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https://math.stackexchange.com/questions/855088/what-is-physical-interpretation-of-dot-product
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What is physical interpretation of dot product? [duplicate]
Consider two vectors $V_1$ and $V_2$ in $\mathbb{R}^3$. When we take their dot product we get a real number. How is that number related to the vectors? Is there any way we can visualize it?
• $u \cdot v = \|u\| \|v\| \cos \theta$
– user61527
Jul 3, 2014 at 7:48
• @T.Bongers With one or two more words, that could be an answer...
– user98602
Jul 3, 2014 at 8:04
Temporarily imagine that $V_2$ is of unit length. Then, $V_1 \cdot V_2$ is the projection of the vector $V_1$ onto the vector $V_2$. Picture here. Now we let $V_2$ have its original length and to do so we multiply the result of the dot product by the new length of $V_2$. (This has the effect of making it not matter which one you pretend has unit length initially.)
You do this sort of thing when you write a vector as a sum of multiples of the standard unit coordinate vectors (sometimes written $\hat{x}, \hat{y}$, and $\hat{z}$). Use the dot product to project your vector onto $\hat{x}$ getting the multiple of $\hat{x}$ that, when assembled with the other components will sum to your vector.
• If $V_1 \cdot V_2$ is the projection of $V_1$ onto $V_2$, then the reverse is also true right, i.e., $V_1 \cdot V_2 = V_2 \cdot V_1$ is the orthogonal project of $V_2$ onto $V_1$? Jun 4, 2020 at 20:26
The dot product ${\bf a}\cdot{\bf b}$ measures the length of ${\bf a}$'s orthogonal projection onto $\bf b$ (the $1$-dimensional subspace it is a part of), scaled by the length of $\bf b$ itself. And conversely. The scaling is nice to have because it means the dot product is bilinear in its two arguments. Physically, it can measure how much of something in one direction moves in a different direction. For instance, suppose water is moving through a net (in the shape of a plane) put in the ocean - and, for simplicity, the water is moving monolithically: the same direction at the same speed at every point - but the direction of movement is not perfectly perpendicular to the net. The dot product of the net's unit normal vector with the water's velocity vector will tell us how much is moving through the net. When this is applied on an infinitessimal scale and then integrated, we can determine how much of something moving with a vector field is displaced through a surface; this is half of the divergence theorem.
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https://www.scala-algorithms.com/MinimumItemRotatedSortedArray/
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# Scala algorithm: Find the minimum item in a rotated sorted array
Published
## Algorithm goal
A rotated sorted array is a sorted array, split into 2 parts, swapped. For example `[1,2,7,9]` can be rotated by changing it to `[7,9,1,2]`. Find the minimum element in this sorted array efficiently.
## Test cases in Scala
``````assert(minItemSortedArray(Array.empty) == None)
assert(minItemSortedArray(Array(1)) == Some(1))
assert(minItemSortedArray(Array(1, 7)) == Some(1))
assert(minItemSortedArray(Array(7, 1)) == Some(1))
assert(minItemSortedArray(Array(9, 1, 7)) == Some(1))
assert(minItemSortedArray(Array(7, 9, 1)) == Some(1))
assert(minItemSortedArray(Array(7, 9, 1, 2)) == Some(1))
assert(minItemSortedArray(Array(7, 9, 1, 2, 4)) == Some(1))
assert(minItemSortedArray(Array(7, 9, 1, 2, 4, 5)) == Some(1))
assert(minItemSortedArray(Array(7, 9, 1, 2, 4, 5, 6)) == Some(1))
assert(minItemSortedArray(Array(6, 7, 8, 9, 1, 2, 4, 5)) == Some(1))
assert(minItemSortedArray(Array(6, 7, 8, 9, 1, 2, 3, 4, 5)) == Some(1))
``````
## Algorithm in Scala
17 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!
## Explanation
The approach to use is very similar to BinarySearch, except for the extra check that there is an extra additional check to find if we have reached the disjunction of the array. (this is © from www.scala-algorithms.com)
## Scala concepts & Hints
1. ### Def Inside Def
A great aspect of Scala is being able to declare functions inside functions, making it possible to reduce repetition.
``````def exampleDef(input: String): String = {
def surroundInputWith(char: Char): String = s"\$char\$input\$char"
surroundInputWith('-')
}
assert(exampleDef("test") == "-test-")
``````
It is also frequently used in combination with Tail Recursion.
2. ### Option Type
The 'Option' type is used to describe a computation that either has a result or does not. In Scala, you can 'chain' Option processing, combine with lists and other data structures. For example, you can also turn a pattern-match into a function that return an Option, and vice-versa!
``````assert(Option(1).flatMap(x => Option(x + 2)) == Option(3))
assert(Option(1).flatMap(x => None) == None)
``````
3. ### Range
The `(1 to n)` syntax produces a "Range" which is a representation of a sequence of numbers.
``````assert((1 to 5).toString == "Range 1 to 5")
assert((1 to 5).reverse.toString() == "Range 5 to 1 by -1")
assert((1 to 5).toList == List(1, 2, 3, 4, 5))
``````
4. ### Stack Safety
Stack safety is present where a function cannot crash due to overflowing the limit of number of recursive calls.
This function will work for n = 5, but will not work for n = 2000 (crash with java.lang.StackOverflowError) - however there is a way to fix it :-)
In Scala Algorithms, we try to write the algorithms in a stack-safe way, where possible, so that when you use the algorithms, they will not crash on large inputs. However, stack-safe implementations are often more complex, and in some cases, overly complex, for the task at hand.
``````def sum(from: Int, until: Int): Int =
if (from == until) until else from + sum(from + 1, until)
def thisWillSucceed: Int = sum(1, 5)
def thisWillFail: Int = sum(1, 300)
``````
5. ### Tail Recursion
In Scala, tail recursion enables you to rewrite a mutable structure such as a while-loop, into an immutable algorithm.
``````def fibonacci(n: Int): Int = {
@scala.annotation.tailrec
def go(i: Int, previous: Int, beforePrevious: Int): Int =
if (i >= n) previous else go(i + 1, previous + beforePrevious, previous)
go(i = 1, previous = 1, beforePrevious = 0)
}
assert(fibonacci(8) == 21)
``````
# Scala Algorithms: The most comprehensive library of algorithms in standard pure-functional Scala
## How our 100 algorithms look
1. A description/goal of the algorithm.
2. An explanation with both Scala and logical parts.
3. A proof or a derivation, where appropriate.
4. Links to Scala concepts used in this specific algorithm, also unit-tested.
5. An implementation in pure-functional immutable Scala, with efficiency in mind (for most algorithms, this is for paid subscribers only).
6. Unit tests, with a button to run them immediately in our in-browser IDE.
### Study our 100 Scala Algorithms: 6 fully free, 100 published & 0 upcoming
Fully unit-tested, with explanations and relevant concepts; new algorithms published about once a week.
### Explore the 22 most useful Scala concepts
To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.
## Subscribe to Scala Algorithms
Maximize your Scala with disciplined and consistently unit-tested solutions to 100+ algorithms.
Use it from improving your day-to-day data structures and Scala; all the way to interviewing.
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https://www.numbersaplenty.com/33203313021231
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Search a number
33203313021231 = 325962529779701
BaseRepresentation
bin1111000110010101111111…
…01011011001000100101111
311100120012112222021122011200
413203022333223121010233
513323000341113134411
6154341220314220543
76664601022664323
oct743127753310457
9140505488248150
1033203313021231
11a64149a656901
123883036424753
13156b09c77c3c2
1482b09836d983
153c8a63767e56
33203313021231 has 12 divisors (see below), whose sum is σ = 48773228167560. Its totient is φ = 21760363335600.
The previous prime is 33203313021209. The next prime is 33203313021271. The reversal of 33203313021231 is 13212031330233.
33203313021231 is a `hidden beast` number, since 3 + 3 + 2 + 0 + 331 + 302 + 1 + 23 + 1 = 666.
It is not a de Polignac number, because 33203313021231 - 27 = 33203313021103 is a prime.
It is a super-2 number, since 2×332033130212312 (a number of 28 digits) contains 22 as substring.
It is a junction number, because it is equal to n+sod(n) for n = 33203313021195 and 33203313021204.
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (33203313021271) by changing a digit.
It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 31264889320 + ... + 31264890381.
It is an arithmetic number, because the mean of its divisors is an integer number (4064435680630).
Almost surely, 233203313021231 is an apocalyptic number.
33203313021231 is a deficient number, since it is larger than the sum of its proper divisors (15569915146329).
33203313021231 is a wasteful number, since it uses less digits than its factorization.
33203313021231 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 62529779766 (or 62529779763 counting only the distinct ones).
The product of its (nonzero) digits is 5832, while the sum is 27.
Adding to 33203313021231 its reverse (13212031330233), we get a palindrome (46415344351464).
The spelling of 33203313021231 in words is "thirty-three trillion, two hundred three billion, three hundred thirteen million, twenty-one thousand, two hundred thirty-one".
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Home » Posts tagged 'Constructivism'
# Tag Archives: Constructivism
## Putting the sense in Number Sense
The best teaching happens when you make a lesson visual, spatial and auditory. That’s why I love teaching kids number sense with a math balance.
Utilizing a math balance in a whole-class setting of twenty-seven kids would be tricky, but at home with one child it’s easy. The balance we own came from Right Start and costs \$25.
5 does not equal 8. It’s so easy to see.
Just like it’s easy to figure out that there are many number combinations that equal 5.
In fact, we spent a full ten minutes just figuring out the number 5!
In pedagogy, we call this “Constructivism”. It means learning a new concept through your own experimentation and discovery. Giving children the full Constructivist experience isn’t always possible, but a math balance makes it a lot easier.
## Math Without Worksheets
One of the best things about teaching math from a Constructivist perspective is the emphasis on metacognition, or “thinking about thinking”. In a good Constructivist classroom the teacher should know, and be constantly assessing, the thinking strategies her students are using to solve problems. One of the ways I accomplished this when I was a teacher was through small group white-board activities. I would group three to five students according to ability level, and let them create and solve word problems on the white-board for me, while I reordered their thoughts and strategies.
From a Constructivist perspective, listening to how children solve problems is where the true art in teaching comes. You need to know when to ask probing questions, when to lead them on to more efficient ideas, and when to pick apart what they are saying. The idea behind Constructivism is not to let kids wildly flounder, but to gently encourage them towards efficiency and accuracy.
My son Bruce(6.5) attends a school where the district uses Houghton Mifflin Math Expressions, which I like, but would not describe as a Constructivist program. Although there are occasionally times built into the curriculum where Bruce is asked to write out his own math problem as part of his homework, or explain his thinking in words and pictures, there doesn’t seem to be the same heavy focus on metacognition that there was in my own classroom.
Last night after dinner, I decided to do an experiment. How would Bruce handle a third grade Constructivist classroom? How would he do if he was in one of my white-board groups, from long ago? It turns out, not so well, at least not without more practice. And let me tell you, after realizing this type of activity was a struggle for him, we will be working on it at least once a week from now on!
Here is our first example. I asked Bruce to tell me a subtraction story problem about the number 263. That was the first bit of difficulty as you can see! Then I asked him to solve the problem with numbers on the left side of the paper, and to keep his work neat, and organized within the box. Second bit of difficulty! I also wanted him to write down his final answer and circle it, but I forgot to articulate this very well, so that was “my bad”. Lastly, I asked Bruce to explain his thinking to me while I reordered his strategies. This is when he really started to flounder.
Okay, let’s try again! If you look at this next example, you can see a slight improvement. The story follows the word problem, his number work stays to the left, and he circled his final answer…but his explanation? On paper it looks okay, but I really had to tease this out of him. It did not come clearly or easily even with me doing the writing for him!
In a Constructivist classroom, by the end of fourth grade I would expect a learner to be able to see a number problem, write a story to go with it, and then write out their proof of how to solve it both in numbers and words. I would expect to see clear thinking, organized work, and neatness. None of that, is as easy as it might sound.
Sometimes, these types of Constructivist activities make certain parents turn vinaceous with annoyance and anger that comes from misunderstanding. I would never expect a child to have to write about every problem they solved. Nor do I think it is fair to hold children back mathematically because they might struggle with reading, writing or language. But doing proof work like this once a week in a small group setting is really helpful for everyone. Teachers get insight into how children are thinking, kids learn from the strategies of each other, and mathematical communication skills get practiced.
As an at-home activity, this has the added bonus of being completely free. I am going to continue working on this type of proof work with Bruce in an Afterschooling setting. I like Houghton Mifflin and I am extremely happy with Bruce’s teachers, but I want him to be successful at work like this too.
## It’s the Teacher NOT the Curriculum, that Makes the Difference!
I recently came across a blog called Out in Left Field whose author espouses the polar opposite of all my views on educational theory. Katharine Beals, PhD, rails against Balanced Literacy Instruction and Constructivist math in particular. Here are links to my own views on why I love Balanced Literacy Instruction and Constructivist math
Katherine Beals takes shots at Bill Gates whom she describes as being misguided, misinformed, and possibly having Asperger’s Syndrome. She also rails against Stanford University professor Keith Devlin, also known as “The Math Guy” on NPR. I haven’t read any of Professor Devlin’s books, but I now want to read all of them! I’m not so sure about Dr. Beals’s book Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School, but I might try reading it anyway just to fairly consider a point of view so opposite than my own. (Note: if you have a child on the Autism spectrum, this book would be of a lot more interest to you. Read the reviews on Amazon, and see why.)
Out in Left Field bugs me for a variety of reasons; she blasts teachers as sometimes being too stupid to teach math, she thinks academics often don’t know what they are talking about, she implies that many mathematicians are cowardly for not speaking up against Reform Math, and she repeatedly professes a belief that rote learning of traditional algorithms is the best way to create mathematical thinkers. But what really bothers me, is Dr. Beals’s general thesis that Reform Math and Balanced Literacy Instruction are B-A-D- Bad!
Teaching with a point of view is not bad, not mater which pedagogy you choose. I could spend the next fifteen minutes telling you why I support the particular education philosophies she hates, but that would be a waste of time. What I know, is that it’s not the curriculum that helps children learn, it’s the teacher
If you give me a group of well-fed, middle class Kindergarteners from moderately stable homes I will teach them to read. If you me a Whole Language curriculum. I will teach them to read! If you give me a Phonics Based program. I will teach them to read! If you give me a Balanced Literacy program. I will teach them to read! Magic pedagogy is not creating readers, good teachers are.
Educators have to teach whatever curriculum the school district hands them. Good teachers deliver the curriculum as instructed, and then use common sense. They see that little Johnny over there is going to be able to read by seeing a new cereal box in front of his breakfast bowl each morning. Great! Let’s make Johnny some patterned books. Little Suzie over there? She really needs more phonics. Bring out the phoneme cards. The reason I like Balanced Literacy Instruction is that it includes both. Teachers have to be flexible!
Now, if you give me forty third graders coming back and forth from Mexico, sleeping next to refrigerators, scared by roving pit-bulls on the playground, no working smoke-detector in my classroom, a principal who downloads pornography in the middle of the school office, no support services whatsoever, and then fail to give me my first paycheck, I’ll give you my 110% best but I can’t make any promises. Even if you give me a phonics based program like Open Court, I might not be able to teach all of those children to read unless you, the community, give me some help. I’m a teacher not a miracle worker.
When I was teaching math at a Constructivist Charter school and I had kids who said, “I’m going to solve this subtraction problem in the traditional way,” and started to borrow and carry, that was just fine with me. It wasn’t okay with all of the teachers at my school, but I was fine with certain kids using traditional algorithms when they wanted to. Kids who have trouble verbalizing, kids who can think faster than they can write, kids who don’t do well in group learning situations… these are students that good teachers make common sense accommodations for.
Good educators teach in ways that accommodate the differentiated learning style of each student. Some kids are going to need to be taught algorithms as a life-raft they cling to. Other kids will become the high-schooler in Academic League who can just look at the question and know the answer. It is unfair to force any one style of learning on all of your students, but it’s not bad to lead into instruction with pedagogy to provide framework and support. As far as pedagogy goes, I think Balanced Literacy Instruction and Constructivism have a lot to offer.
P.S. Ironically, both Dr.Beals and I love Story of the World. 🙂
## Hougton Mifflin Math Expressions, A Review
Those of you familiar with my blog will know that I am a former K-4 teacher who believes in teaching math from a Constructivist perspective. This review of Houghton Mifflin’s Math Expression is based on what I have seen as a parent with my “teacher glasses on”, so to say. I do not have any association with Houghton Mifflin whatsoever.
As a parent, I have had the opportunity to help my son complete the second grade Houghton Mifflin Math Expressions curriculum in a home-study way last year when he was in Kindergarten. Now my role has been simplified (yeah!) to only helping him with his third grade homework. I have also volunteered in my son’s Kindergarten classroom and helped lead many of the small group Kindergarten activities. This gave me a chance to see how the teacher’s guide was written and laid out. I also volunteered to tutor a Kindergartener through my church a few years back, so I got to witness firsthand how an English Language Learner responded to this program.
In general, I am favorably impressed with Math Expressions, but only because as a teacher I have witnessed, and been forced to use, some really awful math programs in the past. (Anyone familiar with Math Their Way?) Houghton Mifflin seems to be trying to strike a balance between Constructivism and traditional algorithm based approaches. This reminds me of the phonics vs. Whole Language debate that resulted in Balanced Literacy Instruction. Math Expressions encourages children to learn to solve arithmetic problems using multiple strategies, but often spoon-feeds the children what these strategies should be.
Pure Constructivists would be very unhappy with Math Expressions because of the way the program directly tells children how to solve problems. This is also a curriculum that usually insists that children “stack” problems (write them vertically) in order to solve equations. Pure Constructivists can sometimes advocate the opposite, and insist that children write problems horizontally. I personally, think children should be able to write problems however they want. On the other hand, Constructivists would be happy with Math Expressions in that it goes beyond borrowing and carrying, as the only way to solve problems.
As a former Kindergarten teacher, I feel very strongly that the Kindergarten curriculum moves way too slowly. The English Language Learner boy I tutored was capable of a lot more than what Math Expressions was having him do. This is also a horrible program for school districts who use the Alternate Day Kindergarten schedule. There is no way you could cover the whole year’s program and only teach math two days a week. On the plus side, the Kindergarten curriculum did include lots of hands-on games and activities to reinforce conceptual learning.
I think my son’s school district has now been using Math Expressions for three or four years. If I recall corectly, they were using Dale Seymour’s Investigations before that. In the past five years, the district’s standardized math scores have gone up 19%, which does not surprise me. Math Expressions seems to be a very “teacher proof” program (although I had that expression!). The teacher guide tells you exactly what to do. It is up to the intelligence and intuition of the teacher herself however, to make this program really great. As with any subject, good teaching is still essential with Math Expressions. Although if your child was stuck with a “bum teacher” (another expression I detest!), they would probably be better off with that teacher using Math Expressions, then a lot of other programs out there.
Finally, I have to mention one thing that is currently bugging me about the third grade program. My son’s homework keeps requiring him to write down his answer numerically and then make a proof drawing of his work. The problem is, my son often solves three digit problems in his head. This is really just a minor annoyance with the program. It is after all, important for mathematicians to be able to explain their thinking and show their work. Unfortunately for Bruce, a proof drawing has nothing to do whatsoever with how he is solving the problem!
If you are a parent reading this whose school district has adopted Math Expressions I would say “Relax! It could be a lot worse.” But if you are looking for ways to support math learning at home, please take a look around my blog because I have lots of ideas for you.
## Right Start Level D
For the past month and half my six year old son Bruce has been working out of the Right Start Level D workbook, which is at the 3rd-4th grade level. Even though it is summer vacation, he is still doing math each day because the rule in our house is that two pages (or one side front and back) of math earn 30 minutes of screen time. So I’m not making Bruce do math all summer, it is his own personal choice.
We do not own the Right Start Level D Teacher’s Guide, but we do have all of the manipulatives at our disposal. I am also familiar with teaching in the Construcvist method and have read the Level C Teacher’s Guide cover to cover. So we even though we are not following the program exactly, I am still able to deliver a lot of meaningful instruction to Bruce, that is a huge step beyond plunking him down on the dining room table and having him do math worksheets.
I don’t know if you can tell from the blown up picture of what he was working on today, but Bruce has quite a sense of humor! He is also still struggling with number reversals. At this point in his math education, I am having him go back and correct the reversals each time. Today however, I chose to ignore them because Bruce was trying to do extra math to earn watching a movie.
We are about 22 out of 150 pages into the Level D workbook, and so far I’m pretty pleased. I think that the workbook can stand alone as an Afterschooling supplement, but that if you were using this program for Homeschooling, you would definitely want to get the Teachers Edition.
## Review: Right Start Level C
We have been using Right Start Level C as part of Bruce’s afterschooling for about seven or eighth months now. We switched over to Right Start, after Bruce completed year of Horizons 1st grade math. I thought Horizons’ first grade program was okay, but that the second grade curriculum focused too much on algorithms. For more information on our experience with Horizons, please see here: https://teachingmybabytoread.com/2011/05/01/horizons-math/
I believe in teaching children math through the Constructivist method, which is where they discover mathematical concepts and strategy themselves, sometiems through hands on discovery. I was very impressed by the philosophy of the Right Start program which stresses understanding over rote memorization. Additionally, I was familiar with Right Start, having used components of the program when I taught 3rd/4th grade at a Charter school.
I decided to shell out out the big bucks and bought the homeschool deluxe set for level C, and I am really glad I did. It has tons of math manipulatives that are useful for Bruce, Jenna, and other math activities we do as well. It also has all of the books, including the Teacher’s Guide. I used the Right Start manipulatives a lot to help explain concepts in Bruce’s school math program, Houghton Mifflin Math Expressions, and we have also used them to help with Life Of Fred Fractions.
The Right Start program has a teacher’s guide that is very creative, detailed, and goes above and beyond what is just in the worksheet book. If you were using Right Start as a stand-alone curriculum, you would really need the teacher’s addition. We were using the program as a supplement to Math Expressions, so we didn’t follow the lessons plans exactly, although Bruce did do almost all of the worksheets.
Since I’m a teacher myself, I read the teacher’s guide almost cover to cover, and then just “winged it”, or taught the lessons intuitively according to all the training I’ve received in teaching mathematics from a Constructivist perspective. But I would definitely recommend following the teacher’s guide, to anyone who was new to the Constructivst approach, or who was using Right Start as their child’s sole mathematics curriculum.
The hallmark of the Right Start program is the abacus, which I was really excited about when the box arrived. My husband is an engineer, who has had the opportunity to work with a lot of coworkers from China, many of whom are abacus devotes. (But a different type of abacus, I should point out.) One of these friends told my husband he could “see the abacus in his mind,” and that’s why he had such exceptional mental math skills. This is the same claim that the author of Right Start makes.
I am still super excited about teaching with an abacus, and intend to do this with Jenna as soon as she is old enough for Level A. The problem with Bruce and the abacus, was that he rejected it from the get-go. You know how there are little babies who reject the pacifier or the bottle? You think, “Did that mother really try hard enough? I mean, did she really try?” Well yes in fact, I did! Bruce would not have anything to do with the abacus at all. Probably his math skills were developed enough already that imposing the abacus into his thinking was something his brain just did not want. He was five years old at the time and had already finished the Horizons first grade workbooks, and half of Hougton Mifflin 2nd grade. This is also party the reason that we could not follow the Right Start lesson plans exactly, because so much of them are abacus based.
Not using the abacus turned out to be okay for our family, because I am not teaching the traditional algorithms of borrowing or carrying to Bruce at this point. The way the Right Start lessons set things up, they use the abacus to teach borrowing and carrying in a manipulative way. So I would have skipped over those parts in the Teacher’s Guide anyway. (For those of you thinking, “What the heck! This lady doesn’t teach borrowing or carrying?”, please see my previous post on subtraction: https://teachingmybabytoread.com/2011/03/15/subtraction/.)
A final point of note. Bruce has almost finished all of Level C, and I’m still stumped by what exact grade level it is. I’ve thought about it a lot, and reread the 2nd, 3rd, and 4th grade standards in our state. I’ve also taught 3rd grade for two years, and a 3rd/4th combo for two years. And yet, I’m still a bit perplexed, because it introduces some concepts that aren’t usually taught in public school until later. In general though, I’d say Level C seems to be in the 2.5 grade – 3.5 grade range. They also have a good placement test online to help you determine which book to choose for your child.
## Square Numbers and Square Roots
Bruce is nearing the very end of Life of Fred Fractions, and one of the last lessons was about square numbers and square roots. He had learned these concepts a while ago, when I taught him the basics of multiplying, but he was unfamiliar with the square root sign. This lesson was a good review. To me, it is also a perfect example of how a Constructivist approach to teaching mathematics solidifies conceptual understanding.
First we built out multiples of 2, 3, and 4. Then we looked to see which arrays were square, and which were rectangle.
Next we labeled all of the numbers. I then asked Bruce to identify the “square” numbers.
Since we hadn’t built out the fives, I had Bruce square 5 on the whiteboard.
We then moved onto the concept of square roots. Bruce is still a bit confused on this point. To be fair, we had just started the square root portion of the lesson when Jenna came running in and scattered all of the blocks! We’ll have to try again later.
## Too Many Algorithims in Life of Fred
Bruce and I are now on chapter 27 of Life of Fred Fractions, and nearing the end.
I still really like the book a lot, but I’m less impressed by it as we near the end. I think the author relies too much on traditional algorithms to teacher mathematical concepts. This is completely contrary to my approach to teaching math, which is Constructivist in philosophy. (For more information on Constructivism, please see my post at: http://teachingmybabytoread.blog.com/2011/03/15/subtraction/)
Earlier in the book, it was easy to do a lot of Constructivist activities and explanations side by side with Life of Fred. To compare, order, reduce, add and subtract fractions for example, Bruce experimented with the Right Start Fraction strips in addition to working with the algorithms taught in Life of Fred. So when the book talked about 2/6 being the same as 1/3, Bruce really understood that well, because he could build those fractions himself.
The fraction strips were also helpful for learning about mixed numbers, and the rules about 0/7 = 0 and 7/7 = 1. In all honesty though, Bruce had a really good understanding of fractions before we even started reading Life of Fred, because of all the times he played Reader Rabbit 2nd Grade math. When he was four and five, we also played lots of games with my homemade fraction cards, such as Fraction War, Capture the Fraction, etc.
I had originally taught him how to reduce fractions, using M’nMs and peanut butter. I’ll have to save the explanation for that one for another time!
Fast forward to now, when we are in the higher chapters of Life of Fred and it is now talking about multiplying fractions, and rules about canceling. Now I can really tell that I never taught past fourth grade, or I probably would have had some tricks up my sleeve to teach these concepts from a Constructivist perspective.
In multiplying fractions, “of” meaning the same thing as “times” makes sense. I’ll be able to explain this if I drag out some M’nMs and peanut butter again. But explaining how canceling works, in a hands-on lesson, still eludes me. If anyone has any ideas please let me know! I’m definitely not satisfied with relying on the algorithm alone, which is what is offered in Life of Fred.
## Subtraction
Bruce finished off his major chapter on subtraction last month, and he wasn’t too keen on it at first. I teach math from a Constructivist perspective, which means enabling children to develop their own meaningful strategies for solving problems, instead of just blindly teaching traditional algorithms. Here’s a nice website that explains more about the Constructivist philosophy: http://mathforum.org/mathed/constructivism.html
Bruce, myself, his classroom teacher, and my husband were all in the trenches there for a few weeks as Bruce explored different strategies for solving triple digit, minus double digit problems with and without regrouping. In normal classroom situations, Bruce would have been exposed to his classmate’s strategies and thinking, which would spur his own ideas, creativity (and showmanship). But since he is working independently through the second grade book, I had to introduce some ideas to get him started.
The first strategy I introduced was solving equations on two abacuses, flipped over on side A, so that they represented 200. (We were starting with problems no greater than 200.) This went on for about a week, and Bruce was not impressed. He does not like using an abacus at all, and so I never got to teach him the side B methods. I was really bummed about this, because my husband worked with an engineer from China, who was just brilliant at math, and Chang said that when he solved problems in his head he could picture the little beads on the abacus sliding. I wanted this for Bruce, but maybe I didn’t introduce the abacus early enough. I’ll know better next time for Jenna.
The second strategy I introduced to Bruce was thinking about the problems in terms of money, and then counting out the equations in pretend change. 236-89 would become \$2.36- .89. Bruce was not too thrilled with this strategy either. He could easily solve problems this way, but under protest.
Finally I broke down and taught him one of the methods the book demonstrated, ungrouping, which uses pictorial representations of hundreds tens and ones. I had resisted showing him this method, because Houghton Mifflin uses it as a precursor to borrowing, which I do not want Bruce to learn until later. But I’m eating a big slice of humble pie right now because this is the method Bruce absolutely loved.
All of a sudden Bruce started tearing through his subtraction work at top speed. He called this strategy “Busting open the hundreds”. I’d usually draw out the squares, lines and dots for him on the white board, and he would erase them and then redraw things as he started working. Pretty soon, he was solving problems in his head, by just looking a the picture and not even erasing anything. Then he didn’t even need the pictures at all.
The way Bruce would solve the above problem is that he would think: “100-89 = 11. 11+36=47 100+47=147” He doesn’t need to do any carrying or traditional algorithms at all, which is a testament to the Constructivist method. Constructivism encourages children to think and understand what numbers really mean, instead of just blinding computing an algorithm, which can stunt their development of number sense. Bruce’s accuracy isn’t 100% yet, but it is on par with your typical second grader. I’ll teach him the traditional methods of borrowing and carrying someday, but not until Bruce can do even harder problems intuitively, in his head.
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https://math.stackexchange.com/questions/1798061/the-largest-product-of-two-n-digit-numbers-which-is-palindrome
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# The largest product of two n-digit numbers which is palindrome
Project Euler: 4 is stated as follows:
## Largest palindrome product
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.
Now I have solved this problem in several ways using programming. One ordinary solution was simply to generate all the products of two 3-digits numbers and pick the largest one. Now this problem can be optimized much further than that, however that is not the point of this question. If one wants to look at a programming solution to this problem, you can find my attempt here.
The first 10 solutions can be found below
1: None x None = None
2: 99 x 91 = 9009
3: 913 x 993 = 906609
4: 9999 x 9901 = 99000099
5: 99979 x 99681 = 9966006699
6: 999999 x 999001 = 999000000999
7: 9997647 x 9998017 = 99956644665999
8: 99999999 x 99990001 = 9999000000009999
9: 999920317 x 999980347 = 999900665566009999
10: 9999999999 x 9999900001 = 99999000000000099999
There is no single digit $a*b$ which can equal a palindrome, since all palindromes are divisible by $11$ and $a,b<10$ since $a$ and $b$ are single digit numbers.
From here a clear pattern emerges. If $n$ is even then the solution is
Solution of the largest palindrome product formed from two even-digit numbers. $$(\underbrace{9 \ldots 9}_{n \text{ times}}) \times (\underbrace{9 \ldots 9}_{n/2 \text{ times}} \ldots \underbrace{0 \ldots 0}_{n/2 - 1 \text{ times}} \ldots 1) = (\underbrace{9 \ldots 9}_{n/2 \text{ times}} \ldots \underbrace{0 \ldots 0}_{n \text{ times}} \ldots (\underbrace{9 \ldots 9}_{n/2 > \text{ times}})$$
Which in a pythonic sense can be written as
nine = '9'*(num/2)
num1 = nine + nine
num2 = nine + '0'*(-1 + num/2) + '1'
product = nine + '0'*(num) + nine
return ((int(num1), int(num2)), int(product))
My question is if a similar pattern can be found for the largest palindrome product formed from two odd digit-numbers.
I know a similar question has been asked before. However my question has still not been answered. The previous question was badly formated and contained factual errors. Eg the largest palindromic product formed from two 7-digit numbers is 99956644665999 not 94677111177649.
• Not all palindromes are divisible by $11$, like $101$ and $131$. – Julián Aguirre May 24 '16 at 14:00
• $3\times3=9$ is the largest palindromic product of a pair of one-digit numbers. – Barry Cipra May 24 '16 at 14:01
• @JuliánAguirre, I think the OP is assuming that the largest palindromic product will have $2n$ digits, in which case it will be divisible by $11$. (My other comment says that the assumption is not warranted when $n=1$.) – Barry Cipra May 24 '16 at 14:03
10 9999996699 9999986701 99999834000043899999
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https://oeis.org/A045616
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This site is supported by donations to The OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A045616 Primes p such that 10^(p-1) == 1 (mod p^2). 15
3, 487, 56598313 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS Primes p such that the decimal fraction 1/p has same period length as 1/p^2, i.e., the multiplicative order of 10 modulo p is the same as the multiplicative order of 10 modulo p^2. [extended by Felix Fröhlich, Feb 05 2017] No further terms below 7.74*10^13 (cf. Fischer's table). 56598313 was announced in the paper by Brillhart et al. - Helmut Richter (richter(AT)lrz.de), May 17 2004 A265012(A049084(a(n))) = 1. - Reinhard Zumkeller, Nov 30 2015 REFERENCES J. Brillhart, J. Tonascia, and P. Weinberger, On the Fermat quotient, pp. 213-222 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971. Richard K. Guy, Unsolved Problems in Number Theory, Springer, 2004, A3. LINKS Richard Fischer, Fermat quotients B^(P-1) == 1 (mod P^2). P. L. Montgomery, New solutions of a^p-1 == 1 (mod p^2), Math. Comp., 61 (203), 361-363. Math Overflow, Is the smallest primitive root modulo p a primitive root modulo p^2?, Jun 09 2010. Helmut Richter, The period length of the decimal expansion of a fraction. Helmut Richter, The Prime Factors Of 10^486-1. Samuel Yates, The Mystique of Repunits, Math. Mag. 51 (1978), 22-28. MATHEMATICA A045616Q = PrimeQ@# && PowerMod[10, # - 1, #^2] == 1 &; Select[Range[1000000], A045616Q] (* JungHwan Min, Feb 04 2017 *) Select[Prime[Range[34*10^5]], PowerMod[10, #-1, #^2]==1&] (* Harvey P. Dale, Apr 10 2018 *) PROG (PARI) lista(nn) = forprime(p=2, nn, if (Mod(10, p^2)^(p-1)==1, print1(p, ", "))); \\ Michel Marcus, Aug 16 2015 (Haskell) import Math.NumberTheory.Moduli (powerMod) a045616 n = a045616_list !! (n-1) a045616_list = filter (\p -> powerMod 10 (p - 1) (p ^ 2) == 1) a000040_list' -- Reinhard Zumkeller, Nov 30 2015 CROSSREFS Cf. A001220, A014127, A123692, A212583, A123693, A111027, A128667, A234810, A242741, A128668, A244260, A090968, A242982, A128669, A039951. Cf. A265012, A049084, A000040. Sequence in context: A230029 A238447 A241977 * A198705 A198624 A198652 Adjacent sequences: A045613 A045614 A045615 * A045617 A045618 A045619 KEYWORD bref,hard,nonn,nice,more AUTHOR Helmut Richter (richter(AT)lrz.de) STATUS approved
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Last modified July 16 04:51 EDT 2018. Contains 312645 sequences. (Running on oeis4.)
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http://www.w3resource.com/python-exercises/numpy/python-numpy-exercise-60.php
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Python NumPy: Convert two 1-D arrays into a 2-D array - w3resource
Python NumPy: Convert two 1-D arrays into a 2-D array
Python NumPy: Array Object Exercise-60 with Solution
Write a Python program to convert (in sequence depth wise (along third axis)) two 1-D arrays into a 2-D array.
Sample array: (10,20,30), (40,50,60)
Sample Solution:-
Python Code:
``````import numpy as np
a = np.array([[10],[20],[30]])
b = np.array([[40],[50],[60]])
c = np.dstack((a, b))
print(c)
```
```
Sample Output:
```[[[10 40]]
[[20 50]]
[[30 60]]]
```
Python Code Editor:
```import numpy as np
a = np.array([[10],[20],[30]])
b = np.array([[40],[50],[60]])
c = np.dstack((a, b))
print(c)```
Improve this sample solution and post your code through Disqus
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https://www.instaclustr.com/seasons-greetings-instaclustr-kafka-christmas-tree-light-simulation/
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# Apache Kafka Christmas Tree Light Simulation – Seasons Greetings From Instaclustr
What would you do if you received a request like this?
Looks like poor old Santa confused us with a company that produces Instant Forests. But maybe Santa knew I’d been trying out Decision Tree Machine Learning (including Random Forests) on our performance data (see previous blogs on Machine Learning with Spark)?
But then I started thinking. Obviously, Santa is “magic” (what online shop can deliver presents to millions of people on Christmas Eve!), so maybe all I had to do was come up with was a simulated virtual tree and Santa could handle the rest?
Where to start? What (in computer science or mathematics) is tree-shaped?
On the first day of Christmas
my true love sent to me:
A Quincunx machine in a Pear Tree
On the second day of Christmas
my true love sent to me:
2 Bean Machines
And a Quincunx machine in a Pear Tree
On the third day of Christmas
my true love sent to me:
3 Galton Boards
2 Bean Machines
and a Quincunx machine in a Pear Tree
On the fourth day of Christmas
my true love sent to me:
4 Pascal’s Triangles
3 Galton Boards
2 Bean Machines
and a Quincunx machine in a Pear Tree
Ok, that’s enough! Ten identical presents are rather boring. A Quincunx machine (also called Bean machine or Galton Board) is a vertical board with nails banged into it in the shape of a Christmas tree.
Here is a clip of one in action.
Balls are dropped from the top (where the “Star” would be on a tree), and bounce either left or right as they hit the nails and drop down to the next level, and so on, until they drop out the bottom. They are collected into bins at the bottom and the height of the bins will eventually approximate a bell curve. Overlaying Pascal’s triangle onto the nails shows the number of different paths that can be taken to get to each bin (as each value is the sum of the two values above it to the left and right, starting with a 1 at the top Star position). The bins towards the middle are reached by more paths and will collect more balls:
Obviously, I’m not the first person to connect these ideas. Here’s a Pascal’s Christmas Tree simulator, a Quincunx simulation, and this blog does a full The 12 days of Pascal’s triangular Christmas!
The Pascal’s Christmas tree simulator (image above) inspired me to use a similar approach for a Christmas tree lights simulator. The tree will be a Galton board, with lights at each nail position (baubles in the above picture). The positions are traditionally rows and columns starting from row 0 at the top, and columns starting from 0 on the left. The star is therefore (0,0). A light will be ON if a ball hits the nail, and will stay on for a second, and then turn OFF. Lights will turn on/off (twinkle!) as balls enter from the top, and drop down to the bottom. If balls drop in fast enough then multiple lights will be on at once.
Time to open up an early Christmas present (Kafka, which is on the Instaclustr roadmap for 2018) and use it to write a scalable Christmas tree lights simulation. Some imagination may be required (perhaps enhanced with a few glasses of Christmas port).
The design choices I had to make were around the number of producers, consumers and topics, what roles they would have, what the message structure would be, and how to handle time.
We’ll start with a single Kafka Producer to drop balls onto the top of the tree (at the Star), with a new ball arriving every second. The “star” is just a simple java producer running in a thread which sends a (0,0) message to the “tree” topic, and sleeps for a second before repeating until the desired number of balls have been released.
Initially, I had thought of using multiple topics to capture the topology of the relationship between the lights, but his would have been too complicated for larger trees. A simpler solution using a single topic (called “tree”) is more obvious. I also decided on a very simple message structure using the Kafka message key as the row value, and the message value as the column. Note that for multiple partition topics this may not be ideal as the key is used for distributing messages across partitions and the small number of row values may not result in a good hash function.
Currently the tree only has the top starlight illuminated all the time. What’s missing? Gravity! To simulate gravity we need a consumer/producer pair, I called this “twinkle”. To twinkle, we receive a message (ball location) from the tree topic, randomly decide if the ball will go left or right, and then publish a message consisting of the new location back to the “tree” topic. Will this work? Not really. This is just an infinite loop, what we really need is a delay queue or explicit timestamp handling, so we can delay the processing of the new ball location until the 1 second ON time has elapsed. A hack for this is to sleep the Twinkle application consumer thread so it only checks for new messages periodically. This is what we have so far.
What’s missing? What should we do with balls that reach the bottom of the tree (the last row)? We could just make them vanish (by not sending a message back to the tree topic). Or better (in the spirit of the Galton Board) let’s add a “count” topic and a Count Consumer to add up the number of balls that fall into each bin under the tree:
The final problem is how to display the tree and lights state? The simplest solution is to have another consumer which subscribes to the “tree” topic and changes the state of the correct lights for each new message in the topic (change of ball location). This is possible and was the approach I tried first. However, the Twinkle and Display consumers have to be in different consumer groups (because of the way the Kafka protocol works, to ensure that they both get every message published to the tree topic), and computing the state and handling timing was tricky:
An improved version computes the state change of the lights in the Tinkle application (step C), and sends a state change message (light location OFF or ON) to the corresponding dedicated topic (Light OFF, Light ON). Every second, the State Display consumer applies all the OFF messages first, and then the ON messages, and then prints the tree lights state (in ASCII). Each “*” is an ON light ON, each “.” is an OFF light.
Here’s a sequence that could be printed for a simple tree with 3 rows, and a single ball dropped in at the top:
Time 1: star lights up (0,0)
## * .. …
Time 2: light at (1,1) ON
## . .*…
Time 3: light at (2,1) ON
## . ...*.
Time 4: All lights OFF
## . ..…
Here’s an (edited) run with 10 rows and 100 balls:
Welcome to the Instaclustr XMAS Tree Simulator!!!!!
## * .. … …. ….. …… ……. …….. ……… ……….
Etc (lots of balls)
## *****..**...**...***.…**..*..**…*..*…....*.***…
Etc (no more balls arriving, eventually end up with all lights OFF)
## . .. … …. ..*.. ..**.. ..**… ..**…. …**…. …..**…
A Happy Normally Distributed Xmas! Counts:
col 0 = 1
col 1 = 2
col 2 = 7
col 3 = 19
col 4 = 28
col 5 = 25
col 6 = 14
col 7 = 4
col 8 = 0
col 9 = 0
Total events counted = 100
More interesting christmas lights with colour could have been simulated by using a richer message structure, e.g. a message number as the key, and a compound value type consisting of (row, col, colour).
Here’s a simplified topology diagram showing just the relationship between producers, topics and consumers.
Is this the best/correct approach for:
• Computing and keeping track of the state of the lights?
• Probably not. Kafka streams and a KTable (which maintains state) may be better. Here’s a blog.
• Handling time?
• Probably not. As I mentioned, using a delay queue or explicit timestamp handling would be better. Essentially I’m using Kafka as a discrete event simulation (DES) which it isn’t really designed for, but in theory, it should work as all you need is events and timestamps. I (briefly) tried using the different timestamp extractors but had a few issues, I suspect that they are designed to work (best) with Kafka streams. So maybe Santa could get a few elves to add some code for this, perhaps using windows.
Will Santa be happy with this? He should be! Given that it’s written in Kafka it will scale massively. It should be easy to increase the speed of the simulation (i.e. run it flat out), increase the size of the tree, and even simulate a forest of trees, each with a slightly different algorithm and/or starting condition, and multiple different ways of displaying the tree/lights. There’s also reprocessing (that I mentioned in this blog), where Kafka persists all the messages, so consumers can choose which messages to process. Consumers could display any historic state of the tree lights.
Canberra was in the news a few years ago with a charity fundraising world record for the number of lights on an artificial Christmas tree. What does ½ a million lights look like?
