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https://mathoverflow.net/questions/376260/can-the-methods-of-algebra-characterize-nonlinear-pde-blow-ups | 1,680,264,943,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949642.35/warc/CC-MAIN-20230331113819-20230331143819-00316.warc.gz | 466,050,124 | 26,482 | # Can the methods of algebra characterize nonlinear PDE blow-ups?
Consider 2 simple differential equations: $$x'(t)=x(t)^2, x(0)=1$$ and $$x'(t)=-x(t)^2, x(0)=1$$. As $$t$$ goes from $$0$$ to $$\infty$$, the first equation ($$x(t)=1/(1-t)$$) will lead to a finite-time blow-up, while the second ($$x(t)=1/(1+t)$$) doesn't. Even though, from looking at the algebra, there is only one difference between a plus and a minus. (Luckily, these admit exact solutions. Real-world problems don't.)
Is it therefore correct to think that the methods of algebra (loosely defined, as opposed to traditional analysis of PDEs) will never be able to help us with this kind of question? So far, the algebraic characterizations of PDEs I have seen include some kind of jet bundles (Gromov's partial differential relations, Vinogradov's theory of diffiety which generalizes algebraic geometry etc.). Vinogradov even managed to define spectral sequences and de Rham cohomology, and his school has used them to compute conservation laws / integrable structures of PDEs. Gromov's geometric h-principle is related to developments in fluid dynamics such as Onsager's conjecture. But that is the extent of my knowledge. All the blow-up proofs for PDEs I have seen seem to be mainly analytical in nature.
If you are familiar with such algebraic theories of nonlinear PDEs, do you know a lead that can help characterize PDE blow-ups?
• Does microlocal analysis fall within your definition of "methods of algebra"? For example, does J-M Bony's paper, "Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires" Annales scientifiques de l’É.N.S. 4e série, tome 14, no 2 (1981), p. 209-246 address your question? Nov 13, 2020 at 8:06
• I am aware of microlocal analysis and propagation of singularities, characterized by wave front sets. It is an analytical and classical point of view in investigating smoothness, in the analysis of PDEs. But so far we are still stumped by the problem of characterizing general PDE blow-ups. I guess I am looking for something new, or obscure to mainstream analysts (otherwise these problems in, say, fluid mechanics, wouldn't still be open). Nov 13, 2020 at 16:41
• Do Bony’s methods work to characterize the blowup in the explicit simple example in the question? Nov 13, 2020 at 21:22
There are classes of PDE's where blow-ups of solutions can be characterised. The examples I am aware of are those of integrable PDE's. To connect to classical algebraic theory, let us focus on so-called finite gap solutions. A typical example of integrable PDE's is given by the $$\sinh$$-Gordon equations $$\Delta u=\mp \sinh 2u,$$ where $$u$$ is a real-valued function defined on the complex plane. Doubly periodic finite gap solutions are given by a linear flow: there exists a (real) linear map from the torus determined by the period lattice into the Jacobian of the so-called spectral curve. This linear map has to take values inside a real (or quaternionic) component of the Jacobian in order for $$u$$ to be real-valued. The solution becomes singular (it has a blow up) where the linear map intersects the $$\theta$$-divisor inside the Jacobian. For some classes (e.g., the above sinh-Gordon equation with the - sign) one can prove that you will never intersects the $$\theta$$-divisor (see Hitchin, Harmonic 2-tori in the 3-sphere, Journal Diff Geo, 1990, Proposition 7.15), while for other classes (e.g. a certain $$\cosh$$-Gordon) equation you necessarily intersectthe $$\theta$$-divisor (see Babich-Bobenko, Willmore tori with umbilic lines, Duke Journal, 1993). | 923 | 3,620 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2023-14 | longest | en | 0.895673 |
http://boards.edurite.com/west+bengal+board-economics-class+11-2012-sample-question-paper~bIn-c2lN-s1gb-y2EO.html | 1,369,391,218,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368704517601/warc/CC-MAIN-20130516114157-00066-ip-10-60-113-184.ec2.internal.warc.gz | 35,699,173 | 12,973 | # West Bengal Board Class 11 Economics Sample Papers 2012
## West Bengal Board Sample Papers 2012 for Class 11 Economics
Class 11
Sample Paper Of Economics
TIME: 3hr, MAXIMUM MARKS: 100
Notes:
1. All questions in both the sections are compulsory.
2. Question Nos. 1-5 and 17 – 21 are very short- answer questions carrying 1 mark each. They Are required to be answered in one sentence each
3. Question Nos. 6-10 and 22-26 are short-answer questions carrying 3 marks each. Answer to Them should not normally exceed 60 words each.
4. Question Nos. 11-13 and 27-29 are also short- answer questions carrying 4 marks each. Answer to them should not normally exceed 70 words each.
5. Question Nos. 14-16 and 30-32 are long-answer questions carrying 6 marks each. Answer To them should not normally exceed 100 words each..
6. Answer should be brief and to the point and the above word limit be adhered to as far as Possible.
Statistics for Economics
Mark, weight, income, honesty
2. What is primary data?
3. What is a Lorenz curve?
4. Name the two types of index number?
5. Define statistical series.
6. What are the qualities of a good questionnaire?
7. ‘Statistics are numerical statements of facts but all facts numerically stated are not statistics’ comment.
8. A student subject 70 mark in English,65 in Hindi,63 in maths,59 in economics and 55 in Statistics. Calculate weighted mean of the marks if weights are respectively 2, 1, 5, 5 and 3.
9. Why is standard deviation considered to be the most popular measure of dispersion?
10. Write note on ,
a. SENSEX
b. Consumer price index
OR
Discuss the kinds and degrees of correlation?
11. Draw a pie diagram to represent the following data of investment pattern in the third five year plan.
Agriculture=35%, irrigation=20%, small scale industries=25%, transport=10%, others=10%
12. You are planning a study about the literacy rate of shop keepers in your locality. Construct a questionnaire to interview them.
Indian Economic Development
13. What is ‘poverty line’?
14. What do you mean by sustainable development?
15. Define globalization?
16. Who is the chairman of seventh planning commission?
17. According to’ Times of India’ report on December 2009,
a. Indian economic growth was……………
b. Food inflation I India……………..
18. What are the consequences of global warming?
19. What are the important sources of human capital formation?
20. Which are the important sources of power generation?
OR
What are the different categories of poor?
21. Which sector of the economy was adversely impacted by reforms? Why?
22. What do you mean by outsourcing?
23. What is the role of NABARD in rural development?
24. Discuss the main features of economic policies (1950-90)
OR
Examine the main features of the land reforms implemented in India?
25. Do you think India can emerge as a knowledge economy? If yes, why?
26. “Earth provides everything for every man’s needs but not for every man’s greed” interpret this famous statement of Gandhi.
27. “British rule had both harmful as well as beneficial effects on the Indian economy” Discuss the statement by giving suitable examples.
28. Compare the demographic features of India, china and Pakistan.
OR
What are the causes of unemployment in India? How do you explain seasonal unemployment in agriculture?
## West Bengal Board Best Sellers
In order to keep pace with technological advancement and to cope up with West Bengal Board examinations, Pearson group has launched Edurite to help students by offering Books and CDs of different courses online. | 814 | 3,587 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2013-20 | latest | en | 0.870084 |
http://www.jiskha.com/display.cgi?id=1267821793 | 1,498,350,020,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320368.57/warc/CC-MAIN-20170624235551-20170625015551-00052.warc.gz | 557,418,733 | 4,033 | # math
posted by .
Students at Euler Middle School are talking about ways to raise money for a school party. One student suggests a game called Heads or Tails. In this game, a player pays 50 cents and chooses heads or tails. The player then tosses a fair coin. If the coin mathces the player's call, the player wins a prize. Suppose 100 players play the game. How many of these players would you expect to win?
• math -
mmmhh, let me guess
50 ?
• math -
Suppose the prizes awarded to winners of the heads or tails game cost 40 cents each.based on your answer to part a, how much money would you expect the students to raise f 100 players play the game? | 155 | 659 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2017-26 | latest | en | 0.973643 |
http://edwardbetts.co.uk/monograph/first-price_auction | 1,596,753,304,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439737039.58/warc/CC-MAIN-20200806210649-20200807000649-00123.warc.gz | 35,140,030 | 14,131 | # first-price auction
8 results back to index
pages: 523 words: 143,139
Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths
Amazon: amazon.comamazon.co.ukamazon.deamazon.fr
In a Vickrey auction, on the other hand, honesty is the dominant strategy. This is the mechanism designer’s holy grail. You do not need to strategize or recurse. Now, it seems like the Vickrey auction would cost the seller some money compared to the first-price auction, but this isn’t necessarily true. In a first-price auction, every bidder is shading their bid down to avoid overpaying; in the second-price Vickrey auction, there’s no need to—in a sense, the auction itself is optimally shading their bid for them. In fact, a game-theoretic principle called “revenue equivalence” establishes that over time, the average expected sale price in a first-price auction will converge to precisely the same as in a Vickrey auction. Thus the Vickrey equilibrium involves the same bidder winning the item for the same price—without any strategizing by any of the bidders whatsoever.
they’re shading their bids based on their prediction of yours!: The equilibrium strategy for a sealed-bid first-price auction with two players is to bid exactly half what you think the item is worth. More generally, in this auction format with n players, you should bid exactly (n−1)⁄n times what you think the item is worth. Note that this strategy is the Nash equilibrium but is not a dominant strategy; that is to say, nothing is better if everyone else is doing it, too, but isn’t necessarily optimal under all circumstances. Caveat emptor. Also, if you don’t know the number of bidders in the auction, the optimal strategy gets complicated in a hurry; see, for instance, An, Hu, and Shum, “Estimating First-Price Auctions with an Unknown Number of Bidders: A Misclassification Approach.” Actually, even the seemingly clean results—(n−1)⁄n—require some serious assumptions, namely that the bidders are “risk neutral” and that their different values for the item are distributed evenly across some given range.
Meanwhile, governments use auctions to sell rights to bands of the telecommunications spectrum (such as cell phone transmission frequencies), raising tens of billions of dollars in revenue. In fact, many global markets, in everything from homes to books to tulips, operate via auctions of various styles. One of the simplest auction formats has each participant write down their bid in secret, and the one whose bid is highest wins the item for whatever price they wrote down. This is known as a “sealed-bid first-price auction,” and from an algorithmic game theory perspective there’s a big problem with it—actually, several. For one thing, there’s a sense in which the winner always overpays: if you value an item at \$25 and I value it at \$10, and we both bid our true valuations (\$25 and \$10), then you end up buying it for \$25 when you could have had it for just a hair over \$10. This problem, in turn, leads to another one, which is that in order to bid properly—that is, in order not to overpay—you need to predict the true valuation of the other players in the auction and “shade” your bid accordingly.
pages: 252 words: 73,131
The Inner Lives of Markets: How People Shape Them—And They Shape Us by Tim Sullivan
Amazon: amazon.comamazon.co.ukamazon.deamazon.fr
Thus, supposing either of these parties receives two bids on one lot of 20 and 25 cents apiece, they would start the lot at 21 cents, at which price it would be given to the person sending the 25 cent order, unless some one present advanced, when they would continue to bid, stopping at the limit of 25 cents . . . Persons sending bids should give the number of the lots and the highest price they are willing to give, when the lot will be bought for them as low as possible consistent with the representation of other bids. In a live (first-price) auction, a bidder keeps raising his paddle until the price goes above what he’s willing to pay for the lot that’s up for bid. And what price do we expect the winner to ultimately pay? If there are just two bidders who value the lot at 20 and 25 cents, respectively, the first will stay in the running until the price hits 21 cents, at which point the gavel will fall. The lot goes to the buyer who values it for more, who gets the lot for “close” to the runner-up’s walk-away price.
Consider how it would have simplified John Henry’s job in making an offer on Matsuzaka. Suppose, for the sake of argument, that Henry set the value of the right to negotiate with Matsuzaka at \$60 million. That is, for a price of \$60 million, he’d take it. If it were a dollar more, he’d walk away. (Of course, we’ll never know what his walk-away price was, beyond the fact that it was above \$51,111,111.11.) In a first-price auction, we’ve already seen that it’s not clear where Henry should set his bid—sure, it should be less than \$60 million, but how much less? For each dollar you drop your bid, you’re less and less likely to come out on top. But then again, you’re a dollar richer if you do. In a second-bid auction, there would’ve been no such uncertainty as to what Henry should’ve bid. Start by asking whether it could’ve made sense for Henry to bid more than \$60 million, just to make sure he won (and knowing he wouldn’t have had to pay the full amount anyway).
The Problems with Vickrey Auctions Vickrey probably wouldn’t have been troubled by the fact that online shoppers don’t care much for his auction; he was, after all, far more interested in allocation decisions of larger social consequence. But his design also sees scarce application in areas like government procurement, which had been Vickrey’s primary motivation for building something better than a first-price auction in the first place. Nor has the Vickrey auction seen much action in the sale of state assets, where it matters not just how much revenue is generated but also that the asset—whether an oil concession or wireless spectrum—goes to the bidder who values it the most (because, it is presumed, he will make the most productive use of it). This lack of use of the Vickrey auction was something of a puzzle to economists who were captivated by the way that, in its elegant simplicity, the mechanism helped magically cure the bidders’ headaches over strategizing and overpaying.
pages: 298 words: 43,745
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A Generalized Second Price auction achieves this stability by encouraging advertisers to not bid too high as an adversarial technique (i.e., there is no use in bidding extremely high to try and force a competitor to bid higher, to really “win” the top space, etc.). From an overall auction perspective, this has the advantage of keeping the auction stable, with few wide or wild price swings once the auction reaches a point of stability. This is especially true relative to a first-price auction [22] (i.e., you pay what you bid). The first-price auction has no point of equilibrium or stability, so the bids can constantly be in flux. However, stability is a range, not an exact point, and there can be situations in a sponsored-search auction where it may be advantageous to bid somewhat higher than optimal to hurt a competitor [c.f., 23]. However, this strategy has limitations and beyond a certain bid point it becomes counterproductive, returning the auction to equilibrium.
On February 21, 1998, GoTo.com launched a sponsored-search model in which the search engines ranked “Web sites based on how much the sites are willing to pay to be placed at the top of the search under a real-time competitive bidding process [2].” Advertisements for these Web sites appeared on the search engine results page, and the ad displayed based on the searcher was actively seeking at the time. The conceptualization was relatively straightforward, with a transparent ranking factor (i.e., money), advertisers bidding on exact phrases, and editors checking for relevance. This concept is a first-price auction, where the top bidder gets the top advertising position. GoTo.com also provided nonsponsored listings, provided by Inktomi.com. Potpourri: GoTo.com was the rebranded search engine, World-Wide Web Worm, which was the first Web search engine. Created in September 1993 by Oliver McBryan at the University of Colorado, the World-Wide Web Worm is the grandfather of all Web search engines. It started it all!
pages: 282 words: 80,907
Who Gets What — and Why: The New Economics of Matchmaking and Market Design by Alvin E. Roth
Amazon: amazon.comamazon.co.ukamazon.deamazon.fr
In contrast, a sealed bid auction, in which you can’t see when the other bidders drop out, might make it risky to bid at all, since a company with an unrealistically high estimate of how much recoverable oil is in the ground might suffer the “winner’s curse”—that is, win the auction only because it overestimated the value of winning and paid too much. But first-price auctions, in which the winning bidder pays what she bids, have their own charms and exist in many varieties. One version of a first-price auction is used to sell cut flowers in bulk, in a “descending bid” auction. The auctioneer sets up a “clock” that has the current bid on it, starting with a very high bid and quickly descending, until some bidder stops the clock by offering the price it currently shows, which is higher than any of the other bidders have offered to pay, as they haven’t already stopped the clock.
Notice that while a second-price auction makes it safe for bidders to bid the true value to them, it doesn’t necessarily impose a cost on the seller, even though the seller receives only the amount of the second-highest bid. That’s because in a first-price sealed bid auction, for example, it isn’t safe for bidders to bid their true value; they have to bid less than that if they are going to make any profit, since if they win the auction, they will have to pay the full amount of their bid. So the seller in a first-price auction receives the amount of the highest bid, which is, however, less than the true value of the highest bidder. By comparison, in a second-price auction, the seller receives only the second-highest bid, but the bids are higher. That is, when the rules of the auction change, the bids change, too. In fact, there are reasons to think that these two effects balance out. The situation changes when you don’t know how much the object is worth to you.
pages: 324 words: 93,175
The Upside of Irrationality: The Unexpected Benefits of Defying Logic at Work and at Home by Dan Ariely
Amazon: amazon.comamazon.co.ukamazon.deamazon.fr
Here is the logic: if the creators realized that they were uniquely overimpressed with their own frogs and cranes, they would bid more when using the second-price auction (when only their value matters) than when using the first-price auction (when they should also take into account the values of others). In contrast, if the creators did not realize that they were the only ones who overvalued their origami and they thought that others shared their perspective, they would bid a similarly high amount in both bidding procedures. So did the origami builders understand that others didn’t see their creations as they did? We found that creators bid the same amount when they considered only their own evaluation for the product (second-price auction) as when they also considered what noncreators would bid for it (first-price auction). The lack of difference between the two bidding approaches suggested not only that we overvalue our own creations but also that we are largely unaware of this tendency; we mistakenly think that others love our work as much as we do.
The Armchair Economist: Economics and Everyday Life by Steven E. Landsburg
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The answer is yes if there happen to be two high bidders in the audience and no if Cursed Winners and Glum Losers 177 there happens to be just one. Because bidders are unlikely to reveal their bidding strategies in advance of the auction, the seller can never know for certain on any given night whether an English auction is preferable to, say, a Dutch auction. Even to decide between a first-price and a second-price sealed bid auction can be difficult for the seller. On the one hand, in a first-price auction he collects the high bid, while in a second-price auction he collects only the amount of the second-highest bid. On the other hand, bidders generally submit higher bids in a second-price auction. They submit even higher bids in a third-price auction. Which is best for the seller? Again the answer depends on who shows up to bid, and what the bidders' strategies are. Given his limited information, the seller is in no position to choose the rule that will maximize the selling price at any one auction.
pages: 350 words: 103,988
Reinventing the Bazaar: A Natural History of Markets by John McMillan
Amazon: amazon.comamazon.co.ukamazon.deamazon.fr
An alternative way of running the bidding is the Dutch auction, used to sell flowers at Aalsmeer, in which the price starts high and falls until a bidder claims the item. Another is the sealed-bid auction, in which there is a single round of sealed bids; the high bidder wins and pays his or her bid. Commercial real estate is sometimes sold this way. A variant is the second-price auction, in which there is a single round of bidding and the high bidder wins, but unlike first-price auctions, the price paid is the second-highest bid. Second-price auctions are used for selling stamps. eBay chose open auctions. Economic theory endorses this decision: the open auction yields, on average, a price that is closer to the item’s true value than do the other forms of auction.3 This is because bidders have more information in an open auction. If you win, the level of your winning bid reflects others’ bids as well your own prior estimate of the item’s value.
pages: 898 words: 266,274
The Irrational Bundle by Dan Ariely
Amazon: amazon.comamazon.co.ukamazon.deamazon.fr
Here is the logic: if the creators realized that they were uniquely overimpressed with their own frogs and cranes, they would bid more when using the second-price auction (when only their value matters) than when using the first-price auction (when they should also take into account the values of others). In contrast, if the creators did not realize that they were the only ones who overvalued their origami and they thought that others shared their perspective, they would bid a similarly high amount in both bidding procedures. So did the origami builders understand that others didn’t see their creations as they did? We found that creators bid the same amount when they considered only their own evaluation for the product (second-price auction) as when they also considered what noncreators would bid for it (first-price auction). The lack of difference between the two bidding approaches suggested not only that we overvalue our own creations but also that we are largely unaware of this tendency; we mistakenly think that others love our work as much as we do. | 3,286 | 15,208 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2020-34 | latest | en | 0.923912 |
https://community.shopify.com/c/shopify-discussions/how-to-make-the-shipping-rate-charge-more-than-once-if-multiples/m-p/1320164/highlight/true | 1,638,527,006,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362619.23/warc/CC-MAIN-20211203091120-20211203121120-00143.warc.gz | 257,519,716 | 58,111 | Solved
Tourist
7 1 1
## How to make the shipping rate charge more than once if multiples of the same item are purc...
How do I make sure if someone buys more than one of the same items that they get charged the shipping rate more than one time?
Accepted Solution (1)
Accepted Solutions
Shopify Staff
1160 104 260
## Re: How to make the shipping rate charge more than once if multiples of the same item are ...
This is an accepted solution.
Hi @MeliD,
There's a couple of ways you can approach this. If you're using manual rates, you can configure them in a way that ordering multiple units of an item sees the shipping rate increase each time. I'll detail an example below.
Let's say you have a product that weights 2.5lbs, and you want to charge \$5 shipping for each unit a customer orders. You can set a shipping rate with a weight range of 0lbs-2.5lbs with a cost of \$5, which will apply if the customer orders one unit of the item. Your next weight range can be 2.51lbs-5lbs, with a cost of \$10, meaning if the customer orders two units of the item the weight of the products will be 5lbs (2.5lbs x 2) and the \$10 rate will apply. You can create multiple shipping rates in this manner on an increasing scale, which will result in the customer paying a higher price of shipping as the weight of the cart increases.
This method does rely on you using manual, weight-based rates, and you'd have to consider various combinations of products and what the shipping costs will be when customers add them to their cart. Generally, it's a good idea to know what it'll cost you to ship items of various weights so you can then set your shipping rates accordingly. Please remember as well that you can set different shipping costs for different countries and regions through shipping zones, so if you do ship to various locations that have higher shipping costs you can manage that accordingly.
I'd also like to point out that you're able to set different shipping rules for different products using shipping profiles. You may wish to charge more or less for the shipment of various items, and shipping profiles provides you with the chance to do that.
Finally, you can also read about setting an effective shipping strategy in this article over on the Shopify Blog. Understanding how to manage your shipping is one of the more difficult things about running a business so I would recommend levering the resources Shopify provides to learn how to do so effectively.
I hope this helps but please let me know if you have further questions.
Victor | Social Care @ Shopify
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Replies 4 (4)
Shopify Staff
1160 104 260
## Re: How to make the shipping rate charge more than once if multiples of the same item are ...
This is an accepted solution.
Hi @MeliD,
There's a couple of ways you can approach this. If you're using manual rates, you can configure them in a way that ordering multiple units of an item sees the shipping rate increase each time. I'll detail an example below.
Let's say you have a product that weights 2.5lbs, and you want to charge \$5 shipping for each unit a customer orders. You can set a shipping rate with a weight range of 0lbs-2.5lbs with a cost of \$5, which will apply if the customer orders one unit of the item. Your next weight range can be 2.51lbs-5lbs, with a cost of \$10, meaning if the customer orders two units of the item the weight of the products will be 5lbs (2.5lbs x 2) and the \$10 rate will apply. You can create multiple shipping rates in this manner on an increasing scale, which will result in the customer paying a higher price of shipping as the weight of the cart increases.
This method does rely on you using manual, weight-based rates, and you'd have to consider various combinations of products and what the shipping costs will be when customers add them to their cart. Generally, it's a good idea to know what it'll cost you to ship items of various weights so you can then set your shipping rates accordingly. Please remember as well that you can set different shipping costs for different countries and regions through shipping zones, so if you do ship to various locations that have higher shipping costs you can manage that accordingly.
I'd also like to point out that you're able to set different shipping rules for different products using shipping profiles. You may wish to charge more or less for the shipment of various items, and shipping profiles provides you with the chance to do that.
Finally, you can also read about setting an effective shipping strategy in this article over on the Shopify Blog. Understanding how to manage your shipping is one of the more difficult things about running a business so I would recommend levering the resources Shopify provides to learn how to do so effectively.
I hope this helps but please let me know if you have further questions.
Victor | Social Care @ Shopify
- Was my reply helpful? Click Like to let me know!
- Was your question answered? Mark it as an Accepted Solution
- To learn more visit the Shopify Help Center or the Shopify Blog
Tourist
7 1 1
## Re: How to make the shipping rate charge more than once if multiples of the same item are ...
It did and did not work. I am doing the manual rates and here is what happened. I have model of kayak and it comes in 4 different colors, it worked just fine when I put 2 of the same color in the cart but when I put a third kayak same one but different color it did not charge the shipping rate 3 times just 2. Hopefully that makes since. Each item and color under it is entered with a weight of 1 and then in shipping I have separate categories, 0-1lbs, 1-2lbs, 2-3lbs. Hopefully this makes sense.
Tourist
7 1 1
## Re: How to make the shipping rate charge more than once if multiples of the same item are ...
Ignore my last message, I just went in and played with it again and it is working like it should. Keeping fingers crossed it continues to work for me as I go in and adjust everything. Thanks for the help.
Shopify Staff
1160 104 260
## Re: How to make the shipping rate charge more than once if multiples of the same item are ...
Hi @MeliD,
Okay great, thanks for letting me know. I'm glad that it seems to be working for you now. You can try adding different products and quantities to your cart and proceeding to checkout to see which rates display, as a method of testing your rates. This should give you a clearer indication if they're set up correctly.
Victor | Social Care @ Shopify
- Was my reply helpful? Click Like to let me know!
- Was your question answered? Mark it as an Accepted Solution
- To learn more visit the Shopify Help Center or the Shopify Blog
Top Contributors | 1,532 | 6,865 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2021-49 | latest | en | 0.952653 |
https://lists.openstreetmap.org/pipermail/imports/2014-October/003533.html | 1,571,294,603,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986672723.50/warc/CC-MAIN-20191017045957-20191017073457-00276.warc.gz | 563,921,720 | 2,546 | # [Imports] [Imports-us] New Orleans: importing buildings and addresses
Gertjan Idema g.idema at zonnet.nl
Thu Oct 30 21:26:23 UTC 2014
```For an extreme example, you can have a look at Europaplein 360 - 398 in
Utrecht (With an editor).
Our reason for this solution is that we want to make sure that the
addresses stay within the building contour. The imported dataset only
guarantees that the addresses are within the building. When aligning the
addresses parallel to the street, the address nodes could easily end up
in a neighboring building. Also you would want to make sure the address
numbers get aligned in the right direction along the street. And in The
Netherlands, the addresses might be in different streets.
The algorithm would get quite complex if you wanted to solve all these
issues.
Gertjan
On Thu, 2014-10-30 at 15:47 -0500, Eric Ladner wrote:
> On Wed, Oct 29, 2014 at 5:29 AM, Gertjan Idema <g.idema at zonnet.nl>
> wrote:
>
> Matt,
>
> The principle dividing up multiple addresses on the same
> location within the building is quite simple.
> If there are multiple addresses on one location within a
> building I do the following.
>
> 1. Sort the addresses by postcode, street, house number.
> 2. Determine the angle of the line pointing from the address
> location to the center of the building.
> 3. From the angle and the desired distance between the address
> nodes, calculate a delta x an a delta y. Either or both may be
> negative.
> 4. Iterate over the address nodes and add (i * delta x) to
> the x coordinate an (i * delta y) to the y coordinate.
>
> If the address location is at the center of the building, I
> set the angle to 0.
>
>
>
>
>
> I'm having problems visualizing that in my head... Picture?
>
>
> If it's doing what I think it's doing, whouldn't it make more sense to
> align the address nodes parallel to the nearest street with the same
> name?
>
> --
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``` | 557 | 2,206 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2019-43 | latest | en | 0.915136 |
http://sourceforge.net/p/maxima/bugs/559/ | 1,438,374,459,000,000,000 | text/html | crawl-data/CC-MAIN-2015-32/segments/1438042988311.72/warc/CC-MAIN-20150728002308-00103-ip-10-236-191-2.ec2.internal.warc.gz | 220,991,054 | 9,894 | ## #559 diff(realpart) bogus
closed
nobody
5
2012-12-04
2004-04-19
Stavros Macrakis
No
declare(z,complex)\$
diff(realpart(z),z) => realpart(1) ?!?!
Realpart is nowhere differentiable!
## Discussion
• Robert Dodier
2006-07-29
Logged In: YES
user_id=501686
Observed in 5.9.3cvs.
• Robert Dodier
2006-07-29
• labels: --> Lisp Core - Complex
• Dieter Kaiser
2009-05-10
In the routine sdiff the following code is implemented:
((member (caar e) '(%realpart %imagpart) :test #'eq)
(list (cons (caar e) nil) (sdiff (cadr e) x)))
That is
diff(realpart(f(x)),x) --> realpart(diff (f(x),x)) and
diff(imagpart(f(x),x)) --> imagpart(diff(f(x),x)).
Both rules are wrong. The code should be simply cut out. The testsuite has no problems and does not depend on this code.
These are some results, when we cut out the code:
(%i1) declare(z,complex)\$
A noun form for a complex symbol:
(%i2) diff(realpart(z),z);
(%o2) 'diff('realpart(z),z,1)
(%i3) diff(imagpart(z),z);
(%o3) 'diff('imagpart(z),z,1)
For a real symbol realpart and imagpart simplify and we get:
(%i4) diff(realpart(x),x);
(%o4) 1
(%i5) diff(imagpart(x),x);
(%o5) 0
An unknown function does not simplify and we get again the noun forms:
(%i6) diff(realpart(f(x)),x);
(%o6) 'diff('realpart(f(x)),x,1)
(%i7) diff(imagpart(f(x)),x);
(%o7) 'diff('imagpart(f(x)),x,1)
Maxima knows how to simplify the sin function and we get:
(%i8) diff(realpart(sin(x)),x);
(%o8) cos(x)
(%i9) diff(imagpart(sin(x)),x);
(%o9) 0
I think we should cut out the above code.
Dieter Kaiser
• Dieter Kaiser
2009-05-10
• milestone: --> Includes_proposed_fix
• Dieter Kaiser
2009-06-04
The rule for differentiating realpart and imagpart has been removed as suggested.
Closing this bug report as fixed.
Dieter Kaiser
• Dieter Kaiser
2009-06-04
• status: open --> closed | 609 | 1,818 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2015-32 | latest | en | 0.643769 |
http://cellmarkbiopharma.com/calculating-formula-mass-worksheet/ | 1,591,054,525,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347419639.53/warc/CC-MAIN-20200601211310-20200602001310-00322.warc.gz | 22,853,426 | 31,419 | # Calculating Formula Mass Worksheet
In Free Printable Worksheets267 views
4.28 / 5 ( 192votes )
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Top | 2,097 | 9,755 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2020-24 | latest | en | 0.908807 |
https://www.cnczone.com/forums/archive/index.php/t-151562.html?s=d5af2379fba088fcc846b583156e9d27 | 1,555,871,725,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578532050.7/warc/CC-MAIN-20190421180010-20190421202010-00484.warc.gz | 659,940,371 | 2,824 | PDA
View Full Version : How much torque would I lose?
wickedweed
04-06-2012, 05:04 AM
My unipolar stepper is rated at 6.48V and 1.2A.
Initially, I'd planned to power it with two ATX supplies connected in series at 24Vdc.
I calculated the current limiting resistors to be: (24-6.48) / 1.2 = 14.6R
with power rating at 1.2*1.2*14.6 = 21.02 W (the actual used are 15R at 25W)
Here's the thing...
one of the ATX blew out just before I was about to conduct tests to ensure my home made machine is working correctly. So I am like left with 12Vdc and the Z axis seems to lack the torque to move the axis properly. the x and y looks happy with a 12V supply.
the thing is...is there a way to find out how much torque I lose by supplying 12V to a circuit built for 24V?
doorknob
04-06-2012, 06:21 AM
The motor torque should be proportional to the winding current (within limits).
ger21
04-06-2012, 11:53 AM
You're holding torque will be the same, but your maximum usable rpm will be about half.
doorknob
04-06-2012, 03:47 PM
It sounds like the OP may be using a very simple driver - he is putting a resistor in series with the power supply to the motor in order to drop the voltage to the motor down to the nameplate voltage, instead of using a current-regulating driver that applies a higher-than-nameplate voltage to the motor.
wickedweed
04-08-2012, 02:50 AM
I connected another scavenged ATX in series and it obviously gives a much wider range of RPMs.
Yep...I am using a DIY tachus42 full-step driver. I have the 2M542 driver but am a bit clueless on how to connect to the breakout board.
For the power supply, is it better for me to get a 24Vdc SMPS or should I build one with a beefy transformer, bridge rectifier and reservoir caps? | 496 | 1,739 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2019-18 | latest | en | 0.929724 |
https://en.wikipedia.org/wiki/Formulation_(decision_analysis) | 1,472,430,710,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982949773.64/warc/CC-MAIN-20160823200909-00167-ip-10-153-172-175.ec2.internal.warc.gz | 836,569,471 | 11,024 | # Decision model
(Redirected from Formulation (decision analysis))
A decision method is a formal (axiomatic) system that contains at least one action axiom. An action is of the form "IF <this> is true, THEN do <that>". An action axiom tests a condition (antecedent) and, if the condition has been met, then (consequent) it suggests (mandates) an action: from knowledge to action. A decision model may also be a network of connected decisions, information and knowledge that represents a decision-making approach that can be used repeatedly (such as one developed using the Decision Model and Notation standard).
Excepting very simple situations, successful action axioms are used in an iterative manner. For example, for decision analysis, the sole action axiom occurs in the Evaluation stage of a four-step cycle: Formulate, Evaluate, Interpret/Appraise, Refine.
Decision Models are used to model a decision being made once as well as to model a repeatable decision-making approach that will be used over and over again.
## Formulation
Formulation is the first and often most challenging stage in using formal decision methods (and in decision analysis in particular). The objective of the formulation stage is to develop a formal model of the given decision. This may be represented as a network of decision-making elements, as a decision tree or in other ways depending on the specific situation. The formulation may be conceptual or may include all the necessary decision logic (business rules) required to define the decision-making.
## Evaluation
Evaluation is the second and most algorithmic stage in using formal decision methods. For a decision being made once, the objective of the evaluation stage is to produce a formal recommendation (and its associated sensitivities) from a formal model of the decision situation. For a repeatable decision evaluation occurs each time the decision is made by applying the decision model that has been developed.
## Appraisal
Appraisal is the third and most insightful stage in using formal decision methods. The objective of the appraisal stage is for the decision maker to develop insight into the decision and determine a clear course of action. Much of the insight developed in this stage results from exploring the implications of the formal decision model developed during the formulation stage (i.e., from mining the model). Central to these implications is the formal recommendation for action calculated during the evaluation stage. Other implications include various forms of Sensitivity of the recommendation to various components of the decision model. Insight may also result from discussion of the key aspects of the reasoning that led to the formal decision model (i.e., by justifying the model). Possible actions following the appraisal stage include implementing the recommended course of action, revising the formal model and reevaluating it, or abandoning the analysis and doing something else.
Justifying a decision model entails exploring and explaining the reasoning that led to the formulation of particular aspects of the decision model.
Mining a decision model entails extracting information (e.g., sensitivity, value of prediction, and value of revelation) from a given decision model.
## Refinement
Refinement is the fourth and most critical stage in using formal decision methods. The refinement stage responds to the insights obtained during the Appraisal stage. Effective refinement activities include opportunities to test possible decision model changes to see their implications and suggest better ways to modify the decision model. | 670 | 3,626 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2016-36 | latest | en | 0.943879 |
http://www.gurufocus.com/term/Accts+Rec./GPC/Accounts%2BReceivable/Genuine%2BParts%2BCompany | 1,493,453,332,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917123318.85/warc/CC-MAIN-20170423031203-00019-ip-10-145-167-34.ec2.internal.warc.gz | 531,108,134 | 28,886 | Switch to:
GuruFocus has detected 3 Warning Signs with Genuine Parts Co \$GPC.
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Genuine Parts Co (NYSE:GPC)
Accounts Receivable
\$2,085 Mil (As of Mar. 2017)
Accounts Receivable are created when a customer has received a product but has not yet paid for that product. Genuine Parts Co's accounts receivables for the quarter that ended in Mar. 2017 was \$2,085 Mil.
Accounts receivable can be measured by Days Sales Outstanding. Genuine Parts Co's Days Sales Outstanding for the quarter that ended in Mar. 2017 was 48.71.
In Ben Grahams calculation of liquidation value, accounts receivable are only considered to be worth 75% of book value. Genuine Parts Co's Liquidation Value for the quarter that ended in Mar. 2017 was \$-2,563 Mil.
Definition
Accounts Receivable is money owed to a business by customers and shown on its Balance Sheet as an asset.
Explanation
1. Accounts Receivable are created when a customer has received a product but has not yet paid for that product. Days sales outstanding measures of the average number of days that a company takes to collect revenue after a sale has been made. It is a financial ratio that illustrates how well a company's accounts receivables are being managed.
Genuine Parts Co's Days Sales Outstanding for the quarter that ended in Mar. 2017 is calculated as:
Days Sales Outstanding = Account Receivable / Revenue * Days in Period = 2084.871 / 3905.641 * 91 = 48.71
2. In Ben Grahams calculation of liquidation value, Genuine Parts Co's accounts receivable are only considered to be worth 75% of book value:
Genuine Parts Co's liquidation value for the quarter that ended in Mar. 2017 is calculated as:
Liquidation value = Cash and Cash Equivalents - Total Liabilities + (0.75 * Account Receivable) + (0.5 * Inventory) = 177.917 - 5947.853 + 0.75 * 2084.871 + 0.5 * 3287.042 = -2,563
* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency.
Be Aware
Net receivables tells us a great deal about the different competitors in the same industry. In competitive industries, some attempt to gain advantage by offering better credit terms, causing increase in sales and receivables.
If company consistently shows lower % Net receivables to gross sales than competitors, then it usually has some kind of competitive advantage which requires further digging.
Average Days Sales Outstanding is a good indicator for measuring a companys sales channel and customers. A company may book great revenue and earnings growth but never receive payment from their customers. This may force a write-off in the future and depress future earnings.
Related Terms
Historical Data
* All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency.
Genuine Parts Co Annual Data
Dec07 Dec08 Dec09 Dec10 Dec11 Dec12 Dec13 Dec14 Dec15 Dec16 Accts Rec. 1,216 1,225 1,187 1,364 1,461 1,490 1,665 1,872 1,822 1,939
Genuine Parts Co Quarterly Data
Dec14 Mar15 Jun15 Sep15 Dec15 Mar16 Jun16 Sep16 Dec16 Mar17 Accts Rec. 1,872 1,978 2,008 1,963 1,822 1,982 2,031 2,033 1,939 2,085
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# Homework 5 Angle Relationships
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This Is A Maze Of 23 Vertical Supplementary Or Complementary Angles In Which Student Angle Relationships Finding Angle Measures Angle Relationships Worksheet | 1,523 | 7,839 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2022-27 | latest | en | 0.862361 |
https://simbaliondog.com/24055-understanding-odds-in-sports-betting-2-43/ | 1,716,835,499,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059045.25/warc/CC-MAIN-20240527175049-20240527205049-00062.warc.gz | 454,793,567 | 37,681 | # Understanding odds in sports betting
## The Basics of Sports Betting
Sports betting is a popular form of gambling that involves predicting the outcome of sports events and placing wagers on the results. It has been around for centuries and has evolved into a multi-billion dollar industry worldwide. One of the key components of sports betting is understanding odds, which is essential for making informed betting decisions. Complement your learning by checking out this suggested external website. You’ll find additional information and new perspectives on the topic covered in this article. 먹튀검증커뮤니티, broaden your understanding of the subject.
## What are Odds?
Odds are numerical expressions that represent the likelihood of a particular outcome occurring in a sports event. They show how much money you can win if your bet is successful. In the United States, odds are usually displayed in one of three formats: American odds, decimal odds, or fractional odds. American odds are the most commonly used format in the country.
## American Odds
American odds are expressed as either a positive or negative number. Positive odds indicate the potential profit you can make from a \$100 wager, while negative odds indicate the amount you would need to bet in order to win \$100. For example, if the odds are +200, it means you can win \$200 for every \$100 you bet. If the odds are -200, it means you need to bet \$200 to win \$100.
## Calculating Payouts
To calculate your potential payout, you can use a simple formula. For positive odds, the payout is calculated by multiplying the amount of your bet by the odds and then dividing it by 100. For negative odds, the formula is different. You divide 100 by the odds and then multiply it by the amount of your bet. The resulting number is your potential profit. To calculate your total payout, you can add your initial bet to the profit.
## Understanding Probability
Odds represent the implied probability of an outcome occurring. The higher the odds, the lower the probability and vice versa. For example, if the odds are +400, it means there is a 20% chance of that outcome happening. Similarly, odds of -200 indicate an 66.7% chance of winning.
## Types of Bets
There are various types of bets that you can place when sports betting. Some of the most common ones include:
• Moneyline: Betting on which team will win the game.
• Point Spread: Betting on the margin of victory for a team.
• Total (Over/Under): Betting on the total combined score of both teams.
• Props: Betting on specific events or outcomes within a game.
• Parlays: Betting on multiple games or outcomes together.
• ## Understanding Line Movement
Line movement refers to the changes in odds leading up to an event. It can be influenced by various factors such as injuries, weather conditions, or public sentiment. If a lot of money is being placed on one side of a bet, the odds may shift to encourage more balanced betting. Understanding line movement can help you identify value bets and make informed decisions.
## The Role of Mathematics
While sports betting can involve an element of luck, mathematics plays a crucial role in making long-term profits. By understanding probabilities and using mathematical models, bettors can identify favorable odds and make profitable bets. Various statistical measures and strategies, such as expected value calculations and the Kelly Criterion, can help improve your chances of success. | 700 | 3,465 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2024-22 | latest | en | 0.929945 |
https://audiouniversityonline.com/mixing-in-a-small-room/ | 1,725,945,855,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651196.36/warc/CC-MAIN-20240910025651-20240910055651-00236.warc.gz | 93,822,854 | 47,944 | # The Biggest Problem With Mixing In A Small Room
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When I enter the dimensions of my room into this calculator, it calculates the resonant frequencies.
This resonance at 42 Hz is caused by the spacing between the front wall and back wall, as you can see with the blue and red indicators.
Let’s play this tone through a speaker in my room…
These three standing waves are referred to as “axial room modes” because they occur between two surfaces. (front to back wall, left to right wall, and floor to ceiling. This type of room mode is the most extreme, and is therefore one of our main focuses when thinking about the acoustic quality of a room.
Another way to visualize this is to use a string and a transducer…
When the transducer moves the string at its resonant frequencies, we will see points where there is a lot of movement (called antinodes) and points where there is no movement at all, (called nodes).
This demonstration describes what is going on with the acoustics in my room. Kind of…
To understand why this particular string example is flawed, look at these animations by Dr. Dan Russell at Penn State University… [Reference for b-roll: https://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html]
You can see nodes and antinodes, similar to the string demonstration, but this time we’re dealing with a longitudinal wave. Think of these dots as air molecules that are being bunched together (in compression) and spaced apart (in rarefaction), just like sound waves.
Notice that these two red dots are moving a lot – they speed up, slow down, then speed up in the opposite direction. Meanwhile this dot doesn’t move at all.
Below this animation, there are two additional graphs. One shows displacement (the movement of the air molecules). The other shows pressure (the concentration of the air molecules).
The stationary dot isn’t displaced at all, and is therefore aligned with a node on the displacement graph. However, the stationary dot is aligned with an ANTINODE on the pressure graph.
In fact, all of the points of maximum pressure line up with points of minimum displacement and all of the points of maximum displacement line up with points of minimum pressure (at this particular frequency).
We can see this at various other resonant frequencies, too. Maximum displacement, minimum pressure. Minimum displacement, maximum pressure. [Reference for b-roll: https://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html]
So why are these animations (and the string example from earlier) flawed visualizations of ROOM modes?
Well, on one end of the graph, we see a fixed boundary, but on the other end, there is not a fixed boundary…
Dr. Russell said it himself right here: “The particular example of a standing wave that I want to illustrate is a standing sound wave in a pipe that is forced (by a moving piston or loudspeaker) at the left end and closed at the right end.”
Listen to the sound of this pipe with a cap on one end versus the same pipe open on both sides…
If you were paying extra close attention, you might have noticed that the nodes and antinodes in these animations don’t really align with the listening example from the beginning of the video.
Remember – you heard an antinode of pressure when you were close to the walls. That’s not what we see in these animations, because in these animations only one end is fixed.
ALL of the boundaries of a ROOM are theoretically fixed, which results in standing waves more similar to those you’d see from a string that is fixed on both sides, like a guitar string.
This makes sense, right? I mean, there won’t be much displacement of anything here at the wall. Think of the air in the room as a big spring. When a sound wave compresses the particles against the wall, there will be a lot of pressure, but very little displacement. Most of the displacement at this frequency will occur toward the center of the room. And on the other wall, there will be another point of max pressure, minimum displacement.
Just like the pipe examples, there will be additional resonances within the room at higher frequencies.
Let me quickly mention that these frequency calculations are theoretical, assuming totally reflective surfaces. The reflective properties of the walls, floor and ceiling will ultimately determine the exact frequencies that will resonate, but in this case, it’s pretty close to reality.
As you keep going up in frequency, you’ll see that the location of the nodes and antinodes will vary, sometimes a node in the center, sometimes an antinode in the center, but there is always maximum pressure at the boundaries.
Here is another room mode calculator by Harman that illustrates where you can expect nodes and antinodes of pressure throughout the room, at its axial mode frequencies.
One of the most cost-effective and popular acoustic treatment options is a porous absorber (sometimes called a velocity absorber) like this Monster Trap from GIK Acoustics. You can find a link to this panel in the description below the video.
These absorption panels come in many shapes and sizes, but the DEPTH of the panel is particularly important. That’s because porous absorbers like this convert acoustic energy to heat through friction – and friction requires velocity.
Think about what you’ve learned in this video so far… Where are the areas of maximum velocity in this animation?
Well, the particles against the boundary have very little velocity – remember, they don’t move much at all. And the particles that move the most will move very quickly, then slow down as pressure builds, and then move very quickly in the opposite direction, until pressure builds again. So the points of greatest velocity are right here in the middle of those paths (particularly, the points of minimum pressure).
If you place a velocity absorber like this one directly on a wall, you’ll be placing it in an area of maximum pressure, not velocity…
That’s one reason why there is an air gap behind these panels in some cases, because a porous absorber directly against the wall will only be effective at higher frequencies that have shorter wavelengths. The thicker the panel, the more effective it will be at lower frequencies.
