rm's cost-minimizing input combination to produce Q = 10 involves no use of capital. (Hint: this is a corner solution.)
b. What must the price of capital down to in order for the rm to use a positive amount of capital, keeping Q at 10 and w at 1?
c. What must Q enhance to for the rm to use a positive amount of capital, keeping w at 1 and r at 50
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http://tahirbal.com/lib/a-brief-guide-to-algebraic-number-theory-london-mathematical-society-student
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math
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By H. P. F. Swinnerton-Dyer
Read or Download A Brief Guide to Algebraic Number Theory (London Mathematical Society Student Texts) PDF
Similar number theory books
Within the spring of 1976, George Andrews of Pennsylvania nation college visited the library at Trinity collage, Cambridge, to ascertain the papers of the past due G. N. Watson. between those papers, Andrews came upon a sheaf of 138 pages within the handwriting of Srinivasa Ramanujan. This manuscript used to be quickly distinctive, 'Ramanujan's misplaced pc.
Noncommutative Geometry and Cayley-smooth Orders explains the idea of Cayley-smooth orders in relevant easy algebras over functionality fields of sorts. particularly, the booklet describes the étale neighborhood constitution of such orders in addition to their relevant singularities and finite dimensional representations.
This quantity comprises refereed papers concerning the lectures and talks given at a convention held in Siena (Italy) in June 2004. additionally incorporated are learn papers that grew out of discussions one of the members and their collaborators. all of the papers are study papers, yet a few of them additionally comprise expository sections which goal to replace the state-of-the-art at the classical topic of certain projective forms and their purposes and new developments like phylogenetic algebraic geometry.
Because the visual appeal of the authors' first quantity on elliptic curve cryptography in 1999 there was super growth within the box. In a few issues, quite aspect counting, the development has been remarkable. different subject matters similar to the Weil and Tate pairings were utilized in new and critical how you can cryptographic protocols that carry nice promise.
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Extra info for A Brief Guide to Algebraic Number Theory (London Mathematical Society Student Texts)
A Brief Guide to Algebraic Number Theory (London Mathematical Society Student Texts) by H. P. F. Swinnerton-Dyer
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https://51airdrop.com/qa/quick-answer-what-if-0-was-not-invented.html
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math
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- Did Aryabhata invented zero?
- Is the number 1 even?
- Is Infinity odd or even?
- Why was the invention of 0 so important?
- Who is the father of 0?
- Is 0 even GMAT?
- Is 0 A number Yes or no?
- What would happen if zero didn’t exist?
- Who Found 0 in India?
- Who is the father of mathematics?
- Who invented math?
- Is 0 an empty set?
- What type of number is 0?
- Is 0 a real number?
- Is 0 even or off?
- Who invented school?
- Who invented calculus?
- Who actually invented zero?
Did Aryabhata invented zero?
Brahmagupta a scholar and mathematician in AD 628 first time defined zero and its operation and developed a symbol for it which is a dot underneath the numbers.
Then, Aryabhatta a great mathematician and an astronomer used zero in the decimal system..
Is the number 1 even?
Even And Odd Numbers – Definition with Examples A number which is divisible by 2 and generates a remainder of 0 is called an even number. … The remainder in the case of an odd number is always “1”. The property by which we classify an integer in math as even or odd is also known as parity.
Is Infinity odd or even?
See infinity is a term, a ‘word’ which we use to describe a never ending number. Its just a mathematical term and not a number. So it is neither odd nor even.
Why was the invention of 0 so important?
Yet for thousands of years we did without it. The Sumerians of 5,000BC employed a positional system but without a 0. … The invention of zero immensely simplified computations, freeing mathematicians to develop vital mathematical disciplines such as algebra and calculus, and eventually the basis for computers.
Who is the father of 0?
Brahmagupta”Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628,” said Gobets. He developed a symbol for zero: a dot underneath numbers.
Is 0 even GMAT?
0 is an even integer (because 2 goes into it 0 times)! 0 is is the only integer that is neither positive nor negative. So if you are asked about “negative numbers,” this doesn’t include zero. But if you are asked about “non-positive” or “non-negative” numbers, this does include zero.
Is 0 A number Yes or no?
The number 0 is the smallest non-negative integer. The natural number following 0 is 1 and no natural number precedes 0. The number 0 may or may not be considered a natural number, but it is an integer, and hence a rational number and a real number (as well as an algebraic number and a complex number).
What would happen if zero didn’t exist?
If we didn’t have zero, then the numbers in the number system wouldn’t go higher than nine. We couldn’t go through life without a zero. If zero wasn’t existent, life would be much different. For example, you couldn’t turn anything higher than 9 for the rest of your life.
Who Found 0 in India?
AryabhataWhat is widely found in textbooks in India is that a mathematician and astronomer, Aryabhata, in the 5th century used zero as a placeholder and in algorithms for finding square roots and cube roots in his Sanskrit treatises.
Who is the father of mathematics?
ArchimedesArchimedes is known as the Father Of Mathematics. He lived between 287 BC – 212 BC. Syracuse, the Greek island of Sicily was his birthplace.
Who invented math?
Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof.
Is 0 an empty set?
The empty set is a set that contains no elements. … There are some important properties of the empty set to remember: The cardinality of the empty set is 0. The empty set is a subset of every set, even of itself.
What type of number is 0?
1 Answer. 0 is a rational, whole, integer and real number. Some definitions include it as a natural number and some don’t (starting at 1 instead).
Is 0 a real number?
The number 0 is both real and imaginary. ): Includes real numbers, imaginary numbers, and sums and differences of real and imaginary numbers.
Is 0 even or off?
For mathematicians the answer is easy: zero is an even number. … Because any number that can be divided by two to create another whole number is even. Zero passes this test because if you halve zero you get zero.
Who invented school?
Horace MannCredit for our modern version of the school system usually goes to Horace Mann. When he became Secretary of Education in Massachusetts in 1837, he set forth his vision for a system of professional teachers who would teach students an organized curriculum of basic content.
Who invented calculus?
Isaac NewtonToday it is generally believed that calculus was discovered independently in the late 17th century by two great mathematicians: Isaac Newton and Gottfried Leibniz.
Who actually invented zero?
MayansThe first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.
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https://t5k.org/glossary/page.php?sort=Unique
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math
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Migration complete - please let us know if anything isn't working.
In mathematics the word unique means exactly one. So when a theorem (such as the division algorithm) states that "there is a unique r such that. . . ," it is telling us there is one such r and only one such r.
Printed from the PrimePages <t5k.org> © Reginald McLean.
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https://www.emergentmind.com/posts/how-many-ants-can-fit-in-an-elephant
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math
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It's not possible to determine exactly how many ants could fit inside an elephant, as it would depend on the size and shape of the ants as well as the size and shape of the elephant.
However, it's safe to say that the number of ants that could fit inside an elephant would be significantly greater than the number of elephants that could fit inside an ant. This is because ants are much smaller than elephants and can fit into spaces that would be much too small for an elephant to enter.
It's worth noting that this question is purely theoretical and has no practical application. Ants and elephants live in different parts of the world and do not interact with each other in a way that would allow one to be placed inside the other.
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https://greencountymga.org/resources/
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math
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- An error has occurred, which probably means the feed is down. Try again later.
Below is a list of helpful links to horticultural websites used by the UW Extension and the SCWMGA.
UW-Extension Green County: http://green.uwex.edu/
Wisconsin MG Program: http://wimastergardener.org/
UW-Extension Info Source: http://fyi.uwex.edu/
UW Plant Disease Diagnostic Clinic: http://labs.russell.wisc.edu/pddc/
UW Madison Dept. of Entomology Insect Diagnostic Lab: http://www.entomology.wisc.edu/diaglab/
UW Soil and Forage Lab: https://uwlab.soils.wisc.edu/
UW Horticulture Site: http://hort.uwex.edu/
UW Landscape Plants of Upper Midwest: http://www.midwestlandscapeplants.org/
Wisconsin Horticulture: http://hort.uwex.edu/
Wisconsin Garden Podcasts: http://fyi.uwex.edu/brownbag/
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http://dolomitisuperski.mobi/antiunitary-operator-92.html
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math
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Calculus and Analysis > Operator Theory > is said to be antiunitary if it satisfies : Wolfram Web Resource. Thanks for the A2A! Unitary operators appear in many places throughout quantum mechanics. The reason is, a unitary operator applied on a quantum. The adjoint (Hermitian conjugate) of an antilinear operator is defined in . An antiunitary operator U is an antilinear operator that preserves the.
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The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, operahor information about the probability amplitude of position, momentum, and other physical properties of a particle.
To keep the notation uniform, call this a ray transformation and this terminological distinction is not made in the literature, but is necessary here since both possibilities are covered while in the literature one possibility is chosen. Linear algebra Functional analysis.
Antiunitary — from Wolfram MathWorld
Other possible states of the universe would actually result in no increase of entropy, in this view, the apparent T-asymmetry of our universe is a problem in cosmology, why did the universe start with a low entropy 7. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself.
It is defined by. The set of all unit ray transformations is thus the group on S. Thus the only two field automorphisms of C that leave the real numbers fixed are the identity map and complex conjugation.
The domain has been decommissioned | Ohio University
Technically, action of time inversion operator contains antiunltary conjugation. Wigner’s theorem — Wigners theorem, proved by Eugene Wigner inis a cornerstone of the mathematical formulation of quantum mechanics.
Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. By this convention the imaginary antiunitafy does not include the unit, hence b.
Two-dimensional representations of parity are given by a pair of quantum states that go into each other under parity. The question of whether this time-asymmetric dissipation is really inevitable has been considered by many physicists, the name comes from a thought experiment described by James Clerk Maxwell in which a microscopic demon guards a gate between two halves of a room.
Turning the paper over is permitted, in elementary geometry the word congruent is often used as follows. All articles that antiunitaryy contain original research Articles that may contain original research from May Due to Wigner’s Theorem these transformations fall into two categories, they can be unitary or antiunitary.
In mathematicsan antiunitary transformationis a bijective antilinear map. As well as their use within mathematics, complex numbers have applications in many fields, including physics, chemistry, biology, economics, electrical engineering. In this way, the numbers are a field extension of the ordinary real numbers. The shape of a triangle is determined up to congruence by specifying two sides and the angle between them SAStwo angles and the side between them ASA or two angles and a corresponding adjacent side AAS.
Congruence permits alteration of some properties, such as location and antiunifary, but leaves others unchanged, like distance and angle s.
An example of congruence. There antiujitary a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. In mathematicsan antiunitary transformationis a bijective antilinear map U: Specifying two sides and an adjacent angle SSAhowever, can yield two distinct possible triangles.
Email Required, but never shown. All articles that may contain original research Articles that may contain original research from May The last triangle is neither similar nor congruent to any of the others. Max Planck is considered the father of the quantum theory.
The second does not conserve the orientation and is obtained from the first class by applying a reflection. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind.
Antiunitary operators are important in Quantum Theory because they are used to represent certain symmetries, such as time-reversal symmetry. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs.
Let G be the group of the universe — that opfrator.
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https://physics.stackexchange.com/questions/83188/if-we-change-the-radius-of-spherical-surface-does-electric-field-or-flux-change
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math
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Suppose a point charge is located at the center of a spherical surface. The electric field at the surface of the sphere and the total flux through the sphere are determined.
1).What happens to the flux and the magnitude of The electric field if the radius of the sphere is halved?
Our teacher said the flux decreases and the filed increases.
A spherical gaussian surface surrounds a point charge $q$. Describe what happens to the: flux through the surface if
2) The radius of the sphere is doubled
Our teacher said the electric flux will not change
3) The shape of the surface is changed to that of a cube
Also the electric flux will not change
So why the electric flux changed in question 1 but in question 2 did not change? And when does the electric flux and electric field change?
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http://www.cwreenactors.com/forum/showthread.php?28817-Yankee-army-rations&p=214623
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math
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Hello all. I have done some searches, but can not find what I am looking for. I am looking for a compleat list of the goods and the amount each soldier was issued. I have found the food items, but not the items such as candles, soap, clothing, and equipment. Can anybody please help?
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http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0005181
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math
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Stokes V Wave Computations in Deep Waterby James E. Dailey,
Serial Information: Journal of the Waterway, Port, Coastal and Ocean Division, 1978, Vol. 104, Issue 4, Pg. 447-453
Document Type: Journal Paper
Abstract: Stokes fifth-order wave theory is widely used in engineering practice to calculate water particle kinematics for the purpose of determining hydrodynamic forces on ocean structures. As shown by Dean, Stokes fifth-order wave theory is appropriate for engineering use primarily in deep water where depth exceeds half the wavelength.In this note, equations for Stokes fifth-order wave theory, as given by Chappelear, are summarized to calculate water particle kinematics, it is necessary to evaluate three parameters by solving simultaneously three nonlinear equations.
Subject Headings: Water management | Wave equations | Particles | Kinematic waves | Engineering profession | Hydrodynamics | Ocean engineering | Parameters (statistics)
Services: Buy this book/Buy this article
Return to search
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https://railroad.net/mechanicville-oneonta-rail-miles-t150919.html
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math
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How does CP come up with their mileage numbering system? I'm assuming that the numbers run along the entire Sunbury Sub from the Canadian border to Sunbury. This pic I took about 1/2 mile south of Nanticoke PA shows the milepoint as 696.65:
http://viewoftheblue.com/photography/ma ... G_2346.JPG
" onclick="window.open(this.href);return false;
That would make it 142 miles from Oneonta (southwest). The milepost at the Canadian border would be something
like 300 if you subtract 167 from the 467 at Mechanicville.
My question is where do the first 300 miles come from, Toronto or somewhere else in Canada?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359082.78/warc/CC-MAIN-20211201022332-20211201052332-00066.warc.gz
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https://www.coursehero.com/file/85854651/127-chemdocx/
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math
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1. A spaceship is found to have a tiny leak that allows the effusion of air into space. Air in the spaceship isa mixture of nitrogen (N2), oxygen (O2), argon (Ar), and trace amounts of other gases.a. Predict which of the three main gases will have the lowest rate of effusion and which will have the highest rate. Explain your answer. (1 point)Since Ar has the highest molar mass it has the lowest rate of effusion and because N2 has the lowest molar mass, it will have the highest rate of effusion.b. Predict how the percentages of the gases in the air will change over time. (1 point)The percentages will change over time to mostly argon, a relative amount of oxygen and little to no nitrogen because it will expend the fastest.c. Argon is found to effuse through the hole at a rate of 1.6 × 10–3mol in 215 s. How much O2would effuse through the hole in the same amount of time? (2 points)There will be 1.80 × 10–3mol of O2 effused through the hole.d. Suppose the three gases were placed at 1.00 atm and 273 K in closed containers, as shown below. A tiny hole is opened in each container, allowing each gas to diffuse into another container filled with neongas. What is the ratio of the rate of diffusion of nitrogen to the rate of diffusion of oxygen? Is this greater than, less than, or the same as the ratio of the rates of effusion for the two gases? (2 points)Nitrogen diffuses at a rate of 1.07 times faster than oxygen. The ratio of the rate of both effusion and diffusion are the same.
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http://blog.darkbuzz.com/2012/10/
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math
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Galina Weinstein has a new paper on Variation of Mass with Velocity: "Kugeltheorie" or "Relativtheorie":
Kaufmann concluded, from 1905 onwards, that the mathematical expression proposed by Alfred Bücherer could also be in accord with his measurements and that one could not definitively decide between that expression and that of Abraham as it was derived from his experiments. In the same paper, Kaufmann noted that the two theories of Lorentz and Einstein yielded the same equations of motion for the electron, and he gave the first clear account of the basic theoretical difference between Lorentz's and Einstein's views.29Lorentz did credit Einstein with having a slightly different approach, but neither expressed any differences in the conclusions, except for minor technical errors. Lorentz said that the chief difference was that Einstein postulated what he had proved. No one saw much difference until several years later when Minkowski's approach became popular, and Einstein adopted it.
In the annual general meeting of the German Society of Scientists and Physicists (Deutsche Gesellschaft der Naturforscher und Ärrzte) in Stuttgart, on the 19th of September 1906, scientists discussed three world pictures, the electromagnetic theories of Abraham, Bücherer, or the other picture based on Lorentz and Einstein's "Principle of Relativity". A discussion revolving around the foundations of physics was held after Planck's lecture. The participants in the discussion were, among others, Kaufmann, Planck, Bücherer, Abraham, Arnold Sommerfeld and others. Scientists did not yet distinguish between Lorentz's theory and Einstein's theory. There were two main theories relating to the electron: Abraham's and Lorentz-Einstein's. An inclination towards Einstein and Lorentz's theories, on the part of scientists such as Planck and Max Laue, was evident.
Walter Kaufmann's 1906 paper says:
Then, a work by H. A. Lorentz appeared in the year 1904, in which the attempt was made to remove the difficulties which sill existed in the optics of moving bodies, by somewhat modified fundamental assumptions on the electron and also on the molecular forces acting in-between the material body-particles. ... Lorentz now showed, that one could arrive at such a result, when it is assumed that the dimensions of all physical bodies, including their individual molecules and electrons, would change their shape in a very specific way with velocity ...Note that Kaufmann is trying to refute Lorentz and Einstein, and considers refuting one the same as refuting the other. Most of the paper just mentions Lorentz without Einstein, such as the section titled, "Comparison with the theories of Abraham, Lorentz and Bucherer."
It is now very remarkable, that, starting from quite different assumptions, Einstein recently arrived at results, which are in agreement with those of Lorentz concerning the consequences accessible to observation, though in which the previously mentioned difficulties of epistemological kind have been avoided. Einstein introduced the principle of relative motion, at least as regards translations, as a postulate. He thus places the theorem at the top, that physical phenomena observable in any rigid system, must be independent from whether the system (together with the observer) is moving relatively to any other system. ... The results accessible to observation are thus the same with respect to both authors; however, while Lorentz only shows that his hypotheses lead to the desired result without excluding that the same can also be achieved in another way, it is shown by Einstein, that when the desired result, namely the principle of relative motion, is placed at the top of the whole of physics, then the kinematics of the rigid body must necessarily be changed in the way stated, and that the equations of electrodynamics must assume the form stated by Lorentz. ...
The measurement results are not compatible with the fundamental assumption of Lorentz-Einstein.
Kaufmann appears to be not aware of Poincare's theory, or how Einstein got the relativity postulate from Poincare.
Kaufmann says Einstein "places the theorem at the top". That is his version of Lorentz's famous statement that Einstein simply postulates what we have deduced. I give a more technical explanation of what this means.
Kaufmann's argument is a little misleading where he says that Einstein showed "that the equations of electrodynamics must assume the form stated by Lorentz." This sounds like a strong statement, but if you read the footnote, Einstein assumes Maxwell's equations in the rest frame, and hence in the moving frame via the relativity principle. So Einstein is really postulating the equations of electrodynamics. It was Lorentz and Poincare who tried to prove the equations for the moving frame, assuming the equations for the rest frame.
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http://www.maths-help.co.uk/Knowldge/Stat/Lottery/Question.htm
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math
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I read that the chance of winning the jackpot in the National Lottery is 1 in 14 million. Is this true? How is it calculated?
In the British National Lottery, six ball are selected at random from
forty-nine numbered balls. Players have to guess which six balls will
be drawn. If they get all six correct, they win the jackpot prize.
We need to work out the total number of possible ways of choosing six
different numbers from forty-nine.
Note that the order of choosing the numbers does not matter.
For example, the numbers 2 , 7 , 34 , 21 , 46 , 11
give the same winning combination as 34 , 11 , 7 , 21 , 2 , 46.
So the total number of possible ways of choosing six balls from forty-nine is
which is equal to
13 983 816
or approximately 14 000 000 (14 million).
Therefore, as you rightly said, the chance of a single ticket winning the
jackpot is approximately one-in-14million
USEFUL TIP: If your calculator has a button marked nCr
you can get the answer directly.
"n" stands for the total number (here n=49)
"r" stands for the number you want to select (here r=6)
So if you type in the sequence 49 nCr 6 =
you should get the result 13 983 816 directly.
nCr is shorthand for the number of different ways of choosing r items from n
where the order does not matter.
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| 1,265 | 23 |
https://learnbright.org/lessons/math/solve-expressions-using-parentheses-and-brackets/
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math
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Our Solve Expressions Using Parentheses and Brackets lesson plan teaches students how parentheses and brackets are used in mathematical expressions and equations. During this lesson, students are asked to use exactly four 4’s to form every integer from 0 to 10, using only the operators +, -, x, ÷, (parentheses), and [brackets]. Students are also asked to solve practice problems that include brackets or parentheses, demonstrating their understanding of the lesson material.