I just had to see if the Kafka Christmas lights simulator was up to the challenge. It was.
A simulated tree with 500,000 lights and 100,000 balls dropped in ran in 555s, processed over 400 million producer + consumer events, and ran 180 times faster than real-time (running flat out), achieving an average throughput of 43 million events per minute, not bad with everything (Kafka broker and java code) running on my laptop. Why stop there? 1 million and 2 million worked fine, can I claim the world record for the most lights on a simulated Christmas tree?
Here’s the code (Java). Note that I made a minor change to the twinkle application to correctly process the Star light. The Star producer now sends a special message (-1, -1) to Twinkle which interprets this as a special case, i.e. an arriving ball with no location yet, and sends a message back to the tree topic with the star location (0,0) and a (0,0) message to the Light ON topic.
Please check out our Spark Streaming, Kafka and Cassandra Tutorial for details on installing and running Kafka and Zookeeper and visit our GitHub to access all Java Code.
## Java Kafka Code
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# Thread: Quantum Mechanics
1. ## Quantum Mechanics
I have the following problems:
a) Under which conditions we can simultaneously measure (with arbitrary precision) two observables which operators does not commute?
b) Does energy and coordinates of particle's momentum are in general simultaneously measurable. Give the conditions under which this physical quantities are simultaneously measurable. Give an example of quantum system having such property.
c) Are there any conditions under which position and square of momentum are simultaneously measurable. Find an example of such conditions.
2. ## My ideas
a) The uncertainity principle goes like that:
$\sigma^2(A) \sigma^2(B) \geq \frac{1}{4} \left| \langle \psi^* | [A, B] | \psi \rangle \right|^2$
So I think the right answer is: "The observables are simultaneously measurable if mean $\langle \psi^* | [A, B] | \psi \rangle$ is zero."
3. ## my ideas II
b)
Let $D_i$ denote differentiation over i-th coordinate. We have one particle with mass m. The energy operator should be like that:
$E = -\frac{\hbar^2}{2m} \nabla^2 = -\frac{\hbar^2}{2m} \sum_i D^2_i$
Momentum operator (coordinate k):
$p_k = -i\hbar D_k$
I will focus on the commutator: $[p_k, E]$
$[p_k, E] = \frac{i\hbar^3}{2m}\left[D_k, \sum_i D^2_i \right] = \frac{i\hbar^3}{2m}\sum_i [D_k, D^2_i]$
I shall assume $i \neq k$:
$[D_k, D^2_i] = D_kD^2_i - D^2_iD_k$
Let's assume the wavefunction belongs to $C^\infty$ class (mathematiclly very restrictive assumption but I consider it as "physical")
As I remember there was some theorem which states that we can change sequence of differentiation (I guess the assumption was that the second derivative is continuous). It was important theorem but I don't remember it's name .
So under this assumptions for wavefunction we should get:
$D_kD^2_i \psi = D_kD_iD_i \psi = D_iD_kD_i \psi = D_iD_iD_k \psi = D^2_iD_k \psi$
So the commutator $[D_k, D^2_i]$ is zero
I guess it is obvious that: $[D_k, D^2_k] = 0$
So $[p_k, E] = 0$
Which means that operators $p_k$, $E$ commute.
Thus we can simulataneously measure momentum and energy with infinite precision.
It seems to me a little strange because the question "Give the conditions under which this physical quantities are simultaneously measurable. Give an example of quantum system having such property." suggests that they should not commute (otherwise giving the example is trivial - any system has such proprety). Could you check if my reasoning is correct?
4. Originally Posted by albi
a) The uncertainity principle goes like that:
$\sigma^2(A) \sigma^2(B) \geq \frac{1}{4} \left| \langle \psi^* | [A, B] | \psi \rangle \right|^2$
So I think the right answer is: "The observables are simultaneously measurable if mean $\langle \psi^* | [A, B] | \psi \rangle$ is zero."
Yes.
-Dan
5. Originally Posted by albi
b)
Let $D_i$ denote differentiation over i-th coordinate. We have one particle with mass m. The energy operator should be like that:
$E = -\frac{\hbar^2}{2m} \nabla^2 = -\frac{\hbar^2}{2m} \sum_i D^2_i$
Momentum operator (coordinate k):
$p_k = -i\hbar D_k$
I will focus on the commutator: $[p_k, E]$
$[p_k, E] = \frac{i\hbar^3}{2m}\left[D_k, \sum_i D^2_i \right] = \frac{i\hbar^3}{2m}\sum_i [D_k, D^2_i]$
I shall assume $i \neq k$:
$[D_k, D^2_i] = D_kD^2_i - D^2_iD_k$
Let's assume the wavefunction belongs to $C^\infty$ class (mathematiclly very restrictive assumption but I consider it as "physical")
As I remember there was some theorem which states that we can change sequence of differentiation (I guess the assumption was that the second derivative is continuous). It was important theorem but I don't remember it's name .
So under this assumptions for wavefunction we should get:
$D_kD^2_i \psi = D_kD_iD_i \psi = D_iD_kD_i \psi = D_iD_iD_k \psi = D^2_iD_k \psi$
So the commutator $[D_k, D^2_i]$ is zero
I guess it is obvious that: $[D_k, D^2_k] = 0$
So $[p_k, E] = 0$
Which means that operators $p_k$, $E$ commute.
Thus we can simulataneously measure momentum and energy with infinite precision.
It seems to me a little strange because the question "Give the conditions under which this physical quantities are simultaneously measurable. Give an example of quantum system having such property." suggests that they should not commute (otherwise giving the example is trivial - any system has such proprety). Could you check if my reasoning is correct?
You are working at it too hard. $[ D_i, D_k ] = 0$ for all i and k, practically by definition.
Give me a bit to think of a system where you might run into a problem. (And remember, your energy function is not quite general: you could have a potential function in there...)
-Dan
6. ## My ideas III
c)
Again I will consider commutator $[x, p^2]$ in one dimensional space (for simplicity).
We have:
$p^2 = -\hbar^2 \frac{d^2}{dx^2}$
So:
$[x, p^2] = -\hbar^2 \left[x, \frac{d^2}{dx^2}\right]$
$\left[x, \frac{d^2}{dx^2}\right] = x\frac{d^2}{dx^2} - \frac{d^2}{dx^2} x$
Let $\psi$ be a wavefunction. We have:
$\frac{d^2}{dx^2} x \psi = \frac{d}{dx} \frac{d}{dx}x\psi = \frac{d}{dx} \left ( \psi + x \frac{d\psi}{dx} \right) = \frac{d\psi}{dx} + \frac{d\psi}{dx} + x \frac{d^2\psi}{dx^2}$
Hence:
$\frac{d^2}{dx^2} x = 2 \frac{d}{dx} + x \frac{d^2}{dx^2}$
Thus:
$\left[x, \frac{d^2}{dx^2}\right] = -2 \frac{d}{dx}$
Finally:
$[x, p^2] = 2\hbar^2 \frac{d}{dx}$
We should have: $\langle \psi^* | [x, p^2] | \psi \rangle = 0$
It is equivalent to:
$2\hbar^2 \int_{-\infty}^{\infty} \psi^*(x) \frac{d\psi(x)}{dx} dx = 0$
I cannot think of any $\psi$ having such property.
7. Originally Posted by topsquark
Give me a bit to think of a system where you might run into a problem. (And remember, your energy function is not quite general: you could have a potential function in there...)
-Dan
I know, but I wanted to consider the simplest case for the beginning.
8. Originally Posted by albi
I know, but I wanted to consider the simplest case for the beginning.
Or maybe I should consider more general case. Maybe $p_k$ and $E$ would not commute if I add the potential?
9. So I got
$[p_k, E] = \frac{-i \hbar^3}{2m} V_k(\mathbf{x})$
Where $V_k = D_k V$
The most trivial case is when: $V = 0$. Maybe the good example would be "infinite potential well" ?
10. Problem c)
I guess i can do that:
$\int_{-\infty}^{\infty} \psi^*(x) \frac{d\psi(x)}{dx} dx = \int z^* dz$
So the problem is to find the curve $\gamma$ for which: $\int_{\gamma} z^* dz = 0$
But still I don't have idea
11. Originally Posted by albi
Finally:
$[x, p^2] = 2\hbar^2 \frac{d}{dx}$
We should have: $\langle \psi^* | [x, p^2] | \psi \rangle = 0$
It is equivalent to:
$2\hbar^2 \int_{-\infty}^{\infty} \psi^*(x) \frac{d\psi(x)}{dx} dx = 0$
I cannot think of any $\psi$ having such property.
Then let's keep it simple: Consider $\psi(x) = sin(x)$.
-Dan
12. Originally Posted by albi
So I got
$[p_k, E] = \frac{-i \hbar^3}{2m} V_k(\mathbf{x})$
Where $V_k = D_k V$
The most trivial case is when: $V = 0$. Maybe the good example would be "infinite potential well" ?
Actually
$[ p_k, E ] \implies [p_k, p^2 + V] = [p_k, V]$
So yes, a constant potential will work for this. So will a step potential, and possibly a delta function potential (don't quote me on this one, I haven't checked it.)
-Dan
13. Originally Posted by topsquark
Then let's keep it simple: Consider $\psi(x) = sin(x)$.
-Dan
That was my first thought, but I rejected it because there is problem with integral (it is not convergent)...
But if we have sin(x) on some finite interval (integer number of periods) than it should work . Thanks for help.
14. Originally Posted by albi
That was my first thought, but I rejected it because there is problem with integral (it is not convergent)...
But if we have sin(x) on some finite interval (integer number of periods) than it should work . Thanks for help.
Yeah, sin(x) is a lousy wavefunction, isn't it?.I was keeping things too simple. Let's be more general and say that any function $\psi(x)$ that is continuous and bounded with $\lim_{x \to \pm \infty}\psi(x) = 0$ that is an even function will do the trick.
-Dan
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1. INTRODUCTION
Sedimentary rocks, with well developed bedding, and schistose metamorphic rocks, exhibit strength anisotropy to some degree when the loading direction varies with respect to their planes of weakness. When constructing underground excavations in rock, it is common to deal with this anisotropy, as the secondary stress field is oriented parallel to the tangent of the excavation boundary. For statistically homogeneous joint direction and spacing there will be regions around the tunnel boundary where the rock strength will attain minimum and maximum values. In particular, for relatively shallow overburdens, intact rock strength is usually not attained, while failure may be exclusively due to joint slip. In such cases the effect and the importance of strength anisotropy depends on the relative size of the problem in point with respect to the size of the rock structural characteristics (Amandie 1996). On account of the rock strength anisotropy, a circular tunnel is subjected to non-uniform deformations around its circumference. The pressure exerted by the rock to a ring support (e.g. a shotcrete or concrete lining) will be non-uniform while bending stresses may be developed. In the present study, such tunnel over stressing is examined numerically.
2. BACKGROUND
Goodman (1989) illustrated the effect of joint slip by its well-known geometrical method that can be used to identify the extent of slip along the periphery of an underground opening. In this methodology the essential information needed are the exact cross section of the opening and the friction angle of the joint planes. Then, with the aid of a simple geometrical construction, zones of joint slip with potential sliding and flexure around a tunnel of any shape can easily be identified. In Figure 1 this is shown for a circular tunnel driven in a rock mass with one joint set dipping at an angle 45° from the horizontal. To identify the zones of layer slip, the tunnel and the layers are drawn in their correct orientation and two lines inclined at φj to the normal to the layers are drawn as tangents to the tunnel periphery. In Figure 1 two values are considered for the joint friction angle, φj =50° and φj =20°. Goodman's geometrical method offers a fast and precise estimation of the zones that may slip at the tunnel periphery in the case of excavating in an anisotropic rock. The required support pressure to prevent any joint slip is also provided by goodman closed form solutions for calculating the extent of the joint slip zones through the rock mass around circular tunnels are presented by Daemon (1983). For a Hoek-Brown rock mass the extent of slip zones has been studied by Kama (1997). According to Daemon the distribution of elastic stresses, at first, is calculated. Then, the elastic shear stress is compared to joint shear strength, considering a Coulomb slip criterion for the joint. The joint is considered to slip, when the elastic shear stress exceeds the joint shear strength. Therefore, slip zones identified by Daemon correspond to excess shear stress contours τ/τp>=1.
This content is only available via PDF.
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For the seasons unit, I’ve done a fair amount of giving students data sets to graph, looking for patterns, similarities, difference. We have been doing so in order to build evidence for or against various claims about what could cause the seasons. I think we’ve learned a lot along the way.
Anyway, there are two observations that have driven student a fair amount of engagement, and I don’t want to forget them:
#1 McCurdo Station in Antarctica has the sun shining on it for 4 straight months, but its average temperature is still below freezing during that time. [If duration was only factor, then we’d expect McCrudo Station to be very hot]
#2 In June, Murfreesboro, TN is 20 degrees hotter than Quito, Ecuador. [Shouldn’t the equator always be hotter?]
One way I’ve gotten some decent leverage in getting students to really initiate with goal-less problems in early kinematics problems is to ask, “If you had taken this trip with a GPS device, what summary trip information could it give you?”
As a class we generate a list of things the GPS device would or should be able to calculate like:
Time of Arrival
Duration of Trip
Final Location
Total Distance Traveled
Average speed (while moving)
Average speed (during entire trip)
I usually tack on a few things, like it could tell us how far we are from where we started (and in what direction). I also say that a good one should also be able to make a graph. I may or may not introduce average velocity.
My job at some point is to connect each of these to formal language and algebraic symbols used in our text. Unfortunately, our text is sloppy with clock readings vs. time intervals. It’s also sloppy with displacement and position. So it’s a little difficult.
I also think it’s cool to have “average speed while moving” be something that the physics text book doesn’t have, and that we’ll have to completely invent our own way of calculating it.
A question I’ve gotten a lot of leverage out the past two semesters is the following one:
You toss your keys straight up to a friend, who is 30m above you leaning out over a balcony. They keys leave your hand with a speed of 25 m/s. Will it get to your friend?
Sure this is a standard boring question. What makes it work is how the show is run. We start off by listing our best guesses about whether it makes it up and the top height they think it gets to: Their answers this semester ranged between 19m and 40m.
In my class, I actually work out this first answer for them (because I’m supposed to model a sample problem), but I ask for their help along the way.
First, I draw a motion map showing how the speed changes at 1s intervals, and we talk about the speed going from 25m/s to 15m/s to 5 m/s, etc, and how the time to the top is when v = 0 m/s. We talk about how much time it takes to get to 0 m/s if you are losing 10 m/s each second: it takes 2.5s to lose 25 m/s. We also talk about the average speed during the trip (12.5 m/s, half way in between 0 m/s and 25 m/s). This, of course, all builds on ideas we built up last week when talking about 1D acceleration problems.
The answer is immediately given as 12.5 m/s * 2.5s = 31.25m
The best guess this time was 32m, and kudos were given to that group.
Lot’s of students then want to talk about why it’s not 40 m (25m + 15m + 10m), and we get to talk about what constantly changing velocity means.
Because of class constraints, I typically re-derive the 31.25m in a way that is more typical of how they are expected to do it: Write down your knowns and unknowns and pick an equation or two to plug away with.
I then send them off to work on the next question. How fast are the keys moving by the time they reach your friend’s hand? Our guesses range between 1.25 m/s and 2.5 m/s.
The right answer is 5 m/s. And students are pretty surprised to find out that we all underestimated the speed. Every group got the right answer. Most students solved the problem by plugging away into equations. One group did so, but didn’t believe that 5 m/s was right, and so they took another approach, using two equations instead of one.
One group took this approach:
In the first second, the ball slows from 25 to 15, with an average velocity of 20 m/s. Thus in the first second, the ball covers 20 m. In the second second, the balls slows from 15 to 5, with an average velocity of 10 m/s. Thus in the second second, the ball covers 10m. That’s 30m covered, with a final speed of 5 m/s. That same group realized that for the first 2 seconds, the average speed was 15 m/s for 2 seconds, also giving 30m of travel.
Last semester, I had a group solve the problem by finding the speed of a ball dropped 1.25 m/s, arguing on the ground of symmetry that it had to be the same.
We ended the problem this semester by talking about the last 1/2 second, where the ball has an average speed of 2.5 m/s for 1/2 second, thus covering the final 1.25m, and why our guesses for the speed were so off.
Simple problem, but lots of places for intuition, lots of places for multiple approaches, and lots of opportunities to talk about velocity, distance, average velocity, and acceleration.
Here is an introduction from a student project in my physics course, who investigated issues of symmetry in projectile motion:
“Why choose this subject to investigate? Out of all the options to research, why this one? The main and best reason I can give to explain why I chose this is just out necessity… In class, …through visualization [of motion diagrams]we began to realize a possible connection between the upward and downward segments of the path. We started to see the motion as reversing itself after the object reached the top of its path. It was from this, that we as a class began to form that idea that if you throw something up at a specific speed, then when it comes back down and gets to the same height that it must be moving at the same speed.”
And here is another introduction from a different student studying the same phenomena
“The purpose of our experiment was to determine if the speed of a ball being thrown up is equal to the final speed of same ball going down. The motivation for this experiment was in part based on Galileo’s own experiments with gravity. Galileo, an Italian physicist, determined that the force of gravity is constant and objects fall at a constant acceleration toward the earth. He determined this by dropping two cannonballs of different size off of the Tower of Pisa. The law of parabolic fall states, “The distance traveled by a falling body is proportional to the square of the time it takes to fall.”
There are likely many different things to see and ways of responding to these different introductions. But, these two different introductions tell the story about the difference between ideas and concepts. Kevin Pugh, an educational psychologist, writes here about ideas: “Ideas are possibilities that must be acted upon and tried out… Ideas are ways of being in the world… They are inseparable from human experience.” Writing about concepts, he states, “Concepts are established meanings (classics)…When intellectual products attain classic status, they become isolated from the conditions in which they had an original significance and from their potential consequences for everyday experience. As a result, their importance is reflexively accepted, but not fully appreciated…”
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main-content
## Über dieses Buch
Interest in the fascinating field of multicriteria optimization and its application to design processes has grown very quickly in recent years. Researchers and practising engineers will find this book an comprehensive presentation of this subject. After an introduction to multicriteria optimization and the advantages of using multicriteria techniques, the first part of the book presents methods and computer procedures for solving multicriteria optimum design problems including interactive methods and knowledge-based systems. The second part presents an extensive range of applications of these methods to design processes in the fol- lowing fields: mechanisms and dynamic systems, aircraft and space technology, machine tool design, metal forming and cast metal technology, civil and architectural engineering, and structures made of advanced materials.
## Inhaltsverzeichnis
### 1. Multicriteria Optimization — Fundamentals and Motivation
Abstract
A well-known statement of the energy principles says that among all possible displacements the actual displacements make the total potential energy an absolute minimum. This means that the application of the principle of minimum potential energy leads to the fundamental equations of the boundary value problem in the theory of elasticity. The principles of mechanics go back to the 17th century. They allowed the formulation of classical problems in numerous fields of the natural and engineering sciences by means of the calculus of variation [1,2]. G.W. Leibniz (1646–1716) and L. Euler (1707–1783) found a suitable mathematical tool for finding the extreme values of given functions by introducing the infinitesimal calculus, with which it is possible to carry out an integrated treatment of energy principles in all fields of mechanics with application to dynamics of rigid bodies, general elasticity theory, analysis of load supporting structures (frames, trusses, plates, shells), the theory of buckling, the theory of vibrations, etc. Some very interesting examples from the field of classical mechanics are the “curve of the shortest falling time” (“brachistochrone”) and the isoperimetric problem investigated by J. Bernoulli (1655–1705) and D. Bernoulli (1700–1782). Another important problem is that of the “smallest resistance of a body of revolution” solved by Sir I. Newton (1643–1727).
H. A. Eschenauer, J. Koski, A. Osyczka
### 2. Optimization Procedure SAPOP — A General Tool for Multicriteria Structural Designs
Abstract
As presented in Chapter 1, it is an important goal of engineering activities to improve and optimize technical designs, structural assemblies and structural components. The task of structural optimization is to support the engineer in searching for the best possible design alternatives of specific structures. The “best possible” or “optimal” structure here applies to that structure which mostly corresponds to the designer’s desired concept and his objectives meeting at the same time operational, manufacturing and application demands. Compared with the “Trial and Error”-method generally used in engineering practice and based on an intuitive empirical approach, the determination of optimal solutions by applying mathematical optimization procedures is more reliable and efficient. These procedures can be expected to be more frequently applied in industrial practice. In order to apply structural optimization methods to an optimization task, both the design objectives and the relevant constraints must be expressed by means of mathematical functions. One example of a design objective is the demand for the maximum degree of stiffness of a structure which can be described by the objective “minimization of the maximum structural deformation”. The design variables are the parameters of the structure, for example the cross-sectional and geometrical quantities, which should be selected in a way that the objective function can be minimized by considering additional conditions. These conditions or constraints are equality and inequality equations which include the mathematical formulation of demands such as permissible stresses, stability criteria etc.
M. Bremicker, H. A. Eschenauer, P. U. Post
### 3. Interactive Multicriteria Optimization in Design Process
Abstract
In this chapter MO-procedures treated in Chapter 2 will be developed into interactive procedures which integrate the decision making process into optimization algorithms. The interactive procedures provide the Decision Maker (DM) with a selection of Pareto-optimal solutions which to some extent are representative for the whole set of available solutions. This procedure consists of a sequence of decision and computation phases. In the decision phase the DM decides whether or not a solution is optimal with respect to his implicit preferences. In the latter case he must give some information about the direction in which he expects to obtain a better solution. In the computation phase the new solution is generated for the next decision phase. The procedure is stopped when the optimal solution which reflects the DM’s preferences is found. Such a dialogue does not only improve the implicit preferences of the decision maker but also supports and simplifies the process of decision making.
H. A. Eschenauer, A. Osyczka, E. Schäfer
### 4. Knowledge Engineering and Multicriteria Optimization
Abstract
Multicriteria optimization is a useful and challenging activity in many disciplines. It provides decision makers with tools for producing better decisions while saving time in the decision process. In the past, computers have assisted in achieving several advancements in the field of multicriteria optimization. In spite of the rapid development of multicriteria optimization techniques, their applications to real world problems have not been legion. There can be many reasons for a decision maker to avoid numerical optimization techniques and resort to conventional trial and error methods based on judgement, intuition and experience. Decision makers who are not experts in optimization techniques usually experience difficulties while using conventional optimization systems. The aim of this chapter is to show how knowledge-based systems technology can be used to overcome some of the shortcomings of earlier optimization systems. It is illustrated how knowledge-based approaches attempt to make multicriteria optimization an easier tool for decision makers to use.
M. Balachandran, J. S. Gero
### 5. Mechanisms and Dynamic Systems
Abstract
The increasing application of industrial robots in different fields of technology augments the demand for further improvement of their performance. Energy consumption and working accuracy especially are becoming more and more important in assessing the efficiency of a robot. One way to improve these factors is the proper balancing of a robot manipulator. There are two main methods of balancing a robot manipulator: 1) by spring mechanisms or 2) by counterweights [1,2]. The problem of the optimum design of a robot spring balancing mechanism is discussed in Chapter 5.2. In this chapter, counterweight balancing of robot arms is the subject of investigation.
J. Koski, A. Osyczka, J. Zajac, F. Pfeiffer, H. H. Müller-Slany, D. H. van Campen, R. Nagtegaal, A. J. G. Schoofs
### 6. Aircraft and Space Technology
Abstract
In the aerospace industry the methods of structural optimization have been integrated into the process of engineering design in many cases. Especially for complex design problems, their application leads to optimal layouts which fulfill all requirements in the best possible manner. Fundamental suggestions for this use in industrial practice were made by L.A. Schmit [1]. Nowadays, mathematical optimization algorithms and finite element methods set the basis for optimization computations with a high rate of generality and efficiency [2]. The additional inclusion of optimization models leads not only to a very modular architecture but also to the direct consideration of all relevant practical demands [3]. A variety of examples of aircraft and spacecraft structures shows the advantages of this procedure [4].
G. Kneppe, H. Baier
### 7. Machine Tool Design
Abstract
Machine tools are the most fundamental and essential machines in industrial manufacturing shops. Performance of machine tools in terms of machine accuracy (high precision) and machine productivity (high working efficiency) greatly depends on the static rigidity and dynamic characteristics of the machine tools [1–3]. Therefore, until now the design optimization of machine-tool structures has been studied intensively [4–8]. Small static and vibrational displacements are mainly evaluated for realizing high machine accuracy. Far smaller displacements. than those existing at the state of machine failure (breakdown), at which the stress is usually known only approximately, must be considered for evaluating the performance of machine tools. That is, the design of machine tools is a displacement criterion design problem. The static rigidity and dynamic characteristics also depend on the design of the machine structures which are composed of structural members and machine elements as well as of joints connecting the structural members and machine elements.
M. Yoshimura, J. Montusiewicz, A. Osyczka, J. Zamorski
### 8. Metal Forming and Cast Metal Technology
Abstract
Traditionally, there appear to be two optimal die designs, the conical die and the perfect die. The former is in general use because of the ease with which it may be manufactured; the latter is not used at all because it is considered to be too costly to manufacture. In essence, the conical die is a “throw-away” die. The advent of extremely hard materials, however, makes it worthwhile to construct long-lasting optimal dies.
W. Stadler, M. Bremicker, H. Eschenauer, H.-W. Wodtke, L. Henrich, K. Schiffner
### 9. Civil and Architectural Engineering
Abstract
The optimization of civil engineering structures usually involves a number of requirements that should be met at the same time in order to obtain a useful design. In the case of single criteria optimization, one of the requirements is selected as the criterion of optimization while the remaining ones are met by including them into the constraints of optimization. However, while using this approach it is necessary to determine a priori the bounds which these requirements should fulfill a priori. Multicriteria (vector) optimization enables the designer to consider effectively all the different, mutually conflicting requirements inherent in the design problem.
St. Jendo, J. S. Gero, M. A. Rosenman
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### angle of rotation calculator
Search: Angle Of Rotation Calculator. Calculate matrix 3x3 rotation X. The sine of the refraction angle of light waves when they change medium is degrees. 109 3. INSTRUCTIONS: Enter the following: () Enter the angle of rotation. The Vector Rotation formula uses quaternions to compute the resulting vector from the specified rotation. Rotation Matrix in 2D Derivation. This calculator for 3D rotations is open-source software. Enter the angle (in degrees) you wish to rotate your shape by (A z-y-z transformation around angles , , ) Mathematically, a 33 rotation matrix is the product of three sequential rotations Here you can enter two known sides or angles and calculate unknown side ,angle or area Depending on the type of triangle and its known a=angle of rotation. or. The angle of helix is 28 o. HOLLOW SHAFT SHEAR STRESS AND ANGULAR DEFLECTION CALCULATOR. Angle of Rotation Calculator. You can position a part so that any face that is at a compound angle is straight up by making two rotations of the part. Clean & Elegant. Tangential velocity vector is always parallel to the radius of the circular path along which the object moves.Tangential velocity vector is always perpendicular to the radius of the circular path along which the object moves.Tangential velocity vector is always at an acute angle to the radius of the circular path along which the object moves.More items Since its terminal side is Output angle format Radians Degrees. C = L / r. Where C is the central angle in radians; L is the arc length; r is the radius; Central Angle Definition. Calculate the new coordinates of a point that has rotated about the z
= s r. = s r. The angle of rotation is often measured by using a unit called the radian. Measure right, acute and obtuse angles in degrees from 0 to 360 free online. Here you can drag the pin and try different shapes: images/rotate-drag.js. This is read as "34 degrees 24 minutes 16 seconds". Conic Sections: Ellipse with Foci Clean & Elegant. Assuming the clock faces are vertical, the vertical rotation ('tilt back') should be zero. Measure of an angle. The angle of rotation is the smallest angle a shape is turned to make it look the same. [ (n - 2) 180]/n. nNumber of threads. If R is the (3x3) rotation matrix, then the angle of rotation will be acos ( (tr ( R )-1)/2), where tr ( R) is the trace of the matrix (i.e. The full rotation is the angle 2 rad, so the resulting angular velocity is: = 2 rad / 23. The Math / Science. Lauren K. Toney, M.S., M.D. 360 /n This calculator for 3D rotations is open-source software. The vector (1,0) rotated +90 deg CCW is (0,1). The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is. Find your angle. Angle of Rotation Calculator The angle of rotation, is the calculation of how many degrees a shape or an object should be turned if it needs to look the same as its original position. To improve this 'New coordinates by rotation of points Calculator', please fill in questionnaire. As a measure of rotation, an angle is the angle of rotation of a ray about its origin. Let rotate the vector around by a large angle , to obtain the new vector Rotation matrices can be constructed from Rotation definition, the act of rotating; a turning around as on an axis This section doesn't assume the angle sum rule, but uses a version of the angle-sum proof to prove the rotation formulae Along with rotational Results are rounded to seven digits. MOMENT: Newton-Meter Dyne-Centimeter Gram-Centimeter Kilogram-Centimeter Kilogram-Meter Newton-Centimeter Pound-Foot Pound-Inch. The Quaternion of Rotation formula, q =f(,V), computes the quaternion which can be used to rotate a point or vector about an axis defined by a vector (V) for a rotation amount defined by an angle (). Each degree is divided into 60 minutes, and each minute further divided into 60 seconds. Converting this angle into radians as follows: Think about 45. Likes: 502. Order of Rotation. 1/n (n - 2) 180. How to Determine the Orientation of an Object Using OpenCVReal-World Applications. One of the most common real-world use cases of the program we will develop in this tutorial is when you want to develop a pick and place system PrerequisitesInstallation and Setup. Find an Image File. Write the Code. Output ImageUnderstanding the Rotation Axes. Calculate an Orientation Between 0 and 180 Degrees. Calculates the new coordinates by rotation of axes This calculator is for a right triangle only! Hope it saves the rest of you a night or two. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. In geometry, an angle. crit = sin-1 (n r /n i) = invsine (n r /n i). For the angle of rotation part please search for view point estimation of objects. Angle of Rotation in Cn Axis formula is defined as the angle through which the rotation about the Axis in the molecule is calculated and is represented as = 2*pi/n or Angle of Rotation in Cn Axis = 2*pi/Order of Rotation Axis. For your reference, this code computes the Euler angles in MATLAB: With rotational symmetry, Calculate angle of rotation by dividing 360 by 2. Click the Quick Analysis tool button and then click the Totals tab. Angle of rotation = {eq}m \cdot \frac{360}{n} {/eq}, where m is the number of divisions between starting and ending points, and n is the That is what you asked for; I estimate a 90% chance that it is not what you want. Angle of Rotation Calculator Calculator "Excellent Free Online Calculators for Personal and Business use. The unit of measurement for the angle can be switched between degrees or radians. Rotating about a point in 2-dimensional space A typical Q angle is 12 degrees for men and 17 degrees for women 0 $\mathrm{m} / \mathrm{s}$ 4CH ANALOG UNIT U8978 Hence for a hexagon, the angle of rotation is 60 degrees Hence for a hexagon, the angle of rotation is 60 degrees. The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is. Example 34 24' 16''. Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high An online double angle calculator can help you to determine all basic double angle identities of the given angle. A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. We know the angle of elevation formula: Angle Of Elevation = a r c t a n ( R i s e R u n) Putting the values of height and horizontal distance in the above formula: Angle Of Elevation = a r c t a n ( 2 1) Angle Of Elevation = a r c t a n ( 2) Angle Of Elevation = 63.434 . Angle of Rotation Calculator The angle of rotation, is the calculation of how many degrees a shape or an object should be turned if it needs to look the same as its original position. The alpha helix (-helix) is a common secondary structure of proteins and is a righthand-coiled or spiral conformation (helix). Output angle format Radians Degrees. 1/n (n - 2) 180 or [(n - 2) 180]/n. If your angle is larger than 2, take away the multiples of 2 until you get a value thats smaller than the full angle. If to an angle 360 or 2, or multiples of those, are added or subtracted, the resulting angle is equal to the original one. The following equation is used to calculate a central angle contained by a circular arc. Rotation about a Point. ILead. Angle of rotation = {eq}m \cdot \frac{360}{n} {/eq}, where m is the number of divisions between starting and ending points, and n is the total number of divisions or slices in a circle. Use the Quick Analysis tool to calculate totals for the selected cells. Home; About; Schedules; News & Events; Contact Us This angle will be stored in the specified field in decimal degrees from true north. The representation of orientation in space is a complex issue. To convert this to a Rotation matrix Quaternion [x, y, z, w] (radians)} Axis with angle magnitude (radians) [x, y, z] Euler angles (radians) Details. The initial side refers to the original ray, and the final side refers to the position of the ray after its rotation. Enter the angle (in degrees) you wish to rotate your shape by (A z-y-z transformation around angles , , ) Mathematically, a 33 rotation matrix is the product of three sequential rotations Here you can enter two known sides or angles and calculate unknown side ,angle or area Depending on the type of triangle and its known Calculate angle of rotation by dividing 360 by 2. 0 360 90 180 270 45 135 225 315 Angle meter Enter angle in degrees. The fixed point is called the center of rotation . This tool is meant for primarily orthogonal polygons rather than organically shaped ones. A central angle is an angle contained between a radius and an arc length. Coterminal Angle Calculator. Of course, this makes sense because the bitmap is rotated inside the same bounds. It uses the rotation of axis (U) and the rotation angle () to compute the quaternion of rotation (q). the sum of the diagonal elements). The Uniform Circular Motion Calculator calculator will calculate: A positive number in the calculated result indicates an anticlockwise direction of rotation. 360. There are many works that estimate the view points of rigid objects. Shares: 251. The initial side refers to the original ray, and the final side refers to the position of the ray after its rotation. It then uses the quaternion vector rotation formula as follows: V' = qVq *. What is Angle Of Rotation Calculator. Rotation angle is backwards. Download scientific diagram | Rotation angle calculation. Angle of Rotation Calculator. Use this tool to determine the trend of a polygon and use the resulting angle to orient symbology such as markers or hatch lines within the polygon. Online angle meter. You know the coordinates of the line that is part of the square: P1, and P2, so you know the difference in X coordinates: P2.X - P1.X. As a measure of rotation, an angle is the angle of rotation of a ray about its origin. dEffective diameter of thread. they adopt dihedral angles such that the dihedral angle of one residue and the dihedral angle of the next residue sum to roughly -105. In the specific rotation equation, one can note that the units that must be used have been explicitly mentioned, i.e. Rotation Matrix; Quaternion; qx: qy: qz: qw: Z-Y-X Euler Angles phi (about x) theta (about y) psi (about z) Angle-Axis Radians Degress Angle(Theta): x: y: z: Advanced Motion Control for Robotics. A resolver is a rotary transformer consisting of a sensor that is used to accurately measure a rotor's angular position relative to the stator, as well as speed of rotation Solver calculate area, sides, angles, perimeter, medians, inradius and other triangle properties 8319 Radians: 2500 Rotations = 15707 This calculator is The angle of rotation. Use this simple tool to accurately calculate how many degrees are in any roof pitch, stair stringer, or any other slope standard or metric. University of Washington Department of Radiology Version 1.0 Last update: August 4, 2013 Please input the following information about your patient: Enter angles as positive numbers and use radio buttons to specify direction of rotation. (V) Enter the x, y and z component of the axis of rotation vector (V) with commas Basic trigonometric formulas are difficult to remember, so, use this online double angle formula calculator for computing all double angle identities such as sin , cos , and tan with the units in degree, radian, and pi radian. What Are Coterminal Angles? Calculate a Resolvers Angle of Rotation What is a Resolver? For quaternions, it is not uncommon to denote the real part first. The five types of angles are: Acute angles (< 90) Right angles (= 90) Obtuse angles (> 90) Straight angles (= 180) Reflex angles (> 180) There is another angle called full angle, which measures 360 degrees and is called a full rotation of the axis. [ 1 Votes ] A clockwise rotation is regarded as a negatives motion, hence a 310 (counterclockwise) rotation is also known as a 50 rotation (because 310 + 50 = 360, a full rotation (turn)). Search: Angle Of Rotation Calculator. Then select a fraction if there is any. A resolver is a rotary transformer consisting of a sensor that is used to accurately measure a rotor's angular position relative to the stator, as well as speed of rotation Solver calculate area, sides, angles, perimeter, medians, inradius and other triangle properties 8319 Radians: 2500 Rotations = 15707 This calculator is Rotation Axis . This form is used in astronomy and defining latitude and longitude.
OUTSIDE DIAMETER : So working out the angle is easy: school level geometry. The angle of refraction of light waves when they change medium is degrees. Angle of Rotation: How big the angle is that you rotate a figure For this example we will say that point is (6,8) Rectangle calculator, formula, work with steps, step by step calculation, real world and practice problems to learn how to find the area, perimeter & diagonal length of a rectangle in A quadrilateral with four congruent angles is a rectangle Angles and their Measure Usually, when a finer measure is needed we just add decimal places to the degrees. The figure to the left has an order of rotation of It will look the same twice Font Size This will compensate for any number of compound angles on the part. Angle Calculator and Further examples . The solution to the problem involves the use of the above equation for the critical angle.
What Are Coterminal Angles? So if we want to program the ActivityBot to rotate degrees we can multiply by 0.284 in order to find the appropriate number of wheel ticks. Please note that the formula for each calculation along with detailed calculations are available below.
Ticks for Angle = * 0.284. 360 The measure of each exterior angle of a regular n-gon is. 360/n. is measured in degrees, where a full circle is 360 degrees. , or calculate the angle between two positions of the mobile device. The direction of the force is perpendicular (at a right angle) to the flow direction and perpendicular to To get the real scale now, along with the most reliable degree of rotation, I had to follow this method. angle of rotation matrix calculator Skip to content. how to find period of rotationConnecting period and frequency to angular velocity | AP Physics 1 | Khan AcademyFinding the Period and Amplitude of a GraphGraphing Sine and Cosine Trig Functions With Transformations, Phase Shifts, Period Domain & Range The converter can therefore also be used to normalize a rotation matrix or a quaternion. (Radians are actually dimensionless, because a radian is defined as Angle of rotation: Lets find the angle of rotation first: $$\theta = \dfrac{1}{2}\cot^{-1}\dfrac{6-2}{4\sqrt{3}} = \dfrac{1}{2}\cot^{-1}\dfrac{\sqrt{3}}{3}$$. The measure of each exterior angle of a regular n-gon is. The amount of rotation is called the angle of rotation and it is measured in degrees. The factors are the lengths of the sides and one of the two angles, other than the right angle Angles associated with polygons So we divide by radius to get a normalized angle: Youll often see this as Take E = 200 GPa, G = 80 GPa Take E = 200 GPa, G = 80 GPa. The Rotational Angle of Alpha Helix formula is defined as the general formula for the rotation angle per residue of any polypeptide helix with trans isomers is given by the equation is calculated using Rotation angle per residue = acos ((1-(4* cos (((Dihedral angles around negative 65 + Dihedral angles around negative 45)/2)^2)))/3).To calculate Rotational Angle of Alpha Helix, Perform, in sequence, a rotation for each possible choice of positions 821 180 degree rotation calculator products are offered for sale by suppliers on Alibaba the first rotation is by an angle about the z-axis using , 2 the first rotation is by an angle about the z-axis using , 2. And here you can choose an angle and see how to rotate different shapes point-by-point. Insert the totals in the empty row below the cell range. Angle Unit (Rotation Axis 0:x, 1:y, 2:z) To improve this 'New coordinates by 3D rotation of points Calculator', please fill in questionnaire. example. Angle formed by the second force to the direction of bar ( 2) Please note that the formula for each calculation along with detailed calculations are available below. Calculate a Resolvers Angle of Rotation What is a Resolver? PPitch. Uniform Circular Motion Calculator. Residues in -helices typically adopt backbone (, ) dihedral angles around (-60, -45). Angle Calculator | Slope to Degrees. Search: Angle Of Rotation Calculator. example Eulers rotation theorem states that, in (3D) space, any displacement of a rigid body in such way that a point on the rigid body remains fixed is equivalent to a single rotation about an axis that passes through the fixed point.Accordingly, such rotation can be described by three independent parameters: two The measure of each interior angle of a regular n-gon is. For illustration purposes, I have attached an image of the line with the angle that I want to calculate. crit = sin-1 (1.000/2.42) = 24.4 degrees. I have put a java applet here which allows the values to be entered and the converted values shown along with a graphical representation of the orientation. Please note that rotation formats vary. Here with the help of a construction angle calculator, you can solve such problems in a fraction of seconds without wasting your precious time. The point rotation calculator executes the original points and transforms them into the new Rotionation axis. Please input the threading information. Coterminal Angle Calculator. x,y,z = vector representing axis of rotation. The calculation, though not difficult, seems messy so we will skip some steps in between. Double-angle trigonometric identities will be used to get to the final result. 1.
per second To improve this 'New coordinates by rotation of axes Calculator', please fill in questionnaire , the above figure corresponds to an alias transformation), is The angle is larger than a full angle of 360, so you need to subtract the total angle until its small Although these Euler Angles can always be used to find Fully Responsive. Try It Yourself. Let rotate the vector around by a large angle , to obtain the new vector Rotation matrices can be constructed from Rotation definition, the act of rotating; a turning around as on an axis This section doesn't assume the angle sum rule, but uses a version of the angle-sum proof to prove the rotation formulae Along with rotational TIR and the Sparkle of Diamonds. We now rotate G in the counter-clockwise direction by an angle . To verify the above formula, we can see that a rotation of 90 degrees = 90 * 0.284 ticks = 25.56 ticks = 26 ticks (rounded up). If the mirror is rotated through an angle the normal is rotated by an angle &phi and thus the angle of incidence increases to +. Lead angle. View question - rotate the aces to eliminate the xy term for 2x^2-72xy+23y^2-80x-60y-125+0 Register Other ways of saying it:"Doing a 360 " means spinning around completely once (spinning around twice is a "720")."I gave the wheel one complete turn looking for holes""It completed one cycle ", meaning it went around exactly once."It was spinning at 200 revolutions per minute" (but people usually say "RPM" instead of "revolutions per minute").More items I am trying to determine the angle of rotation and the calculation that I am using currently is as below: angle = math.atan2(y2-y1,x2-x1)
Conic Sections: Parabola and Focus. This calculator will tell you it's (0,-1) when you rotate by +90 deg and (0,1) when rotated by -90 deg. Leg Rotation Calculator Michael L. Richardson, M.D. Let G be a vector in the x-y plane with a length r and it traces out an angle v with respect to the x-axis. Conic Sections: Parabola and Focus. The angle of rotation is a measurement in mathematics of the amount, or angle, that a figure is rotated around a given point, usually the centre of a circle. Relatively speaking, the critical angle for the diamond-air boundary is an extremely small number. The Uniform Circular Motion Calculator calculator will calculate: A positive number in the calculated result indicates an anticlockwise direction of rotation. The positive value of the pivot point (rotation angle) rotates an object in a counter-clockwise (anti-clockwise) direction first 600 seconds, and then The declination of an object is its angle in degrees, minutes, and seconds of arc above or below the celestial equator Proof by long-hand variant of angle sum proof 5 Axis Rotation Calculator You have a CAD model of a part which you want to mill a face that is at a compound angle. Think about 45. You can use a protractor to measure the specified angle counterclockwise. For this example, well use 28/9 2. Here, is the angle of rotation in the anti-clockwise direction. Take one of the angles - the top right in your example. Click the first Sum button. Enter moment, diameter and length values, select your material and units as required. Calculation of Thread Lead Angle. A parallelogram or rhomboid is a quadrilateral with parallel opposite sides of the same length and opposite angles of the same size 4CH ANALOG UNIT U8978 The positive value of the pivot point (rotation angle) rotates an object in a counter-clockwise (anti-clockwise) direction See full list on calculator A clockwise rotation is considered a negative rotation, so that, for Online angle measurement tool. from publication: Paper No 17.4: 3D Auto-stereoscopic display using pico-projectors and rotating screen |
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# 5.4.1. Experimental Probability
During a football team training, one of the players shot 31 penalty kicks and scored 24 goals while another player shot 20 penalty kicks and scored 10 goals. Which of them should be chosen to shoot a penalty kick?