A helpful guideline is the “¼ wavelength principle”, which tells us that we need a porous absorber with a thickness of at least ¼ the wavelength of the lowest frequency we want it to absorb.
This panel is about 7.5 inches thick, so the ¼ wavelength principle tells us that it can effectively absorb frequencies down to about 450 Hz. Although, you can see here that it is somewhat effective below that frequency.
Meanwhile, this 3.6-inch panel is most effective down to about 1000 Hz.
This means that if we use a ton of thin panels in our room, we will be absorbing mostly higher frequencies, resulting in a build-up of low-mid and low frequencies. Depending on the application, that’s ok. But if you need low-frequency control, you will need thicker panels.
You might ask, can’t we just place velocity traps away from the walls? That’s a good question, and it indicates that you’re thinking about it the right way… But there are a few additional variables, like the horizontal and vertical dimensions of the panel versus the wavelength of sound waves that will simply go around it. Plus, there’s the practicality factor…
I need space to move around for efficiency and creativity more than I need better absorption at low frequencies. And so, I have chosen to use thick panels, placed along the boundaries of my room, with a relatively small air gap behind them.
At a certain point, you’d need panels that are impractically thick to absorb the lowest frequencies. And that’s why there are pressure traps that operate in a way that works best in areas of maximum pressure…
Another reason the relationship between pressure and displacement is important is for selecting the listening position and speaker location.
You might have heard of a guideline referred to as “the 38% rule”. This shouldn’t be taken as a hard fast rule, because (again) the wavelengths that resonate may vary depending on the reflectiveness of the walls and ceilings. But, it’s a helpful starting point.
The 38% rule would suggest that a good starting point for the listening position would be about 38% into the length of your room, as this is where the first few modes in that dimension will be most balanced.
For stereo image, we usually sit directly in the center of the two side walls – so we will be at a complete null for the first two modes. And, with my 8ft ceilings in this room, my listening position ends up at nearly the exact center…
The source location also matters. The room will respond to each resonant frequency most when the source is at a point of maximum pressure. Here’s a helpful animation that illustrates this concept…
The red dot is the position of the speaker on this plane. At the areas of max pressure, the room has the most extreme response to each frequency while the room will theoretically not respond at all if the speaker is in one of the pressure nodes.
If we place our ears in a position where there is a pressure antinode and then move the speaker to a pressure node, we will hear that there is a dip in the room’s response, but we still hear this frequency somewhat because this is a 3-dimensional room, not a 2-dimensional theoretical animation.
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Topic: Orders of magnitude
In the News (Sat 20 Jul 19)
Encyclopedia :: encyclopedia : Orders of magnitude (Site not responding. Last check: 2007-10-21) Thus, an order of magnitude is an approximate position on a logarithmic scale. An order of magnitude estimate of a variable whose precise value is unknown is an estimate rounded to the nearest power of ten. For example, an order of magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. www.hallencyclopedia.com /Orders_of_magnitude (631 words)
Orders of magnitude (time) - Wikipedia, the free encyclopedia The pages linked in the right-hand column contain lists of times that are of the same order of magnitude (power of ten). Rows in the table represent increasing powers of a thousand (3 orders of magnitude). This page was last modified 13:37, 21 July 2006. en.wikipedia.org /wiki/Orders_of_magnitude_(time) (162 words)
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# Binh Nguyen Cong
105 2019 이후 총 참여 횟수
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High Precision Square Root (Inspired by Project Euler 80)
Given a positive integer n which is not a perfect square, write a MATLAB script that will calculate the square root of n truncat...
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Decrypt the cypher using XOR encryption (for beginners)
Inspired by Project Euler n°59 Each character on a computer is assigned a unique code and the preferred standard is ASCII (...
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Pandigital number n°3 (Inspired by Project Euler 32)
After Problem 2319 and 2320. An n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For examp...
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Pandigital number n°2 (Inspired by Project Euler 32)
After <http://www.mathworks.com/matlabcentral/cody/problems/2319 Problem 2319>. An n-digit number is pandigital if it makes u...
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Pandigital number n°1 (Inspired by Project Euler 32)
A little warm-up to begin... An n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For ex...
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I've got the power! (Inspired by Project Euler problem 29)
Consider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5: 2^2=4, 2^3=8, 2^4=16,...
6달 전
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Matlab Basics - Rounding III
Write a script to round a large number to the nearest 10,000 e.g. x = 12,358,466,243 --> y = 12,358,470,000
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Matlab Basics - Rounding II
Write a script to round a variable x to 3 decimal places: e.g. x = 2.3456 --> y = 2.346
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Check that number is whole number
Check that number is whole number Say x=15, then answer is 1. x=15.2 , then answer is 0. <http://en.wikipedia.org/wiki/Whole...
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MATLAB Basic: rounding III
Do rounding towards minus infinity. Example: -8.8, answer -9 +8.1 answer 8 +8.50 answer 8
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해결됨
MATLAB Basic: rounding II
Do rounding nearest integer. Example: -8.8, answer -9 +8.1 answer 8 +8.50 answer 9
6달 전 | 1,460 | 4,988 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2020-16 | latest | en | 0.60261 |
https://www.ncl.ucar.edu/Support/talk_archives/2011/0893.html | 1,696,125,940,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510734.55/warc/CC-MAIN-20231001005750-20231001035750-00743.warc.gz | 984,406,042 | 3,984 | # Re: a question regarding scatter plot
From: Mary Haley <haley_at_nyahnyahspammersnyahnyah>
Date: Mon Apr 04 2011 - 08:24:59 MDT
On Apr 1, 2011, at 10:26 AM, H.Dang wrote:
> Hi Mary,
>
> Thanks for your kind explanation. So my current understanding is that "gsn_csm_xy (wks,ts&time,data,res)" is to plot 2 sets of data. :
>
> 1. ts vs. data(0,:)
> 2. ts vs. data(1,:)
It's more like:
data(0,:) vs ts&time
data(1,:) vs ts&time
"data" is for the Y axis, and ts&time is the X axis. It's not plotting "ts", but the time coordinates associated with "ts".
What you are seeing in this figure is correct. If you were to print the ts&time values, you would see they go from 6113 to 9125, and this is what you see on the X axis.
The data(0,:) values go from 268.0111 to 271.0618, and the data(1,:) values (the line) go from 268.4577 to 270.5234.
The "x" array was simply used as input to "regline", which caculates the regression coefficient.
--Mary
>
> Based on http://www.ncl.ucar.edu/Applications/Scripts/scatter_4.ncl,
>
> x = ispan(0,dimsizes(ts)-1,1)*1.
> ...
> data(0,:) = ts
> data(1,:) = rc*(x-rc@xave) + rc@yave
> ...
> res@xyMarkLineModes = (/"Markers","Lines"/) ; choose which have markers
> ...
> plot = gsn_csm_xy (wks,ts&time,data,res) ; create plot
> end
>
> It firtly plots "ts vs data(0,:)=ts", which should be a line with slope 1. Then it will plot "ts vs data(1,:)=regression line". In both cases, ts is the x-axes, but this code corresponds to the figure http://www.ncl.ucar.edu/Applications/Images/scatter_4_lg.png
>
> Since this figure's x-axes is "time", I don't understand why the code is not like:
>
> plot = gsn_csm_xy (wks,x,data,res)
>
>
> Cheers
> Hongyan
> On Fri, Apr 1, 2011 at 10:13 AM, Mary Haley <haley@ucar.edu> wrote:
> On Mar 31, 2011, at 5:06 PM, H.Dang wrote:
>
>> Hi dear all,
>>
>> I have a question regarding a scatter plot example on NCL website:
>>
>> http://www.ncl.ucar.edu/Applications/Scripts/scatter_4.ncl
>>
>> The last 2 lines are:
>>
>> plot = gsn_csm_xy (wks,ts&time,data,res) ; create plot
>> end
>>
>> The "&time" doesn't work in my NCL, but I can get plots simply use:
>>
>> plot = gsn_csm_xy (wks,ts,data,res) ; create plot
>> end
>>
>> I'm not sure if it's okay if I do it this way.
>
> Dear Hongyan,
>
> It's okay to put "ts" there, as long as the dimensions of ts and data are correct, and that this is what you actually want to plot.
> This call will simply put the "ts" values on your X axis and the "data" values on your Y axis.
>
>
>> And is the x-axes is the pre-defined "x"?
>>
>> x = ispan(0,dimsizes(ts)-1,1)*1.
>
>
> No, it should be set to the values of "ts". That is, the X values will span min(ts) to max(ts).
>
>
> plot = gsn_csm_y(wks,data,res) ; Note, no "ts"
>
> Then "data" would be on your Y axis, and the x axis would be the "ispan" values as you defined above.
>
> --Mary
>
>>
>> Thank you.
>> --
>> Cordially,
>> Hongyan(ΊθΡγ)
>> Tel: 1-519-8884567ext36667
>>
>>
>> _______________________________________________
>> ncl-talk mailing list
>> List instructions, subscriber options, unsubscribe:
>> http://mailman.ucar.edu/mailman/listinfo/ncl-talk
>
>
>
>
> --
> Cordially,
> Hongyan(ΊθΡγ)
> Tel: 1-519-8884567ext36667
>
>
> _______________________________________________
> ncl-talk mailing list
> List instructions, subscriber options, unsubscribe:
> http://mailman.ucar.edu/mailman/listinfo/ncl-talk
_______________________________________________
ncl-talk mailing list
List instructions, subscriber options, unsubscribe:
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Received on Mon Apr 4 08:24:59 2011
This archive was generated by hypermail 2.1.8 : Tue Apr 05 2011 - 09:01:21 MDT | 1,173 | 3,675 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2023-40 | latest | en | 0.848679 |
https://www.physicsforums.com/threads/intergration-by-substitution.111991/ | 1,531,794,783,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589537.21/warc/CC-MAIN-20180717012034-20180717032034-00421.warc.gz | 953,178,169 | 14,535 | # Homework Help: Intergration by substitution
1. Feb 24, 2006
### Hootenanny
Staff Emeritus
The question is to find the following intergal:
$$\int x\cdot u^{\frac{1}{2}$$ where $u = 2x -1$.
$$= \int x\cdot u^{\frac{1}{2}} \;\; \frac{1}{2} du$$
$$u = 2x -1 \Rightarrow x = \frac{u+1}{2}$$
$$= \int \frac{1}{2}(u+1)\cdot u^{\frac{1}{2}} \;\; \frac{1}{2} du \;\; = \int \frac{1}{4}\left( u^{\frac{3}{2}} + u^{\frac{1}{2}}\right) \;\; du$$
$$= \frac{2}{20} u^{\frac{5}{2}} + \frac{2}{12} u^{\frac{3}{2}} = \frac{1}{10} u^{\frac{5}{2}} + \frac{1}{6} u^{\frac{3}{2}}$$
But this isnt going to give me the correct answer. Can anybody see where I've gone wrong? Thank's
2. Feb 24, 2006
### HallsofIvy
If u= 2x- 1 then 2x= u+1 so x= (1/2)(u+1). Substitute THAT for x and the integral becomes
$$\frac{1}{2}\int(u+1)u^{\frac{1}{2}}du= \frac{1}{2}\int (u^{\frac{3}{2}}+ u^{\frac{1}{2}})du$$
That should be easy to integrate.
3. Feb 24, 2006
### Hootenanny
Staff Emeritus
$$\frac{1}{2}\int (u^{\frac{3}{2}}+ u^{\frac{1}{2}})du = \frac{1}{2} \left[ \frac{2}{5} u ^{\frac{5}{2}} + \frac{2}{3} u^{\frac{3}{2}} \right]$$
Is that correct?
4. Feb 24, 2006
### Hootenanny
Staff Emeritus
Or would i have to make a further substitution for $(u^{\frac{3}{2}}+ u^{\frac{1}{2}})$ ?
5. Feb 24, 2006
### TD
That's correct, but don't forget the constant of integration
6. Feb 24, 2006
### Hootenanny
Staff Emeritus
Thank's TD +c
7. Feb 24, 2006
### TD
You're welcome.
To get back to your last question, there is no need for an extra substitution since the integral is lineair, which means that:
$$\int {\alpha f\left( x \right) + \beta g\left( x \right)dx} = \alpha \int {f\left( x \right)dx} + \beta \int {g\left( x \right)dx}$$
So in your case, that gives:
$$\int {u^{\frac{3}{2}} + u^{\frac{1}{2}} du} = \int {u^{\frac{3}{2}} du} + \int {u^{\frac{1}{2}} du}$$
Then you can apply the standard exponent-rule, as you did.
8. Feb 24, 2006
### 0rthodontist
What? He had it completely right the first time. 1/4 is the correct thing to multiply by because dx = 1/2 du. I'm assuming there was a dx in the original integral because otherwise he wouldn't have included the 1/2 du in his second step.
Last edited: Feb 24, 2006 | 889 | 2,221 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2018-30 | latest | en | 0.694558 |
https://emacsdocs.org/docs/elisp/Arithmetic-Operations | 1,726,625,881,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.68/warc/CC-MAIN-20240918000844-20240918030844-00008.warc.gz | 193,166,501 | 7,281 | # 3.6 Arithmetic Operations
Emacs Lisp provides the traditional four arithmetic operations (addition, subtraction, multiplication, and division), as well as remainder and modulus functions, and functions to add or subtract 1. Except for `%`, each of these functions accepts both integer and floating-point arguments, and returns a floating-point number if any argument is floating point.
### `function`1+number-or-markerβ
This function returns `number-or-marker` plus 1. For example,
``(setq foo 4) β 4(1+ foo) β 5``
This function is not analogous to the C operator `++`βit does not increment a variable. It just computes a sum. Thus, if we continue,
``foo β 4``
If you want to increment the variable, you must use `setq`, like this:
``(setq foo (1+ foo)) β 5``
### `function`1-number-or-markerβ
This function returns `number-or-marker` minus 1.
### `function`+\&rest numbers-or-markersβ
This function adds its arguments together. When given no arguments, `+` returns 0.
``(+) β 0(+ 1) β 1(+ 1 2 3 4) β 10``
### `function`-\&optional number-or-marker \&rest more-numbers-or-markersβ
The `-` function serves two purposes: negation and subtraction. When `-` has a single argument, the value is the negative of the argument. When there are multiple arguments, `-` subtracts each of the `more-numbers-or-markers` from `number-or-marker`, cumulatively. If there are no arguments, the result is 0.
``(- 10 1 2 3 4) β 0(- 10) β -10(-) β 0``
### `function`*\&rest numbers-or-markersβ
This function multiplies its arguments together, and returns the product. When given no arguments, `*` returns 1.
``(*) β 1(* 1) β 1(* 1 2 3 4) β 24``
### `function`/number \&rest divisorsβ
With one or more `divisors`, this function divides `number` by each divisor in `divisors` in turn, and returns the quotient. With no `divisors`, this function returns 1/`number`, i.e., the multiplicative inverse of `number`. Each argument may be a number or a marker.
If all the arguments are integers, the result is an integer, obtained by rounding the quotient towards zero after each division.
``(/ 6 2) β 3``
``(/ 5 2) β 2``
``(/ 5.0 2) β 2.5``
``(/ 5 2.0) β 2.5``
``(/ 5.0 2.0) β 2.5``
``(/ 4.0) β 0.25``
``(/ 4) β 0``
``(/ 25 3 2) β 4``
``(/ -17 6) β -2``
If you divide an integer by the integer 0, Emacs signals an `arith-error` error (see Errors). Floating-point division of a nonzero number by zero yields either positive or negative infinity (see Float Basics).
### `function`%dividend divisorβ
This function returns the integer remainder after division of `dividend` by `divisor`. The arguments must be integers or markers.
For any two integers `dividend` and `divisor`,
``(+ (% dividend divisor) (* (/ dividend divisor) divisor))``
always equals `dividend` if `divisor` is nonzero.
``(% 9 4) β 1(% -9 4) β -1(% 9 -4) β 1(% -9 -4) β -1``
### `function`moddividend divisorβ
This function returns the value of `dividend` modulo `divisor`; in other words, the remainder after division of `dividend` by `divisor`, but with the same sign as `divisor`. The arguments must be numbers or markers.
Unlike `%`, `mod` permits floating-point arguments; it rounds the quotient downward (towards minus infinity) to an integer, and uses that quotient to compute the remainder.
If `divisor` is zero, `mod` signals an `arith-error` error if both arguments are integers, and returns a NaN otherwise.
``(mod 9 4) β 1``
``(mod -9 4) β 3``
``(mod 9 -4) β -3``
``(mod -9 -4) β -1``
``(mod 5.5 2.5) β .5``
For any two numbers `dividend` and `divisor`,
``(+ (mod dividend divisor) (* (floor dividend divisor) divisor))``
always equals `dividend`, subject to rounding error if either argument is floating point and to an `arith-error` if `dividend` is an integer and `divisor` is 0. For `floor`, see Numeric Conversions. | 1,226 | 4,018 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2024-38 | latest | en | 0.603236 |
https://codecatch.net/post/a62e37b9-3a82-4572-aefa-7f96841a0bb3 | 1,674,879,026,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499470.19/warc/CC-MAIN-20230128023233-20230128053233-00272.warc.gz | 207,239,458 | 19,058 | ## Invert Binary Tree
2 likes • Oct 15, 2022
JavaScript
## More JavaScript Posts
### Monotonic Array
CodeCatch
0 likes • Nov 19, 2022
JavaScript
```// Time Complexity : O(N)// Space Complexity : O(1) var isMonotonic = function(nums) { let isMono = null; for(let i = 1; i < nums.length; i++) { if(isMono === null) { if(nums[i - 1] < nums[i]) isMono = 0; else if(nums[i - 1] > nums[i]) isMono = 1; continue; } if(nums[i - 1] < nums[i] && isMono !== 0) { return false; } else if(nums[i - 1] > nums[i] && isMono !== 1) { return false; } } return true; };
let nums1 = [1,2,2,3]let nums2 = [6,5,4,4]let nums3 = [1,3,2]
console.log(isMonotonic(nums1));console.log(isMonotonic(nums2));console.log(isMonotonic(nums3));```
### Rings and Rods
CodeCatch
0 likes • Nov 19, 2022
JavaScript
```// There are n rings and each ring is either red, green, or blue. The rings are distributed across ten rods labeled from 0 to 9.
// You are given a string rings of length 2n that describes the n rings that are placed onto the rods. Every two characters in rings forms a color-position pair that is used to describe each ring where:
// The first character of the ith pair denotes the ith ring's color ('R', 'G', 'B').// The second character of the ith pair denotes the rod that the ith ring is placed on ('0' to '9').// For example, "R3G2B1" describes n == 3 rings: a red ring placed onto the rod labeled 3, a green ring placed onto the rod labeled 2, and a blue ring placed onto the rod labeled 1.
// Return the number of rods that have all three colors of rings on them.
let rings = "B0B6G0R6R0R6G9";var countPoints = function(rings) { let sum = 0; // Always 10 Rods for (let i = 0; i < 10; i++) { if (rings.includes(`B\${i}`) && rings.includes(`G\${i}`) && rings.includes(`R\${i}`)) { sum+=1; } } return sum; };
console.log(countPoints(rings));```
```// Vanilla JS Solution:var app = document.getElementById('app');
var typewriter = new Typewriter(app, { loop: true });
typewriter .typeString("I'm John and I'm a super cool web developer") .pauseFor(3000) .deleteChars(13) // "web developer" = 13 characters .typeString("person to talk with!") // Will display "I'm John and I'm a super cool person to talk with!" .start();
// React Solution:import Typewriter from 'typewriter-effect';
<Typewriter options={{ loop: true }} onInit={typewriter => { typewriter .typeString("I'm John and I'm a super cool web developer") .pauseFor(3000) .deleteChars(13) // "web developer" = 13 characters .typeString("person to talk with!") // Will display "I'm John and I'm a super cool person to talk with!" .start(); }}/>```
### Redux Slice
JoeCamRoberon
0 likes • Mar 11, 2021
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```import { createSlice } from "@reduxjs/toolkit";
const alert = createSlice({ name: "alert", initialState: { msg: "", status: "", }, reducers: { set_alert: (state, action) => { return { ...state, msg: action.payload.msg, status: action.payload.status, }; }, clear_alert: (state, action) => { return { ...state, msg: "", status: "", }; }, },});
export const setAlert = (msg, status) => dispatch => { dispatch(set_alert({ msg, status })); setTimeout(() => dispatch(clear_alert()), 4000);};
### getURLParameters
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JavaScript
`const getURLParameters = url =>(url.match(/([^?=&]+)(=([^&]*))/g) || []).reduce( (a, v) => ( (a[v.slice(0, v.indexOf('='))] = v.slice(v.indexOf('=') + 1)), a ), {});`
### MongoDB Connection
CodeCatch
0 likes • Oct 15, 2022
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```const MongoClient = require('mongodb').MongoClient;const assert = require('assert');
// Connection URLconst url = 'mongodb://localhost:27017';
// Database Nameconst dbName = 'myproject';
// Use connect method to connect to the serverMongoClient.connect(url, function(err, client) { assert.equal(null, err); console.log("Connected successfully to server");
const db = client.db(dbName);
client.close();});``` | 1,178 | 4,134 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2023-06 | longest | en | 0.607172 |
https://heavendesigners.com/how-to-measure-wrist-size-in-mm/ | 1,642,537,728,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00080.warc.gz | 371,695,403 | 12,510 | ### How To Measure Wrist Size In Mm
Especially large wrists can match with the largest watch cases (42mm+) wrapping up Male wrists are usually 15cm (5.9in) to 19cm (7.4in) on average, while the female wrists generally measure anywhere between 14cm (5.5in) and 18cm (7in).
Pin Di The Best Products
### Using a ruler, measure in millimetres across the back of your knuckles as shown in the picture below.
How to measure wrist size in mm. Use a ruler or a metric (mm) units to measures the strap or the distance between the case or lugs of the watch. 10 times the number of centimeters plus the number of millimeters over the last centimeter in your measurement equals your wrist measurement in centimeters. Cut out the ruler template as closely to the edge as possible (do not cut off the peak of the marker at 0 centimeters).
Measure the widest width of your wrist a to b. Your watch case diameter should be appropriately matched to the size of your wrist, too. This will give you your regular fit size.
10 x # of cm + # of mm over last cm = wrist measurement in cm. This is a extremely straightforward concept and can help you save time. Place a ruler horizontally across its center and note the reading where the two ends on the inner circle touch the ruler, to get the exact measurment of the diameter.
The average female wrist is between 140mm (5.5 inches) and 170mm (6.7 inches), while the average male wrist is between 165mm (6.5 inches). Most watch straps are measured in millimeter sizes. That means the case size number listed is almost always the diameter of the case, but not the amount of real estate that will be taken up by the watch once it is on your wrist.
Individuals can have larger or smaller wrists and may find the regular fit uncomfortable. The average watch head is about Open your hand (doing so will ensure you get the real size of your wrist when it’s the largest) snuggly wrap a measuring tape around your wrist.
Draw a line on the ruler for dividing the surface area from the paper into 5 equivalent elements. 2.once you have verified that you have printed this sheet correctly. Wrist and strap sizing guide in millimeters
This will give you your loose fit size. Band size is the combined length of the two straps. The size of your watch case diameter should be proportionate with your wrist size.
However, people are different, and so are wrists. Read the size on the measuring tape, preferably in inches or centimeters. Inner diameter of the bangle.
Close your fingers together and bring your thumb to your little finger (as pictured). Hold the strip just below where your wrist bone sits and around where you would normally wear the band, wrap it around your wrist and line that up with the sizes of your watch model. Let’s start out with some basic wrist measurement guidelines and conversions.
Measure the case size of the watch. To determine the length of your watch band follow these 4 steps. Typically, watch measurements are taken with a vernier tool (a pair of measuring calipers), and expressed in millimeters.
Add half a centimeter above the measurement to be safe. Using a strip of paper or tape measurements, wrap it around your hand at the widest point. Depart the ruler around the surface area in the paper until finally you’re ready to remove it.
The easiest way is to measure the case from the 4 o’clock to 10 o’clock position or from the 2 o’clock to 8 o’clock position. To measure a watch case size, place calipers from one side to the opposite side of the case, just above or below the crown, where the case diameter is the smallest. How to determine your bangle size?
If your wrist is 6 inches which is considered as a small wrist, 38 mm should be the ideal size for you. If you are using a plain strip of paper, mark your size with a pen on that paper. To determine your ring size, do the following:to get a rough estimate of the size of the flat surface of your wrist, just measure your wrist size (in millimiters) and divide it by 3.typically, watch measurements are taken with a vernier tool (a pair of measuring calipers), and expressed in millimeters.use a millimeter ruler to measure the string for best results.
Pretend that you were putting on a bangle. How to measure your wrist size (or circumference): To determine your ring size, do the following:to get a rough estimate of the size of the flat surface of your wrist, just measure your wrist size (in millimiters) and divide it by 3.typically, watch measurements are taken with a vernier tool (a pair of measuring calipers), and expressed in millimeters.use a millimeter ruler to measure the string for best results.
This will give you your tight fit size. Cut out the length chart below along the dotted lines. Make sure the palm of your hand is facing up.
Take a bangle that fits you perfectly. Once the ruler is cut out, wrap it around your wrist and tighten it so it fits comfortably. Subtract 10mm from the measurement.
Subtract 12mm from the measurement. 39mm, 40mm, and 42mm range will fit best. To calculate millimeters, there are 10 millimeters in a centimeter.
Subtract 5mm from the measurement. Recommend simply using a tape measure to measure your wrist. Mark off the very first mark, and repeat the method inside the other 4 marks.
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How To Measure Your Wrist For A Bracelet Essential Oil Bracelet Tree Of Life Jewelry Boho Style Jewelry | 1,628 | 7,288 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2022-05 | latest | en | 0.933511 |
https://psichologyanswers.com/library/lecture/read/35168-what-does-it-mean-if-the-divergence-of-a-vector-field-is-zero | 1,638,327,778,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964359082.78/warc/CC-MAIN-20211201022332-20211201052332-00114.warc.gz | 546,077,547 | 6,487 | # What does it mean if the divergence of a vector field is zero?
## What does it mean if the divergence of a vector field is zero?
A vector field with zero divergence everywhere is called solenoidal – in which case any closed surface has no net flux across it.
## Is curl scalar or vector?
(As the curl is a vector, it is very different from the divergence, which is a scalar.) We can draw the vector corresponding to curlF as follows. We make the length of the vector curlF proportional to the speed of the sphere's rotation.
## Is gradient a row or column vector?
In some applications it is customary to represent the gradient as a row vector or column vector of its components in a rectangular coordinate system; this article follows the convention of the gradient being a column vector, while the derivative is a row vector.
## What is gradient vector calculus?
The gradient is a fancy word for derivative, or the rate of change of a function. It's a vector (a direction to move) that. Points in the direction of greatest increase of a function (intuition on why)
## What are the three types of passive transport?
Three common types of passive transport include simple diffusion, osmosis, and facilitated diffusion.
## What is the difference between passive and active transport?
The movement of molecules across a membrane without the input of energy is known as passive transport. When energy (ATP) is needed, the movement is known as active transport. Active transport moves molecules against their concentration gradient, from an area of low concentration to an area of high concentration.
## Is active or passive transport faster?
Active transport is a rapid process. Passive transport is a comparatively slow process.
## What are 4 types of active transport?
CONTENTSAntiport Pumps.Symport Pumps.Endocytosis.Exocytosis.
## What are the two major types of active transport?
There are two types of active transport: primary active transport that uses adenosine triphosphate (ATP), and secondary active transport that uses an electrochemical gradient. An example of active transport in human physiology is the uptake of glucose in the intestines.
## Is osmosis active or passive transport?
Osmosis is a passive transport process during which water moves from areas where solutes are less concentrated to areas where they are more concentrated. Illustration of osmosis. A beaker is divided in half by a semi-permeable membrane.
## What are the two types of transport?
There are two major types of cell transport: passive transport and active transport. Passive transport requires no energy. It occurs when substances move from areas of higher to lower concentration. Types of passive transport include simple diffusion, osmosis, and facilitated diffusion.
## What are examples of passive transport?
Examples of Passive Transportsimple diffusion.facilitated diffusion.filtration.osmosis.
## Is passive transport high to low?
Passive transport is a naturally-occurring phenomenon and does not require the cell to exert any of its energy to accomplish the movement. In passive transport, substances move from an area of higher concentration to an area of lower concentration. ... Passive Transport: Diffusion is a type of passive transport.
## What are examples of active transport?
Here are some examples of active transport in animals and humans:Sodium-potassium pump (exchange of sodium and potassium ions across cell walls)Amino acids moving along the human intestinal tract.Calcium ions moving from cardiac muscle cells.Glucose moving in or out of a cell.A macrophage ingesting a bacterial cell.Meer items...
## Does passive transport require energy?
There are two major ways that molecules can be moved across a membrane, and the distinction has to do with whether or not cell energy is used. Passive mechanisms like diffusion use no energy, while active transport requires energy to get done. | 780 | 3,932 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2021-49 | latest | en | 0.935281 |
http://www.mathskey.com/homework-help/algebra-1-2007/book/9/page/448 | 1,527,397,041,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794868003.97/warc/CC-MAIN-20180527044401-20180527064401-00124.warc.gz | 418,204,538 | 14,432 | Algebra 1, 2007
23
PAGE: 448 SET: Exercises PROBLEM: 23
The equations of linear system are .
Since the coefficient of the y - term in two equations is same. So, eliminate these terms by subtracting the equations.
Write the equations in column form and subtract to eliminate variable y.
.
The resultant equation is and solve it for x.
Divide each side by 6.
Cancel common terms.
.
Substitute the value of in equation 1: and solve for y.
Multiply each side by .
Cancel common terms.
.
The solution is .
The solution is .
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QUESTIONS? LET US HELP. | 229 | 984 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2018-22 | latest | en | 0.9584 |
https://electronics.stackexchange.com/questions/395652/determine-the-voltage-drops-across-the-capacitor | 1,560,749,875,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998376.42/warc/CC-MAIN-20190617043021-20190617065021-00487.warc.gz | 436,076,915 | 35,498 | # Determine the voltage drops across the capacitor
I am having troubles with one type of tasks when preparing for an exam. I think I get the way to solve it when t = 0, but I don't really know what my approach should be when t>0.
That is how I solved it:
//Edit Updated version for t>0. I think it might be correct now. Is it?
• Why your Rth is 3R in the second case? Also as you can see because of 2/3E > 2/5E the capacitor will be charged from 2/5E to 2/3E. Not discharged. – G36 Sep 12 '18 at 14:14
• @G36 As far as I remember we don't have to take these resistors that are in branch where capacitor is placed, so we are left with 2 resistors (R and 2R that are serially connected), but I can be wrong. – James Smith Sep 12 '18 at 14:27
• Why? to find the time constant you need to find the resistance seen from the capacitor terminals. And from the capacitor point of view, the R and 2R are not connected in series. electronics.stackexchange.com/questions/377467/… – G36 Sep 12 '18 at 14:31
• Okey, so Rth will be equal to 8/3R right? – James Smith Sep 12 '18 at 14:56
• Yep, Rth = 8/3R – G36 Sep 12 '18 at 15:02
$$V_0+ V_fe^{-f(r,c)t}$$ | 355 | 1,146 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2019-26 | longest | en | 0.948681 |
https://it.iucr.org/Ea/ch4o1v0001/sgtable4o1o070/ | 1,566,604,618,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027319155.91/warc/CC-MAIN-20190823235136-20190824021136-00440.warc.gz | 515,840,637 | 5,644 | p31m 31m Trigonal/Hexagonal No. 70 p31m Patterson symmetry p-31m
Origin on 31m
Asymmetric unit 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 1/2; x ≤ (1 + y)/2; y ≤ min(1 - xx)
Vertices
0, 0 1/2, 0 2/3, 1/3 1/2, 1/2
Symmetry operations
(1) 1 (2) 3+ 0, 0, z (3) 3- 0, 0, z (4) m x, x, z (5) m x, 0, z (6) m 0, y, z
Generators selected (1); t(1, 0, 0); t(0, 1, 0); (2); (4)
Positions
Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
6 d 1
(1) x, y, z (2) -y, x - y, z (3) -x + y, -x, z (4) y, x, z (5) x - y, -y, z (6) -x, -x + y, z
no conditions
Special: no extra conditions
3 c . . m
x, 0, z 0, x, z -x, -x, z
2 b 3 . .
1/3, 2/3, z 2/3, 1/3, z
1 a 3 . m
0, 0, z
Symmetry of special projections
Along [001] p31m a' = a b' = b Origin at 0, 0, z Along [100] 1m1 a' = 1/2(a + 2b) Origin at x, 0, 0 Along [210] 111 a' = 1/2b Origin at x, 1/2x, 0
Maximal non-isotypic subgroups
I [2] p311 (p3, 65) 1; 2; 3 [3] p11m (cm11, 13) 1; 4 [3] p11m (cm11, 13) 1; 5 [3] p11m (cm11, 13) 1; 6
IIa none
IIb [3] h31m (a' = 3a, b' = 3b) (p3m1, 69)
Maximal isotypic subgroups of lowest index
IIc [4] p31m (a' = 2a, b' = 2b) (70)
Minimal non-isotypic supergroups
I [2] p-31m (71); [2] p6mm (77); [2] p-62m (79)
II [2] h31m (p3m1, 69) | 728 | 1,289 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2019-35 | latest | en | 0.115625 |
https://artofproblemsolving.com/wiki/index.php?title=1962_IMO_Problems/Problem_6&diff=next&oldid=30325 | 1,628,179,126,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046155925.8/warc/CC-MAIN-20210805130514-20210805160514-00245.warc.gz | 120,929,016 | 11,592 | # Difference between revisions of "1962 IMO Problems/Problem 6"
## Problem
Consider an isosceles triangle. Let $r$ be the radius of its circumscribed circle and $\rho$ the radius of its inscribed circle. Prove that the distance $d$ between the centers of these two circles is
$d=\sqrt{r(r-2\rho)}$.
## Solution
<geogebra>d1f93636341cbe0bc2f98c788171d8a55d94f8c8</geogebra> Instead of an isosceles triangle, let us consider an arbitrary triangle $ABC$. Let $ABC$ have circumcenter $O$ and incenter $I$. Extend $AI$ to meet the circumcircle again at $L$. Then extend $LO$ so it meets the circumcircle again at $M$. Consider the point where the incircle meets $AB$, and let this be point $D$. We have $\angle ADI = \angle MBL = 90^{\circ}, \angle IAD = \angle LMB$; thus, $\triangle ADI \sim \triangle MBL$, or $\frac {ID}{BL} = \frac {AI} {ML} \iff ID \cdot ML = 2rp = AI \cdot BL$. Now, drawing line $BI$, we see that $\angle BIL = \frac {1}{2}\angle A + \frac {1}{2}\angle ABC, \angle IBL = \frac {1}{2}\angle ABC + \angle CBL = \frac {1}{2}\angle ABC + \frac {1}{2}\angle A$. Therefore, $BIL$ is isosceles, and $IL = BL$. Substituting this back in, we have $2rp = AI\cdot IL$. Extending $OI$ to meet the circumcircle at $P,Q$, we see that $AI\cdot IL = PI\cdot QI$ by Power of a Point. Therefore, $2rp = PI \cdot QI = (PO + OI)(QO - OI) = (r + d)(r - d)$, and we have $2rp = r^2 - d^2 \iff d = \sqrt {r(r - 2p)}$, and we are done. | 494 | 1,436 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 27, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.8125 | 5 | CC-MAIN-2021-31 | latest | en | 0.780641 |
https://dsp.stackexchange.com/questions/28812/fir-filter-hn-is-palindrome | 1,585,946,734,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370518622.65/warc/CC-MAIN-20200403190006-20200403220006-00336.warc.gz | 444,598,665 | 32,035 | # FIR filter : $h(n)$ is palindrome?
I study condition for fix if filter is a linear phase,but it's not clear in my mind!
I have this $h(n)$: $$h(n) = \begin{cases} \left(\frac{1}{2}\right)^{n} & 0<n<N-1 \\[2ex] 0 & \text{elsewhere} \end{cases}$$ I got the $H(z)$: $$H(z) = \frac {\left(\frac{1}{2}\right)^{N}{z}^{-N}-1}{\frac{1}{2}{z}^{-1}-1}$$ Now, for the phase linear what I do ? I think to verify palindrome property for this $h(n)$, but how ?? or I can finally say that to the form that has definitely not linear ?
$$h[n]=h[N-1-n]\quad \text{or}\quad h[n]=-h[N-1-n]\tag{1}$$
(assuming the impulse response $h[n]$ is zero for $n<0$ and $n\ge N$). Since your filter satisfies neither of the two conditions given by $(1)$ it can't have a linear phase response.
• Thank you, i understand your answer theorically, but you can you do me a practical example for this exercise ? because I think then it would be a fir filter linear phase if it had been $$h(n) = \begin{cases} \left(\frac{1}{2}\right)^{|n|} & 0<n<N-1 \\[2ex] 0 & \text{elsewhere} \end{cases}$$ – P_B Feb 11 '16 at 21:53 | 368 | 1,086 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2020-16 | latest | en | 0.811427 |
https://johnsinclairradio.com/decimal-worksheets-grade-5-printable/ | 1,643,448,850,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304883.8/warc/CC-MAIN-20220129092458-20220129122458-00493.warc.gz | 372,346,005 | 8,268 | # Exemplary Decimal Worksheets Grade 5 Printable
Worksheet. October 13th , 2020.
On this page you find introduction to decimals worksheets, decimal operation worksheets, decimal word problem worksheets, decimal conversion in percents and fractions worksheets, negative decimal worksheets, and many more primary school decimal worksheets. Free math worksheets for grade 5.
Decimal Worksheets Fresh worksheets added in each topic
### This webpage encompasses a combination of printable worksheets based on ordering decimals with a view to enhance 4th grade and 5th grade students' knowledge on decimals and their place values.
Decimal worksheets grade 5 printable. Integers and absolute value worksheets. This practice will help your students fully understand how to use decimals in equations. Most primary students will learn about decimals in grade 4.
Worksheets > math > math by topic > decimals. Print free fifth grade english worksheets, synonyms worksheets, antonyms worksheet, punctuation, capitalization, words joining worksheet. Showing top 8 worksheets in the category decimals grade 5.
A whole number is seperated from its decimal number using a dot(.). Printable decimal worksheets 5th grade. Converting fractions to from decimals worksheets for grade 5.
We have learnt the place value of whole numbers. Decimal number place value system starts from tenths. Therefore students should find the product in each operation.
Our grade 5 addition and subtraction of decimals worksheets provide practice exercises in adding and subtracting numbers with up to 3 decimal digits. Generate free printable worksheets for addition subtraction multiplication and division of decimals for grades 3 7. Practice decimal subtraction to the thousandths with this math worksheet.
Free printable place value worksheets for decimals are for grade 4 through grade 6. Click on the images to view, download, or print them. Writing and evaluating expressions worksheet.
Free decimal worksheets for teachers, parents, and kids. Let students strengthen their fundamental algebraic skills by placing decimal numbers accurately on the number lines in these printable worksheets crafted for 3rd grade and 4th grade kids. Multiply decimal numbers grade 5 worksheet pdf.
Some of the worksheets for this concept are decimal word problems, decimals word problems, grade 5 decimals word problems, all decimal operations with word problems, set 1 word problems decimals, grade 5 supplement, fraction and decimal word problems no problem, decimals practice booklet table of contents. Quadratic equations word problems worksheet. This will take you to the individual page of the worksheet.
Please visit decimal concepts or decimals to view our large collection of printable worksheets. View the full list of topics for this grade and subject categorized by common core standards or in a traditional way. You will then have two choices.
Below, you find the multiply decimal numbers grade 5 worksheet pdf for free. Some of the worksheets displayed are decimals work, decimals word problems, grade 5 decimals work, decimals practice booklet table of contents, math mammoth grade 5 a worktext, rounding decimals introduction packet, grade 5 decimals word problems, multiply the decimals. Students can use this long division worksheet to practice decimal division.
Easily download and print our decimal worksheets. The most basic of all concepts often call for the most rigorous of all practice! Add and subtract decimals up to 3 digits.
Vertical spacing font size and many more. This is a comprehensive collection of free printable math worksheets for grade 5, organized by topics such as addition, subtraction, algebraic thinking, place value, multiplication, division, prime factorization, decimals, fractions, measurement, coordinate grid, and geometry. You can create easy decimal problems to be solved with mental math, worksheets for multiplying by 10, 100, or 1000, decimal long division problems, missing number problems, and more.
Printable worksheets and activities for teaching basic decimal skills and operations with decimals. Exercises here include a wide range of decimal place values up to millionths with a number of simple word problems thrown into the mix for variety! Includes worksheets with only tenths only hundredths only thousandths as well as a mix of all three.
This depends on when and in what grade level students learn about rounding off. A number of pdf worksheets are stacked with a variety of exercises include ordering decimals in place value boxes, using the number line, and using the. On this page you find our rounding off worksheets suited for grade levels 4 and 5 based on the singapore math curriculum.grade 6 students can, of course, also use these worksheets.
This page has worksheets for teaching decimal naming and recognition, as well as decimal addition, subtraction, multiplication, and division. Decimals worksheets and printables use word problems riddles and pictures to encourage a love for math. This assembly of printable worksheets has been meticulously drafted to assist students of grade 5 and above comprehend the use of place values where decimals are involved.
Decimals on a number line worksheets. In addition to that, they might try to figure out the answers mentally, without having to write down intermediary steps.
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Fractions with mango mash. Kids math worksheets, 5th
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Feb 03, 2021 | Audrey Party | 1,317 | 6,651 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2022-05 | latest | en | 0.850396 |
http://www.cfd-online.com/Forums/fluent/35963-how-creat-mesh-gambit-airfoil.html | 1,480,804,725,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541140.30/warc/CC-MAIN-20161202170901-00283-ip-10-31-129-80.ec2.internal.warc.gz | 381,503,748 | 15,041 | How to creat mesh in Gambit for airfoil
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March 8, 2005, 06:29 How to creat mesh in Gambit for airfoil #1 sanjay Guest Posts: n/a hi,Everyone i sanjay umarani doing my PG-in enginering analysis & design, as a part of my study i have to do project work. I have doing my project in CFD analysis of wind tubine airfoil design. I used eppler code to genert the x-y coordinates. In this i have facing some proble to generate the airfoil in Fluent 1) the coordinate points of upper & lower are not equel ? for example -1098 airfoil of 61 cordinates 2) while meshing some c-gird type mesh to be created in that case the element points are not matching it is giving upper 36 & lower 35 it shoud not to be happened in fluent but givien that error why ? if any one know this regard plesae tell me to what is wrong in this case i have waiting your reply sanjay
March 8, 2005, 08:22 Re: How to creat mesh in Gambit for airfoil #2 miguel Guest Posts: n/a HI: Have a look at: http://instruct1.cit.cornell.edu/courses/fluent/ It shows how to mes an airfoil Miguel
March 8, 2005, 23:54 Re: How to creat mesh in Gambit for airfoil #3 sanjay umarani Guest Posts: n/a thanks for your reply i have used the same site & same proble. But the co-ordinate i took was genrated by Eppler Code, in this case it is around 33 upper & 29 lower, if you make correction by making equal points, is their any change of shape will occure or what i have taken is correct i dont now. After all correcting the co-oridante if you go head the it is giving meshing problem. As of my knowledg the mesh element should be equeal. but in this case it is giving upper -76 & lower - 75 is it correct ? if you know about plesae help me by sanjay
March 15, 2005, 04:14 Re: How to creat mesh in Gambit for airfoil #4 white Guest Posts: n/a Using Gambit, try to import your Eppler coordinate using ICEM Input.
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Contact Us - CFD Online - Top | 752 | 2,708 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2016-50 | latest | en | 0.913305 |
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• Apr 9th 2011, 04:13 PM
mushroom
Prove that 9 is a factor of...
Prove that 9 is a factor of:
P(n): $10^(^n^+^1^) + 3 * 10^n + 5$ for all positive integer n
Using the induction method,
I have proven P(1) to be true
P(k): $10^k (10+3) + 5 = 9a$
P(k+1): $10^(^k^+^1^) (10+3) + 5 = ?$
How do I continue? I am new at doing proofs (Worried)
• Apr 9th 2011, 04:31 PM
LoblawsLawBlog
Do you have to use induction? Sometimes that's tedious for problems like this. I would try to rewrite 10 as 9+1 and then use the binomial theorem.
• Apr 9th 2011, 04:33 PM
mushroom
Yes, unfortunately it is required to use the induction method.
• Apr 9th 2011, 05:54 PM
topsquark
Quote:
Originally Posted by mushroom
Prove that 9 is a factor of:
P(n): $10^(^n^+^1^) + 3 * 10^n + 5$ for all positive integer n
Using the induction method,
I have proven P(1) to be true
P(k): $10^k (10+3) + 5 = 9a$
P(k+1): $10^(^k^+^1^) (10+3) + 5 = ?$
How do I continue? I am new at doing proofs (Worried)
$10^{k + 1} (10 + 3) + 5$
$= 10 \cdot 10^k (10 + 3) + 5$
Now use the P(k) step in the form of $10^k(10 + 3) = 9a - 5$
$= 10 (9a - 5) + 5$
And I'm sure you can take it from here.
-Dan
• Apr 9th 2011, 08:49 PM
Soroban
Hello, mushroom!