At the end of the lesson, students will be able to use parentheses and brackets in evaluating numerical expressions containing these symbols.
State Educational Standards: LB.Math.Content.5.OA.A.1
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CC-MAIN-2023-14
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https://communities.bentley.com/products/building/building_analysis___design/w/building_analysis_and_design__wiki/48782/two-basic-principles-of-space-management-for-social-distancing
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math
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There are two basic principles of space management for social distancing:
One can model these two types of space, as follows.
Queue/waiting space can be created using a series of Delay Points (40×40 cm. in the example below) of Capacity 1. Each is set apart at the desired distance, representing floor markings in the distancing area. You may use hexagons (as in the example), or another method to help position distancing marks. Then all the Delay Points should be linked in a string, as shown in the example.
For free circulation space, one can use a Delay Point as an intermediate object. The Delay Point should have a Delay Profile of zero and Capacity calculated to match the density that allows the desired distancing. The Capacity will limit the inflow of people, while with zero delay the Delay Point will send people to the next target, without delay, whenever it becomes available. Please see the diagram below of how the model would change from Normal operation to Distancing operation.
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CC-MAIN-2020-40
| 998 | 4 |
https://blog.lafurniture.cz/ffa-creed-kvj/electromagnetic-spectrum-wavelength-and-frequency-table-efec5d
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math
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Planck Radiation Law years, the distance light travels in one year. The power radiated is In addition to wavelength, the radiation also expressed in frequency. Frequency Violet light has a wavelength of ~400 nm, and a frequency of ~7.5*10 14 Hz. The electromagnetic spectrum is normally given in order of decreasing wavelength or increasing frequency. The frequency of wavelength range for indigo is around 425-450 nm and frequency of 670-700 THz. the various bands in the electromagnetic spectrum. Infrared The low range of the color explains why it is difficult to distinguish this color in the spectral band. the various bands in the electromagnetic spectrum. The entire Electromagnetic waves have crests and troughs similar to (but not identical in behavior to) those of ocean waves. Extremely High Frequency 1 km 100 m Ultraviolet Low for blackbodies at various temperature. proportional to the square of the acceleration. electromagnetic spectrum perform their intended functions. < λ < 0.770 Visible rays are the most familiar form of electromagnetic waves. HF < λ < 1.5 106 > λ > λ < 0.39 The following table gives approximate wavelengths, frequencies, and energies for selected regions of the electromagnetic spectrum. The basic properties of waves mainly include amplitude, wavelength & frequency. Source: ITU-International telecommunication Union: Recommendation ITU-R V.431-7 Nomenclature of the Frequency and Wavelength Bands used in Telecommunications (ITU Legal Affairs Unit - Table 1 reproduction permission, Hebrew translation, July 25, 2014) Three things change: frequency, wavelength and method of production. Forces & Motion. 1018 Waves Extreme Frequency In classical language, ν is the frequency of the temporal changes in an electromagnetic wave.The frequency of a wave is related to its speed c and wavelength λ in the following way. the industry today. Microwaves characteristic frequencies. 30300 GHz luminescence, However, they do so at a wide ra… Cosmic Table 2. E (eV) intensity of radiation as a function of wavelength for a fixed temperature. These properties mainly connected with the intensit… Light emitting < F < 1021 charged particles produce electromagnetic radiation. 6 Reserved. 3003000 Hz Band Can you identify certain characteristics? 1 m 100 mm Visible light makes up just a small part of the full electromagnetic and It is their different wavelengths that cause the different colors of light to separate and become visible when passing through a prism. 330 kHz a higher frequency and a longer wavelength. Medium Frequency: MF: 300–3000 kHz : 1 km – 100 m : High Frequency: HF: 3–30 MHz : 100 m – 10 m : Very High Frequency: VHF: 30–300 MHz: 10 m – 1 m: Ultra High Frequency: UHF: 300–3000 MHz: 1 m – 100 mm : Super High Frequency: SHF: 3–30 GHz : 100 mm – 10 mm: Extremely High Frequency: EHF: 30–300 GHz light has a wavelength of ~400 nm, and a frequency of ~7.5*1014 Hz. Note that when frequency increases, wavelength decreases; c … gamma rays Copyright © 2005 VHF Electromagnetic waves with When light with a continuous Also shown are common objects with sizes similar to the wavelength scale and telescopes that observe in each waveband. Visible light is the portion of the electromagnetic spectrum that is visible to the human … The absorption below shows the intensity distribution predicted by the Plank law in J/(m2s) 3003000 kHz The peak shifts to shorter wavelengths for higher temperatures, and the area (c) The most distant galaxy yet discovered is 12*109 light microwaves, Radio Wave Spectrum Table, See Also: under the curve grows rapidly with increasing temperature. Violet < E < 10-3 EM radiation is classified into types according to the frequency of the wave: these types include, in order of increasing frequency, radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. longer wavelengths and lower frequencies include infrared light, microwaves, and Electromagnetic waves are categorized according to their frequency f or, equivalently, according to their wavelength λ = c/f. diodes 0.577 SpellmanRocks TEACHER. Super The number ν is shared by both the classical and the modern interpretation of electromagnetic radiation. Therefore the frequency of spectrum is defined as the number of complete cycles per second (cps) and also called Hertz according to the name of German physicist H.R Hertz. Wavelength 10-6 This speed is a fundamental constant in physics, and … 330 MHz Full Electromagnetic Spectrum Table, Long Higher rates of velocity The highest energy form of electromagnetic waves are gamma (γ) rays and the lowest energy form are radio waves. E < 10-10 Light distribution of the thermal radiation emitted by an object, we can learn its 1000 km 100 km Electromagnetic waves with shorter wavelengths and higher frequencies Rays or emission of optical radiation as a result of electronic excitation, to Please explore this simple simulations of various molecules interacting with Optical Radiation Spectrum Table, Table 3. radio The human eye sees color over wavelengths ranging roughly from 400 nanometers (violet) to 700 nanometers (red). Near F < 104 0.39 > λ > 0.01 X-rays The notation "eV" stands for electron-volts, a common unit of energy measure in atomic physics. High Atoms and molecules have characteristic resonance frequencies. Infrared 100 m 10 m Ultraviolet 0.1 > λ > 10-7 Figure 16.17 shows how the various types of electromagnetic waves are categorized according to their wavelengths and frequencies—that is, it shows the electromagnetic spectrum. Electromagnetic Wave electromagnetic radiation of different wavelength. This spectrum includes many types of wave that you will recognize including X-rays and infra-red. Figure 2.3.2. All Rights We know that fact, that light can be composed of electromagnetic radiation which is frequently treated like a wave phenomenon. 2 < E < 3 λ < 0.30 < F < 109 luminescence, Compared with human vision, these snakes can sense electromagnetic waves that have: a lower frequency and a shorter wavelength. Wavelength is the distance between any two consecutive identical points on the wave. λ < 10-7 Table 1. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from below one hertz to above 1025 hertz, corresponding to wavelengths from thousands of kilometers down to a fraction of the size of an atomic nucleus. Calculate the wavelength of each. High Frequency HOME Red light has a wavelength of ~700 nm, and a frequency of ~4.3*1014 Table 3. perform their intended functions. Most importantly, it is that part of the electromagnetic spectrum that is detected by the human eye. Electroluminescence. 7x1014 < F < 3x1017 Wave phenomenon all the time electromagnetic wave increases, its energy _____.... Graphical representation of the electromagnetic spectrum plays an important role in the electromagnetic spectrum EMS! And television waves higher frequency ( wavelength ) of violet color velocities particles. Wave phenomenon in behavior to ) those of ocean waves distribution, which peaks at some wavelength is... Fundamental constant in physics, and energies for selected regions of the electromagnetic spectrum telescopes that in. Waves that have: a lower frequency and a frequency of ~4.3 * 1014 Hz waves traveling through have... Techniques and manufacturing steps used in the SI base unit of energy measure in physics! Speed is a light year that pass a given point each second wide ra… frequency band Applications the. Part of the electromagnetic spectrum table, Long Electrical Oscillation, table 2 the time of... Crests and troughs similar to that of light years away, these snakes can sense electromagnetic waves to! Common unit of energy measure in atomic physics include infrared light, X-rays, a! Book presents a version electromagnetic spectrum wavelength and frequency table electromagnetic radiation ( wavelength ) radiation this includes... Wave includes the lowest energy form of electromagnetic radiation and their environment highest. The wavelength lowercase lambda ) and is usually expressed in the spectral.. Wave increases, its energy _____ increases law in J/ ( m2s ) blackbodies! Greek lowercase lambda ) and is usually expressed in frequency spectrum with missing lines authorized for use microwave... Waves traveling through vacuum have a variety of uses peaks at some wavelength or less the divisions the! X-Rays, and … table shows common classification of electromagnetic waves and steps... Many types of wave that you will recognize including X-rays and gamma rays are to... Scale and telescopes that observe in each waveband a speed of light to separate and become visible when through. Particles with thermal energy are changing almost all the time ) to 700 nanometers ( red ) spectrum plays important... Snakes can sense electromagnetic waves band Applications of the various bands in the figure shows! The different colors of light years away in order of decreasing wavelength or increasing frequency the industry today explains! The electromagnetic spectrum electromagnetic spectrum wavelength and frequency table all travel through a vacuum electromagnetic waves tend to travel at which! Energies for selected regions of the electromagnetic spectrum table, Long Electrical,. Learn its temperature frequency … the basic unit for measuring the wavelength provides a distance between two identical! Through or reflects or scatters of matter, it interacts with the and! And can be composed of electromagnetic waves in the electromagnetic spectrum that is, speed... Set characterizes the atoms and molecules and their environment of violet color to the square of electromagnetic! Set of characteristic frequencies color explains why it is difficult to distinguish this in... Frequency … the basic unit for measuring the wavelength of ~700 nm explains why is! Classification of electromagnetic radiation How many meters is a fundamental constant in physics, and gamma rays are the familiar! Higher temperatures, and energies grows rapidly with increasing temperature of energy measure in atomic physics frequencies authorized... Rays, which is all forms of electromagnetic waves traveling through vacuum have a variety of uses =.... Of particles with thermal energy are changing almost all the time light passes through reflects! Table gives approximate wavelengths, that light can be used to identify those atoms molecules! Wavelength range from ~400 nm, and a frequency of ~4.3 * 1014 Hz the peak shifts shorter! Rapidly with increasing temperature, micrometers, or nanometers almost all the time with vision. Wavelengths of different wavelength and frequency ranges of the electromagnetic spectrum, which is forms. By the Plank law in J/ ( m2s ) for blackbodies at various temperature the Planck law gives a distribution! Of complete waves, or wavelengths, frequencies, and a frequency of an electromagnetic wave increases, energy. Rates of velocity change result in higher frequency ( wavelength ) to shorter wavelengths and photon energies distribution! Shown in the figure below rapidly with increasing temperature, a common unit energy. Speed is a fundamental constant in physics, and energies of some regions of the electromagnetic.. Amplitudeis the vertical distance among the tilt of a crest & the axis... Various temperature discovered is 12 * 109 light years away years away you recognize. 3 x 108 ms-1 is normally given in order of decreasing wavelength or frequency... Violet light has a different wavelength molecules which produced it and can be used to identify atoms! The shortest waves are categorized according to their frequency f or, equivalently, according to electromagnetic spectrum wavelength and frequency table frequency or! Many types of wave that electromagnetic spectrum wavelength and frequency table will recognize including X-rays and gamma.! Electron-Volts, a nearly continuous spectrum with missing lines below shows the intensity of radiation as a function wavelength... The continuous distribution, which peaks at some wavelength a ) How meters!, atoms and molecules which produced it and can be used to identify those atoms and molecules emit light a! Sense electromagnetic waves based on classical physics units of light which produced it and can be used to those... Treated like a wave is equal to its frequency multiplied by the Plank law J/... Also expressed in the electromagnetic spectrum radio wave spectrum table, See also: Electroluminescence wide frequency... An extremely wide range of wavelengths, frequencies, and a frequency of ~4.3 * 1014 Hz normally in. In a vacuum at the same speed, but each color has a wavelength range from nm... Vacuum electromagnetic waves based on wavelength and frequency when passing through a vacuum electromagnetic waves a! To many analytical techniques and manufacturing steps used in the semiconductor industry extremely wide range of the spectrum... ) and is usually expressed in the above color spectrum chart, is. Energy measure in atomic physics is similar to ( but not identical behavior... It is their different wavelengths that cause the different colors of light separate! Higher temperatures, and energies for selected regions of the electromagnetic spectrum have special sensory organs that detect infrared! Energy measure in atomic physics are authorized for use in microwave ovens, 900 2560... Each second things change: frequency, wavelength and frequency ranges of the full electromagnetic spectrum the speed. Become visible when passing through a vacuum electromagnetic waves are gamma ( γ ) rays the! A prism, 900 and 2560 MHz light to separate and become visible passing! Wave includes the lowest energy form are radio waves wavelengths are presented light to separate become... Two microwave frequencies are authorized for use in microwave ovens, 900 and 2560.... Distribution of the EMS a different wavelength of uses frequency ( shorter wavelength ) radiation by the wavelength with! Trough & the central axis of the electromagnetic spectrum is the general name given the... Waves tend to travel at speeds which is similar to that of light to separate and become visible passing... As trough & the highest point known as trough & the highest energy form of electromagnetic have! Fixed temperature waves that electromagnetic spectrum wavelength and frequency table: a lower frequency and a frequency of ~4.3 * 10 Hz... Proportional to the known range of frequencies and wavelengths of 10e-6 microns or.... Categorized according to their wavelength λ = c/f that set characterizes the atoms molecules... Physics, and energies for selected regions of the electromagnetic spectrum is given. & frequency spectrum plays an important role in the figure below shorter wavelength ) those atoms and emit.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488534413.81/warc/CC-MAIN-20210623042426-20210623072426-00322.warc.gz
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CC-MAIN-2021-25
| 15,381 | 2 |
https://mahoningvalleylanes.com/qa/can-you-add-two-even-numbers-to-get-an-odd-number.html
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math
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- Why is 13 an odd number?
- What is an even number in math?
- Is 0 an odd or an even number?
- What is the sum of 3 odd numbers?
- Can you add two odd numbers and get an odd number?
- When you add two odd numbers Why is the answer always even?
- What happens when you add an odd number to another odd number?
- When you add an even and odd number?
- Do all prime numbers have to be odd?
- Can you add three odd numbers to get an even number?
- Who is odd number?
- Can you pick 3 watermelons to get a sum of 30?
Why is 13 an odd number?
Odd numbers can NOT be divided evenly into groups of two.
The number five can be divided into two groups of two and one group of one.
Even numbers always end with a digit of 0, 2, 4, 6 or 8.
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31 are odd numbers..
What is an even number in math?
A number which is divisible by 2 and generates a remainder of 0 is called an even number. The remainder in the case of an odd number is always “1”. … The property by which we classify an integer in math as even or odd is also known as parity.
Is 0 an odd or an even number?
The use of the phrase “even number, or the number zero” implies that zero is not even. On the other hand, the mayor is lumping zero together with the even numbers, so he certainly doesn’t think it’s odd. So what is it – odd, even or neither? For mathematicians the answer is easy: zero is an even number.
What is the sum of 3 odd numbers?
Then the sum of three odd numbers can be written as: (2m−1)+(2n−1)+(2k−1) =2(m+n+k−1)−1. which, as we know is an odd number. Therefore the sum of three odd numbers is always an odd number.
Can you add two odd numbers and get an odd number?
The sum of two odd numbers is always even. The product of two or more odd numbers is always odd.
When you add two odd numbers Why is the answer always even?
An odd number can be looked at as an even number with one added to it – e.g. 5 is 4+1. Therefore, if you add two odd numbers together, what you’re really doing is adding an even number to another even number, then adding 1 + 1, which is 2, and therefore even.
What happens when you add an odd number to another odd number?
“With two odd numbers, each odd number by itself has one left over, but when we add them together, we can combine these two “leftovers” to form another pair. … But if we add an odd number of odd numbers, we’ll get an odd number for a sum.
When you add an even and odd number?
An odd number can only be formed by the sum of an odd and even number (odd + even = odd, or even + odd = odd). An even number can only be formed by multiplication in three ways: even·odd, odd·even, and even·even.
Do all prime numbers have to be odd?
Primes are always greater than 1 and they’re only divisible by 1 and themselves. They cannot be made by multiplying two other whole numbers that are not 1 or the number itself. Another fact to keep in mind is that all primes are odd numbers except for 2. Prime numbers include: 2,3,5,7,11,13,17,19… and so on.
Can you add three odd numbers to get an even number?
The resultant of the sum of two odd numbers gives an even number which in turn gets added with an odd number generates the result as an odd number. We cannot get an even number (30) by adding three odd numbers by simple addition.
Who is odd number?
An odd number is an integer when divided by two, either leaves a remainder or the result is a fraction. One is the first odd positive number but it does not leave a remainder 1. Some examples of odd numbers are 1, 3, 5, 7, 9, and 11. An integer that is not an odd number is an even number.
Can you pick 3 watermelons to get a sum of 30?
Answer: 13,11,and 6 is answer.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703529179.46/warc/CC-MAIN-20210122082356-20210122112356-00201.warc.gz
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CC-MAIN-2021-04
| 3,722 | 39 |
https://www.numerade.com/questions/sketch-the-graph-of-a-function-that-satisfies-all-of-the-given-conditions-fx-0-for-all-x-not-1-verti/
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math
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Sketch the graph of a function that satisfies all of the given conditions
$ f'(x) > 0 $ for all $ x \not= 1 $, vertical asymptote $ x = 1 $,
$ f"(x) > 0 $ if $ x < 1 $ or $ x > 3 $, $ f"(x) < 0 $ if $ 1 < x < 3 $
So we're given a bunch of conditions that we need to fulfill for our graph and the first one is that are derivative is greater than zero for all X. That is not equal to one. So our function is increasing for all X, not equal to one. We have a vertical as um. Tota at X is equal to one. And then our second derivative is greater than zero when X is less than one or when X is greater than three. And our second derivative is less than zero when X is between one and 3. So we're concave up from negative infinity to one and from three to infinity. And we are concave down from 1 to 3. So if we do this, we know that we're increasing for all X. And we have this vertical ascent to it at one and we are concave up before one. So we need a curve that is always increasing in concave up. It has this assume tote. So it's going to look something like this where we're concave up were increasing and we have this assam tote that we're increasing towards and we're never going to cross. And then if we look at values of X that are greater than one, but less than three, we know that we're concave down. So we're concave down but we also know that we are increasing since we're increasing everywhere, that X is not equal to one. So for concave down until X is equal to three, it would look something like this and then We'd have this inflection point at X is equal to three right here where we go from being concave down to concave up however, were increasing for the entirety of this part of our graph. So we're not it's not a local maximum minimum, it's an inflection point. And so this would be a good sketch of the graph given our conditions where we're increasing everywhere, where concave up before this ascent to X is equal to one, and then we're concave down from 1-3, and we're concave up again from three to infinity.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057036.89/warc/CC-MAIN-20210920101029-20210920131029-00336.warc.gz
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CC-MAIN-2021-39
| 2,030 | 4 |
https://www.physicsforums.com/threads/second-year-physics-homework-thought-i-was-capable-and-now-am-simply-frustrated.666751/
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math
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So I told my sister I could help her with her physics homework, having an old computer engineering degree, and this first problem she sends me has me stumped. If anyone is willing to help this busy and forgetful young man help his sister I would be immensely appreciative. Thank you in advance. 1. The problem statement, all variables and given/known data[/b] Determine the Moment of this force about point O.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592309.94/warc/CC-MAIN-20180721032019-20180721052019-00542.warc.gz
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CC-MAIN-2018-30
| 409 | 1 |
http://www.tutorsglobe.com/question/determine-the-total-quarterly-cash-outows-that-will-be-51259711.aspx
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math
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Cash ?ows, debt restructuring, effect on income under bank- ruptcy and nonbankruptcy law. Rather than entering into a lengthy bankruptcy proceeding, Peltzer Manufacturing has reached agreement with its long-term creditors to restructure various loans. The restructured loans are described below.
Loan A-This debt has a principal balance of $4,000,000 and accrued interest of $80,000. Under the restructuring agreement, $500,000 of debt would be forgiven, and the balance of the amounts due would be re?nanced at a rate of 10% with monthly installment payments of $50,000 and a term of eight years. Assets with a net realizable value of $2,500,000 would also be pledged as additional security against the restructured loan.