• Aplayer one
• Bplayer two
### Example
During a football team training, one of the players shot 31 penalty kicks and scored 24 goals while another player shot 20 penalty kicks and scored 10 goals. Which of them should be chosen to shoot a penalty kick?
### Solution
Step 1: Determine the probability that player one's penalty kick results in a score.
Divide the player's number of goals by the player's number of penalty kicks.
Step 2: Determine the probability that player two's penalty kick results in a score.
Divide the player's number of goals by the player's number of penalty kicks.
Step 3: Compare the probabilities.
Rename the fractions with a common denominator.
, so player one has a greater probability of scoring a goal. Therefore, player one should be chosen to shoot the penalty kick.
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# Comparing Zager and Zimba
Saw a couple of interesting reads in the last couple of weeks, and they don’t have much overlap.
Tracy Johnston Zager wrote a piece on math apps for kids:
My Criteria for Fact-Based Apps
and Jason Zimba, one of the people behind the Common Core Math curriculum, wrote about how he’s helped his own kids with math here:
Can Parents Help With Math Homework? YES
Giving the timing, I assume the 2nd article was at least in part written to clarify some points in this article from a few weeks ago
Back Off Parents: It’s not your job to teach Common Core Math when helping with homework
where his quote:
“The math instruction on the part of parents should be low. The teacher is there to explain the curriculum,” said Zimba.
got a little more publicity than usual.
What caught my eye in Zimba’s more recent piece was this paragraph:
“Parents can also help at home with skill building and fluency practice—things like memorizing basic math facts. When it comes to skills, practice is essential. It helps students to have someone to flash the cards or pose calculations to them. I have made flashcards that we use at home, and my kids sometimes use digital apps like Math Drills.”
Particularly because Zager’s piece went in nearly the opposite direction when it came to math apps – for example:
“I don’t want to see naked number drills, especially not for 3rd graders. Flashcards embedded in silly or glitzy contexts are still flashcards. I want to see mathematical models like arrays, groups, hundreds charts, and number lines. ”
It certainly appears from the screen shots on the Math Drills app page:
Math Drills on the Itunes web page
that this app wouldn’t meet many (if any) of the criteria that Zager looks for in a math app for kids.
Anyway, both articles are fascinating reads. It is interesting to me to see influential people in math education having ideas that seem almost almost totally opposite of each other.
# Can you believe that a dodecahedron folds into a cube
Last week I saw an incredible post by Simon Gregg:
In Gregg’s post there is an amazing GIF of a dodecahedron unfolding into a cube:
which Gregg found on this other amazing blog post:
The Golden Section, The Golden Triangle, The Regular Pentagon and the Pentagram, The Dodecahedron
After seeing the post I guessed that there would be a way to make the shape from our Zometool set and gave it a shot on Tuesday while the kids were out for the evening:
Playing around with a neat post from Simon Gregg
Today I went through the same exercise with the boys. It took about an hour – because it isn’t obvious, especially for kids, how to make the shapes – but it was so much fun. The project has a great balance between “there’s no way to do this” and “there must be because I just saw it”. Definitely one of the most interesting Zome projects we’ve ever done.
The boys did all of the work on their own. My only suggestion to them was to build the original dodecahedron out of medium blue zome struts. This choice minimizes the number of Zome balls you need later in the project which also minimizes confusing about the shape.
We started by looking at the original gif:
After that the boys decided to build a dodecahedron and along the way the thought that putting a cube on the inside would help:
The shape in the previous video gave them an idea of how the dodecahedron would unfold into a cube. It took probably 20 minutes for them to build the shape representing the folded up doedcahedron. Their approach was to build the cube first and they try to construct the parts on the inside. Understanding all of the rotations and how the various pieces fit together is fairly challenging.
One bit of this shape that the boys found interesting was the shape on the inside, so I had them build that shape next. This part of the build probably took about 15 minutes – even holding the shape in the cube right in front of you, this shape is not super easy to understand:
Finally, I had them connect up the Zome balls inside of the shape to form an icosahedron. It was pretty surprising to me to find this icosahedron hiding inside of this “8 pointed star.” They built that shape and we wrapped up the project:
So, I think this is a fantastic project for kids. The approach that Simon Gregg took with paper is incredible, and if you have a Zometool set you can create the various shapes pretty quickly. I’m still amazed that an dodecahedron can fold up into a cube! Platonic solids are amazing 🙂
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# ofVectorMath length approximations
hey,
since sqrt() is just about the single most cpu heavy thing you can do, it’s nice to have some ways to approximate the length of a vector without using it. so here’s a couple of methods i’ve been using in my own vector classes up til this point, i thought it might be nice to share them - i think they’d go very nicely on the ofxVec2f/3f/4f classes
they both apply Newton’s iterative method for square root approximation, and work very nicely if you pass in a reasonable value for ‘guess’. eg, if you’re tracking the length of a vector over time, with moving endpoints, store the value you got last frame, and use that as your ‘guess’ next frame.
``````
/// not so accurate
float lengthApprox const( float guess = 1.0f )
{ return 0.5f*(guess + lengthSquared()/guess); }
/// a bit more accurate
float lengthApprox2 const( float guess = 1.0f )
{ return lengthApprox(lengthApprox(guess)); }
``````
they will work as is in ofxVec2f, 3f, and 4f.
enjoy…
d
To calculate a vectors length, square the vectors components, add the squares, and take the square root of the sum, which you can see in the following equation:
v = < x, y, z >
||v|| = sqrt[(x * x) + (y * y) + (z * z)]
Another optimization is to offer a function that returns the square of the vector’s length instead. This avoids the square root and often in calculations the square of the distance can be used instead.
… oh and how convenient lengthSquared is already in ofxVectorMath
Out of curiosity I just placed a loop into update() doing 10,000,000 (!) sqrt calculations. Cpu time goes up by 50%. It’s not half as dramatic as I thought.
you mean, 10 million sqrts ups the cpu time from (say) 10% to (say) 15%? or from (say) 10% to (say) 60%?
interesting… i shall have to profile myself…
still, if you need to find nearest neighbour pairs in a set of 1000 3d points, that’s 10 million length() calls just like that.
well you can always set up an outside thread to do the math and have the main thread focus on plugging in the numbers. If you are that concerned about optimizing 2 or 3 sqrt() infused loops then you can go be extreme and use your “guess work” but your precision is going to be way off. You really can’t have gaping errors like 0.1 or 0.5 in physics or vectors since that would be the same as using integers. So suck it up and use sqrt().
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#### Archived
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# when equation = 0
This topic is 6062 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I don't know where my head was back in math class, perhaps up something else, but now I'm regretting not paying attention. Gotta find out when certain equations = 0 e.g. x(x + 3) = 0 when x = 0 or x = -3 Easy enough, but what about 6(x^2 - x - 6) (I figured out it was x = 3 & -2) So what was the method for finding these things? ------------ - outRider - Edited by - outRider on October 15, 2001 10:51:24 PM
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There are a couple ways of doing this. First of all, you can factor the equation. 6(x^2 - x - 6) is equal to 6(x+2)(x-3), and any part of the equation equaling 0 makes the whole thing 0, so x can equal either -2 or 3. Also, there is the quadratic equation, which is (-b +or- sqrt(b^2-4ac))/2a for any equation ax^2 + bx + c = 0. Hope this helps!
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Remember the quadratic equation?
You previous post said you can't figure out 6(x^2 - x - 6) = 0
Ok this is how you do it
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
So, you get 6((1 +/- sqrt(1 + 24)) / (2a))
Simplify you get
6((1 +- 5) / 2)
so the answers you get are
-2 and 3
The Quadratic Equation at its finest :-)
You could have also factored everyting into 6(x+2)(x-3) to get the same answer; the quadratic is better for more complex things.
Edited by - Viscous-Flow on October 15, 2001 11:02:13 PM
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ahhh, i LOVE the quadratic equation
it made me no longer have to factor those damn things
--- krez (krezisback@aol.com)
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I remember the quadratic equation but it doesn''t always give me meaningful answers. The reason I''m doing this is because I have a function g(x) = 3x^4 - 16x^3 + 6x^2 + 72x + 8
g`(x) = 12x^3 - 48x^2 + 12x + 72
To find the critical numbers I''d have to find all the values for x that the equation = 0...
using the quadratic equation after getting it in the form ax^2 + bx + c gets me into decimals and shit... bah, I''ll just factor.
Calculus blows when you have to take it in a CS program.
------------
- outRider -
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Basically the same as using the quadratic formula is completing the square. You have an equation of the form a*x^2+b*x+c=0. You can divide through by a to get x^2+b*x/a+c/a. Then to complete the square you add and subtract one half the x term coefficent squared (x^2+b*x/a+b^2/4a^2)+c/a-b^2/4a^2=0 which is the same as (x+b/2a)^2+c/a-b^2/4a^2 which is the same as (x+b/2a)^2+(4ac-b^2)/4a^2=0. Now to solve for x you move the constant to the right hand side, (x+b/2a)^2=(b^2-4ac)/4a^2, take the square root, x+b/2a=+/-sqrt(b^2-4ac)/2a, and finally subtract b/2a to get the quadratic formula x=-b/2a+/-sqrt(b^2-4ac)/2a or (-b+/-sqrt(b^2-4ac))/2a.
I always have trouble remembering the quadratic formula and find it much easier to remember how to derive it.
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As has been previously mentioned, homework (or school, as opposed to Game Development related) questions should not be posted to this site. The answer to the above problem can be found in ANY elementary calculus text book. It only takes a walk to the library to look it up if you don''t own one yourself. Discovering the answer for yourself gains you far more understanding than someone telling it to you.
Regards,
Timkin
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# Photons and uncertainty principle
Let's assume we have a perfect single-photon source: a device emitting exactly one photon at a time, with defined energy and direction. Let's shoot a photon: we know exactly the position of the photon (starting point and time, velocity) and it's momentum (energy and velocity). Would such a device violate uncertainty principle? Where is the trap?
Just to clarify things, my question essentially is: a particle (e.g., a photon) prepared in an eigenstate of momentum can be found everywhere (at least along the direction of momentum)?
-
The device that shoots the photon has a finite size, and that is the source of uncertainty of photon's position. – Siyuan Ren Aug 21 '12 at 17:02
In your post when you say you 'know' the position and momentum of a single photon you really don't know anything, you are just making a prediction, not making a measurement. In your head you are basically assuming classical physics and using the initial parameters of the system to calculate the final parameters. In order to actually know any properties about a system you will have to perform a measurement, and to really say anything conclusive you will have to do this many times. Take your single photon source and measure the momentum and position of the outgoing photons numerous times - the product of the standard deviation in momentum and position will be greater than $\frac{\hbar}{2}$.
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# BASIC ELECTRICAL SAFETY
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## Kimberly Rae Rama
on 31 August 2014
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#### Transcript of BASIC ELECTRICAL SAFETY
BASIC ELECTRICAL SAFETY
HAZARDS OF ELECTRICITY
Shock – Most common and can cause electrocution or muscle contraction leading to secondary injury which includes falls
Fires – Enough heat or sparks can ignite combustible materials
Explosions – Electrical spark can ignite vapors in the air
Arc Flash - can cause burns ranging from 14,000 degrees f. to 35,000 degrees f
Arc Blast – In a short circuit event copper can expand 67,000 times. The expansion causes a pressure wave. Air also expands adding to the pressure wave
Fundamentals of Electricity
Electrical current is the flow of electrons through a conductor.
A conductor is a material that allows electrons to flow through it.
An insulator resists the flow of electrons.
Resistance opposes electron flow.
Effect of Current Flow
He sweats- and he dies...
Summary - Hazards and Protection
Take Electricity Seriously!!!
Electricity is the second leading cause of death in construction.
Electrocutions make up 12% of construction fatalities annually.
Over 30,000 non-fatal shocks occur each year.
Over 600 deaths occur annually due to electrocution.
Contact with both conductors
Contact with one conductor and ground
With a tool: contact with “hot” metal part and ground (1), (2) & (3)
Severity of the Shock
Severity of the Shock depends on:
Amount of current
Determined by voltage and resistance to flow
Path through the body
Duration of flow through the body
Other factors such as general health and individual differences.
Current Flows in a
Loop or Circuit
Circuits are AC (alternating current) or DC (direct current).
Current is usually AC.
AC current has five parts:
(1) Electrical source
(2) HOT wire to the tool.
(3) The tool itself
(4) NEUTRAL wire returns electricity from the tool
(5) GROUND
Drilling and cutting through cables
Using defective tools, cables and equipment
Failure to maintain clearance distance of 10 feet
Failure to de-energize circuits and follow Lockout/Tagout procedures
Failure to guard live parts from accidental worker contact
Unqualified employees working with electricity
Improper installation/use of temporary electrical systems and equipment
By-passing electrical protective devices
Not using GFCI (ground fault circuit interrupters) devices
Missing ground prongs on extension cords
How Shocks Occur
Current travels in closed circuits through conductors (water, metal, the human body).
Shock occurs when the body becomes a part of the circuit.
Current enters at one point & leaves at another.
Electrical Accidents
Shocks occur in 3 WAYS
Effects of Current Flow...
More than 3 milliamps (ma): painful shock
More than 10 ma: muscle contraction
More than 20 ma: considered severe shock
More than 30 ma: lung paralysis - usually temporary
More than 50 ma: possible ventricular fibrillation (usually fatal)
100 ma to 4 amps: certain ventricular fibrillation (fatal)
Over 4 amps: heart paralysis; severe burns
Luling, La. - A man was electrocuted when his sweat dripped into the electric drill he was using to build a swing set in his backyard, the coroner said.
Richard Miller was pronounced dead Sunday at St. Charles Hospital, said David Vial, St. Charles Parish coroner. Miller, 54, had been using an electric drill in 90 degree heat, Vial said Monday.
“Apparently the man was sweating profusely,” Vial said. “He probably was pushing against the drill with his chest and his perspiration went into the drill itself and made a contact.”
The Associated Press
Controlling Electrical Hazards
Employers must follow the OSHA Electrical Standards (Subpart K)
Electrical installation
Subpart K includes four proactive methods:
Electrical Isolation
Equipment Grounding
Circuit Interruption
Safe Work Practices
Electrical Isolation
We can be safe by keeping electricity away from us. We can:
Insulate the conductors.
Example: The insulation on extension cords.
Elevate the conductors.
Guard the conductors by enclosing them.
Example: Receptacle covers, boxes, & conduit.
Insulating the Conductors
The first way to safeguard workers from electrically energized wires is through insulation.
Rubber and plastic is put on wires to prevent shock, fires, short circuits and for strain relief.
It is always necessary to check the insulation on equipment and cords before plugging them in.
Remember, even the smallest defect will allow leakage!
Elevating Conductors
The second way to safeguard workers from electrically energized wires is by elevating them.
Wires are often elevated by the power company.
It is always necessary to check the location of overhead lines before you begin work each day.
Clearance of worker and any equipment, tools, materials, or scaffold near uninsulated lines is 10 feet!
A worker was attempting to move mobile scaffold.
Scaffold made contact with 7200 volt line.
The worker died.
Guarding the Conductors
The third way to safeguard workers from electrically energized wires is by guarding them.
Covers, boxes, and enclosures are often put around conductors to prevent worker contact.
It is always necessary to check that electrical boxes and panels are covered and free from missing “knock-outs”.
Remember, electric equipment operating at 50 volts or more must be guarded!
Equipment Grounding
We can be safe by providing a separate, low resistance pathway for electricity when it does not follow normal flow (ground prong).
Grounding gives the stray current somewhere to go and keeps you from becoming part of the circuit.
What Must be Grounded?
All circuits and extension cords.
All non-current carrying metal parts.
Portable & semi-portable tools and equipment unless double insulated.
Circuit Interruption
We can be safer by automatically shutting off the flow of electricity in the event of leakage, overload, or short circuit.
Ground Fault Circuit Interrupters (GFCI) are circuit protection (or “overcurrent”) devices that protect you, the worker.
Circuit breakers & fuses protect equipment, not you, because they take too much current & too much time to trip.
Circuit Protective Devices
Circuit Breakers and Fuses
Only protect the building, equipment, and tools from heat build-up!
Never depend on circuit breakers or fuses to prevent shocks!
Ground Fault Circuit Interrupter (GFCI)
Is the only device which will protect the worker from shock and electrocution!
GFCI Protection
All temporary circuits are required to have GFCI protection and
Equipment & cords must be included in an Assured Equipment Grounding Conductor Program
An extension cord is a temporary circuit.
Types of GFCIs: receptacle, circuit breaker
Must be wired correctly and tested.
Assured Equipment Grounding Conductor Program
Requires the following:
-Written program and specific procedures
-Program implemented by a Competent Person (one who is capable of identifying existing and predictable hazards in the surroundings or working conditions which are unsanitary, hazardous, or dangerous to employees, and who has authorization to take prompt corrective measures to eliminate them.
-Equipment grounding conductors must be tested (tools, extension cords, and circuits):
At least every three months for cords & tools
At least every six months for receptacles
Temporary Wiring
There must be separate circuits for electric tools and lighting, each labeled as such.
Light circuits do not require a GFCI. Unless used in a wet location.
Test branch circuits before use.
Maintain vertical clearances.
Insulate wires from their supports.
Extension Cords and Cables
Must be in good shape without splices.
Cannot be secured with staples, nails or bare wire.
Must be protected from damage.
Must have a ground pin.
Should be inspected regularly and pulled from service if defective.
Cannot be repaired with electrical or duct tape. Must be repaired with heat-shrink sleeve or bonding/vulcanizing tape to retain original insulation properties.
Acceptable Cord Types
All cords must meet the National Electric Code’s (NEC) requirement for Hard/Extra Hard type.
Look for markings stamped on cords.
Acceptable Cord Types:
Extra Hard Use Markings: S, ST, SO, STO
Hard Usage Markings: SJ, SJO, SJT, SJTO
No flat cords allowes on construction sites!!!
Safe Work Practices
Before work begins, the employer must determine where exposed and concealed electrical circuits are located.
Once found, warning signs/labels must be posted.
Workers need to know the location, hazards, and protective measures.
Competent Person determines if performance of work could bring contact with energy.
Distance of the worker to the energy source should be considered first.
Tools, materials, and processes should also be considered to see if they could potentially shorten the safe separation distance.
Must not permit work near electric circuits unless the worker is protected by:
De-energizing the circuit and grounding it.
Guarding it effectively by insulation.
Other means (maintaining safe separation)
De-energized circuits and equipment must be locked/tagged out.
No metal ladders for or near electrical work.
No wet hands when plugging or unplugging cords/equipment.
No raising or lowering tools by the cord.
Unless equipment is designed for it, cannot be used in damp and wet locations.
Common OSHA Citations:
.404(b)(1)(i): Branch circuits: GFCI protection/Assured Equipment Grounding Conductor Program
.404(f)(6): Grounding path
.403(b)(2): Equipment installation and use
.404(b)(1)(ii): GFCI
.403(i)(2)(i): Guarding live parts
Hazards
Exposed electrical parts
Ungrounded electrical systems and tools
Damaged power tools and equipment
Using the wrong PPE and tools
All hazards are made worse in wet conditions
Damaged extension cords
Unqualified workers doing electrical work
Protective Measures
Proper grounding
Use GFCI’s
Use fuses and circuit breakers
Guard live parts
Lockout/Tagout
Proper use of flexible cords
Close electrical panels by Competent Person
Employee training
Ensure Competent Person on site
Use proper approved electrical equipment
Qualified person install electrical devices
What is SAFETY?
It is the state of being "safe" (from French sauf), the condition of being protected against physical, social, spiritual, financial, political, emotional, occupational, psychological, educational or other types or consequences of failure, damage, error, accidents, harm or any other event which could be considered non-desirable.
Safety can also be defined to be the control of recognized hazards to achieve an acceptable level of risk.
This can take the form of being protected from the event or from exposure to something that causes health or economical losses.
What is Electricity ?
It is the set of physical phenomena associated with the presence and flow of electric charge. Electricity gives a wide variety of well-known effects, such as lightning, static electricity, electromagnetic induction and electrical current. In addition, electricity permits the creation and reception of electromagnetic radiation such as radio waves.
History of electricity
Long before any knowledge of electricity existed people were aware of shocks from electric fish. Ancient Egyptian texts dating from 2750 BC referred to these fish as the "Thunderer of the Nile", and described them as the "protectors" of all other fish.
Several ancient writers, such as Pliny the Elder and Scribonius Largus, attested to the numbing effect of electric shocks delivered by catfish and torpedo rays, and knew that such shocks could travel along conducting objects. Patients suffering from ailments such as gout or headache were directed to touch electric fish in the hope that the powerful jolt might cure them.
Possibly the earliest and nearest approach to the discovery of the identity of lightning, and electricity from any other source, is to be attributed to the Arabs, who before the 15th century had the Arabic word for lightning (raad) applied to the electric ray.
Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers. Thales of Miletus made a series of observations on static electricity around 600 BC, from which he believed that friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing.
Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber.
Further work was conducted by Otto von Guericke, Robert Boyle, Stephen Gray and C. F. du Fay. In the 18th century, Benjamin Franklinconducted extensive research in electricity, selling his possessions to fund his work. In June 1752 he is reputed to have attached a metal key to the bottom of a dampened kite string and flown the kite in a storm-threatened sky. A succession of sparks jumping from the key to the back of his hand showed that lightning was indeed electrical in nature. He also explained the apparently paradoxical behavior of the Leyden jar as a device for storing large amounts of electrical charge in terms of electricity consisting of both positive and negative charges.
In 1791, Luigi Galvani published his discovery of bioelectricity, demonstrating that electricity was the medium by which nerve cells passed signals to the muscles.
Alessandro Volta's battery, or voltaic pile, of 1800, made from alternating layers of zinc and copper, provided scientists with a more reliable source of electrical energy than the electrostatic machines previously used.
While the early 19th century had seen rapid progress in electrical science, the late 19th century would see the greatest progress in electrical engineering.
n 1887, Heinrich Hertz discovered that electrodes illuminated with ultraviolet light create electric sparks more easily.
In 1905 Albert Einstein published a paper that explained experimental data from the photoelectric effect as being the result of light energy being carried in discrete quantized packets, energising electrons. This discovery led to the quantum revolution.
Full transcript
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Worldwide Scientific Equipment is considering a cash acquisition of Medical Labs for 1.5 million. Medical Labs will provide the following pattern of cash inflows and synergistic benefits for the next 25 years. There is no tax loss carry forward.
Years
1-5 6-15 16-25
Cash inflows (aftertax) \$100,000 \$120,000 \$160,000
Synergestic benefits (aftertax) 15,000 25,000 45,000
The cost of capital for acquiring firm is 9 %. Should the merger be undertaken?
Please see attached for complete details.
#### Solution Preview
See attached file for complete solution.
Since the NPV at -86702 is negative the merger should not be undertaken
Cost of capital= 9%
Year Cash inflow Synergistic benefit Cost Total PV Factor @ 9% Discounted cash flow=
0 (1,500,000) (1,500,000) 1 -1500000 =-1500000*1
1 100,000 15,000 115,000 0.917431 105505 =115000*0.917431
2 100,000 15,000 115,000 0.84168 96793 =115000*0.84168
3 100,000 15,000 115,000 ...
#### Solution Summary
The solution evaluates the NPV of cash acquisition.
\$2.49
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Place Value 1A Value of Underlined Digit - up to Billions 1B Number Words & Expanded Form to Billions 1C Math Vocabulary - "Periods" 1D Compare Numbers "< >" to tens of Millions 1E Ordering Numbers Least to Greatest 1F Problem Solving Place Value: Decimals 2A Decimals - Standard Form 2B Decimals - Word Form 2C Decimals - Value of Underlined Digit 2D Decimals - Compare < > = 2E Decimals - Ordering Least to Greatest 2F Equivalent Decimals 2G Decimals - Problem Solving Whole Numbers & Decimals 3A Addition Properties 3B Add Decimals 3C Subtract Decimals 3D Rounding Whole Numbers to Millions Place 3E Name Place to which Number is Rounded 3F Round Decimals to Underlined Digit 3G Estimate Sums (Round to 100,000) 3H Estimate Differences (Round to 100,000) 3I Addition: 6 and 7 Digits 3J Find Missing Digits in Addition Problem 3K Subtraction: 6 and 7 Digits 3L Subtraction: Find Missing Digits 3M Decimals: Problem Solving Multiplication 4A Multiply 5 & 6 Digit by 1-Digit Number 4B Multiply by 2-digit Number 4C Estimate Products 4D Problem Solving 5A Multiply Decimals and Whole Numbers 5B Multiplication Patterns 5C Multiply Decimals by Decimals 5D Exponents Division 6A Estimate Quotients 6B 1-Digit Divisors 6C Problem Solving 7A Estimate Quotients - Compatible Numbers 7B Divide by 2-Digit Divisors 7C Dividing Decimals 7D Divide Whole Numbers (decimal quotient) 7E Problem solving Graphs and Interpreting Data 8A Vocabulary 8B Range, Mode, Median, Mean 8C Vocabulary 8D Making a Bar Graph 8E Frequency Table 8F Coordinate Grid 8G Make a Line Graph 9A Vocabulary 9B Histogram 9C Stem & Leaf Plot 9D Circle Graph Number Theory 10A Divisibility Rules 10B Prime and Composite Numbers 10C Common Factors - GCF Fractions 10D Write the Fraction Shown by the Model 10E Equivalent Fractions 10F Simplify Fractions 10G Mixed Numbers 11A Least Common Multiple - LCM 11B Least Common Denominator - LCD 11C Equivalent Fractions 11D Compare Fractions 11E Order Fractions 12A Add & Subtract Like Fractions 12B Add & Subtract Unlike Fractions 12C Add Fractions Using LCD 12D Subtract Fractions Using LCD 12E Relate Fractions & Decimals 12F Problem Solving Fractions - Add & Subtract 13A Add Mixed Numbers 13B Subtract Mixed Numbers 13C Subtract Fractions with Renaming 14A Multiply Whole Number by Fraction 14B Multiply a Fraction by a Fraction 14C Multiply Fractions & Mixed Numbers 14D Multiply Mixed Numbers 15A Reciprocals 15B Divide Whole Numbers by Fractions 15C Divide Fractions 15D Problem Solving (multiply fractions) 15E Problem Solving (divide fractions) Measurement: Customary Units 16A Length 16B Capacity and Weight 16C Time Measurement: Metric Units 17A Length 17B Capacity & Mass 17C Temperature Algebra 18A Expressions (Add & Subtract) 18B Expressions (Multiply & Divide) 18C Order of Operations 18D Functions 18E Graphing a Function 19A Equations (Add) 19B Equations (Subtract) 19C Equations (Multiply) 19D Equations (Divide) Geometry 20A Lines 20B Measure Angles 20C Classify Angles 20D Triangles 20E Quadrilaterals 21A Circles 21B Congruent and Similar Figures 21C Transformations 21D Tessellations Perimeter & Area 22A Find Perimeter 22B Area of Squares & Rectangles 22C Area of Parallelograms 22D Area of Triangles Surface Area and Volume 23A Nets and 3-Dimensional Figures 23B Surface Area 23C Estimate and Find Volume Ratio 25A Ratios 25B Ratios and Proportions 25C Equivalent Ratios: use cross products 25D Equivalent Ratios: find the missing number 25E Scale Drawings Probability 26A Probability 26B Outcomes 26C Combinations Percent 27A Understanding Percent 27B Fractions, Decimals & Percents 27C Find Percent of a Number 27D Circle Graphs
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# Find limit x tends to 0 for { x.log(1+2tanx) }/(1-cosx)
Arun
25750 Points
4 years ago
Dear student
x² log ( 1 + 2 tanx) *2 tanx/x* 2 tanx(1 - cosx)
Now put limit
1 * 2 * 2 = 4
Hope it helps
Thanks
2086 Points
4 years ago
write it as
[x/(1 – cosx)]*[log(1+2tanx)/2tanx]*2tanx
so, lim becomes (limit x tends to 0 2xtanx/(1 – cosx))*(limit x tends to 0 log(1+2tanx)/2tanx)
(limit x tends to 0 2xtanx/(1 – cosx))*(limit y tends to 0 log(1+y)/y).....here we have let y= 2tanx
(limit x tends to 0 2xtanx/(1 – cosx))*1
limit x tends to 0 2xsinx/cosx(1 – cosx)
limit x tends to 0 2xsinx(1+cosx)/cosx(1 – cos^2x)
limit x tends to 0 2xsinx(1+cosx)/cosxsin^2x
limit x tends to 0 2x(1+cosx)/cosxsinx
limit x tends to 0 [2(1+cosx)/cosx] * limit x tends to 0 x/sinx
= 4*1
4
kindly approve :)
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# Question: Agnes Hammer is a senior majoring in management science She
Agnes Hammer is a senior majoring in management science. She has been interviewing with several companies for a job when she graduates, and she is curious about what starting salary offers she might receive. There are 140 seniors in the graduating class for her major, and more than half have received job offers. She asked 12 of her classmates at random what their annual starting salary offers were, and she received the following responses:
\$28,500 ..... \$35,500
32,600 ..... 36,000
34,000 .... 25,700
27,500 .... 29,000
24,600 ...... 31,500
34,500 ...... 26,800
Assume that starting salaries are normally distributed. Compute the mean and standard deviation for these data and determine the probability that Agnes will receive a salary offer of less than \$27,000.
View Solution:
Sales0
Views208
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A piston above a liquid in a closed container has an area of 1 m² the piston carries a load of 350 kg what will be the external pressure on the upper surface of a liquid
A piston above a liquid in a closed container has an area of 1m2. The piston carries a load of 350 kg. 3.43 kPa will be the external pressure on the upper surface of the liquid. Solution: The weight of the load is (mass) x (gravity) = (350 kg) x (9.8 m/s²) = 3,430 newtons. (3,430 newtons) / (1 m²) = 3,430 pascals = 3.43 kPa.
Question
Asked 2/7/2019 4:31:35 PM
Updated 11/27/2020 9:22:35 PM
f
Rating
3
A piston above a liquid in a closed container has an area of 1m2. The piston carries a load of 350 kg. 3.43 kPa will be the external pressure on the upper surface of the liquid. Solution: The weight of the load is (mass) x (gravity) = (350 kg) x (9.8 m/s²) = 3,430 newtons. (3,430 newtons) / (1 m²) = 3,430 pascals = 3.43 kPa.
Added 11/27/2020 9:22:35 PM
This answer has been confirmed as correct and helpful.
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A stone falls from a ledge and takes 8 seconds to hit the ground. The stone has an original velocity of 0 m/s. How tall is the ledge? A. 1,254.4 meters B. 39.2 meters C. 78.4 meters D. 313.6 meters
Weegy: A stone falls from a ledge and takes 8 seconds to hit the ground. The stone has an original velocity of 0 m/s. How tall is the ledge? 313.6 meters (More)
Question
Updated 94 days ago|2/16/2024 4:00:56 AM
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Added 94 days ago|2/16/2024 4:00:56 AM
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A stone falls from a ledge and takes 8 seconds to hit the ground. The stone has an original velocity of 0 m/s. d=(1/2)at^2 ; d = 1/2 * 9.8 * 8^2 =; 313.6m.
Added 94 days ago|2/16/2024 4:01:33 AM
This answer has been confirmed as correct and helpful.
A stone falls from a ledge and takes 8 seconds to hit the ground. The stone has an original velocity of 0 m/s. How tall is the ledge? A. 1,254.4 meters B. 39.2 meters C. 78.4 meters D. 313.6 meters
Question
Updated 4/5/2021 11:47:39 AM
A stone falls from a ledge and takes 8 seconds to hit the ground. The stone has an original velocity of 0 m/s. d=(1/2)at^2 ; d = 1/2 * 9.8 * 8^2 =;
d = 313.6m
Added 4/5/2021 11:47:39 AM
This answer has been confirmed as correct and helpful.
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Pre Algebra for Android
Free
Developer's Description
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General Features
+ A reading area that introduces concepts and problem solving steps.
+ A quiz-like area to reinforce concepts and steps introduced in the reading area.
+ A practice area to further reinforce concepts and improve problem solving accuracy and speed.
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There are four general areas:
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Concept Checks quiz you on important concepts and problem solving steps for several topics. These quiz-like areas typically give less than 10 multiple choice questions. The questions are always the same and can be repeated any number of times.
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Outline of Topics
BASICS
A. Numbers
B. Decimals
---- i. Place Value
---- ii. Rounding
C. Fractions
---- i. Equivalent Fractions
---- ii. Reducing
---- iii. Lowest Common Denominator
---- iv. Improper to Mixed Number
---- v. Mixed Number to Improper
D. Exponents
---- i. Evaluation
---- i. Evaluation
F. Absolute Values
G. Conversions
---- i. Fraction to Decimal
---- ii. Decimal to Fraction
H. Inequalities
---- i. Comparisons
FUNDAMENTALS
A. Multiply, Divide, Add, and Subtract
---- i. Integers (positive and negative numbers)
---- ii. Fractions
SIMPLIFYING
A. The Order of Operations
---- i. PEMDAS
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watchtower - 10 months ago 34
R Question
# Sum values using dplyr in R for all combinations of variables
I am relatively new to R programming so I apologize if this question is too basic. I have transactions that show revenue earned from six different types of products. There are three years of transactions. My objective is to find out the sum of products sold for all different combinations of products, which would be
`2^6 - 1 = 64 - 1 = 63`
, for every year. Meaning, I would have
`63*3 = 189`
combinations.
For sake of simplicity, I have created test data using only three variables because I wrote a program using
`while`
loop for one year, which stinks. My objective is to show what I am trying to accomplish. Notwithstanding, I have posted random sample from my original file below.
Here's the test data with only three variables
`Car`
,
`Tire`
, and
`Services`
and
`while`
loop to show you what I am looking for :
`````` dput(Sample_File)
structure(list(Order.ID = c(171, 173, 132, 174, 132, 174, 132,
174, 174), Fiscal.Year = c(2017, 2016, 2016, 2016, 2016, 2016,
2016, 2016, 2018), Car = c(2, 2, 3, 1, 0, 0, 0, 0, 1), Tire = c(0,
0, 0, 1, 0, 1, 0, 1, 1), Services = c(3, 1, 4, 0, 4, 1, 4, 0,
0)), .Names = c("Order.ID", "Fiscal.Year", "Car", "Tire", "Services"
), row.names = c(NA, 9L), class = "data.frame")
``````
Here's my code:
`````` i<-1
Csum <- matrix(rep(0,21),nrow = 7,ncol = 3)
# Row 1 is used when C is ON; T is ON ; S is ON
# Row 2 is used when C is ON; T is ON ; S is OFF
# Row 3 is used when C is ON; T is OFF ; S is ON
# Row 4 is used when C is OFF; T is ON ; S is ON
# Row 5 is used when C is ON; T is OFF ; S is OFF
# Row 6 is used when C is OFF; T is ON ; S is OFF
# Row 7 is used when C is OFF; T is OFF ; S is ON
while (i <= length(Sample_File\$Order.ID))
{
if (Sample_File\$Fiscal.Year[i]!=2016)
{
i<-i+1
next
}
if (Sample_File\$Car[i]!=0 & Sample_File\$Tire[i]!=0 & Sample_File\$Services[i]!=0)#1
{
Csum[1,1] <- Csum[1,1] + Sample_File\$Car[i]
Csum[1,2] <- Csum[1,2] + Sample_File\$Tire[i]
Csum[1,3] <- Csum[1,3] + Sample_File\$Services[i]
}
else if (Sample_File\$Car[i]!=0 & Sample_File\$Tire[i]!=0 & Sample_File\$Services[i]==0) #2
{
Csum[2,1] <- Csum[2,1] + Sample_File\$Car[i]
Csum[2,2] <- Csum[2,2] + Sample_File\$Tire[i]
Csum[2,3] <- Csum[2,3] + 0
}
else if(Sample_File\$Car[i]!=0 & Sample_File\$Tire[i]==0 & Sample_File\$Services[i]!=0) #3
{
Csum[3,1] <- Csum[3,1] + Sample_File\$Car[i]
Csum[3,2] <- Csum[3,2] + 0
Csum[3,3] <- Csum[3,3] + Sample_File\$Services[i]
}
else if(Sample_File\$Car[i]==0 & Sample_File\$Tire[i]!=0 & Sample_File\$Services[i]!=0) #4
{
Csum[4,1] <- Csum[4,1] + 0
Csum[4,2] <- Csum[4,2] + Sample_File\$Tire[i]
Csum[4,3] <- Csum[4,3] + Sample_File\$Services[i]
}
else if(Sample_File\$Car[i]!=0 & Sample_File\$Tire[i]==0 & Sample_File\$Services[i]==0) #5
{
Csum[5,1] <- Csum[5,1] + Sample_File\$Car[i]
Csum[5,2] <- Csum[5,2] + 0
Csum[5,3] <- Csum[5,3] + 0
}
else if(Sample_File\$Car[i]==0 & Sample_File\$Tire[i]!=0 & Sample_File\$Services[i]==0)#6
{
Csum[6,1] <- Csum[6,1] + 0
Csum[6,2] <- Csum[6,2] + Sample_File\$Tire[i]
Csum[6,3] <- Csum[6,3] + 0
}
else #7
{
Csum[7,1] <- Csum[7,1] + 0
Csum[7,2] <- Csum[7,2] + 0
Csum[7,3] <- Csum[7,3] + Sample_File\$Services[i]
}
i<-i+1
}
``````
I have written the code to handle only one year because it was extremely painful to replicate this code for three years. I am looking for a solution that would create a list of 3 data frames, each for three years.
Here's a random sample of size 10 with six variables from original file.
``````dput(Sample_File_Random)
structure(list(Order.ID = c(171, 173, 132, 174, 169, 175, 163,
186, 178, 121), Fiscal.Year = c(2016, 2016, 2017, 2016, 2015,
2016, 2015, 2015, 2015, 2017), Car = c(2, 0, 3, 0, 0, 0, 0, 5346.25,
0, 0), Tire = c(0, 0, 0, 8691.55800460666, 3198, 5, 2, 0, 2,
3282.18), Services = c(3, 0, 4, 0, 0, 0, 0, 0, 0, 0), Insurance = c(4,
0, 0, 4, 0, 4, 0, 0, 0, 0), Accessories = c(94.3, 3749.8, 9308.65,
0, 2, 0, 1, 633.75, 51.44, 0), Finance = c(0, 0, 0, 4, 0, 14800,
0, 0, 0, 0)), .Names = c("Order.ID", "Fiscal.Year", "Car", "Tire",
"Services", "Insurance", "Accessories", "Finance"), row.names = c(NA,
10L), class = "data.frame")
``````
I am really stuck so I would sincerely appreciate any help with vectorizing this..
@ Ronak shah's request: Here's the expected output for
`Sample_File_Random`
``````Output_File
Fiscal.Year Car Tire Services Insurance Accessories Finance
1 2015 0.00 3202.000 0 0 54.44 0
2 2015 5346.25 0.000 0 0 633.75 0
3 2016 2.00 0.000 3 4 94.30 0
4 2016 0.00 0.000 0 0 3749.80 0
5 2016 0.00 8696.558 0 8 0.00 14804
6 2017 3.00 0.000 4 0 9308.65 0
7 2017 0.00 3282.180 0 0 0.00 0
``````
Here is a compact & expressive `dplyr` solution, which proceeds in three steps:
1. create the indicators for whether each of the services is in the basket or not
2. group by the year, and the combinations of the indicators
3. sum the service values by the grouping variables
Here is the code that does this:
``````df_foo %>%
# 1. create the combinations of whether each of the
# products is in the basket or not
mutate_each(
funs(In_Basket = . > 0), Car:Services
) %>%
# 2. group by the year and the basket service indicators
group_by_(.dots = c("Fiscal.Year", grep("_In_Basket", names(.), value = TRUE))) %>%
# 3. sum the service values
summarise_each(
funs(sum(., na.rm = TRUE)), Car:Services
)
``````
This gives the output:
``````Source: local data frame [7 x 7]
<dbl> <lgl> <lgl> <lgl> <dbl> <dbl> <dbl>
1 2016 FALSE FALSE TRUE 0 0 8
2 2016 FALSE TRUE FALSE 0 1 0
3 2016 FALSE TRUE TRUE 0 1 1
4 2016 TRUE FALSE TRUE 5 0 5
5 2016 TRUE TRUE FALSE 1 1 0
6 2017 TRUE FALSE TRUE 2 0 3
7 2018 TRUE TRUE FALSE 1 1 0
``````
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05-25-2012, 12:40 AM PM User | #1 Aboxofdonuts New to the CF scene Join Date: May 2012 Posts: 6 Thanks: 4 Thanked 0 Times in 0 Posts Scientific Notation to standard decimal I'm using java to convert a number that was input by the user in a text box. The user then selects the conversion to do, and then it outputs the converted number to another text box. However, the conversion equations use scientific notation. I want to make another text box that takes the result in scientific notation and turns it into standard decimal format. example: x=1 equation is x*1e-6 first result text box would read 1e-6 second result text box would read 1000000 I've never had to do something like this before, so I'm clueless as to where to even begin. Google proved kinda useless. Couple of ideas but I didn't understand them or couldn't get them to work. Any ideas? Not sure if this will be simple or not lol. Thanks in advanced
05-25-2012, 12:58 AM PM User | #2 xelawho Senior Coder Join Date: Nov 2010 Posts: 2,591 Thanks: 54 Thanked 477 Times in 475 Posts mmm... but doesn't 1e-6 equal 0.000001? javascript has built-in methods for converting to and from exponential numbers: https://developer.mozilla.org/en/Jav...Objects/Number so you can do something like this: Code: ``` ```
05-25-2012, 01:42 AM PM User | #3
Aboxofdonuts
New to the CF scene
Join Date: May 2012
Posts: 6
Thanks: 4
Thanked 0 Times in 0 Posts
Quote:
Originally Posted by xelawho mmm... but doesn't 1e-6 equal 0.000001?
My bad, in the original post I did 1e6 instead of 1e-6.
I was trying the code you used in a brand new dreamweaver file, and if you change the text box to 1e-7 the second text box comes out as scientific notation. Is there a limit to what it can convert? 1e7 works, 1e20 works, but it seems negatives don't.
Some of the equations are like this: 2.47105381e-16 . So I'd hate to have negative numbers not work.
Edit: Just tested my project again, and it seems to automatically convert to decimal when it does the math, however, it only works till a certain amount like stated above.
Now, I'm just scratching my head on this lol.
05-25-2012, 02:47 AM PM User | #4 Old Pedant Supreme Master coder! Join Date: Feb 2009 Posts: 24,965 Thanks: 75 Thanked 4,309 Times in 4,276 Posts No, toPrecision() does *NOT* force scientific notation, at all. Dunno why Xelawho gave you that answer. Actually, if you use toPrecision() [no argument] it is no different than toString(). Only if you give it an argument will it be different. But it still won't FORCE scientific notation. You want toExponential(digits) Example: Code: `````` __________________ An optimist sees the glass as half full. A pessimist sees the glass as half empty. A realist drinks it no matter how much there is.