Quote:
$\text{Prove that 9 is a factor of: }\:10^{n+1} + 3\!\cdot\!10^n + 5\,\text{ for all positive integers }n$
$\text{Verify }S(1)\!:\; 10^2 + 3\!\cdot10 + 5 \:=\:135,\,\text{ a multiple of 9 . . . True!}$
$\text{Assume }S(k)\!:\;10^{k+1} + 3\!\cdot\!10^k + 5 \:=\:9a\,\text{ for some integer }a$
$\text{Add }(9\!\cdot\!10^{k+1} + 27\!\cdot\!10^k)\,\text{ to both sides:}$
. . $10^{k+1} + {\bf9\!\cdot\!10^{k+1}} + 3\!\cdot\!10^k + {\bf27\!\cdot\!10^k} + 5 \;=\;9a + {\bf9\!\cdot\!10^{k+1}} + {\bf27\!\cdot\!10^k}$
. . . . . . . . $10^{k+1}(1 + 9) + 3\!\cdot\!10^k(1+9) + 5 \;=\;9a + 9\!\cdot\!10^{k+1} + 27\!\cdot\!10^k$
. . . . . . . . . . . . $10^{k+1}\cdot 10 + 3\!\cdot\!10^k\!\cdot\!10 + 5 \;=\;9\left(a + 10^{k+1} + 3\!\cdot\!10^k\right)$
. . . . . . . . . . . . . . . . $10^{k+2} + 3\!\cdot\!10^{k+1} + 5 \;=\;\underbrace{9\left(a + 10^{k+1} + 3\!\cdot\!10^k\right)}_{\text{a multiple of 9}}$
We have proved statement $S(k+1).$
The inductive proof is complete. | 1,025 | 2,224 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2017-22 | longest | en | 0.615299 |
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# Quantum Physics.docx
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PHY100H1
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Quantum Physics: Plank’s Constant If Planck’s constant is zero: - First, energy of radiation would be zero. E = h x f. So, h = E/f where h is Planck’s constant, E is energy and f is the frequency of the particle. If that is 0=E/f that means that E= 0 - Second, particles would not have wave properties . Matter wave length (m) = h / mv where h is Planck’s constant, m is mass and v is velocity. When h equals 0, matter wave length would be zero as well. - Third, the uncertainty principle would be meaningless. (Δx)·(Δv) ≈ h/m whereΔx is uncertainty in position, Δv is uncertainty in velocity, h is Plank’s constant and m is mass. If h equals 0, (Δx)·(Δv) would equals 0. Then, there would be no uncertainty because we could predict both velocity and position with pinpoint accuracy. - Forth, when h = 0, there would be no quantum physics and Newtonian physics would be valid. Comments about Planck's Constant 1) Planck's constant proves to have a very small value. 2) The quantity, h, is the central constant of quantum physics. 3) In a universe
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Submit | 422 | 1,592 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2018-17 | latest | en | 0.899245 |
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## How to Calculate Risk Rating | Risk Matrix | Risk Level | Download PPT
Risk rating is a critical aspect of risk management that aids in evaluating and categorizing potential risks within a project, business, or any operational environment. It involves a comprehensive analysis of various factors to determine the likelihood and impact of these risks, thereby allowing organizations to prioritize their mitigation strategies effectively.
### Introduction to Risk Rating
Understanding risk assessment forms the cornerstone of effective risk management. It involves the identification, analysis, and evaluation of potential risks that can impact an organization’s objectives. Risk rating plays a pivotal role in this process by providing a structured approach to quantify and categorize risks based on their severity.
### Components of Risk Rating
#### Identifying Risk Factors
The first step in calculating risk rating involves identifying and listing potential risk factors. These factors can vary widely depending on the nature of the project or business, encompassing aspects such as market volatility, financial risks, operational challenges, and regulatory changes.
#### Creating a Risk Matrix
A risk matrix is a visual representation that maps the likelihood of an event occurring against its potential impact. This matrix is typically divided into various risk levels, aiding in the classification of risks as low, medium, or high.
#### Defining Risk Levels
Each quadrant of the risk matrix corresponds to a specific risk level. Low-risk events are those with minimal impact and low probability, while high-risk events pose a significant threat and have a higher likelihood of occurrence.
### Calculating Risk Rating
Assessing risk involves evaluating the probability of an event occurring and its potential impact on the organization. This evaluation is often done using numerical values assigned to both probability and impact, which are then plotted on the risk matrix.
### Interpreting Risk Levels
Interpreting the risk levels determined through the matrix is crucial. Low-risk events may not require immediate action but necessitate monitoring, while high-risk events demand immediate attention and mitigation strategies.
### Implementing Risk Rating
Integrating risk rating into decision-making processes is vital. Organizations need to consider the assessed risk levels when strategizing, allocating resources, and planning for contingencies.
``Calculating a risk rating or determining a risk level typically involves using a risk matrix, which is a tool that assesses the likelihood and impact of a risk to determine its overall level of risk. Here's a step-by-step guide:``
### Steps to Calculate Risk Rating using a Risk Matrix:
1. Identify Risks: List the potential risks associated with a project, situation, or scenario.
2. Determine Likelihood: Assess the probability or likelihood of each risk occurring. You can use a scale (e.g., low, medium, high) or assign numerical values (e.g., 1-5, with 1 being least likely and 5 being most likely).
3. Assess Impact: Evaluate the potential impact or consequences of each risk if it were to occur. Again, use a scale or numerical values to measure the severity of impact.
4. Create a Risk Matrix: Construct a grid or matrix with the likelihood on one axis (usually horizontal) and impact on the other axis (usually vertical). The matrix will have different levels or categories for likelihood and impact.
5. Assign Ratings: Place each identified risk within the matrix based on its likelihood and impact assessment.
6. Determine Risk Rating: Once each risk is plotted on the matrix, the intersection or position on the grid will indicate its risk rating or level. Generally, risks found in the higher likelihood and higher impact area pose the most significant threat and are labeled as high risk. Risks in lower likelihood and lower impact areas may be low risk.
7. Mitigation Strategies: Based on the risk ratings, prioritize risks that require attention and develop mitigation or risk management strategies for high and moderate-risk areas.
8. Regular Review: Periodically review and update the risk matrix as circumstances change or new information becomes available.
### Example:
Let’s say you have a risk matrix with likelihood ratings of Low, Medium, High (1-3) and impact ratings of Low, Medium, High (1-3).
• If a risk has a high likelihood (3) and a high impact (3), it would be positioned in the top right quadrant of the matrix, signifying it as a high-risk item.
• A risk with low likelihood (1) and low impact (1) would be placed in the bottom left quadrant, indicating a low-risk item.
``Remember, the specific criteria for likelihood and impact, as well as the layout of the matrix, can vary depending on the organization or context. Adjust the scales and categories based on what best fits your needs.``
### Conclusion
In a dynamic business landscape, understanding how to calculate risk rating through a risk matrix is crucial for informed decision-making and proactive risk management. By systematically assessing risks and assigning appropriate levels, organizations can prioritize their efforts and resources effectively to mitigate potential threats.
### FAQs
1. What is a risk matrix, and how does it work? A risk matrix is a visual tool that helps assess risks by plotting their likelihood and impact on a grid. It works by assigning probabilities and impact levels to different scenarios, allowing organizations to categorize risks based on severity.
2. How often should risk ratings be reassessed? The frequency of reassessment depends on various factors like the nature of the project, changes in the environment, or the occurrence of significant events. Generally, it’s good practice to review and update risk ratings periodically, ensuring they reflect current conditions.
3. What are the main challenges in calculating risk rating? Challenges include subjective assessments, biases in evaluating risks, dealing with complex scenarios, and balancing multiple variables that affect the likelihood and impact of risks.
4. Can software tools completely automate risk rating processes? While software tools assist in calculations and data management, human judgment and expertise are crucial in interpreting data, considering contextual factors, and making informed decisions. So, while they automate certain aspects, full automation isn’t advisable.
5. Why is stakeholder involvement crucial in risk assessment? Stakeholders bring diverse perspectives and domain knowledge to risk assessment. Involving them ensures a comprehensive understanding of risks across different areas, enhances risk identification, and increases buy-in for mitigation strategies. | 1,271 | 6,847 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2024-30 | latest | en | 0.93231 |
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## NCERT Solutions for Class 9 Maths Chapter 14
• ### Class 9 Maths Study Material for 2022-23
Class: 9 Maths (English and Hindi Medium) Chapter 14: Statistics
### 9th Maths Chapter 14 Solutions in English & Hindi Medium
Get here the NCERT Solutions for Class 9 Maths Chapter 14 Statistics all exercises which are given below updated for new academic session 2022-23. UP Board Class 9 Students are using NCERT Textbooks now. So, they can also download UP Board Solutions for Class 9 Maths Chapter 14 all Exercises. Download NCERT Solutions and UP Board Solutions Offline Apps based on latest CBSE Syllabus 2022-2023 for all boards who are using NCERT Books 2022-23.
#### Class 9 Maths Exercise 14.1 and 14.2 Solutions in Video
Class 9 Maths Exercise 14.1 Solutions in Video
Class 9 Maths Exercise 14.2 Solutions in Video
#### Class 9 Maths Exercise 14.3 and 14.4 Solutions in Video
Class 9 Maths Exercise 14.3 Solutions in Video
Class 9 Maths Exercise 14.4 Solutions in Video
### What do you understand by data? What are the main data types?
Data: The facts or figures (observation / information collected) which are numerical or otherwise, collected with a definite purpose, are called data.
Data can be further divided into two categories as follows:
Primary data: The data collected by the investigator himself for a definite plan or purpose, is known as primary data.
Secondary data: The data which are not collected directly but obtained from some other sources (published or unpublished), is known as secondary data.
### What is meant by Frequency Distribution of data?
Frequency Distribution: The number of entries of the data having their values lying in a class is defined as the frequency of the class. The table in which the corresponding frequency are written against each class, is called the frequency distribution of the given data.
### What is meant by Class Interval? What is Class size?
Class Interval: Class intervals are the groups in which all the observations are divided. Each class is bounded by two figures or numbers which are called class limits. The difference between the upper limit and the lower of a class is called class size.
### What is a Frequency Polygon?
Frequency Polygon: A frequency polygon is the polygon obtained by joining the mid-points of upper horizontal sides of all the rectangle in the histogram. It can also be drawn independently without drawing histogram. For this we find class mark of each class interval.
#### Important Notes on 9th Maths Chapter 14
Mean: The mean of a number of observations is the sum of the values of all the observations divided by the total number of observations.
Median: Median is that value of the given observation, which divides it into exactly two parts.
Mode: Mode is that value of the given data, which occurs most frequently.
### Give five examples of data that you can collect from your day-to-day life.
Five examples of data that we can collect from our day-to-day life: 1. Height of our classmates or weight of our classmate. 2. Height of first 100 plants near by our locality. 3. Maximum or minimum temperature of a particular month. 4. Time spend for watching TV in a particular week. 5. Rainfall in our city in last 10 years.
### What do understand by primary or secondary data?
When the information was collected by the investigator herself or himself with a definite objective in her or his mind, the data obtained is called primary data. When the information was gathered from a source which already had the information stored, the data obtained is called secondary data.
### What is statistics?
Statistics is the area of study dealing with the presentation, analysis and interpretation of data.
### How many exercises are there in grade 9 Maths Chapter 14 statistics?
There are four exercises in class 9 Maths Chapter 14 (statistics).
In the first exercise (Ex 14.1), there are only two questions.
The second exercise (Ex 14.2) has nine questions and four examples (examples 1, 2, 3, 4).
The third exercise (Ex 14.3) has nine questions and five examples (examples 5, 6, 7, 8, 9).
In the fourth exercise (Ex 14.4), there are 6 questions and 6 examples (examples 10, 11, 12, 13, 14, 15).
So, there are in all 26 questions and 15 examples in class 9 Maths Chapter 14 (statistics).
### How many days, students need to complete chapter 14 of class 9th Maths?
Students need a maximum of 8-10 days to complete chapter 14 of class 9th Maths if they give a minimum of 1-2 hours per day to this chapter. This time also depends on student’s working speed, efficiency, capability, and many other factors.
### What are the main topics in chapter 14 class 9th Maths Book to learn?
The main aim of chapter 14 of class 9th Maths is to make the following things clear to the students:
• 1. Meaning of data.
• 2. Primary data and Secondary data.
• 3. Raw data.
• 4. Range of the data.
• 5. Meaning of frequency.
• 6. Ungrouped frequency distribution table.
• 7. Class-Intervals, class-size, lower class limit, upper class limit.
• 8. Tally marks.
• 9. Grouped frequency distribution table.
• 10. Graphical representation of data
• a. Bar graph.
• b. Histogram.
• c. Frequency polygon.
• 11. Class-marks.
• 12. Measures of central tendency (Ungrouped data).
• a. Mean.
• b. Median.
• c. Mode.
### Is chapter 14 statistics of class 9th Maths difficult to solve?
No, Chapter 14 (statistics) of class 9th mathematics is not challenging. This chapter is nice and very easy, and also, this chapter is the student’s favourite chapter. Students enjoy doing this chapter. | 1,474 | 6,171 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2022-21 | longest | en | 0.87711 |
https://www.transtutors.com/questions/e11-24-depreciation-calculation-replacement-trade-in-onkar-corporation-bought-a-mach-2399513.htm | 1,579,336,654,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250592394.9/warc/CC-MAIN-20200118081234-20200118105234-00075.warc.gz | 1,145,841,003 | 18,026 | # E11-24 (Depreciation Calculation—Replacement, Trade-in) Onkar Corporation bought a machine on J... 1 answer below »
E11-24 (Depreciation Calculation—Replacement, Trade-in) Onkar Corporation bought a machine on June 1, 2013, for $31,800, f.o.b. the place of manufacture. Freight costs were$300, and $500 was spent to install it. The machine’s useful life was estimated at 10 years, with a residual value of$1,900, while the machine’s physical life was estimated at 11 years, with no residual value. On June 1, 2014, a part that was designed to reduce the machine’s operating costs was added to the machine for a cost of $1,980. On June 1, 2017, the company bought a new machine with greater capacity for a cost of$35,000, deliv- ered. A trade-in value was received on the old machine equal to its fair value of $19,000. The cost of removing the old machine from the plant was$75, and the cost of installing the new machine was $1,300. It was estimated that the new machine would have a useful life of 10 years, with a residual value of$4,000. Instructions (a) Assuming that depreciation is calculated on the straight-line basis, determine the amount of any gain or loss on the disposal of the first machine on June 1, 2017, and the amount of depreciation that should be provided during the company’s current fiscal year, which begins on June 1, 2017. The financial statements are prepared under IFRS. (b) How would your answer in (a) change when assuming the financial statements were prepared under ASPE?
Parvez A
Requirement-(a)
For machine purchased on Jun 1,2013:
Cost of the Machine $31,800 Add: Freight Costs$300 Installation costs $500 Total costs of the Machine$32,600 Less: Residual value ($1,900) Depreciable value of the Machine$30,700 Useful life of the Machine 10 years Annual depreciation ($30,700/10 yrs)$3,070
As f.o.b. the place of manufacture, freight costs shall be considered as cost of machine in buyer's books. Also while calculating depreciation, machine's estimated useful life and salvage value should be considered. That is, machine's physical life and salvage value shall be ignored. From above calculation, it is clear that depreciation of $3,070 is charged on the machine for the year 2013. As$1,980 has been debited to machine account on Jun 1,2014, depreciation calculation for rest of 9 years shall be revised as follws:
Total costs of the Machine $32,600 [As calculated above] Less: Depreciation for 2013 ($3,070) [As calculated above] Book value as at Jun 1, 2014 $29,530 Add: Amount debited to machine$1,980 Revised book value of the Machine \$31,510 | 649 | 2,595 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2020-05 | latest | en | 0.951074 |
https://artofproblemsolving.com/wiki/index.php?title=Special:RecentChanges&from=20210517093749&hidemyself=1&hidebots=0&hideminor=1&days=1 | 1,624,159,202,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487655418.58/warc/CC-MAIN-20210620024206-20210620054206-00481.warc.gz | 117,628,305 | 16,026 | # Recent changes
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21:03 2021 AMC 12B Problems/Problem 12 (diff | hist) . . (+631) . . Aop2014 (talk | contribs) (solution was removed for some reason)
20:08 User:MRENTHUSIASM (5 changes | history) . . (+365) . . [MRENTHUSIASM (5×)] 20:08 (cur | prev) . . (-55) . . MRENTHUSIASM (talk | contribs) (→External Links) 20:07 (cur | prev) . . (-4) . . MRENTHUSIASM (talk | contribs) (→External Links) 20:07 (cur | prev) . . (+176) . . MRENTHUSIASM (talk | contribs) (→External Links) 10:58 (cur | prev) . . (+126) . . MRENTHUSIASM (talk | contribs) 09:48 (cur | prev) . . (+120) . . MRENTHUSIASM (talk | contribs)
17:19 1977 AHSME Problems/Problem 28 (2 changes | history) . . (+16) . . [Aopspandy (2×)] 17:19 (cur | prev) . . (+14) . . Aopspandy (talk | contribs) (→Solution 1) 17:19 (cur | prev) . . (+2) . . Aopspandy (talk | contribs)
16:42 User talk:Flamekhoemberish (3 changes | history) . . (+669) . . [MRENTHUSIASM (3×)] 16:42 (cur | prev) . . (+185) . . MRENTHUSIASM (talk | contribs) 15:22 (cur | prev) . . (+7) . . MRENTHUSIASM (talk | contribs) (→Chats) 15:21 (cur | prev) . . (+467) . . MRENTHUSIASM (talk | contribs) (→Chats)
16:30 1995 IMO Problems/Problem 2 (3 changes | history) . . (0) . . [Samrocksnature (3×)] 16:30 (cur | prev) . . (-1,489) . . Samrocksnature (talk | contribs) (→Solution 8 (AM-GM only)) 14:58 (cur | prev) . . (+16) . . Samrocksnature (talk | contribs) (→Solution 8 (AM-GM only)) 14:58 (cur | prev) . . (+1,473) . . Samrocksnature (talk | contribs) (→Solution 7 from Brilliant Wiki (Muirheads) =)
N 15:10 1977 AHSME Problems/Problem 27 (diff | hist) . . (+556) . . Aopspandy (talk | contribs) (Created page with "==Problem== There are two spherical balls of different sizes lying in two corners of a rectangular room, each touching two walls and the floor. If there is a point on each bal...")
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15:09 User:Flamekhoemberish (diff | hist) . . (+160) . . MRENTHUSIASM (talk | contribs) (Flame Kho gave me the permission creating and editing the user page.)
N 15:09 1977 AHSME Problems/Problem 20 (diff | hist) . . (+755) . . Aopspandy (talk | contribs) (Created page with "==Problem== [itex]\begin{tabular}{ccccccccccccc}& & & & & & C & & & & & &\\ & & & & & C & O & C & & & & &\\ & & & & C & O & N & O & C & & & &\\ & & & C & O & N & T & N & O...")
14:54 1990 AIME Problems/Problem 8 (6 changes | history) . . (+1,987) . . [MRENTHUSIASM (6×)] 14:54 (cur | prev) . . (+130) . . MRENTHUSIASM (talk | contribs) (→Solution) 12:08 (cur | prev) . . (+505) . . MRENTHUSIASM (talk | contribs) (→Remark) 11:51 (cur | prev) . . (+973) . . MRENTHUSIASM (talk | contribs) (→Remark) 11:20 (cur | prev) . . (+172) . . MRENTHUSIASM (talk | contribs) 10:49 (cur | prev) . . (+74) . . MRENTHUSIASM (talk | contribs) 10:14 (cur | prev) . . (+42) . . MRENTHUSIASM (talk | contribs) (Added in the diagram. Source: https://gogangsa.com/339)
13:04 2020 AMC 8 Problems/Problem 21 (diff | hist) . . (+142) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:59 2020 AMC 8 Problems/Problem 19 (diff | hist) . . (+142) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:56 2020 AMC 8 Problems/Problem 18 (diff | hist) . . (+141) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:54 2020 AMC 8 Problems/Problem 17 (diff | hist) . . (+139) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:53 2020 AMC 8 Problems/Problem 16 (diff | hist) . . (+142) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:51 2020 AMC 8 Problems/Problem 14 (diff | hist) . . (+141) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:49 2020 AMC 8 Problems/Problem 13 (2 changes | history) . . (+142) . . [Timz2005 (2×)] 12:49 (cur | prev) . . (0) . . Timz2005 (talk | contribs) (→Video Solution by North America Math Contest Go Go Go) 12:47 (cur | prev) . . (+142) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:45 2020 AMC 8 Problems/Problem 12 (diff | hist) . . (+142) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:45 2020 AMC 8 Problems/Problem 11 (diff | hist) . . (+142) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:43 2020 AMC 8 Problems/Problem 10 (diff | hist) . . (+141) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:42 2020 AMC 8 Problems/Problem 9 (2 changes | history) . . (+142) . . [Timz2005 (2×)] 12:42 (cur | prev) . . (+2) . . Timz2005 (talk | contribs) (→Solution 2) 12:40 (cur | prev) . . (+140) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:39 2020 AMC 8 Problems/Problem 8 (diff | hist) . . (+142) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:37 2020 AMC 8 Problems/Problem 6 (diff | hist) . . (+104) . . Timz2005 (talk | contribs) (→Video Solution by WhyMath)
12:35 2020 AMC 8 Problems/Problem 5 (diff | hist) . . (+102) . . Timz2005 (talk | contribs) (→Video Solution)
12:34 2020 AMC 8 Problems/Problem 4 (2 changes | history) . . (+68) . . [Timz2005 (2×)] 12:34 (cur | prev) . . (0) . . Timz2005 (talk | contribs) (→Video Solution 1) 12:32 (cur | prev) . . (+68) . . Timz2005 (talk | contribs) (→Solution 3 (variant of Solution 2))
12:27 1989 AHSME Problems/Problem 24 (4 changes | history) . . (+424) . . [Th1nq3r (4×)] 12:27 (cur | prev) . . (+8) . . Th1nq3r (talk | contribs) (→Solution) 12:26 (cur | prev) . . (+2) . . Th1nq3r (talk | contribs) (→Solution 2) 12:26 (cur | prev) . . (+6) . . Th1nq3r (talk | contribs) (→Solution 2) 12:26 (cur | prev) . . (+408) . . Th1nq3r (talk | contribs) (→Solution)
10:14 1990 AIME Problems (diff | hist) . . (+46) . . MRENTHUSIASM (talk | contribs) (→Problem 8: Added the diagram. Source: https://gogangsa.com/339)
10:12 (Upload log) . . MRENTHUSIASM (talk | contribs) uploaded File:1990 AIME Problem 8.png
09:42 1988 AIME Problems/Problem 8 (2 changes | history) . . (0) . . [MRENTHUSIASM (2×)] 09:42 (cur | prev) . . (+1) . . MRENTHUSIASM (talk | contribs) (Undo revision 156356 by MRENTHUSIASM (talk)) (Tag: Undo) 09:42 (cur | prev) . . (-1) . . MRENTHUSIASM (talk | contribs) (→Solution 1 (Algebra: Generalized)) | 2,762 | 7,120 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2021-25 | latest | en | 0.944091 |
https://hubpages.com/education/How-to-work-out-percentages_ | 1,490,289,847,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218187144.60/warc/CC-MAIN-20170322212947-00130-ip-10-233-31-227.ec2.internal.warc.gz | 782,730,523 | 105,253 | # How to Work Out Percentages - Some Tricks to Help You Work Out Percentages Without A Calculator
"Lisa" , a "social sciences enthusiast" and Mom of three grown kids, writes from personal experience/exposure and/or past research
## Author's Note
If you're looking for conventional/standard ways to do percent problems you'll find several links to "real" math sites by scrolling down toward the end of the main part of this Hub. That isn't the purpose of this Hub; and although I've considered including more conventional approaches here, I think it's most fair to people looking for help with percent problems to direct them to sites that do a better job showing those conventional approaches than I can. After all, that's the sole purpose of those sites. For more on the purpose/intent of this Hub see "More About This Hub" below.
## Some Handy "Tricks" for Doing "Percent Problems"
A Few Notes On The Basics:
In order to find x percent of any number the general way of doing that is to multiply the number by the percentage. Since percentage means hundredths of any number, percentages are written with the decimal point moved two places toward the left-hand side. With whole numbers the decimal point does not show, and since moving the decimal point over one place would indicate tenths, examples of how percentages should be written before multiplying are: .05 (five percent) or .20 (20 percent). An example is find 40% of 80: Multiply 80 (since its a whole number you don't see the decimal point) by 0.40 (which is how percentages can be written, although the 0 before the decimal point isn't really necessary). The answer is 32.
Multiplying any number by any percentage (and remembering to include the decimal points in the answer) will give the percentage.
Quick Tricks
Quick tricks for finding percentages can be used. For example, if one wants to find 30% of a number s/he can start with the original number, mentally move the decimal point over one place (in order to find 10% really quickly) and then multiply that 10% by 3 (because 10 x 3 =30). Any time the percentage involved is divisible by 10 this trick can be used.
Another quick trick for finding 5 percent is to move the decimal point over one place (again, to find 10 percent easily) and divide that result in half (because half of 10 is 5).
Finding percentages that are multiples of 5 (for example, 25) can be done in three steps: Move the decimal point over one place to get 10%, divide that figure in half to get 5%, and then mulitply that figure by 5 (because 5 x 5 = 25).
Also, knowing that 10% equals 1/10th of any number means that finding 10% can also be done by dividing by 10.
Most people are familiar with the fact that a quarter (25 cents) is 1/4th of 100 and that 50 cents is 1/2 of 100. Keeping those basics in mind, one can easy remember that finding 25% of any number means dividing it by 4 and that finding 50% of any number means dividing it by 2.
In the case of something like 75% figuring that out could be done either by using the above divisible-by-5 method or, if its easier, finding 25% and multiplying that by 3 (because 3 x 25 = 75).
A trick for finding 40% might be moving the decimal point over one to get 10% and either remembering that figure or writing it down. Then divide the number for which you're trying to find 40% of by 2. Once you have half of the number subtract that 10% you first figured out - and you've got your 40%.
The finding-10% trick/aid can also be turned into a finding=1% trick/aid. If you move the decimal point over two places you have found 1% of any number. You can easily multiply that 1% to get any other percentage simply by asking "how many 1's are in this percentage?". For example, to find 20 percent you can first find 1% and then multiply that 1% by the 20 (because there are 20 1's in 20). This will also let you find, for example, the 20%.
Finally, there is the issue of figuring out a tip in a restaurant. Again, the quick way (for 15%) is to move the decimal over one place to get the 10%, divide the 10% to figure out what 5% is, and then add together the 10% and 5%. A 20% tip is easier - just get the 10% and multiply it by 2.
## Math Help
This Hub was originally written to show "quick mental tricks" for doing percent problems. It was written with adults in mind and in response to a request. It was not intended to offer more than those quick tricks for common percent problems. The aim was to offer people those tricks they could use in situations involving things like shopping and tipping. Sometimes we need a quick way to figure a tip or sales tax. Sometimes we want to know how much a product will cost when we learn it has a "75%-off price". The aim was to offer a few simple ways people can do percentage problems in their head that can come in handy, and that don't show up too frequently in the "standard" search on doing percentage problems.
When I wrote the Hub I didn't change the wording in the request, and now that it has taken on a nature/life of its own it is clear the title is no longer appropriate or sufficient (to describe the content). I could change the title, of course, but the Hub has found its place in search engines and has turned out to help a lot of people (usually young students) who were having some trouble "getting" how to do percentages. As a result, I don't want to change the title and risk the Hub's "getting lost to the ages".
The nature of the Hub evolved, though, because readers began asking for elaboration on the original approach (the "mental tricks") . From there, readers began asking about percent problems that went beyond the kind one would do using those "mental tricks".
Originally, I had approached writing this Hub (in answer to that question/request someone had posted) as if I were sitting at the dining room table, trying to help a middle-school or junior-high student understand percentage problems. So, it started out "folksy" and in terms that wouldn't show up in math books; and as things evolved and all those questions/comments continued to be posted, I continued to use the same approach.
The way I've seen it, if someone is asking how to figure a percent problem there's a good chance it's because they haven't already become comfortable "doing percents" as taught/being taught in school. So, as questions about finding percents have continued to come in (and as a lot of them have gone way beyond the original intent of this Hub), I've found myself using whatever words or combination of words and techniques I can "pull out of the air" in an attempt to make understanding what "is going on behind a percent problem". People who have trouble "getting" some things in math have that trouble because things like equations on paper don't mean anything to them.
In any case, the Hub has taken directions that weren't the original intent. At the same time, when new questions have been posted I've just figured, "It's easy enough for me to just answer them." As a result, the comments section of this Hub has become very much aimed at people for whom math class and math books haven't happened to be very effective (or wasn't effective enough for them to remember if they were students years ago).
The point is, if you're comfortable with math and having no particular challenge learning from math teachers or books, 1. You either don't need this Hub or else you need one of those conventional "how-to-do-math" sites, from which you can easily find that little extra bit of information you need., and 2. There's a good chance you'll find this particular absolutely "wacky".
If you've always been comfortable learning math there's also a good chance you can't imagine how a perfectly "smart" student may have trouble learning one thing or another, only because an adult hasn't figured out that he needs someone to think up a different way of presenting one thing or another.
Adults who may have, as students, once hit a "stumbling block" on one math thing or another, and adults who have ever had to watch a student struggle with one kind of problem or another (or most of them), will understand why I've left all the questions and answers in the "Comment" section on this Hub.
## More Math Help
0 of 8192 characters used
• 23w 4 years ago
confusingggggggg
• Author
Lisa HW 5 years ago from Massachusetts
Sheila, Sp; sorry I didn't see this for several hours.
In a problem involving dollars and percentages that end in zero, the easiest thing is to keep in mind that a penny is 1% of a dollar (100 pennies), so 1/10 of a penny is 1/10 of a percent.
You can just move the decimal point over two places (toward your left) to find 1%, and once you're found that move it over one more time to get the 1/10 of a percent of the total dollar amount.
After that, you need to remember to subtract what you got for 1/10 of a percent from the total dollar amount that you started with.
• SPSBrown 5 years ago
The discount is 1/10th of a penny. So how do I come about finding out what that discount is for \$390,936.47? Do I multiple \$390,936.47 by .001 to obtain the discount? Or is there are different number other than .001 that I should be using. I was provided with the amount as \$867.12 as the discount for 1/10th of a penny of \$390,936.47. Not sure how they came up with \$867.12, can you help?
• SPSBrown 5 years ago
The discount is 1/10th of a penny. So how do I come about finding what that discount is for \$390,936.47? Do I multiple \$390,936.47 by .001 to obtain the discount?
• Sheila 5 years ago
The discount is 1/10th of a penny. So how do I come about finding what that discount is for \$390,936.47? Do I multiple \$390,936.47 by .001 to obtain the discount?
• Lost 5 years ago
I think I need to see more steps, seems like this stuff skips steps
• ineedhelp 5 years ago
i paid 80 for shoes that was 15 percent off what was my original price?
• adorababy 6 years ago from Syracuse, NY
Thank you for sharing the quick tricks. They brought back old techniques as well.
• sean 6 years ago
James
29,000 minus 3,500 divide 29000 x 100 equals 87.9% drop in gate
i hope this helps and confused you all more
sean
• pc 6 years ago
i dont no how to do much math but everybody who has written is very good at writing news tips witch is really cool one day i hope to be as smart as albert instein and all of you thank you everyone
• kenny 7 years ago
nice bro
• wth 7 years ago
wow, you guys talk waaaayyy to much about math...cbs reading all of it...
• Forest City 7 years ago
If I had \$2220.88 and made \$1.86 interest what would my lowly interest rate be?
• Author
Lisa HW 7 years ago from Massachusetts
Skyman, sorry I haven't seen my e.mail (with comments from Hubs) until a few hours after you posted. If I understand what you want to do, it's just to find averages? In order to find an average you add up each number in a column of the different numbers you have that apply to one thing or another (as in the case of your column of 13 percentages) and then divide what you get by the number of numbers in the column.
In other words, add up your 13 different percentage numbers and divide the total by 13.
• skyman3565 7 years ago
I hope you can help me, I have 13 different percentages and need to work out the average, how?
• Author
Lisa HW 7 years ago from Massachusetts
The conventional way to figure that kind of thing out is to multiply the 250 x .40 (in other words, multiply 250 by 40%).
The quick-trick way to do it is to keep in mind that you can find ten percent and multiply it by 4. There are a few reasons that can make this kind of percent problem much simpler.
You can find 10% (one-tenth) of 250 just by knowing that with 250 there's an imagined/invisible decimal point that is after the 0. All you need to do is move that decimal over one space toward your left to see one-tenth of 250, which is 25.
Now you're dealing with the smaller number (25) that's easier to work with it/multiply in her your head. Also, now you're dealing with only having to moving the decimal point after you're finished.
So, with a problem like this, keep in mind that one-tenth of any number is also one-tenth of 100% (because 100% means "all" of any number).
So all you have to do is think of one-tenth/ten percent of 250 (by mentally moving the decimal point over and "turning it" into 25. Now that you have 10%, all you have to do is multiply that by 4 (because 40% is 4 times 10%).
The answer to your problem is that 100 people were senior citizens (because 25 people would be 10%/one-tenth, and multiply 25 times 4 gets you 100).
You could double-check your answer by thinking of what 60% would be (because 60 and 40 would add up to that 100%). If you think of how 25 is one-tenth/10% of 250 and multiply 25 times 6, you'll get 60%. 6 25's is 150. Double-checking will show you that the 60% (150) added to the 40% you got earlier (100) adds up to the 250.
• Duno 7 years ago
I have a big problem need some help this is my question
At a local cinema, 250 people attended the 8.30pm showing
of a film. 40% of these people were senior citizens.
How many people attending this film were senior citizens?
• wendywu 7 years ago
After reading your great page, does the maths question just want you to work out the %? ie divide \$12 by 10% = 1.20, the x till you get 4.80 = 40%. The book is the same therefore 40%, so the last one must be 3.50 pounds. ie \$7 x 10% = .70 cents, x 4 = 3.20. As Lisa HW says, sometimes we can make it too complicated.
• Author
Lisa HW 7 years ago from Massachusetts
tearing my hairout, sorry I haven't seen your comment until just now (six hours after you posted it). From what you have here, there isn't particularly a percentage problem, as it is a currency conversion one. You can find online currency converters that will convert pounds to dollars and or dollars to lbs. Here's one (but don't go to it until you read the last half of this response to your question, because I don't think the problem is really about the current conversion rate):
http://www.dollars2pounds.com/
I'm not sure what work your daughter's teacher wants her to show, if any, beyond converting the 7 dollar shirt into pounds. The converter above shows that the shirt would 4.28 pounds.
Based on the converter I used just now, the 5 dollar book would be 3.06 pounds. The conversion rate changes. The converter I used shows that the 12 dollar perfume would be 7.34 pounds. The total for the book and perfume are 10.40 pounds. I'm guessing the problem, though, is based on whatever conversion rate is presented - not the current one.
Current conversion rate aside, if you divide the 12 by 4.80; and if you divide 5 by 2.00, you'll see that the teacher's conversion rate is 2.5. Based on that, there would be 2.5 dollars for 1 pound. If you divide the 7.00 by 2.5 you get 2.80 (pounds). The total Baker spent in pounds is 9.60 pounds.
You can double check that by adding up in dollars what he spent (12, 5, and 7), which comes to 24 dollars. If you divide the 24.00 by 2.5 you will get 9.60 pounds.
I'm guessing what the teacher wanted students to know is to first find the conversion rate by dividing dollars by pounds; and then use that to figure out the rest of the problem.
• tearing my hair out! 7 years ago
Could you try and explain this one that came home as my 10 year old daughters homework.
Mr Baker buys some perfume for 12 dollars and a book for 5 dollars,
He calculates that the perfume cost £4.80 and the book cost £2.00
How much would a 7 dollar t-shirt cost in pounds?
Thanks
• jessica 7 years ago
you are wonderful!! i really enjoyed reading all of your responces :) You would make a fabulous teacher!!
• Author
Lisa HW 7 years ago from Massachusetts
says, thanks. Someone else pointed that out. It started with a typo ages ago. I thought I had fixed it. I've removed the errors for now until I go back over it, see what typos was fixed or not fixed, and make whatever corrections have to be made as a result of it.
• 7 years ago
6.25% or 300 is 18.75 not 18.25
• Arty 7 years ago
i dont get it
• jestone 7 years ago from America!
I love math tips! Thanks.
• puppascott 7 years ago from Michigan (As far as you know...)
Read this post right before I posted my version of dealing with percentages. I wanted to make sure i wasn't stepping on toes. Good stuff.
• Author
Lisa HW 7 years ago from Massachusetts
rachael, I don't know if you'll see this note, but I'm posting it anyway. I'm sorry I didn't see your e.mail until long past when my answer would have been helpful to you. Apologies.
• Author
Lisa HW 7 years ago from Massachusetts
steve, thanks (apparently, ibro, a couple of comments up, doesn't think so :) )
• steve. 7 years ago
Wow great site and exellent tips thanks...
• Author
Lisa HW 7 years ago from Massachusetts
To Sandy, who sent me the e.mail, "How do I figure a percentage of 77 out of 300? What would be the percentage?"
The calculator way is to multiply 300 by .77
An easy, in-your-head, way may be to first find 1% and 10% and work from there.
Since you know that 10% (one-tenth) of 300 is 30, you can just move the decimal to see that 1% of 300 is 3 (or you could have just divided the 300 by 100 to get the 3, but sometimes the first way I mentioned can seem clearer to some people).
Since you know that 30 is 10% of 300, all you have to do is multiply 7 times 30 to get 210 (which will you show you what "70 of that 77 percent") is.
Since you don't just want to know what 70% is, and need to know what "that additional 7% is), multiply that "additional 7" by the 3 (because the 3 is 1% of 300; so you're seeing percentages in "single units" for that additional 7).
Anyway, 7 x 3 is 21. So now you would know that the 70 part of that 77% is 210; and you would know that the 7 part of that 77% is 21.
If you add the 210 (70%) to the 21 (7%) you will get the whole 77% of 300.
• Author
Lisa HW 8 years ago from Massachusetts
Thanks, Proud Mom. With what I know you've had going on with your child recently, I can imagine how you may not have much interest in thinking about math right now.
I don't really know what I have for an IQ, but I don't think my fair understanding of junior high math is particularly an indication of much of anything. :) After the day I've had today, I think my IQ is about 45 right now. :)
• Author
Lisa HW 8 years ago from Massachusetts
Thanks, Proud Mom. With what I know you've had going on with your child recently, I can imagine how you may not have much interest in thinking about math right now.
I don't really know what I have for an IQ, but I don't think my fair understanding of junior high math is particularly an indication of much of anything. :) After the day I've had today, I think my IQ is about 45 right now. :)
• Proud Mom 8 years ago from USA
I'm going to have to come back and read this one very s-l-o-w-l-y. But it's looks better than any math book I've seen!!
Wonder what your IQ is?!? :-))))
• Anthony 8 years ago
you need to be a teach, you dont even need a calculator for this...
• Chris 8 years ago
Thanks Lisa for the refresher and tips
• Jaimie that is stuck 8 years ago
What is the 7.65% Social Security/Medicare tax on a paycheck of \$430?
• vindya 8 years ago
Thanks Lisa!!!! You helped me out a great deal with your wonderful explanations, thanks again!
• Author
Lisa HW 8 years ago from Massachusetts
I'm going to use a half gallon (64 ounces) as an example of how to work it out (and assume no evaporation is going to be allowed to happen).
You know that right now you have 32 ounces of alcohol. You need to figure out how much 32 ounces is 35% of. First, you write the 35% as .35.
You know that 32 amounts to .35 of something (call it "x").
A different way to say it is: 35 x (think of it as "35 somethings") = 32.
How do you figure out how what x is? How many "somethings" go into 32 35 times? You would divide 32 ty 35, BUT because you're dealing in a percent you actually divide the 32 by .35 (the way you wrote that 35% above).
By dividing 32 by .35 you would get: 91.42857
You can check that answer by multiplying the 91.42857 by .35 (35 percent), and you'll get 32.
If you round off the answer you'll get 91.43 or 91.4, depending how much you want to round. You could also round to the 91 (because 43 is less than 50).
You're not done yet, though:
Now you need to subtract 64.00 from 91.43 to see how much water to add. 91.43 minus 64.00 = 27.43 ounces. If you didn't round you'd get 27.42857 ounces.
Again, you could double-check by calculating 35 percent of 91.42857. If you multiply that 91.42857 by .35 you will get 32.
Note: It's before 6:00 a.m. on a Monday morning. I'm pretty sure all this works out; and I hope I helped make things clearer; but if anyone notices some error in my wording - I'm not responsible!
• bob 8 years ago
here is one i have a litre of in which fifty percent is alcohol now how much water do i put in to make it 35 percent and or how would i calculate that
• Author
Lisa HW 8 years ago from Massachusetts
Tes, I'm guessing you have too much on your mind. That's probably the biggest reason people have trouble getting math steps. For 30% of 72:
You could first find 300% (which is 3 times 100%) and then move the decimal.
Here's a typical example of a trick to do in your head:
You know that 3 times 7 is 21, so 3 times 70 is 210 (the decimal point moved over one place). You know that 3 times 2 is 6. If you add that 6 to the 210 you got when you multiplied 70 by 3; you'll have 216.
216 is 300% of 72, but you don't want 300%. You want 30%. To find that just move the decimal point over one place toward your left. 216 divided by 10 is 21.60 (don't forget you have to add that zero as a place holder when there is only one digit after the decimal point).
A different approach would be to find 10% of 72 and multiply that by 3 (because 30 is 3 times 10):
To find 10%, just move the decimal point over one place toward your left (in other words divide 72 by 10): Moving the decimal point to show 1/10 (which is 10%) in 72 would result in getting 7.20.
Once you get that 7.20 (which is only 10% of 72) you would want to multiply it by 3 (because, again, 30% is three times 10%). Multiplying that 7.20 (you got when you moved the decimal point over) by 3 (because you need 30% instead of the 10% you now have) will get you 21.60.
Yet another different trick finding 300% and dividing by 10:
Think of the 70 as one thing. Think of the 2 as another thing.
Think of 3 times 70, and you get 210. Think of 3 times 2 and you have 6.
Add the 210 and the 6 - and you have that 216. That's 300% of 72. Now just think of what one-tenth of that would be, and that, of course, would be the 21.60 (because you moved the decimal point over, which is what you do any time you want to find one-tenth of anything).
• Tes 8 years ago
I was trying get to girips with 30% of 72 by hand, i have an exam in london and they, for some reason feel the need to ban calculators!
• Tes 8 years ago
I just dont get it! I must be the dumbest man on the planet! (with poor spelling to!) Im trying to work it out by hand and its just not coming to me what shall i do?
• Author
Lisa HW 8 years ago from Massachusetts
Hi, James. This particular type of calculation goes a little past the kind of "quickie mental tricks" I have for percentages that apply to grocery shopping, tips, and sales taxes. Most people would prefer to use a calculator for this type of calculation.
What you would need to do is figure out the difference between 29000 and 3500 (which is 25500). Because you're interested in what percentage 25500 is of 29000, you would divide the 25500 (the difference) by 29000. After calculating that, you would multiply the answer by 100. Depending on what you're doing you may choose to round, but if you do there will always be a slight discrepancy if you try to "back check" your figures.
(In other words, it used to be 29000 but went down by 25500, so what you need to know is what percentage of that original number (29000) is that 25500. )
You can check your calculations by figuring out what percentage of 29000 the 3500 is (divide 3500 by 29000 and multiply the answer by 100). Once you have what percent (parts of 100%) 3500 is, you can substract that percent from 100 - and you should get an answer that shows what percent of 29000 the 25500 is. (The 3500 is x percent of the original 29000, and the 25500 difference is x percent of the original 29000, and those percentages should add up to 100% of the 29000).
I got 87.9 for 25500; and 12.1 for the 3500. The 87.9 and 12.1 add up to 100%.
I'm including here links to a few sites that do a more "professional" job of explaining how to do this type of calculation (in order of helpfulness, in my opinion). I'm also including a "non-professional" link that adds a simple remark that may be worth including.
This is an excellent one (scroll down to where this type of calculation is done):
http://www.copydesk.org/words/math.htm
Here is one that shows it in a different way:
http://mathcentral.uregina.ca/QQ/database/QQ.09.06...
These three links are also good:
http://www.helpingwithmath.com/by_subject/percenta...
• James 8 years ago
Hi Lisa, i wanted to work out the difference in percentage between two figures. How would I work out the difference (in percentage) between 29,000 and 3,500. Basically both those figures are average attendances for football matches between 2006 and 2007, i wanted to find out how much in a percentage the attendence has dropped in the year. Thanks for your help :)
• James 8 years ago
Hi Lisa, i wanted to work out the difference in percentage between two figures. How would I work out the difference (in percentage) between 29,000 and 3,500. Basically both those figures are average attendances for football matches between 2006 and 2007, i wanted to find out how much in a percentage the attendence has dropped in the year. Thanks for your help :)
• Author
Lisa HW 8 years ago from Massachusetts
Thanks for your nice words, Jen (but - believe me - it's no gift. It's more a matter of survival at the supermarket. :) )
Generally, I'd find 2.45% of any number by using the above "tricks" to find 24% of the number, and move the decimal point over one play to the left-hand side. For example, if you know that 24% of \$100 is, of course, \$24.00; then moving the decimal over one place to the left would give you \$2.40 (which is the 2.4% of \$100.00).
Another approach (that's easy but more complicated than the above quick approach) is:
Turn the 2.4% problem into two different problems: Since 2.4% is 2% plus 4 tenths of a percent, you could easily do it by first thinking of the number you're trying to find the percentage of, moving the decimal point over to get what 1% of that number is. Once you have the 1% you can then make the two different problems.
For example, if the problem is 2.4% of \$100.00, you know immediately that 10% (or 1/10) of \$100.00 is \$10.00. That means that moving the decimal point over one place to the left will show you \$1.00, which is, of course, 1% (1/100) of \$100.00. (All the words I'm using to describe this initial process make it seems like a far bigger deal than really doing it is. )
Once you have your 1% keep that in mind (or write it down), because that's what will let you find your answers easily.
This is when you break the problem down into two very easy problems:
Since you want to find 2.4% you want to find 2% plus 4/10 of one percent.
The first thing is to find 2% by simply multiply the 1% by 2. In this simple case, since 1% is \$1.00, mulitply that \$1.00 by 2 is, of course, \$2.00. You've got your 2% of \$100.00. Keep that figure in mind, or write it down, until you do the second simple problem, which is:
Think about that 1% again (\$1.00). Move the decimal point over one place to get get one-tenth of a percent (because now you're working with the numbers on the right-hand side of the decimal point 2.4%). Moving the decimal point will turn the \$1.00 into .10 (ten cents). Since you now know that .10 is one-tenth of one percent, all you have to do is multiply it by the 4, and you'll get the .40 cents, which is 4/10 of a percent of \$100.00. (Again, all the words make the problem look like a far bigger deal than it really is.)