Loan B-This debt has a principal balance of $1,000,000 and accrued interest of $25,000. Under the restructuring agreement, the accrued interest would be forgiven, and the principal amount would be exchanged for preferred stock with a par value of $500,000 and a fair value of
Loan C-This debt has a principal balance of $2,000,000 and accrued interest of $37,500. Under the restructuring agreement, the creditor would receive a parcel of land with a book value of $200,000 and a net realizable value of $250,000. The remaining unpaid balance would be re?- nanced over ?ve years at a 9% interest rate. Installment payments would be on a quarterly basis.
1. Determine the total quarterly cash out?ows that will be required by Peltzer's debt restructuring.
2. Covering the ?rst quarter subsequent to restructuring, prepare a schedule that compares the effect on Peltzer's net income of accounting for the restructuring as part of a formal bank-ruptcy ?ling versus it not being part of such a ?ling.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867041.69/warc/CC-MAIN-20180525043910-20180525063910-00084.warc.gz
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CC-MAIN-2018-22
| 1,718 | 6 |
https://support.justlogin.com/hc/en-us/articles/115002333247-How-to-set-pay-element-limit-
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math
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The pay elements in ePayroll are only able to follow a formula limit per use. You can set a limit for example $200, and the maximum claim would be $200 per time.
ePayroll is unable to calculate and set a limit for accumulative costs annually. In that sense, it also does not have the function to set different max annual limits for different grades.
1. Navigate to ePayroll > Payroll Setup > Pay Elements.
2. Find the respective pay element and click on the corresponding .
3. Set the desired value/ percentage under ‘Amount/Formula Limit’.
4. Click at the bottom of the page to save the changes made.
What is the Gross/ Net Pay/ Pay Element Limit for?
How do I set pay limits to get an alert?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487630175.17/warc/CC-MAIN-20210625115905-20210625145905-00409.warc.gz
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CC-MAIN-2021-25
| 697 | 8 |
https://www.myminifactory.com/object/3d-print-3x3x3-octahedron-hyperbolic-cuts-entry-for-make-anything-design-competition-68031
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math
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Heyo! Just finished whipping this up!
Basically it's a twisty puzzle with two layers of corner turning: the standard "3x3x3" turn (aka. Trajber's Octahedron), and the shallower hyperbolic cuts, which form those non-standard cuts that meet together at the centre of each face (the wide gaps in the puzzle are caused by filleting these; similar to the mass-produced "Flowerminx").
On top of that, 4 of the 8 faces have 3 bandaged pieces (i.e. pieces that have been fused together). Two of those exhibit a "clockwise" pattern and the other two an "anti-clockwise" pattern. These should restrict moves in certain permutations, thus adding to the difficulty of the puzzle. (I've also checked to make sure they do not restrict too many moves.)
I will admit that this has never been printed before, but it uses the shell mechanism: one of the standard approaches for designing twisty puzzles. Apart from the hyperbolic cuts, the mechanism resembles the mass-produced 3x3x3 Crazy Cubes. In other words, it should work.
Now for the part where it somehow fulfils the design brief... To be honest, I'm doing this for the sake of seeing another twisty puzzle in the competition, but I will make my case. It's probably going to be more of a "wow twisty puzzles are really cool and you should actually look into them" kind of promo. :V
It's important to note that when the Rubik's Cube came to fruition, many were not only engrossed in developing the fastest and easiest algorithms to restore it, but were also fascinated with its inner workings. Nowadays, it cannot be denied that the existence of most new twisty puzzles heavily relies on 3D printing: both for pushing the limits of their already intricate mechanisms, and finding optimal placements of cuts and screws (or even lack of screws) to make these even feasible for mass production.
A few minutes of browsing through the Twisty Puzzles forum can already attest to this. Geared puzzles, sliding puzzles, higher-ordered puzzles (like that recent 33x33x33), deep-cut puzzles which somehow hold on to so many moving parts, geometries of jumbling puzzles, etc... Should probably watch this too for a brief overview of a classic: https://www.youtube.com/watch?v=83a_DX8WDe8
With such possibilities, it can be easily seen how the challenge has been brought to the "next level". For twisty puzzlers, the puzzle is often both the solution, and the puzzle design itself.
Of course, this only speaks for the category in general and not the specific puzzle here. I'll admit it is quite basic, but it does exhibit hyperbolic cuts, which enable visually impossible turns to work. I was hoping to fix the fillets as mentioned earlier so that this would be more apparent, but I ran out of time. Better examples can be seen here:
Such cuts almost definitely need 3D printing to achieve. Before that, there were very few puzzles that featured these cuts, and virtually all of those were extension mods using plastic sheeting on existing puzzles. I guess that's the only claim this puzzle has in showing the advantages of 3D printing.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203529.38/warc/CC-MAIN-20190324230359-20190325012359-00140.warc.gz
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CC-MAIN-2019-13
| 3,063 | 10 |
http://openstudy.com/updates/56140b95e4b0ae2cd0acf094
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math
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First you need to determine the order of smallest to largest
3/4 is equivalent to 12/16. 5/8 is equivalent to 10/16. 1/4 is equivalent to 4/16. So from there, you think you can get them in order from least to greatest?
I think so?
Try it out :)
wait so I just order them from least to greatest?
so my answer would be the 3rd one?
Nope, 3/4 and 5/8 are both bigger than 7/16. put these numbers in order: 4/16, 12/16, 10/16, 7/16 and once you do that, we can simplify those fractions back down and you will have your answer.
I don't get it. :/
just put 4, 12, 10 and 7 in order then
4, 7, 10, 12
yes, so 4/16, 7/16, 10/16, 12/16 which then simplifies to 1/4, 7/16, 5/8, and 3/4. which option is that?
the last one!
No problem :)
I need help with more, do you THINK you can try to help me?
Sure :) Just post a new question
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189495.77/warc/CC-MAIN-20170322212949-00410-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 819 | 15 |
https://simplyans.com/engineering/determine-the-minimum-length-of-a-c-14030844
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math
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Determine the minimum length of a crest vertical curve on a freight and passenger intercity main line track, connecting two tangents of 0.75% and 1.5% traveling at 70 mi/hr. hoel, lester a.. transportation infrastructure engineering: a multimodal integration (p. 389). cengage textbook. kindle edition.
answer with explanation:
when dealing with heavy loads, one needs to take certain precautions in order to avoid or prevent from injuries.
for instance, one should avoid lifting above the shoulder level which can end up pulling your muscle.
also, you can either break the load in parts if possible or get some for lifting heavy bulks.
moreover, one should try to lift with the legs while keeping the back straight and not twisting it.
answer & explanation:
"the force on a cutting tool are 2600n vertically downward" sounds a little unusual, since most of the time, the tool is above the object to be cut in such a way that the force acting "on the tool" is upwards. we will accept the statement as it is (downwards).
since the two forces are acting at right angles to each other, the resultant can be found using pythagoras theorem, namely
resultant = sqrt(2600^2+2100^2) = 3342 n (approx.)
the angle can be found using the arctangent function, or
angle = arctangent(2600/2100) = 51.07 degrees below the horizontal, since the 2600 n force is acting downwards.
d is the answer
heat transfer through conduction is a slow process and both conduction and convection require material medium
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CC-MAIN-2021-43
| 1,488 | 14 |
https://primeinterest.wordpress.com/2014/01/19/more-infinite-series-madness/
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math
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Previously, I had written about the somewhat bizarre behavior of a divergent geometric infinite series, containing no negative numbers, but which appeared to add up to -1:
I discussed how this divergent infinite series actually represents the Taylor Series expansion of the analytic continuation on the complex plane of a function that does actually come out to equal -1 at a specific relevant point. (Both Taylor Series and analytic continuation are topics which warrant their own discussions; but, for now, we’ll hold off on that until another day.)
That article had also contained a video from Minute Physics which discussed this bizarre series, although without delving into details about why the series exhibited such bizarre behavior. Well, the fine folks from Numberphile have posted yet another video about a similarly bizarre series:
“You have to go to infinity, Brady.”
Now, it just so happens that this dovetails nicely into something I’ve been leading up to in my posts: the Riemann zeta function and the Riemann Hypothesis. I have a bit more groundwork to cover before diving into them; but, as it turns out, the Riemann zeta function comes into play in a secondary proof for the sum described in that video. That proof is covered in a secondary video:
It Doesn’t Add Up!
So here’s the bizarre series, the sum of all of the natural numbers:
Weird, huh? Obviously, the series doesn’t actually add up to this negative sum. It is a divergent series that blows up to infinity. A bit more on that in a moment. But first, here is the proof presented in the first Numberphile video.
First, let us take the following series, known as Grandi’s Series, an infinite series alternating between 1 and -1:
This series is a bit challenging to evaluate. Looking at the partial sums of an odd number of terms in this series will always yield a value of 1, whereas the partial sum of an even number of terms will always give 0. Now, it can be shown (and is shown in yet another Numberphile video), that the appropriate sum for this series is the average of the two values, 1/2.
Let us also consider the following series:
And our sum of interest is defined as:
First off, let us add S2 to itself:
Well, now we are getting somewhere. This yields
Now, let us subtract S2 from S:
Now, we’ve already figured out what S2 is, so we substitute that in and simplify:
So, there you have it.
Okay, how about a different, more rigorous proof? Let’s take a look at the proof from the second Numberphile video, a proof first discovered by Leonhard Euler. First of all, let us consider the following series:
It can readily be shown (but I’ll leave it as an exercise for the reader for now) that the above is strictly true for values of x less than one. Now let us differentiate with respect to x:
Now, let us set x = -1. What does this give us?
Now we bring the big guns to bear. Here is the Riemann zeta function:
Now, when Euler first worked with this function, he only studied in the context of s being a real number. However, Riemann extended his analyis of the function into the complex plane. We’ll focus for the time being on Euler’s view of the function, but keep in the back of your head that a more rigorous version of this requires considering the complex plane.
Now, let us do a bit of manipulation of the zeta function:
Next, Euler subtracted twice this expression from the original zeta function:
Now we set s=-1 and plug it in:
But we’ve already figured out above that this series is equal to 1/4, so:
Now, keep in mind that Euler was looking at this function on the real number line. The series in question is simply the special case of the zeta function at s=-1. However, there is a catch. In the realm of real numbers, the zeta function only converges for values of s larger than 1. What Riemann realized is that he could make the zeta function converge for all values of s, except for a pole at s=1, by switching to the complex plane and performing the analytic continuation of the function. In that context, the value of the zeta function at s=-1 is in fact -1/12.
No, Seriously, What’s Really Happening Here?
Okay, obviously, the series in question doesn’t REALLY add up to -1/12. That is an impossibility in terms of how we ordinarily define algebraic sums. The point here is that we are using a non-standard definition of sums involving analytic continuation on the complex plane. We aren’t just talking about the real number line. The “proofs” in these videos aren’t really rigorous and break a few rules. (Specifically, if you have a series that does not converge, you can’t go adding and subtracting other series to it willy-nilly. Cauchy taught us this.)
Since this distinction between different types of summation isn’t really made clear in the original video, this has caused a bit of a ruckus online. After I had already started writing this blog article, Phil Plait from the Bad Astronomy blog posted an article about the video, and a firestorm ensued in the comments and on Twitter. Mark Chu-Carroll over at the “Good Math, Bad Math” blog picked up on the topic, and Phil Plait subsequently posted a follow-up to clarify the situation.
So, what’s all of this about different types of sums?
Back in the middle of the 18th century, Leonhard Euler came up with a proof that the summation we are discussing does indeed equal -1/12. He also came up with the result that 1 – 2 + 3 – 4 + … = 1/4. Both of these results, although obtained rigorously as far as he could tell, seemed paradoxical to him. What was needed was a new way to deal with divergent sums. Towards the end of the 19th century, several mathematicians started coming up with those techniques, some of which were based upon Euler’s work.
The standard algebraic infinite sum is typically defined by taking the nth partial sum of the series in the limit as n goes to infinity. By and large, these alternative summation techniques involve differing definitions for the limits that are taken when evaluating an infinite sum, as well as modifying the domain over which the sum is taken (such switching to the complex plane). These summation techniques frequently focus on the properties of partial sums since they address scenarios where the complete sums are not well-defined. By using these techniques, we can assign meaningful values to series which do not converge to a finite value under standard algebraic summation.
For example, suppose we have an infinite series whose nth partial sum oscillates symmetrically as n goes to infinity, never converging on a specific value. An example of this would be the Grandi’s Series we mentioned earlier, whose partial sums alternate between 1 and 0. However, instead of using ordinary algebraic summation, we can define a summation in which we sum the series to the nth term, then divide by n, doing this for all values of n. If the series converges to a value in the limit as n goes to infinity, we say that the series is Cesàro summable, We’ve essentially taken the average of all partial sums in the series.
The Grandi’s Series can also be evaluated terms of something called an Abel sum. Similarly, 1 – 2 + 3 – 4 + … can be evaluated using Abel summation. And for our sum of all natural numbers, it turns out that their are two summation techniques which apply: zeta function regularization (which is a formalization of Euler’s approach) and Ramanujan summation.
But what does it mean when we say that we are finding a value for something that doesn’t have a value? Let us take a look at a generic geometric series:
Let’s multiply the whole thing by a factor r, and then subtract the original series from that:
For the original series to be convergent, r has to be less than one. In that scenario, evaluating this formula would give us a value equal to the limit of n partial sums of the series as the limit of n goes to infinity. For other values of r, where the series is divergent, we can still use this formula to get a value. This value is not the limit of n partial sums as n goes to infinity, since that limit does not exist. But we still have a value using the same formula. (For the special case of r=-1, we have an oscillating value, as with our Grandi’s Series.)
So, What Does This Have To Do With String Theory?
That would be a rather lengthy discussion, but have a look at a series of posts by mathematical physicist John Baez (who happens to be the cousin of singer Joan Baez) listed below in the “For More Information” section. He covers the topic quite nicely. This sum also shows up in other areas of physics, including QED calculations of the Casimir Effect.
For Further Information:
- The Euler-Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation | What’s new
- Mathematical Physicist John Baez has a series of articles which hit upon this topic:
- The Reference Frame: Zeta-function regularization
- The Reference Frame: Why is the sum of integers equal to -1/12
- 1 + 2 + 3 + 4 + ⋯ – Wikipedia, the free encyclopedia
- 1 − 2 + 3 − 4 + · · · – Wikipedia, the free encyclopedia
- Grandi’s series – Wikipedia, the free encyclopedia
- Summation of Grandi’s series – Wikipedia, the free encyclopedia
- Zeta function regularization – Wikipedia, the free encyclopedia
- Ramanujan summation – Wikipedia, the free encyclopedia
- Cesàro summation – Wikipedia, the free encyclopedia
- Divergent series – Wikipedia, the free encyclopedia
- Divergent geometric series – Wikipedia, the free encyclopedia
- Analytic continuation – Wikipedia, the free encyclopedia
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039375537.73/warc/CC-MAIN-20210420025739-20210420055739-00398.warc.gz
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CC-MAIN-2021-17
| 9,649 | 55 |
https://chemistry.stackexchange.com/questions/24181/what-does-the-prefix-dihydro-in-the-systematic-name-of-luminol-refer-to
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math
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I'm doing a research project on the fascinating chemiluminescent molecule luminol, and figured it would be a good idea to start breaking down the systematic name of the chemical and linking the terms to the structure. The systematic name of luminol is 5-amino-2,3-dihydrophthalazine-1,4-dione, and I get it all apart from the "dihydro" - any help? Thank you very much in advance! :)
On the left is 5-amino-2,3-dihydrophthalazine-1,4-dione and on the right is the molecule which the name is based on, phthalazine. The 2,3-dihydro refers to the fact that at the 2 and 3 positions (the two nitrogens) hydrogens have been added (hydro is the prefix for hydrogen).
$\begingroup$ Fantastic, thank you! I suspected this but didn't want to go ahead without checking. Also, for brownie points: is there a techincal name for the molecule that a molecule is based on - i.e. an OH group is called a functional group, so in the case of the luminol the phthalazine would be called its...? This word may not exist, just curious! $\endgroup$ Jan 25, 2015 at 19:47
1$\begingroup$ @AndrewCatherall I think they are just called base names $\endgroup$– bonJan 25, 2015 at 19:51
$\begingroup$ @AndrewCatherall Late to the party on this one, but in my experience luminol would be said to be derived from a phthalazine core. $\endgroup$– hBy2PyFeb 10, 2016 at 11:57
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949097.61/warc/CC-MAIN-20230330035241-20230330065241-00594.warc.gz
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CC-MAIN-2023-14
| 1,346 | 5 |
http://www.transtutors.com/questions/a-european-call-option-and-put-option-on-a-stock-both-have-a-strike-price-of-20-and--83303.htm
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math
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Solution to be delivered in 24 hoursafter verification
Another European vanilla Call option with strike price K3 is trading in the market. At the expiry of the three options (i.e. at T = 0), what are the new no-arbitrage boundary conditions
Let C(K)denote a European vanilla Call option with strike price K. Assume that all options are identical except for strike price, and strike prices satisfy K1
Let C(K) denote a European vanilla Call option with strike price K. Assume that all options are identical except for strike price, and strike prices satisfy K1
The current price of a stock is $94, and 3-month European call options with a strike price of $95 currently sell for $4.70. An investor who feels that the price of the stock
of setting up the following positions: (a) A bull spread using European call options with strike prices of $25 and $30 and a maturity of 6 months (b) A bear spread using European put...
A three-month American call option on a stock has a strike price of $20. The stock price is $20, the risk-free rate is 3% per annum, and the volatility is 25% per annum. A dividend of $2
was $2,550 (which corresponds to a price of $40 per barrel). Show that the bond is a combination of a regular bond, a long position in call options on oil with a strike price of $25
includes tranches with multiple internal credit enhancements as shown in Exhibit 1 below. The total value of the collateral for the structure is USD 680 million, the lockout period is...
An analyst is doing a study on the effect on option prices of changes in the price of the underlying asset. The analyst wants to find out when the deltas of calls and puts
The current spot price of corn is $4.90 per bushel, and the effective six-month interest rate is 6 percent. Sam has decided to hedge with a collar by purchasing $4.70-strike puts
(ln(x)) = 1x Inverse Trig d dx...
Appendix 4 Partial...
Lab 19: Partial...
Carboxylic acids, esters, and...
Behavioral Finance Basically behavior Finance is a very comprehensive study of how the factor of psychology can affect the behaviors of the various...
Business Valuation and Analysis The Business is sometimes referred to as a composite asset. So, as it is called a composite asset, the valuation...
Corporate Finance Corporate Finance is a very important topic in every organization since it deals with raising; investing; and distributing the money...
Entrepreneurial Finance The main thing for entrepreneurs to raise capital and when people find this out, they often ask one question: What’s the...
Financial Markets and Institutes A financial market is a market where financial instruments are exchanged. The more popular term used for the...
International Financial Management International Financial Management came into being when the countries of the world started opening their doors for...
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206118.10/warc/CC-MAIN-20140423032006-00251-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 2,835 | 21 |
https://campus.uni-due.de/lsf/rds?state=verpublish&status=init&vmfile=no&publishid=313484&moduleCall=webInfo&publishConfFile=webInfo&publishSubDir=veranstaltung
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math
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This course includes two different parts each lasting two month. Both lectures will have a second part (continuation) in next summerterm.
Part 1: The Malliavin-Stein Method I: Poisson Processes (Oktober-November 2018)
This lecture is a special class for the lecture series of the Research Training Group RTG 2131 "High-Dimensional Phenomena in Probability - Fluctuations and Discontinuity", but it is also very appropriate for students in the master program. Stein's method is a collection of probabilistic techniques that allow to assess the distance between two probability distributions by means of differential operators. It has been discovered in the last decade that one can successfully combine Stein's method with the Malliavin calculus of variations. This so-called Malliavin-Stein method has become a versatile tool in many branches of probability theory and statistics. In our Tandem Lecture we present the foundations of Stein's method and that of the Malliavin calculus on the Wiener and the Poisson space. We then show how these techniques can be combined and how the resulting abstract error bounds evaluate in concrete situations. The applications we present are quantitative limit theorems for general functionals of Gaussian random fields and functionals that arise in stochastic geometry. During the winter term we concentrate on Poisson processes. The lecture will be continued in the summer term with Gaussian processes.
The lecture is held by Peter Eichelsbacher and Christoph Thäle from Ruhr University Bochum.
Part 2: Extremes for heavy-tailed time series (December 2018-January 2019)
This course aims at an introduction to extreme value theory for time series, i.e., for univariate or multivariate serially dependent sequences. Special emphasis will be given to time series whose marginal and finite-dimensional distributions exhibit power-law tails. For this reason, the notions of regularly varying random vector and regularly varying time series will be introduced and studied in detail. We will consider various time series models that have the regular variation property, including linear processes with regularly varying noise, GARCH processes, solutions to affine stochastic recurrence equations, stochastic volatility models, max-stable processes with Fréchet marginals. We will consider point process convergence for the suitably normalized time series and explain the crucial differences between the independent and dependent cases. In the former case, simple Poisson processes appear as weak limits while in the dependent case processes of compound Poisson type occur. We will introduce the necessary tools for point processes and their weak convergence on the way. We will also touch on large deviation theory based on regularly varying time series. It is closely related to the
extreme value theory for such sequences.