05-25-2012, 09:45 AM PM User | #5
Philip M
Supreme Master coder!
Join Date: Jun 2002
Location: London, England
Posts: 17,494
Thanks: 200
Thanked 2,471 Times in 2,449 Posts
Quote:
I'm using java to convert a number
This is the JavaScript forum. Java and Javascript are entirely different programming languages, in spite of the confusingly similar names. Rather like Austria and Australia!
You convert a positive or negative scientific format number to standard decimal simply with *1. But 2.47105381e-16 is too big a number for Javascript to handle.
Code:
```<input type = "text" id = "txt1" value = 1e06>
<input type = "text" id = "txt2">
<input type = button value = "Click" onclick = "makeNumber()">
<script type="text/javascript">
function makeNumber() {
var x = document.getElementById("txt1").value;
document.getElementById("txt2").value = x*1;
}
</script>```
Further examples to study:-
Code:
```<script type="text/javascript">
alert (Math.pow(10,21)); // Javascript can display numbers up to 10 ^ 20, thereafter in scientific/exponential notation.
// You can use toFixed() instead of parseFloat() to format positive numbers the way you want up to 20 places of decimals.
// For example (1.23e-7).toFixed(9) will render as 0.000000123
alert (2.47105381e-16.toFixed(20)); // returns positive value
alert ((-2.47105381e-16).toFixed(20)); // using parentheses returns negative value
alert (2.47105381e-16.toFixed(21)); // out of range
// Using .toFixed() with negative numbers requires the value to be placed in parentheses as, due to operator precedence, negative numbers don't return a string.
</script>```
__________________
All the code given in this post has been tested and is intended to address the question asked.
Unless stated otherwise it is not just a demonstration.
Last edited by Philip M; 05-25-2012 at 12:02 PM..
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Intermediate Algebra (6th Edition)
The given set of values is wrong as $c=10$, not $-10$.
RECALL: The standard form of a quadratic equation is $ax^2+bx+c=0$ Write the given quadratic in equation in standard form to obtain: $x^2=-10 \\x^2+10=-10+10 \\x^2+10=0$ The quadratic equation above has: $a=1, b=0, c=10$ Thus, in the given set of values, the value of $c$ must be $10$ and not $-10$.
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# Subtract the numbers: - 932 + 1,911 - 494 - 257 = ? Calculate the numbers difference and learn how to do the subtraction, column subtracting method, from right to left
## The operation to perform: - 932 - 494 - 257
### Stack the numbers on top of each other.
#### And so on...
9 3 2 4 9 4 + 2 5 7 ?
## Add column by column; start from the column on the right.
### Add the digits in the ones column:
#### 1 is the tens digit. Carry it over to the tens column. Write the digit above that column. Add it with the rest of the digits in that column.
1 9 3 2 4 9 4 + 2 5 7 3
### Add the digits in the tens column:
#### 1 is the hundreds digit. Carry it over to the hundreds column. Write the digit above that column. Add it with the rest of the digits in that column.
1 1 9 3 2 4 9 4 + 2 5 7 8 3
### Add the digits in the hundreds column:
#### 1 is the thousands digit. Write it down at the base, next to the hundreds digit.
1 1 9 3 2 4 9 4 + 2 5 7 1 6 8 3
## Now subtract the final numbers above: 1,911 - 1,683 = ?
### Stack the numbers on top of each other.
#### And so on...
1 9 1 1 - 1 6 8 3 ?
## Subtract column by column; start from the column on the right
### Subtract the digits in the ones column:
#### When borrowing, 1 ten = 10 ones. Add 10 to the top digit in the column of the ones: 10 + 1 = 11.
0 1 9 1 11 - 1 6 8 3
#### After borrowing, the subtraction has become: 11 - 3 = 10 + 1 - 3 = 10 + 1 - 3 = 1 + (10 - 3) = 1 + 7 = 8. 8 is the ones digit. Write it down at the base of the ones column.
0 1 9 1 11 - 1 6 8 3 8
### Subtract the digits in the tens column:
#### When borrowing, 1 hundred = 10 tens. Add 10 to the top digit in the column of the tens: 10 + 0 = 10.
8 10 1 9 1 11 - 1 6 8 3 8
#### After borrowing, the subtraction has become: 10 - 8 = 2. 2 is the tens digit. Write it down at the base of the tens column.
8 10 1 9 1 11 - 1 6 8 3 2 8
### Subtract the digits in the hundreds column:
#### 98 - 6 = 2. 2 is the hundreds digit. Write it down at the base of the hundreds column.
8 10 1 9 1 11 - 1 6 8 3 2 2 8
### Subtract the digits in the thousands column:
#### 1 - 1 = 0. 0 is the thousands digit. Write it down at the base of the thousands column.
8 10 1 9 1 11 - 1 6 8 3 0 2 2 8
## The latest numbers that were subtracted
- 932 + 1,911 - 494 - 257 = ? Jan 18 11:38 UTC (GMT) 47,397 - 9,392 = ? Jan 18 11:38 UTC (GMT) - 996 + 1,984 + 568 + 363 = ? Jan 18 11:38 UTC (GMT) 453 + 97 + 167 - 107 - 143 + 116 - 196 = ? Jan 18 11:38 UTC (GMT) - 2,604 + 2,321 - 600 + 1,389 - 180 = ? Jan 18 11:38 UTC (GMT) - 7,120 - 5,670 = ? Jan 18 11:38 UTC (GMT) - 972 - 2,001 + 574 + 364 = ? Jan 18 11:38 UTC (GMT) - 1,014 + 1,069 + 983 - 768 - 377 + 573 = ? Jan 18 11:38 UTC (GMT) - 598 - 457 = ? Jan 18 11:38 UTC (GMT) - 972 - 1,967 + 533 + 330 = ? Jan 18 11:38 UTC (GMT) - 1,064 - 1,134 + 974 + 813 + 384 - 568 = ? Jan 18 11:38 UTC (GMT) - 806 + 270 = ? Jan 18 11:38 UTC (GMT) - 49 - 35 = ? Jan 18 11:38 UTC (GMT) All the numbers that were subtracted by users
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# 30403
## 30,403 is a prime number. Like all primes greater than two, it is odd and has no factors apart from itself and one.
What does the number 30403 look like?
As a prime, it is not composed of any other numbers and has no internal structure.
30403 is a prime number. Like all primes (except two), it is an odd number.
## Prime factorization of 30403:
### 30403
See below for interesting mathematical facts about the number 30403 from the Numbermatics database.
### Names of 30403
• Cardinal: 30403 can be written as Thirty thousand, four hundred three.
### Scientific notation
• Scientific notation: 3.0403 × 104
### Factors of 30403
• Number of distinct prime factors ω(n): 1
• Total number of prime factors Ω(n): 1
• Sum of prime factors: 30403
### Divisors of 30403
• Number of divisors d(n): 2
• Complete list of divisors:
• Sum of all divisors σ(n): 30404
• Sum of proper divisors (its aliquot sum) s(n): 1
• 30403 is a deficient number, because the sum of its proper divisors (1) is less than itself. Its deficiency is 30402
### Bases of 30403
• Binary: 1110110110000112
• Base-36: NGJ
### Squares and roots of 30403
• 30403 squared (304032) is 924342409
• 30403 cubed (304033) is 28102782260827
• The square root of 30403 is 174.3645606195
• The cube root of 30403 is 31.2108416191
### Scales and comparisons
How big is 30403?
• 30,403 seconds is equal to 8 hours, 26 minutes, 43 seconds.
• To count from 1 to 30,403 would take you about eight hours.
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)
• A cube with a volume of 30403 cubic inches would be around 2.6 feet tall.
### Recreational maths with 30403
• 30403 is the same when its digits are reversed! That makes it a palindromic prime number.
• The number of decimal digits it has is: 5
• The sum of 30403's digits is 10
• More coming soon!
MLA style:
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APA style:
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Chicago style:
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The information we have on file for 30403 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!
Keywords: Divisors of 30403, math, Factors of 30403, curriculum, school, college, exams, university, Prime factorization of 30403, STEM, science, technology, engineering, physics, economics, calculator, thirty thousand, four hundred three.
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Edit Article
# How to Create a Spiral with Heart Center of Sinewave Spheres
You'll learn to create a Spiral with a Heart Center made of Sinewave Spheres or Spheroids in the steps that follow, plus dozens of other possible images.
## Steps
• Become familiar with the basic image to be created:
### Part 1 The Tutorial
1. 1
For those of you who have completed the article and workbook therein of How to Acquire a Lemniscate Curve of Sinewave Spheres in Excel (which was based upon having finished How to Create a Lemniscate Spheroid Curve and How to Acquire a Ring of Sinewave Spheres in Excel), doing a SAVE AS of that workbook and starting it under a new name will save quite a bit of time -- just look for MODIFIED and NEW as you go through the steps.
• Otherwise, please follow the steps as laid out in order to create first the Heart and then the Spiral Charts, Open a new Excel workbook and create 3 worksheets (except Chart if you are using Chart Wizard): Data, Chart and Saves. Here is a picture of the Spiral Chart:
2. 2
Set Your Preferences. Open Preferences in the Excel menu and follow the directions below for each tab/icon.
• In General, set R1C1 to Off and select Show the 10 Most Recent Documents .
• In Edit, set all the first options to checked except Automatically Convert Date System . Set Display number of decimal places to blank(as integers are preferred). Preserve the display of dates and set 30 for 21st century cutoff.
• In View, click on show Formula Bar and Status Bar and hover for comments of all Objects . Check Show gridlines and set all boxes below that to auto or checked.
• In Chart, allow show chart names and set data markers on hover and leave the rest unchecked for now.
• In Calculation, Make sure Automatically and calculate before save is checked. Set max change to .000,000,000,000,01 without commas as goal-seeking is done a lot. Check save external link values and use 1904 system
• In Error checking, check all the options.
• In Save, select save preview picture with new files and Save Autorecover after 5 minutes
• In Ribbon, keep all of them checked except Hide group titles and Developer .
3. 3
It helps placing the cursor at cell A16 and doing Freeze Panes. Edit Go To cell range A1:J17288 and Format Cells Number Number Decimal Places 4, Font Size 9 or 10, Fill (from the color wheel) a nice purple fuchsia and make the Border Dark Blue bold Outline.
4. 4
MODIFIED: Enter the upper Defined Name Variables Section (here's a picture AFTER insertion of two new columns at C:D which you are to ignore for now):
• A1: Aligned left, enter Sinewave Spheres in a Spiral Shape and Format Font Apple Chancery or something fancy and nice?
• New: C1: Spiral START Value
• New: C2: Spiral LAST Value
• New: C3: n
• New: D1: 0
• New: D2: "=2*PI()"
• Select cell range C1:D3 and Insert Names Create Names in Left Column, OK.
• New: D3: "=IF(Shrink_To_End="Y",-ABS(Spiral_START_Value-Spiral_LAST_Value),ABS(Spiral_START_Value-Spiral_LAST_Value))"
• New: A2:: Y
• New: B2: Shrink To End
• New: A3: 1
• New: B3: Power
• Select cell range A2:B3 and Insert Names Create Name in Right Column, OK.
• E1: AYE
• E2: BEE
• E3: CEE
• Modified: F1: 36
• F2: .50
• F3: .50
• Select cell range E1:F3 and Insert Name Create in Left Column, OK.
• G1: Stretch_y1
• G2: Enter w/o quotes the formula "=(8.5*(SHRINKER*10))*0.75"
• H1: Stretch_x1
• Modified: H2: Enter w/o quotes the formula "=(8.5*(SHRINKER*10))*2"
• Select cell range G1:H2 and Insert Name Create in Top Row, OK.
• G3: Shrinker
• H3: Enter w/o quotes the formula "=.0025" and Insert Name Define Name Shrinker to cell \$H\$3.
• I1: ROWS
• J1: "=17285-5"
• I2: MAGIC
• J2: Enter w/o quotes the formula "=J1/SPHERES"
• I3: SPHERES
• Modified: J3: 360 is the only number I can get to work at all right..
• Select cell range I1:J3 and Insert Name Create in Left Column, OK.
• MODIFIED: Enter the column heading of rows 4 and 5:
• Modified: A5: Spiral Cos
• Modified: B5: Spiral Sin
• C5: Indicator
• D5: Randy
• E5: t: 0 to nπ
• F5: z1_
• I4 and J4: Charting
• I5: x: No z
• J5: y: With z
• Command+Select cells F1:F3 and I3 and Format Fill yellow.
• Select cell J3 and Format Fill sky blue from the color wheel.
• Select cell range I4:J5 and Format Font italic.
• NEW: Place the cursor in the column headers for C:D (that is, Edit Go To C:D) and Insert Columns. Enter the column variables, headers and column formulas for new columns C:D.
• C2: Enter Spirallic YN and Format Fill kelly green.
• C3: Enter Y and Format Fill yellow.
• Select D2 and enter Spiral RANGE (which coincides with n).
• Select cell C4 and Enter Adjustment. Select cell D4 and enter "=0.25" w/o quotes and do Insert Name Define Name Adjustment to cell \$D\$4. Select C4:D4 and Border Outline Navy Blue bold, fill white, decimal places 4.
• Command+Select cell ranges A1:E3, C2:C3, A2:B2 and A3:B3 and do Border Outline Navy Blue bold,, decimal places 5.
• Select cell C5 and enter SPIRALLIC and do underline.
• Select cell C6 and enter "=IF(Spirallic_YN="Y",Spiral_START_Value+0.00001,1)" and Fill Light Rose colored. Edit Go To cell range C7:C17285 and enter to C7 "=IF(AND(Shrink_To_End="Y",ROW()
• Edit Go To cell range D56:D17285 and Edit Clear Contents. This column is being held in reserve for special effects later.
• Enter the Thickness Looker lookup table. Not using now but we may again later.
• Select cell O5 and enter Thickness Looker.
• Edit Go To cell range O6:O69 and enter 1 into O6 and do Edit Fill Series Column Linear Step Value 1, OK.
• Edit Go To cell range P6:P17 and enter .8 and Fill Down. Enter .85 into P18, .90 into P19, .95 into P20 and .5 into the cell range P21:P69 via Edit Fill Down.
• Select cell range O6:P69 and Insert Name Define Name Thickness_Looker to cell range \$O\$6:\$P\$69 and Format Fill yellow. To the right of P, I have a column I copied and pasted values into P from, as multiplied P by 10, or divided by 100, or subtracted 30, or 50 -- it took a lot of hunting around to get the right values to make the chart come out so you should probably copy the table and paste values for it in the Saves worksheet at some point, including ...
• Select cell O3 and type Thickness and enter to O4 "=VLOOKUP(SPHERES,Thickness_Looker,2)" and do Insert Name Define Name Thickness to cell \$O\$4. Format Fill light blue and border red outline bold.
• MODIFIED: Enter the column formulas:
• Modified: Spiral Cos: Edit Go To cell range A6:A17285 and enter into A6 w/o quotes the following formula, "=(IF(COS((ROW()-6)*PI()/180*Adjustment)<0,(ABS(COS((ROW()-6)*PI()/180*Adjustment))^Power)*-1,COS((ROW()-6)*PI()/180*Adjustment)^Power))" and Edit Fill Down. Format Fill yellow and Border Red bold Outline per cell.
• Modified: Spiral Sin: Edit Go To cell range B6:B17285 and enter into B6 w/o quotes the following formula,"=(IF(SIN((ROW()-6)*PI()/180*Adjustment)<0,(ABS(SIN((ROW()-6)*PI()/180*Adjustment))^Power)*-1,SIN((ROW()-6)*PI()/180*Adjustment)^Power))" and Edit Fill Down. Format Fill yellow and Border Red bold Outline per cell.
• Modified: Indicator: Select cell E6 and enter 1 and select cell E7 and enter 0. Edit Go To cell range E8:E17286; enter w/o quotes the formula, "=IF((ROW()-7)/MAGIC=INT((ROW()-7)/MAGIC),1,IF((ROW()-7)=0,1,0))" and Edit Fill Down. This formula says, 'Take a look at the row I'm in, divide it by the number of rows per sphere (MAGIC) and if that number is an integer, return a 1, otherwise if I'm in the next-to-top row also return a 1, otherwise, return a 0.' So now there is an indicator of where 1 sphere ends and the next one begins, no matter how many spheres the user selects to chart. Format Number Number Custom 0.00000;; to stop the zeros from appearing.
• Modified: Randy: Edit Go To cell range F6:F17285 and Insert Name Define Name Randy to cell range \$F\$6:\$F\$17285. Edit Go To cell range F6:F17286 and enter into F6 w/o quotes the following formula,"=RANDBETWEEN(0,10)/100"and Edit Fill Down. Warning: Make calculation Manual before adding this variable or column into your formulas, especially as a factor, as it can take 20 minutes to calculate and draw the new chart. It is not currently employed, but a copy of its formula has been saved at the bottom of the x and y formulas.
• Modified: t: 0 to nπ: Select cell G6 and enter 0. Select cell G7:G17285 and enter to G7 the formula "=IF(E7=1,2*PI(),2*PI()/(MAGIC*1)+G6)" and Edit Fill Down.
• Modified: z1_: Edit Go To cell range H6:H17285 and enter w/o quotes into H6 the formula "=CEE*COS(AYE*G6)" and Edit Fill Down. Edit Go To cell range H6:H17285 and Insert Name Define Name z1_ to cell range \$H\$6:\$H\$17285.
• Modified: Adj_x1: Edit Go To cell range I6:I17285 and enter w/o quotes into I6 the formula "=IF(E6=1,A6,I5)" and Edit Fill Down. Edit Go To cell range I6:I17285 and Insert Name Define Name Adj_x1 to cell range \$I\$6:\$I\$17285. This makes a constant adjustment as if one were referencing a new center every new sphere from Spiral Cos, else it takes the value just above itself.
• Modified: Adj_y1: Edit Go To cell range J6:J17285 and enter w/o quotes into J6 the formula "=IF(E6=1,B6,J5)" and Edit Fill Down. Edit Go To cell range J6:J17285 and Insert Name Define Name Adj_y1 to cell range \$J\$6:\$J\$17285. This makes a constant adjustment as if one were referencing a new center every new sphere from Spiral Sin, else it takes the value just above itself.
• Modified: x: No z: Edit Go To cell range K6:K17285 and enter w/o quotes into K6 the formula "=(Stretch_x1*(((BEE^2-CEE^2*COS(AYE*G6)*COS(AYE*G6))^0.5 *COS(G6)))+Adj_x1)*SPIRALLIC" and Edit Fill Down. This is the x part of the heart of the sinewave sphere formula from the text, without the z dimension added or multiplied in, which is why it took me so long to discover how to make it work.
• Modified: y: With z: Edit Go To cell range L6:L17285 and enter w/o quotes into L6 the formula "=(Stretch_y1*(((BEE^2-CEE^2*COS(AYE*G6)*COS(AYE*G6))^0.5 *SIN(G6))+z1_)+Adj_y1)*SPIRALLIC" and Edit Fill Down. This is the y part of the heart of the sinewave sphere formula from the text, with the z dimension added in, which is why it took me so long to discover how to make it work. In the spirallic spheroids Garthwaite Curve, the z-dimension is multiplied into both x and y parts. Furthermore, I have made no adjustment for the Golden Mean Long Leg, which I expected to all along, until it worked without it. The other curve doesn't.
• Modified: Select cell K17286 and enter the formula w/o quotes "=K6" and select cell L17286 and enter the formula w/o quotes "=L6". This makes the top connecting line from the last sphere to the first.
• Modified: Planned Error Value -- Select cell K17287 and enter "=SHRINKER^2*(Stretch_x1*(((BEE^2-CEE^2*COS(AYE*G17287)*COS(AYE*G17287))^0.5 *COS(G17287)))+Adj_x1)*Randy" or +Randy, etc. Warning: this can really take a lot of processing time -- set calculation to Manual first.
• Modified: Planned Error Value -- Select cell L17287 and enter "=SHRINKER^2*(Stretch_y1*(((BEE^2-CEE^2*COS(AYE*G17287)*COS(AYE*G17287))^0.5 *SIN(G17287))+z1_)+Adj_y1)*Randy" or +Randy, etc. Warning: this can really take a lot of processing time -- set calculation to Manual first.
• Modified: Edit Go To cell range K6:L17288 and do Format Fill sky blue.
• Modified: Select cell F5 and Format Fill light sea green, font red, Border navy blue outline bold. Copy this cell to J17287. Then do Edit Paste Special Format of this cell to cell E6, E7, G6, K17286 and L17286 to make distinct the format of those cell's formulas/values.
### Part 2 Explanatory Charts, Diagrams, Photos
1. 1
(dependent upon the tutorial data above)
• Create the Heart Chart.
• Modified: Edit Go To cell range [K8:L1446] - a short range -- and from the Ribbon or Chart Wizard select Charts All/Other Scatter Smoothed Line Scatter and Copy or Cut the chart that is atop the data worksheet and paste it to the top left of the Chart worksheet. Hover over the lower right corner until the cursor becomes a double-headed arrow and pull it open to become a large wide rectangle.
• Click in the Plot Area and select Chart Layout from the ribbon and at far left under Current Selection select Series 1, then under that, Format Selection. Set Line to Red, Smoothed line, Weight = 1 pt. and Dashed = Solid. Set Shadow to checked Outer 45 degrees, magenta pink, Size 100%, Blur 0 pt, Distance 30 pt, Transparency 80%. Set Glow to magenta pink Size = 2 pt. 2% transparency, Soft Edges 0 pt. OK.
• Do Current Selection under Chart Layout as Plot Area, Format Selection. No Line, No Glow and No Shadow. Set Fill to Gradient Radial Lower Left Corner, Full Left 0% Orange and Full Right 100% White. No Glow, 3-D is all zeros. OK.
• Do Current Selection under Chart Layout as Chart Area, Format Selection. Fill Gradient color Prussian Blue I think they call it on left 0% to Navy Blue on right 100% Path 0 degrees, Upper Left Corner, Transparency 0%. Line = Auto. Shadow is Unchecked/ No Glow or Soft Edges. 3-D Format is not set. OK.
• The chart handles 360 spheres only at this point.
• The chart's horizontal axis is set to -8 min, +4 Max, and the vertical is set to +/- 4.5.
2. 2
Create the Spiral Chart.
• Here are the settings for the Spiral Chart, in picture form. Spiral_Last_Value has been changed to "=PI()" from "=2*PI()" and Stretch_X1 has been changed to "=(8.5*(SHRINKER*10))*0.8" from "=(8.5*(SHRINKER*10))*2".
• All the Chart formatting settings are the same but the cell range being charted is different -- it's =SERIES(,'DATA 01'!\$K\$8:\$K\$17285,'DATA 01'!\$L\$8:\$L\$17285,1) with the horizontal and vertical scales set to auto-checked.
• Here's another picture of the Spiral Chart:
1. 1
Make use of helper articles when proceeding through this tutorial:
## Tips
• The following graphs may arise from setting Spirallic to the constant 3, Spheres to 35, and Aye to 20 and graphing the series =SERIES(,'DATA 01'!\$K\$8:\$K\$17286,'DATA 01'!\$L\$8:\$L\$17286,1):
• Using the same series, but setting Spheres to 360 and Aye to 36 produces this ring of 30 or 32 "cherries in a ring":
• See also the article: Create a Pink Love Note of Spheres in Form of a Heart
## Warnings
• Errors: If there are unplanned errors or error values, either the sheet in incomplete and needs further input or Lookup Tables for critical variables or perhaps there's a mistake somewhere along the line. If the instructions have been completed and there are still errors, select the cell that has the error value that is furthest left and topmost first. Look for a typo in a formula or unmatched parentheses. Possibly, a Defined Name is wrong -- they need to be input into the formulas exactly as they were defined. Do Insert Name Define to check. If there is a #DIV/0! error, the example does not, so look for a variable that somehow did not get filled in with a value perhaps. At any rate, what to do is select the cell with the error, and after checking all those typical errors, do Tools Auditing Trace Precedents and/or Trace Error. If fixing all the topmost leftmost errors does not fix the rest of your errors on the worksheet, one may need to do it the hard way, from the bottom right upwards then leftwards; that is the slow but sure way to fix all errors.
• Also, errors in the chart data will most likely plot as zeros. This may be acceptable or desirable even. However, if too many lines (or curves) are returning to 0, it may indicate a logical flaw in the data -- or too many tiny values and then perhaps rescaling the chart is needed by inspecting the horizontal and vertical axes and changing them to zero in on the problem. Hover over or click on a data marker on the series plot and then do a search in the proper column by value for that value, and identify its precedents.
## Sources and Citations
• The source workbooks for this article include: "Lemniscate Garthwaite Curve.xlsx" and "Leminscate Sinewave On Sphere p 266.xlsx" and mainly "HEART Sinewave On Sphere p 266.xlsx"
• The Garthwaite Curve shown was first created by Chris Garthwaite in May of 1994 and is based upon the Spherical Helix found on page 264 along with the Sine Wave Sphere on page 266 of "CRC Standard Curves and Surfaces" by David von Seggern, CRC, ANN ARBOR, 1993. ISBN 0-8493-0196-3
## Article Info
Categories: Microsoft Excel Imagery | Graphics
Thanks to all authors for creating a page that has been read 16,811 times.
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### Author Topic: Baccarat unbeatable plan #1 (Read 66960 times)
0 Members and 1 Guest are viewing this topic.
#### AsymBacGuy
• Moderator
• Hero Member
• Posts: 1059
##### Re: Baccarat unbeatable plan #1
« Reply #150 on: June 03, 2019, 11:48:05 pm »
Some shoes are unplayable
You've heard this statement many times from me.
I will try to illustrate my point.
Say the worst driver in the universe is 300 feet behind the finish line and Lewis Hamilton is half a mile behind.
Who would bet Hamilton as winner?
Of course the probability to get Hamilton as winner isn't zero but very close to it.
Translating this into baccarat, per any single shoe it's really really unlikely not to get at least one 3+ banker streak and/or at least one P single and many other "expected" situations.
Nonetheless since any shoe is a finite space, we know that the more we're going through it without finding what we're looking for, higher will be the probabilities to get such unlikely situations.
Even if we finally find a single or a couple of expected situations, the failed previous attempts will pose a serious or letal threat to our bankroll.
When the limited space is more and more consumed and things went in the wrong direction, we risk to place worthless bets.
Good.
What about abandoning our strategic plan and starting to bet what it seem to be predominant?
Wrong choice, imo.
First, quitting our plan trying to get positive outcomes while denying (even temporarily) our studies is a mistake.
If we have ascertained that A>B, A remains favorite period.
Think when you are at a virtual blackjack table getting a positive count of +18 where dealer keep getting 20, 21 and naturals and you are allowed to wager the dealer's side. Are you really interested to wager the dealer's side?
If the answer is yes you should quit gambling immediately.
Second.
If things should go everytime as expected or almost as expected, gambling games wouldn't exist at all.
Even the math advantaged houses rely upon a long term edge.
And even if it would appear contradictory to what I've been sayed so far, sometimes the house hopes that a given shoe will finish ASAP.
Therefore, what not happened so far, especially whether is more "due", is likely to not present for the subsequent portions of the shoe.
More "due" could be interpreted as a kind of balancement, a strong unexpected predominance or a too huge expected predominance.
Third.
Are we willing to guess a random world per every single fkng shoe dealt just because we think that we are able to possede the instincts to do that?
If so, contact NASA or MIT and you'll get more substantial rewards than playing this silly game.
Fourth.
Any single choice we make forms the large picture. More choices = more mistakes. It's a human feature and it has a general value.
It's a proven fact that bad choices will endorse more bad choices and good choices (even made by mistake) will more likely lead to good choices.
In a sense either good and bad choices will distribute more by runs than by singles.
And to get good choices in a row we must first get an initial good choice.
Thus if the shoe we are facing isn't going toward our plan, tell the casino to fk off, that is not to play a dime.
Remember that baccarat outcomes are already preordered and nothing will change their pace.
Final note
If a bac player have found betting lines capable to get a long term edge, this edge will be quite limited hence susceptible to great fluctuations. That's why we should think about the large picture and not about the stupi.d single shoe we're playing at.
as.
Next to edge sorting it's me
Winners don't do different things, they do things differently (Albalaha)
#### roversi13
• Posts: 74
##### Re: Baccarat unbeatable plan #1
« Reply #151 on: June 07, 2019, 07:16:11 am »
I'm not convinced about your theory ,illustrated also in some old your messages ,concerning stop playing if at the beginning of a shoe you have some negative decisions with respect to your attack.
You mentioned 3P+ at the beginning, as very bad also for the rest of the shoe,if you are looking for agglomeration 1 and/or 2 P .
No statistical or mathematical evidence of this theory and my test don't confirm it too.
Several BB agglomerated,even a run of four time BB very frequent....
#### Bally6354
• Hero Member
• Posts: 1121
##### Re: Baccarat unbeatable plan #1
« Reply #152 on: June 07, 2019, 11:17:52 am »
Final note
If a bac player have found betting lines capable to get a long term edge, this edge will be quite limited hence susceptible to great fluctuations. That's why we should think about the large picture and not about the stupi.d single shoe we're playing at.
as.
Hello Asym, I was thinking about what you were saying regarding great fluctuations. I am sure many people would agree and think to themselves ''let's suppose you have a 1 or 2% edge similar to card counting in BJ, then surely the fluctuations would be similar.''
However the difference that I see is that in BJ, the dealer has the same chance to get the good hands as well. It's annoying to sit there for an hour, get a positive true count and then start laying out some decent bets only to see the dealer keep pipping your 19 with a 20 or getting a BJ against your 20. In Baccarat, the dealer doesn't get to come along for the ride if you are reading things well at any given moment in time. They (the Casino) have to take the losses and I see that as a huge difference between the two games.
cheers
Sometimes it is the people who no one imagines anything of who do the things that no one can imagine.
#### alrelax
• B&M Player since 1980
• Hero Member
• Posts: 3728
• Gender:
• 'Caring for Kids' Nonprofit Children's Assistance
##### Re: Baccarat unbeatable plan #1
« Reply #153 on: June 07, 2019, 12:56:00 pm »
Can I please interject here for certain points?
REF:
"Final note. If a bac player have found betting lines capable to get a long term edge, this edge will be quite limited hence susceptible to great fluctuations. That's why we should think about the large picture and not about the stupi.d single shoe we're playing at.
as."
These stupid shoes have made me huge amounts of money as compared to the grind and all the other ones, if played with isolation and then forgotten about as far as what normally happens, if I can borrow and use the word normally as some kind of explanation.
Look at the pictures I post almost on a regular basis.
If I look at the large picture I would lose every session, IMO. Because the large picture brings on too much and too many possibilities that probably will not happen in the same amount of time we are sitting there playing. What is going to happen is that STUPID SHOE with 20-25 Players to 3 Bankers immediately or 20-25 Bankers with 3 Players immediately, or 6 Panda 8s with three of them back to back to back or 15 Players and a few hands later 16 Bankers or two 3 card 8/9s followed by 4 Fortune 7s out of 7 or 8 straight Bankers hands winning or 7 doubles followed by 8 singles followed by 4 sets of 4 followed by (?). And we would missed it all because we are expecting the long run with a calm mixture of what NORMALLY happens.
But either way, with those stupid shoes or the calm normal one, if a player wagers strictly for those stupid crazy shoes as I have mentioned and shown lately and repeatably posted, he will go broke because there are more of the other calm and non-crazy type of shoes. But when he is exposed to those other non-crazy and normal ones he will only make so much that will also disappear on his attempt to continue the same wagering pattern/decisions on ones that appear normal and calm but will not match his wagering, or eventually capitalize on those stupid ones when some other players are pulling down tens of thousands of dollars within a shoe or two. Either way, any repetitive player doing the same thing will lose, either his bank roll or every buy in or just hopefully break even and recoup his losses because he stayed wagering the same on whatever he was attempting for, in dreadful and wrongful wagering consistency decision making/planning.
IMO and experience and realizing profit on those stupid shoes. My thoughts attempted to come out. And not as a put down or a chastising attempt either. As reality.
My full 2 cents on 2 important subject raised by AsymB: https://betselection.cc/alrelax's-blog/two-things-re-presents-long-term-edge-and-stupid-shoes/msg66784/#msg66784
My Blog within BetSelection Board: https://betselection.cc/alrelax's-blog/
Played well over 33,770 shoes of baccarat since I started playing at B&M USA casinos.
"Don't say it's a winning hand until you are getting paid for it".
Played numerous properties in Las Vegas, Reno, Southern California, Atlantic City, Connecticut, South Florida, The South/Southeast as well as most areas of The Midwest.
Baccarat, actually a mixture of Watergate, attacking the Gotti Family and the famous ear biting Tyson fight leading to disqualification and a near riot. Bac has all that more.
EMAIL: Betselectionboard@Gmail.Com
#### AsymBacGuy
• Moderator
• Hero Member
• Posts: 1059
##### Re: Baccarat unbeatable plan #1
« Reply #154 on: June 11, 2019, 12:00:35 am »
Hi and thanks for your replies!
@roversi.
Look, of course I have got a statistical significance about what I'm talking about.
Anytime you are playing a shoe getting a strong P predominance at the start, you are getting a lower probability on certain subsequent "more expected" events as the room to get them is more limited albeit slightly.
It's not to be forgotten that asymmetrical force is very often nullified (inversed) in P predominant shoes, thus B is sailing mainly on a 50/50 proposition.
@bally
You are right, yet in positive counts a bj counter could bet two or more spots thus enlarging the probability to get a natural or a doubling hand.
A luxury we can't have at baccarat, being an on/off single game.
@alrelax
The situations you depicted are quite unlikely being too much left or right deviated from the center of the bell curve, I generally prefer to let them go without betting even if I'd have won a lot wagering on them.
Of course, what I need when I encounter such deviated situations is to be at least one hand ahead as the rest is just a winning streak unless a WL event occures (break even or close to it).
Therefore when in doubt I tend to follow things, even though they are unlikely.
Nonetheless, my records show that I have made more money wagering shoes more adapting to my approach at the start then trying to get a "reverse line" albeit more expected (theoretically).
Naturally, if I think that shoes are not properly shuffled and outcomes tend to get a kind of univocal line I'll ride 'em, partially forgetting my primary plan.
I do not care to be right or wrong, I do care to win.
as.
Next to edge sorting it's me
Winners don't do different things, they do things differently (Albalaha)
#### RickK
• Rising Member
• Posts: 17
##### Re: Baccarat unbeatable plan #1
« Reply #155 on: June 11, 2020, 06:00:42 pm »
as
I took a few steps back in an attempt to try to better understand your thoughts on this thread and others...
"We'll bet a 1-2 unit progression whenever a P single or a P double had come out, in order to get at least a two P 1-2 clustered succession in any order. After winning the first (single) or second (double) event, we stop the betting waiting for another 1 or 2 P situation and going over and over. Meaning we have to wait a 3+ appearance cutting the pattern.
In a word, we'll lose anytime the shoe will present situations as 2-3 or 1-3. Anything different from that (as 1-1, 1-2, 2-1 or 2-2), will go in our favor."
To meet the favorable results in the 2nd paragraph...it "seems" that the 1-2 betting progression would be used such that the initial bet (1) would be to bet that all P1s would go opposite...two wins would result in 1-1 and end of betting sequence...a first win, 2nd loss, third win (2 progression) would result in 1-2....a first loss, 2nd win (2 progression), third win would result in 2-1...and a first loss, 2nd win, 3rd loss, 4th win would result in 2-2...all resulting in "favorable" results.
Two losses in a row, either on first P bet (not listed) or second P bet listed as 2-3 and 1-3 would end the betting sequence as a loss.
#### AsymBacGuy
• Moderator
• Hero Member
• Posts: 1059
##### Re: Baccarat unbeatable plan #1
« Reply #156 on: June 12, 2020, 10:23:18 pm »
Hi Rickk!
The principal aim of this plan is to win just one hand getting a general P 0.75 winning probability. If we are betting toward singles and doubles, we must hope that the third unwanted "3" won't come out after the other two different states (singles and doubles) had come out at least once each.
For example a P 1-1-1-1-1-1-3-1-1-1-1 sequence, despite being so attractive doesn't elicit any betting.
If in the same sequence the 3 would be replaced by a 2 (1-1-1-1-1-1-2-1-1-1-1) we'll get four wins when betting "infinitely" and just one win after the 1 that follows the 2.
The 1-2 unit progression was just an example; actually we generally use a softer 1-1.3 or 1-1.5 progression, meaning that the main effort is focused about singles as doubles are considered just a back-up plan.
Of course the 0.75 P winning probability is extracted from a perfect 50/50 proposition but we know that bac B/P probabilities jump from 0.5/0.5 (sym hands) to 0.5793/0.4207 (asym hands), therefore in no way we could think to really wager each hand by a real 0.5068/0.4932 probability ratio.
Especially when we are restricting at most our range of intervention by quantity and quality factors.
as.
Next to edge sorting it's me
Winners don't do different things, they do things differently (Albalaha)
#### alrelax
• B&M Player since 1980
• Hero Member
• Posts: 3728
• Gender:
• 'Caring for Kids' Nonprofit Children's Assistance
##### Re: Baccarat unbeatable plan #1
« Reply #157 on: November 01, 2020, 10:33:06 pm »
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# What is a hypothesis test for a difference in proportions in MyStatLab?
## What is a hypothesis test for a difference in proportions in MyStatLab?
What is a hypothesis test for a difference in proportions in MyStatLab? A Hypothesis test is a popular way to calculate proportions. Hypothesis test for difference in proportions is quite simple used to calculate proportions of the difference in proportions among samples in an R/BiOS environment. The formula and general formula for the formula of a hypothesis are shown below: In which is Average Difference Summary The most important thing here is to calculate any statistical difference for the proportions of a sample. More or less such a question would be probably referred to as Hypothesis Testing Method, or just Hypothesis Testing Method at the same level as Hypothesis Testing Method has been introduced. The formula and formulation for the formula and formulation of a hypothesis is shown below: Hypothesis testing This chapter, and Hypothesis Testing Method is the framework for creating Hypothesis test for the difference in the proportions of the sample of a given sample. This basic idea is as follows: If you compare two samples that differ by the same proportions of the sample, you will find that the difference that will be noticeable for you will be larger than the difference that would be noticeable for the samples in which those samples differ by a negligible amount. The following steps are required in order to create a Hypothesis Test: Step. To create a Hypothesis Test, First you want to check for any effect on the difference between the samples. A significant effect is not expected for the difference in percentages of a sample because, all the experiments related to a sample that were present in the main-sample table are just not fully tested and do not have that probability for all the samples that will be taken into hypothesis test. To test any effect if no significant in the samples that are tested in one one experiment, check the results of one experiment among the others in the main-sample table. If such as a small effect is expected when you see this that the samples will be full of outliers than do, these tests will be just as useless as trying to separate the difference of two samples in two experiments. For this reason, it is useful to test if two samples actually differ in proportions in the two experiments. In Step 2 go to the main-sample table, you can choose to compare the samples to identify difference in percentages of a sample. The part with the smallest effect will also show that the sample that used to be tested is the one that is part of the main-sample table and that the sample has shifted to the left by a large amount. Step 1. Go to the the main-sample table and check the results of one experiment among the others in the sample table. If none of these experiments is significant, then you can conclude that the difference will be small and will be noticeable. If the first one is significant, then you have two cases to test the difference other than one experiment. If one experiment is insignificant and then another one is significant, thenWhat is a hypothesis test for a difference in proportions in MyStatLab? A hypothesis test click here to read based on a difference in the distribution of the scores with a one-tailed response distribution as determined by the null hypothesis. Every hypothesis test is possible, but each hypothesis test is only useful if the hypotheses of the hypothesis test share some criterion for determining its null hypothesis which is described in the hypothesis test (given that this false-noise is smaller than that from not being the null hypothesis).
## Pay Someone With Apple Pay
In my domain of real work, these hypotheses test the difference in the distribution of the score with no hypothesis in place of the null distribution of the score as can be seen by the null-equals-place theorem. This difference is attributed to a difference in the null-distribution, but this does not mean its falsity. It means that the differences between the distribution of the score with no hypothesis and the null-distribution of the score are a failure of the hypothesis test. This is the second example where a non-normal distribution fails to be a null hypothesis. The solution to this error has been discussed at the link. (1) A null hypothesis test is: f = (0, x(1), x(2), \dots, x(n)) Let us show that this is a null hypothesis test. This test makes use of the distribution of x(1), x(2), …, x(m) – A normal distribution. The distribution of a null-distribution f = (x(1), {x(2), \dots, x(m))} This normal distribution is also a null-distribution because it is not a null distribution with no probability. In fact, that is the distribution of x(1), x(2), …, x(n) with a null-distribution as before. Our new test says that we can have two distributions with the same null-shaped distribution but different probability distributions – f = {What is a hypothesis test for a difference in proportions in MyStatLab? I’m a computer scientist and I’m a researcher, and I’m looking for this ‘assignment’ question I’m looking for. I’m doing a clinical test for a difference in proportions in my main dataset, and I’m assuming it’s significant and how do I proceed? Can I somehow quantify this by number and then compute a result. The result is 0.0731/PC – meaning a 0.0731, if I were to do a “M” would 2.96. Yet this report only shows 0.0731/PC*10.01? Not even my report in the book (or some of the scientific articles I read!!!) I’m assuming my report is equal or less than the average of two different reports when using the association test – a previous study by the same author has only shown a small share of 2.96, adding to other comparisons. Note that in this comparison if the 2.
## Pay Someone To Take My Test
96 statistic was for 0.0731/PC this one would give a larger number? So, I would take the last 0.0731/PC but then I would take the odd 0.0731/PC and apply me to the my test. My best thought is that if you have a prior paper which is too large to see in my dataset, then would this be the work? I might reach an interesting conclusion by only having one test on this table. Here is the code if you could post it for e.g: \documentclass{article} \usepackage{tikz} \usepackage{amsmath} \usepackage{onblur} \usepackage{fancyhdr} \usepackage{chimera} \usepackage{amsfonts} \newcommand*{\test}[1]{\setbox0=0pt{\hbox{\hskip1.0pt}}
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5.3 T-Bill Futures Example
office (412) 9679367
fax (412) 967-5958
toll-free 1 (800) 214-3480
5.3 Binomial Option Pricing: N-Period Derivation
I
n the two-period case, we can write the call option value with respect to risk-neutral probabilities p as:
This two-period form can be rearranged into a form that allows the general structure to be deduced.
Written in this form, the general formula for n-periods is
That is, we are summing over the 2n possible paths that the underlying stock price can take. Note, however, that because u, d, and r are constants, the option pricing problem is not path-dependent.
In this case, a path can be defined in terms of some number of realized upticks and some number of realized downticks that sum to n. With this observation, let m be the smallest number of upticks for which a path is in-the-money. We can ignore any path with less than m upticks because the call option will finish out-of-the-money.
Thus, if we let m be the smallest integer such that Sumdn-m > X, then we can simplify the general formula by eliminating all stock paths with fewer than m upticks:
Since we know that the option will finish in-the-money on all these paths, we no longer need to take the max, and so we get:
This expression still has the simple form of the two-period model. The second term is the (risk-neutral) probability that the call option will be in-the-money multiplied by the exercise price, all discounted by the risk-free rate. Therefore, it is the discounted value of the expected payment.