Now that you know that 2% of your \$100.00 is \$2.00; and that .4% of \$100.00 is .40 cents, all you have to do is add them together. You get \$2.40 (which is, of course, the \$2.40 you would get by figuring out 24% and moving the decimal place over one place).
In other words turn the problem into two little problems, dealing separately with the numbers on each side of the decimal point . Then add them together.
Thanks again, for your kind words. :)
• Aussie Woman 8 years ago
G'day Lisa
I finally do get it - you've put it so simply & I could use my calculator (at last!) to follow. You have a gift & it's so generous of you to share it with people.
My question is - Please can you tell me how do I get 2.4% of something - I thought about cheating and rounding it up to 3% to make it easier - but that doesn't improve my knowledge at all. I can understand when it's .25% or .75% but what about this sort of thing how do I calculate that?
Thank you so much for being you
Jen
• Jess Ba-ad 8 years ago from Philippines
We usually grab a calculator when we need some math. This info is so useful when there is no calculator at hand. Thanks
• brain ache!! 8 years ago
Thanks for all your help needed to look up on percentages for a test im taking and you've really helped :-)
• Author
Lisa HW 8 years ago from Massachusetts
It did go through, but after I replied to your first post I thought of something I should have included:
Actually, yesterday I did run into a \$700,000 house I wouldn't mind buying if I had the extra money. Do you think I could hire myself out as a "Sixth-grade, math-homework-doer" and earn enough to buy that 14-room house, which always looks so great at Christmas time? :)
In the interest of full disclosure, I was a kid who had no trouble learning math in elementary school, but when I got to seventh grade I was put in an "experimental modern math" class (which came to be the math that is now taught in schools). I did ok until my family moved, and because the new school didn't have the same math program the other school had, I was put in yet another and more advanced "modern math" class for a couple of years.
Maybe it was the sudden jump, or maybe it was the teacher, but from then on I never could see how that particular math "related to real life". I had my good grades in high school math under certain circumstances, but my inability to find high-school math "applicable to real life" (bizarre as that sounds to anyone who knows better, including my more mature and present self) made it close to impossible for me to "waste my free time" on math homework (!!!). So, whatever homework I did I did in English class (where the material came easily to me and didn't require paying attention).
As a kid, I blamed myself for not being able to make myself do what I truly wanted to do and knew I should be doing. I was about 40 years old when I finally figured out that I hadn't been lazy or careless. I had been without a teacher who knew enough to just point out how math applies to real life and gives us a new way to approach problem solving - even when the problem isn't a mathematical one.
Kindergarten and first-grade children are routinely shown the "apples and oranges" problems, but when kids get to sixth grade or so, and the math is no longer about simply adding and substracting, I think adults sometimes don't realize that some kids (maybe most) still need to see how something like Algebra is used in real-life problem-solving. Sometimes, too, maybe kids need to learn not just one way to find something like percentages, but a number of different little tricks that - when they see them - will help them see how it all fits together.
I grew up to be a person who is ok with math. In fact, I grew up to be a person who actually uses Algebra in my real-life problem-solving, even though I've chosen to work in areas that are more words- or people-focused. Still, I know the schools are full of kids who are - to one degree or another - like I was, with some having their grades only mildly affected but others having their academic journey more seriously harmed.
In a way I feel like a fraud, presuming to attempt to offer tricks on even something as elementary as percentages; but then again, there's a part of me that thinks there's a chance a "non-math" person may be able to explain things to another "non-math" person in a way the other person relates to more.
I don't over-estimate the degree to which my little percentages hub may be of any help to anyone; but if it turns out that it's of a little help to a few students who, for one reason or another, didn't quite catch on in class, then, to me, that makes the half hour or so I spent writing so much more well spent than it would have been on some other activities.
Again, thanks for your kind words. (I suppose, though, I'll have to wait on that 14-room house for now. Maybe if I'd had a better love of math when I was in sixth grade I would have become an architect or engineer, instead of dreaming of becoming an English teacher or social worker. :))
• compu-smart 8 years ago from London UK
Not sure if this went through the stystem, but i just wanted to say that you should have a donation button on this page for all your hard-good work your doing!!
Good job;)
• Author
Lisa HW 8 years ago from Massachusetts
Chikka, Math isn't always as hard as it can seem to be when you're in school. I'm not a math teacher, and math has never been my favorite subject (whatsoever); but when somehow all the things they try to teach in school just seem a lot easier once you get old enough to kind of see how easy things really are.
Something a lot of students don't realize is when they're "all nervous" and tense about homework or school subjects brain chemicals can actually change and make concentrating on what you're trying to learn more difficult.
What I recall about being around your age is not seeing math the way I eventually came to see it. As a student, I saw it as a bunch of unrelated things that were used to find numbers (or something like that). Once I got older I started to see that math is like a giant puzzles that makes one, big, picture (or whole) and that doing things like finding fractions and percents were really just different ways of seeing the pieces of that puzzle.
Another simple way to imagine math is to always kind of keep that picture of 100 pennies in your mind. You can imagine how you could multiply that dollar's worth of pennies by any number you want, or if there were a way to cut the pennies into tiny, equal, pieces, you'd be dealing with fractions (of 1). Math, though, is little more than ways of playing with those "pennies". Another way to see how math is nothing more than something that represents real stuff in the world might be to get something like a thousand Bingo chips or Poker chips; or else cut some paper into thousands of equal pieces and just play with it. Divide it into little groups of paper, add groups together, stack them up in equal stacks, and then make new stacks with different amounts of them.
I guess my point is that it's important not to think of numbers as "just numbers on paper" and math operations as "just isolated things you have to learn". While more advanced math can certainly seem a little trickier, in terms of drawing a connect connection to something like stacks of Poker chips or pennies, if you can get very comfortable seeing how 6th-grade math is pretty much a matter of that "whole" puzzle with all those different ways of altering the pieces of it; it may give you a sense of feeling more sure and ready to take on the more advanced math later.
I can give you some words to describe what I have on my desk right now, and you'll know that the words I type represent something very real and concrete. For example: cup of coffee, stapler, telephone. You have no problem knowing exactly what the words represent. Well, if I gave you a number that number would represent something every bit as concrete and real as the coffee cup, stapler, and phone are. If I tell you I have 4 books on my desk and tell you I'll take one away, you'll automatically imagine how I now have 3 books on my desk. The number of books I mentioned tells you nothing about what the books are, how big they are, or what color covers they have. Numbers represent, as you know, how many of anything there is, was, or will be. Numbers do a separate job than words do, but the thing with math is that it is about learning tricks for playing with numbers.
Maybe it would help if you could try to always imagine how every number in the world represents a poker chip or a part of poker chip.
Finally, something else that may possibly help you get a stronger feel for the way numbers fit together: Take a piece of paper, rule off ten or eleven vertical colums and, maybe, 20 horizontal rows. If you haven't already done this (or if it has been a while) start by making a multiplication chart with numbers 1 through 20 down the left-hand side, and numbers 1 through 10 or so across the top.
You'll find filling in the chart fairly easy, but as you fill it in notice there's a real "system going on" to the whole thing. Then try a different kind of multiplication chart. Try setting it up the say way but imagining, say, that you'll be paid 5.00 an hour for work. Down the side put something like "Week 1", Week 2", "Week 3" etc. and across the top head the columns with, say, 1 hour, 2 hours, 3 hours, etc.
Imagine how much you could make working different numbers of hours each week, and then once you have your whole chart done you could notice how you could do easily check on something like, "If I worked for 20 hours a week how much will I have at the end of Week 4?" "If I worked for 12 hours a week how much would I have by the end of Week 3?" It doesn't have to be hours worked. It could be number of DVD's you'll be collecting, number of music files, or anything. The point is if you make yourself some charts when you have a little fre e time you'll start to get a real feel for how math is that bunch of puzzles pieces that fit together.
Someone hasn't managed to help you feel sure of math. If you take a little time to make yourself some multiplication tables (strange as that may seem) you'll be using what you already know, as well as noticing a few things you may have missed along the way. You'll be the one in charge of setting up your own math problems and what you'll do with them. It's one of the best ways to get that proverbial "hands on" experience and knowledge.
I hope all these words haven't just been a giant bore to you (or anyone else), but when people can really see the relationship of numbers to real life things (even though sometimes though things are abstract) math can be pretty easy.
• Author
Lisa HW 8 years ago from Massachusetts
6th Grader: Sorry I took a while to see this, but here's my response:
• Chikka that is confused 8 years ago
Lisa Hw your rea;ling smart at phsical and mental mathematics. If only you were here to help me with the thery But your not But reading all the Comments you posted can help me a little, WHY does mathematics have to be so HARD I'm only in grade 6 for crying out loud. Only 6 more years in school :(. Some one please help me!!!!!
Sincerely,
A confused 6th Grader That needs alot of help
• Chikka that is confused 8 years ago
There's this equation that says, 55% of 72 = ? But the thing is that I came up to the Ans: 95.4 and I'm confused because the answer is even larger than the real estate number set which is (72). Can someone PLEASE help we with this with sugar and ice-cream on top!!!??
Sincerely,
• compu-smart 8 years ago from London UK
Great hub!!
Very detailed explanations..
• Rob 8 years ago
Could you tell me how to work out what the % difference is between £16 & £17. Many Thanks
• trai 8 years ago
thanks this helps i knew tis b4 but forgot it i haven't used presentages in a while
• E. parker 9 years ago
thank you your page really help out an old timer like myself going back to school is a hard thing to do after you,v been out of it for so long.Thank again
• Author
Lisa HW 9 years ago from Massachusetts
• 7th grade kid 9 years ago
wow thank i got a A on my test
• Author
Lisa HW 9 years ago from Massachusetts
Well, it is the 580 multiplied by .06 (the .06 represents 6 1/100ths). The answer is 34.80.
Another way to do it is to quickly realize that 10% of 580 can be found by moving the decimal point over one place, and getting 58.00. 1% of 580 can be found by moving the decimal point over yet one more place (5.80).
You can then find 6% by multiplying the 5.80 by 6 (because 6 equals 6 1's). Again, of course, you will get 34.80.
• Confused 9 years ago
So what is the percentage of 6% in 580 ?
• Author
Lisa HW 9 years ago from Massachusetts
Oh noo..... don't tell me that. :) Let's see: One percent equals one one-hundredth of any whole. If you cut up a giant pie into one hundred pieces each of those pieces would equal one percent. Ten of those pieces would equal ten percent.
To find the percent of any number write a decimal point followed by the percent you want to find. For example, to write 40% as .40. What that means is 40 one-hundredths of the whole. To find something like 40% of any number multiply that number by the .40 (40% written in a way that lets you multiply). You'll get a number that shows that 40% of the whole is.
The trick for finding 40% quick is to remember that 40 is 4 times 10. Finding 10% is easy because to do that you just move the decimal point on place. (For example, 10% of 80 is 8. Finding 40% is just a matter of finding that 10% and multiply by 4 (because 4 x 10 equals 40).
• mistress 9 years ago
i still dont get it
• lauralong 9 years ago from East Texas
Good tips, I always forget and have to call my husband...
• MrMarmalade 9 years ago from Sydney
Thanks for very good lesson
• Albert 9 years ago
wow thanks alot u helped greatly. i owe u.
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• ### How to Calculate Pints, Quarts, Gallons to and from Pounds.
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• Author
Lisa HW 5 years ago from Massachusetts
Thank you, everyone for your comments, kind words, and questions. They've helped raise issues beyond the original intent of this Hub, and if it weren't for the comments and questions I wouldn't have thought to include a whole lot of things that I hope may have been helpful to someone. Sincerely appreciated.
• llololollollo 5 years ago
omg tanks i was strugaling!
• Author
Lisa HW 5 years ago from Massachusetts
Shannon, if, by any chance, you're having trouble finding your own comment (Oct 11, 2011) and my reply, look farther up (toward the middle of the comments). I've discovered some "technical issue", and I don't know what to do about it right now.) In any case, your comment and mine are both there.
• Author
Lisa HW 5 years ago from Massachusetts
Shannon: I approved your comment for posting here, but for some reason it isn't showing up. (Technical problem I'm having.) I was going to re-type it here, but now I can't seem to find your version of it either.
In any case, you asked about problems such as finding out what percentage of 40 27 is, or how to find out something like what percentage of 50 13 is.
You would find the answer to that kind of percent problem this way:
First you divide the 27 by 40.
Then you multiply the answer by 100.
In the example of what percent of 50 13 is,
you would divide the 13 by 50.
Then you multiply the answer by 100, and you'll get 26%. (13 is 26% of 50).
You can check this one easily by thinking of this:
13 is 13% of 100. So, because 50 is half of 100, 13 would make "twice as much of a percentage". (Two times 13 is 26.)
Basically, what you want to figure out (for example, in the one with 27 and 40) is, "How can I chop this 40 into equal 27 equal little bits. That's why you divide the 27 by 40. Once you see what each of those equal little bits are "worth", you need to multiply them by the 100 because that's what will show you what percentage of 40 the number, 27, is.
I hope this helps. (And I'm sorry that I seem to have done something to make posting your comment a "technical problem". We've had some changes in settings on HubPages, and maybe I've done something wrong with my setting.)
• Shannon. 5 years ago
I'm doing a test tomorrow on this stuff, and I'm not sure how to work out things like 27 out of 40 as a percentage, I understand that to find 13 out of 50 as a percentage is just how many times can you fit 50 into 100 which is 2 then times 13 by 2 as well to get the answer I'm just very confused on how to find out numbers like 40 and others that you cant fit equally into 100 :/ Can anybody help pleaseee!
• ruach 5 years ago
it is a awesome site
• Author
Lisa HW 5 years ago from Massachusetts
Note to "Lost" (I don't really know what you're comment isn't showing up, but I'll reiterate it for anyone reading: "Lost" commented that s/he is "lost" because it "seems like the above info skips some steps").
Reply: Hi, Lost. I'm sorry the info isn't helpful. The Hub does skip steps because the aim was to try to offer people "quickie" tips for finding percentages in their head. A better resource for the conventional way to work out percentages can be found in the gray block near the top of this Hub, which contains links to math help.
If you have a question about any of quick-trick examples I've included here, feel free to ask; and I'll do my best to clarify anything. :)
• Chris 5 years ago
Lisa HW, Your dedication to this posting has been astounding to me. Your efforts are definitely appreciated!
• anonamous 6 years ago
exuse me, how do you work out 21 percent of something? i'm very stuck and urgently need help! thank you. :)
• Author
Lisa HW 6 years ago from Massachusetts
Sim, probably the quickest way to find something like 35% of anything, might be to do something like think of what 10% is and then divide that in half to get 5%. For 35% (because there are 7 5's in 35), multiply what you got for 5% by 7.
With something like 25% of anything (or, as you say, 50% of something), just dividing by 4 or 2 (whichever applies) is easiest.
• Sim 6 years ago
Sorry the example was for you to let me know what the 65% and the 69% would be as they are both only worth 25% or 35% of 60%.
So what would 65% be as a 25% of 60% and
what would 69% be as a 35% of 60%
if that makes sense?
obviously if the grade was 25%,25%,50% it would make it easier as we would merely half or quarter the grade to find out what it is of the %age.
Thanks.
• Sim 6 years ago
Yes Lisa,
You are quite right in your second-guessing.
40% of the whole module comes from the one exam result
and the other 60% is coming from two parts - online test 35% of that 60% and the assignment being the 35% of the 60%. Each of the pieces of work are worth 100 marks.
40% and 60% adding together to make the whole 100% for the module.
Ok so let's just say I throw some random numbers out here for you to make understanding a bit simpler for me as im currently not well AT ALL so this is all still a bit confusing,
These are examples;
For the 25% of the 60% online test I got 65%(MARKS OUT OF 100)
For the 35% of the 60% assignment I got 69%(MARKS OUT OF 100)
For the 40% exam I got 73% (MARKS OUT OF 100)
Thanks for the help so far..!! x
• Author
Lisa HW 6 years ago from Massachusetts
Sim, I shouldn't be second-guessing what you say here; but I'm wondering if what they're saying is that 40% of the grade will be based on a test; and the other 60% made up of the other two (assignment and exam) combined (with the assignment making up 35% of the whole grade, and the test making up the 25% of the whole grade. (25% and 35%, of course, add up to the 60 - so I was just wondering if that's what they doing.)
Having said that (and if it's going to 25% of 60, etc.), if I were aiming to do it quickly I'd think of 10% of the whole grade and first multiply it by 4. That's the 40% quickly. What's left would be the 60%.
From there I'd find 10% of that number (the 60%)and multiply it by 2 to get 20% of the 60%. Keeping in mind what that 10% of the 60% was, I'd think of half that (5% is half of 10, of course) and add it to the 20% to get the 25% of that 60%).
I'd do the same kind of thing to get the 35% of 60% (get the 10%, multiply it by 3 to get 30%; then after half of 10% to get the 35).
(I still suspect they're saying 40% of the grade will be based on the exam, 35 based on the assignment, and 25 based on the test. Maybe I'm wrong, of course. :) )
• Sim 6 years ago
For my university grades this year in one module they have decided to make life difficult for us.
The total marks come in the form of
a test (25% of 60%)
an assignment (35% of 60%)
an examination (40%)
Quite clearly the 40% won't be the difficult one to figure out, but I'm a bit baffled on figuring the 25% and 35% of 60%.. Help here please?
• Diane Inside 6 years ago
Hey lisa just loved the refresher. I always get befuddled when I go to the market and it is a 30% off sale. Ha Ha. Now I can remember how to work that out to see what the savings would be. Thanks.
• wt1s3rv3r 6 years ago
Good Post!
• BESBES 6 years ago
If you know what 15% of an amount is, how can you find out what the total amount is (100%)? I use to know how to figure it when I was in school but don't remember it now.
• Author
Lisa HW 6 years ago from Massachusetts
ss sneh, I was unaware of that particular percentage. LOL
• ss sneh 6 years ago from the Incredible India!
Hi! Do you know the percentage of Google finding- "how to work out percentages" - this hub? 99.999999% ! -- Thanks
• rajeev 6 years ago
18 people as top management working in a company of a total manpower 1570
what is percentage of the management
how it calculate
• Author
Lisa HW 6 years ago from Massachusetts
Ivan, it does affect me. It's nice to think that the Hub has helped someone with a test in school. Thank you for coming back to share that nice piece of information.
• Ivan 6 years ago
Hi Lisa. This may not affect you but thanks to ur site I got 97% on my percentage and decimal test I showed my friend the site and he showed the teacher now the page is in our school bookmarks lol
• Author
Lisa HW 6 years ago from Massachusetts
sean w, thanks. The way you posted isn't just "an easier way" - it's pretty much THE way (as in "the way people learn in school how to do that kind of percentage problem). :)
I'm not so much addressing you here (since you seem to be all set when it comes to percentages now :) ); but you raised a point worth addressing about how there are pretty easy ways to do math problems; and how about how, in some ways, I've made things appear a lot more difficult by using a lot of words to try to explain how things are done.
This Hub began only as a "quick-mental-tricks" Hub, and it turned into one with people asking percentage-problem questions beyond quick mental tricks. Questions have come from young students, people who are having trouble with percentages, had trouble with that particular type of math problem in school, or just forgot.
Pretty much most of what I've offered in the Comments section (anything outside the "main Hub" here) is a matter of my assuming whoever has asked how to do one kind of problem or another could use someone to explain in a way other than the way math books or math teachers explain (because the "more conventional way" of teaching how to a percentage doesn't always work well for some people).
So what's here (as far as my responses to questions goes), is a whole lot of wordiness (and even "wackiness", at least within the context of math) that comes from my kind of stabbing-in-dark and trying to think of some "non-standard" way to make what's going on with percentage problems clearer to anyone who isn't comfortable with them.
One reason people forget what they learned in math (whether it's with percentage problems or other kinds of problems) is that they don't see "what's going on behind the written equation". It can look like "nothing but numbers/letters on paper" (even if they know what each number/letter represents and so can do the equation). What often happens is people learn how to do one kind of math problem in school, and then they forget a few years letter because they never really learned "what was going on behind the equation" enough for it to stay with them. It was just "one more kind of math problem to memorize".
I just thought it might be worth pointing out that if someone is looking for the "standard way" to do a percentage problem they'll be better off going to one of the links offered here. People looking for any quick mental tricks for doing percentages usually understand they won't be getting the "standard" way of doing things.
How all the comments seemed to evolve into being "regular" percentage-problem questions, I'm not sure - but that explains why there's so many unconventional approaches to doing things on this particular Hub. :)
sean (although the above wasn't particularly aimed at you and was instead aimed at kind of explaining to anyone else who reads from now on); thanks for pointing out something that never occurred to me (as a result of how this Hub started out as one thing and evolved into something else). This Hub has been up for awhile, and it has kind of evolved over time. You've given me some ideas of for making it better than it is now, so thanks.
• sean w 6 years ago
hi Sean
original price 240 special offer price 210
240 - 210 = 30
then 30/240 = 0.125 x 100 = 12.5%
cheers
sean w
• Author
Lisa HW 6 years ago from Massachusetts
Sean, this gets beyond the "mental-tricks" category, but what you'd do is first see that at \$210, you'd be paying \$30 less. That \$30 is what you'd be focusing on.
You either want to know what percent of \$240 the \$30 is (because that will tell you what percent the price was reduced), or else you want to know what percent of \$240 the \$210 is (because that would tell you what percent you'd be paying - with whatever the difference between that and 100% is showing the percent reduction) (But forget this approach for now. I'm only mentioning it as something to keep in mind if a problem is ever easier to do by doing it this way.)
If you think of "percents" as "units" instead (or too), it can make seeing how this kind of problem works seem less complicated. I'm going to use the word, "units," because I think it can make it easier to describe what's happening in this type of problem.
Since you want to know what percent of \$240 the \$30 is, you first want to think about dividing up that \$30 into 240 equal "pieces". Why? Because you need to know the relationship between 30 and 240.
As you know, to figure out how many equal "pieces" you could divide the 30 into, you'd divide 30 by the 240 (and it would be easier to do that on a calculator, although you don't have to. It's just that I don't have a quick mental trick for this kind of percent problem).
Once you divide 30 by 240, you see that it comes out to 0.125
Here's the word, "units", comes in: The way to remember that you have to divide the smaller number by the larger one is to imagine how you have to come up with however many equal "units" ("pieces") would "go to"/"go with" each of the (in this case) 240 individual dollars (or "units"/"pieces").
So, you divide the \$30 difference in price by the original \$240 price, and you get the 0.125
Then just multiply that 0.125 by 100 because you want to know what relationship 100 of those 0.125 "units" would have to \$30.
Just by moving the decimal point over two places you can see that 0.125 by 100 is 12.50. If you feel more comfortable with doing it on a calculator, you'll get the same thing by multiply by a 100 on that.
You can double-check your math by finding 12.5% of 240 - and you'll see that it's 30.
Looking at the problem the other way (seeing what percent 210 is of 240), you can see that if 30 is 12.5%, 210 is 87.5% of the original 240 (because you're subtracting the 12.5 from 100% and seeing that what's left is 87.5)
Hope this helps.
• Sean 6 years ago
So how would you do a percent decrease or increase with an unknown percentage. Lets say you went to buy a dining room table that originally sold for \$240 and since it was a floor model it was reduced to \$210, what is the percent decrease from the original price?
• Author
Lisa HW 6 years ago from Massachusetts
sian-a, before I leave this for now, there is one quick mental trick that's different from the approach I used above:
With something like 40% of 45 I might "turn that 45 into 90", because that's divisible by 10 and would make using the above "tricks" easier.
Of course, since 90 is two times what 45 is, I'd have to divide the answer I got by 2.
So, I might do something like:
Turn the 45 into 90.
Think of 10% of 90 (which is, of course, 9)
To get 40% of 90 I'd know to multiply the 9 by 4
(because 9 is 10% and there are 4 10%'s in 40%)
So, since I know that 4 x 9 is 36, I'd see that 40% of 90 is 36.
Since I didn't really want 40% of 90 and really wanted 40% of 45, I'd have to think of what half of 36 is (and that's 18).
18 is 40% of 45, and you'll see (be able to check) that if multiply 45 by .40 on a calculator or paper.
There you have the 40% of 45 (with a somewhat odd approach, I know. :) )
• Author
Lisa HW 6 years ago from Massachusetts
sian-a, (I don't know if you're asking for an example of a "mental trick" or just how to figure out that particular kind of percentage problem). I'm going to go with just "how to figure it out" (no mental tricks for now), because I want to answer you but I don't quite have the time right now to write out how, exactly, I'd do that kind with a "mental trick". It takes a little time to think up how to explain something in a way I think may be easy to read) I figure, if you're asking how to do that percent in general, you need a quick answer. If you're just interested in a "mental quick-trick" to do it, I imagine it isn't any emergency. :)
Mental tricks aside, the simple answer to that one is multiply 45 by .40 either on paper or with a calculator.
Another way might be to move the decimal point to get 10% (4.5), and then multiply that by 4 (because there are 4 10%'s in 40%). (Someone might wonder what would even be the benefit of doing something like this approach on a calculator or paper, and the only benefit might be that for a student who's not comfortable with percentages, it can sometimes help to make a problem seem simpler (and then to change it back to what may have seem like a more difficult problem).
• sian-a 6 years ago
how do you work out 40% of 45 ?
• Author
Lisa HW 6 years ago from Massachusetts
Ivan, not only do (and will) I remember you, but I mentioned you (and your "thing" about my age) to my sister over the weekend. LOL (She's around my age, so she sees the humor in my discomfort with admitting my precise age on the Internet.)
• Ivan 6 years ago
Dang Lisa you so smart lol I hope you remember me from comments above you rule
• Author
Lisa HW 6 years ago from Massachusetts
PC, Hi. I think there's a chance you just did a little something wrong with the calculator or missed a step (or something like that). I'm assuming you may have done a "percent trick" and were then checking it on the calculator?
If you were finding 5% of 763 you could do it first by thinking of how 10% of 763. All you do to get that is look at the 763, know it would have a decimal point after it (if the decimal point weren't invisible) (so it would be 763. ) and then move that decimal point you put in over one place toward your left hand. (so 10% would be 76.30)
Then all you do is divide that 10% (76.30) in half (because you know that 5 is half of 10).
Anyway, I'm going to guess about what you may have done (although I can't guess about that 1678-thing; I think that was a calculator thing, maybe):
If the problem were to find 50 percent of 763, to do that on a calculator you'd multiply 763 by .50 (which is what 50 percent would look like if you wrote it out). If you multiply 763 (punch that in first on that calculator) by .50 (forget the percent key on the calculator for now and just use the multiplication key) by .50 you'll get 381.5. Sometimes it's easy (in your head) to just think of dollars while you're doing percents. Turn everything into dollars - and if you weren't really dealing in dollars with the original problem, you can "turn things back into non-dollars" after you've done the math. It just helps you keep in mind where the decimal points and zeros go along the way).
Since 50% is half of 763, to check that 381.5 answer all you would do would be multiply the 381.5 times 2 to make sure there are really 2 381'5's in 763.
If you were finding five percent of 763 the five percent should look like this .05 (and you'd multiply the 763 by .05 either on a calculator or on paper).
For the most part, I can't really think of too many times you'd need to divide if you were either using the mental tricks here to find percent, or else using a calculator or paper to find percent. Usually, it's a matter of multiply by whatever percent you need to know.
The one reason I think you may have been dividing (if you were trying to do a percent problem) was if you were trying to approach the problem by finding 10% first and then dividing that in half to find 5%.
If you were trying to find half of 10%, you would have first seen that to get 10% of 763 you'd move the decimal point over one place toward your left hand (after you pictured an invisible decimal point being after the 3), you get 76.30. So if it were dollars, 10% of 763.00 would be 76.30.
If you originally had wanted to find five percent (.05) of 763, you'd need to divide that 76.30 (10%) you got in half (because 5 is half 10).
If you divide the 76.30 (ten percent) in half you get 38.15 (so that would 5 percent of 763).
Another guess about why you may have been dividing:
If you were trying to find fifty percent of 763 you could get that by dividing 763 by 2 - not by fifty percent. Again, if you're finding percent on a calculator, you multiply, putting in the "starting number".
If you trying to find fifty percent of 763, the reason you'd divide by 2 is because fifty percent is half of one-hundred percent.
There are four kinds of percent problems that are super easy to do in your head (which is why you can sometimes start with one of them and take it from there):
100% is all done for you with any number.
50% always means "just divide in half"
10% is easy because you just move the decimal point.
1% can be found by moving the decimal point 2 places over.
Keep in mind that if you find 1% you always multiply by whatever percent/number you want to find (that can help you feel like you understand percents better and can make what's happening with percents a little clearer for you).
Hope some of this helps.
• PERCENTS CHANGE!! 6 years ago
Hey, Im a 6th grader, I suck at math. So I read a few comments and stuff and went oh, I can do this!! so using my calculator I divide .5 into 763...and got 1678...I DONT KNOW HOW!!! Help!!
• Author
Lisa HW 6 years ago from Massachusetts
Ivan - nope. Not 60, 70, or 80. LOL If you really have to push the age thing, I'm in my 50's (and still getting over the fact that I'm in not in my 40's, so that's as much I can make myself admit. LOL ) I'm not all that knowledgeable, but thanks for the compliment. I just try not to write or talk about the stuff I don't know and stick with the stuff I do. LOL
• Ivan 6 years ago
Lol sorry so are you like 60? That sounds right lol I'm just wondering cause iv never met a person as knowledgeable as you haha
• Author
Lisa HW 6 years ago from Massachusetts
Maybe what the 15% confusing thing was that it showed up in the kind of problem that could be done most easily in a couple of different steps. The "tricks" I'm offering here are based on the more basic math facts that a lot of people are really comfortable with, even if they aren't finished with school or aren't "math people".
As I showed above, it's easy to find 10% of something. Since you can't find 5% the same way, the next-easiest thing to do is find 10% and divide it half (because finding 10% is simple, and because you know that 5 if half of 10).
Or, the other easy way would be to think of 1% and multiply that by 5.
What I'm trying to offer are "tricks" or different ways to figure percentages either in your head or without a lot of figuring on paper. I'm not offering the "usual" way of figuring percentages a lot of times here, because I was aiming to show those "quick tricks". So I can see how there are places where such odd tricks may not make sense to some people. :)
• Author
Lisa HW 6 years ago from Massachusetts
Ivan - LOL. Nowhere near 80! I was in elementary school in the 1960s, and those teachers were - like - my grandmother's age (and she was born in 1881, so that's where I came up that era). My mother was in her 40's. If her mother had been alive she would have been in her 70's. With the exception of one, young, kindergarten, teacher; the youngest of the teachers in that school was way older than my mother - and the rest of them only got older from there!! A couple/few of them may have been born between, say, 1900 and 1920.
confused kid, I'm kind of confused about your post too. I'm just going take a couple of guesses about what you're asking. Please overlook it if I don't understand what you mean exactly:
If what you're asking if how to find 10% that's a really easy thing to do. 10% is always one-tenth of any number. All you have to do is look at (or think of) the number you want to find 10% of, and move its decimal point over. Since numbers don't always show up with decimal points (because the decimal point isn't really required for whole numbers), first you just have to think where the decimal point should.
For example, if the number is 33 you need to (at least while you're figuring ten percent) think of how the decimal point would be 33.0. Later you can take out the decimal point, but for figuring 10%/one-tenth, it makes things easy.
If the number you wanted 10% of was 105, you'd add the decimal point like this: 105.0
Once you know where the decimal point (even an invisible one) is in any number, all you have to do is move it one place over toward your left hand to find one-tenth (10%) of it. So, if you wanted 10% of 450: First you put in the decimal that you can't see (450.0). Then you move that decimal point over one place toward your left hand. It will look like this": 45.00 Since you're dealing with a whole number (like 450) you don't need those zeros after the decimal point. Because, when there is nothing but zeros after a decimal point it means you have a whole number.
So, once you see that 10% of 450(.0) shows up to be 45.00 you can drop off the zeros. You now have 45.
If you're looking for 10% of 15: You can see that 15 is a whole number. It's not 15.5 or 15.7, or anything like that. It's just plain, old, 15. All you do is add that invisible decimal point to 15. You add it right after the 15, so it should look like this (at least while you're doing your figuring): 15.0
Now, you move the decimal point over one place toward your left hand, and it will look like this: 1.50 That's 10% of 15. Since you can't drop off the 5 (because the only thing you can ever drop off are zeros that follow a decimal point); you'll see that 10% of 15 is 1.5. (You can drop off that zero because it's at the end).
In other words, any time you want to find 10% of any number all you have to do is divide that number by 10.
To find 1% you move the decimal point TWO places over toward your left hand. The good thing about finding 1% is that you can multiply 1% by whatever percentage-number you need to. If you want to find 4% of 50, all you have to do is find 1% of 50 (the way I showed above) and then multiply that 1% by 4.
There are other ways of finding percents that may make sense for a lot of people (especially someone who uses a calculator), so the only benefit to the approaches I'm showing here is they tend to make finding percentages easier (and something you can often do in your head).
Hope some of this is a little more helpful. Feel free to ask for further clarification if there's a chance I can make it any less confusing. :)
• confused kid 6 years ago
this is stupid i said suppose u don't no the percentage eg.10% and they just say find the percentage of 15
• Ivan 6 years ago
Hehe this is great Lisa but if your teachers are born late 1800s aren't you like 80? Not that it's bad because you know so so much
• Author
Lisa HW 6 years ago from Massachusetts
Ivan, thank you for such nice words. I'm glad it was helpful (because sometimes people come to this Hub hoping to find it helpful and seeing it didn't help them very much). We (HubPages) writers get comments sent to us through e.mail, so when I see a question show up I'm always glad to at least try to answer it. This Hub is a different kind of Hub than a lot of the other Hubs I've written. I wrote in because someone asked how to do percents, so I figured these "tricks" might be helpful to someone. It turns out there are a lot of people (often students) looking for help on how to do one kind of math problem or another.
I'm not all that "smart" (trust me on that LOL ). With something like basic math stuff, though, a person doesn't need to be particularly great with math to find a few handy tricks.
I'd describe myself as "being confident with basic math problems", and because students and learning are something I've spent a lot of time thinking about (I have three grown kids who went through the public school system), I'd like to try to answer your question about how I got "confident" with this particular kind of math thing.
One thing that I think got me off on good footing with basic math was that I went to an old fashioned elementary school (no frills and not even a lot of the most common things, like a cafeteria or gym). The teachers were elderly (and I mean "elderly" - like born in the latest 1800's). They taught the basics in all subjects, but they were pretty good at it. So I think it's important that kids in the first few years of school learn the most basic things, like "math facts" (multiplication tables). Everything after learning those basic math facts is based on them.
Sixth grade was a lost year for me because the teacher was senile (truly senile - I'm not being funny). In seventh grade I was put in an "experimental math class", but then my parents moved and the new school didn't have the same kind of "experimental math". So halfway through the year I was "completely turned off" of math because I was fed up that I hadn't just been put back in a "regular" math class, rather than being jumped ahead to math that was more advanced than the the "experimental" math had been. I stopped doing all math homework for 7th and 8th grade. I was a thirteen-year-old girl with "better things to think about". LOL For high school I had matured, and so I "shaped up" once I got into math like Algebra and Geometry. I even took an extra math course (Business Math) because I thought something that "practical" might be useful.
Once I had been "separated from my earlier interest in math) when that sixth-grade teacher was as ineffective as she was, I never regained any particular enthusiasm for, or interest in, math. Maybe it was me (although I think it's this way for a lot of students, especially girls), but there were never any teachers who managed to know how to share their own enthusiasm (if they had any in the first place) for math.
Although I somehow managed to often get good grades; to me, math class was always a matter of teachers "droning on and on", or else (because math teachers usually used the board to show how things were done) I'd get aggravated because I'm not a "visual" learner. I'm an "auditory" learner.
I'd pick up a good part of what the teacher was saying, but I wasn't super confident with a lot of it. Then, because I wasn't interested in math, I'd get agitated when homework time came (and being agitated means being stressed; being stressed means having trouble concentrating because "stress hormones" rise and actually affect our ability to concentrate).
What I realized I needed to do was "never mind about the right terms" and even "never mind about how teachers say to do one thing or another"; and instead, put things (in my head) in my own terms and "find my own way to being more comfortable with" different things in math. Of course, that doesn't always cut it with a "show-your-work" kind of quiz or test; but where it did "cut it" was that I had the confidence to think I had "the right" to figure out my own ways of "getting to know math better" (rather than seeing it as a subject that "belonged" only to people who love it.
The words used in math aren't interesting words to a lot of students in the process of trying to learn it. Students who lean toward having stronger verbal-related skills can find math words so boring it can seem as if they all run into each other, and none of them particularly stands out as "memorable" or "interesting". A lot of the "droning on and on" just doesn't capture the attention of some students, and a lot of the people who teach math aren't particularly "verbal" people. They're "math" people.
My tip to any student who sometimes feels like he's "drowning" with one kind of math problem or another would be to "make yourself a life-line" by taking whatever you already have learned about math, putting things in words that make whatever you do already know seem more "catchy", and using that to pull yourself to "dry ground".
If you take whatever you already DO know, and "make it yours" by "mentally playing with it" (on paper if you need to), it can put you on that much better footing to then use the "sureness" you've built for yourself for learning the next thing in math. I guess the thing is there can be a gap betweeen what teachers try to teach and what students actually completely learn. Students (maybe particularly "verbal" students) need to find a way to fill in that gap in some way that works for them.
Students can't fill in that gap with anything but what they already have (in terms of knowledge of math). What they usually "have" is SOME knowledge of the subject and their own way of using words, as well as their own set of things that will make "seeing" the subject easier for them.
A lot of students don't have the confidence to try to think of their own ways of filling in that gap. In fact, a lot of students are not encouraged to do that. They're often told, "Here's what you need to do, and you need to do it this way." A lot of students think, "There's the teacher. The teachers knows the subject. Here's me. I don't like this subject, and I don't know it. End of story."
One student may never eventually "love" the subject; but trying to make it more "catchy" in one's mind by "playing with" what one already knows can at least eliminate having to overcome the fact that a student finds math tediously uninteresting. If a student can get to the point where he's at least comfortable with whatever he already knows, math no even needs to be interesting. It's then "turned into" something that's "matter-of-fact" to learn.
I think the challenge, though, is that students are pretty much on their own when it comes to that "figuring out ways to fill in that gap". They need to know how they best learn, how they can best recall things, and how to make something more interesting for themselves. They need to have enough confidence to say, "I need to do this my way, just for now, until I learn it better." I think they also need teachers and parents who understand that, for some students, "doing it my way first" helps fill in that "gap" (so they can then go on and do it "the right way").
I don't know if any of this is at all helpful. The length of my response probably very much backs up my claim that I'm more of a "verbal" person than a "math" person. LOL
• Ivan 6 years ago
Wow thanks for answering I get it now your the best and also it's cool how you still answer questions even though you made this 2 years ago!!! Lots of people just make a site answer 2 questions and leave. You need a donation button lol how are u so smart? How did u learn I really need to know because I get slot of presure from parents cause there both doctors but anyway I really appreciate what you do for us ur a legend u rock
• Author
Lisa HW 6 years ago from Massachusetts
I'm not completely sure if I understand your question correctly, but finding 45 percent of 20 in your head (of, if you need it, making a couple of quick notes on a scrap of paper) is easy. There are a few different ways you could use "quick tricks".
One easy way would be to aim to first figure out 5% percent, and because you already know that there are 9 5's in 45, all you'd have to do is multiply 5 percent by 9.
The quick way to find 5% if to think of 10% (because you know that there are 2 10's in 20.
So, first you see that 10% of 20 is 2. That means, of course, that half of 10% (5%) is 1.
Since you started out knowing that there are 9 5's in 45, all you have to do is multiply 9 by 1 in your head - and you've got your 45% of 20. 9 x 1 is, of course, 9 (which is 45% of 20).
-----
Another approach to some problems like this one:
When I first look at the 45% of 20 problem, my instinct is to think of how I already know that 45 is half of 90. That means if I figure out 90% all I have to do is think of what half of that is (or figure out what half of it is) to get 45%.
Finding 90% is easy because 90 is 10 less than 100, so all I have to do is see what 10% is - and then substract that from 20 to get 90%. Since it's easy to know that 2 is 10% (one tenth) of 20, and it's easy to know that if I substract 2 from 20 I'll get 18 (and, again, since 45% if half of 90%), I can easily see that 45% of 20 is 9.
-----
Another approach might be this:
Find (or think of) 40% of 20 first, then find (or think of) 5% of 20 - and add them together.
It's easy to find 40% by thinking of what 10% (one-tenth) of 20 is; and then multiplying it by 4 (because 40 amounts to 4 times 10).
So, since you know that one-tenth (10%) of 20 is 2, all you have to do is multiply 2 times 4 to get 8 or 40%. (Some people may want to jot that down until they get the 5% that they're going to add to the 8 they came up with when they figured out the 40% of 20.
Figuring out 5% is easy with this approach because you already figured out 10%. So, you just think of how half of the 10% (2 in the problem here) is 1.
Now all that needs to be done is add that 1 you just got to the 8 you got when you figured out how much 40% of 20 is - and you've got the 9.
In answer to your question about "timing by 100" you wouldn't do that if you had a problem like "find .45 of 20". You'd do that if the problem was one like: "What number is 9 45% of?"
If you're doing a problem like the 45% of 20 one, you don't really need to think about the decimal point unless/until you see that one is needed later. Calculators show percentage with the decimal point, so you can see exactly where the calculator is at any point in your calculations. When you're doing a problem like this in your head you can just think of 45% as "45" and deal with adding any decimal points later. For example, with a number like "20" the decimal point is "invisible" but would be after the zero.
If the problem were different, and were "find 0.045 of 20" you would use the same mental tricks as for 45% (.45) of 20, but then you'd know that you had to move the decimal point (even if you start out with an invisible decimal point in 20). The reason you'd move the decimal point over one place would be because you wanted to show that "9" (45%) divided by 10. So, instead of 9 (9.0), .045% of 20 would be .09 (because you moved that invisible decimal point that we don't see after 9 over one place (and added a zero in order to show that the decimal point had been moved over one place).
When the calculator shows that decimal point it's showing that you're finding 45 one-hundredths of 20 (because one-hundredths are "one-percents"). If there wasn't a decimal point it would look like you're multiplying 20 x 45.
When you do these "quick tricks" to find percentages, you kind of already have it in your head that finding percent; and when you do something like find 10% (one-tenth) because it's easy, you've already done the "dividing" you need to "get you into a percent mode" with whatever you do from there.
• Ivan 6 years ago
Lisa you have a great site your really smart! But is doing a percentagethe calculaterway which is making it a decimal like .45 of 20 really hard? Because i don't get the timeing by 100 thing please reply!!!
• Author
Lisa HW 6 years ago from Massachusetts
pam, the way you have the .10% written, that's one-tenth of a percent. Ten percent could be written .10 (one-tenth) or else 10%, but since, if you were to add the "invisible decimal point", you'd write 10.0 for ten; with both the decimal and percent sign it makes it one-tenth of a percent. (With both the decimal and percent sign, there's an "invisible zero" before the decimal point.
With the problem you posted, I'm going to use 10% to keep things simple. You can always move the decimal point later if you really want one-tenth of a percent.
I'm also going to use the word, "units" instead of "percents", because it can seem simpler:
If some original number was reduced by 10%, that would mean the 1,605,837 is 90 percent (or 90 "individual percents/units") of that original number.
Since you the 1,605,837 makes up 90 "units" of the original number you need to divide the 1,605,837 by 90 in order to see what one "unit" is.
Once you know what one "unit" is you can multiply that number by 100 to figure out what the original 100% was.
When you divide the 1,605,837 by 90 ("units") you get 17,842.63. If you multiply that by 100 (which you can, of course, just do by moving the decimal point over two places), you get 17,84263.
You can check your answer by finding 90% of 17,84263 and seeing that it's 1,604,837.
The above example is going with the problem that the 1,605,837 was what happened when you reduced a larger number by 10% (ten percent).
If it was reduced, instead, by a tenth of a percent you'd move the decimal point accordingly. You'd still start out by finding what number each of those 90 "units" represents.
There are other ways to do this kind of problem, but I think this way is the simplest for someone not entirely comfortable with percents, or just someone who likes to reduce the risk of making a mistake with a zero or decimal point somewhere earlier in the problem.
I just always find kind of using 10% as a "base" if possible makes things a lot simpler.
• pam 6 years ago
If your beginning amount is reduced by .10% and the result is 1,605,837; what was the beginning amount? Also is the .10% 1/tenth of a percent or is it 10 percent?
• Author
Lisa HW 6 years ago from Massachusetts
karina, I never thought much about them (I have other math things I hate, but not percentages). From what I've seen, though, I guess you're far from alone. :)
• karina 6 years ago
omg i totally hate percentages well anyway thanx 4 the lesson i learned something about this subject!....
• Author
Lisa HW 6 years ago from Massachusetts
To increase by a percentage, you would simply multiply the number by 100 percent plus whatever the percentage is. For example, if you want to add 20% of 100 you would either use a calculator to get 120% of 80; or else you could do some such problems in your head:
Since you already know that 80 is 100% of itself, you just have to figure out what 20% is and add that. An easy trick is to think of how 2 times 8 is 16 (if you do that you're leaving off the zero in the 80 in your head, but it makes it easy).
Then all you need to do is add 16 to 80 (which is 100% of itself).
Another quick trick to find that extra 20% is to think of 10% of 80 (easy - it's 8) and multiply that 8 by 2 (because you know 20% is 2 times 10% percent).
To decrease a number (as in the example of 20% and 80) you could either use the tricks to get the 20% and just substract that.
Or else, you could substract the 20% from 100 (which you can easily do in your head) and come up with 80. Once you have that you know you'll be looking for 80% of 80.
You could, of course, either use a calculator or write it out on paper and find find 80% of 80 the "usual way". Or, you could do one that easy in your head:
Since you know you'll be looking for 80% of 80, you go back to thinking up 10% of 80 (8) and multiply it by 8 (since 80 is 8 times 10).
So the only difference with a decreasing-by-a-percentage problem is that you first subtract the percentage from 100 to figure how what percentage you're really looking for - and then you use the tricks to find that percent.