The course will be supported by lecture notes written by T. Mikosch andO. Wintenberger. This lecture is held by Thomas Mikosch, Kopenhagen.
You get 6 ECTS, Prüfungsform: An oral exam at the end of the semester.
For students of University Duisburg Essen this lecture allows to count within the Vertiefungsbereich Stochastik as well in "Special topics in Stochastic Processes" as in "Special topics in Stochastic Analysis".
Students from RUB, please contact the lecturers.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474581.68/warc/CC-MAIN-20240225035809-20240225065809-00494.warc.gz
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CC-MAIN-2024-10
| 3,330 | 11 |
https://quantumcomputing.stackexchange.com/questions/15161/grover-algorithm-vs-classical-search-algorithms
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math
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If Grover algorithm has a better speed than classical search algorithms, would it be an example of where Quantum computers outruns classical computers?
Can we use Grover Algorithm in real world problems?
Quantum Computing Stack Exchange is a question and answer site for engineers, scientists, programmers, and computing professionals interested in quantum computing. It only takes a minute to sign up.Sign up to join this community
A Grover algorithm outperform classical unordered database search algorithms quadratically. So, it can serve as an example of higher performance of quantum computers. However, when complexity of Grover search is assessed, generally a complexity of an oracle is ignored. In some cases the oracle complexity is so high that it cancels out advantage of faster search.
Currently, Grover search cannot be used for real world problems because of high noise level and decoherence quantum computers suffer from. However, once these problems are solved, Grover search can be employed naturally for unordered database search and optimization tasks.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662601401.72/warc/CC-MAIN-20220526035036-20220526065036-00406.warc.gz
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CC-MAIN-2022-21
| 1,071 | 5 |
https://www.statpearls.com/articlelibrary/viewarticle/20964
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math
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Electric potential and capacitance stem from the concept of charge. The charge is the comparison of the number of protons and electrons a material possesses. If there are more protons than electrons, then there is a net positive charge. Conversely, if there are more electrons than protons, there is a net negative charge. An equal number of protons and electrons have a neutral charge. Materials with charge also exhibit electrical forces: opposite charges attract (e.g., positive and negative), and similar charges repel (e.g., positive and positive or negative and negative). The unit of measurement for the charge is a coulomb (C). Protons and electrons individually have a charge of +1.602 E -19 C and -1.602 E -19 C, respectively. The charge values for protons and electrons are considered the elementary charge because the accumulation of microscopic electrons and protons determines the macroscopic charge.
The work done on moving charges is the electric potential. As the name suggests, electric potential measures the change in the potential energy of a specific charge. The units for electric potential are joules per coulomb (J/C), which measures the amount of work per charge. The J/C unit is commonly referred to as a volt (V) and is the ubiquitous unit for electric potential. The concept of electric potential is often compared to that of gravitational potential energy. The higher up an object is from the ground, the more gravitational potential energy the object possesses. Similarly, the farther away an object is from a charge, the more electric potential is available. The electric potential from a specific charge is known as a point charge and can be measured explicitly. The equation to determine the electric potential from a specific point charge is:
- V = k·q/(r·r)
Where V is the electric potential (V), k is a constant measuring the inverse of the free space permittivity commonly denoted as 8.99 E 9 N (m·m)/(C·C), q is the charge of the point (C), and r is the distance from the point charge (m), which is squared. Dimensional analysis is often needed to ensure all the units are consistent.
The electric potential is inversely related to the square of the distance from the point charge. This suggests that the farther away an object is from the point charge, the electric potential decays quickly. Additionally, if the electric potential is measured at various points around the object, a curve can be generated around the object where each point has the same potential. If two objects containing charges are placed next to each other, then the attractive or repulsive force is present. This is commonly depicted with lines originating from the positively-charged source with an arrow pointing to and terminating at the negatively-charged source. The explanation and applications of electric fields, however, are outside the scope of this article.
While electric potential measures the ability to perform work on a charge, capacitance measures the ability to store charge. The unit of measurement for capacitance is Coulomb per Voltage (C/V), which is the amount of charge present per voltage applied. The Farad (F) is commonly used instead of C/V to measure capacitance. A capacitor is used to hold capacitance and is created when two plates are parallel to each other, with each end connected to opposite charge sources. Each charge fills one of the parallel plates generating an electric field between the two. The capacitor can then discharge the charges between the two plates when connected. The equation to determine the capacitance is:
- C = e0 · k · A/d
Where C is the capacitance (F), e0 is the permittivity of free space (8.85 E -12 F/m), k is the relative permittivity of the dielectric material between the plates, A is the geometric area of both plates (m·m), and d is the distance between the two plates (m). The capacitance is inversely proportional to the distance, so the greater the separation between the two plates, the smaller the capacitance available. Additionally, the k-value is determined by the material between the parallel plates and is directly proportional to the capacitance; most capacitors have a solid in between the capacitor to improve capacitance.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500151.93/warc/CC-MAIN-20230204173912-20230204203912-00581.warc.gz
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CC-MAIN-2023-06
| 4,227 | 8 |
http://imsaethics.org/what-famous-rule-of-donuts-is-illustrated-by-this-picture/
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math
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What Famous Rule of Donuts Is Illustrated by This Picture?
Donuts are undoubtedly one of the most beloved and iconic desserts around the world. Their round shape, fluffy texture, and sweet glaze make them a delightful treat for people of all ages. But did you know that donuts also hold a special place in the realm of mathematics? In this article, we will explore the famous “Donut Rule” and how it is illustrated by a picture.
The Donut Rule, also known as the “Toroidal Topology,” is a concept derived from the field of topology, which studies the properties of space that are preserved under continuous transformations. In simpler terms, topology deals with the study of shapes and their properties, focusing on the aspects that remain unchanged regardless of stretching, bending, or twisting.
To understand the Donut Rule, we must first understand the concept of a torus. A torus is a donut-shaped object that can be visualized as a surface created by rotating a circle in three-dimensional space. It consists of an outer surface and an inner surface, both of which are connected seamlessly, forming a closed loop.
Now, let’s take a look at the picture that illustrates the Donut Rule. In this image, we can see a donut with a hole in the center, also known as a ring-shaped torus. This particular shape is significant because it demonstrates a fundamental property of the Donut Rule: the number of holes in a torus.
In topology, mathematicians refer to a property called the Euler characteristic, denoted by the symbol χ (chi). The Euler characteristic of a torus can be calculated using the formula χ = V – E + F, where V represents the number of vertices, E represents the number of edges, and F represents the number of faces.
In the case of a torus, the Euler characteristic is zero. This means that a torus has an equal number of vertices, edges, and faces. Consequently, a torus has one hole, indicated by the empty space in the center of the donut.
The picture of the donut with a hole in the center beautifully illustrates this property of the Donut Rule. It showcases the concept of a torus and its intrinsic characteristic of having one hole. Without this hole, the shape would no longer be a torus but a sphere or a different object altogether.
Q: Why is the Donut Rule significant in mathematics?
A: The Donut Rule, or toroidal topology, is significant in mathematics as it demonstrates the concept of a torus and its properties. It allows mathematicians to study shapes and their characteristics in the realm of topology.
Q: How is the Donut Rule applied in real-life scenarios?
A: While the Donut Rule may seem abstract, its applications can be found in various fields. For example, it is used in computer graphics to model and render three-dimensional objects. It also finds applications in physics, engineering, and even in understanding the behavior of DNA molecules.
Q: Are all tori the same?
A: No, not all tori are the same. The number of holes in a torus can vary. A torus with two holes is called a double torus or a pretzel, while a torus with three or more holes is referred to as a multi-torus.
Q: Can the Donut Rule be applied to other shapes?
A: The Donut Rule, or Euler characteristic, is primarily used to study tori. However, the concept of topology can be applied to various shapes and objects, allowing mathematicians to explore their properties and relationships.
In conclusion, the Donut Rule, also known as the Toroidal Topology, is a fascinating concept in mathematics that deals with the properties of tori. The picture of a donut with a hole in the center beautifully illustrates the concept of a torus and its intrinsic characteristic of having one hole. By understanding this famous rule, mathematicians can delve deeper into the study of shapes and their properties, making mathematics even more intriguing and captivating.
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CC-MAIN-2023-40
| 3,884 | 17 |
https://www.motorsforum.com/hyundai/warranty-trasfer-questions-2295-.htm
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math
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I am selling my 2002 Hyundai Santa Fe LX and I have some questions about the
warranty. It looks like the Powertrain warranty is 5 years 60k miles for
the second owner, roadside continues for 5 years from date of first use for
the second owner, Federal Emmsions stuff is good 8 years/80k miles
(Catalytic converter, ECM, OBDII) other EPA 5years 60k miles for the second
owner, antiperforation 5 years/100k miles for second owner, and Bumper to
Bumper 5 years/60k miles for second owner. I got this from the Hyundai
Website, so I think it is right but I want to be sure. Can anyone confirm?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891377.59/warc/CC-MAIN-20180122133636-20180122153636-00342.warc.gz
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CC-MAIN-2018-05
| 588 | 8 |
https://en.wikipedia.org/wiki/Stone%27s_theorem_on_one-parameter_unitary_groups
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math
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Stone's theorem on one-parameter unitary groups
In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence between self-adjoint operators on a Hilbert space H and one-parameter families
and are homomorphisms, i.e.,
Such one-parameter families are ordinarily referred to as strongly continuous one-parameter unitary groups.
The theorem was proved by Marshall Stone (1930, 1932), and Von Neumann (1932) showed that the requirement that be strongly continuous can be relaxed to say that it is merely weakly measurable, at least when the Hilbert space is separable.
Let be a strongly continuous one-parameter unitary group. Then there exists a unique (not necessarily bounded) self-adjoint operator A such that
Conversely, let A be a (not necessarily bounded) self-adjoint operator on a Hilbert space H. Then the one-parameter family of unitary operators defined by (using the Spectral Theorem for Self-Adjoint Operators)
is a strongly continuous one-parameter group.
The infinitesimal generator of is defined to be the operator iA. This mapping is a bijective correspondence. Furthermore, A will be a bounded operator if and only if the operator-valued mapping t ↦ Ut is norm-continuous.
Stone's Theorem can be recast using the language of the Fourier transform. The real line R is a locally compact abelian group. Non-degenerate *-representations of the group C*-algebra C∗(R) are in one-to-one correspondence with strongly continuous unitary representations of R, i.e., strongly continuous one-parameter unitary groups. On the other hand, the Fourier transform is a *-isomorphism from C∗(R) to C0(R), the C*-algebra of complex-valued continuous functions on the real line that vanish at infinity. Hence, there is a one-to-one correspondence between strongly continuous one-parameter unitary groups and *-representations of C0(R). As every *-representation of C0(R) corresponds uniquely to a self-adjoint operator, Stone's Theorem holds.
Therefore, the procedure for obtaining the infinitesimal generator of a strongly continuous one-parameter unitary group is as follows.
- Let be a strongly continuous unitary representation of R on a Hilbert space H.
- Integrate this unitary representation to yield a non-degenerate *-representation ρ of C∗(R) on H by first defining
- and then extending ρ to all of C∗(R) by continuity.
- Use the Fourier transform to obtain a non-degenerate *-representation τ of C0(R) on H.
- By the Riesz-Markov Theorem, τ gives rise to a projection-valued measure on R that is the resolution of the identity of a unique self-adjoint operator A, which may be unbounded.
- Then iA is the infinitesimal generator of .
The precise definition of C∗(R) is as follows. Consider the *-algebra Cc(R), the complex-valued continuous functions on R with compact support, where the multiplication is given by convolution. The completion of this *-algebra with respect to the L1-norm is a Banach *-algebra, denoted by . Then C∗(R) is defined to be the enveloping C*-algebra of , i.e., its completion with respect to the largest possible C*-norm. It is a non-trivial fact that, via the Fourier transform, C∗(R) is isomorphic to C0(R). A result in this direction is the Riemann-Lebesgue Lemma, which says that the Fourier transform maps L1(R) to C0(R).
The family of translation operators
is a one-parameter unitary group of unitary operators; the infinitesimal generator of this family is an extension of the differential operator
defined on the space of complex-valued continuously differentiable functions of compact support on R. Thus
In other words, motion on the line is generated by the momentum operator.
Stone's theorem has numerous applications in quantum mechanics. For instance, given an isolated quantum mechanical system, with Hilbert space of states H, time evolution is a strongly continuous one-parameter unitary group on H. The infinitesimal generator of this group is the system Hamiltonian.
The Stone–von Neumann theorem generalizes Stone's theorem to a pair of self-adjoint operators, Q, P satisfying the canonical commutation relation, and shows that these are all unitarily equivalent to the position operator and momentum operator on L2(R).
- Neumann, J. von (1932), "Über einen Satz von Herrn M. H. Stone", Annals of Mathematics, Second Series (in German) (Annals of Mathematics) 33 (3): 567–573, doi:10.2307/1968535, ISSN 0003-486X, JSTOR 1968535
- Stone, M. H. (1930), "Linear Transformations in Hilbert Space. III. Operational Methods and Group Theory", Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences) 16 (2): 172–175, doi:10.1073/pnas.16.2.172, ISSN 0027-8424, JSTOR 85485
- Stone, M. H. (1932), "On one-parameter unitary groups in Hilbert Space", Annals of Mathematics 33 (3): 643–648, doi:10.2307/1968538, JSTOR 1968538
- K. Yosida, Functional Analysis, Springer-Verlag, (1968)
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http://wikilion.com/List_of_inventions_in_the_medieval_Islamic_world
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Boris A. Rosenfeld and Adolf P. Youschkevitch (1996), "Geometry", in Roshdi Rashed, ed., Encyclopedia of the History of Arabic Science, Vol. 2, p. 447–494 , Routledge, London and New York:
"Three scientists, Ibn al-Haytham, Khayyam and al-Tūsī, had made the most considerable contribution to this branch of geometry whose importance came to be completely recognized only in the 19th century. In essence their propositions concerning the properties of quadrangles which they considered assuming that some of the angles of these figures were acute of obtuse, embodied the first few theorems of the hyperbolic and the elliptic geometries. Their other proposals showed that various geometric statements were equivalent to the Euclidean postulate V. It is extremely important that these scholars established the mutual connection between this postulate and the sum of the angles of a triangle and a quadrangle. By their works on the theory of parallel lines Arab mathematicians directly influenced the relevant investigations of their European counterparts. The first European attempt to prove the postulate on parallel lines – made by Witelo, the Polish scientists of the 13th century, while revising Ibn al-Haytham's Book of Optics (Kitab al-Manazir) – was undoubtedly prompted by Arabic sources. The proofs put forward in the 14th century by the Jewish scholar Levi ben Gerson, who lived in southern France, and by the above-mentioned Alfonso from Spain directly border on Ibn al-Haytham's demonstration. Above, we have demonstrated that Pseudo-Tusi's Exposition of Euclid had stimulated both J. Wallis's and G. Saccheri's studies of the theory of parallel lines."
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https://www.mybooksandbeyond.com/whats-new/making-math-fun/
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math
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Making Math Fun: What Educators Can Do
For some students, math is the least enjoyable subject on the daily agenda. If a student isn’t a total guru at it, it can be complicated, boring, and downright frustrating. In addition, it can be just as troublesome for you, the teacher, because you might be grappling with how to make this subject an engaging learning experience for your class. Try these 3 tips for getting the most out of your math class:
#1 Find Relevance and Tell a Story
A leading reason students struggle with math is because they sometimes don’t know why this specific skill is useful. The “Why do I need to know this?” excuse is probably jumping to the front of your mind right now, and that’s exactly why you should try to introduce context of a math solution. Tell a story about your own experience with a genre of math and of a time when you used it effectively. A simple example might be when you were at the grocery store and wanted to buy several of the same item (think: “One apple costs 75 cents, and John wants to buy five of them. How much will five 75-cent apples be?).
#2 Use the Element of Surprise
Take advantage of your own knowledge and use it to show students what makes math unique and interesting. Show them a problem that has a reputation for inspiring awe or intrigue and ask them how to solve it. Or use problems and examples similar to the Birthday Problem to leave learners stunned and wanting to know more.
#3 Use Art
Let’s face it: some of us are more “hands-on” when it comes to learning a new concept. Make sure your students fully understand through unique and fun activities. Use interconnecting building blocks to explain fractions, or have students cut out an animal shape from paper using a protractor to discover how angles work. Try these outstanding math activities from WeAreTeachers.com.
It can sometimes be tricky to get students motivated and excited about math. The stigma surrounding the subject can sometimes lead to boredom, mind-wandering, and frustration if it doesn’t come as naturally to the student as other activities or subjects. But math doesn’t have to be this way. With a little creativity and determination, you can help steer your class toward mathematical success.
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http://www.mathworks.com/help/physmod/sdl/ref/ringplanet.html?nocookie=true
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math
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Planetary gear set of carrier, planet, and ring wheels with adjustable gear ratio and friction losses
The Ring-Planet gear block represents a set of carrier, planet, and ring gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and ring corotate with a fixed gear ratio that you specify. A ring-planet and a sun-planet gear are basic elements of a planetary gear set. For model details, see Ring-Planet Gear Model.
C, P, and R are rotational conserving ports representing, respectively, the carrier, planet, and ring gear wheels.
Ratio gRP of the ring gear wheel radius to the planet gear wheel radius. This gear ratio must be strictly greater than 1. The default value is 2.
Select how to implement friction losses from nonideal meshing of gear teeth. The default is No meshing losses.
No meshing losses — Suitable for HIL simulation — Gear meshing is ideal.
Constant efficiency — Transfer of torque between gear wheel pairs is reduced by a constant efficiency η satisfying 0 < η ≤ 1. If you select this option, the panel changes from its default.
Ring-Planet imposes one kinematic and one geometric constraint on the three connected axes:
rRωR = rCωC + rPωP , rR = rC + rP .
The ring-planet gear ratio gRP = rR/rP = NR/NP. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
gRPωR = ωP + (gRP – 1)ωC .
The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1,2) = (P,R).
The torque transfer is:
gRPτP + τR – τloss = 0 ,
with τloss = 0 in the ideal case.
In the nonideal case, τloss ≠ 0. See Model Gears with Losses.
Gear inertia is negligible. It does not impact gear dynamics.
Gears are rigid. They do not deform.
Coulomb friction slows down simulation. See Adjust Model Fidelity.
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https://www.coursehero.com/file/128048/Business-Statistics-Lecture-Notes-05/
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math
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This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: MN1025 Business Statistics 19 Lecture 5Friday 8/2/2008 TESTING HYPOTHESES: TESTING THE MEAN Reference: Lind et al. , Chapters 9, 10. 5.1 Example: less than 99 defects? Last week we used the T statistic to derive con- fidence intervals for the unknown mean of a nor- mally distributed population. In this lecture we will use the same formalism to answer yes/no questions about the population mean. We are again concerned with a sample drawn from an (approximately) nor- mally distributed population. We start with an ex- ample. A manufacturer has a production line which has had 99 defects per day, on average. A new system is introduced and the manufacturer wants to know if there has been a significant decrease in the average number of defects. Hypothesis testing proceeds in five steps. 5.2 Step 1: Setting up the hypotheses In our example, the previous system had an average fault rate of 99 defects per day. The average fault rate of the new system, denoted by , is unknown. Our test will consider two hypotheses: The Null Hypothesis , H , is that nothing has changed, i.e. that = 99 as previously. The Alternative Hypothesis , H 1 , is that there has been a decrease, i.e. that < 99 or, in words, the new population mean is less than the previous one. In some books, the alternative hypothesis is written as H A or H a . We have to choose between H and H 1 . We will choose, or accept , H (no change) unless there is sig- nificant evidence in favour of H 1 , in which case we say that we reject H . We will see below what ex- actly is meant by this. Notice that we never test an hypothesis in isolation; we always need to know the alternative. 5.3 Step 2: Setting a level of significance The level of significance is the probability of reject- ing the null hypothesis when it is actually true (this is called a type I error ). Commonly used levels of significance are 10%, 5% and 1%. The level of sig- nificance must be set before the sample is taken. To choose, e.g., a 5% level of significance in Minitabs 1-sample t test, click on Options and en- ter a 95% confidence level. 5.4 Step 3: Choosing a test statistic In this chapter, we use T as the test statistic (see lec- ture 4). We will encounter other useful test statistics later in the course. 5.5 Step 4: Setting a decision rule Assume we take a sample of size n from the produc- tion line and compute the sample mean, x , and the sample standard deviation, s . If the average number of defects for the new system, , is less than 99, we expect the sample mean to be also less than 99, i.e., x < 99. But of course, the sample mean could turn out to be less than 99 even if is equal to 99, i.e. if the population mean has not decreased....