The first term is the discounted value of the expected revenue. Unlike the expected payment, the expected revenue is not equal to S times the probability of the call being in-the-money, because the revenue depends on the stock price (while the payment does not). Rather, we calculate the expected revenue, as done in the formula.
Using the definition of p, this can be rewritten as
Let q = pu/r. Then, using the binomial distribution notation, the present value of the call option equals
Next, we consider the limiting behavior of this pricing model as n gets larger. This is described in topic 5.4, Binomial Option Pricing: Limiting Results, and formally derived in the technical appendix to this chapter.
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Faq
# Question: How to make 3d round in autocad?
Moreover, how do you make 3D curves in AutoCAD?
1. Enter the radius at the prompt.
2. Enter A and enter a degree of curve.
3. Enter C and enter a degree of chord.
Also the question is, how do I rotate a circle in AutoCAD 3D?
1. Click Home tab > Modify panel > Rotate 3D. Find.
2. Select the object to rotate (1).
3. Specify the start point and endpoint of the axis about which the objects are to be rotated (2 and 3).
4. Specify the angle of rotation.
1. Do one of the following: Click Home tab Draw panel Circle drop-down Center, Radius. Find. Click Home tab Draw panel Circle drop-down Center, Diameter. Find.
2. Specify the center point.
3. Specify the radius or diameter.
On an isometric drawing, circles appear as ellipses and arcs as elliptical arcs. You must properly align isometric circles and arcs with the appropriate isometric plane.
Contents
## How do I make curves smooth in AutoCAD?
On the command line, enter OPTIONS. Go to Display > Display resolution section. Increase the value of Arc and circle smoothness.
## How do I round corners in AutoCAD?
We can use the Fillet command to “cut corners” and “round” our edges without doing any math. Once we specify our corner’s radius, the command will automatically join both lines to each other. The “Multiple” option allows us to continuously Fillet many intersections without having to initiate the command repeatedly.
INTERESTING: Can I open AutoCAD file online?
## What is a curve in 3D modeling?
Curve Modelling: Another type of modelling that relies on curves to generate surface geometry. Curve modelling can be both parametric (based on geometric and functional relationships) or freeform, and rely on NURBS (nonuniform rational B-splines) to describe surface forms.
## How do you rotate a 3D object?
Rotate the 3D object around its Y axis: Move the pointer over the rotation handles until a green rotation ring appears, then drag the green ring. Rotate the 3D object around its Z axis: Move the pointer over the rotation handles until a blue rotation ring appears, then drag the blue ring.
## What is the use 3D Rotate command?
Specifies a method for defining the axis of rotation. Object. Aligns the axis of rotation with an existing object. You select one of the following object types: Line.
## How do you use 3D alignment?
1. Click Home tab Modify panel 3D Align. Find.
2. Select the objects that you want to align.
3. Specify either one, two, or three source points and then the corresponding first, second, or third destination points. The first point is called the base point.
## What are the six different options for creating a circle in AutoCAD?
To create circles, you can specify various combinations of center, radius, diameter, points on the circumference, and points on other objects.
## Which is the option to create a circle?
On the Insert tab, click Shapes. Under Basic Shapes, click Oval. Click where you want the oval to start, and drag to draw the shape. To draw a circle, press Shift while you drag.
INTERESTING: How to make architectural drawings in autocad?
## What is 3 point circle in AutoCAD?
Click on the 3-Point command. To draw a circle by selecting 3 points from the drawing scheme of Autocad, you need to click on the pop-up menu as shown by green arrow above then click on the 3-Point circle command in Autocad. Specify the first point.
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Oxford loan in the US : The B-School Application
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# Oxford loan in the US
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Joined: 29 Mar 2010
Posts: 22
Schools: Oxford (admitted), Cambridge (admitted + $), LBS (waitlisted) Followers: 0 Kudos [?]: 2 [1] , given: 1 Oxford loan in the US [#permalink] ### Show Tags 20 May 2010, 07:42 1 This post received KUDOS Oxford R1 & R2 admits/alumni, How did you get a loan (in the US) for tuition/living expenses? Last edited by xandy on 21 May 2010, 06:21, edited 1 time in total. Intern Joined: 03 Jun 2009 Posts: 20 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Oxford loan in the US [#permalink] ### Show Tags 20 May 2010, 11:24 Sorry would mind sharing if we can expect to hear about scholarship awards when they announce acceptances or do they notify about finances separately? Current Student Joined: 01 Nov 2009 Posts: 197 Location: Finland Schools: Cambridge/Judge '11 Followers: 5 Kudos [?]: 17 [0], given: 0 Re: Oxford loan in the US [#permalink] ### Show Tags 20 May 2010, 23:32 At least Cambridge and Oxford seem to notify of scholarships separately. Intern Joined: 03 Jun 2009 Posts: 20 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Oxford loan in the US [#permalink] ### Show Tags 21 May 2010, 12:35 Thanks for the reply, approximately how long after being admitted did Oxford get back to you regarding scholarship$$? Current Student Joined: 01 Nov 2009 Posts: 197 Location: Finland Schools: Cambridge/Judge '11 Followers: 5 Kudos [?]: 17 [0], given: 0 Re: Oxford loan in the US [#permalink] ### Show Tags 23 May 2010, 23:38 I can't remember. I think a few weeks. Intern Joined: 08 Feb 2010 Posts: 47 Schools: Oxford '11 Followers: 1 Kudos [?]: 13 [0], given: 11 Re: Oxford loan in the US [#permalink] ### Show Tags 26 May 2010, 09:08 xandy wrote: Oxford R1 & R2 admits/alumni, How did you get a loan (in the US) for tuition/living expenses? Xandy, You can apply for a Stafford Loan, which covers up to$20,500 for tuition/living expenses. Due to changes in the gov't funding of these loans, I think you won't be able to apply before June. Also, I believe that a Grad Plus loan is an option for those needing additional funding. You should def contact Jenny Roberts or Maria Poole (SBS US loan team) for details concerning timing and your particular situation:
J
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Re: Oxford loan in the US [#permalink]
### Show Tags
27 May 2010, 06:51
you can also get student loans from banks...i got mine from Canada but i imagine it wouldn't be too different in the US. these loans should be able to cover your full year's tuition and expenses.
_________________
Oxford Round 1 - interview invite 10/30/09, admit 12/11/09, ATTENDING 2010
Re: Oxford loan in the US [#permalink] 27 May 2010, 06:51
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# two roll mill with lenght mm
Published June 14, 2013 Practical Roll Techniques: Nip & Crown
Dispense a length of two papers equivalent to 12" greater than the face length of the mating rolls. 2. ... The nip impression is not a continuous profile across the face length of the roll, because the sensors are on centers of 45 cm, 60 cm, and 75 cm. If there are ...
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# Functions: Why, How, and Anatomy (in JS)
Dec 6, 2018 · 6 min read
First things first: why do we even need a function? Let’s suppose for a moment that you’ve completed much of your studies and you are now a developer. You’re really good. You’re so good, in fact, that you have a brilliant idea and begin making your new app. Suddenly, you’re getting investors and venture capital. Now you need a team. And eventually, you’re spending less time coding and more time schmoozing with people who can fund you and creative teams.
With all the telephone calls and business meetings you decide it’s time to get an assistant. Some days you have important lunches with team members and investors, but on any other day, you generally get lunch from a restaurant down the street. You decide that it’s time that your assistant do this for you.
Your brand new assistant arrives and the first day you tell them to go get you a bacon cheeseburger, onion rings, and a Coca-Cola at the restaurant down the street. You give your assistant the name of the restaurant, driving directions, explain to them how to charge the meal to the company and tell them to return with your food. Everything goes according to plan and you’re happily using the extra time answering your pile of emails while the assistant does the tedious stuff.
A couple of days later you have no business meetings scheduled and you ask your assistant to go get your lunch. At this point, you would expect the assistant to know which restaurant you mean, which food, the directions to the restaurant and how to charge it to your company. If the assistant couldn’t remember this basic information and you had to give it every single time you asked for lunch, then that assistant would likely be fired shortly.
Enter the function. We want our assistant to do the same series of tasks by saying one short command “Go get me lunch”. In code, this might look something like this:
This is the definition of a function. It begins with the word “function”. The function is named “goGetMeLunch”. The parentheses will later hold what are known as “parameters” but we’ll get to those later.
This function definition specifies the series of events that should happen every time we tell it to run. It is a block of code that is in a state of waiting and will not execute until we “call” it. Programmers typically talk about “calling” a function. This means that we are executing the function.
So how do we call/execute/invoke a function? We simply say its name and include a pair of parentheses.
This is the console output:
So now we have a function set up for our assistant. Every time we say goGetMeLunch(); they will perform the set of tasks that ultimately bring your lunch back to you.
But at this point, you may notice a problem Every time you ask them to go get you lunch they perform all those tasks exactly as written. It also means that all you ever get back is a bacon cheeseburger, onion rings, and a Coca-Cola. At this point, the code for that may look a bit like this:
And this is the console output:
Currently, there is no code to change your order. Maybe you don’t want the same thing all the time. We also need a way to tell our assistant to change our food order to whatever we want at the time we call it.
Enter parameters and arguments. Parameters appear in the parentheses after the function name in the function definition. These will “catch” our arguments. Arguments are the information we’re sending into the function. Parameters are variables that will last as long as the function is executing. So where we have the variable declarations inside the function that are set to always be the same thing, we can move those into the definition as parameters.
Here I’ve moved the variables up into the parentheses by the function name. These are now parameters. Remember, nothing happens with this function until we call it. Currently, mainDish, side, and drink have no values. But we’re about to give them some and we do this at the moment we call/execute the function. Note that I’ve now changed the comment about ordering my usual lunch to reflect that they are going to order a main dish, a side, and a drink regardless of what those are that day.
Here we have three separate days that we send our assistant to get lunch. Each time we’re ordering something different. The strings inside the parentheses are what we’re ordering and they are known as “arguments”. These are what we’re sending into the function for it to work with. Our parameters and our arguments will match up one to one.
On Tuesday mainDish will be assigned “barbeque chicken”, side will be assigned “corn on the cob”, and “ice tea” willl be assigned to drink. On Wednesday, mainDish will be assigned “caesar salad”, side will be assigned “baked potato”, and drink will be assigned “lemonade”. This same pattern happens for Thursday. The parameters accept the arguments coming into the function and work as a variable declaration.
And here is the console output. As you see, because the function was run three times, there will be three logs to the console.
We always want our assistant to drive to the restaurant, order our food, wait for the food, pick up the order, and come back to us with it. It would be ridiculous and redundant to have to specify those things every time. But we still need it flexible enough that we can change part of that information to suit our needs at the time we require it.
A function is a way to repeat a certain sequence of events every time we ask it to run. Some of the information may change and some may not. It can also be used to give us back some result if we’re doing a calculation or an evaluation of some data. But I hope this helps explain a bit both about why we use them and how we use them.
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Homework_4_solution(1)
# Homework_4_solution(1) - 1 EE113 Homework 4 Problem 4.7...
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Unformatted text preview: 1 EE113 Homework 4 Problem 4.7 Consider the moving average system with exponential weighting y ( n ) = 1 M + 1 M summationdisplay k =0 λ k x ( n − k ) where | λ | < 1 . Is the system linear? causal? time-invariant? stable? Solution: Yes, it is linear, causal, time-invariant, and stable. The reason is (a) for linearity: for the input sequence αx 1 ( n ) + βx 2 ( n ) , where α and β are two constant scalars, the output sequence y ( n ) should be y ( n ) = 1 M + 1 M summationdisplay k =0 λ k [ αx 1 ( n − k ) + βx 2 ( n − k )] = α M + 1 M summationdisplay k =0 λ k x 1 ( n − k ) + β M + 1 M summationdisplay k =0 λ k x 2 ( n − k ) = αy 1 ( n ) + βy 2 ( n ) where y k ( n ) is the output sequence for the input sequence x k ( n ) . (b) for causality: the output y ( n ) only depends on the input { x ( n ) ,x ( n − 1) ,...,x ( n − M ) } for any n . (c) for time-invariability: for the input sequence x 1 ( n ) is a shifted version of x ( n ) ,i.e.,x 1 ( n ) = x ( n − m ) for any constant integer m , the output sequence y 1 ( n ) should be y 1 ( n ) = 1 M + 1 M summationdisplay k =0 λ k x 1 ( n − k ) = 1 M + 1 M summationdisplay k =0 λ k x ( n − m − k ) = y ( n − m ) which is the shifted version of y ( n ) by the same shifts m as the input sequence x 1 ( n ) . (d) for stability: if the input sequence x ( n ) is bounded by | x ( n ) | ≤ B x < ∞ , then the output sequence y ( n ) can be bounded as | y ( n ) | = vextendsingle vextendsingle vextendsingle 1 M + 1 M summationdisplay k =0 λ k x ( n − k ) vextendsingle vextendsingle vextendsingle ≤ 1 M + 1 M summationdisplay k =0 | λ k | · | x ( n − k ) | ≤ 1 M + 1 M summationdisplay k =0 | λ | k · B x = B x ( M + 1) 1 − | λ | M +1 1 − | λ | October 25, 2011 DRAFT 2 Problem 4.9 True or False: (a) A relaxed system is linear. (b) A linear system is relaxed. Solution: (a) A relaxed system is not necessarily linear. Here is a counterexample: y ( n ) = x 2 ( n ) u ( n ) (b) A linear system is relaxed. This can be shown by contradiction. Say there is a linear, but not relaxed system S such that y ( n ) = S [ x ( n )] where x ( n ) is the input sequence and y ( n ) is the output sequence. There should be a time instant n o such that the input sequence x ( n ) = 0 if n ≤ n o but the output sequence y ( n o ) negationslash = 0 . Then it can be verified that the linearity does not hold at the time instant n o because S [ αx ( n o )] = S [ α × 0] = S [0] = S [ x ( n o )] = y ( n o ) negationslash = αy ( n o ) for a nonzero constant scalar α October 25, 2011 DRAFT 3 Problem 4.11 The response of a linear time-invariant system to x ( n ) = u ( n ) is y ( n ) = 0 . 5 n u ( n ) . Find its response to δ ( n ) ....
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## This note was uploaded on 01/24/2012 for the course EE 113 taught by Professor Walker during the Fall '08 term at UCLA.
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# $$\frac{2}{3} + \frac{4}{5}$$ is _______.
This question was previously asked in
CTET Dec 2018 Paper I (L - I/II: Hindi/English/Sanskrit)
View all CTET Papers >
1. $$\frac{6}{8}$$
2. $$1\frac{6}{15}$$
3. $$1\frac{7}{15}$$
4. $$\frac{8}{15}$$
Option 3 : $$1\frac{7}{15}$$
$$\frac{2}{3} + \frac{4}{5}$$
$$\frac{(5\times2)+(3\times4)}{15}$$
$$\frac{(10+12)}{15}=\frac{22}{15}=1\tfrac{7}{15}$$
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# Potential Energy problem
## Homework Statement
A 1kg block rests on earth's surface. How much energy is required to move the block very far from the earth, ending up at rest again?
## Homework Equations
U = -G(m1m2)/r
Uf-Ui= -W (W= work internal)
U=mgy
## The Attempt at a Solution
I know that my final potential energy will be zero, and because the object ends at rest i can say my final kinetic energy will also be zero. Not sure where to go from here, or what equation to use.
CompuChip
Homework Helper
You are on the right track... as you say, the final total energy will be zero.
Can you also say something about the initial energy?
So assuming i use the equation Kf + Uf = Ki + Ui the left side of the equation goes to zero. Im then only left with my initial conditions, and my Ki = 1/2mv^2 and U=mgy..? or does U= -G (Mm)/r ...?
CompuChip
Homework Helper
So assuming i use the equation Kf + Uf = Ki + Ui the left side of the equation goes to zero. Im then only left with my initial conditions,
Exactly.
and my Ki = 1/2mv^2
Where v is the initial velocity (which is ... ?)
and U=mgy..? or does U= -G (Mm)/r ...?
Yes. The whole idea is that they are the same at or very close to the surface of the earth. You can easily show this yourself, if you equate the two,
$$- \frac{G M m}{r} = m g r$$
where r is the distance from the center of the earth, you can solve this for g:
$$g = - \frac{G M}{r^2}$$.
Just plug in the numbers for r at (or negligibly close to) the surface of the earth, at 6400 km from the center, and you will find a value very close to the usually quoted value of g = -9.81 m/s².
(This also explains the reason that g varies between different locations on earth: since the earth is not a perfect sphere, its radius changes a bit from one point to another. It is a bit smaller at the poles, so g will be a bit larger there than at the equator).
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# Counter (digital)
(Redirected from Digital counter)
A counter circuit is usually constructed of a number of flip-flops connected in cascade. Counters are a very widely used component in digital circuits, and are manufactured as separate integrated circuits and also incorporated as parts of larger integrated circuits.
## Electronic counters
In electronics, counters can be implemented quite easily using register-type circuits such as the flip-flop, and a wide variety of classifications exist:
• Asynchronous (ripple) counter – changing state bits are used as clocks to subsequent state flip-flops
• Synchronous counter – all state bits change under control of a single clock
• Decade counter – counts through ten states per stage
• Up/down counter – counts both up and down, under command of a control input
• Ring counter – formed by a shift register with feedback connection in a ring
• Johnson counter – a twisted ring counter
• Modulus counter.
Each is useful for different applications. Usually, counter circuits are digital in nature, and count in natural binary. Many types of counter circuits are available as digital building blocks, for example a number of chips in the 4000 series implement different counters.
Occasionally there are advantages to using a counting sequence other than the natural binary sequence—such as the binary coded decimal counter, a linear feedback shift register counter, or a Gray-code counter.
Counters are useful for digital clocks and timers, and in oven timers, VCR clocks, etc.[1]
### Asynchronous (ripple) counter
Asynchronous counter created from two JK flip-flops
An asynchronous (ripple) counter is a single d-type flip-flop, with its J (data) input fed from its own inverted output. This circuit can store one bit, and hence can count from zero to one before it overflows (starts over from 0). This counter will increment once for every clock cycle and takes two clock cycles to overflow, so every cycle it will alternate between a transition from 0 to 1 and a transition from 1 to 0. Notice that this creates a new clock with a 50% duty cycle at exactly half the frequency of the input clock. If this output is then used as the clock signal for a similarly arranged D flip-flop (remembering to invert the output to the input), one will get another 1 bit counter that counts half as fast. Putting them together yields a two-bit counter:
Cycle Q1 Q0 (Q1:Q0)dec
0 0 0 0
1 0 1 1
2 1 0 2
3 1 1 3
4 0 0 0
You can continue to add additional flip-flops, always inverting the output to its own input, and using the output from the previous flip-flop as the clock signal. The result is called a ripple counter, which can count to 2n - 1 where n is the number of bits (flip-flop stages) in the counter. Ripple counters suffer from unstable outputs as the overflows "ripple" from stage to stage, but they do find frequent application as dividers for clock signals, where the instantaneous count is unimportant, but the division ratio overall is (to clarify this, a 1-bit counter is exactly equivalent to a divide by two circuit; the output frequency is exactly half that of the input when fed with a regular train of clock pulses).
The use of flip-flop outputs as clocks leads to timing skew between the count data bits, making this ripple technique incompatible with normal synchronous circuit design styles.
### Synchronous counter
A 4-bit synchronous counter using JK flip-flops
In synchronous counters, the clock inputs of all the flip-flops are connected together and are triggered by the input pulses. Thus, all the flip-flops change state simultaneously (in parallel). The circuit below is a 4-bit synchronous counter. The J and K inputs of FF0 are connected to HIGH. FF1 has its J and K inputs connected to the output of FF0, and the J and K inputs of FF2 are connected to the output of an AND gate that is fed by the outputs of FF0 and FF1. A simple way of implementing the logic for each bit of an ascending counter (which is what is depicted in the adjacent image) is for each bit to toggle when all of the less significant bits are at a logic high state. For example, bit 1 toggles when bit 0 is logic high; bit 2 toggles when both bit 1 and bit 0 are logic high; bit 3 toggles when bit 2, bit 1 and bit 0 are all high; and so on.
Synchronous counters can also be implemented with hardware finite-state machines, which are more complex but allow for smoother, more stable transitions.
A circuit decade counter using JK Flip-flops (74LS112D) - erratum: Vcc=5V, not 12V on drawing
A decade counter is one that counts in decimal digits, rather than binary. A decade counter may have each (that is, it may count in binary-coded decimal, as the 7490 integrated circuit did) or other binary encodings. "A decade counter is a binary counter that is designed to count to 1010b (decimal 10). An ordinary four-stage counter can be easily modified to a decade counter by adding a NAND gate as in the schematic to the right. Notice that FF2 and FF4 provide the inputs to the NAND gate. The NAND gate outputs are connected to the CLR input of each of the FFs." A decade counter is one that counts in decimal digits, rather than binary. It counts from 0 to 9 and then resets to zero. The counter output can be set to zero by pulsing the reset line low. The count then increments on each clock pulse until it reaches 1001 (decimal 9). When it increments to 1010 (decimal 10) both inputs of the NAND gate go high. The result is that the NAND output goes low, and resets the counter to zero. D going low can be a CARRY OUT signal, indicating that there has been a count of ten.
### Ring counter
Main article: Ring counter
A ring counter is a circular shift register which is initiated such that only one of its flip-flops is the state one while others are in their zero states.
A ring counter is a shift register (a cascade connection of flip-flops) with the output of the last one connected to the input of the first, that is, in a ring. Typically, a pattern consisting of a single bit is circulated so the state repeats every n clock cycles if n flip-flops are used.
### Johnson counter
Main article: Johnson counter
A Johnson counter (or switch-tail ring counter, twisted ring counter, walking ring counter, or Möbius counter) is a modified ring counter, where the output from the last stage is inverted and fed back as input to the first stage.[2][3][4] The register cycles through a sequence of bit-patterns, whose length is equal to twice the length of the shift register, continuing indefinitely. These counters find specialist applications, including those similar to the decade counter, digital-to-analog conversion, etc. They can be implemented easily using D- or JK-type flip-flops.
## Computer science counters
Main article: Register machine
In computability theory, a counter is considered a type of memory. A counter stores a single natural number (initially zero) and can be arbitrarily long. A counter is usually considered in conjunction with a finite-state machine (FSM), which can perform the following operations on the counter:
• Check whether the counter is zero
• Increment the counter by one.
• Decrement the counter by one (if it's already zero, this leaves it unchanged).
The following machines are listed in order of power, with each one being strictly more powerful than the one below it:
1. Deterministic or non-deterministic FSM plus two counters
2. Non-deterministic FSM plus one stack
3. Non-deterministic FSM plus one counter
4. Deterministic FSM plus one counter
5. Deterministic or non-deterministic FSM.
For the first and last, it doesn't matter whether the FSM is a deterministic finite automaton or a nondeterministic finite automaton. They have the same power. The first two and the last one are levels of the Chomsky hierarchy.
The first machine, an FSM plus two counters, is equivalent in power to a Turing machine. See the article on counter machines for a proof.
### Web counter
Main article: Web counter
A web counter or hit counter is a computer software program that indicates the number of visitors, or hits, a particular webpage has received. Once set up, these counters will be incremented by one every time the web page is accessed in a web browser.
The number is usually displayed as an inline digital image or in plain text or on a physical counter such as a mechanical counter. Images may be presented in a variety of fonts, or styles; the classic example is the wheels of an odometer.
Web counter was popular in the 1980s and 1990s, later replaced by more detailed and complete web traffic measures.
### Computer based counters
Many automation systems use PC and laptops to monitor different parameters of machines and production data. Counters may count parameters such as the number of pieces produced, the production batch number, and measurements of the amounts of material used.
## Mechanical counters
Main article: Mechanical counter
Mechanical counter wheels showing both sides. The bump on the wheel shown at the top engages the ratchet on the wheel below every turn.
Several mechanical counters
Early IBM tabulating machine using mechanical counters
Long before electronics became common, mechanical devices were used to count events. These are known as tally counters. They typically consist of a series of disks mounted on an axle, with the digits 0 through 9 marked on their edge. The right most disk moves one increment with each event. Each disk except the left-most has a protrusion that, after the completion of one revolution, moves the next disk to the left one increment. Such counters were used as odometers for bicycles and cars and in tape recorders, fuel dispensers, in production machinery as well as in other machinery. One of the largest manufacturers was the Veeder-Root company, and their name was often used for this type of counter.[5]
Hand held tally counters are used mainly for stocktaking and for counting people attending events.
Electromechanical counters were used to accumulate totals in tabulating machines that pioneered the data processing industry.
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# reddit is a platform for internet communities
[–] 0 points1 point (0 children)
Are you a blank page in a notebook, waiting to be filled with countless drawings of cocks?
[–] 0 points1 point (0 children)
That's actually not what the schwarzchild radius is. Its the distance from the center of a black hole such that the escape velocity at that distance exactly equals the speed of light.
[–] 2 points3 points (0 children)
I'll mount your carbon frame any day...
;)
[–] 0 points1 point (0 children)
[–] 0 points1 point (0 children)
I thought it was hilarious. Not something I'd appreciate as "music," but I can appreciate it all the same. This has been my jam for the past week or so: https://www.youtube.com/watch?v=Ae0nwSv6cTU
[–] 0 points1 point (0 children)
Messed around with it for a few minutes - here is a quick overview of how this website actually works:
• There are six sets of 26 sounds, each assigned to a specific letter on the keyboard (6*26=156 sounds total)\
• Pressing spacebar cycles between different "sets" of twenty-six noises. All the sets are similar, but distinct in their organization.
• Organization within the sets is divided into groups of three, with a single group of two, and a single group of one. This organization is vertical/diagonal in the keyboard layout which continues across the whole keyboard.
• Example: The subset (Q,A,Z) of any of the six primary sets will be a specific sound type, with Q, A, and Z all being slightly different. A really clear example of these differences can be seen with (R,F,V).
• Sets of two and one are (O,L), and (P).
Have fun! Really like the website by the way, thanks for posting.
[–] 3 points4 points (0 children)
~3.26 years, but it's much simpler to convert to LY for that, yes? I definitely see what you mean. I was just thinking that parsecs are really only useful in one niche area (distance measurements through parallax), and so converting to a different unit defeats the purpose of having parsecs in the first place.
[–] 1 point2 points (0 children)
Yes, but aren't parsecs a useful unit to have? Much easier to create a separate system of measurement for stellar parallax than to mix arcseconds and centimeters.
I suppose solely for the conversion factor it could be useful, but apart from that, it seems silly to use centimeters in any calculation where you would otherwise use parsecs.
[–] -1 points0 points (0 children)
Why the hell would anyone ever need to convert from parsecs to centimeters?
[–] 0 points1 point (0 children)
The fact that he's named chef and has chef's mustache seems a pretty good indicator that they also had apocalypse now In mind.
[–] 3 points4 points (0 children)
[–] 1 point2 points (0 children)
Huh, one of my favorites. I felt the same way as you after I read it for the first time; I think what put me off was how the opening section seems like a complete non sequitur until later on in the story...but after reading it a few more times I love it with a passion. Honestly, all of Huxley's writing appeals to me, it just makes sense. He writes in a very logical structure, yet still words ideas in ways that leave the overall "vibe" open to interpretation. His essays are great too: The Oddest Science, and Music at Night are two of my favorites.
[–] 1 point2 points (0 children)
The smallest possible radius of a black hole is determined by its mass. The "Schwarzchild radius" is exactly this: the radial limit of a spherical mass such that the escape velocity of an object placed on the surface of that sphere would equal the speed of light (it's the same thing as the event horizon, which honestly sounds way cooler).
Therefore, this size limit must be directly proportional to the mass of an object, and G (6.67 x 10-11 [N m2 / kg2 ]) and c (~300,000 m/s) must be thrown in there somewhere. In the end, it comes out like this: REH = 2Gm/c2.
So if we put in the mass of Earth to this equation, we can figure out how dense (and tiny) the Earth would have to be in order for its escape velocity to exceed the speed of light.
RSchwarzchild = (2(6.67 x 10-11 ) (5.9721986 x 1024 kg))/(2.998 x 108 )2
= (7.97×1014 m3 / s*2) / (8.988×1016 m2 / s2)
At this point, the seconds2 cancel out, and m3 is divided by m2, leaving...meters!
= 0.008867 meters
= 8.867 mm
= tiny as fuck
So technically, a black hole can be as small as you want, as long as it's dense enough. This logic sort of breaks up at a subatomic scale, mainly because nobody has any idea what would happen if a few loose atoms were somehow brought to the requisite density. It's impossible, really; in order for something to naturally become a black hole its mass has to be large enough that it can overcome the forces of electron degeneracy (which keeps white dwarfs from collapsing), and neutron degeneracy (which is the only thing keeping neutron stars from collapsing to their Schwarzchild radii). A star must be greater than 1.44 solar masses (maximum stable mass of W.D) in order to exceed the Chandrasekhar limit and go from a white dwarf to either a neutron star, or a black hole. So the prospect of a black hole less massive than that is possible on paper, but never realistically possible.
Edit: Formatting
Edit 2: Density! D = m/v!
MEarth= 5.9721986 x 1024 kg
VTinyEarth/BlackHoleThingy = 2.92×10-15 km³ or 2.92 cm3
so DTinyEarth/BlackHoleThingy = 2045000000000000000000000 kg/cm3
[–] 0 points1 point (0 children)
You Probably Know: Frank Zappa
You May Know: Captain Beefheart
You Probably Don't Know: Melody's Echo Chamber
You Don't Know: The Envy Corps
[–] 1 point2 points (0 children)
Salsa
[–] 3 points4 points (0 children)
US to decide whether the classification of marijuana is actually a dangerous drug
classification of marijuana is a dangerous drug
[–] 0 points1 point (0 children)
Sleep Dirt gets my vote, one of my favorite albums. I'd also recommend Studio Tan; who doesn't like Greggery Peccary?
[–] 6 points7 points (0 children)
atlas + progressively saggier ass = metaphor representing the natural aging of the human body (ass?), and the associated philosophication
[–] 0 points1 point (0 children)
54
[–] 1 point2 points (0 children)
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http://tobydriscoll.net/blog/trefethen-bau-matlab-julia-lecture-8-gram-schmidt/
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# Trefethen & Bau & MATLAB & Julia, Lecture 8: Gram-Schmidt
This lecture is about the modified Gram-Schmidt method and flop counting. The notebooks are here.
I’m lost.
Almost as an afterthought I decided to add a demonstration of the timing of Gram-Schmidt compared to the asymptotic
n_ = collect(50:50:500);
time_ = zeros(size(n_));
for k = 1:length(n_)
n = n_[k];
A = rand(1200,n);
Q = zeros(1200,n); R = zeros(600,600);
tic();
R[1,1] = norm(A[:,1]);
Q[:,1] = A[:,1]/R[1,1];
for j = 2:n
R[1:j-1,j] = Q[:,1:j-1]'*A[:,j];
v = A[:,j] - Q[:,1:j-1]*R[1:j-1,j];
R[j,j] = norm(v);
Q[:,j] = v/R[j,j];
end
time_[k] = toc();
end
using PyPlot
loglog(n_,time_,"-o",n_,(n_/500).^2,"--")
xlabel("n"), ylabel("elapsed time")
I noticed that while the timings were similar, Julia lagged MATLAB just a bit. I decided this would be a great chance for me to see Julia’s prowess with speedy loops firsthand.
Compare the vectorized and unvectorized Julia versions here:
Look at the last line–it’s allocating 1.4GB of memory to make the nested loop version happen! I thought perhaps I should use copy to create v in each pass, but that change didn’t help. I even tried writing my own loop for computing the dot product, to no avail.
It did help a little to replace the line in which v is updated with
v = broadcast!(-,v,Q[:,i]*R[i,j])
The bang on the name of the function makes it operate in-place, overwriting the current storage. Apparently Julia will create some syntactic sugar for this maneuver in version 0.5. Here it reduced the memory usage to 1.1 GB.
Julia’s reputation is that it’s great with loops, especially compared to MATLAB and Python. As a Julia newbie I recognize that there may still be only a small change I need to make in order to see this for myself. But I feel as though having to use that broadcast!, or even the more natural .= that may be coming, is already too much to ask. I’m frustrated, confused, and disappointed.
##### Toby Driscoll
###### Professor of Mathematical Sciences
My research interests are in scientific computation, mathematical software, and applications of mathematics in the life sciences.
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# Is Experimentation Random?
#1
I’m playing in a game and invested heavily in experimentation early on. So far there have been 7 galactic cycles and my scientists have unlocked experimentation 5 of those times- the last 3 in a row!! The other two were in terraforming. This seems way out of balance. If it is really random maybe I should go to vegas.
#2
As far as I know and have read here, yes I believe it’s supposed to be completely random.
I would love to know what algorithm is used to decide it though!
#3
I just use pythons radom.choice method to pick a tech from a list of all techs.
You should definitely buy a lottery ticket.
#4
first game, i just got experimentation 3 out of 4 cycles. exp, bank, exp, exp… algorithm definitely needs a change.
a co-worker has gotten exp, bank, exp … so far.
#5
This Dilbert strip comes to mind: http://dilbert.com/strips/comic/2001-10-25/
#6
I posted this on the G+ page in response to a suggestion on the issue:
An alternative solution would be to decide how many hits in the same thing you would accept in a row before you got a hit in everything else.
So if you say experimentation must give you a hit in everything once before it can cycle again, every 7 cycles you’d take the list [1,2,3,4,5,6,7], randomize that, and pull the next tech out of the list each turn.
If, for example, you wanted to allow for the possibility of hitting 2 in a row you’d do the same thing, except every 14 cycles and using a list like [1,1,2,2 … 7,7].
I think that would be kinda nice, and would lend a little strategic predictability to experimentation.
#7
To echo jon/Dilbert’s comment, random is random.
If you get HyperSpace 5 times in a row, the odds are still 1 outa 7 you’ll get it again. I’ve played enough that I’ve seen (mostly) different tech each time … and below is a screenshot (click to see big) where I got Weapons five outa six times … but a teammate (it was a team-based game) was our Weapons dude …
I think Experimentation is one of the better aspects of the game (and don’t think the random nature should be changed) … although its importance diminishes later one.
BTW, I’ve heard rumors that Experimentation might be biased for the AFK’ers … if so, I actually think that is a GREAT move.
#8
AFKers are not cheating on Experimentation, but thats a good idea because it would mostly hidden and could be chalked up to randomness
#9
Without tipping the scales too much, I’m all for giving the AFK’ers some advantages.
I.e. being able to trade even if not in Scan range, making moves/trading/etc. intra-turn, and yea, biasing experimentation. That is until you get the full sentient AI working and they start attacking players to take over the galaxy!
#10
But you still want noobs to eventually become veterans, right ?
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# math
posted by .
Raymond has exactly 360 square inches of cardboard to make a box. He wants two of the dimensions to be 6 inches and the other one to be a whole number of inches. How many different size boxes can he make?
• math -
Width = 6 in.
Height = 6 in.
Length = L in.
As=2(W*h) + 2(L*h) + (2W*L) = 360in^2. = max. surface area.
2(6*6) + 2(L*6) + 2(6*L) = 360,
72 + 12L + 12L = 360,
24L = 360 - 72 = 288,
L = 12 in. = max length.
Lmin 1 in. = min whole number.
He can make 12 different sizes(L = 1 to
12in).
## Similar Questions
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2. ### Math
Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.
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6. ### Algebra
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8. ### Sgt
raymond wants to make a box that has a volume of 360 cubic inches. He wants the height to be 10 inches and the other two dimensions to be whole numbers of inches. How many different-size boxes can he make?
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https://proofwiki.org/wiki/Sequence_Converges_to_Within_Half_Limit
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# Sequence Converges to Within Half Limit
## Theorem
### Sequence of Real Numbers
Let $\sequence {x_n}$ be a sequence in $\R$.
Let $\sequence {x_n}$ be convergent to the limit $l$.
That is, let $\displaystyle \lim_{n \mathop \to \infty} x_n = l$.
Suppose $l > 0$.
Then:
$\exists N: \forall n > N: x_n > \dfrac l 2$
Similarly, suppose $l < 0$.
Then:
$\exists N: \forall n > N: x_n < \dfrac l 2$
### Sequence of Complex Numbers
Let $\sequence {z_n}$ be a sequence in $\C$.
Let $\sequence {z_n}$ be convergent to the limit $l$.
That is, let $\displaystyle \lim_{n \mathop \to \infty} z_n = l$ where $l \ne 0$.
Then:
$\exists N: \forall n > N: \cmod {z_n} > \dfrac {\cmod l} 2$
### Sequence in Normed Division Ring
Let $\struct {R, \norm {\, \cdot \,} }$ be a normed division ring with zero $0$.
Let $\sequence {x_n}$ be a sequence in $R$.
Let $\sequence {x_n}$ be convergent in the norm $\norm {\, \cdot \,}$ to the following limit:
$\displaystyle \lim_{n \mathop \to \infty} x_n = l \ne 0$
Then:
$\exists N: \forall n > N: \norm {x_n} > \dfrac {\norm l} 2$
## Also see
This is used in the Quotient Rule for Sequences.
Although this result seems a little trivial, it is often crucial to know that a sequence will be "eventually non-zero" so we know we can legitimately divide by it.
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http://metric-calculator.com/converter_qt_to_l.htm
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# Quarts to Liters (qt to l) Conversion Calculator
This converter provides conversion of quarts to liters (qt to l) and backwards.
Enter quarts or liters for conversion:
Select conversion type:
Rounding options:
Conversion Chart
quarts to liters Conversion Table: 1 qt = 0.9464 l2 qt = 1.8927 l3 qt = 2.8391 l4 qt = 3.7854 l5 qt = 4.7318 l6 qt = 5.6781 l7 qt = 6.6245 l8 qt = 7.5708 l9 qt = 8.5172 l10 qt = 9.4635 l11 qt = 10.4099 l12 qt = 11.3562 l13 qt = 12.3026 l14 qt = 13.2489 l15 qt = 14.1953 l16 qt = 15.1416 l17 qt = 16.088 l18 qt = 17.0344 l19 qt = 17.9807 l20 qt = 18.9271 l21 qt = 19.8734 l22 qt = 20.8198 l23 qt = 21.7661 l24 qt = 22.7125 l25 qt = 23.6588 l26 qt = 24.6052 l27 qt = 25.5515 l28 qt = 26.4979 l29 qt = 27.4442 l30 qt = 28.3906 l31 qt = 29.3369 l32 qt = 30.2833 l33 qt = 31.2296 l34 qt = 32.176 l35 qt = 33.1224 l36 qt = 34.0687 l37 qt = 35.0151 l38 qt = 35.9614 l39 qt = 36.9078 l40 qt = 37.8541 l41 qt = 38.8005 l42 qt = 39.7468 l43 qt = 40.6932 l44 qt = 41.6395 l45 qt = 42.5859 l46 qt = 43.5322 l47 qt = 44.4786 l48 qt = 45.4249 l49 qt = 46.3713 l50 qt = 47.3177 l 51 qt = 48.264 l52 qt = 49.2104 l53 qt = 50.1567 l54 qt = 51.1031 l55 qt = 52.0494 l56 qt = 52.9958 l57 qt = 53.9421 l58 qt = 54.8885 l59 qt = 55.8348 l60 qt = 56.7812 l61 qt = 57.7275 l62 qt = 58.6739 l63 qt = 59.6202 l64 qt = 60.5666 l65 qt = 61.5129 l66 qt = 62.4593 l67 qt = 63.4057 l68 qt = 64.352 l69 qt = 65.2984 l70 qt = 66.2447 l71 qt = 67.1911 l72 qt = 68.1374 l73 qt = 69.0838 l74 qt = 70.0301 l75 qt = 70.9765 l76 qt = 71.9228 l77 qt = 72.8692 l78 qt = 73.8155 l79 qt = 74.7619 l80 qt = 75.7082 l81 qt = 76.6546 l82 qt = 77.6009 l83 qt = 78.5473 l84 qt = 79.4937 l85 qt = 80.44 l86 qt = 81.3864 l87 qt = 82.3327 l88 qt = 83.2791 l89 qt = 84.2254 l90 qt = 85.1718 l91 qt = 86.1181 l92 qt = 87.0645 l93 qt = 88.0108 l94 qt = 88.9572 l95 qt = 89.9035 l96 qt = 90.8499 l97 qt = 91.7962 l98 qt = 92.7426 l99 qt = 93.6889 l100 qt = 94.6353 l
1 quart (qt) = 0.946353 liter (l). Quart (qt) is a unit of Volume used in Standard system. Liter (l) is a unit of Volume used in Metric system. The US liquid quart equals to 0.946352946 liters.
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https://python-bloggers.com/2021/05/naive-bayes-classification-in-nlp-tasks-from-scratch/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+Python-bloggers+%28Python-bloggers%29
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In this tutorial, we will get the Bayesian Score of each word as well as of the whole Subject Line. The score will indicate the chance of a Subject Line and/or token being “spam”. You can find the dataset here. We have used the same dataset, in the Email Spam Detector Tutorial, so feel free to compare the Bayesian approach with the Logistic Regression.
import pandas as pd
import numpy as np
import re
from collections import Counter
import string
## Theory and Formulas
#### So how do you train a Naive Bayes classifier?
• The first part of training a naive bayes classifier is to identify the number of classes that you have.
• You will create a probability for each class. $$P(D_{pos})$$ is the probability that the document is positive. $$P(D_{neg})$$ is the probability that the document is negative.
Use the formulas as follows and store the values in a dictionary:
$$P(D_{pos}) = \frac{D_{pos}}{D}\tag{1}$$
$latexP(D_{neg}) = \frac{D_{neg}}{D}\tag{2}$
Where $$D$$ is the total number of documents, or Subject Lines in this case, $$D_{pos}$$ is the total number of positive SL and $$D_{neg}$$ is the total number of negative SL.
#### Prior and Logprior
The prior probability represents the underlying probability in the target population that a SL is positive versus negative. In other words, if we had no specific information and blindly picked a SL out of the population set, what is the probability that it will be positive versus that it will be negative? That is the “prior”.
The prior is the ratio of the probabilities $$\frac{P(D_{pos})}{P(D_{neg})}$$.
We can take the log of the prior to rescale it, and we’ll call this the logprior
$$\text{logprior} = log \left( \frac{P(D_{pos})}{P(D_{neg})} \right) = log \left( \frac{D_{pos}}{D_{neg}} \right)$$.
Note that $$log(\frac{A}{B})$$ is the same as $log(A) – log(B)$. So the logprior can also be calculated as the difference between two logs:
$$\text{logprior} = \log (P(D_{pos})) – \log (P(D_{neg})) = \log (D_{pos}) – \log (D_{neg})\tag{3}$$
#### Positive and Negative Probability of a Word
To compute the positive probability and the negative probability for a specific word in the vocabulary, we’ll use the following inputs:
• $$freq_{pos}$$ and $$freq_{neg}$$ are the frequencies of that specific word in the positive or negative class. In other words, the positive frequency of a word is the number of times the word is counted with the label of 1.
• $$N_{pos}$$ and $$N_{neg}$$ are the total number of positive and negative words for all documents (for all SLs), respectively.
• $$V$$ is the number of unique words in the entire set of documents, for all classes, whether positive or negative.
We’ll use these to compute the positive and negative probability for a specific word using this formula:
$$P(W_{pos}) = \frac{freq_{pos} + 1}{N_{pos} + V}\tag{4}$$
$$P(W_{neg}) = \frac{freq_{neg} + 1}{N_{neg} + V}\tag{5}$$
#### Log likelihood
To compute the loglikelihood of that very same word, we can implement the following equations:
$$\text{loglikelihood} = \log \left(\frac{P(W_{pos})}{P(W_{neg})} \right)\tag{6}$$
The overall probability of each SL is:
$$p = logprior + \sum_i^N (loglikelihood_i)$$
where we sum up loglikelihoods of each word in the SL plus the logprior.