• nathan 6 years ago
How do you work out the percentage increase/decrease from one number to another?
• Author
Lisa HW 6 years ago from Massachusetts
stephanie, it's not clear to me what you mean. If you're looking for percents that are related to the price of something, it's all kind of the same thing.
Please overlook it if my attempt to clarify/be helpful shows that I don't really know what you were looking for: If you're looking for prices (for example 50 percent of ten dollars) the ten dollars would be written as 10.00 (with that decimal point showing 10 dollars and no cents/change).
If you're writing prices you always know that there are spaces for however many dollars are in the price, then there's the decimal point, followed by however much change is also in the price. Ten dollars and ninety-nine cents would, of course, look like \$10.99
So, to find any percentage of any price, you would picture how it would be written first (or imagine it in your head); and you'd figure out the percentage with the decimal point in mind.
If the problem were simple enough you wouldn't have to do that, though. For example fifty percent of ten dollars means "half" of ten dollars dollars. Since you know that five is half of ten, you'd easily known that five dollars (\$5.00) is fifty percent (50%) of ten dollars (\$10.00).
One reason for using decimals (besides needing to use them when change is involved) is that it makes figuring out the percentage pretty easy. All you have to do is picture (or write down) how the price would look in numbers, and use that decimal point that's in all prices (if they're written out correctly) to help you figure the percent you're looking for.
Again, apologies if I don't "get it" with regard to the kind of thing you're looking for. I've just taken a wild shot at guessing what additional information may possibly be helpful.
Feel free to post with an example of the kind of problem you want to solve. I may or may not see it right away (depending on if you post at all, but I'll be back to try to answer as soon as I can).
• stephanie 6 years ago
this isn't the one i am looking for.i am looking for the one that is for the price nat decimals
• Author
Lisa HW 6 years ago from Massachusetts
whatever: Looks to me, then, like you fit real well here.
• whatever 6 years ago
losers al of u
• meet 6 years ago
thanks for ur help
• Dot I 7 years ago
Hi I am wanting to know if a question asks;if you got \$60.00 and spent \$14.50,what is the percentage you spent(14.50)what's the fastest way to calculate this?thank you
• Author
Lisa HW 7 years ago from Massachusetts
kenny, thanks.
• kenny 7 years ago
thanks this is really nice way very eassy.............
• Author
Lisa HW 7 years ago from Massachusetts
Dan, to find out what percent of 1199 the 700 is you would divide the 700 by the 1199 (on a calculator - this one I don't have a quick mental trick for) and multiply the answer by 100. It comes out to 58.38198 (and if you round you'll get 58.4%).
If you check for 58.4% of 1199 you'll see that it's a "hair over" 700.
If you wanted more accuracy you can, of course, use the calculator for the above steps and instead don't round anything up or down.
(I hope I worded this right and didn't "do any oversights". It's 7 in the morning here - no coffee yet. LOL.)
• Author
Lisa HW 7 years ago from Massachusetts
Rod, hi. I'll try (although sometimes it can be tricky to figure out how much or how little to say and still hope to make something easy). I'm not sure I can make it shorter, but maybe I can make it simpler. I'm going to try to separate all the ideas with a lot of spacing, to make reading easier.
If you don't do this already, sometimes when you're reading about math stuff it can help if you whisper what you're reading to yourself (or even read aloud). That helps you get the information in through your ears, and sometimes listening to "math stuff" is easier than try to "make your eyes" get the message to your head.
I guess the main idea is to try to make all the numbers smaller, so they're easier to work with in your head (if the problem is one that you can do that with).
The one thing you have to know (or keep in mind if you already know it) is that every number has a decimal point, whether it shows or not. If you have something like \$5.00 (to find some percent of) you can see the decimal point. If you're talking about 500 apples you can't see the decimal point, but you know it comes after the second 0, and just doesn't show up.
So, if you had to find 20% of 500 apples you could come up with 10% easily, because all you have to do is move the decimal point (either on paper or in your head) over one place (toward your left hand).
First you picture that 500 (apples) really has an invisible decimal point after it (like 500. - but you can't see it.)
So, even though you really want to find 20%...
First find 10% because it's really easy to do. (If you move the decimal point over one place toward your left hand you'll get 50 (or 50. if you imagine the invisible decimal point).
Now that you know 10% of 500 is 50 it's really easy to just think of two times 50 in order to find 20% (because you know that two 10's make 20). 2 times 50 is 100. That means that 20% of 500 is 100.
If you want to make the numbers even smaller and easier to deal with (on a problem like this one)...
Instead of finding 10% to make things easier, find 1%.
The reason it can help to find 1% first is because all you need to do to find the 20% (which is really what you want to do) is multiply 1% times 20 (because 20 1%'s will be 20%).
For example, with the 500 all you have to do is know that because percent always involves hundredths, 1% is 5.
(1% of 300 would be 3. 1% of 600 would be 6. etc. etc.)
If you need to move the decimal point toward your left hand in order to find 1% you would move it two places. At the bottom I'll make a comment about moving the decimal point over.
So, now that you've figured out that 1% of 500 is 5; if you want to know what 20% is you just multiply that 5 times 20. (5 "single/1 percents" times 20, because you really want to end up knowing what 20% is).
Why? Because there are 20 1-percents in 20 percent.
To check that the answer is right here's what you can think of:
100% always means ALL of something. 20% means PART of something. If you know that there are 5 20's in 100, the way to check your answer is to think of how many 20's (or how many "twenty percents) there are in 100. You probably already know in your head that there are 5 20's in 100.
That would mean that if you think of how of the answer you got for 20% (which was 100) and multiply times 5 it will show that you end up with the 500 (apples) you started with.
Moving the decimal point over one place toward your left hand means "dividing the number by 10". "Dividing by 10 is the same thing as finding 10%.
Moving the decimal point over two places toward your left hand means "dividing the number by 100". Dividing the number by 100 and finding 1% are the same thing.
With a little trickier kind of problem like: 13% of 500 you could do something like...
Think of 10% of 500 (by moving the decimal point so to get 50 instead of 500). So now you know that 50 is 10% of 500, but you really need to know what 13% is. Remember that 50 is 10% and then do step two:
Think of 1% of 500.
(Either by picturing moving the decimal point over two places and getting 5; or else by thinking of one tenth of the 50 you got (because there are 10 "single percents" in 10%).
1% of 500 is 5.
Now that you know 1% is 5 all you need to do to figure out how much that extra 3% is (that we left out of the 13% when we only figured out how much 10% is).
Just multiply the 5 you got for 1%) by 3 (because you really want 3%, not just 1%). 5 times 3 is 15.
To figure out 13% of 500 then, just add the 10% and the 3% you got (which was 50 for the 10% and 15 for the 3%).
Since 50 plus 15 equals 65, that means that 65 is 13% of 500.
Rod, I know this one example of percents of 500 doesn't really do it; but what would probably help you get how to figure out many percentages in your head would be if you think up problems yourself, finding different percentages of 100.
Find 10% of 100 (it's easy - remember? Just move the decimal point over one place).
Find 20% of 100. Just find different percentages of 100 (simple ones at first, like 40%, 50%, etc.).
Then try to find things like 45% of 100 or 65% of 100.
(To find 45% find 40% and 5% and add them together. To find 65% find 60% and 5% and add them together.)
(To find 40% think of 10% first and then multiply it times 4. To find 60% think of 10% first and multiply that times 6.)
To find 5% of a number think of what 1% and then multiply that by 5. To find 6% of a number think of what 1% is and multiply that by 6. etc. etc.
Hope some of this helps.
• dan 7 years ago
oh and one more think sorry Lisa
1199 is the price and i picked it up for \$700 what is that as a discount off 1199? I know 30% off 1000 is 700
• Rod 7 years ago
I'm a 6th this year and when i read your working out strategy, I didn't really get it. Can you explain it a little shorter and easier to understand?
Thanks!
• dan 7 years ago
Thanks a lot for that Lisa
I think i might have made a mistake in my question though here is what i'm trying to do:
I sold 37 units this month and the same month last year i sold 33 so what is the % increase here? Also lets say i sold 875 last year and only 370 this year how do i wrk that out as a negative??
Sorry and many thanks!
• Author
Lisa HW 7 years ago from Massachusetts
dan, you would divide the 310 by 387 (first) and then multiply the answer by 100. In this case, you'd have to round up at the end. (More later).
First, as a way of helping show what's going on, the reason you need to divide the 310 by 387 is that 387 represents "the whole", so you have to "assign" equal 387 "equal parts" in relation to the 310 "units". It's Step 1 in seeing the relationship between each of the 310 "units" to the "whole", 387. In other words, in order to know what number you'll be dealing with, you have to "break up" each of the 310 "units" in a way that relates to the 387.
So, if you divide 310 by 387 you get: 0.801034 (rounding down would get you 0.801. The next step is to multiply that by 100 (by simply moving the decimal point two places toward your right hand - or by using a calculator if you want).
From there you have: 80.1%
If you check to find 80.1% of 387 you'll get 309.987, and if you round up (to make up for the fact that you rounded down earlier), you'll see that 310 just about 80.1% of 387.
If you hadn't rounded down above, and if you multiply 387 by the 0.801034 you'll get just a tiny bit over 310 (but not enough to round up).
So - with a problem like this, divide the smaller number by the bigger number, and then multiply what you get by a 100.
Essentially, what you're doing with this kind of problem is trying to see a relationship between 310 "units" and 387, so you have to divide. The problem is that there isn't even one "387" in 310, so you're going to get equal "pieces" that don't amount to one whole "piece". If you picture trying divide 310 cookies by 387 you can imagine the bits you'd have to break them into. Because, with percentages, you're dealing with a larger number than "all those bits", and because percentages are about hundreths, that's why you multiply by 100 after dividing.
• dan 7 years ago
hi Lisa
i need to work out what 310 is as a percentage of 387
I'm not sure how to work out negative percentages??
Thanks
• nawid 7 years ago
thank you
• grace 7 years ago
great thanx yo rock i totally get it
• Author
Lisa HW 7 years ago from Massachusetts
Artisan, thank you. If you are, you're not alone - that's for sure. :)
• Artisan Walker 7 years ago from Springfield, Oregon
Thank you for this. Clearly written and easy to understand -- even for someone mathematically challenged such as myself.
• emather 7 years ago from United Arab Emirates
i really had problems. thanks for this great hub
• Author
Lisa HW 7 years ago from Massachusetts
dogboy, to find something like 10% of, say, 50 you'd imagine that with the 50 the decimal point (which isn't ever written for whole numbers) would be after the zero (like 50. ). If you were dealing with 50 dollars it would, of course, be written out 50.00. So, keeping in mind where the decimal point (written or not written) is with any number...
To find something like 10% you would move the decimal point over once toward your left. With the 50. you'd move it from being after the zero to being after the 5, which would give you the 5 as 10% (1/10th) of 50.
• dogboy 7 years ago
you keep mentioning move the decimal point over one....LEFT OR RIGHT ? Just to make it perfectly clear.......Ü
• Author
Lisa HW 7 years ago from Massachusetts
Del, great. :) Thank you.
• Del 7 years ago
Just what I was looking for thanks a lot:)
• Deccan Chargers 7 years ago
very nice article.....
keep up the good work ....
thanks ....
Good article on working out percentages thanks, maryladd
• Author
Lisa HW 7 years ago from Massachusetts
Author's Note: Somewhere in my account I ran into a comment that pointed out an error. That comment isn't showing up here, even though I approved it; so I don't quite know what's going on there.
In any case, I will return later to look for both the comment and the error pointed out by it. There's been a lot of a quick typing and "math gymastics" going on when I've tried to do things quickly here - so, again, I'll be back to correct the error and see whatever happened to that comment.
• Author
Lisa HW 7 years ago from Massachusetts
William, I'm not sure how your comment relates to the subject; but I have to admit it adds a little "lightness" to an otherwise boring topic. :)
• William 7 years ago
In the words of R. Kelly, "Everybody feelin freakyyyyy!!!!!"
• Author
Lisa HW 7 years ago from Massachusetts
andromida, thanks. :)
• syras mamun 7 years ago
Excellent hub topic.I think your tips gonna help me to figure out restaurant tip in a few seconds.
• Author
Lisa HW 7 years ago from Massachusetts
Sexy jonty, thank you for the kind words. :)
• Sexy jonty 7 years ago from India
Very well written hub .....
very much informative ......
Thank you very much for your great hub, for good advice, good wishes and support. Thanks for sharing your experience with all of us.
• Author
Lisa HW 7 years ago from Massachusetts
Chris, just another overlooked "grounding" tip: Since you know that 4 x 80 is 320 (because you know that 4 x 8 is 32, and you're just dealing with the extra zero/tens), you'd also know that 320 is higher than 300. That means you can know that the answer to "what percent of 800 is 300" is going to be between the 30 and 40 (%) - in other words, in the 30's.
• Author
Lisa HW 7 years ago from Massachusetts
Chris, you need to figure out what percent of 800 300 is. The way to do that is to divide 300 by 800, and then multiply that by 100. What you're essentially doing is figuring out how "800 units" can be equally divvied up among 300 "units". Then, because percent is hundredths, that's why you multiply by 100.
In this case, you'll find that 300 is 37.5 percent of 800, so that's your answer.
A different way to do it is to realize that 8 is 1% of 800 (percent is hundredths, and you get that by moving the decimal over two places; so you can do it in your head). Once you know what 1% is you ask, "How many 1%'s go into 300?" If you divide 300 by 8 you'll see that you get the 37.5 as well.
Just as a tip for getting a rough idea of how big a number you're looking for: You know that half (50%) of 800 is 400, so you'd know ahead of time that because 300 is less than 400 you'll be looking for a percentage under 50%.
Another "grounding" tip: You know that 10% of 800 is 80, so it's easy to know that 20% would be twice that (160). 30% would be three times 80 (240). At this point you may see that the 240 is getting kind of close to the 300; and, again, you know that 50% is 400. Again, this kind of thing can give you some "grounding" about the ballpark you're looking for.
• chris 7 years ago
im really struggling the best way to work out this problem please, please help out of 800 shoppers 300 shop more than three times a week. What percentage of the shoppers shop more than three times a week? i know theres got to be an easy way
• Author
Lisa HW 7 years ago from Massachusetts
Kristi, I don't have any quickie mental tricks for that (and actually, I've been sick for a couple of weeks and can't really concentrate to write). So, I'm including this link, which shows the conventional way to figure out that type of problem:
http://www.ehow.com/how_2364017_percentage-numbers...
Actually, here's a site that will do the calculation for you:
http://lachie.net/maths/percent.html
I may think of a mental trick for that in the near future. Sorry not to be of more help.
• Kristy 7 years ago
Ok, how do I find out what the percentage is of something? If I am making something and I add 3.5 oz. base ingredients and add.5 oz. of another ingredient, what is the percentage of the .5 oz to the whole thing?
• Author
Lisa HW 7 years ago from Massachusetts
Serina, first you'd figure out how much 25% is. A quick way is to divide the number you're dealing with by 4.
Another way is to figure in your head: What is 10% of the number in question. Then think of half of that 10%. (which will tell you what 5% is). Multiply whatever number is 10% by 2 (because you want 20%) and then add the number you got for 5%.
Now that you have whatever 25% is, you want to find 22%. The easiest way is to think of what 10% is by moving the decimal point over one place. Multiply the number you got (for 10%) by 2 (because 20 is two times as much as 20).
Now think of what 1% is by moving the decimal point over one more place (from where it was after you got the 10%). Again, multiply the number you get (for 1%) by 2 (to account for that extra 2 over the 20%).
Add the number you got as 20% to the number you got as 2%, and that's 22%.
• serena 7 years ago
How would you work out 22% of 25%???
• meggie moo 7 years ago
all sounds like archish to me (language bezzies made up don't get it) thanx though
• abc 7 years ago
i still dont get it (:sos:)
• Author
Lisa HW 7 years ago from Massachusetts
Tiffany, you'd need to know the total number of votes in addition to how many votes someone got. From there you would use the same approach you use to find out what percent of one number another number is. In other words, if there were a total of, say, 500 votes you'd need to figure, "161 is what percent of 500". If I understand the type of "product discount" percentage problem you mentioned correctly, this would be an example of that:
Product used to sell for \$100. Today it's on sale for \$80. To find out the percentage of the "discount" you'd first consider the \$20 difference; and then ask "what percent of \$100 is \$20". That step, there, is the same as you'd use for the voting question (minus the dollar/cents factor).
• Tiffany 7 years ago
How do I determine the percent of each person's percentage of the vote. For example, if a person got 161 votes, how do I get the percentage of that number of votes. It might read 161 or "percentage. What are the steps?
I know how to get percentage of a product discount and so on, no problem.
thanks
• Author
Lisa HW 7 years ago from Massachusetts
Ibro, this site was prepared in answer to someone's request about how to find percentages. It was the aim to show some quick tricks to help people figure it percentages easily (maybe at the supermarket or when figuring out a restaurant tip, etc.)
I used a casual, "non-math", style of wording because I figured if someone has trouble with figuring percentages they are either very young or else people who benefit more from "non-math"/more casual explanations.
I have no doubt that this page is not what a lot of people, looking for math information, will be looking for. Based on feedback/traffic it gets, however, it is apparently what has answered some people's question about how to figure percentages easily. Based on several nice e.mails I've gotten from junior-high age students, they are generally the "audience" for this site; but based on those e.mails, I have to say that I don't call it "BS" if a page has helped even a few kids learn their math. My thinking has been that the world is full of more "formal" or "advanced" sites/books and even people who teach math, and none of it apparently got through to some of those kids who e.mailed me (at least when it came to figuring out percentages).
So, this page is an "unfancy"/"folksy" attempt to share some quick percentages tricks with anyone who has/had trouble with doing that. Nobody is pretending it's anything more important or useful than that. I have no doubt many people will find it is "BS" (that's ok), and I do think it's unfortunate if it hasn't been helpful to you, as you had thought. I hope you found the kind of helpful information you were looking for, and remind you that search engines don't always "know" exactly what you're looking for, and send you a bunch of different sites in search results.
• ibro 7 years ago
i think this site help me a lot but the site was BULLSHIT
• Anuj Tripathi 7 years ago
That is excellent. I liked it Lisa. As I am looking forward to the Management aptitude exam , this tutorial would be the boon for me.
Please do write some other articles on various other tricks.
• Author
Lisa HW 7 years ago from Massachusetts
wonderful, sorry if it didn't help. If you have the time, and want to ask a specific question, I'd be happy to try to be help.
you really help me thank you
• wonderful 7 years ago
i hate it does not helr
• Author
Lisa HW 7 years ago from Massachusetts
JPSO138, this hub has surprised me. It was a request I saw ages ago, and I thought, "I can answer that easily enough - think I'll answer the request." It has surprised me that anyone other than the person who made the request has even looked it. Based on the surprising number of e.mails I've gotten from this hub, I guess a lot of junior-high aged students seem to have liked it. It's not my best piece of writing, by any means, but I kind of like that it has apparently been useful to some students.
• JPSO138 7 years ago from Cebu, Philippines, International
This will surely increase your ranking.... Very detailed explanation.
• Author
Lisa HW 8 years ago from Massachusetts
Not sure I understand if the question is related to an above comment, or just a question about 1% on its own; but I'm assuming a general question:
If you have "all of" something (any number) it is like having 100 equal little pieces of it. Those "equal little pieces of it" are 100 little "pieces" in the form of a single percent each (1%).
Showing 1% of any number is done by moving the decimal point over two places in the direction of your left hand. After you move the decimal point, if there are a string of number after it you either round them up/down (in a situation like when you're figuring out sales tax); or you could leave them until all the "figuring out" has been done before rounding (or choosing not to).
You can think of it as if any number is something like a cake. A small number is a small cake, and the the bigger the number the bigger the cake; still, what 1% is this: If you cut any "cake" (number) into 100 little pieces, each will represent 1%.
50 pieces of that "cake" means 50 little pieces that are each made up of 1%. (50%) 25 pieces of "cake" means, of course, 25%.
• Maths confused ? 8 years ago
what is 1%
• Author
Lisa HW 8 years ago from Massachusetts
Linda, first you have to figure out the difference between the original 57,500 and the new 62,250. You probably already know that you just just substract the 57,500 from the 62,250 - and get 4,750.
The way to figure out what percent of 57,500 the 4,750 is would be:
Divide the 4,750 by 57,500 (on a calculator is always easiest), get the answer, and the multiply that answer by 100. In this case you need to round, because there's a string of numbers beyond the "hundredths" space in the answer.
If you divide 4,750 by 57,500 you get 0.082609. You then can round it off.
A kind of backwards way to find the same thing (just so you can maybe see what's going on with this type of problem) is this:
You can figure out how many "4,750's" go into 57,500. Since it cannot be evenly divided, you'll come up with a figure that represents a fraction of the 57,500.
If you divide 57,500 by 4,750 you get 12.10526. That tells you what part/fraction of 57,500 the 4,750 is.
Since you need to know what percentage of the whole 57,500 it is (and since 57,500 is 100%, or ALL, of itself); you can divide 100 by that 12.10526 to come up with a percentage too. Again, you need to round.
(I hope I wasn't too late responding here, and I hope I didn't make any stupid errors - kind of bleary eyed at this time of night, but I didn't know if anyone else would see your comment and respond.) (Actually, I did make a stupid error but caught at least that one. )
• Linda 8 years ago
Help! I'm a 6th grade student trying to find out how what percent of increase is it when you start at 57,500 and increase it to 62,250?
• Author
Lisa HW 8 years ago from Massachusetts
Laura, I'm not quite sure exactly how to interpret your question. (Maybe it's me, and it's late - but I'm assuming you want an answer quickly.)
Moving the decimal point over 1 place (toward your left) will divide a number by tenths. With an example like 600 (you shouldn't see the decimal point, but I'll add where it's "implied") would be 600. If you move it once toward your left you'll essentially divide 600 by 10 (60.) Move it once more to your left, and you divide it by 10 again and get 6. (Again, the decimal points shouldn't be there, or else they should have a zero after them.)
To further divide the above example by ten, you would move the decimal point in 6 (or 6.0 once toward your left and get .6 (6 tenths). Move it again once, and you have .06 (there zero makes a "spacer" in this case).
With 6.5 you're dealing with one whole number (the 6) and the .5 (5 tenths because it is one place after the decimal point).
Assuming you need to move the decimal point at all (there is such a thing as 6.5%, but I'm assuming that isn't the case here), you would move the decimal point in 6.5 over once toward your left and get .654 to reflect a percentage (hundredths and a little more than you may want/need). Depending on how accurate you want to be, you could leave .654 or else round the 4 (and because 4 is less than 5 you would drop it off to round things off).
If you were to try to check your math "backward" by using the .65 you would find it just slightly off; but if you checked it by using the .654 you would come up with an accurate figure that proved your math was correct.
• Laura R. 8 years ago
I need to know how to change the decimal place that appears on your answer. it comes out with tenths, I need it to be with the hundreths. Instead of 6.5, I need 6.54. Can anyone help?
• Author
Lisa HW 8 years ago from Massachusetts
Thanks, kashifmahmood. They come in handy during grocery shopping too. :)
• kashifmahmood 8 years ago from Web
I love maths/calculations and have always been good at it. These simple yet very essential tips really help to save time specially during apptitute tests ;)
• Author
Lisa HW 8 years ago from Massachusetts
The "usual" way would be to simply multiply 90 by .78.
You need to figure out 70% and 8% and add them together to get 78%. Figure out 70% by knowing that 10% of 90 is 9. Multiply the 9 that 9 by 7 (get 63). Then know that since 9 is 10% of 90, .9 is 1% of 90. Multiply 9 x 8 (get 72), but because 9 is 10% (not 1%) you need to add the decimal that will divide the 72 by 10. (7.2). In other words, when thought of that 10% of 90 (9) that would get you the 70% because 70 is a two-digit number and ends with 0.
Because the 8 is in the "ones column" (as compared to the 7 in 70 that's in the "tens column") you have to add that decimal that will turn the 72 you get when you multiply 9 x 8 and make it one-tenth of 72, which is 7.2.) 63 (which is 70%) and 7.2 (which is 8 percent) equal 70.2 when added together.
From a slightly different approach:
Another mental trick may be to think of what 1% of 90 is (.9 because you've moved the decimal point over two places). From there, temporarily forget about the decimal point.
Break down the 78 into 70 and 8.
Think of how 7 x 9 = 63 Because you want to five 70% (not 7%) percent, though, and because there is that 0 after the 7 in 70, by not returning that decimal point "mentally removed" you are allowing for the fact that 70 is ten times 7. In other words, don't return the decimal point you took out if you're looking for a "two-digit percent" like 70.
Next, multiply 8 x .9. This time, though, return that decimal you mentally removed because 8 x 9 will get you 72 but because you really should have been multiply .9 (which is 1% of 90) by 8, you have to return that decimal point.
All these words make it all seem complicated; but the mental actions involved go really quickly.
So, what you end up with is that you have come up with 70% of 90 (63) and 8% percent of 90 (7.20). Then just add the 63 and the 7.2 (because you're adding 70% plus 8%) - and you'll get the 70.2 (which is 78% of 90).
A quicker trick may be to instead figure out the easier 22% of 90 and then substract that from 90 to get the 78%. The reason this may be easier is because all you have to do is find the 1% and double it.
If you figure out the 20% by thinking of how 1% of 90 is .9 (so remove the decimal point before figuring out 20%), you'll end up with 18.
If you then divide that by 10 (because 2% is one-tenth of 20%), you'll end up with 1.8.
Since 18 plus 1.80 = 19.8 - that's what 22% of 90 is.
Then substract the 19.8 from the 90 - and you end up with 78% of 90.
The only reason I suggest the "22% approach" in this case is that 22 has the same number (2) to deal with. It can make things that much simpler when figuring out things mentally. Also, because 2 is so close to 1, it makes things that much easier again.
Sometimes how to mentally figure out a percentage can best be approached by first asking what would be the simplest and most "mental-friendly" approach.
Yet one other approach (maybe the quickest):
Aim to figure out the 22% (because it's the smaller and easier number) and later subtract that from the 90.
You know that 10% of 90 is 9, so 20% of 90 will be 18.
Now figure out 2% (because you need to figure out 20% and also 2% to get 22%) by knowing that that 2% is one-tenth of 20%. Once you know that 20% is 18 you can easily realize that 2% is 1.8 (the decimal point made the difference).
From there, simply add the 18 to the 1.8, and you'll get the 19.8. You will have the 22% of 90, so all you have to do is substract that 19.8 from 90 to get 78%
A quick mental trick to substract something like 19.8 from 90 is to think of the "nearest easy number" (in this case, 20) and substract that from 90. (90 minus 20 is 70). Because you know that substracting 20 from 90 is subtracting a little more than the 19.8 you have to think of the difference between 20 and 19.8 to know how much you need to substract from the answer you got (because you substracted slightly more than than the 19.8). In this case, the difference between 19.8 and the 20 you used for convenience is .2. So add the .2 to the 70 you got when substracted 20 from 90.
• kareem 8 years ago
so how wou;d you find 78% of 90
• highschoolmusicalrocks 8 years ago
ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
• Author
Lisa HW 8 years ago from Massachusetts
Lee, for a problem like finding out "what \$463 is 35% of":
There is a response to "James'" comment above that tells how to get the answer to such a problem; but there are also links (show in the response to James) that may be explain that kind of calculation better. :)
• Lee"YaY 8 years ago
how would you find the ordinary price of an item if the item is \$463 because it was 35% off. how would u find the original price of it..
• Author
Lisa HW 8 years ago from Massachusetts
6 is 6% of 100. 94 made pick-ups would be 94%.
• LACIE 8 years ago
QUESTION? 6 MISSED PICKUPS IS WHAT OUT OF 100%.
• Ursula 8 years ago
Thank you so much I finally got it!!!!
• petz 8 years ago
I get it...tnx!
• Author
Lisa HW 8 years ago from Massachusetts
It's not, but if whatever is already here is of use to any junior high people, all the better.
• A Guy 8 years ago
Is this a Junior High Math Study Board?
• esocial 8 years ago from California
Timely topic, thanks! WHo can't use this?!
• Author
Lisa HW 8 years ago from Massachusetts
Thank you. A donation button sounds good to me, but I don't think HubPages would approve. :)
• compu-smart 8 years ago from London UK
Good job:) | 30,460 | 119,201 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2017-13 | longest | en | 0.936986 |
http://www.calculatorx.com/math/trigonometry/arccos/arccos-of-3.htm | 1,506,094,249,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818688997.70/warc/CC-MAIN-20170922145724-20170922165724-00245.warc.gz | 413,210,270 | 6,569 | # What is the arccos of 3 ?
## What is the arccos of 3 ?
What is the arccosine of 3 ?
arccos 3 = ?
## Real arccos function
The arccosine is the inverse cosine function.
Since the cosine function has output values from -1 to 1,
the arccosine function has input values from -1 to 1.
So arccos x is undefined for x=3.
arccos 3 is undefined
## Complex arccos function
x = arccos(3)
cos(x) = cos(arccos(3))
cos(x) = 3
From Euler's formula
cos(x) = (eix + e-ix) / 2
(eix + e-ix) / 2 = 3
eix + e-ix = 6
Multiply with eix
e2ix + 1 = 6eix
y = eix
y2 - 6y + 1 = 0
y1,2 = (6 ± √32)/2
y1 = 5.828427 = eix
y2 = 0.171573 = eix
Apply ln on both sides gives the solution for arccos(3):
x1 = ln(5.828427) / i
x2 = ln(0.171573) / i | 299 | 740 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2017-39 | longest | en | 0.623523 |
https://www.slideshare.net/iamsudip03/brick-masonary-47967723 | 1,563,347,654,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195525094.53/warc/CC-MAIN-20190717061451-20190717083451-00475.warc.gz | 846,492,225 | 41,967 | Successfully reported this slideshow.
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# BRICK MASONRY
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### BRICK MASONRY
1. 1. BRICK MASONRY PRESENTED BY: SUBHENDU SAMUI 12001312049 SUDIP HOR 12001312050 SUKESH DEY 12001312051 SUKHOMOY DAS 12001312052 SUMANTA BAIDDO 12001312053
2. 2. OVERVIEW INTRODUCTION DEFINATION UNIQUENSS CHARACTERISTIC OF BRICK ADVANTAGE MANUFACTURNG TYPES SIZE JOINT TOOLS TECHNICAL TERMS ORIENTATION RULES BOND CLASSIFICATION TESTS OF BRICK DEFECTS CONCLUSION
3. 3. Brick bonds are an essential part of wall structure. "brick" is a standard-sized weight- bearing building unit. Several bricks are laid together in stacks. Mortar paste is placed on top of each to form a firm bond. are laid to form the structure. There are different ways in which bricks are termed as bonds.
4. 4. WHAT IS BRICK-MASONARY BRICK :- Brick is a building unit ,which is in the form of rectangular block in which length to breadth ratio is 2 but height can be different. MASONARY :-Construction of building unit bonded together with mortar. BRICK MASONRY:-The art of laying bricks in mortar in a proper systematic manner gives homogeneous mass which can withstand forces without disintegration, called Brick masonry.
5. 5. BRICK MASONRY-UNIQUENESS FIRE RESISTANCE SIZE DURABILITY WORAKABILITY ECONOMICAL
6. 6. CHARACTERISTIC OF BRICKS Brick will not burn, buckle or melt. Brick will not rot and allow Termites to invade. Brick will not rust and corrode. Brick will not dent. Brick will not fade from the Sun’s UV Rays. Brick will not be damaged by high winds , rain or hail. Brick will not require constant maintains. Brick will not devalue. Brick will not limit your personal expression. Brick will not limit your design options.
7. 7. ADVANTAGES OF BRICK MASONRY The Brick masonry is cheaper than compared to stone masonry. Bricks are of uniform size. Bricks are very workable . Brick blocks don’t need any dressing. Bricks are very light in weight. No complicated lifting devices are necessary in brick work. There is no problem to its availability. They do not require transportation from long distances. Brick work can be done by the less skilled labours also. Bonding strength is very good and brick work is more durable.
8. 8. MANUFACTURING OF BRICKS
9. 9. TYPES OF BRICKS MASONRY Bricks Masonry Brick work in mud Brick work in cement
10. 10. BRICK WORK IN MUD The mud is used to fill up the joints. Thickness of the mortar joint is 12 mm. Cheapest Maximum height of wall is 4 m.
11. 11. BRICK WORK IN CEMENT 1st Class Cement of lime mortar is used. The surface and edges of bricks are sharp. The thickness of mortar joints doesn’t exceed 10mm 2nd Class Ground moulded bricks are used. Bricks are rough and shape is slightly irregular. The thickness of mortar joint is 12 mm. 3rd Class Bricks are not hard ,rough surface with distorted shape. Used for temporary structures. Used in places where rainfall is not heavy.
12. 12. SIZES OF BRICK Nominal size :-A standard metric brick has coordinating dimensions of 225 x 112.5 x 75 mm (9” x 4.5” x 3”) Architectural size :- Working dimensions (actual dimensions)of 215 x 102.5 x 65 mm (8.5” x 4” x 2.5”)
13. 13. MASONRY JOINT Weathered joint :-Mortar joint has sloped (downwards) edge. Concave joint :-Joint concave inwards. Vee joint :-Mortar joint is the form of V. Flush joint :-Mortar joint is flush with the brick surface. Raked joint :-A large portion of the mortar joint is raked out not a safe ,impermeable joint. Stripped joint :- A medium large portion of the mortar joint is a safe permeable joint. Struck joint :-Mortar joint has aslope (upwards) edge.
14. 14. TOOLS USED IN BRICK MASONRY Trowel Plumb bob Hammer Spirit level Mason square Steel tape
15. 15. BRICK COURSES & CLOSURES QUEEN CLOSURE: A brick cut in half down its length. KING CLOSURE : A brick cut a corner & joining middle points of width and length of the brick. THREE QUARTER BAT : A brick cut to three-quarters of its length, and laid with its long, narrow side exposed. HALF BAT: A brick cut in half across its width and laid in the wall structure. QUARTER BAT: A brick cut to a quarter of its length.
16. 16. ORIENTATION OF BRICKS STRETCHER: A brick laid with its long narrow side exposed. HEADER: A brick laid flat with its width at the face of the wall. SOLDIER: A brick laid vertically with the long narrow side of the brick exposed. SAILOR: A brick laid vertically with the broad face of the brick exposed.
17. 17. RULES FOR GOOD BRICK BONDING Uniform in size. Bricks arranged uniformly throughout the wall. Bats are used as little as possible. The bricks in the interiors of wall laid as headers, that is, across the wall. The lap not more than 2 and one-fourth(1/4) inches. The vertical joints in every other course should be vertically over one another.
18. 18. BONDS IN BRICK-WORK 1. English bond. 2. Flemish bond. 3. Header bond. 4. Stretcher bond. 5. Facing bond. 6. English cross bond. 7. Brick on edge bond. 8. Dutch bond. 9. Raking bond. 10. Garden wall bond
19. 19. FLEMISH-BOND This bond has one stretcher between headers, with the headers centered over the stretchers in the course below. When a course begins with a stretcher, the course will ordinarily terminate with a stretcher at the other end. Brickwork that appears as Flemish bond from both the front and rear is Double Flemish bond.
20. 20. ENGLISH BOND Bricks are laid in alternate courses of headers and stretchers. There is a chance of penetration of damp through transverse joints. Queen closures are inserted next to headers to produce overlap. English bonds are the strongest but it is to be noted that the continuous vertical joints are to be avoided. Appearance is not as good as Flemish bonds.
21. 21. SUSSEX BOND This bond has three stretchers between every header. the headers are centered above the midpoint of three stretchers in the course below. Generally used as garden walls and are relatively cheaper than other bonds.
22. 22. GARDEN-WALL BOND Used for 9 inch wall. Used when a fair face is required on both sides. Wall is composed of three or four courses of stretchers alternating with one of headers. It is mostly used in construction of garden wall.
23. 23. HEADER BOND Heading or Header Bond is laid on headers. Used for round quick sweeps . Should never be used in straight work as it is very week. This bond is used for facing of curved surface and footings in foundations.
24. 24. STRETCHER BOND Bricks are laid in stretchers. Used in walls of half – brick in thickness. Due to its constant occurrence in the last position it is also called Chimney Bond, Running Bond. This bond doesn’t develop proper internal bond.
25. 25. QUALITIES OF GOOD BRICKS 1. Bricks should be uniform in shape & standard in size. 2. Bricks should give a clear metallic ringing sound when struck with each other. 3. Bricks should show a bright homogeneous & free from voids. 4. Bricks should be well brunt and possess sharp edges. 5. Colour of the bricks should be uniform and bright. 6. Bricks should be sufficiently hard & no impression should be left on bricks surface when scratched with finger nail. 7. Bricks should have crushing strength above 5.50N/mm”. 8. The bricks should not break when it dropped from a height of about 1 m. 9. The bricks should not absorb water more than 20% by weight when soaked in cold water for 24 hrs. 10. The bricks should not show any deposits of white salts when allowed to dry in shade.
26. 26. CLASSIFICATION OF BRICKS FIRST CLASS BRICKS :- This are table moulded. Surface & edges are sharp, square ,smooth , straight. Well brunt & have uniform texture ,metallic ringing when struck against each other. Used for superior work. SECOND CLASS BRICKS :- This are ground moulded brick. Surface are rough. The quality of this bricks are inferior. THIRD CLASS BRICKS :- The surface & edges are rough. Does not create any metallic sound. Used for temporary & unimportant structure. FOURTH CLASS BRICKS :- This bricks are over brunt. Irregular shape & dark colour. Used in floor , foundation, roads.
27. 27. TESTS FOR BRICKS 1) Absorption:- The brick should not absorb water more than 20% of dry weight. 2) Crushing strength:- As per BIS 1077-1957 the minimum crushing strength of bricks is 3.5 N/mm2 3) Hardness :- Brick is treated to be sufficient hard if no impression could be made on the surface of the brick by finger nail. 4) Soundness :- Two bricks when struck with each other should emit metallic ringing sound. 5) Structure :- It should be homogeneous ,compact ,and free from any defects. 6) Shape & size :- Standard size (190 X 90 X 90 mm) and shapes should be truly rectangular with sharp edges and smooth surface.
28. 28. DEFECTS IN BRICK MASONRY Sulphate attack :- Sulphate salts present in bricks work react with alumina content of cement .It occur in boundary walls. Crystallization of salts from bricks :- Occur in masonry made out of brick which contain excessive soluble salts.This phenomenon is also known as efflorescence. Corrosion of embedded iron or steel :- Iron or steel embedded in brick work gets corroded in the presence of dampness .On corrosion the metal expands in volume and tends to crack the brick work.
29. 29. CONCLUSION Masonry boasts an impressive compressive strength (vertical loads) but is much lower in tensile strength unless reinforced. Brick masonry increases the thermal mass of a building and thereby resists fire. Masonry tends to be heavy and must be built upon a strong foundation, such as reinforced concrete, to avoid settling and cracking. | 2,839 | 10,071 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2019-30 | latest | en | 0.772475 |
https://www.gradesaver.com/textbooks/science/physics/CLONE-afaf42be-9820-4186-8d76-e738423175bc/chapter-7-for-thought-and-discussion-page-130/4 | 1,723,330,036,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640826253.62/warc/CC-MAIN-20240810221853-20240811011853-00599.warc.gz | 619,999,927 | 12,284 | ## Essential University Physics: Volume 1 (4th Edition)
Potential energy can be negative, for where the ground is can be considered an arbitrary definition. For instance, if I were to say that the ground was the floor while a different person said the ground was the top of a table, neither of us would be wrong. Therefore, anything below whatever is defined to be ground level has negative potential energy. Kinetic energy, however, equals $mv^2$. $v^2$ and can never be negative, for it is squared, and mass can never be negative, so kinetic energy will never be negative. | 126 | 575 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2024-33 | latest | en | 0.96856 |
http://slideplayer.com/slide/4063569/ | 1,501,246,561,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500550967030.98/warc/CC-MAIN-20170728123647-20170728143647-00025.warc.gz | 308,458,883 | 25,962 | # Physics 7C lecture 07 Potential Energy
## Presentation on theme: "Physics 7C lecture 07 Potential Energy"— Presentation transcript:
Physics 7C lecture 07 Potential Energy
Thursday October 17, 8:00 AM – 9:20 AM Engineering Hall 1200
To use gravitational potential energy in vertical motion
Goals for Chapter 7 To use gravitational potential energy in vertical motion To use elastic potential energy for a body attached to a spring To solve problems involving conservative and nonconservative forces To determine the properties of a conservative force from the corresponding potential-energy function To use energy diagrams for conservative forces
Introduction How do energy concepts apply to the descending duck? We will see that we can think of energy as being stored and transformed from one form to another.
Gravitational potential energy
Energy associated with position is called potential energy. Gravitational potential energy is Ugrav = mgy. Figure 7.2 at the right shows how the change in gravitational potential energy is related to the work done by gravity.
A piece of fruit falls straight down. As it falls,
Q7.1 A piece of fruit falls straight down. As it falls, A. the gravitational force does positive work on it and the gravitational potential energy increases. B. the gravitational force does positive work on it and the gravitational potential energy decreases. C. the gravitational force does negative work on it and the gravitational potential energy increases. D. the gravitational force does negative work on it and the gravitational potential energy decreases. Answer: B
A7.1 A piece of fruit falls straight down. As it falls, A. the gravitational force does positive work on it and the gravitational potential energy increases. B. the gravitational force does positive work on it and the gravitational potential energy decreases. C. the gravitational force does negative work on it and the gravitational potential energy increases. D. the gravitational force does negative work on it and the gravitational potential energy decreases.
The conservation of mechanical energy
The total mechanical energy of a system is the sum of its kinetic energy and potential energy. A quantity that always has the same value is called a conserved quantity. When only the force of gravity does work on a system, the total mechanical energy of that system is conserved. This is an example of the conservation of mechanical energy. Figure 7.3 below illustrates this principle.
An example using energy conservation
Refer to Figure 7.4 below as you follow Example 7.1. Notice that the result does not depend on our choice for the origin.
B. less than 10.0 m/s but greater than zero C. greater than 10.0 m/s
Q7.2 You toss a kg baseball straight upward so that it leaves your hand moving at 20.0 m/s. The ball reaches a maximum height y2. What is the speed of the ball when it is at a height of y2/2? Ignore air resistance. v2 = 0 y2 v1 = 20.0 m/s m = kg y1 = 0 A m/s B. less than 10.0 m/s but greater than zero C. greater than 10.0 m/s D. not enough information given to decide Answer: C
A7.2 You toss a kg baseball straight upward so that it leaves your hand moving at 20.0 m/s. The ball reaches a maximum height y2. What is the speed of the ball when it is at a height of y2/2? Ignore air resistance. v2 = 0 y2 v1 = 20.0 m/s m = kg y1 = 0 A m/s B. less than 10.0 m/s but greater than zero C. greater than 10.0 m/s D. not enough information given to decide
(Ignore air resistance.)
Q7.3 As a rock slides from A to B along the inside of this frictionless hemispherical bowl, mechanical energy is conserved. Why? (Ignore air resistance.) A. The bowl is hemispherical. B. The normal force is balanced by centrifugal force. C. The normal force is balanced by centripetal force. D. The normal force acts perpendicular to the bowl’s surface. E. The rock’s acceleration is perpendicular to the bowl’s surface. Answer: D
A7.3 As a rock slides from A to B along the inside of this frictionless hemispherical bowl, mechanical energy is conserved. Why? (Ignore air resistance.) A. The bowl is hemispherical. B. The normal force is balanced by centrifugal force. C. The normal force is balanced by centripetal force. D. The normal force acts perpendicular to the bowl’s surface. E. The rock’s acceleration is perpendicular to the bowl’s surface.
A. the block on the curved track B. the block on the straight track
Q7.4 The two ramps shown are both frictionless. The heights y1 and y2 are the same for each ramp. A block of mass m is released from rest at the left-hand end of each ramp. Which block arrives at the right-hand end with the greater speed? A. the block on the curved track B. the block on the straight track C. Both blocks arrive at the right-hand end with the same speed. D. The answer depends on the shape of the curved track. Answer: C
A7.4 The two ramps shown are both frictionless. The heights y1 and y2 are the same for each ramp. A block of mass m is released from rest at the left-hand end of each ramp. Which block arrives at the right-hand end with the greater speed? A. the block on the curved track B. the block on the straight track C. Both blocks arrive at the right-hand end with the same speed. D. The answer depends on the shape of the curved track.
When forces other than gravity do work
Refer to Problem-Solving Strategy 7.1. Follow the solution of Example 7.2.
Work and energy along a curved path
We can use the same expression for gravitational potential energy whether the body’s path is curved or straight.
Energy in projectile motion
Two identical balls leave from the same height with the same speed but at different angles. Follow Conceptual Example 7.3 using Figure 7.8.
Motion in a vertical circle with no friction
Follow Example 7.4 using Figure 7.9.
Motion in a vertical circle with friction
Revisit the same ramp as in the previous example, but this time with friction. Follow Example 7.5 using Figure 7.10.
Moving a crate on an inclined plane with friction
Follow Example 7.6 using Figure 7.11 to the right. Notice that mechanical energy was lost due to friction.
Work done by a spring Figure 7.13 below shows how a spring does work on a block as it is stretched and compressed.
Elastic potential energy
A body is elastic if it returns to its original shape after being deformed. Elastic potential energy is the energy stored in an elastic body, such as a spring. The elastic potential energy stored in an ideal spring is Uel = 1/2 kx2. Figure 7.14 at the right shows a graph of the elastic potential energy for an ideal spring.
Situations with both gravitational and elastic forces
When a situation involves both gravitational and elastic forces, the total potential energy is the sum of the gravitational potential energy and the elastic potential energy: U = Ugrav + Uel. Figure 7.15 below illustrates such a situation. Follow Problem-Solving Strategy 7.2.