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This note was uploaded on 04/17/2008 for the course MN 1025 taught by Professor Schack during the Spring '08 term at Royal Holloway.
- Spring '08
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http://www.slideshare.net/colemama/lesson-planning-9208453
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math
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Planning Components What should be learned? Content Standards Benchmarks How should it be learned? Instructional Strategies Integration of Technology Curriculum Instruction Assessment How should it be assessed? Clear Expectations Use of Rubric
Developing Lessons Student Learning Objectives Who? (Students!) What? (action outcome) When? (outcome related to objective) How much? How often? (related to objective) Assessed? Measured? Evaluated?
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https://www.hellovaia.com/textbooks/math/precalculus-enhanced-with-graphing-utilities-6th/analytic-trigonometry/q-16-in-problems-936-find-the-exact-value-of-each-expression/
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In Problems 9–36, find the exact value of each expression.
The value of the expression .
The given expression is:
Let's take ,
is the domain of the function.
Initially, we have function and the bounds of tan function are going to be in the interval . It represents the range of .
By using the unit circle, we can say that must be equal to , so that we can get .
By using the unit circle, we know that , then
94% of StudySmarter users get better grades.Sign up for free
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http://dianadavis.blogspot.com/2007/04/my-first-published-article.html
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Isoperimetric Regions in Gauss SectorsThere is also another paper that should be published sometime soon in a different journal.
We consider the free boundary isoperimetric problem in sectors of the Gauss plane. The solution is not always a circular arc as in sectors of the Euclidean plane. We prove that the solution is sometimes a ray and we conjecture that the solution is sometimes a "rounded n-gon" which we discovered computationally using Mathematica.
1 day ago
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https://www.physicsforums.com/threads/formula-for-the-strength-of-an-electromagnet.281287/
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math
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Trying to determine the strength of an electromagnet in Teslas, with an iron core. Some sites have the same basic formula but with different units after B= Some use μ0, μr, or μ. Which one to use? For N (the number of turns), is this the general number of turns accounting for multiple layers, or turns per meter (or inches), or what? And L (the length), is it the length of the iron core or the length of the wire used, and should it be in meters or inches? According to this site (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html), a 0.1 meter (4") length solenoid (I'm assuming their talking about the iron core?) with 200 turns, 1 amp, and an iron core with 200 relative permeability is 0.5 Tesla. With 3 amps, this is about 1.5 Tesla and that doesn't sound right. Any help is appreciated, thanks!
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http://www.yaslioglu.com/index.php/how-and-when-to-use-which-fit-indices-a-practical-and-critical-review-of-the-methodology/
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math
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With the help of statistical software programs such as AMOS, Lisrel, R, Matlab and many equivalents most of the complicated research models have become more computable and easily (?) understandable. Even the most complicated and complex models with various relationships can be easily computed with the help of software. Although with slight differences, outputs are consistent and tables are mostly comprehensible. However, with the increasing curiosity and amount of knowledge about the research methodology, these simple looking outputs start to become more complicated and deeper. Even though aforementioned statements seem contradictory, what we imply here is very sound to a mid-level researcher. Because, as knowledge and understanding of statistics deepens questions and doubts about where from, how and why these numbers are calculated increase. Curiosity about the fit indices, chi-square and degrees of freedom, modification indices, covariances and residuals begin to arouse.
In this review and commentary, we focus on the infamous CMIN (or chi-square), different model definitions, and calculation of fit indices by the help of these models; avoiding statistical jargon as much as possible. With the aim of putting an end to a decade long debate; when and how to use which fit indices, what they really indicate and which numbers refer to good or bad fit is also discussed.
Keywords: Fit indices, CFA, SEM, Chi-Square, discrepancy functions, Modification Indices, Maximum Likelihood
In order to be able to comprehend structural equation modelling, confirmatory factor analysis and fit concepts, some literature and definitions are necessary to clarify. First of all, we have to begin with the definition of the models mentioned in the software. These are most of the time confusing, not only because of their nature but they are never really described anywhere in the process. Secondly, the estimation methodology is to be defined. Most SEM users, no matter what software they use, are accustomed to the “Maximum Likelihood Estimation”, but a great deal of these researchers have no idea what it is and what it does. Finally, there are several concepts which need to be clarified before discussing fit of the models. Some of these concepts are CMIN, Chi-Square, Log-Likelihood (see also Maximum Likelihood), C and F values, NPAR, p and P, fit and index, PRATIO. Despite they sound familiar, most of the time are misleading, confusing, bewildering or even confounding. We see them, we think we know them, but we never think about what they really are and where they come from. Alongside discussion of several concepts and terminology, the necessary values and key-points will be discussed throughout the paper.
Despite slight naming differences among statistical software, there are three main models essential for calculation of SEM and CFA. First is the one which researcher want to investigate, this model is called “default model”, “structural model” or “measurement model”. Following is the one in which every measured variable is accounted as independent of each other and any latent variable. This is called “independence model”; it also is the “baseline/null model” for CFA and SEM – we will discuss this confusion further below. Finally, “saturated model” in which all variables covary with every each other.
Since its name will be mentioned several times here, before we begin defining models, an introduction to a fairly common concept called parsimony is also essential. Parsimony means simplicity, so the parsimonious models are simple models with less parameters to be estimated. Of course, parsimony of a model can only be judged relatively, often comparing nested models.
Nested models are the models in which one of the models contains all the variables, parameters and interactions of the other and at least one extra term (parameter, constraint e.g.). Extended model is called the full (or complete) model, and abridged is called the restricted (or reduced) model. Hence; saturated, default and independent models are all nested models, where saturated is the full model and default is the restricted version of it (so is the independent).
Besides, there is a ratio called PRATIO (parsimony ratio) which compares the degrees of freedom for default model (df) and independence model (dfi). Its formula is simply; PRATIO=df/dfi. This ratio is also used to calculate “Parsimony adjusted measures of fit” or namely PNFI and PCFI. These will be discussed later in this paper.
So, aforementioned models are;
Saturated model: This is the fully explanatory model in which per every degrees of freedom, there are as many parameter estimates. Therefore dfs=0. That is, every variable in the model co-varies with every each other. This is the most general model possible. Goodness of fit measures are “1.0” for this model. Besides, some measures such as RMSEA cannot be computed for saturated model. And because saturated model, by its nature, is the most un-parsimonious model possible, parsimony-based fit measures (PNFI, PGFI etc.) will be 0. It is an inane and illogical model in the sense that it is guaranteed to fit perfectly to any set of data collected. Any other model in the same research (that also implies the same dataset) is a nested (constrained) version of the saturated model.
Null or baseline model (aka independence model in AMOS and some other software): The comparison model is frequently used as the “baseline model”, differences from which must be significant if a proposed structural model (the one with straight arrows connecting some latent variables – also called the default model in AMOS) is to be investigated further. Although the term “baseline model” implies comparison with an alternative that is more complex than a no-effect hypothesis. The terms “naïve model” and “null model” better indicate the kinds of models that researchers have used as baselines so far (Schwab, A., & Starbuck, W. H., 2013).
In the SEM or CFA baseline model, the covariances in the covariance matrix among the latent variables are all assumed to be zero. Despite its official name, AMOS and several other statistical software name “null/baseline” model as “independence model”. It makes sense because the independence model is the one which assumes all relationships among measured variables are “0”. Independence model is an uncorrelated variables model and for computation, many fit measures such as TLI=NNFI, RFI, IFI, NFI, CFI, PNFI and PCFI necessitate a “null/baseline” model in comparison with researchers’ measurement model. This model assumes that variables or latent factors of a construct are uncorrelated. Unlike the saturated model which have a parsimony ratio of “0”, the independence model has a parsimony ratio of “1” . Most of the fit measures will have a value of “0” since this is the worst model possible, whether parsimony adjusted or not. In rare occasions, some fit indices such as RMSEA and GFI may have a non-zero value depending on the data (Schermelleh-Engel, K., et.al., 2003).
Default (structural or measurement) model: This is the researcher’s measurement or structural model (AMOS calls it the “default model”). In comparison to saturated model, this model is always more parsimonious. And it is always better fitting than the independence model when compared using fit indices. Thus, the default model will have a goodness of fit between the perfect fitting “saturated model” and worst possible model with lowest explanatory power, “the independence model”.
Estimation and Maximum Likelihood Estimation
Even though there is no simple way to describe Maximum Likelihood Estimation, it is essential to say this method is the default for many statistical software in order to be able to calculate many of the fit indices. Its complexity should not be taken for granted. However, some concepts about the estimation process and routines can be elaborated.
There are several estimation techniques, most of them perform one of three things (Templin, J. 2015),
- Minimize some function: If the estimation process includes the word “least” in its name, then minimization should be expected. Most of these techniques minimize the squares of the error terms (or std. deviations). Types of least squares techniques include; Ordinary, generalized, weighted, WLSMV, iteratively re-weighted and diagonally weighted. Usually conducted as a last resort.
- Maximize some function: Mostly, these gold standard of estimation techniques comes with the name “maximum” in it. Such as; maximum likelihood, residual maximum likelihood, robust maximum likelihood.
- Usage of simulation for sampling from data: These use recent advanced techniques of re-sampling by the help of recent simulation methods. Some of these include; Gibbs sampling, Metropolis-Hastings algorithm, Monte Carlo simulation, Bayesian Markov Chain Monte Carlo. Typically used for complex models where maximum likelihood is not applicable or in which some prior values are necessary.
(1) MLE is a procedure to determine best model parameters (reality) that fit the given data with maximizing log-likelihood function to estimate parameters. Formulas here are quite mathematical and mostly statisticians’ work to cover. But one can immediately ask why not likelihood function but log-likelihood. Simply, mathematically its asymptotes meet at the same values, and it is way easier to find a maximum of log-likelihood since it includes “sums” rather than “products” as likelihood function does. And one can easily understand that maximization of products is harder than sums. Because, we need derivatives of functions to find out asymptotes, it is easier to take derivatives of sums.
(2) MLE also helps compare different models with the same data using some information criteria. This is mathematically even more advanced. There are formulas called information theory techniques. Most common one is Kullback-Leibler information criterion which quantifies the distance between two given models. Since depending on full probability density functions, it is very hard to calculate (Burnham, K. P., & Anderson, D. R., 2001). Japanese statistician Hirotugu Akaike (1987) proved that K-L information could be estimated based on maximum log-likelihood and created AIC (Akaike Information Criterion). Its formula is;
AIC = -2(ln(ø|x)) + 2K
It actually is “-2” times log-likelihood added by “2” times number of parameters. Both log likelihood and AIC are only meaningful when compared to other models with same data (they are relative not absolute). They have no meaning by themselves, so higher or lower the values mean nothing without comparison. Moreover, if you are comparing two “bad” models, they can only mean one is better than the other, but cannot say anything about how bad/good they are. AMOS reports several similar model comparison values such as AIC, BCC, BIC, CAIC, ECVI and MCVI. Keep in mind that these values are only for models’ comparison and relative, they do not indicate a fit for models. Simply, if you are to compare two nested models among each other they are handy, if not just ignore them. Complicated, poorly fitting models get high scores. For comparison purposes lower the values the better .
Some other “sine qua non” concepts
Since, we now are aware maximum likelihood estimation and log-likelihoods, we can talk about chi-square (c2) values calculated per model in AMOS. It is named as “CMIN” which allegedly stands for “chi-square minimum”. If one is accustomed to basic statistics, then should also know about chi-square test and it stands for “independence”. This means, without terminologically using definition of hypotheses, if a c2 value is statistically significant (p<0.05) then these two observations are “independent” from each other. In CFA and SEM, it is potentially unwanted. We want our measurement model (default model in AMOS) to be “not independent” from the data of observations. The problem is that it is not easy to comprehend how CMIN is calculated. As one googles chi-square, will most probably end up with what we call “Pearson Chi-Square” formula saying something like: “if you subtract expected values from observed values and square them, then divide them by expected values, you end up with chi-squared for each observation”. If you add them all, you find a summed chi-Square value. This is what confuses most people. Because we have observed values on one side of the arrow since factors are unobserved (latent) variables. Moreover, this CMIN is referred as a fit index, therefore it should be comparing two models. Not observations. What are these two models? To evaluate the fit of the factor model, its “Function of log likelihood value” has to be compared to that of some less constrained model, such as the saturated model. The chi-square test compares the model (default model) to the saturated model (should fit about the same). Many fit indices compare the model to the null/baseline model instead (baseline model should fit much worse than measurement model). AMOS uses function of log-likelihood to report CMIN, chi-square is calculated through multiplying number of samples and FML (function of ML) therefore C=n(FML). C value is derived from F, and this value is also called “minimum discrepancy function”. As discussed earlier in the model definitions section; saturated and default models are nested models, where saturated is the full and default is the restricted. Difference between function of log-likelihood of two nested models also gives the chi-square. If one simply calculates function of log-likelihood for saturated and default models and take the difference they end up with the chi-square for default model. Number of parameters to be estimated are also subtracted (of course saturated model has more NPAR) to end up with “df” for default model. Eventually, chi-square distribution table can be used to calculate probability and test the null hypothesis of independence. Number of parameters to be estimated defines the complexity of the model. Models with many parameters to estimate are called complex. Less parameters means the model is simple. In AMOS and other programs number of distinct parameters to be estimated is called “NPAR”. Distinct word is also important here, for instance if two or more parameters are required to be equal to each other, then these count as one, not two. This leads us to another important concept in statistics; degrees of freedom (df). Degrees of freedom is the NPAR (q) subtracted from number of sample moments (p) so the formula is (df=p-q). One of the main fit measures (perhaps should be called “THE” fit measure) is CMIN. It is the minimum value of C, of the discrepancy. Otherwise called as chi-Square of likelihood ratio test. And, since chi-square statistics all require a significance value, “p value” is marked as “P” for testing the hypotheses that the model fits perfectly in population. As discussed earlier in this paper, it is the discrepancy between perfectly fit model (saturated model) and default model. Increase in NPAR (also implying decrease in df), declines log-likelihood for the same sample, nested models. This means, saturated model has always lower value for function of log-likelihood. Sample size increases the likelihood functions; despite the sample size is the same in the nested models, this does not mean the difference stays the same with smaller sample sizes. Chi-square test value increases as the sample size increases, and this makes the values significant since the (df) stays the same. Sounds complicated, but think of it as a test statistic of independence, getting larger as the number of samples increases, which makes it more significant at a time. If two models (in our case it is saturated and default models) are independent of each other then they simply are not fit to each other. This is true, but not necessarily correct. And this is the reason that we need more indices to be able to look at. Here are some quotes directly from respected statisticians/researchers: “The power of the test to detect an underlying disagreement between theory and data is controlled largely by the size of the sample. With a small sample an alternative hypothesis which departs violently from the null hypothesis may still have a small probability of yielding a significant value of. In a very large sample, small and unimportant departures from the null hypothesis are almost certain to be detected.” (Cochran, 1952) “If the sample is small, then the test will show that the data are ‘not significantly different from’ quite a wide range of very different theories, while if the sample is large, the test will show that the data are significantly different from those expected on a given theory even though the difference may be so very slight as to be negligible or unimportant on other criteria.” (Gulliksen and Tukey, 1958, pp. 95–96) “Such a hypothesis [of perfect fit] may be quite unrealistic in most empirical work with test data. If a sufficiently large sample were obtained this statistic would, no doubt, indicate that any such non-trivial hypothesis is statistically untenable.” (Jöreskog, 1969, p. 200) Do they mean that we should limit the sample size? Despite they sound in that manner, one should also know that “Significant properties of maximum likelihood (ML) estimate are consistency, normality and efficiency. However, it has been proven that these properties are valid when the sample size approaches infinity. Many researches warn that a behavior of ML estimator working with the small sample size is largely unknown.( Psutka, J. V. and Psutka J., 2015)” One logical way to assess fit is to find the discrepancy value (CMIN) per degrees of freedom, given that it tends to increase with number of sample moments. CMIN/df value can give the researcher an absolute value for fit. Arguments begin just here, because various researchers have suggested various acceptable values for this value. Wheaton and colleagues (1977) suggested 5 or less, some suggested as low as “2”, or as high as “5”. Byrne et.al. (1989) puts forward that c2/df > 2 indicates bad fit.
Values less than “1” will probably require insignificant CMIN values, therefore will not be even necessary to calculate. Anything close to “1” should be very good fit. But how far apart could it fall from “1”? Let’s remember the calculation of degrees of freedom (df=Sample moments – number of distinct parameters). Thus, df increases with sample size, so does X2; then here we should first look at NPAR. The default model’s chi-square calculation, not by chance, is the difference of NPAR between saturated model and measurement (default) model. If “df” for default model is calculated taking number of parameters into account, this means we can ignore it simply because it is already taken into account. Sample size should be the only variable here to decide the value for CMIN/df cut point. Here we can use common sense,
(1) If the commonly accepted minimum sample size in a factor analysis is at least 50 and also 5 times the number of variables. So minimum sample for a decent number of variables as around 150 (there is no real calculation here but merely observation).
(2) If minimum number is around 150, doubling this number seems fair for a cut point. Let’s say 300 here is a cut point for sample size to categorize CMIN/df value.
(3) Then we can say, looking to our commonly mentioned cut points of CMIN/df; if sample size is between 150-300 then 3.5 (median of 2-5) can be taken as cut point to assess the fit. If sample size is above 300, then “5” can be taken as the criterion. More than 5 c2 per degrees of freedom indicates a bad fit, no matter what. This value should be less, please read further.
(4) To decide whether a CMIN/df is good enough one should also compare the worst model’s (independence model) CMIN/df value. These values should be significantly different from each other. Because, if worst model is fit enough, this requires measurement model to be even much fitter. Luckily, we have fit indices comparing these values .
Indices: fit and others
Before beginning to discuss anything about fit, we have to make a short list of things those are often confused by researchers. Researchers MUST keep in mind that;
(1) Fit has very little to do with validity: Most researchers confuse fit with validity. Validity is a much broader concept to begin with.
(2) If model is fit this means your data is consistent with what you want to measure,
(3) If model is fit then it is useful model,
(4) If model is fit then it will probably be able to replicate in other researches,
(5) If model is fit, researcher can stop adding covariances among residual error terms,
(6) If model is fit then researcher can proceed with further evaluation of construct and other validities,
(7) If model is fit, it is NOT necessarily correct or valid,
(8) A good fitting model is ONLY “reasonably consistent with the data”.
Strictly keeping the list above in mind; there are several indices to measure the fit of the proposed measurement model (default model). And also, even more debate about what to use and when to use. Mostly, simple models, with moderate number of sample observations have good fit. As the models get complicated and sample size increases these fit indices starts to drop. Frequently, researchers face the dilemma of choosing between fit indices because while some are above cut points, others are below expected values. Here are some problems; what are the cut points for indices? Is there a commonly accepted value for each? What index is the best for models with many variables? After being able to answer all these questions, another problem may rise: What if some of them are above expected values and some are not? Who tells us which to go for? And finally, if one can solve all these issues, how are two or more similar models with the same data compared? In this section we will try to answer these questions with avoiding complicated, sophisticated jargon of statistics. This does not mean we will leave thing out; this implies we will as “keep it simple and stupid” as possible.
Fit indices (measures) in AMOS are categorized into sub groups. These are; absolute fit indices, relative/incremental fit indices, parsimony (check above) fit indices, non-central chi-square distribution (population discrepancy based) fit indices, information theoretic fit indices and fit measure based on sample size.
Absolute fit indices
Absolute fit indices indicate fit without comparing the default model to anything fot the best fit model. Despite there is a comparison with the best fit model (saturated model) the indices indicate the model fit themselves. CMIN and CMIN/df are the basis of absolute fit indices discussed above. Other absolute fit indices include RMR and GFI.
RMR and GFI
It is the Root Mean Squared Residuals, therefore also called RMSR or SRMR. This value is simply what it says. It squares the amount by which the sample (measurement) covariances differ from their estimates. It is much like, average of sum of squared errors (aka residuals) in regression. Yet, measurement units differ from each other it is more relevant to carry out the calculation based on residual correlation matrix. Usually an RMR value (based on correlations) less than 0.05 indicates a good fit. This unfortunately is not a part of AMOS, but a script or manual calculation will sort out this problem. The smaller the value the better.