## Coding
Let’s get our hands dirty by building the formulas above.
# load the data and set the spam=1 and ham=0
# convert the text into lower case and remove the puncuations
df['target'] = df.target.map({'spam':1, 'ham':0})
df['text'] = df.text.apply(lambda x:x.lower())
df['text'] = df.text.apply(lambda x:x.translate(str.maketrans('', '', string.punctuation)))
df
# Get the V Freq
V_freq = Counter(" ".join(df['text'].values.tolist()).split(" "))
# Get the V
V = len(V_freq.keys())
# get the freq_pos
freq_pos = Counter(" ".join(df.loc[df.target==1]['text'].values.tolist()).split(" "))
# get the freq_neg
freq_neg = Counter(" ".join(df.loc[df.target==0]['text'].values.tolist()).split(" "))
# get the number of positive and negative documents
D_pos = sum(df.target==1)
D_neg = sum(df.target==0)
# get the number of unique positive and negative words
N_pos = len(freq_pos.keys())
N_neg = len(freq_neg.keys())
logprior = np.log(D_pos/D_neg)
def word_loglikelihood(w):
w = w.lower()
if w in V_freq:
p_w_pos = (freq_pos.get(w,0)+1 / (N_pos+V))
p_w_neg = (freq_neg.get(w,0)+1 / (N_neg+V))
return np.log(p_w_pos/p_w_neg)
else:
return(0)
Let’s see the score of some words, like “lovable” and “free“.
As we can see, the word “free” has a high score (>0) which means that this word is more related to spam emails. On contrary, the word “lovable” has a very low score (<0) which means that this word is not related to spam emails.
Let’s create a function that returns the score of the whole subject line by adding up the word likelihood of each word plus the logprior.
def text_loglikelihood(mytxt):
mytxt = mytxt.lower().split(" ")
score = logprior
for w in mytxt:
score+= word_loglikelihood(w)
# print(w,word_loglikelihood(w))
return(score)
Get the score of the first SL from our data frame:
text_loglikelihood(df.iloc[0]['text'])
We get:
-107.49288547485799
which implies that this SL is more likely to be Ham.
## Make Predictions
Let’s say that we want to make predictions for all the SL. We will add two columns. The score and the label of the prediction by taking values 0 and 1, where 1 is when the score is positive and 0 otherwise.
df['score'] = df.text.apply(lambda x:text_loglikelihood(x))
df['prediction'] = df.score.apply(lambda x:int(x>0))
# confusion matrix
df.groupby(['target','prediction']).size().reset_index()
Finally, the accuracy on the train dataset is 99.5%
np.mean(df.target==df.prediction)
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# CBSE Class 11 Computer Science Sample Paper Set S
Read and download PDF of CBSE Class 11 Computer Science Sample Paper Set S designed as per the latest curriculum and examination pattern for Class 11 issued by CBSE, NCERT and KVS. The latest Class 11 Computer Science Sample Papers have been provided with solutions so that the students can solve these practice papers and then compare their answers. This will help them to identify mistakes and improvement areas in Computer Science Class 11 which they need to study more to get better marks in Class 11 exams. After solving these guess papers also refer to solved Class 11 Computer Science Question Papers available on our website to build strong understanding of the subject
## Sample Paper for Class 11 Computer Science Pdf
Students can refer to the below Class 11 Computer Science Sample Paper designed to help students understand the pattern of questions that will be asked in Class 11 exams. Please download CBSE Class 11 Computer Science Sample Paper Set S
### Computer Science Class 11 Sample Paper
CBSE Class 11 Computer Science Sample Paper Set S.Sample Papers are the very important for every student. The sample papers should be practiced to gain extra marks in examinations. The sample papers have been prepared based on pattern of last year examinations and as per latest changes in the syllabus. Students, teachers and parents can download all CBSE educational material and very well prepared worksheets from this website. All CBSE educational material is developed by our panel of teachers, have also been submitted by CBSE teachers and students.
1.a. What are escape sequences ?mention 5 of them
b. Why is it important to include iostream.h in c++ programs?
c. Give a command to delete files with extension .BAK from directory NEW. The command must confirm before deleting files.
d. Explain briefly the difference between
1)COPY and MOVE command.
2)strcmp() and strcmpi()
e. Differentiate between 1, ‘1’, “1”
2.a. How 2’s complement of number is obtained? Explain with help of an example.
b. Make a binary addition of 34 and 24.
c. Give header files for (3)
setw(),sizeof() , cos(), floor() , isupper() , isalpha()
d. Convert the following numbers into its equivalent codes.
i. (0011.01)2 = (?)8
ii. (2b7)16 = (?)2
iii. (342)8 = (?)10
i. (EA5A)16 -> (?)8
3.
a. Will the following program execute successfully? If not, state the reasons. (2) #include<conio.h>
{
float c; int vowels=0.0; others=0;
cout<<”enter char”;
while((c>=’A’)&&(c<=’Z’))
{
switch(c)
{
case ‘A’ :
case ‘E’ : case ‘I’ : case ‘A’:vowels++;
default : others++; } } cout<<vowels<<others;}
b. Find the O/p of following c++ statements(if ANY,assume the header files are there and the statements are in main function
1) unsigned int x=5; int y=-6;
if(x<y) cout<<”t”; else cout<<”f”;
2) for(i=0;i<5;i++)
{ j=pow(i,2); if((j%2)==0) { continue;} else cout<<j;}
c. Give the value for a,b,d,e for c=4 in each
a= ++c + ++c; b=c++ + ++c; d=++c + c++; e=c++ + 2*c++;
Please click the below link to access CBSE Class 11 Computer Science Sample Paper Set S.
## More Study Material
### Sample Paper Computer Science Class 11
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https://www.deepdyve.com/lp/springer_journal/pointwise-and-internal-controllability-for-the-wave-equation-y00QvAJd8i
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# Pointwise and Internal Controllability for the Wave Equation
Pointwise and Internal Controllability for the Wave Equation Abstract. Problems of internal and pointwise observation and control for the one-dimensional wave equation arise in the simulation of control and identification processes in electrical engineering, flaw detection, and medical tomography. The generally accepted way of modelling sensors and actuators as pointlike objects leads to results which may make no apparent physical sense: they may depend, for instance, on the rationality or irrationality of the location for a point sensor or actuator. We propose a new formulation of sensor (actuator) action, expressed mathematically by using somewhat unconventional spaces for data presentation and processing. For interaction restricted to an interval of length ε , the limit system of observation (or control) now makes sense when ε tends to zero without a sensitive dependence on the precise location of the limiting point. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals
# Pointwise and Internal Controllability for the Wave Equation
, Volume 46 (3) – Dec 19, 2002
18 pages
/lp/springer_journal/pointwise-and-internal-controllability-for-the-wave-equation-y00QvAJd8i
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-002-0747-1
Publisher site
See Article on Publisher Site
### Abstract
Abstract. Problems of internal and pointwise observation and control for the one-dimensional wave equation arise in the simulation of control and identification processes in electrical engineering, flaw detection, and medical tomography. The generally accepted way of modelling sensors and actuators as pointlike objects leads to results which may make no apparent physical sense: they may depend, for instance, on the rationality or irrationality of the location for a point sensor or actuator. We propose a new formulation of sensor (actuator) action, expressed mathematically by using somewhat unconventional spaces for data presentation and processing. For interaction restricted to an interval of length ε , the limit system of observation (or control) now makes sense when ε tends to zero without a sensitive dependence on the precise location of the limiting point.
### Journal
Applied Mathematics and OptimizationSpringer Journals
Published: Dec 19, 2002
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# Homework Help: Need lots of help!
1. Jun 1, 2009
### brittney1993
Need lots of help! :D
1. The problem statement, all variables and given/known data
A new rectangle with the word “STROM” is to be constructed inside the mat of an outside rectangle. The width of the mat surrounding the rectangular “STROM” logo will be the same. The area of the boundary around the word “STROM” will be the same as the logo itself. Determine the uniform width of the boundary.
2. Relevant equations
i made a picture of it including the measurements from the sheet:
http://img188.imageshack.us/img188/4315/strompic.jpg [Broken]
3. The attempt at a solution
294.5 inches x 72 inches = 21204 inches
i really dont know what to do, please show me step-by-step directions on how to solve this so I can understand and learn from it. Thanks!!!!:)
Last edited by a moderator: May 4, 2017
2. Jun 1, 2009
### sylas
Re: Need lots of help! :D
You'll learn even better when you show us the step by step solution! You've done the first step correctly. The units are "square inches". Now there's more information you were given. Can you find any other areas? What else has an area in this problem?
3. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
i dont know what to do :(
how am i to find the uniform width of the boundary??
4. Jun 1, 2009
### sylas
Re: Need lots of help! :D
Step by step. Don't worry about the width yet. Can you find the area of anything else? There's the logo for example. What do you know about its area?
5. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
well there weren't any measurements given to the logo, so how would i go about finding its area? as far as i know, the measurements from the mat rectangle have to do with something with its area, right? i cant seem to figure it out though. =\
6. Jun 1, 2009
### sylas
Re: Need lots of help! :D
Try this sentence: "The area of the boundary around the word “STROM” will be the same as the logo itself."
Can that help tell you the area of the logo itself? You've already obtained the total area.
7. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
i still don't get it. :( i only got the total area which is 21204 inches. so you're saying its the same? so the logo's area is 21204 inches as well?
ah damn i suck at this...lol.
8. Jun 1, 2009
### sylas
Re: Need lots of help! :D
Hang in there; you're still ok. You got the first bit yourself, and now you're going to get the next.
The total area is 21204. That area is a logo, and also a fixed width boundary.The logo is the same area as the boundary, and together they equal 21204.
Whats the area of the logo? What's the area of the boundary?
Cheers -- sylas
9. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
10602? i divided the total area by 2.
10. Jun 1, 2009
### sylas
Re: Need lots of help! :D
That's right.
Now the next bit is going to take a bit of algebra. There are several ways of doing it but they all get the same answer.
Use a variable "w" to represent the width of the boundary. The logo is a smaller rectangle inside the big one. What is its length and width? You won't be able to give them as numbers just yet, but you can get an expressing using "w".
11. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
huh? I don't get it. :( so I have 10602 as the area, and now I need the legnth and width of it.
10602 = L x W
how do I get the length & width when i have the areA?
12. Jun 1, 2009
### sylas
Re: Need lots of help! :D
One approach I use with this sort of problem is to give variables, for everything, and then write down as many equations as I can.
For example. You have used L and W for the length and width of the logo. Now also use B for the width of the boundary.
Can you write expression using L, W and B for the length and width of the whole mat?
Length: 294.5 = ???[L,W,B]
Width: 72 = ???[L,W,B]
I'm also a big fan of drawing pictures. You can label your diagram with L, W and B, to show what lengths and widths they refer to in the problem.
13. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
can you just give me the answer? i know thats probably the right way to learn in ur opinion, but hear me out. if you give me the answer then i can see how you got there by going backwards. i think that'd be better because i really can't figure this out and I'm not really understanding you :(
14. Jun 1, 2009
### sylas
Re: Need lots of help! :D
Sorry. There are rules here about how we do this. I am probably not explaining as well as I could, and you can help me with that as well.
Here's the diagram I suggested for you, labeled with L, W and B.
Can you give n expression in terms of the variables for the total length?
294.5 = ???
15. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
294.5 = n
???
16. Jun 1, 2009
### sylas
Re: Need lots of help! :D
That's using a new variable for the total length, and you know its value. I often use variables for known values also.
But what I am asking now is for a new expression, which captures something you know about the problem. Specifically, the total length "n" can be given in terms of your other variables L, W and B in the diagram.
n = ???
Replace the ??? with an expression involving the other variables.
17. Jun 1, 2009
### brittney1993
Re: Need lots of help! :D
is it...
294.5 = l + 2b
72 = w + 2b
18. Jun 1, 2009
### sylas
Re: Need lots of help! :D
That's right!
You now have given three equations, with three unknowns. The other one is the equation you gave back in [post=2220405]msg #11[/post].
You want to find "b". You can re-arrange the two equations here into the form
L = ???
W = ???
where ??? are expressions using "b". You use these expressions for L and W in your earlier equation in [post=2220405]msg #11[/post], you will have one equation, with one variable, and you have to solve that for the answer.
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# Convert 5.33 Feet to Inches
## How many inches in 5.33 Feet?
5.33 Feet is equal to 63.96 Inches
## Explanation of 5.33ft to Inches Conversion
Feet to Inches Conversion Formula: in = ft × 12
According to 'feet to inches' conversion formula if you want to convert 5.33 (five point three three) Feet to Inches you have to multiply 5.33 by 12.
Here is the complete solution:
5.33 ft × 12
=
63.96″
(sixty-three point nine six inches )
## How to write 5.33 Feet in height?
You could write 5.33 Feet as simple as 5.33ft or 5.33'
## About "Feet to Inches" Calculator
This converter will help you to convert Feet to Inches (ft to in). For example, it can help you find out how many inches in 5.33 Feet? (The answer is: 63.96). Enter the number of Feet (e.g. '5.33') and hit the 'Convert' button.
5.33' = 63.96″
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# Centripetal Force: Banked Curve
## Homework Statement
A 1200 kg car travels around a curve banked at 42.5 degrees in a circular path of radius = 150m, but the ramp is only 55m long. The force of friction on the car is 9000N, calculate the speed of the car.
So:
θ (angle the incline makes with the horizontal) = 42.5
mass = 1200 kg
Friction = 9000 N
Fc= FNx + FFx
Fc= mv2 / r
## The Attempt at a Solution
The car does not move in the y-plane, therefore:
Ff + Fg + FN = 0
FN = (mg + Ffsinθ)/cosθ
Solve for FN and I got 24213.83512 N
Then I used the value of FN to find FNx and added FFx to it.
Then I multiplied by the radius, divided by the mass and took the square root leaving me with 54m/s.
However, when I use the formula found on this page http://en.wikipedia.org/wiki/Banked_turn" [Broken] I got 67 m/s.
Which one is right? And If I'm wrong, where did I go wrong?
Last edited by a moderator:
LawrenceC
How did you apply the 9000N to the equations on the Wiki site?
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# passenger storage track lenght.
I have come up with the figure in the neighborhood of 24'-25' feet for the length of through tracks to hold 10 passenger cars (figuring 12" each) plus
the turnout clearance for #6 turnouts. This makes it tough to get into a 12' x 13' room because it uses up two complete walls. Am I anywhere close on the length needed for these though ladder tracks?
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<%-name%>
On 13/03/2011 2:49 PM, Pintlar wrote:
For a ten car train, you need 10ft plus the clearance length of two #6 turnouts, total 12ft. So where do you get the 24 foot from? Are you planning to put these tracks end to end? Or store two trains end to end? What about reserving one side of the room for the storage tracks, and building shorter parallel through tracks?
What kind of layout are you planning/building? Without some sense of your overall plans, it's tough to understand your problem, let alone suggest solutions.
I'll toss one out anyhow: Unless you stand well back, you can't see a complete 10-car passenger train in HO, certainly not in a 12'x13' room. So planning for such long trains in such a small space isn't needed. You can easily get away with trains of two locomotives + 5 cars, or about 6-1/2 feet. If you plan the layout as a series of scenes, the view blocks (both physical and psychological) that separate the scenes will add to the illusion of a long trains, since you will find it difficult to see both ends of a train at the same time.
HTH, if not, come back with more background to you problem.
Wolf K.
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<%-name%>
I'm considering the two circles each larger than 24" radius to accommodate the entrance to the ladder tracks. ******************************************************
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<%-name%>
12" would be 87' in H0. Yeah, about 90' is typical for passenger cars. One *could* 'cheat' and use shortened cars -- Athearn used to make passenger cars that were about 70 scale feet long -- not truely scale correct, but could be used as part of "selective compression" to make things fit better in a smaller space)... Or use shorter trains -- 5-6 cars rather then 10 -- another "selective compression" trick.
--
Robert Heller -- 978-544-6933
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<%-name%>
Robert Heller wrote:
Wolf hit the mark with his statement that the length of train one can view in a single glance/scene is all that is required. An exception might be one of those interminable goods trains one meets at level crossings when one is late. The length one can see in a scene is dependant on how far away one can stand from the track. Generally we build layouts to fill the available space and so have minimal human space very close to the tracks. The viewable length is usually about 1-2m. One can build view blocks such as stands of trees, raised terrain, city buildings etc to break the view where there are long open stretches. For my layout I set the maximum train length at 2.5m (8') As I run 1932 German trains my passenger coaches are shorter than US. (240mm - 9") One difficulty is that there are occasions when I can't fit one of each relevant type of coach into a train: 2 locos/Post/luggage/3rd class/ 2nd+1st/sleeper/restaurant/sleeper/ 2nd/3rd. For goods trains (freight) the prototype limit was 100 axles - the model limit is about 50 axles. The main feature of the layout is banking trains up a steep section of main line - adding banking locos means the trains have to be shorter so I get into the odd situation where the heavier the train represented, the shorter it is. Still, the problem is largely in my head because the 2.5m length is much longer than can be viewed at one look.
Greg.P.
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# python - user input - set
i want to write a python code where user input a number and i want to insert in between the right place.
for example user input 35, i want to insert between 30 and 40.
a = int(input("Enter a number: "))
s1 = set([10,20,30,40,50])
pepr
This is not possible if you want to use the set type. Set does not preserve the order of arguments. Using a list in the set([10, 20, 30, 40, 50]) is just a convention. You can also use a tuple (immutable), but it would look syntactically slightly confusing -- like set((10, 20, 30, 40, 50)) -- because of the doubled parentheses. Or, at least, it it would be more error prone -- even though the error would be revealed very soon.
So, you may want to use the list without converting it to the set type.
Assuming that the list is sorted, you can traverse the list in a loop and search for the index of the leftmost value that is greater (or greater-or-equal) than the inserted value. Then you can use the list.insert() method to insert it.
Unless it is a homework (to write such loop), it is better to use the standard Python module bisect to search for the position. The module even implements the handy function bisect.insort_left(a, x, lo=0, hi=len(a)), that does exactly what you may want. (Here a is the list used as an array, x is the inserted value. The other two arguments are optional.)
SOLUTION
aikimark
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
I tried using list.
l1 = [10,20,30,40,50]
index = 0
n=15
for e in l1:
if e < n:
index += 1
else:
break
print l1.index(e)
l1.insert(l1.index(e),n)
print l1
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# x and y intercepts.
• Oct 11th 2009, 02:10 PM
nautica17
x and y intercepts.
I need to find the x and y intercepts of this:
f(x) = x^3 - 4x
The y-intercept is just zero right? So how about the x's? I haven't done this in a while. Do you just factor this or do you do something else? I know it's easy.. but I'm having a major brain fade here. (Headbang) I'm guessing the x is on -4 and 4?
Edit: I think I got it. x-intercepts are on (-2,0) and (2,0)?
• Oct 11th 2009, 02:21 PM
Quote:
Originally Posted by nautica17
I need to find the x and y intercepts of this:
f(x) = x^3 - 4x
The y-intercept is just zero right? So how about the x's? I haven't done this in a while. Do you just factor this or do you do something else? I know it's easy.. but I'm having a major brain fade here. (Headbang) I'm guessing the x is on -4 and 4?
Edit: I think I got it. x-intercepts are on (-2,0) and (2,0)?
The y-intercept is given by f(0), so the y-intercept is zero. The x intercept is occurs when \$\displaystyle y=0=x^3-4x\$, so just solve this equation.
• Oct 11th 2009, 02:33 PM
Barthayn
Quote:
Originally Posted by nautica17
I need to find the x and y intercepts of this:
f(x) = x^3 - 4x
The y-intercept is just zero right? So how about the x's? I haven't done this in a while. Do you just factor this or do you do something else? I know it's easy.. but I'm having a major brain fade here. (Headbang) I'm guessing the x is on -4 and 4?
Edit: I think I got it. x-intercepts are on (-2,0) and (2,0)?
The x-intercepts are (x-2)(x+2) and 0.
• Oct 11th 2009, 05:55 PM
mr fantastic
Correction in red:
Quote:
Originally Posted by Barthayn
The x-intercepts are the solutions to (x-2)(x+2)=0 and x = 0.
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4 256 ounces per cubic decimeter [oz/dm³] in grams per cubic foot
oz/dm³ to g/ft³ unit converter of density
4 256 ounces per cubic decimeter [oz/dm³] = 3 416 585.27 grams per cubic foot [g/ft³]
ounces per cubic decimeter to grams per cubic foot density conversion cards
• 4 256
through
4 280
ounces per cubic decimeter
• 4 256 oz/dm³ to g/ft³ = 3 416 585.27 g/ft³
• 4 257 oz/dm³ to g/ft³ = 3 417 388.04 g/ft³
• 4 258 oz/dm³ to g/ft³ = 3 418 190.81 g/ft³
• 4 259 oz/dm³ to g/ft³ = 3 418 993.58 g/ft³
• 4 260 oz/dm³ to g/ft³ = 3 419 796.35 g/ft³
• 4 261 oz/dm³ to g/ft³ = 3 420 599.12 g/ft³
• 4 262 oz/dm³ to g/ft³ = 3 421 401.89 g/ft³
• 4 263 oz/dm³ to g/ft³ = 3 422 204.66 g/ft³
• 4 264 oz/dm³ to g/ft³ = 3 423 007.43 g/ft³
• 4 265 oz/dm³ to g/ft³ = 3 423 810.19 g/ft³
• 4 266 oz/dm³ to g/ft³ = 3 424 612.96 g/ft³
• 4 267 oz/dm³ to g/ft³ = 3 425 415.73 g/ft³
• 4 268 oz/dm³ to g/ft³ = 3 426 218.5 g/ft³
• 4 269 oz/dm³ to g/ft³ = 3 427 021.27 g/ft³
• 4 270 oz/dm³ to g/ft³ = 3 427 824.04 g/ft³
• 4 271 oz/dm³ to g/ft³ = 3 428 626.81 g/ft³
• 4 272 oz/dm³ to g/ft³ = 3 429 429.58 g/ft³
• 4 273 oz/dm³ to g/ft³ = 3 430 232.35 g/ft³
• 4 274 oz/dm³ to g/ft³ = 3 431 035.12 g/ft³
• 4 275 oz/dm³ to g/ft³ = 3 431 837.89 g/ft³
• 4 276 oz/dm³ to g/ft³ = 3 432 640.65 g/ft³
• 4 277 oz/dm³ to g/ft³ = 3 433 443.42 g/ft³
• 4 278 oz/dm³ to g/ft³ = 3 434 246.19 g/ft³
• 4 279 oz/dm³ to g/ft³ = 3 435 048.96 g/ft³
• 4 280 oz/dm³ to g/ft³ = 3 435 851.73 g/ft³
• 4 281
through
4 305
ounces per cubic decimeter
• 4 281 oz/dm³ to g/ft³ = 3 436 654.5 g/ft³
• 4 282 oz/dm³ to g/ft³ = 3 437 457.27 g/ft³
• 4 283 oz/dm³ to g/ft³ = 3 438 260.04 g/ft³
• 4 284 oz/dm³ to g/ft³ = 3 439 062.81 g/ft³
• 4 285 oz/dm³ to g/ft³ = 3 439 865.58 g/ft³
• 4 286 oz/dm³ to g/ft³ = 3 440 668.35 g/ft³
• 4 287 oz/dm³ to g/ft³ = 3 441 471.11 g/ft³
• 4 288 oz/dm³ to g/ft³ = 3 442 273.88 g/ft³
• 4 289 oz/dm³ to g/ft³ = 3 443 076.65 g/ft³
• 4 290 oz/dm³ to g/ft³ = 3 443 879.42 g/ft³
• 4 291 oz/dm³ to g/ft³ = 3 444 682.19 g/ft³
• 4 292 oz/dm³ to g/ft³ = 3 445 484.96 g/ft³
• 4 293 oz/dm³ to g/ft³ = 3 446 287.73 g/ft³
• 4 294 oz/dm³ to g/ft³ = 3 447 090.5 g/ft³
• 4 295 oz/dm³ to g/ft³ = 3 447 893.27 g/ft³
• 4 296 oz/dm³ to g/ft³ = 3 448 696.04 g/ft³
• 4 297 oz/dm³ to g/ft³ = 3 449 498.81 g/ft³
• 4 298 oz/dm³ to g/ft³ = 3 450 301.57 g/ft³
• 4 299 oz/dm³ to g/ft³ = 3 451 104.34 g/ft³
• 4 300 oz/dm³ to g/ft³ = 3 451 907.11 g/ft³
• 4 301 oz/dm³ to g/ft³ = 3 452 709.88 g/ft³
• 4 302 oz/dm³ to g/ft³ = 3 453 512.65 g/ft³
• 4 303 oz/dm³ to g/ft³ = 3 454 315.42 g/ft³
• 4 304 oz/dm³ to g/ft³ = 3 455 118.19 g/ft³
• 4 305 oz/dm³ to g/ft³ = 3 455 920.96 g/ft³
• 4 306
through
4 330
ounces per cubic decimeter
• 4 306 oz/dm³ to g/ft³ = 3 456 723.73 g/ft³
• 4 307 oz/dm³ to g/ft³ = 3 457 526.5 g/ft³
• 4 308 oz/dm³ to g/ft³ = 3 458 329.27 g/ft³
• 4 309 oz/dm³ to g/ft³ = 3 459 132.03 g/ft³
• 4 310 oz/dm³ to g/ft³ = 3 459 934.8 g/ft³
• 4 311 oz/dm³ to g/ft³ = 3 460 737.57 g/ft³
• 4 312 oz/dm³ to g/ft³ = 3 461 540.34 g/ft³
• 4 313 oz/dm³ to g/ft³ = 3 462 343.11 g/ft³
• 4 314 oz/dm³ to g/ft³ = 3 463 145.88 g/ft³
• 4 315 oz/dm³ to g/ft³ = 3 463 948.65 g/ft³
• 4 316 oz/dm³ to g/ft³ = 3 464 751.42 g/ft³
• 4 317 oz/dm³ to g/ft³ = 3 465 554.19 g/ft³
• 4 318 oz/dm³ to g/ft³ = 3 466 356.96 g/ft³
• 4 319 oz/dm³ to g/ft³ = 3 467 159.73 g/ft³
• 4 320 oz/dm³ to g/ft³ = 3 467 962.49 g/ft³
• 4 321 oz/dm³ to g/ft³ = 3 468 765.26 g/ft³
• 4 322 oz/dm³ to g/ft³ = 3 469 568.03 g/ft³
• 4 323 oz/dm³ to g/ft³ = 3 470 370.8 g/ft³
• 4 324 oz/dm³ to g/ft³ = 3 471 173.57 g/ft³
• 4 325 oz/dm³ to g/ft³ = 3 471 976.34 g/ft³
• 4 326 oz/dm³ to g/ft³ = 3 472 779.11 g/ft³
• 4 327 oz/dm³ to g/ft³ = 3 473 581.88 g/ft³
• 4 328 oz/dm³ to g/ft³ = 3 474 384.65 g/ft³
• 4 329 oz/dm³ to g/ft³ = 3 475 187.42 g/ft³
• 4 330 oz/dm³ to g/ft³ = 3 475 990.19 g/ft³
• 4 331
through
4 355
ounces per cubic decimeter
• 4 331 oz/dm³ to g/ft³ = 3 476 792.95 g/ft³
• 4 332 oz/dm³ to g/ft³ = 3 477 595.72 g/ft³
• 4 333 oz/dm³ to g/ft³ = 3 478 398.49 g/ft³
• 4 334 oz/dm³ to g/ft³ = 3 479 201.26 g/ft³
• 4 335 oz/dm³ to g/ft³ = 3 480 004.03 g/ft³
• 4 336 oz/dm³ to g/ft³ = 3 480 806.8 g/ft³
• 4 337 oz/dm³ to g/ft³ = 3 481 609.57 g/ft³
• 4 338 oz/dm³ to g/ft³ = 3 482 412.34 g/ft³
• 4 339 oz/dm³ to g/ft³ = 3 483 215.11 g/ft³
• 4 340 oz/dm³ to g/ft³ = 3 484 017.88 g/ft³
• 4 341 oz/dm³ to g/ft³ = 3 484 820.65 g/ft³
• 4 342 oz/dm³ to g/ft³ = 3 485 623.41 g/ft³
• 4 343 oz/dm³ to g/ft³ = 3 486 426.18 g/ft³
• 4 344 oz/dm³ to g/ft³ = 3 487 228.95 g/ft³
• 4 345 oz/dm³ to g/ft³ = 3 488 031.72 g/ft³
• 4 346 oz/dm³ to g/ft³ = 3 488 834.49 g/ft³
• 4 347 oz/dm³ to g/ft³ = 3 489 637.26 g/ft³
• 4 348 oz/dm³ to g/ft³ = 3 490 440.03 g/ft³
• 4 349 oz/dm³ to g/ft³ = 3 491 242.8 g/ft³
• 4 350 oz/dm³ to g/ft³ = 3 492 045.57 g/ft³
• 4 351 oz/dm³ to g/ft³ = 3 492 848.34 g/ft³
• 4 352 oz/dm³ to g/ft³ = 3 493 651.11 g/ft³
• 4 353 oz/dm³ to g/ft³ = 3 494 453.87 g/ft³
• 4 354 oz/dm³ to g/ft³ = 3 495 256.64 g/ft³
• 4 355 oz/dm³ to g/ft³ = 3 496 059.41 g/ft³
Foods, Nutrients and Calories
POTATO CHIPS, UPC: 071104501120 contain(s) 536 calories per 100 grams or ≈3.527 ounces [ price ]
ENRICHED MACARONI PRODUCT, UPC: 026825009936 weigh(s) 58.12 gram per (metric cup) or 1.94 ounce per (US cup), and contain(s) 364 calories per 100 grams or ≈3.527 ounces [ weight to volume | volume to weight | price | density ]
Foods high in Copper, Cu, foods low in Copper, Cu, and Recommended Dietary Allowances (RDAs) for Copper
Gravels, Substances and Oils
CaribSea, Freshwater, African Cichlid Mix, Original weighs 1 121.29 kg/m³ (69.99985 lb/ft³) with specific gravity of 1.12129 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Oxalonitrile, liquid [C2N2] weighs 953.7 kg/m³ (59.53755 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-508B, liquid (R508B) with temperature in the range of -106.67°C (-160.006°F) to -6.65°C (20.03°F)
Weights and Measurements
A binary number is a number that consists of these two (2) symbols or digits zero (0) and one (1)
The pressure forces on any solid surface by liquid or gas, do not apply to any single point on that surface. Instead, these forces are spread equally along the whole surface.
st/US tbsp to long tn/l conversion table, st/US tbsp to long tn/l unit converter or convert between all units of density measurement.
Calculators
Calculate Ideal Body Weight and Adjusted Body Weight
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# mix_d17O: Mixing curves in triple oxygen isotope space In isogeochem: Tools for Stable Isotope Geochemistry
mix_d17O R Documentation
## Mixing curves in triple oxygen isotope space
### Description
mix_d17O() produces mixing curves between two endmembers (A and B) in triple oxygen isotope space (d18O vs. D17O).
### Usage
mix_d17O(
d18O_A,
d17O_A,
D17O_A,
d18O_B,
d17O_B,
D17O_B,
lambda = 0.528,
step = 10
)
### Arguments
d18O_A d18O value of component A (‰). d17O_A d17O value of component A (‰). D17O_A Alternatively, the D17O value of component A (‰). d18O_B d18O value of component B (‰). d17O_B d17O value of component B (‰). D17O_B Alternatively, the D17O value of component B (‰). lambda Triple oxygen isotope reference slope. Default 0.528. step Output resolution, i.e., step size. Default 10%.
### Details
If both d17O and D17O values are specified for a component, the function uses the d17O values for the calculations.
### Value
Returns a data frame:
1. d18O value of the mixture at x% mixing (‰).
2. D17O value of the mixture at x% mixing (‰).
3. relative amount of component B in the mixture (%): from 100% A and 0% B to 0% A and 100% B.
4. d17O value of the mixture at x% mixing (‰).
d17O_c() calculates equilibrium calcite d18O, d17O, and D17O values for a given temperature.
### Examples
# The two functions below yield the same output.
mix_d17O(d18O_A = d17O_c(10, -1)[1], d17O_A = d17O_c(10, -1)[2],
d18O_B = d17O_c(100,0)[1], d17O_B = d17O_c(100, 0)[2])
mix_d17O(d18O_A = d17O_c(10, -1)[1], D17O_A = d17O_c(10, -1)[3],
d18O_B = d17O_c(100,0)[1], D17O_B = d17O_c(100, 0)[3])
isogeochem documentation built on March 31, 2023, 8:30 p.m.
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# Economics/Math
posted by .
1. Assume that q and z are two random variables that are perfectly positively correlated. q takes the value of 20 with probability 0.5 and the value of zero with probability 0.5, while z takes the value of 10 with probability 0.5 and the value of zero with probability 0.5. What is the covariance of q and z?
(A) 50.
(B) 100.
(C) 0.
(D) 1.
(E) There is not enough information to tell.
• Economics/Math -
You state that q and z are perfectly positively correlated. This alone says the covariance of q and z is 1. The rest of the information you provide is a red herring.
• Economics/Math -
Thank you for responding. The solution, however, is shown as 100. Wouldn't the coorelation coefficient be 1 but not necessarily the covariance?
## Similar Questions
1. ### Economics/Statistics
1. Assume that q and z are two random variables that are perfectly positively correlated. q takes the value of 20 with probability 0.5 and the value of zero with probability 0.5, while z takes the value of 10 with probability 0.5 and …
2. ### Math
A box contains a one-dollar bill, a five-dollar bill, a ten-dollar bill, and a twenty-dollar bill. Two bills are chosen in succession without replacement. Use a tree diagram to list the sample space for this experiment and then answer …
3. ### Probability
Let X be a random variable that takes non-zero values in [1,∞), with a PDF of the form fX(x)=⎧⎩⎨cx3 if x≥1, 0,otherwise. Let U be a uniform random variable on [0,2]. Assume that X and U are independent. …
4. ### probability
For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1. Let Ui=X1+X2+⋯+Xii,i=1,2,…. …
5. ### Probability
For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between −1 and 1. Let Ui=X1+X2+⋯+Xii,i=1,2,…. …
6. ### statistics
A researcher finds that two continuous, random variables of interest, X and Y, have a joint probability density function (pdf) given by: f(x,y)={cxy 0<=x<=1,0<=y<=1,x+y=>1, .........0 otherwise where c is a constant. …
7. ### statistics
A researcher finds that two continuous, random variables of interest, X and Y, have a joint probability density function (pdf) given by: f(x,y)={cxy 0<=x<=1,0<=y<=1,x+y=>1, .........0 otherwise where c is a constant. …
8. ### math
A bag contains 5 red and 4 green apples. Michael takes one apple at random from the bag. His sister Ashley then takes an apple at random from he bag. What is the probability that the two apples are the same colour?
9. ### Probability
Let X be a random variable that takes non-zero values in [1,∞), with a PDF of the form fX(x)=⎧⎩⎨cx3,0,if x≥1,otherwise. Let U be a uniform random variable on [0,2]. Assume that X and U are independent. …
10. ### Probability and Statisics
Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that a SRS of size 200 would come within plus or minus 3 percentage points of this true value. In other words, …
More Similar Questions
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1. Hello all ,just a simple question from me for a change, when electricity or energy/force hits an object of mass,
but that energy would be a constant force , example a laser pointed at a wall.
Would that energy beam, the laser, have any difference in any energy out put along the beam.
Meaning, at the start of flow nearest to the laser, would it have a different energy level than the point of contact of the beam on the wall.
And on the wall point of contact, would the energy level build, and create a back up of charge back to the starting point?
2. ### Related Discussions:
3. Originally Posted by theorist
Hello all ,just a simple question from me for a change, when electricity or energy/force hits an object of mass,
but that energy would be a constant force , example a laser pointed at a wall.
Energy and electricity are not the same thing. A laser is not electricity.
Would that energy beam, the laser, have any difference in any energy out put along the beam.
Apart form a small energy loss due to absorption by the atmosphere, the energy would not change. (It can't change - conservation of energy.)
And on the wall point of contact, would the energy level build, and create a back up of charge back to the starting point?
The energy level would "build" to some extent if the laser warmed the wall where it hit. This would soon be balanced by the heat being lost by conduction and radiation. You wouldn't get a continuous increase. And no, this would have no effect at all on the laser.
There would no "back up of charge" (whatever that means) because no charge is being transferred.
Charge is not energy. Electricity is not charge. Energy is not electricity. etc.
4. Why is theorist still allowed to post in the science sub-forae?
5. Originally Posted by Strange
Originally Posted by theorist
Hello all ,just a simple question from me for a change, when electricity or energy/force hits an object of mass,
but that energy would be a constant force , example a laser pointed at a wall.
Energy and electricity are not the same thing. A laser is not electricity.
Would that energy beam, the laser, have any difference in any energy out put along the beam.
Apart form a small energy loss due to absorption by the atmosphere, the energy would not change. (It can't change - conservation of energy.)
And on the wall point of contact, would the energy level build, and create a back up of charge back to the starting point?
The energy level would "build" to some extent if the laser warmed the wall where it hit. This would soon be balanced by the heat being lost by conduction and radiation. You wouldn't get a continuous increase. And no, this would have no effect at all on the laser.
There would no "back up of charge" (whatever that means) because no charge is being transferred.
Charge is not energy. Electricity is not charge. Energy is not electricity. etc.
Thank you Strange for answering my Physics question.
6. Electricity is a type of energy , in other words it is a property of some sub atomic particles other forces may give shock to human being but a different type of shock
7. Electricity is not a "thing"; it is a set of things related to electric charge and the movement of charge.
Specifically, neither electricity nor charge are a type of energy.
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AddMultiple - Maple Help
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# Online Help
###### All Products Maple MapleSim
LinearAlgebra[Modular]
AddMultiple
add multiple of a mod m Matrix or Vector to another
Calling Sequence AddMultiple(m, mult, A, B, order, 'sparse') AddMultiple(m, mult, A, B, C, 'sparse')
Parameters
m - modulus A - Matrix or Vector, including subspec B - Matrix or Vector, including subspec order - ordering of output object sparse - (optional) controls behavior of operation mult - (optional) multiplier, default is 1 C - output Matrix or Vector, including subspec
Description
• The AddMultiple function performs the operation $\mathrm{mult}B+A$ placing the output in a new object, or in C, depending on calling sequence. All of A, B, and C must be mod m Matrices or Vectors, and mult must be a scalar.
The first calling sequence returns a new mod m Matrix or Vector for the result with the specified ordering, order, or the ordering of the input objects A and B.
Note: If A and B have different ordering, order must be specified.
The second calling sequence places the output of the computation into C, returning NULL.
Note: The parameter C can be the same Matrix or Vector as A or B as long as the operation is performed with direct overlap. For example, if A and C are the same Matrix, the operation involving the entry ${A}_{i,j}$ must have the result going to ${C}_{i,j}$.
• The multiplier, mult, is an optional parameter. However, if it is not specified, it is assumed to be 1. The multiplier must be in the range $0..m-1$. This function can be used to perform Matrix or Vector subtraction by the selection of $\mathrm{mult}=m-1$. This is coded efficiently, that is, without multiplication.
• If specified, the optional keyword 'sparse', is only applicable if the multiplier is not $1$ or $m-1$ and the datatype is a hardware datatype. It indicates that the algorithm checks for zero entries before performing multiplications. This typically provides an efficiency gain if matrices have 10% or more entries in B equal to zero. This is not implemented for the integer datatype, as it typically provides very little gain.
Note: In cases for which sparse does not apply but has been specified, the option is ignored.
• The AddMultiple function allows the use of sub-Matrix and sub-Vector specifications for both input and output Matrices or Vectors. For example, the function can be used to add a row of a Matrix to a row Vector, placing the result in the column of another Matrix.
• Note: If the used portion of A or B, and C overlap, but not directly, the behavior of AddMultiple is undefined.
• This command is part of the LinearAlgebra[Modular] package, so it can be used in the form AddMultiple(..) only after executing the command with(LinearAlgebra[Modular]). However, it can always be used in the form LinearAlgebra[Modular][AddMultiple](..).
Examples
> $\mathrm{with}\left(\mathrm{LinearAlgebra}\left[\mathrm{Modular}\right]\right):$
> $A≔\mathrm{Mod}\left(13,\mathrm{Matrix}\left(4,4,\left(i,j\right)↦\mathrm{rand}\left(\right)\right),\mathrm{integer}\left[\right]\right)$
${A}{≔}\left[\begin{array}{cccc}{10}& {0}& {8}& {12}\\ {2}& {6}& {0}& {11}\\ {9}& {2}& {11}& {7}\\ {4}& {11}& {12}& {11}\end{array}\right]$ (1)
> $B≔\mathrm{Mod}\left(13,\mathrm{Matrix}\left(4,4,\left(i,j\right)↦\mathbf{if}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}i=j\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{then}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}1\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{else}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}0\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{end}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{if}\right),\mathrm{integer}\left[\right]\right)$
${B}{≔}\left[\begin{array}{cccc}{1}& {0}& {0}& {0}\\ {0}& {1}& {0}& {0}\\ {0}& {0}& {1}& {0}\\ {0}& {0}& {0}& {1}\end{array}\right]$ (2)
Default multiplier and new output Matrix (A+B).
> $\mathrm{AddMultiple}\left(13,A,B\right)$
$\left[\begin{array}{cccc}{11}& {0}& {8}& {12}\\ {2}& {7}& {0}& {11}\\ {9}& {2}& {12}& {7}\\ {4}& {11}& {12}& {12}\end{array}\right]$ (3)
Chosen multiplier of 2 (A+2*B).
> $\mathrm{AddMultiple}\left(13,2,A,B\right)$
$\left[\begin{array}{cccc}{12}& {0}& {8}& {12}\\ {2}& {8}& {0}& {11}\\ {9}& {2}& {0}& {7}\\ {4}& {11}& {12}& {0}\end{array}\right]$ (4)
Replace A with the result.
> $\mathrm{AddMultiple}\left(13,2,A,B,A\right):$
> $A$
$\left[\begin{array}{cccc}{12}& {0}& {8}& {12}\\ {2}& {8}& {0}& {11}\\ {9}& {2}& {0}& {7}\\ {4}& {11}& {12}& {0}\end{array}\right]$ (5)
Add row 3 of A to row 2 of A, with output in column 1 of B.
> $\mathrm{AddMultiple}\left(13,A,3,'\mathrm{transpose}',A,2,'\mathrm{transpose}',B,1..-1,1\right):$
> $A,B$
$\left[\begin{array}{cccc}{12}& {0}& {8}& {12}\\ {2}& {8}& {0}& {11}\\ {9}& {2}& {0}& {7}\\ {4}& {11}& {12}& {0}\end{array}\right]{,}\left[\begin{array}{cccc}{11}& {0}& {0}& {0}\\ {10}& {1}& {0}& {0}\\ {0}& {0}& {1}& {0}\\ {5}& {0}& {0}& {1}\end{array}\right]$ (6)
Construct a larger Matrix and identity Matrix, using larger modulus.