Motion with elastic potential energy
A. Ugrav and Uel are both increasing.
Q7.5 A block is released from rest on a frictionless incline as shown. When the moving block is in contact with the spring and compressing it, what is happening to the gravitational potential energy Ugrav and the elastic potential energy Uel? A. Ugrav and Uel are both increasing. B. Ugrav and Uel are both decreasing. C. Ugrav is increasing; Uel is decreasing. D. Ugrav is decreasing; Uel is increasing. E. The answer depends on how the block’s speed is changing. Answer: D
A7.5 A block is released from rest on a frictionless incline as shown. When the moving block is in contact with the spring and compressing it, what is happening to the gravitational potential energy Ugrav and the elastic potential energy Uel? A. Ugrav and Uel are both increasing. B. Ugrav and Uel are both decreasing. C. Ugrav is increasing; Uel is decreasing. D. Ugrav is decreasing; Uel is increasing. E. The answer depends on how the block’s speed is changing.
A system having two potential energies and friction
In Example 7.9 gravity, a spring, and friction all act on the elevator. Follow Example 7.9 using Figure 7.17 at the right.
Conservative and nonconservative forces
A conservative force allows conversion between kinetic and potential energy. Gravity and the spring force are conservative. The work done between two points by any conservative force a) can be expressed in terms of a potential energy function. b) is reversible. c) is independent of the path between the two points. d) is zero if the starting and ending points are the same. A force (such as friction) that is not conservative is called a nonconservative force, or a dissipative force.
Frictional work depends on the path
Follow Example 7.10, which shows that the work done by friction depends on the path taken.
A. greater than the rate at which you do work on the block.
Q7.12 You push a block up an inclined ramp at a constant speed. There is friction between the block and the ramp. The rate at which the internal energy of the block and ramp increases is A. greater than the rate at which you do work on the block. B. the same as the rate at which you do work on the block. C. less than the rate at which you do work on the block. D. not enough information given to decide Answer: C
A7.12 You push a block up an inclined ramp at a constant speed. There is friction between the block and the ramp. The rate at which the internal energy of the block and ramp increases is A. greater than the rate at which you do work on the block. B. the same as the rate at which you do work on the block. C. less than the rate at which you do work on the block. D. not enough information given to decide
Conservative or nonconservative force?
Follow Example 7.11, which shows how to determine if a force is conservative or nonconservative.
Conservation of energy
Nonconservative forces do not store potential energy, but they do change the internal energy of a system. The law of the conservation of energy means that energy is never created or destroyed; it only changes form. This law can be expressed as K + U + Uint = 0. Follow Conceptual Example 7.12.
Q7.9 Fx The graph shows a conservative force Fx as a function of x in the vicinity of x = a. As the graph shows, Fx = 0 at x = a. Which statement about the associated potential energy function U at x = a is correct? x a A. U = 0 at x = a B. U is a maximum at x = a. C. U is a minimum at x = a. D. U is neither a minimum or a maximum at x = a, and its value at x = a need not be zero. Answer: B
A7.9 Fx The graph shows a conservative force Fx as a function of x in the vicinity of x = a. As the graph shows, Fx = 0 at x = a. Which statement about the associated potential energy function U at x = a is correct? x a A. U = 0 at x = a B. U is a maximum at x = a. C. U is a minimum at x = a. D. U is neither a minimum or a maximum at x = a, and its value at x = a need not be zero.
Q7.10 Fx The graph shows a conservative force Fx as a function of x in the vicinity of x = a. As the graph shows, Fx = 0 at x = a. Which statement about the associated potential energy function U at x = a is correct? x a A. U = 0 at x = a B. U is a maximum at x = a. C. U is a minimum at x = a. D. U is neither a minimum or a maximum at x = a, and its value at x = a need not be zero. Answer: C
A7.10 Fx The graph shows a conservative force Fx as a function of x in the vicinity of x = a. As the graph shows, Fx = 0 at x = a. Which statement about the associated potential energy function U at x = a is correct? x a A. U = 0 at x = a B. U is a maximum at x = a. C. U is a minimum at x = a. D. U is neither a minimum or a maximum at x = a, and its value at x = a need not be zero.
D. Any of the above could be correct.
Q7.11 Fx The graph shows a conservative force Fx as a function of x in the vicinity of x = a. As the graph shows, Fx > 0 and dFx/dx < 0 at x = a. Which statement about the associated potential energy function U at x = a is correct? x a A. dU/dx > 0 at x = a B. dU/dx < 0 at x = a C. dU/dx = 0 at x = a D. Any of the above could be correct. Answer: B
D. Any of the above could be correct.
Fx The graph shows a conservative force Fx as a function of x in the vicinity of x = a. As the graph shows, Fx > 0 and dFx/dx < 0 at x = a. Which statement about the associated potential energy function U at x = a is correct? x a A. dU/dx > 0 at x = a B. dU/dx < 0 at x = a C. dU/dx = 0 at x = a D. Any of the above could be correct.
Force and potential energy in one dimension
In one dimension, a conservative force can be obtained from its potential energy function using Fx(x) = –dU(x)/dx Figure 7.22 at the right illustrates this point for spring and gravitational forces. Follow Example 7.13 for an electric force.
Force and potential energy in two dimensions
In two dimension, the components of a conservative force can be obtained from its potential energy function using Fx = –U/dx and Fy = –U/dy Follow Example 7.14 for a puck on a frictionless table.
Energy diagrams An energy diagram is a graph that shows both the potential-energy function U(x) and the total mechanical energy E. Figure 7.23 illustrates the energy diagram for a glider attached to a spring on an air track.
Force and a graph of its potential-energy function
Figure 7.24 below helps relate a force to a graph of its corresponding potential-energy function.
A. at x = a B. at x = b C. at x = c D. at x = d
Q7.6 The graph shows the potential energy U for a particle that moves along the x-axis. The particle is initially at x = d and moves in the negative x-direction. At which of the labeled x-coordinates does the particle have the greatest speed? Answer: B A. at x = a B. at x = b C. at x = c D. at x = d E. more than one of the above
A7.6 The graph shows the potential energy U for a particle that moves along the x-axis. The particle is initially at x = d and moves in the negative x-direction. At which of the labeled x-coordinates does the particle have the greatest speed? A. at x = a B. at x = b C. at x = c D. at x = d E. more than one of the above
A. at x = a B. at x = b C. at x = c D. at x = d
Q7.7 The graph shows the potential energy U for a particle that moves along the x-axis. The particle is initially at x = d and moves in the negative x-direction. At which of the labeled x-coordinates is the particle slowing down? Answer: A A. at x = a B. at x = b C. at x = c D. at x = d E. more than one of the above
A7.7 The graph shows the potential energy U for a particle that moves along the x-axis. The particle is initially at x = d and moves in the negative x-direction. At which of the labeled x-coordinates is the particle slowing down? A. at x = a B. at x = b C. at x = c D. at x = d E. more than one of the above
E. misleading question—there is a force at all values of x
The graph shows the potential energy U for a particle that moves along the x-axis. At which of the labeled x-coordinates is there zero force on the particle? A. at x = a and x = c B. at x = b only C. at x = d only D. at x = b and d E. misleading question—there is a force at all values of x Answer: D
A7.8 The graph shows the potential energy U for a particle that moves along the x-axis. At which of the labeled x-coordinates is there zero force on the particle? A. at x = a and x = c B. at x = b only C. at x = d only D. at x = b and d E. misleading question—there is a force at all values of x | 3,834 | 15,375 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2017-30 | latest | en | 0.88099 |
https://scicomp.stackexchange.com/questions/30909/is-this-the-correct-way-for-solving-coupled-1d-pdes-using-finite-difference-meth | 1,632,435,272,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057447.52/warc/CC-MAIN-20210923195546-20210923225546-00498.warc.gz | 546,366,862 | 41,761 | # Is this the correct way for solving coupled 1d PDEs using finite difference methods?
I am trying to solve the following coupled PDEs:
$$C_e\frac{\partial u(x,t)}{\partial t} = k_{ed}\frac{\partial^2u(x,t)}{\partial^2x} - G_{el}(u(x,t) - v(x,t)) + S(x,t)$$ $$C_l\frac{\partial v(x,t)}{\partial t} = k_{ed}\frac{\partial^2v(x,t)}{\partial^2x} + G_{el}(u(x,t) - v(x,t))$$
where $$k_{ed}$$, $$G_{el}$$ are constants and $$C_e = \gamma u(x,t)$$ and $$C_l$$ are specific heats and $$S(x,t) = I_0 exp(-\frac{x}{\delta}-\frac{(t - 2t_p)^2}{t_p^2})$$ is the laser pulse source term.
I use finite difference methods to solve the above equations as follows:
$$u^{f+1}_i = u^f_i + \frac{k_{ed}dt}{\Delta x^2}(u^f_{i+1} -2u^f_i + u^f_{i-1}) + dt(-G_{el}(u^f_i - v^f_i) + S^f_i)$$ and $$v^{f+1}_i = v^f_i + \frac{k_{ed}dt}{\Delta x^2}(v^f_{i+1} -2v^f_i + v^f_{i-1}) + dt(G_{el}(u^f_i - v^f_i))$$
Where $$(f,i)$$ are mesh in time and space as $$F\Delta t = T_{total}, f = 0,1,2 ... F$$ and $$N\Delta x = L, i = 0,1,2,... N$$ where $$T_{total}$$ and $$L$$ are the total integration time and length respectively. I have implemented the above in python:
import numpy as np
import matplotlib.pyplot as plt
# sample parameter §§ Gold
la0 = 429 # conductivity in W/mK
gma = 62.8 # thermal constant J/m^3K^2
Cl = 2.6*10**6 # phonon specific heat in J/m^3K
Gel = 3.5*10**16 # lelectron phonon coupling constant
tau_e = 0.04 # e relaxation t const
tau_l = 0.6 # l relaxation t const
Tm = 300
L = 100 # sample thickness in nm
# Laser pulse parameters
T = 6
R = 0.93 # reflectivity
I0 = 100 # fulence in J/m^2
tp = 0.1 # in ps
zz0 = 15.3 # penetration depth in nm
#F = 0.5
def las(x,t):
pt = 0.93*((1-R)/(zz0*tp))*I0*np.exp(-(x/zz0)-2.772*((t-2*tp)**2/tp**2))
return pt
def I(x):
tin = Tm
return tin
a = la0 # Ked
def solver_FE(I, a, las, L, T):
"""
"""
import time; t0 = time.clock() # For measuring the CPU time
dt = 0.001
Nt = int(round(T/float(dt)))
t = np.linspace(0, Nt*dt, Nt+1) # Mesh points in time
dx = 1
Nx = int(round(L/dx))
x = np.linspace(0, L, Nx+1) # Mesh points in space
F = a*(dt/dx**2)
u = np.zeros(Nx+1)
u_n = np.zeros(Nx+1)
v = np.zeros(Nx+1)
v_n = np.zeros(Nx+1)
# Set initial condition u(x,0) = I(x)
for i in range(0, Nx+1):
u_n[i] = I(x[i])
v_n[i] = I(x[i])
for n in range(0, Nt):
# Compute u, v at inner mesh points
for i in range(1, Nx):
u[i] = u_n[i] + (-F*(u_n[i-1] - 2*u_n[i] + u_n[i+1]) + dt*(-Gel*(u_n[i] - v_n[i]) + las(x[i], t[n])))/(gma*u_n[i])
v[i] = v_n[i] + (-F*(v_n[i-1] - 2*v_n[i] + v_n[i+1]) + dt*(Gel*(u_n[i] - v_n[i])))/(Cl)
# Insert boundary conditions
u[0] = 0; u[Nx] = 0
v[0] = 0; v[Nx] = 0
# this step is to save each value of v and u in each time step before updating it, such that I can plot u and v with respect to time.
ut = np.array([])
vt = np.array([])
for m in range(0, Nt):
ut = np.append(ut,u)
vt = np.append(vt,v)
# Switch variables before next step
u_n, u = u, u_n
v_n, v = v, v_n
t1 = time.clock()
return u_n, v_n, x, t, t1-t0 # u_n holds latest u
u, v, x, t, cpu = solver_FE(I, a, las, L, T)
#fig = plt.figure(1)
##t = np.linspace(0, T, h)
#plt.plot(t,u,'r',label=r'$$T_e$$')
#plt.plot(t,v,'b',label=r'$$T_l$$')
##plt.plot(t,sol0[:,2],'g',label=r'$$T_s$$')
#plt.ylabel('$$Temperature$$',fontsize=20)
#plt.xlabel('Delay',fontsize=20)
#plt.legend(loc='best')
#plt.show()
##
fig = plt.figure(2)
#t = np.linspace(0, T, h)
plt.plot(x,u,'r',label=r'$$T_e$$')
plt.plot(x,v,'g',label=r'$$T_l$$')
#plt.plot(t,sol0[:,2],'g',label=r'$$T_s$$')
plt.ylabel('$$Temperature$$',fontsize=20)
plt.xlabel('length',fontsize=20)
plt.legend(loc='best')
plt.show()
fig = plt.figure(3)
#t = np.linspace(0, T, h)
plt.plot(t,las(0,t),'r',label=r'$$T_e$$')
#plt.plot(x,v,'g',label=r'$$T_l$$')
#plt.plot(t,sol0[:,2],'g',label=r'$$T_s$$')
plt.ylabel('$$Intensity$$',fontsize=20)
plt.xlabel('Delay',fontsize=20)
plt.legend(loc='best')
plt.show()
while running it I get the following errors:
RuntimeWarning: overflow encountered in double_scalars
u[i] = u_n[i] + F*(u_n[i-1] - 2*u_n[i] + u_n[i+1]) + dt*(-Gel*(u_n[i] - v_n[i]) + las(x[i], t[n]))
C:/Users/jayas/OneDrive/Documents/Python Scripts/llg/diff_ttm_v_test.py:90: RuntimeWarning: overflow encountered in double_scalars
v[i] = v_n[i] + F*(v_n[i-1] - 2*v_n[i] + v_n[i+1]) + dt*(Gel*(u_n[i] - v_n[i]))
C:/Users/jayas/OneDrive/Documents/Python Scripts/llg/diff_ttm_v_test.py:89: RuntimeWarning: invalid value encountered in double_scalars
u[i] = u_n[i] + F*(u_n[i-1] - 2*u_n[i] + u_n[i+1]) + dt*(-Gel*(u_n[i] - v_n[i]) + las(x[i], t[n]))
C:/Users/jayas/OneDrive/Documents/Python Scripts/llg/diff_ttm_v_test.py:90: RuntimeWarning: invalid value encountered in double_scalars
v[i] = v_n[i] + F*(v_n[i-1] - 2*v_n[i] + v_n[i+1]) + dt*(Gel*(u_n[i] - v_n[i]))
I guess that I am doing somewhere wrong while calculating the inner mesh points. Can anyone lemme know whats going wrong in here and ideas to rectify it?
• What is the stability criterion for selecting your timestep for this differential equation? Jan 21 '19 at 20:58
• my stability criteria in this case is: F < = 0.5 Jan 21 '19 at 21:23
• Double checking your equations, they seem to be non-linear but your FD looks like a linear iteration. Jan 21 '19 at 21:41
• My advice, use FD to transform your PDEs to a system of transient ODEs and use scipy's odeint to integrate in time. It is optimized and robust, it will be difficult to optimize your own time-marching scheme to do better. Why reinvent the wheel? Jan 22 '19 at 19:41
• @nluigi Do you have an example or some implementations for such coupled PDEs? Jan 23 '19 at 17:27
This doesn't answer your question directly but instead suggests an alternate strategy. In general, unless you are interested in experimenting with numerical methods, I recommend using an existing PDE solver instead of trying to write one yourself. This advice is particularly true for numerically-challenging problems, like yours appears to be.
Since you are interested in Python, I have written a FiPy version of your problem, as shown below.
Unfortunately, I can't say that FiPy easily obtained a solution. But I have done some numerical experimentation and made a few observations. First, I should acknowledge that I don't understand much about the physics of these equations.
1. I changed your boundary conditions to zero-flux at the ends to be consistent with your initial conditions.
2. The laser pulse doesn't seem to be adding much heat to the system; the temperatures as a function of time change very little from the initial values. The temperature changes are so small, I have been plotting the difference in temperature compared with the initial conditions.
3. The large value of Gel appears to make the problem very numerically stiff and more difficult to solve. I've been experimenting with values several orders of magnitude less.
The Python code using the FiPy PDE solver is:
import numpy as np
import fipy
# sample parameter Gold
la0 = 429 # conductivity in W/mK
gma = 62.8 # thermal constant J/m^3K^2
Cl = 2.6e6 # phonon specific heat in J/m^3K
Gel = 3.5e16 # lelectron phonon coupling constant
#Gel=1e10 # reduce value to improve numerics
tau_e = 0.04 # e relaxation t const
tau_l = 0.6 # l relaxation t const
Tm = 300.
L = 100 # sample thickness in nm
# Laser pulse parameters
T = 6.
T=1
R = 0.93 # reflectivity
I0 = 100 # fulence in J/m^2
tp = 0.1 # in ps
zz0 = 15.3 # penetration depth in nm
#F = 0.5
def las(x,t):
pt = 0.93*((1-R)/(zz0*tp))*I0*np.exp(-(x/zz0)-2.772*((t-2*tp)**2/tp**2))
return pt
def I(x):
tin = Tm
return tin
a = la0 # Ked
nx = 100
dx = L/nx
mesh = fipy.Grid1D(nx = nx, dx = dx)
x = mesh.cellCenters[0]
#pt25 = mesh._getNearestCellID(([25.],))
u = fipy.CellVariable(name="u", mesh=mesh)
v = fipy.CellVariable(name="v", mesh=mesh)
valueLeft = 0
valueRight = 0
applyDirichletConstraint=False
if(applyDirichletConstraint):
u.constrain(valueRight, mesh.facesRight)
u.constrain(valueLeft, mesh.facesLeft)
v.constrain(valueRight, mesh.facesRight)
v.constrain(valueLeft, mesh.facesLeft)
else:
pi=np.math.pi
#Gumv = Gel*(u-v) # explicit source terms are not appropriate for this stiff system
Gumv = fipy.ImplicitSourceTerm(Gel, var=u) - fipy.ImplicitSourceTerm(Gel, var=v)
time = fipy.Variable()
eqn0 = fipy.TransientTerm(gma*u, var=u) == fipy.DiffusionTerm(a, var=u) - Gumv + las(x,time)
eqn1 = fipy.TransientTerm(Cl, var=v) == fipy.DiffusionTerm(a, var=v) + Gumv
eqn = eqn0 & eqn1
steps = 5000
dt = T/steps
ival = I(x)
u.setValue(ival)
v.setValue(ival)
centerX=([L/2.],)
uCenter = [u(centerX)[0]]
vCenter = [v(centerX)[0]]
ts = [0.]
t = 0
for step in range(steps):
time.setValue(t+dt/2.)
eqn.solve(dt=dt)
uCenter.append(u(centerX)[0])
vCenter.append(v(centerX)[0])
t += dt
ts.append(t)
# plot difference from intial value
uCenter = np.asarray(uCenter) - Tm
vCenter = np.asarray(vCenter) - Tm
import matplotlib.pyplot as plot
plot.subplot(211);
plot.title('nx=%d, dt=%12.3e, Gel=%g' % (nx, dt, Gel))
p1=plot.plot(ts, uCenter)
plot.grid(b='on')
plot.xlabel('Time')
plot.ylabel('u at center')
plot.subplot(212);
p2=plot.plot(ts, vCenter)
plot.grid(b='on')
plot.xlabel('Time')
plot.ylabel('v at center')
plot.savefig('plot.pdf')
plot.show() | 3,161 | 9,192 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 26, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2021-39 | latest | en | 0.688897 |
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# AWA scores
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Joined: 06 Jun 2003
Posts: 59
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03 Feb 2004, 14:12
I received my official score last week (Q41, V39, 710) but was disappointed to see AWA score of 4.5. Can some of the folks who have recently taked the GMAT post their AWA scores?
Thanks.
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Joined: 15 Dec 2003
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03 Feb 2004, 14:15
Hey bluefox, I got my scorecard yesterday and got 5.5. I simply used a combination of the OA and PR templates
_________________
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Paul
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Joined: 19 Jul 2003
Posts: 63
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Location: Florida
### Show Tags
03 Feb 2004, 17:57
Hi there. I'm not sure that too many schools worry a lot about the AWA.
I was wondering if you could re post your breakdown. You say you got Q41 and V39. That corresponds to a ballpark of 650 most of the time.
I'm not trying to call you out on anything believe me. I think you probably made a typo, but I think it would help me if you gave your breakdown. That way I could learn more from your post. Thanks.
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Paul
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03 Feb 2004, 22:01
http://www.gmatclub.com/phpbb/viewtopic.php?t=3775
bluefox got q48v39
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Paul
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Joined: 12 Jul 2003
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04 Feb 2004, 09:58
I got a 5.5 using the PR template. Not sure it really matters though for US Citizens.
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04 Feb 2004, 09:58
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# AWA scores
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Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 794 | 2,671 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2017-43 | latest | en | 0.909519 |
https://www.pobonline.com/articles/95107-state-plane-coordinates-vs-surface-coordinates-part-3 | 1,618,768,496,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038507477.62/warc/CC-MAIN-20210418163541-20210418193541-00582.warc.gz | 1,037,864,625 | 21,779 | As I stated earlier in this series, state plane coordinates are based on conformal map projections. Since we¿re surveyors, we can't think of a map projection as used only for paper maps - but this concept may be hard for some people to grasp.
There are many definitions of map projections. One reference states, a map projection is a systematic representation of all or part of a surface of a round body, especially the earth, onto a plane (Snyder). Another reference says, a projection is a means of transferring points on one surface to corresponding points on another surface (Buckner). When surveying or mapping a large area, a projection is required. No matter what projection is used, there will be distortions. If the survey or map covers a small area -like a town - distortions may not be visible, but they do exist. Determine what distortion is the least objectionable, and select that projection for the survey or map.
With few exceptions, there are three developable surfaces which are the basis of most map projections: the cylinder, cone and plane. A developable surface can be "cut" and unrolled to form a plane. This is shown in Figure 1. For illustrative purposes, let's describe these surfaces on a global basis.
Cylinder
• Surface touches the equator throughout its circumference.
• The meridians of longitude will be projected onto the cylinder as equidistant straight lines perpendicular to the equator.
• The parallels of latitude are projected as lines parallel to the equator, and mathematically spaced for certain characteristics.
• The Mercator Projection is the best known example, and its parallels must be mathematically spaced (see Figure 2).
Cone
• If a cone is placed over the globe, with its peak along the polar axis of the earth and with the surface of the cone touching the globe along some particular parallel of latitude, a conic projection can be produced (see Figure 3).
• The meridians are projected onto the cone as equidistant straight lines radiating from the peak.
• The parallels are projected as lines around the circumference of the cone in planes perpendicular to the earth¿s polar axis, spaced for the desired characteristics.
Plane
• A plane tangent to one of the earth's poles is the basis for polar azimuthal projections. An azimuthal projection is one on which the directions or azimuths of all points are shown correctly with respect to the center.
• The group of projections is named for the function, not the plane, since all tangent-plane projections on a sphere are azimuthal.
• The meridians are projected as straight lines radiating from a point, but they are spaced at their true angles instead of the smaller angles of the conic projections. One example is shown in Figure 4.
• The parallels of latitude are complete circles, centered on the pole.
We are interested in modifications to the characteristics described above.
1. The cylinder or cone may be secant to or cut the globe at two parallels instead of being tangent to just one. This provides two standard parallels.
2. The plane may cut through the globe at any parallel instead of touching a pole.
3. The axis of the cylinder or cone can have a direction different from that of the polar axis, while the plane may be tangent to a point other than a pole. This type of modification leads to important oblique, transverse and equatorial projections, in which most meridians and parallels are no longer straight lines or arcs of circles.
This will be the topic of the next column, because the modifications are used in the state plane coordinate system. | 740 | 3,584 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2021-17 | latest | en | 0.91969 |
http://mathhelpforum.com/statistics/5248-combinations.html | 1,480,879,905,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541361.65/warc/CC-MAIN-20161202170901-00192-ip-10-31-129-80.ec2.internal.warc.gz | 179,832,187 | 11,837 | Here is the problem:
A sequence of letters of the form abcba is an example of a palindrome of five letters.
a. If a letter may appear more than twice, how many palindromes of five letters are there? of six letters?
b. Repeat part a under the condition that no letter appears more than twice.
I do not know how to go about doing this problem. Any help would be appreciated. thanks.
2. Hello, ashkash!
I used Brute Force . . . and started making a list.
A sequence of letters of the form ABCBA is an example of a palindrome of five letters.
(a) If a letter may appear more than twice,
how many palindromes of five letters are there? of six letters?
With five letters, consider the first three letters.
3 different letters: . $ABC\;\;\Rightarrow\;\;ABCBA$
2 different letters: . $\begin{array}{ccc}ABA\;\;\Rightarrow\;\;ABABA \\ AAB\;\;\Rightarrow\;\;AABAA \\ ABB\;\;\Rightarrow\;\;ABBBA\end{array} \begin{array}{ccc}* \\ * \\ *\end{array}$
. . Only one letter: . $AAA\;\;\Rightarrow\;\;AAAAA\;\;\;\:*$
With six letters, again consider the first three letters.
3 different letters: . $ABC\;\;\Rightarrow\;\;ABCCBA$
2 different letters: . $\begin{array}{ccc}ABA\;\;\Rightarrow\;\;ABAABA \\ AAB\;\;\Rightarrow\;\;AABBAA \\ ABB\;\;\Rightarrow\;\;ABBBBA\end{array} \begin{array}{ccc}* \\ * \\ * \end{array}$
. . Only one letter: . $AAA\;\;\Rightarrow\;\;AAAAAA\;\;\;\:*$
(b) Repeat part (a) under the condition that no letter appears more than twice.
Disregard answers in (a) marked with an asterisk $(*).$
3. for the question you need to consider all 26 letters of the alphabet and not just a,b,and c.
4. Originally Posted by ashkash
for the question you need to consider all 26 letters of the alphabet and not just a,b,and c.
Would $AAAAA$ be a valid combination?
5. yes, it would.
6. As soroban pointed out all you have to consider is the first three letters, each is independent of the other...
Here's an example problem. Flip a coin. After one flip you have only two possible outcomes (2^1):
$\boxed{\begin{array}{cc}H\\T\end{array}}$
After two flips you get four possible outcomes (2^2):
$\boxed{\begin{array}{cccc}HH\\HT\\TH\\TT\end{array }}$
After three flips you get eight possible outcomes (2^3):
$\boxed{\begin{array}{cccccccc}HHH\\HHT\\HTH\\HTT\\ THH\\THT\\TTH\\TTT\end{array}}$
You can see that after each flip the outcome multiplies by two (because a flip can give 2 different results)
Now your problem can give 26 different results per letter, and only 3 letters matter. Therefore we get the answer of 26^3
you get the same answer with 6 places as well
7. Hello again, ashkash!
If we are considering all 26 letters of the alphabet,
. . we simply append a permutation factor.
With five letters, consider the first three letters.
3 different letters: . $ABC\;\;\Rightarrow\;\;ABCBA$ . . . one way
There are $26$ choices for the " $A$",
. . $25$ choices for the " $B$",
. . and $24$ choices for the " $C$".
Hence, there are: . $26\cdot25\cdot24 \times 1 \:=\:15,600$ ways.
2 different letters: . $\begin{array}{ccc}ABA\;\;\Rightarrow\;\;ABABA \\ AAB\;\;\Rightarrow\;\;AABAA \\ ABB\;\;\Rightarrow\;\;ABBBA\end{array}$ . . . three ways
There are $26$ choices for the " $A$"
. . and $25$ choices for the " $B$".
Hence, there are: . $26\cdot25 \times 3 \:=\:1950$ways.
Only one letter: . $AAA\;\;\Rightarrow\;\;AAAAA$ . . . one way
There are $26$ choices for the " $A$".
Hence, there are: . $26 \times 1 \:=\:26$ ways.
Therefore, there are: . $15,600 + 1950 + 26 \:=\:\boxed{17,576\text{ ways.}}$
8. just to clear confusion: $\underbrace{\overbrace{15600+1950+26}^{\text{Sorob }\!\!\text{an's Way}}=17576=\overbrace{26^3}^{\text{my way}}}_{\text{both ways give the same answer}}$ | 1,125 | 3,725 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2016-50 | longest | en | 0.812181 |
https://fractalforums.org/fractal-mathematics-and-new-theories/28/parabolic-julia-sets/3091/msg29680 | 1,627,879,976,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154304.34/warc/CC-MAIN-20210802043814-20210802073814-00195.warc.gz | 285,119,871 | 20,252 | • August 02, 2021, 06:52:55 AM
### Author Topic: Parabolic Julia sets (Read 5640 times)
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• Fractal Frankfurter
• Posts: 541
##### Re: Parabolic Julia sets
« Reply #90 on: July 07, 2021, 08:56:27 PM »
can I use your program to find triangle that I can use as a trap a forward orbit of interior points ?
#### marcm200
• 3e
• Posts: 1013
##### Re: Parabolic Julia sets
« Reply #91 on: July 08, 2021, 01:52:35 PM »
can I use your program to find triangle that I can use as a trap a forward orbit of interior points ?
In principle, you could use the TPC to detect interior regions that do not touch the boundary of the Julia set, if you provide their location (i.e. two of the three triangle points). The code is actually not ready for release (a lot of superfluous routines no longer used, I plan on uploading it to my GitHub page shall I succeed in the symbolic numbers or bivariate analysis), but if you don't mind those complications, I can send you the source files.
A few conditions on your triangle must be met:
• it must contain an attracting periodic point, preferrably deep within, to succeed
• the dynamics near/inside the triangle must be strongly contracting such that the triangle not only gets smaller with iteration but also rotates in such a manner, that it fits inside the initial shape - and as that triangle has two narrowing tips, that might turn out tricky, i.e. needing a higher iteration count than the periodic length
• as I use IA, overestimation poses a substantial problem. I have not been able to successfully prove a triangle for f[4] so far. So longer cycles probably won't work as of now.
• there's quite heavy symbolic calculations currently performed which may take some time. And the longer the symbolic expression, the greater the influence of overestimation becomes
To prove a region is actually interior to a Julia set, I would recommend a different approach based on cell-mapping/affine arithmetics which I once used for area bounds:
1. Approximate a periodic point (rounding errors are not of concern here).
2. Place a simple polygon with that point as roughly the center and convert it to an affine form (for rectangles, I have a routine here, for other polygons I would need to do it manually.
3. Perform 1 to n iterations with solely affine arithmetics.
4. During iteration, additionally convert the affine form into a complex interval (but only use the AF for iteration). This enlarges the region and check, whether that complex interval lies inside the initial polygon (if the initial shape is a rectangle, that's easy, for axis-parallel triangles - 2 of 3 side - it is manageable, for other forms it gets costly). If inside, the initial shape is contained in the Julia set's interior
5. Then check other small polygons (probably complex squares represented by one pixel) to see if they iterate to the initial polygon (attracted by that point) to get more regions. Fuse geometrically connected regions to a larger shape.
6. Finally you can place your desired trap somewhere in geometrically connected regions that lie inside.
#### marcm200
• 3e
• Posts: 1013
##### Re: Parabolic Julia sets
« Reply #92 on: July 19, 2021, 06:26:24 PM »
After implementing bivariate subdivision to arrive at tighter ranges for the triangle parameterizations, it was now possible to prove triangles being in the filled-in Julia set for derivatives other than real +1 and -1.
For $$z^2+i\cdot z$$ with a parabolic (derivative = i) fix-point at the origin, the following triangle is interior by f[4](ABD):
$A(0,0)\\ B(-0.25,0)\\ D(-0.25,0.125)$
An automatically generated proof is in the attached file.
Bounding the range of bivariate polynomials was simply achieved by partitioning the domain [0..1] x [0..1] into smaller tiles; evaluating the polynomial via standard interval arithmetics and taking the union of all those miniranges which usually is much tighter than evaluating the polynomial in the entire domain.
The left image shows the output of the assisted TSA placing the triangle from above (yellow) as initial interior. Black is additional interior that forward maps into the triangle or other black regions. Earlier levels (not shown) depict less black, and especially the petal-like structures are bigger, so I think this will also converge to the full interior at ever higher refinements.
Interesting is the right image. The initial triangle only has half the width and height - and now it only shows a windmill-like pattern which only slightly changes at higher levels.
Is this only a momentary output? And at (much?) deeper refinements it will also converge to the full interior?
Maybe the small triangle is contained fully in one attracting petal (a guess) - and the pre-images form a proper subset of the filled-in Julia set, so no detection of the entire interior will occur? - while the larger triangle extends over the petal's boundary and catches regions attracted by the petal?
• Fractal Frankfurter
• Posts: 541
##### Re: Parabolic Julia sets
« Reply #93 on: July 19, 2021, 07:43:14 PM »
My naive analysis :
I draw critical orbit, which in parabolic case is an n=th arm ( dostorted ) star. Here n= 4
Each arm of the star is a skeleton of attracting petal ( it is also used in the parabolic chessboard )
Then I draw external rays that land on the parabolic fixed point , here 1/15, 2/15, 4/15, 8/15
Near fixed point the exterior parts are very thin so (aproximately) any triangle which has fixad point on its vortex and is between 2 external rays maybe parabolic petal
The bigger triangle the better
Here my image
In my method the grey petals are repelling petals ( or points which do not escape or not attracts), like on the gif image
HTH
#### marcm200
• 3e
• Posts: 1013
##### Re: Parabolic Julia sets
« Reply #94 on: July 20, 2021, 09:32:28 AM »
Near fixed point the exterior parts are very thin so (aproximately) any triangle which has fixad point on its vortex and is between 2 external rays maybe parabolic petal
Do you have a constructive proof that one can fit a (small) triangle between those rays and located at the parabolic point? It would be interesting to see a (probably) different approach than the parameterization/IA I use.
• Fractal Frankfurter
• Posts: 541
##### Re: Parabolic Julia sets
« Reply #95 on: July 20, 2021, 04:41:58 PM »
Do you have a constructive proof that one can fit a (small) triangle between those rays and located at the parabolic point?
unfortunately I am not a mathematician = I'm not good in prooving. It is more experimental and geometric (IMHO)
#### marcm200
• 3e
• Posts: 1013
##### Re: Parabolic Julia sets
« Reply #96 on: July 23, 2021, 05:16:53 PM »
"z^2-1.25 - indirect"
For the quartic mapping
$g(z) := z^4+(2\cdot\sqrt{2}-2)\cdot z^3+(2-3\cdot\sqrt{2})\cdot z^2-z$
with a parabolic fix-point at the origin, the following triangle could be proven to reside in the filled-in Julia set (see the attached text file).
$A(0,0) \\ B(-0.0625,0) \\ D(-0.0625,0.03125) \\$
g(z) was derived from the function-of-interest f(z) := z^2-1.25 by
• using the 2-iterate f[2](z) to split the parabolic 2-cycle from f into two parabolic fix-points
• conjugating to a translation that moves one parabolic point to the origin
The proven triangle was then converted back to one that resides in the filled-in Julia set of f, by reversing the translation and constructing a smaller right triangle that lies inside the proven one with double-representable coordinates, which results in:
$A_f( 6949350\cdot 2^{-25} , 0 )\\ B_f( 4852199\cdot2^{-25} , 0 )\\ D_f( 4852199\cdot2^{-25} , 1048575*2^{-25} )$
This was then marked during the TSA analysis using x-axis symmetry (image below, yellow). The computation also converges as in higher refinements the gray shrinks quite substantiually.
Zooming near the yellow tip shows a nice feature (upper right): The set-in triangle has very smooth boundaries, the "triangle" on the other side of the parabolic periodic point (here in the 2-cycle) has a stair-case boundary, because it forward-maps (in 2 steps) into the yellow one and its ragged boundary is a result of the rectangular shape of the bounding box.
Technical details
• initially all numbers different from 0 and 1 were hidden in temporary variables to get cancellation during the symbolic construction of the final rational function
• actual numbers were inserted in a symbolic number format that knows rules for square-root arithmetics over positive numbers (especially sqrt(a^2*b)=a*sqrt(b) for positive integers)
• currently, a subset o algebraic irrationals are accepted: linear combinations of sqrt expressions
• on my list were transforming f in different ways: rational parabolic point and irrational coefficients or vice versa, constructed either by translation or scaling by conjugation (but not all were tested)
• the successful proof takes about 15 min using a fixed-point number type on base 10^9 with 392 . 180 decimals before and after the radix point set at compile time. Evaluation of expressions is done in standard interval arithmetics using Horner's scheme
• Fractal Frankfurter
• Posts: 541
##### Re: Parabolic Julia sets
« Reply #97 on: July 23, 2021, 08:30:32 PM »
"z^2-1.25 - indirect"
cool. The parameter c is on the real axis = it is a real number ( not complex). It is a "easy" case. I have used circle with parabolic point on it's boundary as an attracting petal
Radius and position of the circle was found by Trial and error method forward iterating of critical point : radius = half of the distance between point of the critical orbit and parabolic point
For other cases ( c is a complex number) one can use triangles inside sectors around parabolic points ( defined by the external rays landing on the parabolic point / critical orbit )
https://arxiv.org/abs/math/0505036v2
« Last Edit: July 24, 2021, 07:10:51 AM by Adam Majewski, Reason: mv »
#### marcm200
• 3e
• Posts: 1013
##### Re: Parabolic Julia sets
« Reply #98 on: July 24, 2021, 09:54:41 AM »
cool. The parameter c is on the real axis = it is a real number ( not complex). It is a "easy" case.
From an implementational point of view, it was quite a demanding case: period-2 cycle with combined 4 petals lead to heavy symbolic expressions, irrational coordinates of a periodic point and the need to find a triangle inside another one.
But you're right insofar that I haven't tried a compound complex number as a coefficient up to now. I'm curious to see how that will work out next (or not).
• Fractal Frankfurter
• Posts: 541
##### Re: Parabolic Julia sets
« Reply #99 on: July 24, 2021, 01:02:06 PM »
i see it in a geometric way ( orbits , curves, , sets), but you of course see deeper because you are mathematicien. I hope that you program will let me find attracting petals for smth like "A quad. Julia set with 987 parab. petals i"
#### marcm200
• 3e
• Posts: 1013
##### Re: Parabolic Julia sets
« Reply #100 on: July 24, 2021, 02:29:24 PM »
I hope that you program will let me find attracting petals for smth like "A quad. Julia set with 987 parab. petals i"
Could you post the specific parameters?I seem to not be able to get more than an image without description.
But 987 petals - that would be a record! And 987 iterations at least till an initial triangle gets back to its starting petal. So I suppose an explicit symbolic equation is out of the equestion for that and one would attempt this via iterated, reliable arithmetics, maybe a rotated square that consists of two triangles with one tip at the parabolic point and then use affine arithmetics, but one would lose the cancellation capacity of symbolic calculations ...
• Fractal Frankfurter
• Posts: 541
##### Re: Parabolic Julia sets
« Reply #101 on: July 24, 2021, 03:37:04 PM »
Could you post the specific parameters?I seem to not be able to get more than an image without description.
But 987 petals - that would be a record!
There are many examples but the simplest example is 1/987 ( or 1/n in general)
Mandel gives : c = 0.250010131066671 +0.000000064494660 i
One can do it manually in c :
Code: [Select]
gcc c.c -lm -Walla@zalman:~/Dokumenty/c\$ ./a.outRoot point between period 1 component and period 987 component = c = 0.2500101310666710+0.0000000644946597*IInternal angle (c) = 1/987Internal radius (c) = 1.0000000000000000
Here is the full c program:
Code: [Select]
/*gcc c.c -lm -Wall./a.outRoot point between period 1 component and period 987 component = c = 0.2500101310666710+0.0000000644946597*IInternal angle (c) = 1/987Internal radius (c) = 1.0000000000000000*/#include <stdio.h>#include <math.h> // M_PI; needs -lm also#include <complex.h>/* c functions using complex type numbers computes c from component of Mandelbrot set */complex double Give_c( int Period, int p, int q , double InternalRadius ){ complex double c; complex double w; // point of reference plane where image of the component is a unit disk // alfa = ax +ay*i = (1-sqrt(d))/2 ; // result double t; // InternalAngleInTurns t = (double) p/q; t = t * M_PI * 2.0; // from turns to radians w = InternalRadius*cexp(I*t); // map to the unit disk switch ( Period ) // of component { case 1: // main cardioid = only one period 1 component c = w/2 - w*w/4; // https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set/boundary#Solving_system_of_equation_for_period_1 break; case 2: // only one period 2 component c = (w-4)/4 ; // https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set/boundary#Solving_system_of_equation_for_period_2 break; // period > 2 default: printf("higher periods : to do, use newton method \n"); printf("for each q = Period of the Child component there are 2^(q-1) roots \n"); c = 10000.0; // bad value break; } return c;}int main (){ int period = 1; double InternalRadius = 1.0; // internal angle in turns as a ratio = p/q int p = 1; int q = 987; complex double c = Give_c(period, p, q, InternalRadius); printf("Root point between period %d component and period %d component = c = %.16f%+.16f*I\n",period, q, creal(c), cimag(c)); printf("Internal angle (c) = %d/%d\n",p, q); printf("Internal radius (c) = %.16f\n",InternalRadius); return 0;}
« Last Edit: July 24, 2021, 04:58:40 PM by Adam Majewski, Reason: descr »
• Fractal Frankfurter
• Posts: 541
##### Re: Parabolic Julia sets
« Reply #102 on: July 24, 2021, 04:05:14 PM »
List of all roots between period 1 and period 987 components
Code: [Select]
Root point between period 1 component and period 987 component = c = 0.2500101310666710+0.0000000644946597*I Internal angle (c) = 1/987Root point between period 1 component and period 987 component = c = 0.2500405213927559+0.0000005159415960*I Internal angle (c) = 2/987Root point between period 1 component and period 987 component = c = 0.2501620395922977+0.0000041270309808*I Internal angle (c) = 4/987... The message exceeds the maximum allowed length (80000 characters).
and the program
Code: [Select]
/*gcc c.c -lm -Wall./a.outRoot point between period 1 component and period 987 component = c = 0.2500101310666710+0.0000000644946597Internal angle (c) = 1/987Internal radius (c) = 1.0000000000000000*/#include <stdio.h>#include <math.h> // M_PI; needs -lm also#include <complex.h>// numer of hyberolic components ( and it's centers ) of Mandelbrot set int GiveNumberOfCenters(int period){ //int s = 0; int num = 1; int f; int fMax = period-1; //sqrt(period); // https://stackoverflow.com/questions/11699324/algorithm-to-find-all-the-exact-divisors-of-a-given-integer if (period<1 ) {printf("input error: period should be positive integer \n"); return -1;} if (period==1) { return 1;} num = pow(2, period-1); // minus sum of number of center of all it's divisors (factors) for (f=1; f<= fMax; ++f){ if (period % f==0) {num = num - GiveNumberOfCenters(f); } } return num ;}int ListNumberOfCenters(int period){ int p=1; int pMax = period; int num=0; if (period ==1 || period==2) {printf (" for period %d there is only one component\n", period); return 0;} for (p=1; p<= pMax; ++p){ num = GiveNumberOfCenters(p); printf (" for period %d there are %d components\n", p, num); } return 0;}/* c functions using complex type numbers computes c from component of Mandelbrot set input: Period : positive integer n<d InternalRadius in [0.0, 1.0] */complex double Give_c( int Period, int n, int d , double InternalRadius ){ complex double c; complex double w; // point of reference plane where image of the component is a unit disk // alfa = ax +ay*i = (1-sqrt(d))/2 ; // result double t; // InternalAngleInTurns if (Period<1 ) {printf("input error: period should be positive integer \n"); return 10000.0;} t = (double) n/d; t = t * M_PI * 2.0; // from turns to radians w = InternalRadius*cexp(I*t); // map to the unit disk switch ( Period ) // of component { case 1: // main cardioid = only one period 1 component c = w/2 - w*w/4; // https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set/boundary#Solving_system_of_equation_for_period_1 break; case 2: // only one period 2 component c = (w-4)/4 ; // https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set/boundary#Solving_system_of_equation_for_period_2 break; default: // period > 2 printf("period = %d ; for higher periods : not works now, to do, use newton method \n", Period); printf("for each Period >2 there are more then 1 components.\nHere are 2^(p-1) - s = %d components for period %d\n", GiveNumberOfCenters(Period), Period); printf("to choose component use: it's center or external ray or angled internal address \n"); c = 10000.0; // bad value break; } return c;}void PrintAndDescribe_c( int period, int n, int d , double InternalRadius ){ complex double c = Give_c(period, n, d, InternalRadius); printf("Root point between period %d component and period %d component = c = %.16f%+.16f*I\t",period, d, creal(c), cimag(c)); //printf("Internal radius (c) = %.16f\n",InternalRadius); printf("Internal angle (c) = %d/%d\n",n, d); }/*https://stackoverflow.com/questions/19738919/gcd-function-for-cThe GCD function uses Euclid's Algorithm. It computes A mod B, then swaps A and B with an XOR swap.*/int gcd(int a, int b){ int temp; while (b != 0) { temp = a % b; a = b; b = temp; } return a;}int ListAllBifurcationPoints(int period, int d ){ double InternalRadius = 1.0; // internal angle in turns as a ratio = n/d int n = 1; //int d = 987; if (period<1 ) {printf("input error: period should be positive integer \n"); return 1;} if (period >2) {printf("input error: not works now. TODO \n"); return 2;} // n/d = local angle in turns for (n = 1; n < d; ++n ){ if (gcd(n,d)==1 )// irreducible fraction { PrintAndDescribe_c(period, n,d,InternalRadius); } } return 0;}int main (){ int period = 1; double InternalRadius = 1.0; // internal angle in turns as a ratio = p/q int n = 1; int d = 987; complex double c; //c = Give_c(period, n,d , InternalRadius); //PrintAndDescribe_c(period, n,d , InternalRadius); ListAllBifurcationPoints(period,d); //ListNumberOfCenters(period); return 0;}
« Last Edit: July 25, 2021, 10:56:20 AM by Adam Majewski »
#### marcm200
• 3e
• Posts: 1013
##### Re: Parabolic Julia sets
« Reply #103 on: July 29, 2021, 12:36:26 PM »
"Compound complex"
$f(z) := z^2 + (-\frac{1}{2}+i\cdot \frac{1}{2}\cdot \sqrt{3})\cdot z$
with a parabolic fix point at z=0 with 3 petals, the triangle
$A(0,0) \\ B(-0.125,0) \\ D(-0.125,0.0625)$
resides inside the filled-in Julia set.