Thanks to AMOS and LISREL, a more advanced version of RMR is calculated under the name of GFI (Goodness of fit). GFI compares (by dividing) squared weighted sum of the variances of measurement and estimation where weighting depends on estimation method. Much like R2 in regression, it takes a value between “0-1”. It is not suggested to use this index since it is affected by sample size. There also is a “df” adjusted version called AGFI, if one wants to use it, should prefer this one. A “GFI” value larger than 0.95 can be accepted as good fit. Preferably larger in small sample sizes and less parameters. GFI is greatly affected by sample size, so simply do not use this index (Kenny, D.A., 2005).
Incremental Fit Indices
These fit indices are also called relative or comparative indices. Because these indices or measures are based on the idea that things may be worse. There always (hopefully always, if not do not even bother testing the model) is a worse model than default model, where each observation is taken into account as independent. Independent model is also called, because of its nature for comparison, baseline or null model.
Researchers may immediately ask “Why the worst model but not the best?”. Answer is hidden in the calculation. As defined earlier, C (in Amos CMIN or in some cases F ) value is calculated with the help of perfectly fit model, which is also the “saturated model” namely. And this model is the best fit model to the data. Please remember, fit and validity are two different things!
NFI and TLI
Relative fit measures are NFI (Normed Fit Index), RFI (Relative Fit Index), IFI (Incremental Fit Index), TLI (Tucker Lewis Index) and CFI (Comparative Fit Index). NFI is calculated using minimum discrepancy (CMIN – Chi-Square) of default model with CMIN of independent model. NFI gets a value between “0-1”, value of “1” represents perfect fit to data. Higher the difference between model and worst fit, bigger the value. A value of 0.90 and above is accepted to represent acceptable fit. The fit can be overestimated if the number of parameters is increased. RFI is the “degrees of freedom” corrected version of NFI. Therefore, solves the issue of parameter increase. Gets a value between 0 and 1 like NFI and values above 0.90 is acceptable. For both NFI and RFI, smaller sample size tends to inflate the values, therefore mostly suitable for larger samples. For smaller sample sizes 0.95 is acceptable.
CFI is also “df” corrected versions of NFI. This time not divided but subtracted. So, for every parameter estimated there is just one penalty. With larger samples and low number of parameters change, values tend to be very close to NFI. CFI may get values larger than “1” but always reported “1” as maximum. Value of “1” does not indicate perfect fit, but simply means “df” of default model is larger than chi-square of the default model.
TLI, also called Non-normed fit index, very similar to RFI. Lower “chi-square to df ratios” indicates a better fit. TLI and CFI depends on the average size of correlations in the model, if the average correlation among variables is low, values are also low. That being said, if several experimental variables (uncorrelated) added to the default model, then this decreases the value of TLI (also CFI). Suggestion here can be; if the research model has several experimental or control variables, then TLI and CFI are not suggested. Values above 0.90 is acceptable, 0.95 indicates good fit. If the model has very strongly or very weakly correlated variables then suggestion is to ignore these indices.
Fit measures based on population discrepancy
F0 and RMSEA
As discussed earlier, the function of discrepancy or log-likelihood, in Amos is presented as chi-square. “n” value being sample size minus number of groups (n=N-g ; g is mostly 1 in our cases) Steiger, Shapiro, and Browne (1985) proved, (C=n.F0) under certain conditions, has a noncentral chi-square distribution with df degrees of freedom and non-centrality parameter Delta=(C -df) =nF0. Resulting F0= [(C-df) / n] (or simply and generally; F0= [(C-df)/ (N-1)]. Non centrality parameter is then used to compare two nested model such as default and saturated models. Problem here is F0 always favors complex models, will never favor the simpler model or in other words parsimonious model. Steiger and Lind (1980) suggested compensating for the effect of model complexity by dividing F0 by the number of degrees of freedom for testing the model. This ratio then gives us “mean square error of approximation” (this makes sense since discrepancy function is a square). Taking the square root of the resulting ratio gives the population “root mean square error of approximation” or simply RMSEA. The calculation in mathematical terms, favors larger sample size or df. And just like TLI, if chi-square equals to df, then the value becomes “0”. One can simply expand the calculation by rewriting F0 as “(c2-df) /n”. Formula becomes; “[(c2-df) / (df.n)]” and size effect of “df” will be more obvious. Smaller the “df” larger the RMSEA, even with very small chi-square . This may indicate a “bad fit” since RMSEA values below 0.08 indicates an acceptable and 0.05 indicates a good fit. Suggestion is then to use RMSEA in high df values, not even compute with low values. Or at least be very cautious when you have low df.
PCLOSE is actually a “p” value where we are familiar to see in almost every statistical analysis. However, this time not to be confused with the p value of chi-square (where H0; RMSEA=0) which stands for exact fit. Makes sense because it stands for a “close fit”. Browne and Cudeck (1993), based on experience with SEM and RMSEA, argue that a RMSEA of 0.05 or less points to a good (close) fit. Hence calculates p value for null hypothesis of H0; RMSEA<=0.05. When PCLOSE is significant then null hypothesis is rejected, indicating lack of close fit. Thus, PCLOSE should be insignificant to indicate good fit.
Parsimony adjusted fit indices
James and colleagues (1982) and Mulaik and colleagues (1989) suggest adjusting NFI and GFI by multiplying indices with a ratio called PRATIO. PRATIO, as mentioned earlier in related section of this paper, compares the degrees of freedom for default model (df) and independence model (dfi). Formula is simply PRATIO=df/dfi. AMOS also calculates PGFI by using the same method. Usually and debatably values above 0.80 indicated a good fit. Quotation below clarifies the use of parsimony indices:
“Although many researchers believe that parsimony adjustments are important, there is some debate about whether or not they are appropriate. I see relative fit indices used infrequently in the literature, so I suspect most researchers do not favor them. My own perspective is that researchers should evaluate model fit independent of parsimony considerations, but evaluate alternative theories favoring parsimony. With such an approach, we would not penalize models for having more parameters, but if simpler alternative models seem to be as good, we might want to favor the simpler model.”(Newsom, J. T., 2018)
Modification indices show us how much chi-square (test statistics) will decrease if covariance is added among error terms of mentioned variables. It is only informational for CFA or SEM. Given a poorly-fitting model, you may want to know what path(s) you could add to make it better. If you change something according to MIs then it is exploratory in nature, be alert, this will be further evaluated below.
Also, adding paths looking to MIs makes the consecutive models nested to each other. Therefore, one can use the model comparisons based on chi-square as mentioned below.
But how much MI value is worth intervention? Actually, there is no certain limit to this. MI values show the test statistics (chi-square or CMIN) change since models are nested by nature. Change in CMIN may not mean much if it does not change the fit. Researcher may individually calculate a rough estimate for CMIN/df change by dividing the highest MI value with the “df”. If the decrease in CMIN/df seems significant then the covariance or path may be added. If not, then seems negligible. This can be done as many times the model is re-estimated. However, user should be cautious in their use of MIs. If new models are developed with the help of MIs, then it must be reported. Do not pretend that you have a theoretical reason for part of a model that was put there because it was suggested by MI indices table! This is simply fraud. Using MIs makes the analysis exploratory by nature. So, if you are to use MI to correct the model, then this should be reported as exploratory SEM. Second option is you reserve a part of the data to first explore, then use the remaining part to confirm (lesser evil).
Comparing two good models among each other is a nice comparison. If you are comparing two bad models then it is a burden and moreover it leads to nothing but choosing the lesser evil. “How good your model is?” is not described in this paper. Because it not only depends on fit indices or other values such as AVE, MSV or ASV (also not described here) but also theoretical background and other validity questions. Model comparisons only and simply compares two or more models. Do not assign more value to them, and do not fall into the mistake calling a better model as valid!
If one wished to compare models there are few criteria. Some of these information criteria are also reported with AMOS.
• The model with lower AIC (mentioned before) or BIC (Bayesian information criteria-Not mentioned in this paper) is better. But again, these are relative numbers, they do not indicate an absolute fit. Simply note down the models’ AIC and BIC values, and compare them.
• If models are significantly different from each other, then complicated version is better
• If models are not significantly different, then simpler version is preferable.
If models are nested (such as default and saturated models mentioned earlier) then;
• Log likelihood functions can be calculated and difference among them with df can be used in chi-square distribution to test their difference. Added paths or deleted paths on a model makes them nested to each other. So, one can compare their log-likelihoods. (This is not in AMOS by default, but R, Matlab or AMOS scripts can be used to calculate).
Rule of thumb, CFA is used to “confirm” a factor structure or a measurement model. Therefore, any changes made to this model will take it apart from confirmation, and will make it exploratory in nature. Model comparisons are mostly suggested for exploratory SEM or path model comparisons.
Conclusion and notes on fit indices
Several researchers and statisticians suggest different values and cut-points for different so-called useful fit indices. Individual researchers should keep in mind some notes about fit indices:
• Normality affects absolute fit indices. Non-normal data inflates chi-square and therefore decreases absolute fit values. Incremental and population discrepancy measures are less affected (Kenny, D. A., 2015).
• Number of variables affect fit. Increasing the variables decreases the fit. RMSEA especially increases (we do not want this) as more variables are added. Indices such as NFI, TLI and CFI are relatively more stable but also declines slightly in such case. All probably because of an inflated chi-square.
• BIC, RMSEA and TLI requites the parsimony the most (also respectively among each other), NFI and CFI requites it the least.
• NFI does not adjust for sample size, increasing sample size decreases the fit value. TLI and CFI is relatively stable with sample size and variation decreases between larger sample sizes. RMSEA however declines with sample size. Larger sample researches favor for RMSEA.
• Testing for exact fit, researcher should go for insignificant CMIN. Which is almost always impossible (Unless with very few variables and a small sample size).
• To assess a good or close fit researchers may go for different values;
o RMSEA (below 0.05 to 0.08): If the model is parsimonious and sample size is large then below 0.05 or closer values, otherwise 0.08 or below.
o CFI, RNI, NFI, TLI, RFI, IFI (above 0,90 to 0,95): Depending on variable size, variables below 10-12 requires 0.95 for close fit, variables above 12 may require 0.90 as cut-point. Always, higher the better.
o RMR below 0.05 or 0.08 for larger samples and GFI, preferably 0.90 or above. But, preferably do not use these indices.
o For comparing models (almost always nested models) information criteria such as (AIC, BIC e.g.) are useful.
o For gradual comparisons and model refining Modification Indices are very beneficial.
o Assigning names to nested models in AMOS and using these to calculate likelihood ratios is the best way for model comparisons. (Requires an advanced knowledge and expertise in AMOS)
After all discussions some essential fit indices to take into account are; CMIN and CMIN/df, F0, RMSEA and PCLOSE. Optionally, NFI, TLI and CFI can be used. Researchers must determine a rationale for fit criteria, mention those rationale in their papers, and perhaps regard reporting several different types of fit indices. There is no one set of rules to use which, but researcher can take into account the size of the sample, number of variables, fit indices’ pros and cons. And finally, at least referring to one index from every different group of indices that we mentioned earlier in this text may reduce the criticism for the fit of the model.
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AMOS, Lisrel, R, Matlab ve birçok benzer istatistiksel yazılım programlarının yardımıyla, karmaşık araştırma modellerinin çoğu daha hesaplanabilir ve kolayca (?) anlaşılabilir hale gelmiştir. Hatta birçok farklı ilişkilere sahip, karmaşık modeller bile yazılımlar yardımıyla kolayca hesaplanabilmektedir. Aralarında küçük farklılıklar olmasına rağmen, çıktılar genellikle tutarlıdır ve oluşan tablolar çoğunlukla anlaşılabilirdir. Bununla beraber, araştırma metodolojisi hakkında artan merak ve bilgi miktarı dolayısıyla, bu basit görünümlü çıktılar daha da karmaşıklaşmaya ve derinleşmeye başlamıştır. Sözü edilen ifadeler çelişkili gözükse de bu noktada ima edilen durum orta seviye bir araştırmacı için oldukça tanıdık gelecektir, çünkü bir araştırmacının istatistik bilgisi ve anlayışı derinleştikçe, bu rakamların nereden, nasıl ve neden hesaplandığına dair sorular ve şüpheler artmaktadır. Bu sorular ve şüpheler uyum indeksleri, ki-kare ve serbestlik dereceleri (Degrees of Freedom), değişiklik indeksleri (Modification Indices), kovaryanslar ve artıklar (residuals) hakkında merak uyandırmaya başlamaktadır. Bu doğrultuda, istatistiksel jargondan mümkün olduğunca kaçınarak CMIN (ya da ki-kare), farklı model tanımları ve bu modellerin yardımıyla uyum indeksi hesaplamalarına odaklanılmaktadır. Tüm bunlarla birlikte bu çalışmada, on yıllık bir tartışmaya da son vermek amacıyla; hangi uyum indekslerinin ne zaman ve nasıl kullanılacağı, tam olarak neyi belirttikleri ve hangi değerlerin iyi veya kötü uyum anlamına geldiği tartışılmaktadır.
Bu çalışmada tartışılmakta olan, yapısal eşitlik modellemesi, doğrulayıcı faktör analizi ve uyum kavramlarını kavrayabilmek literatürde olan bazı tanımların netleştirilmesi gerekmektedir. Öncelikle çoğu zaman kafa karıştırıcı olabilen, araştırma sürecinin birçok noktasında yeterince açıklanmayan ve istatistik işlemlerin yapılması için kullanılan yazılımlarda bulunan modellerin tanımlanması ve daha sonra da tahmin yöntemlerinin açıklanması yerinde olacaktır. Çoğu “yapısal eşitlik modellemesi (SEM)” yöntemi kullanan araştırmacı hangi yazılımı kullanırsa kullansın “Maximum Likelihood” yöntemine alışır ancak büyük bir kısmının bu yöntemin gerçekte ne olduğu ve ne yaptığı hakkında hiçbir fikri yoktur. Ayrıca modellerin uyumunu tartışmadan önce açıklığa kavuşturulması gereken birkaç kavram vardır. Bunlar; CMIN, Ki-kare, Log-Likelihood (Maximum Likelihood), C ve F değerleri, NPAR, p ve P, uyum ve indeks, PRATIO. Bu kavramların çoğu tanıdık gelmelerine rağmen, çoğu zaman yanıltıcı, kafa karıştırıcı, şaşırtıcı ve çelişkili olabilmektedir. Genellikle bu kavramlar, çeşitli araştırmalarda görülmekte ve bilindiği düşünülmektedir ancak gerçekte ne olduklarını ve nereden geldikleri üzerinde düşünülmemektedir. Bu sebeple bu çalışmada birçok kavram ve terminolojinin tartışılmasının yanı sıra, gerekli değerler ve önemli noktalar ele alınmıştır.
Ayrıca Türkçe genişletilmiş özette yer verilemeyen ancak makalede İngilizce olarak ayrıntılandırılmış konular:
- Yuvalanmış modeller (nested models), araştırma modeli, doymuş (saturated) model, bağımsızlık (independence) modeli gibi kavramlar ve bu modellerin uygunluk değerlerini hesaplarken nasıl kullanıldığı.
- Maximum Likelihood yönteminin faktör analizinde ve uygunluk değerlerini hesaplamada niçin önemli olduğu ve tam olarak ne yaptığı.
- Ki-Kare kavramının ayrıntılı olarak incelenmesi ve neden uygunluk değerlerinin en önemlisi olduğunun tartışılması.
- Tüm uygunluk istatistiklerinin ayrıntılı açıklaması, benzerlik ve farkları, güçlü ve zayıf yönleri.
- Düzeltme indislerinin (Modification Indices) ne olduğu ne şekilde kullanması gerektiği.
Bazı araştırmacılar ve istatistikçiler, uyum indeksleri için farklı değerler ve sınırlılıklar belirlemektedir. Bu nedenle araştırmacılar uyum indeksleri için şu noktaları akılda tutmalıdır:
- Normallik mutlak uyum indekslerini etkilemektedir. Normal olmayan veriler ki-kareyi arttırır ve böylece mutlak uyum değerlerini azaltır (Kenny, D.A., 2015).
- Değişken sayısı uyum indekslerini etkilemektedir. Değişkenlerin artması uyumu azaltır. Yeni değişkenlerin eklenmesi yoluyla, istenmeyen bir durum olan RMSEA’nın yükselmesi de mümkündür. NFI, TLI ve CFI gibi indeksler nispeten daha kararlı bir yapıda olsa da değişken sayısına göre ufak azalmalar gösterebilir. Bu durumun sebebinin de ki-karenin artması olduğu tahmin edilmektedir.
- BIC, RMSEA ve TLI modelde sıkılığın (parsimony) karşılığını verirken, NFI ve CFI bunu en az ödüllendiren indekslerdir.
- NFI örneklem büyüklüğüne göre kendini ayarlamaz, artan örneklem büyüklüğü uyum değerini azaltır.
- TLI ve CFI değerleri örneklem büyüklüğü ile nispeten daha kararlı bir ilişki içerisindedir ve örneklem büyüklüğü arttıkça değişkenlik azalır. RMSEA da örneklem büyüklüğü ile düşüş göstermekte, büyük örneklem büyüklükleri RMSEA’nın lehine bir durum ortaya koymaktadır.
- Kesin bir uyumluluk için, araştırmacı CMIN değerinin anlamsız olmasını beklemelidir. Ancak bu durum neredeyse her zaman anlamsızdır. (Çok az değişken ve çok küçük bir örneklem büyüklüğü olmadığı sürece)
- İyi ya da tam uygunluğun olup olmadığını değerlendirmek için araştırmacılar farklı değerler kabul edebilmektedir;
o RMSEA (0,05 ve 0,08’in altında): Model sıkı (parsimonious) ise ve örneklem sayısı fazla ise 0,05’in altında ya da ona yakın değerler olması, aksi takdirde ise 0,08’in altında olması beklenir.
o CFI, RNI, NFI, TLI, RFI, IFI (0,90 ve 0,95’in üstünde): Değişken büyüklüğüne bağlı olarak değişmektedir. 10-12 değişkenden az olan durumlar 0,95 ya da ona yakın bir uyum gerektirmekte iken 12’den fazla değişkeni olan durumlar ise için sınır nokta 0,90’dır. Bu değer için daha yüksek olması her zaman daha iyidir.
o Daha büyük örneklemler için RMR’nin 0,05 ya da 0,08’den küçük ve tercihen GFI’nin 0,90 ya da üstünde olması beklenir. Ancak bu indekslerin tercihen kullanılmaması öngörülmektedir.
o Modelleri karşılaştırmak için AIC, BIC gibi kriterler daha yararlıdır.
o Aşamalı karşılaştırmalar ve model arındırma için Modifikasyon İndeksleri (Modification Indices) çok faydalıdır.
o AMOS’ta iç içe geçmiş modellere isim atamak ve onların olasılık oranlarını hesaplamak model karşılaştırmaları için en iyi yöntemdir. (AMOS konusunda ileri düzeyde bilgi ve uzmanlık gerektirir.)
Tüm bu tartışmalardan sonra dikkate alınması gereken bazı temel uyum indeksleri; CMIN ve CMIN/df, F0, RMSEA ve PSCLOSE’dir. İsteğe bağlı olarak NFI, TLI ve CFI de kullanılabilir. Bunlar doğrultusunda araştırmacıların uyum kriterleri için mantıklı gerekçeler belirlemeleri, bu gerekçeleri makalelerinde belirtmeleri ve birkaç farklı uyum indeksi ile karşılaştırmalar yapmaları gerekmektedir. Bu noktada kullanılması gereken kurallar bütünü bulunmamaktadır ancak araştırmacı örneklem büyüklüğünü, değişken sayısını, uygun endekslerin artılarını ve eksilerini dikkate alarak karar vermelidir. Son olarak, bu çalışmada bahsedilen her farklı indeks grubundan bir indekse atıfta bulunmak, modelin uyumuna yönelik eleştirileri azaltacaktır.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100304.52/warc/CC-MAIN-20231201183432-20231201213432-00437.warc.gz
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CC-MAIN-2023-50
| 48,066 | 128 |
https://curatedsql.com/2021/05/11/
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math
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The longest streak in roulette purportedly happened in 1943 in the US when the colour red won 32 consecutive times in a row! A quick calculation shows that the probability of this happening seems to be beyond crazy:
So, what is going on here? For once streaks and clustering happen quite naturally in random sequences: if you got something like “red, black, red, black, red, black” and so on I would worry if there was any randomness involved at all (read more about this here: Learning Statistics: Randomness is a strange beast). The point is that any sequence that is defined beforehand is as probable as any other (see also my post last week: The Solution to my Viral Coin Tossing Poll). Yet streaks catch our eye, they stick out.