> $N≔100:$
> $p≔65535:$
> $A≔\mathrm{Mod}\left(p,\mathrm{Matrix}\left(N,N,\left(i,j\right)↦\mathrm{rand}\left(\right)\right),\mathrm{float}\left[8\right]\right)$
> $B≔\mathrm{Mod}\left(p,\mathrm{Matrix}\left(N,N,\left(i,j\right)↦\mathbf{if}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}i=j\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{then}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}1\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{else}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}0\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{end}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{if}\right),\mathrm{float}\left[8\right]\right)$
Time addition of 327*B to A 2000 times.
> $t≔\mathrm{time}\left(\right):$
> $\mathbf{for}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}i\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{to}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}2000\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{do}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\mathrm{AddMultiple}\left(p,327,A,B,A\right)\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathbf{end}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{do}:$$\mathrm{time}\left(\right)-t$
${0.224}$ (7)
Time addition of 327*B to A 2000 times using sparse.
> $t≔\mathrm{time}\left(\right):$
> $\mathbf{for}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}i\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{to}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}2000\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{do}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\mathrm{AddMultiple}\left(p,327,A,B,A,'\mathrm{sparse}'\right)\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathbf{end}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{do}:$$\mathrm{time}\left(\right)-t$
${0.091}$ (8)
See Also
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Hello and welcome to our community! Is this your first visit?
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# Thread: Non repeating Random Number Generator
1. ## Non repeating Random Number Generator
My first post here guys
Basically I'm wondering what I can do to avoid a randomly generated number being repeated in the same column.
This is the code I'm using....I'm trying to generate 3 random numbers between 1 and 10 without using the same number twice.
Help??....
-------------------
function newCard()
{
for (var i=0; i<1; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
document.getElementById("square" + i).innerHTML = newNum;
}
for (var i=9; i<10; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
document.getElementById("square" + i).innerHTML = newNum;
}
for (var i=18; i<19; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
document.getElementById("square" + i).innerHTML = newNum;
}
• Code:
```var Nus=[-1,-1,-1];
function newCard()
{
for (var i=0; i<1; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
while (newNum==Nus[0]) newNum = Math.floor(Math.random() * 9) + 1;
Nus[0]=newNum;
document.getElementById("square" + i).innerHTML = newNum;
}
for (var i=9; i<10; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
while (newNum==Nus[1]) newNum = Math.floor(Math.random() * 9) + 1;
Nus[1]=newNum;
document.getElementById("square" + i).innerHTML = newNum;
}
for (var i=18; i<19; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
while (newNum==Nus[2]) newNum = Math.floor(Math.random() * 9) + 1;
Nus[2]=newNum;
document.getElementById("square" + i).innerHTML = newNum;
}```
• Originally Posted by vwphillips
Code:
```var Nus=[-1,-1,-1];
function newCard()
{
for (var i=0; i<1; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
while (newNum==Nus[0]) newNum = Math.floor(Math.random() * 9) + 1;
Nus[0]=newNum;
document.getElementById("square" + i).innerHTML = newNum;
}
for (var i=9; i<10; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
while (newNum==Nus[1]) newNum = Math.floor(Math.random() * 9) + 1;
Nus[1]=newNum;
document.getElementById("square" + i).innerHTML = newNum;
}
for (var i=18; i<19; i++)
{
var newNum = Math.floor(Math.random() * 9) + 1;
while (newNum==Nus[2]) newNum = Math.floor(Math.random() * 9) + 1;
Nus[2]=newNum;
document.getElementById("square" + i).innerHTML = newNum;
}```
I replaced my text with what you wrote above and left the
at the very top of the code.
It still gives me the same results :-(
• Code:
```Array.fromRange = function(start, end) {
var arr = [];
while(start <= end)
arr.push(start++);
};
Array.prototype.shuffle = function() {
for(var i = this.length; i > 1; --i)
this.swap(i - 1, Math.floor(Math.random() * i));
return this;
};
Array.prototype.swap = function(i, j) {
var t = this[i];
this[i] = this[j]
this[j] = t;
};
//////////////////////////////////////
var rands = Array.fromRange(1, 10).shuffle();
var num1 = rands.pop();
var num2 = rands.pop();
var num3 = rands.pop();```
• Originally Posted by Trinithis
Code:
```Array.fromRange = function(start, end) {
var arr = [];
while(start <= end)
arr.push(start++);
};
Array.prototype.shuffle = function() {
for(var i = this.length; i > 1; --i)
this.swap(i - 1, Math.floor(Math.random() * i));
return this;
};
Array.prototype.swap = function(i, j) {
var t = this[i];
this[i] = this[j]
this[j] = t;
};
//////////////////////////////////////
var rands = Array.fromRange(1, 10).shuffle();
var num1 = rands.pop();
var num2 = rands.pop();
var num3 = rands.pop();```
sorry if i'm being stupid...but i'm a relatively new java programmer and learning slowly. could you please explain what this does as it doesn't work for me when i replace my code with this....just comes up blank again!
•
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View the step-by-step solution to:
# Jetson Co. sold 20,400 units of its only product and incurred a \$53,368 loss (ignoring taxes) for the current year as shown here. During a planning...
Jetson Co. sold 20,400 units of its only product and incurred a \$53,368 loss (ignoring taxes) for the current year as shown here. During a planning session for year 2012’s activities, the production manager notes that variable costs can be reduced 50% by installing a machine that automates several operations. To obtain these savings, the company must increase its annual fixed costs by \$154,000. The maximum output capacity of the company is 40,000 units per year.
JETSON COMPANY
Contribution Margin Income Statement
For Year Ended December 31, 2011
Sales \$ 773,160
Variable costs 618,528
Contribution margin 154,632
Fixed costs 208,000
Net loss \$ (53,368 )
Jetson Co. sold 20,400 units of its only product and incurred a \$53,368 loss (ignoring taxes) for the current year as shown here. During a planning session for year 2012’s activities, the production manager notes that variable costs can be reduced 50% by installing a machine that automates several operations. To obtain these savings, the company must increase its annual fixed costs by \$154,000. The maximum output capacity of the company is 40,000 units per year. JETSON COMPANY Contribution Margin Income Statement For Year Ended December 31, 2011 Sales \$773,160 Variabl e costs 618,528 Contri bution margin 154,632 Fixed costs 208,000 Net loss \$ (53,368)
JETSON CO.
Sales
VC
Contribution Margin
Fixed Cost
Net Loss
Solution 1 Breakeven in \$ Sales Amt in \$
Price per unit % of Sales
\$773,160
38
100%
\$618,528
30
80%
\$154,632
8
20%
\$208,000
\$(53,368)...
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http://www.kylesconverter.com/length/shaku-to-ropes
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# Convert Shaku to Ropes
### Kyle's Converter > Length > Shaku > Shaku to Ropes
Shaku Ropes (rope) Precision: 0 1 2 3 4 5 6 7 8 9 12 15 18
Reverse conversion?
Ropes to Shaku
(or just enter a value in the "to" field)
Please share if you found this tool useful:
Unit Descriptions
1 Shaku:
Shaku was standardized to exactly 10/33 meters (SI base unit). Originally based on the length of the forearm this unit may also be referred to as a Japanese foot. 1 Shaku ≈ 11.93 in ≈ 0.9942 ft ≈ 0.30303 m.
1 Rope (H):
Rope is former English unit measuring 20 feet in length. Other variations exist. In SI Units a rope of 20 feet is 6.096 meters. 1 rope = 6.096 m.
Conversions Table
1 Shaku to Ropes = 0.049770 Shaku to Ropes = 3.4797
2 Shaku to Ropes = 0.099480 Shaku to Ropes = 3.9768
3 Shaku to Ropes = 0.149190 Shaku to Ropes = 4.4739
4 Shaku to Ropes = 0.1988100 Shaku to Ropes = 4.971
5 Shaku to Ropes = 0.2485200 Shaku to Ropes = 9.9419
6 Shaku to Ropes = 0.2983300 Shaku to Ropes = 14.9129
7 Shaku to Ropes = 0.348400 Shaku to Ropes = 19.8839
8 Shaku to Ropes = 0.3977500 Shaku to Ropes = 24.8548
9 Shaku to Ropes = 0.4474600 Shaku to Ropes = 29.8258
10 Shaku to Ropes = 0.4971800 Shaku to Ropes = 39.7678
20 Shaku to Ropes = 0.9942900 Shaku to Ropes = 44.7387
30 Shaku to Ropes = 1.49131,000 Shaku to Ropes = 49.7097
40 Shaku to Ropes = 1.988410,000 Shaku to Ropes = 497.097
50 Shaku to Ropes = 2.4855100,000 Shaku to Ropes = 4970.9695
60 Shaku to Ropes = 2.98261,000,000 Shaku to Ropes = 49709.6954
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https://www.pythonsos.com/data-structures/adjacency-matrix-in-python/
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When working with graphs, one common representation is the adjacency matrix. An adjacency matrix is a square matrix used to represent a finite graph. Each cell of the matrix represents an edge between two vertices. In Python, we can represent an adjacency matrix using a nested list or a NumPy array.
## Option 1: Using a Nested List
One way to represent an adjacency matrix in Python is by using a nested list. Each element of the outer list represents a row in the matrix, and each element of the inner list represents a cell in the matrix.
``adj_matrix = [[0, 1, 0], [1, 0, 1], [0, 1, 0]]``
In this example, we have a graph with three vertices. The adjacency matrix is represented by a 3×3 nested list. The value 1 in the matrix indicates an edge between two vertices, while the value 0 indicates no edge.
## Option 2: Using a NumPy Array
Another way to represent an adjacency matrix in Python is by using a NumPy array. NumPy is a powerful library for numerical computing in Python, and it provides efficient array operations.
``````import numpy as np
adj_matrix = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]])``````
In this example, we import the NumPy library and create a 3×3 NumPy array to represent the adjacency matrix. The array elements can be accessed and manipulated using NumPy’s array indexing and slicing operations.
## Option 3: Using a Graph Library
If you are working with graphs extensively, it might be beneficial to use a graph library that provides built-in functionality for working with adjacency matrices. One popular graph library in Python is NetworkX.
``````import networkx as nx
adj_matrix = [[0, 1, 0], [1, 0, 1], [0, 1, 0]]
In this example, we import the NetworkX library and create a graph object using the adjacency matrix. NetworkX provides various algorithms and functions for graph analysis and manipulation.
After considering the three options, the best choice depends on the specific requirements of your project. If you only need basic operations on the adjacency matrix, using a nested list or a NumPy array would be sufficient. However, if you require advanced graph analysis and manipulation, using a graph library like NetworkX would be more appropriate.
Rate this post
### 9 Responses
1. Dorothy Deleon says:
Option 1 seems old school, but hey, if it gets the job done, why not? 🤷♀️
2. Braylon Stone says:
Option 2 all the way! NumPy arrays be flexin with their efficient calculations. 🚀
3. Dior says:
Option 3 seems cool, but Im all for simplicity. Option 1 FTW! 🙌🏼
4. Brayden says:
Option 3 seems fancy, but I prefer the simplicity of Option 1. What about you guys? #AdjacencyMatrixDebate
5. Samira Herrera says:
Option 3 is a no-brainer, who needs the hassle of nested lists or arrays?
6. Carly says:
Option 3 seems cool, but wouldnt Option 1 be simpler for beginners? 🤔
1. Elijah says:
Sure, Option 1 might be simpler for beginners, but wheres the fun in taking the easy route? Option 3 offers a chance to challenge yourself and grow. Embrace the complexity, my friend, and see what youre truly capable of.
7. Rowan Soto says:
Option 2 using NumPy array seems like the coolest way to tackle adjacency matrix. #TechGeek
8. Zen says:
Option 4: Using emojis 🤔🔢📊. Because who doesnt love a graph that speaks in smileys? 😄😎
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https://betterlesson.com/lesson/563862/wp-solve-a-2-step-problem-involving-integers?from=consumer_breadcrumb_dropdown_lesson
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# WP: Solve a 2-step problem involving integers
3 teachers like this lesson
Print Lesson
## Objective
SWBAT solve 2-step problems involving integers.
#### Big Idea
Students will break out their vocabulary foldables to help navigate through real world problems involving multi-step integer problems.
## Bell Ringer
10 minutes
Have students sit in their Individual Think Time seats. Students will be handed the bell ringer as they walk in the door. Students are to get started on the bell ringer right away with no talking. Students will have an opportunity to work with their peer groups during the student activity section. Students will be given 10 minutes to grapple through the bell ringer on their own. Students should show their work on each problem and be prepared to defend their answers. If students are unable to answer the problems, have the students write what they do not understand. Students are not allow to write I don’t know any of it. Students must write specific questions that will help their peers and you to help them through what they do not understand. It is helpful to walk the room to check for understanding. For students who may struggle be sure during this time you encourage them to write why.
## Student Activity
10 minutes
After students have worked for 10 minutes on their own, have the students pair up with a peer or group. Students should discuss what they were able to accomplish, what they did not understand, and how they were able to solve the problems. What strategies did they use? What in the problem gave them trouble? The pairs or groups should share out for 10 minutes. During this time you will be able to engage with the groups through effective questioning. Depending upon where the student struggles, will depend upon your questioning. You are an awesome educator and you know your students better than anyone. Use questioning that will evoke further thinking and not yes or no questions that will give them the answer.
## Whole Group Discussion/Direct Instruction
15 minutes
: During this time you will be able to allow students to share out their thinking with the whole group. Post the assignment on the smartboard, document camera, or other means for the whole group to see the assignment. During this time students are able to share out how they solved the problem. You may have the student come to the smartboard and work out the problem while he or she explains their strategy, or they may talk through the process they used to solve the problem and you can write what they are explaining. During this time the rest of the group will critique the work of the students sharing out. Did anyone else solve the problem the same way? Does everyone agree with the way the student solved the problem, if not why? Did anyone else get the same response, but solve the problem in a different way? During this time it is important that students are able to share out their thinking whether correct or incorrect. This will allow you to understand how your students are thinking. It is important to validate correct thinking and correct mistakes made. This time period is a time in which direct instruction will also take place. You will allow students the opportunity to share their thinking, and also go through the correct process in solving the problems
## Closing/Exit Ticket
5 minutes
This is the time in which you will summarize your lesson. You will go through the important emphasis of the lesson. What did you want your students to be able to do once the lesson concludes? How will you know they gained the understanding you wanted them to gain? Exit tickets are a great way to formatively assess if students understood the objective of the lesson.
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https://www.coursehero.com/file/6288562/Quiz17A/
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# Quiz17A - Name Section UFID Show all of your work to...
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Unformatted text preview: Name : Section : UFID: Show all of your work to receive credit. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. MAC1140, Quiz 17 1. A chemist is analyzing a 1000g sample of a radioactive substance. She nds that after 2 hours, 250g of the substance remains, while the rest has decayed into other elements. (a) Find a and b in the exponential decay model y = ae-bt to describe this situation as a function of time (hint: nd the half-life rst) (b) How long will it take until there is only 100g of substance left? 2. A microbiologist is testing how dierent environments aect the growth of a strain of bacteria. There will be 1000 bacteria initially. From previous experiments, He expects the bacteria to reach 2000 in number after one hour, and to eventually reach 11,000 in number. He wants to set up a logistic growth model, but all he remembers from MAC1140 is that a logistic growth model follows the form a , where y will represent the amount of bacteria. y= -rt 1 + be (a) What is a in the model? (Hint: what happens to e-rt as t gets bigger?) (b) What is b in the model? (Hint: use the initial amount of bacteria, when t = 0) (c) What is r in the model? (Hint: what is y when t = 1?) ...
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https://teoria.com/en/articles/2020/cents/02.php
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#### The Mathematical Ratio of Intervals
The mathematical operation we must use to determine the size of an interval is division. When we divide the frequencies, both thirds have the same size or mathematical ratio (1.25):
325 / 260 = 1.25
162.5 / 130 = 1.25
This number, or mathematical ratio, allows us to calculate major thirds based on any note. By multiplying we get an ascending major third and by dividing we get a descending major third. Starting from a 440, we get the upper C# and the lower F:
Note Frequency Ascending major third (C#5) Descending major third (F4)
A4 440 Hertz 440 * 1.25 = 550
440 / 1.25 = 352
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https://www.helpingwithmath.com/resources/games/3oa4-unknown-factor01/3oa4-unknown-factor01.html
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# Multiplication and Division with Unknown Numbers (1 of 2)
SKIP
NEXT
GO!
There is another version of this game here where you can practice with multiplication facts form other tables (e.g. 6x , 9x ,etc). There is also a listing of many more multiplication and division games here.
A Multiplication/ Division Game - By HelpingWithMath.com
### Related Resources
The resources listed below are aligned to the same standard, (3OA04) re: Common Core Standards For Mathematics as the Multiplication game shown above.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?
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http://au.metamath.org/mpegif/anandis.html
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Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > anandis Structured version Unicode version
Theorem anandis 805
Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)
Hypothesis
Ref Expression
anandis.1
Assertion
Ref Expression
anandis
Proof of Theorem anandis
StepHypRef Expression
1 anandis.1 . . 3
21an4s 801 . 2
32anabsan 788 1
Colors of variables: wff set class Syntax hints: wi 4 wa 360 This theorem is referenced by: 3impdi 1240 dff13 6007 f1oiso 6074 omord2 6813 fodomacn 7942 ltapi 8785 ltmpi 8786 axpre-ltadd 9047 faclbnd 11586 pwsdiagmhm 14773 tgcl 17039 grpoinvf 21833 ocorth 22798 fh1 23125 fh2 23126 spansncvi 23159 lnopmi 23508 adjlnop 23594 brbtwn2 25849 heicant 26253 mblfinlem2 26256 ismblfin 26259 ftc1anclem6 26299 ftc1anclem7 26300 ftc1anc 26302 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 This theorem depends on definitions: df-bi 179 df-an 362
Copyright terms: Public domain W3C validator
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http://www.sjsu.edu/faculty/watkins/gravdisk.htm
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San José State University
applet-magic.com
Thayer Watkins
Silicon Valley
USA
Gravitational Force in a Thin Disk of Matter
For mass distributed in a spherical arrangement there are some marvelous theorems that simplify the analysis. These include:
• The gravitational force exerted by a spherical shell or a spherical ball on an outside point is the same as if the entire mass were concentrated at the center of the sphere.
• For a point within a spherical shell there is no net force.
Such theorems do not hold for matter not distributed spherically. In particular they do not hold for matter distributed in a thin disk. To see why the internal statics of matter distributed in a disk is completely different from that of matter distributed in a sphere consider first the case of a spherical shell.
Take any point P within the spherical shell and construct a circular cross section cone with its apex at P. Let dΩ be the solid angle for the cone and σ be the areal mass density on the spherical shell. Let r1 and r2 be the distance from the point P to the shell along the axis of the cone. The cone subtends an area of dΩr1² in one direction and dΩr2² in the other direction.
The mass acting on the point P along the axis of the cone is then σdΩr1² in one direction and σdΩr2² in the other. The net gravitational along the axis of the cone is
#### dF = GσdΩr1²/r1² − GσdΩr2²/r2² which reduces to dF = GσdΩ − GσdΩ = 0
Thus for any direction the net force is zero.
For a ring let ρ be the linear mass density. For an arbitrary P within the ring pass a line through P and construct two lines which have an angle with the line of ½dθ.
The net force on a unit mass at P is
#### dF = G(ρr1dθ)/r1² − G(ρr2dθ)/r2² which reduces to dF = Gρdθ/r1 − Gρdθ/r2and further dF = Gρdθ(1/r1 − 1/r2)
Thus there is a net attraction toward the point on the ring which is closest to P.
To make the analogy with the spherical shell closer consider a cylindrical band of width b. The areas subtended by two planes separated by an angle dθ are (r1dθ)b and (r2dθ)b. The net force is then
#### dF = Gbr1dθ/r1² − Gbr2dθ/r2² which reduces to dF = Gbdθ(1/r1 − 1/r2)
Therefore there is a net attraction to the closer point on the cylindrical band.
For mass outside of a ring there is a net attraction toward the ring. Thus for mass near the edge of a disk there is a net radial force toward the center of the disk. For mass near the center of the disk, the attraction of the outer part of the disk outweighs the attraction toward small mass near the center. Thus there is a net radial attraction away from the center of the disk and over time the disk would evolve toward a ring shape. Matter exactly at the center would be held in balance.
## The Gravitational Attraction of a Ring
Consider mass distributed throughout a thin ring of radius R at a uniform linear density of ρ. The polar coordinate system has its origin at the center of the ring. An element at radius R and angle θ has xy coordinates of (Rcos(θ), Rsin(θ)) has a distance s from the point at r and angle 0 (xy coordinates (r, 0)) given by
#### s² = (r−Rcos(θ))² + (Rsin(θ))² which reduces to s² = R² + r² − 2rRcos(θ)
The gravitational force at (r, 0) due to an infinitesimal element of length Rd&heta; located at (R, θ) has a magnitude of G(ρRdθ)/s². The radial component of the force is the important factor. Let φ be the angle between the radial line to (R, 0) and the point (R, θ). This is the angle the force makes with the radial line to (r, 0). The cosine of the angle φ of the force is equal to (r−Rcos θ)/s. Thus the radial component of the force due to the infinitesimal element is
#### dFr = Gρ[R(r−Rcos(θ))/s³]dθ
The tangential component of the total force, by symmetry, vanishes. The total force is then simply the integral of this expression from 0 to 2π radians; i.e.,
#### Fr = Gρ∫02π[R(r−Rcos(θ))/s³]dθ or, equivalently Fr = GρR∫02π[(r−Rcos(θ))/s³]dθ
The mass M of the ring is 2πRρ so the above formula may be put into the form
#### Fr = GM(1/2π)∫02π[(r−Rcos(θ))/s³]dθ
This expression may be simplified by dividing the numerator and denominator of the integrand by r. The numerator then becomes (1−(R/r)cos(θ)). The denominator, which is s³/r, is better expressed as r²(s³/r³). (The factor r² will later be brought outside of the integration.) Since
#### s³/r³ = (s/r)³and s = (r² + R² − 2rRcos(θ))½s/r reduces to ((1 + (R/r)² − 2(R/r)cos(θ))½
Letting the ratio (R/r) be denoted as ζ the force can be expressed as
#### F = ((GM/r²)(1/2π)∫02π[(1−ζcos(θ))/(1+ζ²−2ζcos(θ))3/2]dθ or, equivalently F = (GM/r²)H(ζ) where H(ζ) = (1/(2π))∫02π[(1−ζcos(θ))/(1+ζ²−2ζcos(θ))3/2]dθ
There might be an analytical evaluation of H(ζ) but for now a numerical evaluation will suffice. However it is easily seen that as ζ → ∞ (which corresponds to r<<R) H → 0 and that as ζ → 0 (which corresponds to r>>R) H → 1.
ζ H(ζ) 0.1 1.007570999 0.3 1.073742106 0.5 1.245620571 0.7 1.692441706 0.8 2.270761711 0.9 4.642991428 1.0 0.0 1.1 -3.449766463 1.2 -1.106285155 1.3 -0.615289403 1.4 -0.402346904 1.5 -0.28477633 1.6 -0.211925335 1.7 -0.163423773 1.8 -0.12945636 1.9 -0.104743953 2.0 -0.08621929
This is for a thin ring. For a disk there has to be an integration from 0 to Rmax. The mass of an infinitesimal ring is proportional to R² so this has to be taken into account as well. In terms of the above, this would involve integrating ζH(ζ) from 0 to Ζ.
#### F = ∫0Rmax(GM(R)/r²)H(ζ)dR = ∫0Rmax(GπρR²/r²)H(ζ)dR = Gρ∫0Rmaxζ²H(ζ)dR
In the last formula the variable of integration can be changed from R to ζ=R/r, which means that dR=rdζ. Thus
#### F(Ζmax) = Gρ∫0Ζmax(ζ²H(ζ))dζ
(To be continued.)
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Post subject: ConfusedPosted: Fri Jan 16, 2009 11:48 am
Joined: Fri Jan 16, 2009 7:10 am
Posts: 7
Just confused
I saw that last year the passmark for Tiffin, intially, was 229. I assume that the maximum was 280/281.
The difference between the highest achieveable mark and the passmark is therefore 51/52.
I was told that to pass the Tiffin exam you need to achieve a score comparable to 95% ie getting 5 or so questions wrong.
How do they make a difference of say 5 marks in each paper ( or a total of 10 over both papers) into 25 marks (50 marks overall).
Having read some of the posts I understand that there is some age standardisation but can they stretch it to that extent ?
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Post subject: % needed in testsPosted: Fri Jan 16, 2009 12:37 pm
Joined: Fri Jan 09, 2009 12:27 pm
Posts: 77
I'm not sure where you found the 95 % pass mark figure, but I think that to obtain a standardised score of about 118 in a Tiffin paper, 80 % is nearer the mark for a child born around the middle of the school year, though of course, this will vary each year, according to the ability of all the children taking the test. 95 % (4 questions wrong in a 80 question paper) may well get you 140 if you are born in the Summer.
I know of someone who appealed and was told that their child had gained 65/80 in one test with a standardised score of 121 and gained 57/80 in the other with a standardised score of 108.
Hope this helps.
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Post subject: Posted: Fri Jan 16, 2009 12:39 pm
Joined: Thu Oct 02, 2008 3:31 pm
Posts: 188
Location: London
hi there and welcome
you can't make that calculation
there is no linear relation between the number of wrong answers and the pass mark, you cannot equate 5 questions to 25 marks
why?
consider that the majority of children are close to the average, so they all make a very similar number of right answers
one or two additional right answers can make a child jump 50 places, if you have 1500 applications
instead if the child is very very bad, all questions wrong, or very very good, all questions right, one or two questions more or less does not make a difference in the ranking
if you look in this forum you can also find the more mathematical explanation,
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Post subject: Posted: Fri Jan 16, 2009 1:15 pm
Joined: Fri Jan 16, 2009 7:10 am
Posts: 7
Runningmum, the 95% was merely from the rumourmill.
The figures you mention were revealing however I suppose you have to take into account Giulio's comments about one or two marks suddenly moving a candidate 50 places.
Giulio, thanks for the information, I don't really understand the mathematics of it, but will search for those articles.
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Post subject: Posted: Sat Jan 17, 2009 8:50 am
Joined: Fri Jan 16, 2009 7:10 am
Posts: 7
Runningmum, with reference to the person who appealed because their child scored 121 and 108 would this not have given an aggregated score of 229 ?
I was under the impression that the initial cut off mark, last year, was 229 and then moved down to about 224 when the lists were finally closed. Did they appeal to Tiffin Girls or Boys ?
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Post subject: Tiffin scoresPosted: Sat Jan 17, 2009 10:56 am
Joined: Fri Jan 09, 2009 12:27 pm
Posts: 77
Hi TMTY
Unfortunately it was an appeal for Tiffin Girls and the final cut off that year was at 230. She is now enjoying life at Nonsuch.
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Post subject: Posted: Sat Jan 17, 2009 11:47 am
Joined: Fri Jan 16, 2009 7:10 am
Posts: 7
Thanks Runningmum.
What a great score as well, just shows how much more competitive the girls school is, the boys is hard enough !
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# Emily Reed
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# Nonlinear spring energy problem
• lzh
## Homework Statement
The stretch of a nonlinear spring by an amount x requires a force F given by:
F=40x-6x^2
where F is in Newtons and x is in meters.
What is the change in potential energy U when the spring is stretched 2m from its equilibrium position?
U=.5kx^2
= .5(kx)x
F=kx
## The Attempt at a Solution
F=40(2)-6(2)^2=80-24=56N
U=.5(56N)(2)=56J
Thats what I thought would work, but 56J is no the correct answer. What am I doing wrong?
F=-dU/dx
use this
So it'd be:
56N(2m)=-dU
dU=-112?
Am I not getting this?
## Homework Statement
The stretch of a nonlinear spring by an amount x requires a force F given by:
F=40x-6x^2
where F is in Newtons and x is in meters.
What is the change in potential energy U when the spring is stretched 2m from its equilibrium position?
U=.5kx^2
= .5(kx)x
F=kx
## The Attempt at a Solution
F=40(2)-6(2)^2=80-24=56N
U=.5(56N)(2)=56J
Thats what I thought would work, but 56J is no the correct answer. What am I doing wrong?
The trick here is to recognize that F=40x-6x^2 which is not the same as F=kx.
Now U(x) = $$\int^x_0\,F(x) dx\,=\,\int^x_0\,kx\,dx$$
http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html#pe2
http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html#pe
Oh, I see!
Thanks, I got it!
f=-dU/dx
integrating both sides
20x^2 -2x^3=-U
put x=2
U=-64J
change would be 64...and work done would be 64 J
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# Grab your calculator and do the multiplication
Your last odds versus you successful the Mega Hundreds of thousands Jackpot are calculated to be one hundred seventy five,711,536 or clearly said 175 million, 711 thousand, 5 hundred 36 30-6 to at least one (175,711,536 to one). Now you know the way to compute the odds of winning the Mega Thousands and thousands Lottery.
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It won’t make a difference if it is the Florida, Ohio, Texas, PA or NJ Lottery. This system or formula provides the true odds. Florida Lottery is 6/fifty three. Big apple Lottery is six/fifty nine. The Ohio Lottery, Lottery sambad morning Massachusetts Lottery, Wisconsin Lottery, and the Condition of Washington Lottery carry a six/forty nine lottery numbers ratio. Illinois Lottery carries a six/fifty two.
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The chances of you effectively matching the selection on the 3rd ball to generally be drawn is currently one/fifty four from the whole quantity of balls remaining from the drum. Along with the third ball faraway from the drum and sitting down with one other two successful quantities, your odds of accurately matching the fourth ball is lowered to 1/fifty three.
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The Powerball Lottery calculations are determined by a 1/fifty nine for the initial five white balls and one/39 with the “pink” electricity ball. The 1st list of multipliers is 59x58x57x56x55. This team totals 600,766,320. Now divide 600,766,360 by one hundred twenty (1x2x3x4x5). Your new complete is 5,006,386. There exists a one/39 opportunity to capture the “pink” ball. 39 x five,006,386 offers you the true odds of successful the Powerball Jackpot, specifically 195,249,054 to one.
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A Decide five/39 ball Lottery video game components appears like this: (one/39, one/38, one/37, one/36, 1/35) for a total of sixty nine,090,840 divided by 120 (1x2x3x4x5) for the odds of 1/575,757 of profitable the Jackpot such as the Illinois Little Lotto. Other States While using the identical five/39 lottery quantities consist of the NC Lottery, Ga and Florida Lottery Fantasy five, and Tennessee Lottery’s Decide on five. Virginia Lottery’s Dollars 5 carries a five/34 vary.
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# Preposterous products: the perfect solution to 'uneven slice' spats
"He got a bigger slice of that cake than me!" Oh, how many times I've heard that in my life; and I'm not even an HR Director. The problem of fairly parsing a pie, cake or other round treat has bedeviled parents as long as there have been children and round treats. So why was the answer, so obvious, thousands of years in the making?
Thankfully, the Fair Share Cake Plate solves the problem ( but not cheaply; \$45 will buy a lot of even-up cake). The platter, which resembles a large compass with degree demarcations on the periphery, will allow you to cut slices precisely alike. Of course, a little geometry will come in handy. Here's a cheat-sheet.
Cutting into 12 slices = 30 degrees per slice
16 slices = 22.5 degrees
24 slices = 15 degrees
31 slices = no cake for you!
And don't even mention the problem of a cut that wanders as it plunges through the Z axis.
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# Argument (complex analysis)
"Arg (mathematics)" redirects here. For argument of a function, see Argument of a function.
Figure 1. This Argand diagram represents the complex numbers lying on a plane. For each point on the plane, arg is the function which returns the angle φ.
In mathematics, arg is a function operating on complex numbers (visualized in a complex plane). It gives the angle between the line joining the point to the origin and the positive real axis, shown as φ in figure 1 opposite, known as an argument of the point (that is, the angle between the half-lines of the position vector representing the number and the positive real axis).
## Definition
Figure 3. Two choices for the argument φ
Arguments are defined in two equivalent ways:
• Geometrically, in relation to an Argand diagram, arg z is the angle φ from the positive real axis to the vector representing z. The numeric value is given by the angle in radians and is positive if measured counter-clockwise.
• Algebraically, an argument of the complex number z = x + iy is any real quantity $\phi$ such that
$z = x + i y = r \cos \phi + i r \sin \phi \$
for some positive real r. The quantity r is the modulus of z, written
$r = |z| = \sqrt{x^2 + y^2} \ .$
The names amplitude[1] or phase[2] are sometimes used equivalently.
Under both definitions, it can be seen that the argument of any (non-zero) complex number has many possible values: firstly, as a geometrical angle, it is clear that whole circle rotations do not change the point, so angles differing by an integer multiple of radians (a complete circle) are the same. Similarly, from the periodicity of sin and cos, the second definition also has this property.
## Principal value
Figure 4. The principal value Arg of the blue point at 1+i is π/4. The red line here is the branch cut and corresponds to the two red lines in figure 2 seen vertically above each other).
Because a complete rotation around 0 leaves a complex number unchanged, there are many choices which could be made for φ by circling the origin any number of times. This is shown in figure 3, a representation of the multi-valued (set-valued) function, where a vertical line cuts the surface at heights representing all the possible choices of angle for that point.
When a well-defined function is required then the usual choice, known as the principal value, is the value in the open-closed interval (−π, π], that is from −π to π radians, excluding −π itself (−180 to +180 degrees). This represents an angle of up to half a complete circle from the positive real axis in either direction, the angle φ is constrained to lie between −π and π radians. This portion of the surface is shown hatched in red in figure 2, and projected onto the plane in figure 4.
### Notation
The principal value sometimes has the initial letter capitalized as in Arg z, especially when a general version of the argument is also being considered. Note that notation varies, so arg and Arg may be interchanged in different texts.
Some authors define the range of the principal value as being in the closed-open interval [0, 2π).
The set of all possible values of the argument can be written in terms of Arg as:
$\arg{z}=\{\operatorname{Arg} z+2\pi n:n\in \mathbb Z\}$.
## Covering space
Figure 2. The arguments of the complex plane are plotted vertically. arg measures the angle of points, shown by the fact that the outward radial lines, which have constant angle to the real axis, lie on the surface. The layered structure shows that each point has infinitely many arguments, each one corresponding an intersection between a vertical line through the point and the sheet. The red hatching indicates the surface corresponding to the principal value. See larger version.
In informal situations, arg may be left not well-defined, for instance arg z(t) where z depends on a parameter t may change by every time z goes around the origin. This idea can be made more precise by considering z(t) as being defined not on the complex plane but on a covering space. Polar coordinates excluding the origin and with an unconstrained angle provide such a space, in this case arg is defined by:
\begin{align} \arg \colon \mathbb{R}^+\times\mathbb{R} &\to \mathbb{R} \\ (r,\ \phi) &\mapsto \phi \end{align}
The covering space has as base space the punctured complex plane. This is equivalent to the product of a positive non-zero radius and an angle on a unit circle that is:
$\mathbb{C}\smallsetminus\{0\} = \mathbb{R}^+ \times \mathbb{S}^1$
The principal value Arg then maps the unit circle component of this representation to the interval (−π, π].
## Computation
The principal value Arg of a complex number given as x+iy is normally available in math libraries of many programming languages using the function atan2( ) or some language specific variant. The value of atan2(y, x) is the principal value in the range (−π, π].
Many texts say the value is given by arctan(y/x), as y/x is slope, and arctan converts slope to angle. This is correct only when x > 0, so the quotient is defined and the angle lies between π/2 and π/2, but extending this definition to cases where x is not positive is relatively involved. Specifically, one may define the principal value of the argument separately on the four half-planes x > 0, x < 0 (separated into two quadrants if one wishes a branch cut on the negative x-axis), y > 0, y < 0, and then patch together.
$\operatorname{Arg}: \mathbb{C} \smallsetminus \{0\} \to \left(-\pi,\pi\right]$
$\operatorname{Arg}(x + iy) = \operatorname{atan2}(y,x) = \begin{cases} \arctan \frac{y}{x} & \qquad x > 0 \\ \frac{\pi}{2} - \arccot \frac{y}{x} & \qquad y > 0 \\ -\frac{\pi}{2} - \arccot \frac{y}{x} & \qquad y < 0 \\ \pi + \arctan \frac{y}{x} & \qquad x < 0, y \ge 0 \\ -\pi + \arctan \frac{y}{x} & \qquad x < 0, y < 0 \\ \text{undefined} & \qquad x =y = 0 \end{cases}$
For the variant where Arg is defined to lie in the interval [0, 2π), the value can be found by adding to the value above when it is negative.
Alternatively, the principal value can be calculated in a uniform way using the tangent half-angle formula, the function being defined over the complex plane but excluding the origin:
$\operatorname{Arg}(x + iy) = \begin{cases} 2 \arctan \left( \frac{y}{\sqrt{x^2+y^2}+x} \right) & \qquad x > 0 \text{ or } y \ne 0 \\ \pi & \qquad x < 0 \text{ and } y = 0 \\ \text{undefined} & \qquad x = 0 \text{ and } y = 0 \end{cases}$
This is based on a parametrization of the circle (except for the negative x-axis) by rational functions. This version of Arg is not stable enough for numerical use but can be used in symbolic calculation.
## Identities
One of the main motivations for defining the principal value Arg is to be able to write complex numbers in modulus-argument form (the modulus of z = x + iy is |z| = √(x2 + y2), the length of the vector on the Argand diagram). Hence for any complex number z,
$z = \left| z \right| e ^ { i \operatorname{Arg} \left( z \right) }$.
This is only really valid if z is non-zero but can be considered as valid also for z = 0 if Arg(0) is considered as being an indeterminate form rather than as being undefined.
Some further identities follow. If z1 and z2 are two non-zero complex numbers then
$\operatorname{Arg}\left(z_1 z_2\right) \equiv \operatorname{Arg}(z_1) + \operatorname{Arg}(z_2) \pmod {(-\pi,\pi]}$
$\operatorname{Arg}\left(\frac{z_1}{z_2}\right) \equiv \operatorname{Arg}(z_1) - \operatorname{Arg}(z_2) \pmod {(-\pi,\pi]}$
If z ≠ 0 and n is any integer then
$\operatorname{Arg}\left(z^n\right) \equiv n \operatorname{Arg}(z) \pmod {(-\pi,\pi]} .$
### Example
$\operatorname{Arg}\left(\frac{-1- i}{i}\right) \equiv \operatorname{Arg}(-1-i) - \operatorname{Arg}(i) = -\frac{3\pi}{4} - \frac{\pi}{2} = -\frac{5\pi}{4} \equiv \frac{3\pi}{4} \pmod {(-\pi,\pi]}$
## References
### Notes
1. ^ Knopp, Konrad; Bagemihl, Frederick (1996). Theory of Functions Parts I and II. Dover Publications. p. 3. ISBN 0-486-69219-1.
2. ^ Dictionary of Mathematics (2002). phase.
### Bibliography
• Ahlfors, Lars (1979). Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable (3rd ed.). New York;London: McGraw-Hill. ISBN 0-07-000657-1.
• Beardon, Alan (1979). Complex Analysis: The Argument Principle in Analysis and Topology. Chichester: Wiley. ISBN 0-471-99671-8.
• Borowski, Ephraim; Borwein, Jonathan (2002) [1st ed. 1989 as Dictionary of Mathematics]. Mathematics. Collins Dictionary (2nd ed.). Glasgow: HarperCollins. ISBN 0-00-710295-X.
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## Thursday, January 5, 2012
### Math Game- Racing Rectangles
Racing Rectangles
Racing Rectangles is a game that can help reinforce arrays and multiplication. Students, working in pairs, take turns rolling two dice. Each student must choose a different colored marker or crayon to use. The student outlines and fills in a rectangle that matches what they rolled.
For example, if the student rolled a 4 and 3, that student would fill in a 4x3 rectangle on the grid. The player then writes the total number of squares inside the rectangle.
A player loses a turn when his or her rectangle cannot fit on the game board. Play continues back and forth until neither player can't draw a rectangle.
Students count up their total of squares they colored.
The winner is the one with the highest number of squares filled in.
Here is an example of what a game board might look like...
Enjoy!
1. Hi Mary:
I think I'd like to use this when we review area next month. Thanks--as always--for sharing!
Kim
2. Awesome game! My students have begun learning how to multiply and we have already studied area-- a perfect activity for centers!
3. Love it! Thanks so much for sharing!
Jennifer
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Simplify logo.75 log2 0.125
Question
# Simplify logo.75 log2 0.125
JEE/Engineering Exams
Maths
Solution
155
4.0 (1 ratings)
( begin{array}{l}quad log _{frac{3}{4}}left(log _{2} frac{1}{(0.125)^{1 / 4}}right) =log _{frac{3}{4}}left(log _{2}(0.125)^{-1 / 4}right) =log _{frac{3}{4}}left(log _{2}(0.5)^{-3 / 4}right) =-log _{frac{3}{4}}left(log _{2}left(frac{52)}{4}right)^{frac{3}{4}}right. =log _{3 / 4}left(frac{-3}{4} times log _{2}(25)right. = & log _{3 / 4}left(-frac{3}{4} log _{2} 2^{-1}right) = & log _{3 / 4} 3 / 4 = & =pm text { Alusi }end{array} )
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# Solving a time-dependent structural mechanics problem with Finite Element
I'm trying to solve a time-dependent structural mechanics problem with Finite Element. I modified one of the last samples in the "Solving Partial Differential Equations with Finite Elements" Tutorial.
The following equations should ideally represents a beam initially at rest and then stimulated by a sinusoidal force per unit volume directed ad the $y$ axis.
Needs["NDSolveFEM"]
\[CapitalOmega] = Rectangle[{0, 0}, {5, 1}];
mesh = ToElementMesh[\[CapitalOmega]];
mesh["Wireframe"];
op = {Inactive[
Div][({{0, -((Y \[Nu])/(1 - \[Nu]^2))}, {-((Y (1 - \[Nu]))/(
v[x, y, t], {x, y}]), {x, y}] +
Inactive[
Div][({{-(Y/(1 - \[Nu]^2)),
0}, {0, -((Y (1 - \[Nu]))/(2 (1 - \[Nu]^2)))}}.Inactive[
Grad][u[x, y, t], {x, y}]), {x, y}],
Inactive[
Div][({{0, -((Y (1 - \[Nu]))/(2 (1 - \[Nu]^2)))}, {-((
u[x, y, t], {x, y}]), {x, y}] +
Inactive[
Div][({{-((Y (1 - \[Nu]))/(2 (1 - \[Nu]^2))),
v[x, y, t], {x, y}]), {x, y}]} /. {Y -> 10^3, \[Nu] ->
33/100};
Subscript[\[CapitalGamma], D] =
DirichletCondition[{u[x, y, t] == 0., v[x, y, t] == 0.}, x == 0];
ic = {
u[x, y, 0] == 0, v[x, y, 0] == 0,
Derivative[0, 0, 1][u][x, y, 0] == 0,
Derivative[0, 0, 1][v][x, y, 0] == 0
};
{uif, vif} =
NDSolveValue[{op == {0, Sin[t]}, Subscript[\[CapitalGamma], D],
ic}, {u, v}, {x, y} \[Element] mesh, {t, 0, 2 \[Pi]},
Method -> {"PDEDiscretization" -> {"MethodOfLines",
"TemporalVariable" -> t,
"SpatialDiscretization" -> {"FiniteElement"}}}];
My real problem is different and more complex but the result is the same
NDSolveValue::tvic: t cannot be used as the temporal independent variable because the conditions {u[x,y,0]==0,v[x,y,0]==0,(u^(0,0,1))[x,y,0]==0,(v^(0,0,1))[x,y,0]==0} for that dimension do not constitute sufficient initial conditions given at only one value of t. >>
NDSolveValue::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >>
I tried different forms of the force (also op == {0,0} which should end with the stationary solution) and also adding $t>0$ ad a predicate under DirichletCondition without success.