I focus on the sets $$z^2+z\cdot e^{2\pi\cdot i\frac{p}{q}}$$, as those allow me to set the fix point at the origin, and in particular at rationally complex coordinates that are exactly representable. As sine and cosine of angles being a rational multiple of 2*pi are algebraic integers, I looked for values of the denominator q where the degree was suitable for my implementation, i.e. 1, 2 or - if larger - a degree=2 in disguise. The values 3,5,6 were then selected. The above set is p/q=1/3 (literature below).
As the seed was irrationally complex, for the TSA I needed to use small complex intervals to construct an image. Those, however, will comprise values from outside the unicritical parameter-space as the parabolic seed is on the boundary. As I use outward rounding and basic operations, inclusion property of interval arithmetics assures that area that maps into the triangle (or other detected inteior) under the interval seed is true interior of the filled-in parabolic Julia set of interest.
Here I used $$z^2+([-16777216..-16777216]+i\cdot [29058990..29058991])*2^{-25}\cdot z$$.
The image's lower left pixel's coordinates are $$3056\cdot w-4 + i\cdot (2544\cdot w-4)$$ and the width of a pixel w=8/8192.
The proof-of-concept stage is now completed. In principle, the TPC could prove triangles for many Julia sets, provided enough time and memory. For z^2+c there is the difficulty that one usually is not able to describe a periodic point in exactness for longer cycles or larger petal number, so I had to resort to the z^2+A*z case which in principle could be conjugated to one another. Would one extend the symbolic number capabilities to more than square roots, it should be possible to get sets with a larger number of petals. However, I suspect the time needed to grow tremendously large (I currently stop a set if after 1 day there's no answer of the TPC in either success or failure).
Literature
Lehmer DH. A note on trigonometric algebraic numbers.
Besin S, DeAngelo V. The minimal polynomial of sin(2pi/p) and cos(2pi/p).
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by Mr Rebooted | 6,157 | 22,538 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2021-31 | latest | en | 0.918855 |
https://www.calculus-online.com/exercise/6030 | 1,679,451,349,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943749.68/warc/CC-MAIN-20230322020215-20230322050215-00513.warc.gz | 782,154,257 | 57,525 | # Calculating Limit of Function – A quotient of exponential functions – Exercise 6030
### Exercise
Evaluate the following limit:
$$\lim _ { x \rightarrow \infty} \frac{2^{x+1}+3^{x+1}}{2^x+3^x}$$
$$\lim _ { x \rightarrow \infty} \frac{2^{x+1}+3^{x+1}}{2^x+3^x}=3$$ | 105 | 268 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 2, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2023-14 | longest | en | 0.339163 |
https://brainmass.com/physics/classical-mechanics/units-conversion-volume-density-and-other-physical-quantities-24622 | 1,716,018,457,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057327.58/warc/CC-MAIN-20240518054725-20240518084725-00114.warc.gz | 126,356,808 | 7,692 | Purchase Solution
# Units conversion, volume density and other physical quantities.
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A corner construction lot has the shape of a right triangle. If the two sides perpendicular to each other are 37 m long and 42.3 m long, respectively, what is the length of the hypotenuse?
75. The lightest solid material is silica aerogel, which has a typical density of only about
3
0.10 g/cm . The molecular structure of silica aerogel is typically 95% empty space.
3
What is the mass of one 1m of silica aerogel?
79. A light-year is a unit of distance corresponding to the distance light travels in a vacuum in 1 year.
8
If the speed of light is 3.00 x 10 m/s, what is the length of a light-year in meters?
85. The Channel Tunnel, or "Channel" which runs under the English Channel between Great Britain and France, is 31 mi long. (There are actually three separate tunnels.) A shuttle train that carries passengers through the tunnel travels with an average speed of 75 mi/h. On average, how long, in minutes, does it take the shuttle to make a one-way trip through the Chunnel?
87. A student wants to determine the distance of a small island from the lakeshore. He first draws a 50-m line parallel to the shore. Then, he goes to the ends of the line and measures the angles of the lines of sight from the island relative to the line he has drawn. The angles are 30 degrees and 40 degrees. How far is the island from the shore?
89. Suppose you are paying \$1.20 for 1 gal of gas. Then the United States switches to SI units, and you find that gas costs \$0.32/L. Which is the greater cost for gas?
93. A rectangular block has the dimensions 2.8 cm, 9.5 cm, and 8.7 cm. Estimate the volume of the block in cubic centimeters.
95. A cylindrical drinking glass has an inside diameter of 8.0 cm and a depth of 12 cm. If a person drinks a completely full glass of water, how much water (in liters) will be consumed?
99. A car is driven 13 miles east and then a certain distance due north and ends up at a position of 25 degrees north of east.
a) The distance traveled by the car due north is 1) less than, 2) equal to, or 3) greater than 13 miles. Why?
b) What distance does the car go due north?
101. A hollow spherical ball of radius 12 cm is filled with water. What is the mass of water inside the sphere, in kilograms?
##### Solution Summary
Full answers to several miscellaneous problems in the areas of units conversion, volume density and other physical quantities.
##### Basic Physics
This quiz will test your knowledge about basic Physics.
##### Introduction to Nanotechnology/Nanomaterials
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Test your knowledge of moon phases and movement.
##### Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
##### Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics. | 721 | 3,114 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2024-22 | latest | en | 0.932616 |
http://www.swcombine.com/forum/thread.php?thread=56566&page=0 | 1,544,521,195,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823614.22/warc/CC-MAIN-20181211083052-20181211104552-00275.warc.gz | 493,066,718 | 5,555 | 2133 active members
164 are online
Year
20
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14
Time
02:41:35
Guest
Message CentreRPG CentreQuestion Centre
Archives » Need some help with space station weight and ships
Year 13 Day 265 8:16
i have just got myself a new Luxury Space Colony was going to use it as a base and storage. what i want to know is how many ships i can store in there.
Cargo Stats for the station:
Weight: 83,256 T
Volume: 16,000 m³
Weight Cap: 69,380 T
Volume Cap: 13,454 m³
what i want to store is the X-ceptor
Weight: 30 T
Volume: 500 m³
Weight Cap: 0.0700 T
Volume Cap: 0.5000 m³
i have 22 of these so would i be able to store them all in there?
Year 13 Day 265 8:33
I'm going to assume your question is about something other than basic math (or that you don't know what to calculate).
To determine what a container can hold, you take the Weight Cap and Volume Cap of the container. Now, you take the Weight and Volume of the entities you want to put into the container.
Container (station)
Weight Cap: 69,380 T
Volume Cap: 13,454 m³
Entity (X-ceptor)
Weight: 30 T
Volume: 500 m³
You have 22 entities.
Total Weight: 30 T * 22 = 660 T
Total Volume: 500 m³ * 22 = 11,000 m³
660 T < 69,380 T - OK
11,000 m³ < 13,454 m³ - OK
So, yes, you are able to store them all in there.
Year 13 Day 265 8:50
cool thank you. sorry it was kind of a noob question, but i did not know what one you go by was it just the weight or the volume. thank you for the help :D
Year 13 Day 265 18:02
We use both.
____________ | 464 | 1,496 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2018-51 | latest | en | 0.925041 |
https://math.stackexchange.com/questions/2525578/whats-wrong-with-this-alternative-notion-of-lebesgue-inner-measure-sup-of-sums | 1,582,846,758,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146907.86/warc/CC-MAIN-20200227221724-20200228011724-00392.warc.gz | 407,824,033 | 30,967 | # What's wrong with this alternative notion of Lebesgue inner measure: sup of sums of lengths of collections of closed intervals contained in the set?
Given a subset $E\subseteq\mathbb{R}$, with the length of a closed Interval $I = [a,b]$ given by $l(I)=b - a$, the Lebesgue outer measure $\lambda^*(E)$ is defined as
$\lambda^*(E) = \operatorname{inf} \{ \sum_{k=1}^\infty l(I_k) : {(I_k)_{k \in \mathbb N}} \text{ is a sequence of closed intervals with } E \subset \bigcup_{k=1}^\infty I_k \}$.
One might define a similar notion (I'll call it $\beta$) by $\beta(E) = \operatorname{sup} \{\sum_{k=1}^\infty l(I_k) : {(I_k)_{k \in \mathbb N}} \text{ is a sequence of closed intervals with} \bigcup_{k=1}^\infty I_k \subset E \}$. I would have thought this would be called "Lebesgue inner measure" but that seems to mean something different.
1) This notion $\beta$ is conspicuously missing from textbooks. Why?
My guess is that maybe $\beta(I)> l(I)$ for some closed interval $I$? I say that because the proof that that can't happen with Lebesgue outer measure (i.e. that $l^*(I)=l(I)$) uses the Heine-Borel Theorem which requires that the collection of closed intervals be a cover of $I$.
2) Are there nice sufficient conditions for $\beta(E)$ to be equal to the Lebesgue outer measure $l^*(E)$? For example, are they equal if E is Lebesgue measurable?
Because then $\beta({\bf{Q}}^{c}\cap[0,1])=-\infty$ but the inner measure of ${\bf{Q}}^{c}\cap[0,1]$ coincides with the outer measure, which the value is $1$.
We should take $\sup\emptyset=-\infty$. | 475 | 1,558 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2020-10 | latest | en | 0.907404 |
http://isabelle.in.tum.de/repos/isabelle/diff/0bec0d1d9998/src/HOL/Library/positivstellensatz.ML | 1,556,203,549,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578721468.57/warc/CC-MAIN-20190425134058-20190425160058-00095.warc.gz | 91,722,210 | 2,217 | src/HOL/Library/positivstellensatz.ML
changeset 63211 0bec0d1d9998 parent 63205 97b721666890 child 63648 f9f3006a5579
``` 1.1 --- a/src/HOL/Library/positivstellensatz.ML Wed Jun 01 17:46:12 2016 +0200
1.2 +++ b/src/HOL/Library/positivstellensatz.ML Wed Jun 01 19:23:18 2016 +0200
1.3 @@ -615,10 +615,10 @@
1.4 in
1.5 if c1 * c2 >= @0 then acc else
1.6 let
1.7 - val e1' = linear_cmul (Rat.abs c2) e1
1.8 - val e2' = linear_cmul (Rat.abs c1) e2
1.9 - val p1' = Product(Rational_lt(Rat.abs c2),p1)
1.10 - val p2' = Product(Rational_lt(Rat.abs c1),p2)
1.11 + val e1' = linear_cmul (abs c2) e1
1.12 + val e2' = linear_cmul (abs c1) e2
1.13 + val p1' = Product(Rational_lt (abs c2), p1)
1.14 + val p2' = Product(Rational_lt (abs c1), p2)
1.16 end
1.17 end
1.18 @@ -653,11 +653,11 @@
1.19 let val d = FuncUtil.Ctermfunc.tryapplyd t x @0 in
1.20 if d = @0 then inp else
1.21 let
1.22 - val k = (Rat.neg d) * Rat.abs c / c
1.23 + val k = ~ d * abs c / c
1.24 val e' = linear_cmul k e
1.25 - val t' = linear_cmul (Rat.abs c) t
1.26 + val t' = linear_cmul (abs c) t
1.27 val p' = Eqmul(FuncUtil.Monomialfunc.onefunc (FuncUtil.Ctermfunc.empty, k),p)
1.28 - val q' = Product(Rational_lt(Rat.abs c),q)
1.29 + val q' = Product(Rational_lt (abs c), q) | 568 | 1,623 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2019-18 | latest | en | 0.212346 |
http://www.absoluteastronomy.com/topics/David_Mermin | 1,369,295,552,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368703001356/warc/CC-MAIN-20130516111641-00027-ip-10-60-113-184.ec2.internal.warc.gz | 318,828,476 | 4,838 | David Mermin
# David Mermin
Discussion
Encyclopedia
Nathaniel David Mermin is a solid-state physicist
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
at Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
best known for the eponymous Mermin-Wagner theorem
Mermin-Wagner theorem
In quantum field theory and statistical mechanics, the Mermin–Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d ≤ 2...
and his application of the term "Boojum
Boojum (superfluidity)
In the physics of superfluidity, a boojum is a geometric pattern on the surface of one of the phases of superfluid helium-3, whose motion can result in the decay of a supercurrent. A boojum can result from a monopole singularity in the bulk of the liquid being drawn to, and then "pinned" on a...
" to superfluidity, and for the quote "Shut up and calculate!"
Together with Neil W. Ashcroft, Mermin has written an esteemed textbook, Solid State Physics, and numerous popularizations of physics and mathematics.
## Mermin’s foot
Mermin has contributed to special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
with two books and several articles. In Its About Time (2005) he suggests that the English foot be slightly modified:
Henceforth, by 1 foot we shall mean the distance light travels in a nanosecond. A foot, if you will, is a light nanosecond (and a nanosecond, even more nicely, can be viewed as a light foot). …If it offends you to redefine the foot … then you may define 0.299792458 meters to be 1 phoot, and think "phoot" (conveniently evocative of the Greek φωτος, "light") whenever you read "foot".
This adaptation of a physical unit is one of several ploys that Mermin uses to draw students into space-time geometry. | 566 | 2,495 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2013-20 | latest | en | 0.897989 |
https://darkskiesfilm.com/how-much-is-125-as-a-fraction/ | 1,679,854,460,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00702.warc.gz | 233,583,782 | 10,600 | # How much is 125 as a fraction?
## How much is 125 as a fraction?
So, 125% as a fraction is 5 / 4.
### What is 1/3 in a calculator?
1/3 = 13 ≅ 0.3333333 Spelled result in words is one third.
#### What is 3/4 to the power of 3 as a fraction?
3/4^3 = 2764 = 0.421875.
How do I turn 0.125 into a fraction?
0.125 = 125/1000. We can reduce this to lowest terms by dividing the numerator and denominator by 125 to get the equivalent fraction 1/8.
What is 0.125 simplified?
1/8
Answer: 0.125 as a fraction is equal to 1/8. Now we can reduce 125/1000 to the lowest terms by dividing and multiplying the numerator and denominator by 125 to get the equivalent fraction, that is, 1/8.
## What is 1/3 of a fraction?
Answer: The fractions equivalent to 1/3 are 2/6, 3/9, 4/12, etc.
### How do you put fractions in a calculator?
The numerator is the top number in the fraction. Type the numerator into your calculator, then push the divide button. Next, type the bottom number into the calculator, which is the denominator. Hit the equal sign to get your decimal.
#### How do I turn into a fraction?
Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.
What is 0.125 as a fraction and percent?
Answer: 0.125 as a fraction is equal to 1/8. Let us first convert the decimal into a fractional form. Now we can reduce 125/1000 to the lowest terms by dividing and multiplying the numerator and denominator by 125 to get the equivalent fraction, that is, 1/8.
How do you find 1/3 of a whole?
Answer: The number is 1/3 which can also be written as 0.33 Hence, the number 1/3 is not a whole number, since it is in fractional form and whole numbers do not include fractions or decimals.
## What is 1 3 equal to as a fraction?
### How do you raise to a 1/3 power?
Fractional Exponents For example, take “125 raised to the 1/3 power,” or 125^1/3. The denominator of the fraction is 3, so you’re looking for the 3rd root (or cube root) of 125. Because 5 x 5 x 5 = 125, the 3rd root of 125 is 5. Thus, 125^1/3 = 5. | 643 | 2,199 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2023-14 | longest | en | 0.92004 |
https://thesis.library.caltech.edu/5726/ | 1,718,676,952,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861746.4/warc/CC-MAIN-20240618011430-20240618041430-00697.warc.gz | 506,825,734 | 6,483 | CaltechTHESIS
A Caltech Library Service
# Permutation decomposition of (0,1)-matrices and decomposition transversals
## Citation
Henderson, John Robert (1971) Permutation decomposition of (0,1)-matrices and decomposition transversals. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/J1Z1-SK19. https://resolver.caltech.edu/CaltechTHESIS:04212010-092257716
## Abstract
The central problem of this thesis is the study of sums of disjoint partial permutation matrices ("permutation decompositions"). This problem has as its origin the result of G. Birkoff that an ordern (0,1)-matrix having k l's in every row and column can be written as a sum of k permutation matrices (partial permutation matrices of "size" and order n). The thesis divides into two main parts. In the first part (Chapters II, III) we first deal with the existence of permutation decompositions of a given (0, 1)-matrix where each of the summands has a specified size and secondly, with some applications consisting of reformulating certain identification problems of Combinatorics in terms of permutation decompositions. The general existence problem remains unsolved. For more than two distinct sizes in the proposed permutation decomposition of a (0, 1)-matrix A, a more subtle invarient than numbers of l's in submatrices of A is required. The second part of this thesis is concerned with "transversals" of permutation decompositions. The specific goal is to make some contribution toward resolving the conjecture of H. J. Ryser that every odd order latin square has a "transversal". Chapter IV is preliminary, and deals with "generalized traces" of 3-dimensional (0, 1)-matrices. A more fruitful approach is considered in Chapter V. There the conjecture of Ryser is generalized and the apparently central concept of a "square" n-tuple of positive integers is introduced. Such square "lists" are characterized in terms of tournament score vectors. A weaker structure than a latin square, that of a "pair configuration", is also introduced and for such structures the concept of a square list is more intimately connected with the existence of a "transversal". The generalized conjecture is proven only in special cases.
Item Type: Thesis (Dissertation (Ph.D.)) Mathematics California Institute of Technology Physics, Mathematics and Astronomy Mathematics Public (worldwide access) Ryser, H. J. Unknown, Unknown 24 August 1970 CaltechTHESIS:04212010-092257716 https://resolver.caltech.edu/CaltechTHESIS:04212010-092257716 10.7907/J1Z1-SK19 No commercial reproduction, distribution, display or performance rights in this work are provided. 5726 CaltechTHESIS Tony Diaz 21 Apr 2010 21:33 20 Dec 2019 19:32
## Thesis Files
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Repository Staff Only: item control page | 653 | 2,813 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2024-26 | latest | en | 0.890799 |
https://www.studypool.com/discuss/376093/geometry-question-please-help?free | 1,495,667,602,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607871.54/warc/CC-MAIN-20170524230905-20170525010905-00120.warc.gz | 932,403,778 | 14,093 | Mathematics Tutor: None Selected Time limit: 1 Day
is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the image . If the slope and length of are m and l respectively, what is the slope of ?
a) 1.3 m
b) 1.3 l
c) 1.3 (m + l)
d) m
Feb 6th, 2015
c) 1.3 (m + l)
Feb 6th, 2015
I did not type it right. There is XY in the beginning
XY is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the image XY . If the slope and length of XY are m and l respectively, what is the slope of XY?
Feb 6th, 2015
...
Feb 6th, 2015
...
Feb 6th, 2015
May 24th, 2017
check_circle | 235 | 652 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2017-22 | longest | en | 0.862173 |
https://www.physicsforums.com/threads/how-is-entropy-defined-by-boundary-area-in-holographic-principle.282286/ | 1,477,403,972,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720153.61/warc/CC-MAIN-20161020183840-00145-ip-10-171-6-4.ec2.internal.warc.gz | 970,887,535 | 14,023 | # How is entropy defined by boundary area in Holographic Principle?
1. Dec 31, 2008
### skeleton
Reference: http://en.wikipedia.org/wiki/Holographic_Principle
The principle states that the description of a volume of space should be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. For a black hole, the principle states that the description of all the objects which will ever fall in is entirely contained in surface fluctuations of the event horizon.
Leonard Susskind, in his book "The Black Hole War", reflects on quantum gravity whereby the total amount of information (bits) that can be stored within a spactial volume is no more than that which can reside on its spatial boundary. This would be calculated in terms of plank length.
Surface area of box, A = 2*(L.l*L.w + L.w*L.h + L.l*L.h))
Internal volume of box, V = L.l*L.w*L.h
In Euclidean space, V>A except for L.l, L.w, L.h < 6 and other trivial proportions.
Can anyone illustrate (or direct me to) the mathematics that validates the Holographic Principle?
2. Jan 2, 2009
### skeleton
Still curious ... Bump. | 270 | 1,144 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2016-44 | longest | en | 0.887522 |
https://oeis.org/A062017/internal | 1,709,425,574,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476137.72/warc/CC-MAIN-20240302215752-20240303005752-00814.warc.gz | 412,629,101 | 2,900 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062017 Numbers with all even digits which can be factored into two numbers (> 1) one with all odd digits and the other with all even digits. 1
%I #14 Dec 20 2021 18:47:41
%S 0,6,20,22,24,26,28,40,42,44,60,62,66,68,84,88,200,204,220,222,226,
%T 228,240,242,246,248,260,262,264,266,280,284,286,400,408,420,424,426,
%U 440,442,444,448,460,462,468,484,600,602,604,606,620,622,624,626,628,660
%N Numbers with all even digits which can be factored into two numbers (> 1) one with all odd digits and the other with all even digits.
%H David A. Corneth, <a href="/A062017/b062017.txt">Table of n, a(n) for n = 1..10000</a>
%e 0 = 0 * 1, 44 = 4 * 11 and 60 = 15 * 4 are terms.
%Y Cf. A062015.
%K nonn,base,easy
%O 1,2
%A _Amarnath Murthy_, Jun 01 2001
%E Corrected and extended by _Matthew Conroy_ and _Frank Ellermann_, Jun 11 2001
%E 0 prepended and offset changed to 1 by _David A. Corneth_, Dec 20 2021
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Last modified March 2 19:19 EST 2024. Contains 370498 sequences. (Running on oeis4.) | 483 | 1,389 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2024-10 | latest | en | 0.765068 |
http://www.cs.au.dk/~gerth/pub/esa10.html | 1,529,377,204,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267861752.19/warc/CC-MAIN-20180619021643-20180619041643-00026.warc.gz | 382,103,202 | 2,188 | # On Space Efficient Two Dimensional Range Minimum Data Structures
## Gerth Stølting Brodal, Pooya Davoodi, and S. Srinivasa Rao
In Proc. 18th Annual European Symposium on Algorithms, volume 6347 of Lecture Notes in Computer Science, pages 171-182. Springer Verlag, Berlin, 2010.
## Abstract
The two dimensional range minimum query problem is to preprocess a static two dimensional m by n array A of size N=m· n, such that subsequent queries, asking for the position of the minimum element in a rectangular range within A, can be answered efficiently. We study the trade-off between the space and query time of the problem. We show that every algorithm enabled to access A during the query and using O(N/c) bits additional space requires Ω(c) query time, for any c where 1 ≤ cN. This lower bound holds for any dimension. In particular, for the one dimensional version of the problem, the lower bound is tight up to a constant factor. In two dimensions, we complement the lower bound with an indexing data structure of size O(N/c) bits additional space which can be preprocessed in O(N) time and achieves O(clog2 c) query time. For c=O(1), this is the first O(1) query time algorithm using optimal O(N) bits additional space. For the case where queries can not probe A, we give a data structure of size O(N·min{m,log n}) bits with O(1) query time, assuming mn. This leaves a gap to the lower bound of Ω(Nlog m) bits for this version of the problem.
Online version
esa10.pdf (215 Kb)
DOI
10.1007/978-3-642-15781-3_15
Slides
esa10.pdf (1110 Kb), esa10.pptx (654 Kb)
BIBTEX entry
```@incollection{esa10,
author = "Gerth St{\o}lting Brodal and Pooya Davoodi and S. Srinivasa Rao",
booktitle = "Proc. 18th Annual European Symposium on Algorithms",
doi = "10.1007/978-3-642-15781-3_15",
isbn = "978-3-642-15780-6",
pages = "171-182",
publisher = "Springer {V}erlag, Berlin",
series = "Lecture Notes in Computer Science",
title = "On Space Efficient Two Dimensional Range Minimum Data Structures",
volume = "6347",
year = "2010"
}
``` | 545 | 2,038 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-26 | latest | en | 0.797252 |
https://numbersworksheet.com/double-digit-multiplication-worksheets-grade-5/ | 1,638,472,674,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362287.26/warc/CC-MAIN-20211202175510-20211202205510-00357.warc.gz | 445,133,534 | 8,918 | # Double Digit Multiplication Worksheets Grade 5
Double Digit Multiplication Worksheets Grade 5 – Are you aware how you can increase using numbers worksheets to help enhance your child’s reading through and writing skills? I will reveal how by supplying you with an understanding of the key benefits of numbers worksheets. If you comprehend some great benefits of employing a printable pack structure, it will be possible to make use of this load formatting from the class placing for improving your child’s capabilities with numbers and also other studying/writing activities. You will be able to train your youngster the advantages of counting from one to fifteen, determine sizeable and modest products, create an easily readable list, identify animals and identify the parts of the auto, plus much more.
It is possible to modify these to meet your child’s certain requires. That is amongst the most essential benefit of the numbers worksheets. This can be accomplished by changing the graphics, producing particular listings for youngsters with autism or any other particular demands, or you can develop a different formatting to fit your child’s amount of being familiar with. You may also utilize the worksheets being a exciting teaching instrument to produce your child’s numbers and recognizing styles with them. You may also utilize them along with other training resources for example publications, storybooks, and DVDs. Employing a variety of these power tools enables you to adopt your child’s studying to the next level.
They are utilized to teach your child basic math skills. That’s an additional benefit in the numbers worksheets. Upon having worked tirelessly on working on your child’s capabilities with amounts and identification, it is possible to start learning subtraction, addition, and multiplication. Once your child has perfected these skills, they can work on general issue resolving which will allow them to have a head start once they get into school.
Ultimately, you should use the worksheets to construct and enhance your child’s basic math expertise. Worksheets can present how subtractions are completed, as an example, or the best way to understand the visible difference from a beneficial number and a adverse number, by making use of true-daily life example. It is possible to strengthen your child’s standard capabilities and then make them more adept at advanced mathematics, by incorporating activities that reinforce recent skills with new ones.
Numbers worksheets enable you to be creative inside your educating of your own child. They motivate your child to participate in the present and lessons the direction they learn because they are far more productive from the activity. In addition, worksheets aid create their memory, increase their great motor expertise, and improve their vocabulary at the identical time. By doing this, you are aiding your child to be a much better thinker as well as a far more competent learner.
You may want to come up with a few alterations for the worksheets to fit your child’s understanding type. You can do so by simply taking away or adding towards the workout routines which you have selected to use within the worksheets. When you do this, you can easily create worksheets that are far more designed for your tiny one’s learning style and suit their understanding strategies. Simply by making small modifications to your worksheets, you can actually convert their studying in a more fun experience that is certain to positively impact their minds. | 639 | 3,535 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2021-49 | latest | en | 0.926278 |
https://cacm.acm.org/magazines/2010/6/92487-puzzled-solutions-and-sources/fulltext | 1,632,197,688,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057158.19/warc/CC-MAIN-20210921041059-20210921071059-00541.warc.gz | 202,176,871 | 8,275 | Last byte
# Puzzled: Solutions and Sources
View as: Print Mobile App ACM Digital Library Full Text (PDF) In the Digital Edition Share: Send by email Share on reddit Share on StumbleUpon Share on Hacker News Share on Tweeter Share on Facebook
The Intermediate Value Theorem says that if you go continuously from one real number to another, you must pass through all the real numbers in between. You can use it to prove the Ham Sandwich Theorem; here's how it can be used to solve Puzzles 1 and 2:
Solution. Puzzle 1 asked us to prove that the programmers who spent Saturday climbing and Sunday descending Mt. Baker were, at some time of day, at exactly the same altitude on both days.
It's easily done. For any time t, let f(t) be the progammers' altitude on Sunday minus their altitude on Saturday; f(t) starts off positive in the morning and ends up negative at night, so at some point must be 0.
An equivalent, and perhaps more intuitive, way to see this is to imagine that the programmers have twins who were instructed to climb the mountain on Sunday exactly as the programmers climbed it the day before. Then, even if their paths up and down were different, there is some point at which the programmers and their twins must pass one another in altitude.
2. Inscribing a Lake in a Square.
Solution. Puzzle 2 asked us to show that, given any closed curve in the plane, there is a square containing the curve, all four sides of which touch the curve. The idea of the proof is both simple and elegant. Start with a vertical line drawn somewhere west of the curve. Gradually shift the line eastward until it just touches the curve. Repeat with a second line, drawn east of the curve and moving gradually west, so we now have another vertical line touching the curve on its east side. Now bring a horizontal line down from the north until it touches the curve and another from the south, thus inscribing the curve in a rectangle.
But what we want is not merely a rectangle but a square. Suppose the rectangle is taller than it is wide (as it would be in, say, Lake Champlain). Now slowly rotate the four lines together clockwise, keeping all four outside but still touching the curve. After 90 degrees of rotation, the picture is exactly the same as before, only now, the previously long vertical lines of the rectangle are the short horizontal sides.
At some point in the rotation process, the original vertical lines and horizontal lines were all the same lengthand, at exactly that point, the curve was inscribed in a square.
3. Curves Containing the Corners of a Square.
Solution. The third puzzle was (as usual) unsolved, frustrating geometers for more than a century. For a discussion see http://www.ics.uci.edu/~eppstein/junkyard/jordan-square.html, including reference to an article by mathematician Walter Stromquist ("Inscribed Squares and Square-like Quadrilaterals in Closed Curves," Mathematika 36, 2 (1989), 187197) in which he proved the conjecture for smooth curves. See also Stan Wagon's and Victor Klee's book Old and New Unsolved Problems in Plane Geometry and Number Theory (Mathematical Association of America, 1991).
### Author
Peter Winkler (puzzled@cacm.acm.org) is Professor of Mathematics and of Computer Science and Albert Bradley Third Century Professor in the Sciences at Dartmouth College, Hanover, NH.
### Footnotes
All readers are encouraged to submit prospective puzzles for future columns to puzzled@cacm.acm.org.
DOI: http://doi.acm.org/10.1145/1743546.1743575
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.
No entries found | 863 | 3,941 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2021-39 | latest | en | 0.950164 |
https://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/login?o=dnclcdr&s=id=%22100CCU00392033%22.&searchmode=basic | 1,627,186,416,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046151563.91/warc/CC-MAIN-20210725014052-20210725044052-00329.warc.gz | 422,529,104 | 21,494 | # 臺灣博碩士論文加值系統
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令$\mathcal{G}$表示一個圖類別,無向圖$G$是一個探測$\mathcal{G}$圖(probe $\mathcal{G}$ graph),假如我們可以在$G$中找到一個Independent Set並且在這個Independent Set中加邊,使得加完邊後的圖是一個$\mathcal{G}$圖類別中的圖,根據定義,圖類別$\mathcal{G}$是探測圖類別$\mathcal{G}$的一個子類別。給定一圖$G$，假如$G$中的任兩點在任何連通的導出子圖(induced sugraph)的距離和在$G$中的距離相同,我們稱$G$為保距圖 (distance-hereditary graph),二分保距圖(bipartite distance-hereditary graph)既是保距圖也是二分圖(bipartite graph),托勒密圖(ptolemaic graph)是弦圖(chordal graph)的子圖類別滿足圖中不含有導出子圖為gem的圖,二分保距圖和托勒密圖都是保距圖的子圖類別,在本篇論文中,我們設計了三個時間複雜度為 $O(nm)$ 的辨識演算法,用來辨識保距圖的探測圖 (probe distance-hereditary graphs),二分保距圖的探測圖 (probe bipartite distance-hereditary graphs),托勒密圖的探測圖 (probe ptolemaic graphs)。
Let $\mathcal{G}$ denote a graph class. An undirected graph $G$ iscalled a {\em probe $\mathcal{G}$ graph} if one can make $G$ a graphin $\mathcal{G}$ by adding edges between vertices in someindependent set of $G$. By definition graph class $\mathcal{G}$ is asubclass of probe $\mathcal{G}$ graphs. A graph is {\em distancehereditary} if the distance between any two vertices remains thesame in every connected induced subgraph. {\em Bipartitedistance-hereditary graphs} are both bipartite and distancehereditary. {\it Ptolemaic graphs} are chordal and induced gem free.Both bipartite distance-hereditary graphs and ptolemaic graphs aresubclasses of distance-hereditary graphs. In this dissertation, wepropose $O(nm)$-time algorithms to recognize probedistance-hereditary graphs, probe bipartite distance-hereditarygraphs, and probe ptolemaic graphs where $n$ and $m$ are the numbersof vertices and edges of the input graph respectively.
1 Introduction 12 Preliminaries 6 2.1 Notation 6 2.2 Properties of DHGs and its subclasses 8 2.3 Properties of probe DHGs and its subclasses 14 2.4 An $O(n^3)$-time recognition algorithm 193 Partially partitioned probe DHG 22 3.1 Twins 22 3.2 Kernel probe graphs and Algorithm B 25 3.3 Non-biconnected probe graphs without twins and Algorithm R 41 3.4 Time complexity of the main algorithm 454 Partially partitioned probe BDHG 48 4.1 False twins 49 4.2 Kernel probe graphs and Algorithm B1 51 4.3 Non-biconnected probe graphs without false twins and Algorithm R1 59 4.4 Time complexity 665 Partially partitioned PPtG 68 5.1 Some properties for reducing the problem size 69 5.2 Algorithm PPtG 87 5.3 Time complexity 946 Conclusion 97 6.1 The recognition of unpartitioned probe G graphs 97 6.2 The Hamiltonian cycle problem 98
[1] H. J. Bandelt, and H. M. Mulder, Distance-hereditary graphs, Journalof Combinatorial Theory, Series B 41 (1986), pp. 182–208.[2] D. Bayer, V. B. Le, and H.N. de Ridder, Probe threshold and probetrivially perfect graphs, Theoretical Computer Science 410 (2009),pp. 4812–4822.[3] A. Berry, E. Cohen, M. C. Golumbic, M. Lipshteyn, N. Pinet, A.Sigayret, and M. Stern, Recognition chordal-bipartite probe graphs,Research Report LIMOS/RR-07-09, 2007.[4] A. Berry, M. C. Golumbic, and M. Lipshteyn, Recognizing ChordalProbe Graphs and Cycle-Bicolorable Graphs, SIAM Journal on Dis-crete Mathematics 21 (2007), pp. 573–591.[5] A. Brandstädt, V. B. Le, and J. P. Spinrad, Graph classes: A sur-vey, SIAM Monographs on Discrete Mathematics and Applications,Philadelphia, 1999.[6] D. B. Chandler, M.-S. Chang, T. Kloks, J. Liu, and S.-L. Peng, Recog-nition of probe cographs and partitioned probe distance hereditarygraphs, Proceedings of the 2nd International Conference on AlgorithmicAspects in Management (AAIM 2006), LNCS 4041 (2006), 267–278.[7] D. B. Chandler, J. Guo, T. Kloks, and R. Niedermeier, Probe ma-trix problems: totally balanced matrices, Proceedings of the 3rd Inter-national Conference of Algorithmic Aspects on Management (AAIM2007), LNCS 4508 (2007), pp. 368–377.[8] D. B. Chandler, M.-S. Chang, T. Kloks, J. Liu, and S.-L. Peng, Par-titioned probe comparability graphs, Theoretical Computer Science396 (2008), pp. 212–222.[9] D. B. Chandler, M.-S. Chang, T. Kloks, V. B. Le, and S.-L. Peng,Probe ptolemaic graphs, Proceedings of the 14th Annual Interna-tional Computing and Combinatorics Conference (COCOON 2008),LNCS 5092 (2008), pp. 468–477.[10] D. B. Chandler, M.-S. Chang, A. J.J. Kloks, J. Liu, and S.-L. Peng, Onprobe permutation graphs, Discrete Applied Mathematics 157 (2009),pp. 2611–2619.[11] D. B. Chandler, M.-S. Chang, T. Kloks, and S.-L. Peng, Probe graphs.Manuscript, 2009http://www.cs.ccu.edu.tw/~hunglc/ProbeGraphs.pdf[12] G. J. Chang, A. J. J. Kloks, J. Liu, and S.-L. Peng, The PIGsfull monty - a floor show of minimal separators, Proceedings of the22nd Annual Symposium on Theoretical Aspects of Computer Science(STACS 2005), LNCS 3404 (2005), pp. 521–532.[13] G. J. Chang, T. Kloks, and S.-L. Peng, Probe interval bigraphs (ex-tended abstract), Electronic Notes in Discrete Mathematics 19 (2005),pp. 195–201.[14] M.-S. Chang, T. Kloks, D. Kratsch, J. Liu, and S.-L. Peng, On therecognition of probe graphs of some self-complementary classes of per-fect graphs, Proceedings of the 11th Annual International Computingand Combinatorics Conference (COCOON 2005), LNCS 3595 (2005),pp. 808–817.[15] M.-S. Chang, L.-J. Hung, and P. Rossmanith, Probe bipartite distance-hereditary graphs, Proceedings of National Computer Symposium 2009:Workshop on Algorithms and Bioinformatics, pp. 16–27.[16] M.-S. Chang, L.-J. Hung, and P. Rossmanith, Probe distance-hereditary graphs, Proceedings of the 16th Computing: the AustralasianTheory Symposium (CATS 2010), CRPIT 109 (2010), pp. 55–64.[17] M.-S. Chang and L.-J. Hung, Recognition of probe ptolemaicgraphs (Extended Abstract), Proceedings of International Workshopon Combinatorial Algorithms (IWOCA 2010), LNCS 6460 (2011),pp. 286–290.[18] M.-S. Chang, L.-J. Hung, T. Kloks, and S.-L. Peng, Block-graph width,Theoretical Computer Science 412 (2011), pp. 2496–2502.[19] M.-S. Chang, L.-J. Hung, and P. Rossmanith, Recognition of probedistance-hereditary graph graphs, accepted by Discrete Applied Math-ematics.[20] B. Courcelle and S. Olariu, Upper bounds to the clique width of graphs,Discrete Applied Mathematics 101 (2000), pp. 77–114.[21] B. Courcelle, J. A. Makowsky, U. Rotics, Linear time solvable optimiza-tion problems on graphs of bounded clique-width, Theory ComputingSystems 33 (2000) pp. 125–150.[22] A. D’Atri and M. Moscarini, Distance-hereditary graphs, Steiner trees,and connected domination, SIAM Journal on Computing 17 (1988),pp. 521–538.[23] M.C. Golumbic, H. Kaplan, and R. Shamir, Graph sandwich problems,Journal of Algorithms 19 (1995), pp. 449–473.[24] M. C. Golumbic, M. Lipshteyn, Chordal probe graphs, Discrete AppliedMathematics 43 (2004), pp. 221–237.[25] M. C. Golumbic, F. Maffray, and G. Morel, A characterization of chainprobe graphs, Annals of Operations Research 188 (2011), pp. 175–183.[26] P. L. Hammer and F. Maffray, Completely separable graphs, DiscreteApplied Mathematics 27 (1990), pp. 85–99.[27] A. Hertz, Slim graphs, Graphs and Combinatorics 5 (1989), pp. 149–157.[28] P. Hlinˇ en´ y and S. Oum, Finding branch-decomposition and rank-decomposition, SIAM Journal on Computing 38 (2008), pp. 1012–1032.[29] E. Howorka, A characterization of distance-hereditary graphs, TheQuarterly Journal of Mathematics 28 (1977), pp. 417–420.[30] E. Howorka, A characterization of ptolemaic graphs, Journal of GraphTheory 5 (1981), pp. 323–331.[31] R.-W. Hung, S. C. Wu, and M.-S. Chang, Hamiltonian cycle problemon distance-hereditary graphs, Journal of Information Science and En-gineering 19, pp. 827–838.[32] L.-J. Hung, T. Kloks, and C. M. Lee, Trivially-perfect width, inProceedings of International Workshop on Combinatorial Algorithms(IWOCA 2009), LNCS 5874 (2009), pp. 301–311.[33] J. L. Johnson and J. Spinrad, A polynomial-time recognition algorithmfor probe interval graphs, Proceedings of the 12th Annual ACM-SIAMSymposium on Discrete Algorithms (SODA 2001), pp. 477–486.[34] J.-M. Lanlignel and E. Thierry, Pruning graphs with digital searchtrees. Application to distance hereditary graphs, Proceedings of the17th Annual Symposium on Theoretical Aspects of Computer Science(STACS 2000), LNCS 1770 (2000), pp. 529–541.[35] V. B. Le and H. N. de Ridder, Characterisations and linear-time recog-nition of probe cographs. Proceedings of the 33rd International Work-shop on Graph-Theoretic Concepts in Computer Science (WG 2007),LNCS 4769 (2007), pp. 226–237.[36] V. B. Le, Two characterization of chain partitioned probe graphs, An-nals of Operations Research 188 (2011), pp. 279–283.[37] R. M. McConnell and J. P. Spinrad, Construction of probe intervalgraphs, Proceedings of the 13th ACM-SIAM Symposium on DiscreteAlgorithms (SODA 2002), pp. 866–875.[38] R. M. McConnell and Y. Nussbaum, Linear-time recognition of probeinterval graphs, Proceedings of the 17th Annual European Symposiumon Algorithms (ESA 2009), LNCS 5757 (2009), pp. 349–360.[39] S. Oum, Rank-width and vertex-minors, Journal of Combinatorial The-ory, Series B 95 (2005), pp. 79–100.[40] S. Oum, Graphs of bounded rank-width. PhD Thesis. Princeton Univer-sity, Princeton (2005).[41] S. Oum, Approximating rank-width and clique-width quickly, ACMTransactions on Algorithms 5, No. 1, Article 10, 2008.[42] P. E. Zhang, A. Schon, S. G. Fischer, E. Cayanis, J. Weiss, S. Kistler,and E. Bourne, An algorithm based on graph theory for the assem-bly of contigs in physical mapping of DNA, Bioinformatics 10 (1994),pp. 309–317.
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簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室 | 3,590 | 9,928 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2021-31 | latest | en | 0.510922 |
http://mathhelpforum.com/algebra/213145-basic-algebra-help-print.html | 1,498,357,729,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320386.71/warc/CC-MAIN-20170625013851-20170625033851-00513.warc.gz | 253,884,283 | 3,468 | # Basic Algebra help
• Feb 15th 2013, 10:40 AM
ROCKCDXX
Basic Algebra help
I'm taking a real estate course and brushing up on my math. I'm doing a practice test from my book and this problem has me stumped, and there's no explanation for it in the book.
The value of a house today is \$37,500. It has been depreciating (losing value) 2.5% per year. What was the value of the house 10 years ago?
So as I understand it the equation should look like: x-(x0.025(10)=37,500
which breaks down to x-x0.25=37,500
or x minus 25% of x equals 37,500 if I'm not writing it correctly above... Am I right so far? How do I finish this?
• Feb 15th 2013, 10:48 AM
sakonpure6
Re: Basic Algebra help
If the house costs 37500 now and it is depreciating 2.5 % every year, then to find it's value 10 years ago we need to increase the property value which is 37500 by 2.5 % for 10 years and the equation to solve this would be (1+0.025)^10(37500). We do (1+0.025) because we are increasing the value by 2.5 percent. The 10 is the number of years ( it is also the x variable).
the answer is about \$48003 and you can check this by depreciating this value by 2.5% for 10 years which will give your initial house value of \$37500
• Feb 15th 2013, 10:53 AM
ROCKCDXX
Re: Basic Algebra help
2.5% of the original value is not the same as 2.5% of the current value... the answer should be \$50000 I believe, but I don't know how to get there...
• Feb 15th 2013, 10:56 AM
sakonpure6
Re: Basic Algebra help
Quote:
Originally Posted by ROCKCDXX
2.5% of the original value is not the same as 2.5% of the current value... the answer should be \$50000 I believe, but I don't know how to get there...
if it is loosing 2.5% every year, then if you go back in time, the price should also increase 2.5% every year.
• Feb 15th 2013, 11:00 AM
ROCKCDXX
Re: Basic Algebra help
right but by 2.5% of the unknown number
• Feb 15th 2013, 11:01 AM
sakonpure6
Re: Basic Algebra help
??
value of property 10 years ago= (1.025)^10years (property value now)
• Feb 15th 2013, 11:15 AM
ROCKCDXX
Re: Basic Algebra help
Never mind I figured it out... for future reference, knowing the house has depreciated 25% over 10 years, 37500 represents 75% of the original value... 37,500/75%= 50,000... thanks for the help anyway
• Feb 16th 2013, 03:31 AM
ibdutt
Re: Basic Algebra help
You need to use the formula for Compound interest i.e., A = P ( 1 + r/100)^n, where A is amount, P - principal, r rate and n time. In this case we will have to take rate as negative since it is depreciation. | 790 | 2,535 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2017-26 | longest | en | 0.925523 |
https://deltaclicks.com/variations-of-domino/ | 1,722,794,456,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640408316.13/warc/CC-MAIN-20240804164455-20240804194455-00533.warc.gz | 157,136,556 | 11,523 | # Variations of Domino
Those of you who don’t know what domino is may be wondering what makes it so appealing. The simple answer is that domino is a family of tile-based games. The rectangular tiles have two square ends and are marked with the number of spots on each. Players take turns laying out the tiles in a row until they reach the desired number. Depending on the number of spots on each domino, they are said to be worth one point or one unit.
In a domino game, each player plays a tile onto the table. The tile must touch the end of the domino chain. In some variations, a player may play a tile that contains a particular number on one end of the chain, but not on the other. In other versions, the player must chip out the remaining tiles and then play the last one. Those who reach the lowest score at the end of the game win.
The pips on a domino serve as identifying marks for matching purposes. There are 28 dominos in a set. The faces of each tile have different numbers of spots and pips. The tiles are typically laid down in lines, but can also be arranged in an angular pattern. The rules of dominoes are as simple as those for playing a card game. Its popularity has led to numerous variations.
In a traditional game of domino, a player starts by placing a tile face-up on the table. The next player must match one end of the domino to a portion of the first tile. Sometimes, players can join multiple dominos on the same line. Those who do not have dominoes to play must draw from an empty table or draw from the unused tiles. The winner is the first to complete their chain.
One of the most common versions of domino is the Block game, which involves two players. A player starts with a double-six set of dominoes, and alternately extends the line of play until he or she reaches the desired number of pip values. Upon completing this task, the winner scores the total pip count of the losing player’s hand. This game is played in pairs or fours, and can be challenging for the novice as well as the advanced.
The game of domino originated in China, where the earliest mention of dominoes is found in the Book of Wulin (translated as “the book of dominos”). In the late eighteenth century, the game became popular in France, where it was named after a black and white hood worn by Christian priests during the winter. Interestingly, the domino game is still popular in many parts of Latin America. In the Arctic, Inuits play a game that is similar to Western Dominoes. These games were probably an imitation of Western games.