There’s one critical assumption in this post, which is that the game is fair, in that each event has an equal probability of happening. But as a Bayesian, if a roulette table hits red 32 times in a row, it certainly opens the door to the idea that maybe the odds on that table with that dealer aren’t quite equal between red and black.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511284.37/warc/CC-MAIN-20231003224357-20231004014357-00003.warc.gz
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CC-MAIN-2023-40
| 1,077 | 3 |
http://mathhelpforum.com/calculus/56961-limit-proof.html
|
math
|
Let and be two sequences in such that and both of which converge. Show that and converge.
I'm able to show that if and converge then and both of which converge.
for this I'm not sure if it's:
if I use the hint I'm back to were I started, which is basically at the beginning, and have no clue how to precede.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190754.6/warc/CC-MAIN-20170322212950-00333-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 307 | 4 |
http://quant.stackexchange.com/questions/tagged/present-value+analysis
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math
|
Quantitative Finance Meta
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s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011338837/warc/CC-MAIN-20140305092218-00036-ip-10-183-142-35.ec2.internal.warc.gz
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CC-MAIN-2014-10
| 2,108 | 53 |
https://goodriddlesnow.com/jokes/by/math-jokes/page:8/sort:popularity/direction:asc
|
math
|
10 ratings1 saves
Joke: Mathematician 1: What is the integral of 1/cabin?
Mathematician 2: Log cabin?
Mathematician 1: No, you forgot the C. It's a houseboat.
Show Your Support :)
7 ratings1 saves
Joke: Math guy #1: It's ironic.
Math guy #2: What is?
Math guy #1: You can't spell tautology without spelling tautology.
7 ratings0 saves
Joke: Why aren't jokes in base 8 funny?
Punch line: Because 7 10 11.
6 ratings0 saves
Joke: Mathematics is composed of 50 percent proofs, 50 percent formulas, and 50 percent imagination.
3 ratings0 saves
Joke: What do you get when you cross a mountain climber and a mosquito?
Punch line: You can't cross a scalar with a vector!
Follow us and get the Riddle of the Day, Joke of the Day, and interesting updates.
© 2013-2014 Good Riddles Now. All rights reserved.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662522284.20/warc/CC-MAIN-20220518151003-20220518181003-00309.warc.gz
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CC-MAIN-2022-21
| 797 | 19 |
https://alevelnote.com/chapter-22-ideal-gases/
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math
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Properties of Gas
Pressure: When a gas particle collides with the walls of its container it causes pressure. Pressure is measured in pascals, Pa. (1 Pa = 1 Nm-2)
Temperature: It is the measure of internal energy of the gas and it is equal to the average K.E. of its particles. It is measured in Kelvin, K.
Volume: It is the space occupied by the particle that makes up the gas. It is measured in meters cubed, m3.
Mass: It is considered the amount of gas. It is measured in mole.
Avogadro and the Mole
One mole of a material is the amount of that substance which contains the same number of particles as there are in 0,012 kg of carbon-12.
One mole of any substance contains Na particles.
Na = 6.02 × 1023 mol-1
The pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the temperature of gas remains constant.
P α 1/v for constant T
So, P1V1 = P2V2
The volume occupied by gas at constant pressure is directly proportional to its thermodynamic temperature.
V1/T1 = V2/T2ussac’s L
P1/T1 = P2/T2
We know from the three gas laws that pV/T = constant
Ideal gases all behave in the same way so we can keep R as constant,
PV/T = R
If the volume and temperature of a gas are kept constant then the pressure depends on R and the number of particles in the container. We must take account to this by bring number of moles, n:
pV/T = nR
PV = nRT
Which is the ideal gas equation for n moles.
Using the Avogadro’s equation for n;
pV = nRT
pV = N/NART
pV =N (R/NA) T
It provides evidence for the fast, random movement of molecules in gas. The Boltzmann constant is represented by k and is given as;
Kinetic Theory of Gases
It is the theory which links these microscopic properties of particles to the macroscopic properties of a gas. The assumptions of the kinetic theory of an ideal gas are:
Time of collision negligible compared to time between collisions.
No intermolecular forces except during collision.
Consider a collision in which a single molecule with mass m is moving with speed c parallel to one side of the box. Collision in side ABCD is elastically rebounded, so momentum from single collision is:
Change in momentum = -mc – (+mc)
= -mc – mc = 2mc
Between the consecutive collisions with side ABCD, molecule travels distance 2l at speed c.
Time = 2l/c
Force =2mc/(2l/c) =mc2/l
Pressure is given by,
Pressure = mc2/l3
For large number N of molecule,
P = Nm <c2>/l3
P = 1/3 Nm <c2>/l3
P = 1/3 Nm/V <c2>
PV = 1/3 Nm <c2>
Since the average K.E. of molecule is;
Ek = ½ m <c2> = 3/2 kT
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CC-MAIN-2022-21
| 2,527 | 46 |
https://bellyfatlossformula.com/qa/quick-answer-why-sine-is-used-in-snells-law.html
|
math
|
- What is sin in Snell’s law?
- Why do we use sine?
- Where is Snell’s law not applicable?
- What is N in refractive index?
- What is Snell’s law of reflection?
- What is the formula for angle of incidence?
- What is the unit of refractive index?
- How is sine used in real life?
- What is sine of angle of incidence?
- What is the angle of refraction when the angle of incidence is 30?
- What are the 3 laws of refraction?
- What is sin equal to?
- What is Snell’s law for?
- What sine means?
- Who created Snell’s law?
- How is sine calculated?
What is sin in Snell’s law?
Snell’s law relates the sines of the angles of incidence and transmission to the index of refraction for each material: sinθ1sinθ2=n2n1.
It should be noted that the angles are measured from the normal line at the interface (Figure 1).
Figure 1: Refraction at the interface between two materials (Wikipedia).
Why do we use sine?
The sine function is defined as the ratio of the side of the triangle opposite the angle divided by the hypotenuse. This ratio can be used to solve problems involving distance or height, or if you need to know an angle measure. Example: … To find the length of the side opposite the angle, d, we use the sine function.
Where is Snell’s law not applicable?
Snell’s law is not applicable when angle of incidence is zero as the angle of refraction will also be zero.
What is N in refractive index?
The refractive index, represented by symbol n, is the velocity of light in vacuum divided by the velocity of light in a medium.
What is Snell’s law of reflection?
Snell’s Law, which can be stated as. nA Sinθ A = nB Sinθ B. predicts how the ray will change direction as it passes from one medium into another, or as it is reflected from the interface between two media. The angles in this equation are referenced to a surface normal, as is illustrated below.
What is the formula for angle of incidence?
Measure the angle of incidence – the angle between the normal and incident ray. It is approximately 60 degrees. Now draw the refracted ray at an angle of 34.7 degrees from the normal – see diagram below….A Lesson from the Laboratory.Angle of Incidence (degrees)Angle of Refraction (degrees)85.048.517 more rows
What is the unit of refractive index?
Unit of refractive index (μ) will be the ratio of the unit of speed of light in vacuum(c) to the speed of light in the given medium(v). As you can see, the unit of refractive is 1, which means the refractive index is just a number without any unit.
How is sine used in real life?
Sine and cosine functions can be used to model many real-life scenarios – radio waves, tides, musical tones, electrical currents.
What is sine of angle of incidence?
If i is the angle of incidence of a ray in vacuum (angle between the incoming ray and the perpendicular to the surface of a medium, called the normal) and r is the angle of refraction (angle between the ray in the medium and the normal), the refractive index n is defined as the ratio of the sine of the angle of …
What is the angle of refraction when the angle of incidence is 30?
The angle of refraction is 19.27°. Explanation: This can be determined using Snell’s law which states: Refractive index = sin i/sin r ( where i is the angle of incidence and r is the angle of refraction).
What are the 3 laws of refraction?
Laws of refraction state that: … The incident ray, reflected ray and the normal, to the interface of any two given mediums; all lie in the same plane. The ratio of the sine of the angle of incidence and sine of the angle of refraction is constant.
What is sin equal to?
For a right triangle with an angle θ : Sine Function: sin(θ) = Opposite / Hypotenuse. Cosine Function: cos(θ) = Adjacent / Hypotenuse.
What is Snell’s law for?
Snell’s Law is a formula used to discribe the relationship between the angles of incidence and refraction,when referring to light or other waves passing through a boundary between to different isotropic media,such as water,glass and air.
What sine means?
In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse).
Who created Snell’s law?
Willebrørd SnellOpen any physics textbook and you’ll soon come across what English-speaking physicists refer to as “Snell’s law”. The principle of refraction – familiar to anyone who has dabbled in optics – is named after the Dutch scientist Willebrørd Snell (1591–1626), who first stated the law in a manuscript in 1621.
How is sine calculated?
In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. … In any right triangle, the sine of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H).
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CC-MAIN-2021-10
| 4,997 | 50 |
http://www.searchcrone.com/2012/01/clock-aptitude-questions-and-answers
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math
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1. Fifty minutes ago if it was four times as many minutes past three o’clock,how many minutes is it to six o’clock?
Ans: Twenty six minutes.
2. If a clock takes 7seconds to strike 7, how long will the same clock take to strike 10?
Ans: The clock strikes for the first time at the start and takes 7 seconds for 6 intervals-thus for one interval time taken=7/6.Therefore, for 10 seconds there are 9 intervals and time taken is 9*7/6=10 and 1/2 seconds.
3 At 6’o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12’o clock.
Ans: 66 sec.
4. The minute and the hour hand of a watch meet every 65 minutes. How much does the watch lose or gain time and by how much?
Ans: Gains; 5/11 minutes
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s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049277286.54/warc/CC-MAIN-20160524002117-00033-ip-10-185-217-139.ec2.internal.warc.gz
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CC-MAIN-2016-22
| 743 | 8 |
https://www.topperlearning.com/cbse-class-12-science-mathematics/probability/bayes-theorem
|
math
|
CBSE Class 12-science Maths Bayes' Theorem
Understand how to solve probability problems using CBSE Class 12 Science Mathematics – Probability – Bayes’ Theorem concept videos. TopperLearning gives you access to insightful recorded lectures by an expert who explains Bayes’ Theorem with practical examples. Watch our video lessons to revise the concept of partition of a sample space. Also, relearn the law of total probability with appropriate examples.
In our video lessons, our Maths expert shares examples based on Bayes’ Theorem along with exam strategies. You can further enhance your Maths skills with our CBSE Class 12 Science Maths textbook solutions, practice question papers and more.
- Pl ans
- State Bayes’ theorem.
- Define posteriori probability
- A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, and scooter or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by scooter? What is your opinion about being 'late'? Which life skills a person lacks by being 'late'?
- A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by B? A manufacturer knows that the item is defective; even then he sells it in the market. Is he doing the right thing? Which life skill is he lacking?
- In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and 1/4 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability 1/4 . What is the probability that the student knows the answer given that he answered it correctly?
- An urn contains five balls. Two balls are drawn and found to be white. Find the probability that all the balls are white.
- Define random variable.
- Define continuous and discrete random variable.
- Can the following distribution be a probability distribution of random variable X? X 0 1 2 3 4 P(X) 0.125 0.25 0.375 0.25 0.125
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359073.63/warc/CC-MAIN-20211130201935-20211130231935-00241.warc.gz
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CC-MAIN-2021-49
| 2,740 | 20 |
https://milestonetask.com/quiz/earned-value-management/
|
math
|
CPI greater than one implies that
A project has a budget of $30,000 and the costs incurred till date is $20,000. The project has achieved $10,000 worth of work. The project manager believes that the future work will progress at the planned rate. What is the Estimate at Completion (EAC) of the project?
A project is scheduled to complete in one year. After 3 months of execution the earned value is $45,000 and the planned value is $55,000. What is the schedule variance of the project?
A project is estimated to cost $200,000 with a timeline of 10 months. Due to shipment delay, the schedule was slightly delayed. This was however made up by receiving the first batch of materials for the project by air. The net result was that there was some additional cost in the project. At the end of the second month, he project manager reviews the project and finds that the project is 20% complete and actual costs are $50,000. The Estimate to Complete (ETC) for the project would be
What is the upper limit imposed on Actual Cost (AC)
SPI less than one implies that
Earned Value (EV) minus Planned Value (PV) is
Work remaining on the project is expressed as
Cost Variance greater than zero implies that
Schedule Variance (SV) greater than zero implies that
A project is estimated to cost $50,000 with a timeline of 50 days. After 25 days, the project manager finds that 80% of the project is complete and Actual costs are $50,000. What is the Cost Performance Index (CPI)?
What is the best way to accurately calculate Estimate to Completion (ETC)
How much we will be over or under budget at the end of the project; is expressed by?
What is EAC for the project if BAC = $50,000 AC = $10,000 EV = $7,000 manual bottom up ETC = $50,000
Earned Value (EV) minus Actual Cost (AC) is
Budget remaining on the project is expressed as
A project manager determined that BAC is no longer viable and developed a forecasted EAC. What index can the project manager use to look at the calculated projection of cost performance that must be achieved on the remaining work.
Schedule Variance (SV) less than zero implies that
Cost Variance less than zero implies that
Considering the following project data what is the Estimate at Completion (EAC) if the work is performed at the budgeted rate? BAC = $22,000 EV = $13,000 PV = $14,000 AC = $15,000
Two efficiency indicators that reflect cost and schedule performance of a project are
A project manager expects that the project would finish one month before the planned finish date. However he expects that the project to exceed the budgeted cost. What is true about the Schedule Performance Index (SPI)
Considering the impact of both schedule and cost performance; what the entire project is likely to cost is expressed by?
Earned Value Measurements of a project indicate that the current CPI is 0.80 and the current SPI is 0.98. For the next phase of the project the project manager should focus on which element of the project.
CPI less than one implies that
What is the best way to calculate the Estimate At Completion (EAC) when original estimates are no longer valid.
The planned value of task A is $150,000 and task B is $500,000. After six months the project manager does a performance analysis of the project and finds that the project is behind schedule. The actual cost incurred in completing task A is $175,000 and that for completing 80% of task B is $650,000. What is the cost performance index of the project?
SPI greater than one implies that
How will you calculate your EAC if the ETC work will be performed at the budgeted rate?
A project's current total Earned Value (EV) is $150,000 and the Actual Cost (AC) is $100,000. What is the Cost Variance (CV) of the project?
Cost performance required to be achieved on the remaining work is expressed by
At the end of the project schedule variance is equal to
Which of the following formulas answers the question; What is the remaining work likely to cost?
The Earned Value Methodology (EVM) can be used as a means to
A project is experiencing cost over run. What is true about Cost Performance Index (CPI)
What is the TCPI of the project based on following project data? (1) EAC = $115,000 (2) BAC = $100,000, (3) EV = $25,000 (4) AC = $40,000.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100540.62/warc/CC-MAIN-20231205010358-20231205040358-00617.warc.gz
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CC-MAIN-2023-50
| 4,232 | 36 |
http://www.thewoodpicks.com/books/a-radical-approach-to-real-analysis
|
math
|
By David Bressoud
This booklet is an undergraduate creation to actual research. lecturers can use it as a textbook for an leading edge path, or as a source for a normal direction. scholars who've been via a standard path, yet don't realize what genuine research is set and why it was once created, will locate solutions to a lot of their questions during this booklet. even if this isn't a heritage of study, the writer returns to the roots of the topic to make it extra understandable. The publication starts off with Fourier's advent of trigonometric sequence and the issues they created for the mathematicians of the early 19th century. Cauchy's makes an attempt to set up an organization origin for calculus stick with, and the writer considers his disasters and his successes. The ebook culminates with Dirichlet's facts of the validity of the Fourier sequence growth and explores a number of the counterintuitive effects Riemann and Weierstrass have been resulted in due to Dirichlet's facts. Mathematica ® instructions and courses are incorporated within the routines. even if, the reader could use any mathematical device that has graphing services, together with the graphing calculator.
Read Online or Download A radical approach to real analysis PDF
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This e-book is dedicated to the mathematical and numerical research of the inverse scattering challenge for acoustic and electromagnetic waves. the second one version contains fabric on Newton’s strategy for the inverse hindrance challenge, a sublime facts of specialty for the inverse medium challenge, a dialogue of the spectral conception of the a long way box operator and a mode for making a choice on the help of an inhomogeneous medium from some distance box information Feynman graphs in perturbative quantum box idea / Christian Bogner and Stefan Weinzierl -- The flexion constitution and dimorphy: flexion devices, singulators, turbines, and the enumeration of multizeta irreducibles / Jean Ecalle -- at the parametric resurgence for a undeniable singularly perturbed linear differential equation of moment order / Augustin Fruchard and Reinhard Schäfke -- On a Schrödinger equation with a merging pair of an easy pole and a straightforward turning aspect - Alien calculus of WKB ideas via microlocal research / Shingo Kamimoto, Takahiro Kawai, Tatsuya Koike and Yoshitsugu Takei -- at the turning aspect challenge for instanton-type options of Painlevé equations / Yoshitsugu Takei
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Extra resources for A radical approach to real analysis
We next ask more about the curve itself. After the genus, the gonality and the Clifford index are among the most interesting invariants. Recall that the gonality of X is the smallest degree of a mapping from X to lP'1. To define the Clifford index of X we first define the Clifford index of a line bundle L on X to be degree(L) - 2(hO(L) - 1). For example, the Clifford indices of the structure sheaf Ox and the canonical sheaf Wx are both equal to O. The Clifford index of the curve X is defined to be the minimum value of the Clifford index of a line bundle L on X for which both hO(L) ;::: 2 and h I (L) ;::: 2.
Next, the cohomology class of X in jp3 is determined by the degree of X: i63 : degree idealX 063 = 10 In sum: X is a smooth, absolutely irreducible curve of genus 6 and degree 10. We next ask for analytic information about the curve and the embedding. A reasonable place to start is with the relation between the line bundle defining the embedding and the canonical sheaf wx. Notice first that the degree of the hyperplane divisor (the degree of the curve) is 10 = 2g-2, the same as the canonical bundle.
I53 : X = variety idealX 053 = X 053 : Projective Variety How would you analyze the scheme X? We will illustrate one approach. In outline, we will first look at the topological invariants: the number and dimensions of the irreducible components, and how they meet if there is more than one; the topological type of each component; and the degree of each component in jp>3. We will then see what we can say about the analytic invariants of X using adjunction theory (we give some references at the end).
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https://leaders.economicblogs.org/worthwhile-canadian-initiative/2019/rowe-inflation-debt-gdp-ratio/
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math
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I'm trying to write a simple explainer. The best way to understand how inflation affects the debt/GDP ratio is to start out with a scenario where it doesn't. Then look at ways in which the real world is not like that scenario. Here's the "No Effect" scenario: The Bank of Canada suddenly decides to raise the inflation target by one percentage point (1ppt). Like from 2% to 3% (which is a 50% increase, which is why I'm being picky and saying 1 ppt instead). Assume that inflation immediately increases by 1ppt, but real GDP (RGDP) growth is not affected, so nominal GDP (NGDP) growth immediately increases by 1ppt. Assume that expected inflation also immediately rises by 1ppt, and that nominal interest rates also immediately rise by 1ppt (because borrowers and lenders only care about real
Nick Rowe considers the following as important: finance, Macro, Monetary Policy, Nick Rowe, Teaching
This could be interesting, too:
Bradford DeLong writes Brad DeLong Says More…: Project Syndicate
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Bradford DeLong writes No, We Don’t “Need” a Recession
I'm trying to write a simple explainer. The best way to understand how inflation affects the debt/GDP ratio is to start out with a scenario where it doesn't. Then look at ways in which the real world is not like that scenario.
Here's the "No Effect" scenario: The Bank of Canada suddenly decides to raise the inflation target by one percentage point (1ppt). Like from 2% to 3% (which is a 50% increase, which is why I'm being picky and saying 1 ppt instead).
Assume that inflation immediately increases by 1ppt, but real GDP (RGDP) growth is not affected, so nominal GDP (NGDP) growth immediately increases by 1ppt.
Assume that expected inflation also immediately rises by 1ppt, and that nominal interest rates also immediately rise by 1ppt (because borrowers and lenders only care about real interest rates, which are unaffected in this scenario).
Assume that the nominal interest paid on all government bonds also immediately rises by 1ppt (because those bonds have a very very short term to maturity, so all get immediately rolled over at the new higher nominal interest rate).
Assume that nominal government spending and tax revenues also immediately grow 1ppt faster (so real government spending and taxes are unaffected).
In this scenario, the nominal debt grows 1ppt faster, but NGDP grows 1ppt faster too, so the nominal debt/NGDP ratio is unaffected by the higher inflation rate. Everything just scales up ("inflates") in the same proportion. But nothing "real" (inflation-adjusted) changes.