• I can't look at it right now, try to put t in first position. Commented May 18, 2015 at 16:15
• @user21 Thanks, tried, but unfortunately nothing changes. But, sorry, I made some confusions while translating from my real problem to this simplified version, I'l try to update the question soon... Commented May 18, 2015 at 17:54
This works:
Needs["NDSolveFEM"]
\[CapitalOmega] = Rectangle[{0, 0}, {5, 1}];
mesh = ToElementMesh[\[CapitalOmega]];
mesh["Wireframe"];
op = {Inactive[
Div][({{0, -((Y \[Nu])/(1 - \[Nu]^2))}, {-((Y (1 - \[Nu]))/(2 \
(1 - \[Nu]^2))), 0}}.Inactive[Grad][v[t, x, y], {x, y}]), {x, y}] +
Inactive[
Div][({{-(Y/(1 - \[Nu]^2)),
0}, {0, -((Y (1 - \[Nu]))/(2 (1 - \[Nu]^2)))}}.Inactive[
Grad][u[t, x, y], {x, y}]), {x, y}],
Inactive[
Div][({{0, -((Y (1 - \[Nu]))/(2 (1 - \[Nu]^2)))}, {-((Y \
\[Nu])/(1 - \[Nu]^2)), 0}}.Inactive[Grad][u[t, x, y], {x, y}]), {x,
y}] + Inactive[
Div][({{-((Y (1 - \[Nu]))/(2 (1 - \[Nu]^2))),
v[t, x, y], {x, y}]), {x, y}]} /. {Y -> 10^3, \[Nu] ->
33/100};
Subscript[\[CapitalGamma], D] =
DirichletCondition[{u[t, x, y] == 0., v[t, x, y] == 0.}, x == 0];
ic = {u[0, x, y] == 0, v[0, x, y] == 0};
{uif, vif} =
NDSolveValue[{D[{u[t, x, y], v[t, x, y]}, t] + op == {0, Sin[t]},
Subscript[\[CapitalGamma], D], ic}, {u, v}, {t, 0,
2 \[Pi]}, {x, y} \[Element] mesh,
Method -> {"PDEDiscretization" -> {"MethodOfLines",
"TemporalVariable" -> t,
"SpatialDiscretization" -> {"FiniteElement"}}}]
You only need to specify derivatives of the initial condition up to degree one less then the time derivative - zero in this case. (For a wave equation, you'd specify the first derivative of the initial condition)
• I'm very sorry for posting this stupid question. And of course you are right, the initial condition on speed is not necessary. When translating from my real problem to a simplified version to poste here I forgot to include the inertial forces, i.e. the right Cauchy's equation of motion is something like op + {0 - Derivative[2, 0, 0][u][t, x, y], Sin[t] - Derivative[2, 0, 0][v][t, x, y]} == {0, 0} and with this equation the ic on speed are required and NDSolve doesn't complain. My real problem is still there, but is not related with this question at this point. Thanks and sorry again. Commented May 18, 2015 at 18:29
• @unlikely, that's alright. Sometimes this happens when one tries to simplify things. I am looking forward to see your final application ;-) Commented May 18, 2015 at 18:32
• It is mandatory to put t independent variable before {x,y} or {x,y,z} spatial variables? It appears that the error messages are related to the use of [x,y,z,t] as arguments for unknowns... I'm develoving different models for my problem, (2D stationary, 3D stationary, and 3D time dependent) so for me it is more natural to add independent variables of more realistic model at the end, at least for the final resulting InterpolatingFunction(s)... Commented May 19, 2015 at 8:33
• @unlikely, for now yes. It works for some cases to have the t last but not all yet. Commented May 19, 2015 at 13:00
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# Binary search simple explanation atydoryz722215185
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What is Russian Peasant Multiplication Why does it work, , how is the Russian peasant algorithm connected to binary numbers.
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In computers Different bases are often used in computers Binarybase 2) is used because at the most simple level, computers can only deal with 0s , 1s.
Binary search simple explanation.
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Aug 19, for math., 2016 How to Convert Binary to Hexadecimal This article will explain how to convert binarybase 2) to hexadecimalbase 16 Whether it is for coding Some say Banc De Binary is a ad more about my experience with this binary options broker , is it not., find out if BBinary is a fraud, May 21, 2011 Colour eaking up an image into pixels like this makes it possible for a computer to store it Each pixel is stored in order as a series of binary.
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A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate. Introduces the concepts behind different number bases, and shows how to convert between decimalbase ten) and binarybase two) numbers.
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| 1,708,638,596,000,000,000
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# The SI unit 1 cubic meter per second is equal to ________.
This question was previously asked in
SSC JE Mechanical 14 Nov 2022 Shift 2 Official Paper
View all SSC JE ME Papers >
1. 1000 litres per second
2. 10 litres per second
3. 1 litre per second
4. 100 litres per second
Option 1 : 1000 litres per second
Free
General Awareness Mock Test
17.8 K Users
20 Questions 20 Marks 12 Mins
## Detailed Solution
Explanation:
Cubic meters per second:
• A cubic meter per second (m3·s−1, m3/s, cumecs or cubic meter per second in American English) is a derived SI unit of flow rate equal to that of a cube with sides of one metre (1000 mm) (39.37 in) in length exchanged or moving each second.
Since 1 m3 = 1000 liters
• The SI unit of 1 cubic meter per second is equal to 1000 liters per second.
• It is popularly used for water flow, especially in rivers and streams.
Concept:
Discharge or Rate of flow:
• It is defined as the amount of fluid flowing through a section of channel or a pipe per unit time.
• The discharge may be expressed in terms of weight of flowing fluid per unit time or mass of flowing fluid per unit time or volume of flowing fluid per unit time through a channel or pipe.
• The units of discharge for liquids are m3/s or litres/s.
• The units of discharge for gases are N/s or kg/s.
Note:
• In case of incompressible fluid, the discharge is usually expressed as the volume of flowing fluid per unit time (volume flow rate of the fluid).
• Whereas, in case of compressible fluid, the discharge is expressed as the weight of flowing fluid per unit time.
Let us consider a fluid flowing through a pipe;
A = cross-sectional area of pipe
V = average velocity of flowing fluid through the pipe
$$v$$ = specific volume = $$\frac{1}{\rho}$$
m = Mass flow rate
Discharge, $$Q = AV=mv$$ (m3/s)
or $$m=\frac{AV}{v}$$$$=\rho{A}{V}$$ (kg/s)
or $$mg = \rho{g}AV$$
$$W=\rho{g}AV$$ (N/s)
The SI unit of Q will be 1 cubic metre per second.
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# Search for tag: "percent to decimal conversion"
#### How to Convert a Percent to a Decimal | Part 2 of 2 | Convert 135% and 12.5% to a Decimal
In this video we learn how to Convert a percent to a decimal. We Convert each percent to a decimal. We convert 135% and 12.5% to a decimal. The steps we followed on how to convert a percent to a…
From MinuteMath 0 likes 1 plays
#### How to Convert a Percent to a Decimal | Part 1 of 2 | Convert 6% and 78% to a Decimal
In this video we learn how to Convert a percent to a decimal. We Convert each percent to a decimal. We convert 6% and 78% to a decimal. The steps we followed on how to convert a percent to a…
From MinuteMath 0 likes 2 plays
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Solubility > Dissolution/precipitation
Dissolution of Montmorillonite, only occuring 1 cell at a time
(1/1)
ravreeland:
Hello, I am new to PHREEQc and been having trouble. I looked in the manual and the forum and couldn't find an answer to the problem I am having.
I am trying to model the affect of pH in a clay column in terms of the clay dissolving. What my problem is, my model is only dissolving the clay in cell 1, and won't start dissolving the clay in cell 2 until cell 1 has completely dissolved. The pH changes in the rest of the cells, but the amount of clay does not. I feel like its because I have not set up the code correctly. One thing that I can think of that is possibly happening is that the material dissolved in cell 1 is not allowing the rest of the cells to dissolve because of equilibrium balance.
My questions are if the dissolution should happen one cell at a time? If it is not, what can I do to fix it?
Thank you very much for your time.
TITLE pH Study
#This is a commit
SOLUTION 0 MgCl2 #solution to be flowed into the cells at cell 1
units mmol/kgw #molality
# default --> 1 kg of solution
temp 25.0
pH 1.0 charge # need this pH to be around 0, 1 or 2.
pe 12.5 O2(g) -0.68
H(1) 0.016 #0.016 should be the molility of 37% HCl solution
# need to add H(1) to it for solution to reach pH target.
Cl 10
SOLUTION 1-10 Initial solution for column
units mmol/kgw #molality
temp 25.0
pH 10.0 charge
pe 12.5 O2(g) -0.68
#Cl 20 # helps with the other cells, but they are still not disolving. AKA just starts lower
EQUILIBRIUM_PHASES 1-10
Ca-Montmorillonite 0 0.1
#[name of mineral] [saturation index] [amount]
-force_equality false
TRANSPORT # 1D simulation
-cells 10 #designates the number of cells in 1D
-lengths 10*0.01
-flow_direction forward
-shifts 100 #number of times solution is shifted to next higher cell
-time_step 1 #seconds
-initial_time 0
-punch_cells 1-10
-punch_frequency 1
SELECTED_OUTPUT
-file pH_precipTest_1.sel #name of file where results are written
-reset false # sets some options to false, see user manual
-step # prints out the advection shift number of transport calculations
-distance true
-totals H(1) Cl Ca Si Al S #prints out concentration in molatity of list
-water true #prints mass of water, perhaps in Kg
-equilibrium_phases Ca-Montmorillonite #prints out two lines, moles of each phase, and moles transferred
-pH true
#this is to print out other custom stuff to output
USER_PUNCH
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Coursework-Planning, Biology Investigating energy provided by different foods Variables to consider: Storage/Ageing of food Food preparation Composition of food Heating during preparation Mass of food Aim I intend to investigate the amount of energy released when you burn two different types of food. One product will be intended for slimming, the other will be non slimming. I am going to test the variable composition of food. I will be using biscuits, bread, cheese and crisps for my experiment. Prediction I think that the food intended for slimming will have less energy than the non-slimming food. I think this, because in order to successfully lose weight, you have to lower your energy intake, and the non-slimming foods contain more energy than foods intended for slimming.
I think that slimming foods will provide approximately one third less fat that foods not intended for slimming. Our bodies need energy to survive, and the food we eat gives us energy. This is used for all the activities in every day life. The fuel for respiration is our food. glucose + oxygen carbon dioxide + water + energy The number of overweight people in the UK has been steadily rising, and more than half of the population is now overweight. There are several reasons why people are getting heavier.
Our environment and lifestyle make it difficult for us to keep a healthy weight, and there are many more high-fat foods readily available now. It's official: Britain is the most obese country in Europe. This is the reason why many people turn to slimming products as an easy way to lose weight. This equation applies to a healthy person, but in an overweight person, some of the energy input is turned into excess energy, and is stored as fat.
Non-slimming food contains less energy, so there is less energy to be stored as fat. Energy in = (food and drink) Energy out (metabolism, and activity) Energy is measured in kilojoules (kJ). This unit of energy used to be called the calorie, which is why some foods say 'low calorie' on the box. Our food consists of three main substances: carbohydrates, proteins and fats.
They all have different energy values.
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Potassium Chlorate: Molar Mass, Properties, Uses, and Safety Precautions
Potassium chlorate is a chemical compound that has found numerous applications in various industries. It is a white crystalline substance composed of potassium (K), chlorine (Cl), and oxygen (O). It is highly soluble in water and is known for its oxidizing properties.
The chemical formula for potassium chlorate is KClO3. It consists of one potassium atom (K), one chlorine atom (Cl), and three oxygen atoms (O).
Molar Mass of Potassium Chlorate
The molar mass of potassium chlorate (KClO3) can be calculated by summing the molar masses of its constituent elements:
1. Potassium (K): 39.10 g/mol
2. Chlorine (Cl): 35.45 g/mol
3. Oxygen (O): 16.00 g/mol.
Calculate the molar mass of potassium chlorate:
Molar mass of KClO3 = (1 x molar mass of K) + (1 x molar mass of Cl) + (3 x molar mass of O)
= (1 x 39.10 g/mol) + (1 x 35.45 g/mol) + (3 x 16.00 g/mol)
= 39.10 g/mol + 35.45 g/mol + 48.00 g/mol
= 122.55 g/mol
The molar mass of potassium chlorate (KClO3) is 122.55 g/mol.
Potassium Chromate Formula, Uses, Solution and Indicator Preparation
Decomposition
Potassium chlorate (KClO3) decomposes when heated to release oxygen gas (O2) and leave behind potassium chloride (KCl) as a residue.
2KClO3(s) → 2KCl(s) + 3O2(g)
In this reaction, the solid potassium chlorate breaks down into solid potassium chloride and oxygen gas. This property of potassium chlorate to decompose and release oxygen gas has various practical applications, including its use in pyrotechnics and as an oxygen source in emergency situations.
Properties of Potassium Chlorate
The properties of potassium chlorate is essential to appreciate its various applications.
1. It is typically found in the form of odorless, white crystals.
2. It is highly soluble in water, which makes it suitable for various chemical processes.
3. It is a powerful oxidizing agent, meaning it can provide oxygen to support combustion reactions.
4. When heated to this decomposes and releasing oxygen gas and leaving behind potassium chloride (KCl).
Potassium Nitrate Molar Mass, Formula and Uses
Uses of Potassium Chlorate
Potassium chlorate has a diverse range of uses, including:
1. It is a key ingredient in fireworks and safety matches due to its ability to provide oxygen for combustion.
2. It is used in the synthesis of various chemicals, including dyes and pharmaceuticals.
3. It is employed to generate oxygen gas in emergency oxygen packs and self-contained breathing apparatus (SCBA) used by firefighters.
4. It is use in agriculture as an herbicide to control weed growth.
Safety Precautions
Here some safety precautions to keep in mind:
Storage
Store potassium chlorate in a cool, dry place away from flammable substances and organic materials.
Handling
Wear appropriate protective gear, including gloves and safety goggles, when handling this compound.
Avoid Contamination
Do not mix potassium chlorate with incompatible substances, as it may lead to hazardous reactions.
Avoid Heat Contact
Keep potassium chlorate away from open flames and heat sources to prevent spontaneous ignition.
Disposal
Dispose of potassium chlorate waste following local regulations and guidelines.
Conclusion
It is a versatile chemical compound with a range of important applications. Its oxidizing properties make it valuable in pyrotechnics, chemical synthesis, and emergency oxygen production.
Potassium Permanganate: Molar Mass, Density
BANTI SINGH
Hi I'm Banti Singh, a Chemical Engineer! Welcome all of you to my blog. If you got the information right? Share the information. All of you Thank you
Thanks to visit this site.
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# Yahoo Web Search
1. Sort by
1. ### Buy or Sell: Chicago Bulls are the 5th best team in the NBA going into this season?
...should make a nice playoff run I am so excited to see what they do. D-Rose is one of my favorite players!
12 Answers · Sports · 21/07/2010
2. ### Grand theft auto question?
...a minuet later) you get an additional \$102,500 and so on and so forth. I did this for like two hours and now I have a couple million and I'...
1 Answers · Games & Recreation · 08/05/2008
3. ### Top ten most expensive paintings?
...! \$43+ million out of pocket. By the way, the title of this painting is not the artist doing his Rocky Balboa impression; "Yo" means "I" in ...
4 Answers · Arts & Humanities · 26/02/2007
4. ### Ok i keep getting a different answer than my teacher on my hw and i want to know if im doing something wrong?
Simply subtract the old value from the new value, then divide by the old value. Multiply the result by 100 and slap a % sign on it. That's your percent change. 146400-102500 = 43900 43900/102500 = 0.4282 0.4282 x 100 = 42.82%
1 Answers · Education & Reference · 13/07/2008
5. ### Calculate the average speed of a complete round trip in which the outgoing 250 is covered at 85 , followed by?
...60= 50/17+1+25/6=(300+102+425 )/102=827/102 avg speed= 500 divided by 827/102 = 500*102/827=61.67 km /h
2 Answers · Science & Mathematics · 28/06/2012
6. ### Accounting. Working out break even.?
You're right. For part 2...you make \$10 per box, so to get a \$6,000 profit you need to sell \$6,000 / 10 = 600 boxes in addition to the 3,500 = 4,100 boxes. 4,100 boxes x \$25 per box = \$102,500.
7. ### Economics Help?
...rate of 5%, so that in 6 months I would receive 100,000*(1+0,05/2)=\$102,500. 3) Buy the T-Note futures contract (for \$100,000 of...
2 Answers · Social Science · 21/12/2006
8. ### Service ESC just turned on, on my 2007 Saturn Aura XR how do i fix it?!?
ESC = Electronic Stability Control. It's possible that there was just a stray signal or momentary misalignment that caused the condition. However, if the code won't reset with turning off ignition, take your car to a...
2 Answers · Cars & Transportation · 05/08/2014
9. ### Career Options!!!!?
... - \$105,400 (this isn't the entry level job) * Lawyer - \$102,500 * Pharmacist - \$94,500 * Optometrist - \$91,000 Since...
2 Answers · Education & Reference · 22/06/2008
10. ### How many of these US Companies are supporting your US Presidential Candidate?
... \$81,750 Avenue Capital Group \$80,400 Ernst & Young \$78,250 do the corporations choose before we do ? ronpaul2008.com
6 Answers · Politics & Government · 25/08/2007
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# Terms of a Proportion - Definition and Examples
What are the terms of a proportion? A proportion can be written in a couple of ways as shown below.
• a / b = c / d
• a:b = c:d
The four terms of a proportion are the terms a, b, c, and d.
## More examples showing what the terms of a proportion are
a.
4 / 5 = 12 / 20
The terms of the proportion are 4, 5, 12, and 20.
b.
e / f = g / h
The terms of the proportion are e, f, g, and h.
c.
x / y = x2 / y2
The terms of the proportion are x, y, x2 and y2.
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Learn
As seen in the previous exercise, Kotlin allows us to combine or chain arithmetic expressions in order to achieve more complex calculations. When doing so, we must keep in mind the order in which each expression gets evaluated.
Most programming languages follow a certain order of operations (similar to PEMDAS) when evaluating such expressions. In Kotlin, this order looks like:
1. Parentheses
2. Multiplication
3. Division
4. Modulus
6. Subtraction
You may have noticed that we skipped over the E (Exponents) in PEMDAS. This is because Kotlin does not have an exponent operator and instead relies on the `.pow()` function to calculate exponentiation. We’ll cover this more in-depth in the following exercise.
Let’s see a few examples of compound arithmetic expressions:
``````println(5 + 8 * 2 / 4 - 3) // Prints: 6
println(3 + (5 + 5) / 2) // Prints: 8
println(3 * 2 + 1 * 7) // Prints: 13``````
Another rule to keep in mind is when an expression contains sister operations such as multiplication and division or addition and subtraction, side by side. The compiler will evaluate this expression in a left to right order. For example:
``println(3 + 16 / 2 * 4) // Prints: 35``
Since we have division, `/`, and multiplication, `*`, side by side, the left to right order goes into effect and the expression evaluates as such:
Keep in mind both sets of rules when creating complex arithmetic expressions.
### Instructions
1.
In Operations.kt, we’ve set up multiple arithmetic expressions that are missing arithmetic operators.
Add an arithmetic operator in place of `___` to complete each expression.
• `answer1` should be `14`
• `answer2` should be `3`
• `answer3` should be `11`
Note: You will see an error in the terminal on the right if there are still any `___` present in your code. The error should go away after you’ve replaced each `___` with the correct operator.
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# 4
(Thanks to Mark Xu for comments on these notes.)
These are some notes on tensor networks, the mapping from boolean circuits to tensor networks, and how #SAT can be written as a tensor network contraction.
# Definitions and Notation
## What is a tensor?
A rank- tensor is an array of numbers with integer indices, e.g. is a rank-3 tensor. The range of each index is called its bond dimension. So for instance the Kronecker delta tensor used in physics is given by
and is a tensor with two indices, each of bond dimension 3. Meanwhile the Levi-Civita symbol
is a tensor with three indices each of dimension 3.
## What is a tensor contraction?
A contraction is a specification of dot products to perform between tensors. For instance
says to form the tensor by contracting with along the second index of and the first index of .
A tensor can also be contracted with itself, forming a trace. For instance
says that we trace over the second and third indices of to form .
Often times the summation is written just with indices and no symbol using Einstein summation notation. In this notation, indices are summed over if they appear in an expression exactly twice. This notation is unambiguous because contraction is only defined over pairs of indices.
## What is a tensor network?
A tensor network is a specification of which contractions are desired between one or more tensors. They are often drawn diagrammatically in penrose notation as
Here has three indices, , two of which are free (meaning they are not involved in any contraction) and one of which is linked to an index of , which itself has a further free index .
# Representing Boolean Circuits
A boolean circuit with inputs can be written as a tensor network as follows. For further references see here.
First, each input is mapped from False/True to a vector which is either or . These vectors can be contracted with tensors representing the various boolean gates. For instance
This has the property that
That is, implements an OR gate. An AND gate can be similarly constructed:
Note that an AND tensor can also be used to copy a wire, because
Finally, NOT gates are just given by
so that
In this way, we can construct a tensor network which, when contracted against the vectors representing its inputs, results in a vector representing its output.
# #SAT
#SAT is the problem of counting the number of instances of a boolean circuit which output True. We can represent this problem in a tensor network as follows:
(1) Map the boolean circuit to a tensor network with input indices and output index . The result might look like
If we contract some combination of against the input indices then the resulting tensor network will equal either (if the boolean circuit would have produced True with that input) or (otherwise).
(2) Contract an instance of against . Because is orthogonal to , and both have unit norm, the resulting tensor network now produces the scalar 1 if the inputs are set to a combination of so that and the scalar 0 otherwise.
(3) Make a copy of this tensor network, with input indices .
(4) Construct a new tensor network which specifies the contraction of the network and its copy, linking each with the corresponding . This might look as follows:
This network has no free indices and so produces a scalar when contracted. The contraction can be written as a sum over all possible values of the indices , so that scalar equals the number of input instances satisfying the boolean circuit.
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# How Temperature Affects Reaction Rate
By: • Research Paper • 822 Words • February 27, 2010 • 1,379 Views
Page 1 of 4
Lab Report: How Temperature affects Reaction Rate
Aim:
The Aim is to investigate how temperature can affect Reaction Rate. The experiment will be performed by heating equally sized and weighted lime stones with equal amounts and concentration of Hydrochloric acid at different temperatures. The temperatures will be 35˚C and 40˚C. We will measure the reaction rates by observing gas release of the reaction between lime stones and Hydrochloric acid. The amount of gas release at different temperatures will be compared afterwards to see if temperature can affect Reaction Rate.
Hypothesis:
I predict that the higher the temperature, the higher the Reaction Rate will be. Therefore I predict that the Reaction rate of the 40˚ C heated Lime Stones and HCL acid will be higher than the 35˚ C heated Lime Stones and HCL acid. I predict this because I know that when the temperature is raised, particles move faster and collide more frequently. Therefore if temperature is raised, the Reaction rate will increase. The increase in temperature will allow Reaction rate to rise and also increase amount of molecules being thermally activated (give enough energy to collide). I also predict that Reaction rate will increase roughly by a double for each 10˚ C. In this case, I suppose the Reaction rate will increase roughly by a half for 5˚C increased temperature.
Variables:
The independent variable is the one that is changed by the scientist:
 Temperature in ˚C, at which the HCl acid and Lime Stones will be heated
The dependent variable changes in response to the change the scientist makes to the independent variable:
 Rate of Reaction, measured by observing how much gas (in cmі) is produced
 Amount of molecules activated (given enough energy to collide)
 How fast the particles move
 How energetic the molecules will collide
The controlled variables are quantities that a scientist wants to remain constant:
 Size of Lime Stones
 Amount of Lime Stones
 Amount of Hydrochloric Acid
 Concentration of Hydrochloric Acid
Apparatus:
 Tripod
 Gauze
 Bunsen Burner
 Delivery Tube
 Stand and Clamp
 Gas Syringe (100 cmі)
 2x 20g Lime stones (small pieces)
 2x 20cmі of 0.2M Hydrochloric Acid (HCl)
 Thermometer (capable to measure until 100˚ C)
 Stop watch
 Eye Protection
 Bung
Diagram:
Method:
1. Collect the apparatus, as listed in the ‘Apparatus’ list
2. Set up Apparatus as shown in the diagram. The Apparatus should be set up without the bung, delivery tube and the gas syringe at first as they are not required until later on in the experiment.
3. Heat the flask with 20 cmі Hydrochloric acid until it reaches the temperature of 35˚C
4. Turn off heat immediately and take the thermometer out of the flask
5. Place the 20g of Lime Stone in the flask and immediately block the top of the flask with bung. The bung must be connected to the delivery tube, which will be connected to the Gas Syringe (as shown in diagram).
6. Record the results/Reaction Rate by observing the amount of gas produced each 15 seconds (in regular intervals).
7. Keep recording until no more reaction can be seen.
8. Repeat
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FLAC3D Theory and Background • Constitutive Models
# Anisotropic-Elasticity Ubiquitous-Joint Model
This model combines the logic of the anisotropic elastic model with that of the ubiquitous-joint model (note that “weak plane” and “joint” are used interchangeably in the text). The new model has a single orientation of weakness, which matches the orientation of the plane of elastic isotropy. The criterion for failure on the plane, whose orientation is given, consists of a local Mohr-Coulomb yield criterion with tension cutoff. The model can be used to simulate the behavior of layered material, such as clay shales, and account for slip conditions in the direction of layering (weak plane direction).
In the FLAC3D/3DEC implementation, new stresses are evaluated for each step using the elastic-anisotropic incremental laws. The new stresses are analyzed for yielding on the weak plane and updated accordingly using the joint flow rule. The local shear flow rule is non-associated, and the local tension flow rule is associated.
Consider a local system of reference axes, with $$x'$$ and $$y'$$ in the “weak” plane, and the $$z'-$$ axis normal to it. This axis is a principal direction of elasticity. Also, any two perpendicular directions $$x'$$ and $$y'$$, which are principal directions of elasticity, can be selected in the isotropic plane. The incremental elastic strain-stress relations used in the local axes are as follows:
(1)$\begin{split}\begin{matrix} \Delta \sigma_{1'1'} = a_{11} \Delta \varepsilon^e_{1'1'} + a_{12} \Delta \varepsilon^e_{2'2'} + a_{13} \Delta \varepsilon^e_{3'3'} \\ \\ \Delta \sigma_{2'2'} = a_{12} \Delta \varepsilon^e_{1'1'} + a_{11} \Delta \varepsilon^e_{2'2'} + a_{13} \Delta \varepsilon^e_{3'3'} \\ \\ \Delta \sigma_{3'3'} = a_{13} \Delta \varepsilon^e_{1'3'} + a_{12} \Delta \varepsilon^e_{2'2'} + a_{33} \Delta \varepsilon^e_{3'3'} \\ \\ \Delta \sigma_{1'2'} = 2G \Delta \varepsilon^e_{1'2'} \\ \\ \Delta \sigma_{1'3'} = 2G' \Delta \varepsilon^e_{1'3'} \\ \\ \Delta \sigma_{2'3'} = 2G' \Delta \varepsilon^e_{2'3'} \end{matrix}\end{split}$
where
(2)$\begin{split}\begin{matrix} a_{11} = {{E'-{\nu'}^2 E} \over {(1+\nu)[(1-\nu)E' - 2{\nu'}^2 E]}} E \\ \\ a_{12} = {{\nu E'+{\nu'}^2 E} \over {(1+\nu)[(1-\nu)E' - 2{\nu'}^2 E]}} E \\ \\ a_{13} = {{\nu E'} \over {(1-\nu)E' - 2{\nu'}^2 E}} E \\ \\ a_{33} = {{(1-\nu) E'} \over {(1-\nu)E' - 2{\nu'}^2 E}} E \end{matrix}\end{split}$
and
$$E = E_{1'}= E_{2'}$$ Young’s moduli in the plane of isotropy $$E'= E_{3'}$$ Young’s moduli in the direction normal to the plane of isotropy $$\nu = \nu_{1'2'}$$ Poisson’s ratio characterizing lateral contraction in the plane of isotropy when tension is applied in this plane $$\nu' = \nu_{1'3'} = \nu_{2'3'}$$ Poisson’s ratio characterizing lateral contraction in the plane of isotropy when tension is applied in the direction normal to it $$G = G_{1'2'}$$ shear modulus for the plane of isotropy, and $$G_{1'2'} = E_{1'}/[2(1+\nu_{1'2'})]$$. $$G' = G_{1'3'} = G_{2'3'}$$ shear modulus for any plane normal to the plane of isotropy.
The conversion of stress and strain tensors from local to global axes and vice-versa is obtained by the application of the usual matrix rotation operations.
Let $$\tau$$ be defined as the magnitude of the tangential traction component on the weak plane:
(3)$\tau = \sqrt{\sigma^2_{1'3'} + \sigma^2_{2'3'}}$
Also, $$\gamma$$ is the strain variable associated with $$\tau$$:
(4)$\gamma = \sqrt{\varepsilon^2_{1'3'} + \varepsilon^2_{2'3'}}$
The local incremental stress-strain equations (Equation (1)) expressed using the above generalized stress and strain components are:
(5)$\begin{split}\begin{matrix} \Delta \sigma_{1'1'} = a_{11} \Delta \varepsilon^e_{1'1'} + a_{12} \Delta \varepsilon^e_{2'2'} + a_{13} \Delta \varepsilon^e_{3'3'} \\ \\ \Delta \sigma_{2'2'} = a_{12} \Delta \varepsilon^e_{1'1'} + a_{11} \Delta \varepsilon^e_{2'2'} + a_{13} \Delta \varepsilon^e_{3'3'} \\ \\ \Delta \sigma_{3'3'} = a_{13} \Delta \varepsilon^e_{1'3'} + a_{12} \Delta \varepsilon^e_{2'2'} + a_{33} \Delta \varepsilon^e_{3'3'} \\ \\ \Delta \tau = 2G \Delta \gamma \end{matrix}\end{split}$
Yield and Potential Functions, Plastic Corrections, and Large-Strain Update to Orientation
The yield and potential functions, plastic corrections, and large-strain update to orientation are similar to those joint-related sections described in the ubiquitous-joint model.
Implementation Procedure
The coefficients of the global elasticity matrix are computed and stored in the initialization phase. New stresses are estimated using the elasticity matrix and the total strain increments for the step. The global stress tensor then is resolved in the local axes of the weak plane, and the local yield conditions are tested. If yielding is detected, a relevant local stress correction (derived using the flow rule) is calculated as described above. The stress correction then is resolved into global axes and added to the elastic stress estimate. Finally, in large strain, adjustment of the weak plane orientation is performed to account for rigid body rotations.
ubiquitous-anisotropic Model Properties
Use the following keywords with the zone property (FLAC3D) or block zone property (3DEC) command to set these properties of the anisotropic-elasticity ubiquitous-joint model.
ubiquitous-anisotropic
dip f
dip angle [degrees] of weakness plane
dip-direction f
dip direction [degrees] of weakness plane
joint-cohesion f
joint cohesion, $$c_j$$
joint-dilation f
joint dilation angle, $$\psi_j$$. The default is 0.0.
joint-friction f
joint friction angle, $$\phi_j$$
joint-tension f
joint tension limit, $$\sigma^t_j$$. The default is 0.0.
normal v
normal direction of the weakness plane, ($$n_x$$, $$n_y$$, $$n_z$$)
normal-x f
$$x$$-component of the normal direction to the weakness plane, $$n_x$$
normal-y f
$$y$$-component of the normal direction to the weakness plane, $$n_y$$
normal-z f
$$z$$-component of the normal direction to the weakness plane, $$n_z$$
poisson-normal f
Poisson’s ratio characterizing lateral contraction in the plane of isotropy when tension is applied normal to the plane, $${\nu}'$$ = $$\nu_{13}$$ = $$\nu_{23}$$
poisson-plane f
Poisson’s ratio characterizing lateral contraction in the plane of isotropy when tension is applied in the plane, $$\nu$$ = $$\nu_{12}$$
shear-normal f
shear modulus for any plane normal to the plane of isotropy, $$G'$$ = $$G_{13}$$ = $$G_{23}$$
young-plane f
Young’s modulus in the plane of isotropy, $$E$$ = $$E_1$$ = $$E_2$$
young-normal f
Young’s modulus normal to the plane of isotropy, $$E'$$ = $$E_3$$
Notes
• Only one of the two options is required to define the elasticity: bulk modulus $$K$$ and shear modulus $$G$$, or Young’s modulus $$E$$ and Poisson’s ratio $$\nu$$. When choosing the latter, Young’s modulus $$E$$ must be assigned in advance of Poisson’s ratio $$\nu$$.
• Only one of the three options is required to define the orientation of the weakness plane: dip and dip-direction; a norm vector ($$n_x, n_y, n_z$$); or three norm components: $$n_x$$, $$n_y$$, and $$n_z$$.
• The tension cut-off is $${\sigma}^t = min({\sigma}^t, c/\tan \phi)$$.
• The joint tension limit used in the model is the minimum of the input $$\sigma^t$$ and $${c_j}/{\tan \phi_j}$$.
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All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
perplexus dot info
BRIAN = LINDA = LEVIK = CORAL (Posted on 2006-12-08)
Can you find a five-figure number, with distinct digits between 1 and 9, which satisfies all of the following encoded equations?
BRIAN x 2 = CONGA
LINDA x 3 = NAILER
LEVIK x 4 = VARIED
CORAL x 6 = NESTED
Repeated letters within an equation indicate the replication of digits. However, the same letter in different equations does not necessarily refer to the same digit.
See The Solution Submitted by Josie Faulkner Rating: 4.3750 (8 votes)
Comments: ( You must be logged in to post comments.)
Subject Author Date re(3): the programmatic way Josie Faulkner 2006-12-09 03:40:16 re(2): the programmatic way Charlie 2006-12-08 23:38:55 re: the programmatic way Josie Faulkner 2006-12-08 18:57:20 re: Solution ala verbose Josie Faulkner 2006-12-08 18:53:25 re: Busy Busy Busy [spoiler] Josie Faulkner 2006-12-08 18:49:28 Busy Busy Busy [spoiler] Vernon Lewis 2006-12-08 15:50:41 the programmatic way Charlie 2006-12-08 11:02:45 Solution ala verbose Leming 2006-12-08 10:08:45
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# Lorenz Curve
Reviewed by Vineeth | Updated on Aug 27, 2020
Catalogue
## Introduction
Lorenz curve is a pictorial portrayal of inequality in income or inequality in wealth. It was developed by Max Lorenz in the year 1905. Mr Lorenz was an American economist. The graph outlines wealth or income against the population on the horizontal axis, while the vertical axis depicts income or wealth. Therefore, an x value of 54 and a y value of 12.4 says that the bottom 54% of the total population is in control of 12.4% of the overall wealth or income.
A Lorenz curve is generally co-occurred with a straight line having a slope of 1 and depict absolute balance in wealth or income distribution. The Lorenz curve lies underneath and represents the real distribution. The area across the straight and curved line is the Gini coefficient. It expressed as a ratio of the area below the straight line. The Gini Coefficient is one of the measurements of inequality.
## Why Lorenz Curve is important?
Lorenz curve is mostly used in representing economic inequality. However, it can also be used in representing inequalities in the distribution in any process or system. The level of unequal distribution increases when the Lorenz curve drifts away from the baseline. In economics, the Lorenz curve is used to represent inequality of either income or wealth. Note that wealth and income should not be used synonymously as it is possible that an individual with high net worth can have low income and an individual with a high income have a low net worth.
## Industry Impact
The Gini coefficient, which is used to show the level of inequality ranges between 0%(0) to 100% (1). A Gini coefficient of 0 correlates to absolute equality. This says that all individuals possess an equal amount of wealth or income. The absolute equality which is plotted as a Lorenz curve is a straight diagonal line whose slope is always 1. This is because the area across the curve will be zero, and hence the Gini coefficient will also turn out to be a zero. A Gini coefficient of 1 shows that one individual account for all the incomes earned or all the wealth.
## Conclusion
Lorenz curve is typically used to describe inequality in the income. It can also be used to depict inequality in other systems. The area between the straight and curved lines represent the Gini coefficient.
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Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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## #1 2011-08-19 23:57:05
bobbym
Online
### Squares and circles.
Problem was just posed by ganesh.
#### ganesh wrote:
Find the ratio of the areas of the incircle and circumcircle of a square.
I know there is a lot of ways to do this but supposing you did not have any idea how to solve this. Geogebra to the rescue!
1) Make a 4 sided regular polygon. ( a square )
2) Use the 3 point circle option to draw the outer circle using 3 of the vertices of the square.
3) Draw the diagonal line segments to get the center of the square.
4) Put a point F on the square. Make that line segment from the center to F parallel with the x axis.
5) use the point and radius circle option to make a point from the center of the square to f.
6) Get areas of both circles.
7) Take the ratio:
8) use one of the free vertices to expand the inner circle. Find the new areas. What do you deduce?
Looks like the ratio of the areas is 1 / 2. Not rigorous but definitely enough to go to war with!
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
## #2 2011-08-20 01:33:00
anonimnystefy
Real Member
Offline
### Re: Squares and circles.
hi bobbym
i solved this before,and it is very easy.
the radius of the inner circle is a/2 where a is the side of the square.so it's area is A1=pi*a^2/4
the radius of the outer circle is a/sqrt(2).it's area is A2=pi*a^2/2.
Last edited by anonimnystefy (2011-08-20 01:33:26)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
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Three Phase System
Definition: The system which has three phases, i.e., the current will pass through the three wires, and there will be one neutral wire for passing the fault current to the earth is known as the three phase system. In other words, the system which uses three wires for generation, transmission and distribution is known as the three phase system. The three phase system is also used as a single phase system if one of their phase and the neutral wire is taken out from it. The sum of the line currents in the 3-phase system is equal to zero, and their phases are differentiated at an angle of 120º
The three-phase system has four wire, i.e., the three current carrying conductors and the one neutral. The cross section area of the neutral conductor is half of the live wire. The current in the neutral wire is equal to the sum of the line current of the three wires and consequently equal to √3 times the zero phase sequence components of current.
The three-phase system has several advantages like it requires fewer conductors as compared to the single phase system. It also gives the continuous supply to the load. The three-phase system has higher efficiency and minimum losses.
The three phase system induces in the generator which gives the three phase voltage of equal magnitude and frequency. It provides an uninterruptible power, i.e., if one phase of the system is disturbed, then the remaining two phases of the system continue supplies the power.The magnitude of the current in one phase is equal to the sum of the current in the other two phases of the system.
The 120º phase difference of the three phases is must for the proper working of the system. Otherwise, the system becomes damaged
Types of Connections in Three-Phase System
The three-phase systems are connected in two ways, i.e., the star connection and the delta connection. Their detail explanation is shown below.
Star Connection
The star connection requires four wires in which there are three phase conductors and one neutral conductor. Such type of connection is mainly used for long distance transmission because it has a neutral point. The neutral point passes the unbalanced current to the earth and hence make the system balance.
The star connected three phase systems gives two different voltages, i.e., the 230 V and 440V. The voltage between the single phase and the neutral is 230V, and the voltage between the two phases is equal to the 440V.
Delta Connection
The delta connection has three wires, and there is a no neutral point. The delta connection is shown in the figure below. The line voltage of the delta connection is equal to the phase voltage.
Connection of Loads in Three Phase System
The loads in the three-phase system may also connect in the star or delta. The three phase loads connected in the delta and star is shown in the figure below.
The three phase load may be balanced or unbalanced. If the three loads (impedances) Z1, Z2 and Z3 has the same magnitude and phase angle then the three phase load is said to be a balanced load. Under balance condition, all the phases and the line voltages are equal in magnitude.
5 thoughts on “Three Phase System”
1. Thank you for your information.
The value label on the first figure is wrong. The phase difference between two consequence peak is 120. The second peak (phase 2) is at 210 …
The phase 1 ends up its period at 360, so on…
2. ODYEK CARLOS KIM
Thanks so much for the knowledge you people have added to me. I have understood how 3 phase works. Thanks
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## anti aliasing filter
Started by 6 years ago10 replieslatest reply 6 years ago236 views
Hi,
I want to sample a signal in 5 GHz and I assume there is a white noise of level m0.
Because I want design an antialiasing filter, when I sampled this signal this noise in higher frequency is replicated to desire frequency band.
How can I calculate total noise level in desired band? or maximum noise level in desired band?
I mentioned that noise in frequency 0-5GHz ,5-10GHz, 10-15GHz, …, 0.995-1THZ,1- 1.005THZ, 1.005-1.01THZ, … is replicated to 5GHz desired frequency.
Thanks.
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You need to look at integrated noise after the filter which is given by (m0)*(equivalent noise bandwidth of filter). For example: if you use a first order filter, the integrated noise is (m0)*(pi/2)*(w_3dB). Depending on the filter order, the equivalent noise bandwidth will change.
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but,
suppose: fs is frequence sample and fb is desired band and k is an integer value from minus infinity to plus infinity.
then we know when we sampled a signal noise in k*fs+fb frequency in original signal is replicated to fb desired bandwidth, so noise is increased.
i want to know whats maximum value of noise after sampling and how calculted, or how can i approximate or evaluate noise in desired band after sampling
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A white noise has infinite energy, if you do not filter the signal before sampling, you will have infinite noise energy. However, a true white noise do not exist in real-world. The thermal noise is not a real white noise, as its power density decays to zero at extremely high frequency. Also, your ADC, and all other components before him, has limited pass-band. So, you need to know the pass-band of your system in order to get an answer for your question.
Check this reference
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thanks for answer, your are right, but mathematically we impose white noise is extended to infinity. i want a method to find total noise power to estimate the level of noise to design anti aliasing filter ripple in pass band and stop band
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I have never design an analog anti-aliasing filter. However, I know that If you are going to model your input as a white noise, you have to set a band limit to your filter, a frequency point where full attenuation is obtained after it.
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You are sampling at $$F_s$$. Just from sampling, the signal at any frequency $$f$$ gets contributions from $$f \pm F_s, f \pm 2F_s, \cdots$$.
If the noise is truly white and uncorrelated, then the total noise power from aliasing will add -- not the noise amplitude. So, let $$y(f)$$ be your signal after filtering and before sampling at frequency $$f$$. The total noise power in your sampled signal is:
(sorry for the math-messing; this forum needs a preview mode)
$x_n \left ( f \right )^2 = \sum_{k=1}^\infty \left( y \left( f + k F_s \right)^2 + y \left( f - k F_s \right)^2 \right)$
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if i want design a 14 bit adc with supply voltage as 1v then total noise in pass band must be smaller than 1 LSB=(1/2^14).
if we assume a white noise then whats the max value of noise in pass band and stop band with attention to this that noise in upper frequencies are replicated to our pass band after sampling.
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But you didn't. What's missing? I can't tell.
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hi
your formula, that you write is completely correct.but it does not determine any way to calculate gain in stop band OR SLOPE of gain in stop band for getting special noise level in desired band.
suppose thermal noise level in 0-5GHZ is m0 and also to infinity frequency. we know noise in frequency 5ghz to infinity is replicated after sampling to desired band namely 0-5ghz.
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