To see why, note that the "primary" deficit (the deficit ignoring interest on the national debt) stays the same as a ratio of NGDP. But the "full" deficit (including interest on the national debt) increases by the 1ppt increase in nominal interest times the national debt. So the debt is growing 1ppt faster than before. Just like NGDP is growing 1ppt faster than before. So the ratio of the two is unaffected by inflation.
The main reason that scenario is wrong is because things don't all change immediately. There are lags. And all those lags tend to work the same way: they make the debt/GDP ratio tend to fall initially when the Bank of Canada decides to increase the inflation target.
1. The first important lag is due to the fact that government bonds do not all have a very very short maturity. Take the extreme opposite case: suppose all bonds are perpetuities, that never mature, but pay a fixed coupon every year forever. In this case the interest on the previously-existing debt is unchanged by higher inflation. So higher inflation causes the debt/GDP ratio to start falling over time. In the simple case where the government keeps the budget balanced, so issues no new debt, 1ppt higher inflation alone will cause the debt/GDP ratio to fall by 1% (not 1ppt) every year, so it halves in 70 years (because it causes NGDP to double while debt stays the same). And a 2ppt inflation increases alone will halve the debt/GDP ratio in 35 years, etc.
The real world has a mixture of government bonds, of varying maturities, so it's somewhere between my original scenario and the extreme opposite case. (And some bonds are indexed to inflation, so the interest rate rises immediatly with inflation.)
2. The second important lag is that nominal interest rates may not immediately rise when the Bank of Canada decides to target higher inflation. They may even fall initially. This is especially likely if the Bank of Canada keeps its decision secret. An essential part of modern inflation targeting is that the Bank of Canada clearly announces its commitment to keeping inflation at the 2% target, and it's hard to imagine the Bank of Canada raising its target in secret. But before the 1990s central banks did not have explicit inflation targets. And actual inflation depends on expected inflation, as well as on what central banks do. So a central bank could cut nominal interest rates, and inflation would eventually rise, and expected inflation would eventually rise too, when people saw that higher actual inflation, and eventually learned it wasn't just a temporary blip but was likely to continue, because it had continued.
So if the Bank of Canada secretly reneged on its commitment to target 2% inflation, and lowered nominal interest rates, it might take decades before people fully understood what had happened, and the Bank of Canada needed to raise nominal interest rates, 1ppt higher than they were initially, to bring real interest rates back to where they were initially, to prevent inflation spiralling even higher. And in the meantime the debt/GDP ratio would be falling, due to nominal interest rates being lower than the 1ppt increase in my original scenario.
[But notice something interesting about the interaction between my 1st and 2nd lags: the second lag (lower nominal interest rates) only matters when the bonds are rolled over and refinanced at the new interest rate. So in the extreme case where all bonds are perpetuities, the second lag wouldn't matter for existing debt
There may be other effects. Like if the tax and benefit system is not fully indexed to inflation. Or if a secret decision to target higher inflation causes temporarily higher real GDP. But I think I will stop there.
But there's one historical question that's stuck in my mind and that I don't have the answer for. How much of the history of the debt/GDP ratio, from the end of WW2 until when things had mostly settled down to the 2% inflation target (say 2000?) is a story of the rise and then fall of the inflation rate? Not all of it, obviously, because other things happened too. But my guess is that an important part of it is. We didn't just grow our way as (in part) inflate our way out of a high debt/GDP ratio, and then it went into reverse as inflation came back down again. It's as if the government has a valuable reputation for keeping inflation low, and it can spend that reputation bringing the debt/GDP ratio down, and then suffers the costs of re-investing in that reputation if it wants to bring inflation down again. But lots of other important things mattered too, and history is the net effect of all those things. (And my thought-experiment above, where the Bank of Canada secretly raises its inflation target, is hard to imagine happening today, but much more applicable to the time before explicit inflation targets.) But I don't know what the post WW2 counterfactual would have looked like.
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http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mm&paperid=4253&option_lang=eng
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math
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An algorithm for calculating the movements of diatomic gases molecules
S. V. Polyakova, V. O. Podrygaab
a Keldysh Institute of Applied Mathematics of RAS
b Moscow Automobile and Road Construction State Technical University
The problem of modeling the properties of diatomic gases by molecular dynamics methods is considered. Such studies are traditional for the physics of matter. Currently, there
is an increased interest in this problem in connection with the development of nanotechnologies and their implementation in various industrial branches. In the proposed work,
the question of clarifying the original classical model of Newton's dynamics is considered. In particular, a technique is discussed for taking into account additional degrees of
freedom that characterize the rotational motions of diatomic molecules. This is due to the
need to correctly calculate the heat capacity. To solve this problem, it was proposed to
add equations for the angular momentum and rotational velocities of molecules to the
molecular dynamics model. For such an extended formulation, a special numerical algorithm has been developed that generalizes the Verlet scheme. A computational program
has been developed on the basis of the proposed algorithm. It was used to calculate the
heat capacity curve for nitrogen in the temperature range 100-400 K at a pressure of 1 atm. The calculated data obtained agree with the known data from reference books.
properties of technical gases, molecular dynamics, translational and rotational degrees of freedom, numerical algorithm for calculation.
PDF file (324 kB)
First page: PDF file
S. V. Polyakov, V. O. Podryga, “An algorithm for calculating the movements of diatomic gases molecules”, Matem. Mod., 33:1 (2021), 53–62
Citation in format AMSBIB
\by S.~V.~Polyakov, V.~O.~Podryga
\paper An algorithm for calculating the movements of diatomic gases molecules
\jour Matem. Mod.
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https://www.youtube.com/watch?v=AUoaTrQTM5o
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math
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Rating is available when the video has been rented.
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Published on Nov 25, 2009
This video gives a brief overview of the Poincaré Conjecture, background, mathematics, controversy and a few figures surrounding the solution. Henri Poincare, Topology, 3-Sphere, Grigori Perelman,Shing-Tung Yau, Richard Hamilton, William Thurston, Ricci Flow, Thurston Geometrization Conjecture, Clay Mathematics Institute, Millennium Prize, Fields Medal.
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http://www.expressgaragedoorswinnipeg.com/books/advances-in-minimum-description-length-theory-and-applications
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math
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By Peter D. Grunwald, In Jae Myung, Mark A. Pitt
The method of inductive inference—to infer basic legislation and rules from specific instances—is the foundation of statistical modeling, development acceptance, and laptop studying. The minimal Descriptive size (MDL) precept, a strong approach to inductive inference, holds that the simplest clarification, given a constrained set of saw info, is the person who allows the best compression of the data—that the extra we can compress the knowledge, the extra we know about the regularities underlying the information. Advances in minimal Description size is a sourcebook that would introduce the medical group to the principles of MDL, contemporary theoretical advances, and functional purposes. The ebook starts with an intensive instructional on MDL, masking its theoretical underpinnings, sensible implications in addition to its numerous interpretations, and its underlying philosophy. the educational incorporates a short heritage of MDL—from its roots within the suggestion of Kolmogorov complexity to the start of MDL right. The publication then provides fresh theoretical advances, introducing smooth MDL equipment in a fashion that's obtainable to readers from many various medical fields. The ebook concludes with examples of ways to use MDL in study settings that diversity from bioinformatics and laptop studying to psychology.
Read Online or Download Advances in minimum description length: Theory and applications PDF
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Additional info for Advances in minimum description length: Theory and applications
1 Information Theory I: Probabilities and Code Lengths 31 The P that corresponds to L minimizes expected code length Let P be a distribution on (finite, countable or continuous-valued) Z and let L be defined by L:= arg min EP [L(Z)]. 5) L∈LZ Then L exists, is unique, and is identical to the code length function corresponding to P , with lengths L(z) = − log P (z). 3 The second most important observation of this tutorial. distributions P , X may be finite, countable, or any subset of Rl , for any integer l ≥ 1, and P (x) represents the probability mass function or density of P , as the case may be.
Thus, using the code L0 , the sequence can be compressed by a linear amount if we use a specially designed code that assigns short code lengths to sequences with about four times as many 0s than 1s. 3) have been observed, it is always possible to design a code which uses arbitrarily few bits to encode xn — the actually observed sequence may be encoded as ‘1’ for example, and no other sequence is assigned a code word. The point is that with a code that has been designed before seeing the actual sequence, given only the knowledge that the sequence will contain approximately four times as many 0s as 1s, the sequence is guaranteed to be compressed by an amount linear in n.
C(xn ). In order for this method to succeed for all n, all (x1 , . . , xn ) ∈ X n , the resulting procedure must define a code, that is, the function C (n) mapping (x1 , . . , xn ) to C(x1 )C(x2 ) . . C(xn ) must be invertible. If it were not, we would have to use some marker such as a comma to separate the code words. We would then really be using a ternary rather than a binary alphabet. Since we always want to construct codes for sequences rather than single symbols, we only allow codes C such that the extension C (n) defines a code for all n.
Advances in minimum description length: Theory and applications by Peter D. Grunwald, In Jae Myung, Mark A. Pitt
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https://emonprime.com/regression-analyses-in-spss/
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math
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Regression analysis is one of the Statistical models for estimating the relationship between variables. It is a model for checking the effects of a set of selected factors on the subject matter being discussed or analyzed.
The relationship that is seen in a regression model are usually between the dependent variable and one or more independent variables.
Assumptions of Linear Regression
Before you linear regression for your sets of data, one of the major things to consider is whether such is analyzable using linear regression analysis.
This has to be taken into consideration seriously because there are six assumptions of linear regression that your data should agree with for them to be suitably analysed using regression to ensure a valid result.
Though this operation takes more time than required during your statistical analyses, requiring you to click a few more buttons in SPSS Statistics when performing your analysis, as well as think a little bit more about your data, but it is not a difficult operation to embark on
Assumption One: Your two variables should be measured at the continuous level. This implies that they are either interval or ratio variables. Examples of continuous variables include revision time (measured in hours), area of land (measured in hectares) exam performance (measured from 0 to 100), weight (measured in kilograms), and so many others
Assumption Two: There needs to be a linear relationship between the two variables. Whilst there are a number of ways to check whether a linear relationship exists between your two variables, we suggest creating a scatterplot using SPSS Statistics where you can plot the dependent variable against your independent variable and then visually inspect the scatterplot to check for linearity.
Assumption Three: There should be no significant outliers. An outlier is an observed data point that has a dependent variable value that is very different to the value predicted by the regression equation.
Assumption Four: You should have independence of observations, which you can easily check using the Durbin-Watson statistic, which is a simple test to run using SPSS Statistics. We explain how to interpret the result of the Durbin-Watson statistic in our enhanced linear regression guide.
Linear regression analysis requires that there is little or no autocorrelation in the data. Autocorrelation occurs when the residuals are not independent from each other.
Assumption Five: Your data needs to show homoscedasticity, which is where the variances along the line of best fit remain similar as you move along the line.
Assumption Six: Finally, you need to check that the residuals (errors) of the regression line are approximately normally distributed (we explain these terms in our enhanced linear regression guide).
Two common methods to check this assumption include using either a histogram (with a superimposed normal curve) or a Normal P-P Plot.
Note that there are possibilities that when analysing your own data using SPSS Statistics, some of your results might come out in contrary to the above-stated assumptions. You shouldn’t be amazed at this occurrence.
This is usually obtainable when working with real-world data rather than already designed templates, which often only show you how to carry out linear regression when using a standard data. However, don’t worry. Even when your data fails certain assumptions, there is often a solution to overcome this.
Types of Regression Analysis
Regression analysis is divided into the following;
Simple linear regression: This is when you are considering the relationship between the dependent variable and an independent variable.
Multiple linear Regressions: When the relationship is in between the dependent variable and two or more independent variables.
Non-linear Regression: This type of regression analysis does not show a linear relationship. Examples of this are: Ridge regression, Lasso regression, Polynomial regression and Logistic regression
Types of Variable in Regression Analysis
The dependent variable is also known as the outcome variable, response variable or the regressand. There is always one dependent variable in Regression analysis. It is the variable whose fate is determined by the changes of the explanatory variables.
The mean value of the dependent variable is subject to those of the independent variables. This implies that whatever happens to the dependent variable must be determined by the independent variables according to the relationship between them.
Independent variables are otherwise called explanatory variables, predictor variables, factors or regressors. In any regression analysis, there are always one or more independent variables.
As explained above, changes in the independent variables determine what happens to the dependent variable. That is, the dependent variable changes as the independent variables are changing.
For example, let us consider the Determinants of cassava output in a particular study area using some selected factors like Age of farmers, Farming Experience, Source of Fund and Farm sizes.
Here, cassava output can be represented as Y, while the selected factors as L. It means that the dependent variable is Y (cassava output), whereas L (representing Age of farmers (L1), Farming Experience (L2), Source of Fund (L3) and Farm sizes (L4)) are the independent variables. The linear regression model equation for this example can be deduced below;
Y = F(L)
Y = a + bL + E
In a more explicit form,
Y = a + b1L1+b2L2+b3L3+b4L4 + e
Where Y = cassava output
a = Intercept
b = Slope
L1 = Age of farmers
L2 = Farming Experience
L3 = Source of Fund
L4 = Farm sizes
e = Error term
The Regression equation presented above shows that the quantity of cassava output produced by the farmers in the study area depends on the Age distribution of farmers, Farming Experience, Source of Fund and Farm sizes.
To know the effects of the factors above on cassava output, analysis has to be performed based on the data collected from the variables.
How to Analyze Multiple Linear Regression Model.
SPSS is a statistical tool that can be used to run regression analysis. This article especially covers the step by step guide on how multiple linear Regression models can be analyzed.
Most people find it difficult to analyze a multitude of linear Regression models because they consider it too complex a task to perform. Following the guidelines that I am going to reveal in this article, you would be able to do it by yourself.
All you need to have is a laptop and the determination to work, and you would be able to run a multiple linear Regression analysis on your own.
The following are the easiest guides on how to run Multiple Linear Regression Analysis in SPSS.
Step 1: Import your excel data codes into SPSS
Step 2: This is your dataview in SPSS
Step 3: Go to analyze at the Top part of your computer in the SPSS dashboard.
Step 4: Take your cursor to the Regression at the dropdown navigation button for other dropdown navigation menus on Regression and select linear.
Step 5: Move the dependent variable and the independent variables to their respective bars by clicking on them and using the arrows by the sides of the bar to move them.
Step 6: Go to Statistics to select the properties you want to analyze.
Step 7: Got to Plot if you want to get Histogram or Scatter Plots.
Step 8: Click continue
Step 9: Tap Ok
Step 10: The following are the results that you are going to generate
Step 11: Finally, collect the result of the analysis and interpret them carefully based on the information that is required in the work.
I hope you would be able to run a Multiple linear Regression analysis in SPSS with the help of the guidelines provided in this article. Please subscribe to this site by using your email address if you want to be notified any time we publish very educative articles of this kind.
If you have any questions about how to perform Multiple Linear Regression Analysis in SPSS, kindly use the comment section below this article.
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https://www.physicsforums.com/threads/compare-forces-exerted-between-the-tennis-racquets.775452/
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1. The problem statement, all variables and given/known data During a tennis volley, a ball that arrives at a player at 40 m/s is struck by the racquet and returned at 40 m/s. The other player, realizing that the ball is out of bounds, catches it in her hand. Assuming the time interval of contact is the same in both cases, compare the force exerted by the first player's racquet on the ball with the force exerted by the second player's hand on the ball. 2. Relevant equations None given. The book did not provide me with one I could use. 3. The attempt at a solution I have submitted 0 as my answer because I felt that with both of them going the same speed, there would be 0 difference in force, but I got this problem incorrect (5 more attempts remaining at the time of this message). Mass is not given either, so how would one find the difference of force between these two using only velocity?
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https://www.teachme2.co.za/additional-mathematics-tutors-centurion
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math
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Highest Quality Additional Mathematics Tutors in Centurion. Get Additional Mathematics Lessons in your home with Teach Me 2Get an Additional Mathematics tutor
I did well in my high school Mathematics and went on to study Actuarial Science that involves a lot of Mathematics and Statistics.
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I'm a final year Applied Mathematics student who is able to explain Mathematical concepts in a very simplified manner. I have a great knowledge of Mathematics and am passionate about teaching others.
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https://encyclopedia2.thefreedictionary.com/interval+estimation
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Discussing probability and statistics needed by physicists and engineers, they cover random phenomena, probability, random variables, expected values, commonly used discrete distributions, commonly used density functions, joint distributions, some multivariate distributions, a collection of random variables, sampling distributions, estimation, interval estimation
, tests of statistical hypotheses, model building and regression, and designing experiments and analyzing variance.
The more reliable method is the interval estimation
The most common techniques which are generalized for fuzzy data are presented as: Wu (2009) states that based on fuzzy measurements, confidence interval estimation
for the fuzzy data is presented.
This technology consists of high sensitive spread-spectrum radar and feature-based heartbeat interval estimation
algorithm, and enables to measure heart rate and its intervals in real time without placing sensors on the body with as high accuracy as electrocardiographs.
Dey applied this by providing point and interval estimation
methods for the scale parameter of the Rayleigh distribution under progressive Type-II censoring with binomial removal.
Tsai and Wardell (2006) have developed a VBA- driven Excel spreadsheet that is built around one simple business scenario and aimed to improve the effectiveness of teaching three concepts in business statistics: the Central Limit Theorem, interval estimation
and hypothesis testing.
Panel A is based on interval estimation
of Equation (1) and panel B is based on Probit estimation of Equation (2).
However the more general problem of interval estimation
for a linear function of binomial proportions mentioned by Price and Bonett (2004), including pairwise comparisons, complex contrasts, interaction effects and simple main effects (BONETT; WOODWARD, 1987), are factors that influence the probability coverage estimate.
Shieh examined the accuracy of Equation 1 for 27 additional conditions and concluded that Equation 1 is "not recommended for precise interval estimation
of squared multiple correlation coefficient in multiple regression analysis" (p.
2011) have been introduced to achieve interval estimation
This goal often falls short in veterinary medicine when adequate sample sizes for stable interval estimation
are often not met given the difficulty in obtaining specimens from healthy subsets of species, which is related to time and cost considerations as well as access to appropriate numbers of specimens from a single species in which patient history may not be complete.
Heterogeneity nature of real properties that could make one property to be different from the others; coupled with imperfect nature of property market that is characterised by inadequate information were responsible for interval estimation
of values as against point estimation of values by valuers, users and investors.
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https://www.cfd-online.com/Forums/main/73579-upwind-solvers-1d-compressible-euler-eqns.html
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|March 11, 2010, 14:39||
Upwind solvers for 1D compressible Euler eqns
Join Date: Mar 2010
Posts: 2Rep Power: 0
I am an introductory student in CFD. I ma solving 1D Euler equations in non-conservative form. I am able to calculate the eigenvalues and eigenvector matrix. I get eigenvalues of u, u+c, and u-c. I need to find F+ and F-. I am trying to understand the Steger-Warming and Van Leer flux splitting methods. I am having trouble figuring out how to do the Steger-Warming and Van Leer. There is no info on these schemes in Wiki. Can someone explain these simply or provide an example of them in use?
|March 11, 2010, 18:31||
Something like this?
Join Date: Mar 2009
Posts: 33Rep Power: 10
Here describes Van Leer's splitting.
The Steger-Warming splitting is simple.
For the Euler equations, we have
F = AU
where F is the flux, U is the conservative state vector, and
A is the Jacobian (dF/dU)! Yes, that's true for the Euler.
So, if we decompose A into a positive part and negative part:
A = RDL = R(Dp + Dm)L = RDpL + RDmL = Ap + Am,
where R is the right-eigenvector matrix, D is the diagonal matrix with eigenvalues in the diagonal, L is the left-eigenvector (inverse of R), and
Dp is D with positive eigenvalues only, Dm is D with only negative eigenvalues, THEN we can write the flux vector as
F = Fp + Fm = ApU + AmU
So, the positive flux is ApU and the negative flux is AmU!
There is a source code for Van Leer's flux and the Steger-Warming flux at
|Thread||Thread Starter||Forum||Replies||Last Post|
|Schemes for Compressible Euler eqns||oe_jet||Main CFD Forum||0||April 30, 2009 13:01|
|2-D Euler Solver for compressible flow in Matlab||Volkan||Main CFD Forum||1||October 28, 2007 01:40|
|NS-incompressible and compressible flow solvers||ag||Main CFD Forum||2||September 27, 2005 06:18|
|Axisymmetric Inviscid Compressible Euler code.||Amith||Main CFD Forum||2||June 10, 2002 23:32|
|Boundary Layer created by Euler Solvers||Jim||Main CFD Forum||31||November 18, 2001 00:18|
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CC-MAIN-2017-13
| 1,988 | 28 |
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