Regardless of the domino game type, you can find a variety of sets to suit any occasion. Double-six and double-nine sets are commonly used to play “standard” domino games. The standard game is played with double-six and double-nine domino sets, and has four players. This game is popular worldwide, and there are many variations of the game. Just be sure to check out the variations of the game and the rules for the different versions of the game. | 655 | 3,004 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2024-33 | latest | en | 0.958513 |
https://republicofsouthossetia.org/question/the-taste-test-for-ptc-phenylthiocarbamide-is-a-favorite-eercise-in-beginning-human-genetics-cla-14888865-89/ | 1,638,449,422,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362219.5/warc/CC-MAIN-20211202114856-20211202144856-00066.warc.gz | 550,380,899 | 13,728 | ## The taste test for PTC (phenylthiocarbamide) is a favorite exercise in beginning human genetics classes. It has been established that a sing
Question
The taste test for PTC (phenylthiocarbamide) is a favorite exercise in beginning human genetics classes. It has been established that a single gene determines whether or not an individual is a “taster.” If 70% of Americans are “tasters” and 20 Americans are randomly selected, what is the probability that a at least 17 are “tasters”? b fewer than 15 are “tasters”?
in progress 0
1 week 2021-11-23T17:33:15+00:00 1 Answer 0 views 0
(a) 0.1071
(b) 0.4164 .
Step-by-step explanation:
We are given that a single gene determines whether or not an individual is a “taster.” 70% of Americans are “tasters” and 20 Americans are randomly selected.
We can take this situation as of Binomial distribution i.e.;
where, n = number of trials or number of samples
x = required success
p = probability of success
So, here success is that gene determines individual to be a “taster.” i.e.
p = 0.70 and also n = 20
(a) Probability that at least 17 are “tasters” = P(X >= 17)
For this we will use binomial probabilities table in which less than probabilities are given so;
P(X >= 17) = 1 – P(X <=16) = 1 – 0.8929 = 0.1071.
(b) Probability that fewer than 15 are “tasters” = P(X < 15)
P(X < 15) = P(X <= 14) = 1 – 0.5836 = 0.4164 . | 404 | 1,384 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2021-49 | latest | en | 0.915217 |
http://nrich.maths.org/public/leg.php?code=97&cl=3&cldcmpid=542 | 1,502,904,447,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886102309.55/warc/CC-MAIN-20170816170516-20170816190516-00065.warc.gz | 285,531,015 | 10,132 | # Search by Topic
#### Resources tagged with Circles similar to Kissing Triangles:
Filter by: Content type:
Stage:
Challenge level:
### There are 62 results
Broad Topics > 2D Geometry, Shape and Space > Circles
### Floored
##### Stage: 3 Challenge Level:
A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?
### Pie Cuts
##### Stage: 3 Challenge Level:
Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).
### Square Pegs
##### Stage: 3 Challenge Level:
Which is a better fit, a square peg in a round hole or a round peg in a square hole?
### Angle A
##### Stage: 3 Challenge Level:
The three corners of a triangle are sitting on a circle. The angles are called Angle A, Angle B and Angle C. The dot in the middle of the circle shows the centre. The counter is measuring the size. . . .
### The Pillar of Chios
##### Stage: 3 Challenge Level:
Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .
##### Stage: 4 Challenge Level:
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
### The Pi Are Square
##### Stage: 3 Challenge Level:
A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?
### Curvy Areas
##### Stage: 4 Challenge Level:
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
### Semi-detached
##### Stage: 4 Challenge Level:
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
### F'arc'tion
##### Stage: 3 Challenge Level:
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .
### Bull's Eye
##### Stage: 3 Challenge Level:
What fractions of the largest circle are the two shaded regions?
### Crescents and Triangles
##### Stage: 4 Challenge Level:
Triangle ABC is right angled at A and semi circles are drawn on all three sides producing two 'crescents'. Show that the sum of the areas of the two crescents equals the area of triangle ABC.
### A Chordingly
##### Stage: 3 Challenge Level:
Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.
### Partly Circles
##### Stage: 4 Challenge Level:
What is the same and what is different about these circle questions? What connections can you make?
### Intersecting Circles
##### Stage: 3 Challenge Level:
Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?
### Squaring the Circle
##### Stage: 3 Challenge Level:
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .
### An Unusual Shape
##### Stage: 3 Challenge Level:
Can you maximise the area available to a grazing goat?
### Coins on a Plate
##### Stage: 3 Challenge Level:
Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.
### Circles, Circles Everywhere
##### Stage: 2 and 3
This article for pupils gives some examples of how circles have featured in people's lives for centuries.
### Not So Little X
##### Stage: 3 Challenge Level:
Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?
### Salinon
##### Stage: 4 Challenge Level:
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
### Semi-square
##### Stage: 4 Challenge Level:
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
### Like a Circle in a Spiral
##### Stage: 2, 3 and 4 Challenge Level:
A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
### Blue and White
##### Stage: 3 Challenge Level:
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
### Pi, a Very Special Number
##### Stage: 2 and 3
Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.
### Circle Packing
##### Stage: 4 Challenge Level:
Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...
### Rolling Around
##### Stage: 3 Challenge Level:
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
##### Stage: 4 Challenge Level:
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .
##### Stage: 4 Challenge Level:
The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
### Tied Up
##### Stage: 3 Challenge Level:
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
### Arclets Explained
##### Stage: 3 and 4
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
##### Stage: 4 Challenge Level:
Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
### Efficient Packing
##### Stage: 4 Challenge Level:
How efficiently can you pack together disks?
### Some(?) of the Parts
##### Stage: 4 Challenge Level:
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
### Fitting In
##### Stage: 4 Challenge Level:
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .
### Efficient Cutting
##### Stage: 3 Challenge Level:
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
##### Stage: 2, 3 and 4 Challenge Level:
A metal puzzle which led to some mathematical questions.
### Three Tears
##### Stage: 4 Challenge Level:
Construct this design using only compasses
### LOGO Challenge 11 - More on Circles
##### Stage: 3 and 4 Challenge Level:
Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .
### LOGO Challenge 12 - Concentric Circles
##### Stage: 3 and 4 Challenge Level:
Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.
### LOGO Challenge - Circles as Animals
##### Stage: 3 and 4 Challenge Level:
See if you can anticipate successive 'generations' of the two animals shown here.
### What Is the Circle Scribe Disk Compass?
##### Stage: 3 and 4
Introducing a geometrical instrument with 3 basic capabilities.
### LOGO Challenge 10 - Circles
##### Stage: 3 and 4 Challenge Level:
In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.
### Round and Round
##### Stage: 4 Challenge Level:
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
### Three Four Five
##### Stage: 4 Challenge Level:
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
### Squaring the Circle and Circling the Square
##### Stage: 4 Challenge Level:
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
### Get Cross
##### Stage: 4 Challenge Level:
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
### Circumspection
##### Stage: 4 Challenge Level:
M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.
### Rolling Coins
##### Stage: 4 Challenge Level:
A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .
### Holly
##### Stage: 4 Challenge Level:
The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface. | 2,290 | 10,041 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2017-34 | latest | en | 0.85978 |
http://mathoverflow.net/questions/45116/total-space-of-the-line-bundle-mathcalo1-over-mathbbpn?sort=oldest | 1,461,897,446,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860110356.23/warc/CC-MAIN-20160428161510-00058-ip-10-239-7-51.ec2.internal.warc.gz | 110,212,042 | 16,461 | # Total space of the line bundle $\mathcal{O}(1)$ over $\mathbb{P}^n$
It is well known that total space of the tautological line bundle $\mathcal{O}(-1)$ over projective space $\mathbb{P}^n$ is closed subvariety of $\mathbb{P}^n\times\mathbb{A}^{n+1}$. My question is how to realize total space of $\mathcal{O}(1)$ over $\mathbb{P}^n$ in such manner, i.e. I need an embedding of $Tot(\mathcal{O}(1))$ in simple variety and defining equations. Thanks.
-
It is the complement $\mathbb{P}^{n+1} - \{x\}$ of a point in a projective space.
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Shouldn't $\mathbb{P}^{n+1}\setminus\{x\}\to \mathbb{P}^n$ be the tautological line bundle? – Fei YE Nov 7 '10 at 1:59
The tautological line bundle contains a divisor, isomorphic to $\mathbb{P}^n$, with normal bundle of degree $-1$ (namely, the zero section). On the other hand every effective compact divisor in $\mathbb{P}^{n+1}-\{x\}$ has a positive normal bundle. In particular, a hyperplane avoiding $x$ has normal bundle of degree $1$. The projection from the point identifies the complement of $x$ with the total space of this normal bundle. – Tony Pantev Nov 7 '10 at 2:20
Thank you, Tony. Maybe you know such simple description of $Tot(O(n))$ for $n>1$ also? – Klim Puhov Nov 8 '10 at 14:23
You can get $Tot(\mathcal{O}(n))$ in a similar manner by deleting a point from a weighted projective space. But this is more contrived. And is not really better than thinking of $Tot(\mathcal{O}(n))$ as a toric variety. So this probably is not what you want. – Tony Pantev Nov 9 '10 at 1:22
@TonyPantev would you mind saying which weighted projective space contains the total space of $\mathcal{O}(n)$ and how to think of it as a toric variety? – PrimeRibeyeDeal Apr 5 at 1:45
Dear Luther King, since you ask for equations, let me add them to Tony's beautifully geometric answer.
Consider $\mathbb P^{n+1}$ with homogeneous coordinates $(z_0:z_1:\ldots:z_{n+1})$ and $\mathbb P^{n}$ enbedded as the hyperplane $z_0=0$. If $x\in\mathbb P^{n+1}$ is the point $x=(1:0:\ldots:0)$, the required total space $T=Tot \mathcal O_{\mathbb P^{n}}(1)$ is the complement $T=\mathbb P^{n+1} \setminus \{x\}$ of $x$ in $\mathbb P^{n+1}$. The fiber of our bundle $\mathcal O_{\mathbb P^{n}}(1)$ at the arbitrary point $(0:z_1:\ldots:z_{n+1}) \in \mathbb P^n$ is the set of all $(\lambda:z_1:\ldots:z_{n+1})$ with $\lambda \in k$ (base field) .
The one-dimensional vector space structure on the fiber is given by $(\lambda:z_1:\ldots:z_{n+1})+(\mu:z_1:\ldots:z_{n+1})=(\lambda +\mu:z_1:\ldots:z_{n+1})$ and similarly for products by scalars. Beware that we definitely do not have an isomorphism from our fiber to $k$ defined by $(\lambda:z_1:\ldots:z_{n+1})\mapsto \lambda$: this is not even a well-defined map. This is not surprising: after all $\mathcal O_{\mathbb P^{n}}(1)$ is not a trivial bundle!
A more canonical approach (edited) Readers of the canonical faith may suppress coordinates as follows.
Consider a $k$ - vector space $V$ of dimension $n+1$, its projectivization $\mathbb P (V)$ and its embedding $\mathbb P (V) \to \mathbb P (k \oplus V)$ sending the point $\mathbb P (l) \in \mathbb P (V)$ to the point $\mathbb P (0\oplus l) \in \mathbb P (k \oplus V)$. The vector bundle $\mathcal O _{\mathbb P (V)} (1)$ then has as total space the open subset $T\subset \mathbb P (k \oplus V)$ obtained by deleting $x=\mathbb P (k \oplus 0)$ from $\mathbb P (k \oplus V)$ i.e. $T= \mathbb P (k \oplus V)\setminus x$. The fiber over $\mathbb P (l)$ [identified with $\mathbb P (0\oplus l)$] is $\mathbb P (k \oplus l)\setminus x$, a vector space of dimension one with origin the point $\mathbb P (0 \oplus l)$ but with no prefered isomorphism to $k$.
Elementary geometry It may clarify the above to recall that given a one dimensional projective space $\mathbb P$ over $k$, if you delete a point $x$ from it you get a one dimensional affine space $\mathbb P \setminus x$ and if you choose in it an origin, you get a one dimensional vector space, but that vector space has no prefered isomorphism with the vector space $k$.
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Thanks for detailed answer, Georges! – Klim Puhov Nov 7 '10 at 20:22
For me the best description of $Tot(O(1))$ is the tautological --- as the relative spectrum of the sheaf of algebras $A = O \oplus O(-1) \oplus O(-2) \oplus \dots$ on $P^n$: $$Tot(O(1)) = Spec_{P^n}(A).$$ This allows to work with $Tot(O(1))$ more effectively than any other description. For example, a coherent sheaf on $Tot(O(1))$ can be represented by a quasicoherent sheaf $F$ on $P^n$ together with a morphism $F(-1) \to F$ inducing on $F$ a structure of an $A$-module.
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Yes, I know about such description, but for my purposes the above one is preferable. – Klim Puhov Nov 7 '10 at 20:35 | 1,538 | 4,725 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2016-18 | longest | en | 0.778697 |
http://doc.sumy.ua/prog/pb/cookbook/ch10_06.htm | 1,521,463,902,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257646914.32/warc/CC-MAIN-20180319120712-20180319140712-00648.warc.gz | 80,706,819 | 3,776 | Полезная информация
## 10.5. Passing Arrays and Hashes by Reference
### Problem
You want to pass a function more than one array or hash and have each remain distinct. For example, you want to put the "Find elements in one array but not in another" algorithm from Recipe 4.7 in a subroutine. This subroutine must then be called with two arrays that remain distinct.
### Solution
Pass arrays and hashes by reference, using the backslash operator:
`array_diff( \@array1, \@array2 );`
### Discussion
See Chapter 11, References and Records, for more about manipulation of references. Here's a subroutine that takes array references and a subroutine call that generates them:
```@a = (1, 2);
@b = (5, 8);
@c = add_vecpair( \@a, \@b );
print "@c\n";
`6 10`
sub add_vecpair { # assumes both vectors the same length
my (\$x, \$y) = @_; # copy in the array references
my @result;
for (my \$i=0; \$i < @\$x; \$i++) {
\$result[\$i] = \$x->[\$i] + \$y->[\$i];
}
return @result;
}```
A potential difficulty with this function is that it doesn't check to make sure it got exactly two arguments that were both array references. You could check explicitly this way:
```unless (@_ == 2 && ref(\$x) eq 'ARRAY' && ref(\$y) eq 'ARRAY') {
If all you plan to do is `die` on error (see Recipe 10.12), you can usually omit this check, since dereferencing the wrong kind of reference triggers an exception anyway. | 376 | 1,409 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2018-13 | latest | en | 0.795909 |
https://ai.stackexchange.com/questions/tagged/reward-functions?tab=Votes | 1,620,440,866,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988831.77/warc/CC-MAIN-20210508001259-20210508031259-00057.warc.gz | 114,315,951 | 43,959 | # Questions tagged [reward-functions]
For questions about rewards functions (e.g. in the context of reinforcement learning, which may be denoted as $R(s, a)$).
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765 views
### Counterexamples to the reward hypothesis
On Sutton and Barto's RL book, the reward hypothesis is stated as that all of what we mean by goals and purposes can be well thought of as the maximization of the expected value of the cumulative ...
370 views
### Why is the reward in reinforcement learning always a scalar?
I'm reading Reinforcement Learning by Sutton & Barto, and in section 3.2 they state that the reward in a Markov decision process is always a scalar real number. At the same time, I've heard about ...
2k views
### What are other ways of handling invalid actions in scenarios where all rewards are either 0 (best reward) or negative?
I created an OpenAI Gym environment, and I would like to check the performance of the agent from OpenAI Baselines DQN approach on it. In my environment, the best possible outcome for the agent is 0 - ...
577 views
### How do we define the reward function for an environment?
How do you actually decide what reward value to give for each action in a given state for an environment? Is this purely experimental and down to the programmer of the environment? So, is it a ...
183 views
### Why does a negative reward for every step really encourage the agent to reach the goal as quickly as possible?
If we shift the rewards by any constant (which is a type of reward shaping), the optimal state-action value function (and so optimal policy) does not change. The proof of this fact can be found here. ...
250 views
### How are the reward functions $R(s)$, $R(s, a)$ and $R(s, a, s')$ equivalent?
In this video, the lecturer states that $R(s)$, $R(s, a)$ and $R(s, a, s')$ are equivalent representations of the reward function. Intuitively, this is the case, according to the same lecturer, ...
109 views
### How to improve the reward signal when the rewards are sparse?
In cases where the reward is delayed, this can negatively impact a models ability to do proper credit assignment. In the case of a sparse reward, are there ways in which this can be negated? In a ...
279 views
### How do I convert an MDP with the reward function in the form $R(s,a,s')$ to and an MDP with a reward function in the form $R(s,a)$?
The AIMA book has an exercise about showing that an MDP with rewards of the form $r(s, a, s')$ can be converted to an MDP with rewards $r(s, a)$, and to an MDP with rewards $r(s)$ with equivalent ...
292 views
### What are some best practices when trying to design a reward function?
Generally speaking, is there a best-practice procedure to follow when trying to define a reward function for a reinforcement-learning agent? What common pitfalls are there when defining the reward ...
312 views
### Can the rewards be stochastic when the transition model is deterministic?
Suppose we have a deterministic environment where knowing $s,a$ determines $s'$. Is it possible to get two different rewards $r\neq r'$ in some state $s_{\text{fixed}}$? Assume that $s_{\text{fixed}}$ ...
74 views
### How should I handle invalid actions in a grid world?
I'm building a really simple experiment, where I let an agent move from the bottom-left corner to the upper-right corner of a $3 \times 3$ grid world. I plan to use DQN to do this. I'm having trouble ...
245 views
### Why does shifting all the rewards have a different impact on the performance of the agent?
I am new to reinforcement learning. For my application, I have found out that if my reward function contains some negative and positive values, my model does not give the optimal solution, but the ...
89 views
### Can rewards be decomposed into components?
I'm training a robot to walk to a specific $(x, y)$ point using TD3, and, for simplicity, I have something like ...
109 views
### How to apply Q-learning when rewards is only available at the last state?
I have a scheduling problem in which there are $n$ slots and $m$ clients. I am trying to solve the problem using Q-learning so I have made the following state-action model. A state $s_t$ is given by ...
88 views
### Why is the reward function $\text{reward} = 1/{(\text{cost}+1)^2}$ better than $\text{reward} =1/(\text{cost}+1)$?
I have implemented a simple Q-learning algorithm to minimize a cost function by setting the reward to the inverse of the cost of the action taken by the agent. The algorithm converges nicely, but ...
113 views
### Why is the equation $r(s', a, s') =\sum_{r \in \mathcal{R}} r \frac{p\left(s^{\prime}, r \mid s, a\right)}{p\left(s^{\prime} \mid s, a\right)}$true?
I am referring to eq. 3.6 (page 49) based on Sutton's online book and can be found in an image below. I could not make sense of the final derivation of the equation $r(s, a, s')$. My question is ...
468 views
### What are the pros and cons of sparse and dense rewards in reinforcement learning?
From what I understand, if the rewards are sparse the agent will have to explore more to get rewards and learn the optimal policy, whereas if the rewards are dense in time, the agent is quickly guided ...
261 views
### Is a reward given at every step or only given when the RL agent fails or succeeds?
In reinforcement learning, an agent can receive a positive reward for correct actions and a negative reward for wrong actions, but does the agent also receive rewards for every other step/action?
152 views
### How does the initialization of the value function and definition of the reward function affect the performance of the RL agent?
Is there any empirical/theoretical evidence on the effect of initial values of state-action and state values on the training of an RL agent (the values an RL agent assigns to visited states) via MC ...
56 views
108 views
### What are proxy reward functions?
The understanding I have is that they somehow adjust the objective to make it easier to meet, without changing the reward function. ... the observed proxy reward function is the approximate solution ...
83 views
### What is the difference between success rate and reward when dealing with binary and sparse rewards?
In OpenAI Gym "reward" is defined as: reward (float): amount of reward achieved by the previous action. The scale varies between environments, but the ...
132 views
### How to define a reward function in POMDPs?
How do I define a reward function for my POMDP model? In the literature, it is common to use one simple number as a reward, but I am not sure if this is really how you define a function. Because this ...
63 views
### How can I go from $R(s)$ to $R(s,a)$ in this specific MDP?
I'm trying to implement a research paper, as explained in this other post, here the author of the paper assumed R as a function of both states and actions, while the code (and the MDP) I'm using to ...
27 views
I have been training some kind of agent to reach a target using a Q-learning based approach, and I have tried two different types of rewards: Long-term reward: $\mathrm{reward} = - \mathrm{distance}(\... 0answers 22 views ### How can I discourage the RL agent from drawing in a zero-sum game? My agent receives$1, 0, -1$rewards for winning, drawing, and losing the game, respectively. What would be the consequences of setting reward to$-1$for draws? Would that encourage the agent to win ... 0answers 36 views ### How to combine two differently equally important signals into the reward function, that have different scales? I have two signals that I want to use to model my reward. The first one is the CPU TIME: running mean from this diagram: The second one is the MAX RESIDUAL from this diagram: Since they are both ... 1answer 89 views ### How can I implement the reward function for an 8-DOF robot arm with TRPO? I need to get an 8-DOF (degrees of freedom) robot arm to move a specified point. I need to implement the TRPO RL code using OpenAI gym. I already have the gazebo environment. But I am unsure of how to ... 1answer 794 views ### What is the reward system of reinforcement learning? Can you describe this reward system in more detail? I understand that the environment sends a signal indicating whether or not the action taken by the agent was 'good' or not, but it seems too simple. ... 1answer 160 views ### What is the difference between a fitness function and a reward function? In reinforcement learning (RL), the reward function (RF), which can be denoted as$r(s)$,$r(s, a)$,$r(s, a, s')$,$r(s, s')$depending on its specific definition, provides the learning signal, which ... 1answer 51 views ### If the reward function of an environment depends on some initial conditions, should I create a separate environment for each condition? I would like some guidance on how to design an Environment for a Reinforcement Learning agent where the stopping conditions and rewards for the environment change based on an initial set of input ... 1answer 65 views ### What is the relationship between the reward function and the value function? To clarify it in my head, the value function calculates how 'good' it is to be in a certain state by summing all future (discounted) rewards, while the reward function is what the value function uses ... 1answer 42 views ### How to scale all positive continuous reward? My RL project has all positive continuous rewards for every step and the goal is to have the maximum cumulative reward (episodic reward). The problem is that the rewards are too close and all between ... 1answer 115 views ### What is the optimal value function of the shifted version of the reward function? Similarly to this question that I asked some time ago, what is the optimal value function of the shifted (by some constant$c$) version of some reward function? More precisely, let's assume that$r(s, ...
I am working on an RL problem where the time when the agent obtains the reward for taking action $a$ in time step $t$ is stochastic. In fact, there is no immediate reward for taking action $a$ in time ... | 2,308 | 10,085 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2021-21 | latest | en | 0.919978 |
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Book Id: WPLBN0002828324 Subjects: Non Fiction, Technology, Digital Art Collections: Technology, Literature, Fine Arts, Naval Science, Authors Community, Art ► Abstract Table of Contents DetailsEGYPTIAN HIEROGLYPHS ² 4 - 23 RADIO DIAGRAMS ² 24 - 36 TV SHOW ² 37 - 44 ELECTRICAL CIRCUITS ² 45 - 54 MARINE FAUNA ² 55 - 76
Book Id: WPLBN0001235170 Subjects: Non Fiction, Technology, Education ► Abstract Full Text Search Details...art 1 Overview 1 Conventional engineering and new engineering 1 Part 2 Electrical engineering 2 Example problems that illustrate elect... ... 15 3 The electrical resistance form of the problems in Chapter 2 41 4 Wh... ...rm of the problems in Chapter 2 41 4 Why electrical behavior V{I} should replace electrical resistance V/I 54 ... ... resistance V/I 54 5 Stability of resistive electrical systems 64 6 Inductance,... ... ix • Nonlinear electrical devices have enabled instantaneous and world wide comm... ...ers 2 and 3, note that: • Problems 2.5/1, 2.6/1, and 2.6/4 concern proportional circuits. They can be solved in a simple and direct manner using... ...sistance methodology. • Problems 2.5/2 and 2.6/2 concern very simple nonlinear circuits. They can be solved in a simple and direct manner using... ...logy. • Problems 2.5/3, 2.6/3, 2.6/5, and 2.6/6 involve more complex non- linear circuits. They can be solved in a simple and direct manner using... ... illustrate how behavior methodology is used to solve problems that concern series circuits, and series-parallel circuits. 2.4 A preview of the...
Book Id: WPLBN0002096508 Subjects: Non Fiction, Military Science, Education ► Abstract Full Text Search Details...ble. I!!E:::.. I: Don't think for a minute that the same rationale isn't ued today for unsecured circuits that e: ~ happen to use sophisticated transm... ...level links. as in the case of all the ciphony equipments I've mentioned so far. or for tactical circuits that we will. in due course. cover. Still. w... ...e said. sharply limits the number of digits we can use to describe speech to beencrypted on such circuitswith a consequent lou orquality ofinteWgibili... ... to the big bed· plant voice equipments we ought to talk aboul. That's the subject of "approved" circuits. Way back with the KO-6. we were having diff... ... handled. transmitted, and stored: and in the case of TOP SECRET information. this order forbids electrical transmission ezcept in encr:-'pted form. o... ...f a chrOnology for you. In brief: any time a machine is used to process classified infor mation electrically, the various switches, contacts, rela)'l... ...ueezingthrough with them? Masking, which is the notioD of deliberately creating a lot or ambient electrical DOise to over ride. jam. smear out or oth... ... 3,200 feet and, typically, at more than 1000 feet, even when they were operated in a very noisy electrical environment. One such teat Was conducted. ... ...c::=-..:::::::: F"--:: 5---:.:-. i === - .- =--= ~: 1 -· ... = _. -- SBCkE'i NufOltM hysical aDd electrical.paration between thOle cimJita cazr,yiD1 c...
Book Id: WPLBN0001235233 Subjects: Non Fiction, Psychology, Education ► Abstract Full Text Search Details... the air. This is directed, specifically formed energy, intended to trigger certain circuits in the recipient brain. It should come as no surprise i... ...herapy has clear physiological effects upon the brain of the patient (blood volume, electrical activity, discharge and absorption of hormones, etc.)... ...he air. This is a directed, specifically formed energy, intended to trigger certain circuits in the recipient brain. It should come as no surprise i... ...herapy has clear physiological effects upon the brain of the patient (blood volume, electrical activity, discharge and absorption of hormones, etc.)... ...lled Rapid Eye Movement (REM). It is also associated with changes in the pattern of electrical activity of the brain (EEG). A dreaming person has th... ...he uterus contracts and the muscles at the base of the tongue enjoy a relaxation in electrical activity. These facts would indicate that dreaming is...
Book Id: WPLBN0002096505 ► Abstract Full Text Search Details...dustries: petroleum, light indus- tries, natural gas, mining, petrochemical, electrical, automotive plants (under con- struction), and food processing... ...nsport aircraft Airfields: none Telecommunications: international land- line circuits to Spain and France; 1 AM station; about 12,800 telephones (43.5... ...ent Major industries: foods, iron and steel, machinery, textiles, chemicals, electrical, paper and pulp Crude steel: 5.3 million metric tons pro- duce... ...(1986) Exports: \$352 million (f.o.b., 1985); sugar and sugarcane byproducts, electrical parts, clothing Imports: \$552 million (f.o.b., 1985); food- st... ...port equipment, alumina for refining, petro- leum products, food, beverages, electrical equipment, chemical products Major trade partners: most trade ... ... \$139.6 million (f.o.b., 1984 est); textiles, petroleum products, machinery, electrical equipment, motor vehicles, chemicals, Pharmaceuticals Major tr... ...switching centers; satellite communications, long- haul point-to-point radio circuits, regional cable and wire landlines, directional radio- relay, an... ...hones (25 per 100 popl.); 10 AM, 14 FM, 29 TV stations; tropospheric scatter circuits to Greece and Turkey; 3 submarine coaxial cables; 1 Atlantic Oce... ...2,439 m Telecommunications: small, modern system using cable and radio-relay circuits; 900,000 telephones (23.5 per 100 popl.); 47 AM, 33 FM, 86 TV st...
Book Id: WPLBN0002096873 Subjects: Non Fiction, Social Sciences, Technology ► Abstract Full Text Search Details... page after end of this chapter. Brain, Our Hard Drive; Neurons, Its Circuits The brain is our system‘s hard drive; neurons, its circuits. ... ...ry did a host of inventors set in motion the development of devices using electrical power that belong in any listing of Information Technologies. ... ...ate call until morning vote totals had confirmed it. 1960s Integrated circuits replace transistors. Plain-paper copying machine. 1969 See...
Book Id: WPLBN0002097024 Subjects: Non Fiction, Technology, History of Technology ► Abstract Full Text Search Details...nd the globe to head for the beaches. Brain, our hard drive; neurons, its circuits The brain is our system‘s hard drive; neurons, its circuits. Ou... ...ry did a host of inventors set in motion the development of devices using electrical power that belong in any listing of Information Technologies. ... ...ate call until morning vote totals had confirmed it. 1960s Integrated circuits replace transistors. Plain-paper copying machine. 1969 See...
Book Id: WPLBN0002110121 ► Abstract Full Text Search Details... BUILDING THE SMART GRID SMART GRIDS sense and respond to changes in electrical systems sparked by either suppliers or consumers, in order to ... ...r-secure smart grid. A so-called microgrid, a small-scale version of an electrical distribution and storage system, will be established to ensure... ...2011 · HAWAII BUSINESS like those prepared with stem cells and electric circuits for the space-shuttle experiment. Nearby, regenerative- cell scie...
Book Id: WPLBN0002096913 Subjects: Non Fiction, Fine Arts, Art History ► Abstract Full Text Search Details...rm in the century of tectonics; - impersonal personalized texts; - the electrical shock; - the translation of the impossible into the possible, ... ...eality: the twisting of the modern life in sophisticated electronic short circuits, of which some are dangerous. It raises the protestation concerni... ...t are more or less intent, through brilliant objectives (surrealist short circuits), but objectives with a magma of derision. The paradoxist poet te... ...monstrated enough ability in the expressiveness of negation. The semantic circuits obtained in paradoxism are of a revealing illumination and libera... ...he aesthetics of its non-) and for this it counts on the paradoxist short-circuits. Concomitantly, a literary experience edifies itself, able to eng... ...lashing technique of the century, but in its personal mode: futurist short-circuits appear to it like some insignificant stings. As its specific load...
Book Id: WPLBN0002097100 ► Abstract Full Text Search Details... each circuit of an electric network. Thus in effect Kirchoff replaced each electrical network by its underlying graph and showed that it is not nec... ...f a graph determined by any of its spanning trees will suffice. A contrived electrical network N, its under lying graph G and a spanning tree T are ... ...sed by Kirchoff to generate a “cycle basis” for the cycles in the graphs of electrical networks. Now we consider enumeration of the spanning trees o... ...gar, 8 1973, 43- 48. 12. Chvatal, V., and Erdos, P., A note on Hamiltonian Circuits, Discrete Maths (2) 1972 111-113. 13. Craiger, J.P., R.J. Weiss...
Book Id: WPLBN0001235286 Subjects: Non Fiction, Philosophy, Science ► Abstract Full Text Search Details...ch other and of the nucleus. They are allowed to interact only through the average electrical field (which is the charge of the nucleus and the cha... ...approximation of the field. This process is repeated until the final charge and the electrical field distribution agree with the input to the SE. R... ...he air. This is a directed, specifically formed energy, intended to trigger certain circuits in the recipient brain. It should come as no surprise i... ...herapy has clear physiological effects upon the brain of the patient (blood volume, electrical activity, discharge and absorption of hormones, etc.)...
Book Id: WPLBN0002097045 ► Abstract Full Text Search Details...aph or a subgraph glued bigraph. A bitree is a connected bigraph without any circuits. Now we proceed on to define cut-set in a connected bigra... ...offered by financial institutions / government o Obtaining irrigational and electrical facilities from government o Usage of technological equip...
Book Id: WPLBN0001235224 Subjects: Non Fiction, Education, Economics ► Abstract Full Text Search Details...asing quality with lower prices. Think about the vast improvement on both scores in electrical appliances. The VCR and PC of yesteryear cost thrice ... ...ct them to change their chemical reactions, the compounds that they contain, other electrical and chemical parameters, hormones, enzymes, catalysts... ...lled Rapid Eye Movement (REM). It is also associated with changes in the pattern of electrical activity of the brain (EEG). A dreaming person has th... ...he uterus contracts and the muscles at the base of the tongue enjoy a relaxation in electrical activity. These facts would indicate that dreaming i... ...uality even as prices decrease. Think about the vast improvement on both scores in electrical appliances. The VCR and PC of yesteryear cost thrice ... ...he air. This is a directed, specifically formed energy, intended to trigger certain circuits in the recipient brain. It should come as no surprise i... ... the air. This is directed, specifically formed energy, intended to trigger certain circuits in the recipient brain. It should come as no surprise i...
Book Id: WPLBN0001235225 Subjects: Non Fiction, Religion, Philosophy ► Abstract Full Text Search Details...asing quality with lower prices. Think about the vast improvement on both scores in electrical appliances. The VCR and PC of yesteryear cost thrice ... ...ct them to change their chemical reactions, the compounds that they contain, other electrical and chemical parameters, hormones, enzymes, catalysts... ...lled Rapid Eye Movement (REM). It is also associated with changes in the pattern of electrical activity of the brain (EEG). A dreaming person has th... ...he uterus contracts and the muscles at the base of the tongue enjoy a relaxation in electrical activity. These facts would indicate that dreaming i... ...uality even as prices decrease. Think about the vast improvement on both scores in electrical appliances. The VCR and PC of yesteryear cost thrice ... ...he air. This is a directed, specifically formed energy, intended to trigger certain circuits in the recipient brain. It should come as no surprise i... ... the air. This is directed, specifically formed energy, intended to trigger certain circuits in the recipient brain. It should come as no surprise i...
Book Id: WPLBN0001235260 Subjects: Non Fiction, Philosophy, Technology ► Abstract Full Text Search Details... the information about compatibility is inscribed in binary code and silicon circuits, rather than the molded plastic of a razor cartridge? What if en... ... a terrible decision, at least in my opinion, likely to be rejected by other Circuits and perhaps even eventually by the Supreme Court. But for the mo... ...ized and as well understood as valves, screws, capacitors, or resistors. The electrical engineer told to build a circuit does not go out and invent he... ...g, with biological black boxes that perform all of the standard functions of electrical or mechanical engineering—measuring flow, reacting to a high si...
Book Id: WPLBN0001235240 Subjects: Non Fiction, Education, Technology ► Abstract Full Text Search Details...ccess on it. As technologies such as digital ink and printable integrated circuits mature - hardware and software will have completed their inevitab... ...commercial e-mail messages a day over his three 45- megabit-per-second DS3 circuits. "If you were getting \$40,000 a month for each circuit," Scelson ... ...and of the nucleus. They are allowed to interact only through the average electrical field (which is the charge of the nucleus and the charge distri... ...ion of the field. This process is repeated until the final charge and the electrical field distribution agree with the input to the SE. Recursion ...
Book Id: WPLBN0001235244 Subjects: Non Fiction, Education, Internet ► Abstract Full Text Search Details...d spring-mounted needles to pass through the holes in each card, creating an electrical loop that ad- vanced the reader’s tally for a particular hole ... ...event sandbagging is seen, for example, in Webster Electric Co. v. Splitdorf Electrical Co., 264 U.S. 463 (1924) (denying claims of patent infringemen... ... 1, 2007). 23. See Gordon E. Moore, Cramming More Components onto Integrated Circuits, E- , Apr. 19, 1965, available at http://download.inte...
Book Id: WPLBN0002097015 Subjects: Non Fiction, Education, Science ► Abstract Full Text Search Details...s the self-awareness of ones own entire body. After death; the neural organic circuits of the human tool-brain cease to function. How could any ene... ...brain cease to function. How could any energy pattern relying on these neural circuits remain intact and not decompose, not fall apart and dissipate... ...ets for addictive substances. But then again… so are gas stations, so are electrical power plants. If there was any unbiased study done on the ... ...ing their infrastructures… reducing the entire population to beggardom with no electrical power, no water supply, no hospitals, no schools, no bridge... ...c charges were found… they were put into Leyden jars… Jars, laden with an electrical charge that could jar you loose from your dulled deadened aw... ...ic shock. It was used as a parlor trick to excite the ladies. What kind of electrical charge was found first? Static electricity. Dead electrici... ...l instinctive level. After the instinct-keys are punched. The subconscious circuits in the body of the computer go through complex, convoluted pa... ...re are no workers working at any job. So all the national infrastructures of electrical power, mass media, all forms of transportation, all governme... ... the invention of microchips: tiny decapitated heads with their own tiny brain circuits that could perform more complicated functions than the first ...
Book Id: WPLBN0001235216 Subjects: Fiction, Science, Future ► Abstract Full Text Search Details...ble to prove or disprove it in the future. Is it possible that there is an electrical or chemical reason for some people to think that they have had ... ...ng on your television set. It works, you don‘t have to know about all the circuits and science behind it. So if somebody tells you there is a god tha... ...entists have duplicated these out of the body experiences in people using electrical stimulation of certain brain areas. ―Another area of ...
Book Id: WPLBN0002118117 Subjects: Fiction, Drama and Literature, Literary fiction Collections: Literature, Language, Sociology, Education, Authors Community, Adventure ► Abstract Full Text Search Details.... Dreams meant that he was more than a mere carbon organism jilted around by electrical activity in the circuitry within the result of hornomal activi... ...d then it slowly abated, lost and tangled within new neurons, new electronic circuits with thoughts successfully attempting to understand his bitterne...
Book Id: WPLBN0000677125 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...the bird is neither seen nor heard; the torpid atmosphere, deprived of its electrical conditions, echoes neither the whirr of its wings nor its joyous... ...av- ing a centre and a principal of life, guaranteeing to each other their circuits, absorbed and absorbing like plants, and form- ing a vast Whole en...
Book Id: WPLBN0000661751 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details... Pekin had any right to expect. The Emperor returned after the briefest of circuits; he descended in great pomp from his throne, with the severest res... ... one who depends simply on an infinite memory, but also on an infinite and electrical power of com- bination; bringing together from the four winds, l...
Book Id: WPLBN0000661677 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details... one who depends simply on an infinite memory, but also on an infinite and electrical power of com- bination; bringing together from the four winds, l... ...as steadily as may be supposed. The emperor returned after the briefest of circuits; he descended in great pomp from his throne, with the severest res...
Book Id: WPLBN0000665854 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...s, i.e., those fires resulting from the col- lapse of buildings, damage to electrical systems, overturn- ing of stoves, and other primary effects of t... ...glass, ruined all equipment not already destroyed by the blast, ruined all electrical wir- 21 The Atomic Bombings of Hiroshima and Nagasaki ing, plum... ...7 months to get into operation. In addition to the damage sustained by the electrical and gas systems, severe damage to the water supply system was re... ...The majority of the fires were of secondary origin starting from the usual electrical short-circuits, broken gas lines, overturned stoves, open fires,... ...he fires were of secondary origin starting from the usual electrical short-circuits, broken gas lines, overturned stoves, open fires, charcoal brazier... ... the explosion itself or by the collapse of buildings contain- ing stoves, electrical fixtures, or any other equipment which might produce what is kno...
Book Id: WPLBN0000660062 ► Abstract Full Text Search Details...iesce. Let us take our bloated noth- ingness out of the path of the divine circuits. Let us un- learn our wisdom of the world. Let us lie low in the L... ...extrudes the old leaf? The law of nature is alternation for evermore. Each electrical state superinduces the oppo- site. The soul environs itself with... ...ficiency to all men’s eyes. In like manner, let a man fall into the divine circuits, and he is enlarged. Obedi- ence to his genius is the only liberat...
Book Id: WPLBN0000661439 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...ell entretied, braced in the beams, Stout as a horse, affectionate, haughty, electrical, I and this mystery here we stand. Clear and sweet is my soul,... ... or outside of pavement and land, Belonging to the winders of the circuit of circuits. One of that centripetal and centrifugal gang I turn and talk li... ...ng the tent ropes,) In the freshness the forenoon air, in the far stretching circuits and vistas again to peace restored, To the fiery fields emanativ...
Book Id: WPLBN0000655832 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...zen in the group. Educated in Morocco, Bahaji returned to Germany to study electrical engineering at the Technical University of Hamburg-Harburg. He s... ...occan, came to Germany in 1993, moving to Hamburg two years later to study electrical engineering at the T echnical University .A witness has recalled... ...uring familiarization flights near New Y ork—a target they referred to as “electrical engineering. ”According to Binal- shibh, the other pilots did no... ... Some callers were unable to connect with 911 operators, receiving an “all circuits busy” message. Standard operating procedure was for calls relat- i... ...e lead vehicle and a van; the proposed briefing the- ater had no phones or electrical outlets. Staff scrambled to prepare another room for the Preside... ...bh, Mar. 7, 2003; Oct. 11, 2003. Binalshibh since has denied that the term electrical engineering was used to refer to a potential nuclear target desp...
Book Id: WPLBN0000678927 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...that the mixture of large bod- ies of fresh and salt water may disturb the electrical equilibrium? Even during our occasional visits to this part of S... ... Darwin tempted to be explained, I believe by Mr. Murray, by their similar electrical condition. The circumstance of spiders of the same species, but ... ...arm than in cold countries; and I have sometimes imagined that a disturbed electrical condition of the atmosphere was most favourable to its productio... ...s, which it was neces- sary either to leap over or to avoid by making long circuits. We slept on the road, and next morning reached Valdivia, whence I...
Book Id: WPLBN0000662362 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...and miles; for so much at the least, it was likely to prove, including the circuits to which they were often compelled by rivers or hostile tribes, fr... ...igura- tion of clouds prevailed; this he took as a collateral proof of his electrical hypothesis. His own headaches, too, which in all probability wer...
1|2 Records: 1 - 20 of 29 - Pages: | 5,218 | 22,896 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2020-50 | latest | en | 0.723772 |
http://www.brightstorm.com/qna/question/7846/ | 1,369,367,308,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368704134547/warc/CC-MAIN-20130516113534-00003-ip-10-60-113-184.ec2.internal.warc.gz | 369,108,561 | 9,800 | Quick Homework Help
# how do you find the area of a traprzoid with a base of ten a heaght of six and a top of six. ⚑ Flag
by ruth027 at January 11, 2011
the formula is: h(b1+b2)/2 or height( base 1 +base 2)/2 to get the area
GURUKID January 11, 2011
48
yankeekid January 11, 2011
Use the formula: A=h1/2(b+b2)
Emmylou January 11, 2011
use A=height( base 1 +base 2)/2
azngk January 15, 2011 | 155 | 400 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2013-20 | latest | en | 0.88989 |
https://boardgames.stackexchange.com/questions/7366/when-should-you-side-lands-in-and-out/7368 | 1,656,372,810,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103344783.24/warc/CC-MAIN-20220627225823-20220628015823-00756.warc.gz | 189,002,145 | 62,667 | # When should you side lands in and out?
Some Magic writers advise players to side out a land when on the draw in Limited, in order to improve the probability of drawing a strong starting hand.
• Is it reasonable to do the same (side out a land on the draw) in Constructed? And, if so, why isn't it commonly done?
• Assuming you have a good reason to have land in your Constructed sideboard in the first place (usually cards like Wasteland), when is it strategically beneficial to bring in extra lands instead of only making spell-for-spell substitutions?
A recent case of this was in pre-Avacyn Restored Standard. There were some versions of UB Control that had 3 Nephalia Drownyards main-deck and another one in the sideboard.
In a control mirror with both decks full of reactive cards, the player who has mana advantage usually wins the game, because he or she can play many spells in one turn (e.g. play a threat, counter a removal spell against it, then counter the opponent's counter).
With lands in the sideboard, this deck could side in an extra land, taking out a removal spell. This way they would hit their land drops more easily and have another win condition in the deck, since milling was the best win condition in UB mirrors.
For reference, the 2nd place finisher of GP Baltimore 2012, as Hackworth pointed in the comments, used 2 lands in his sideboard. Its player goes so far as to say that Nephalia Drownyard is "the only card that matters in the mirror."
For the first question, I would say that while the same mathematics work for constructed as well, sideboarding lands just for mana balance reasons in constructed does not seem reasonable.
Firstly, in constructed the impact of a single land on the mana balance of your deck is smaller than in limited due to larger decksize (and the effect is quite small to begin with).
Secondly, in limited you have infinite lands in your sideboard, while in constructed you would have to remove a real card from the sideboard to fit in a land. Since the sideboard cards in constructed typically are very high impact cards in the right situation, this cost is quite significant, and likely higher than any benefit from potentially better mana balance.
• But the mana-balance part of the question just involves siding out a land on the draw, and putting that one land back into your maindeck on the play. This doesn't actually require keeping any land in your sideboard. May 15, 2012 at 12:57
• That is correct, I did not consider that. I would suspect that one remaining issue which is more likely to be valid in constructed, is that the number of lands is only part of the issue. You also need to have the right colors of lands. Since constructed decks often include many colors, it is likely more problematic to ensure a good distribution when changing the mana base, and I would suspect most don't find it worth the extra testing required (note: I'm not a very good magic player, so I don't really know the pro's reasoning). May 15, 2012 at 14:03
Tengfred has already made what I think is the crucial point here: your constructed sideboard allotment is a parsimonious 15 cards. If you're spending slots on the ability to subtly rejig your mana balance between games on the play and on the draw, you're probably doing it wrong.
Having said that, if you can genuinely only find 14 nonland cards that would improve your deck in any imaginable scenario, then I can imagine worse things than a land in the 15th slot. An extra land is almost always going to be a better draw against a creatureless deck than a removal spell, for instance!
• I think both of you misunderstood the question - the question is not about having a land in your sideboard, but about going from say 24 land and 36 non-land in the deck to 23 land and 37 non-land when you are sideboarding on the draw - you are not replacing one land with another. Since your first turn will have a draw, having 8 cards on your first turn and 52 left in deck change the odds of drawing your land enough to make it possibly viable. Sep 14, 2021 at 15:52 | 910 | 4,078 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-27 | longest | en | 0.968002 |
https://thekingofrome.com/winning-percentage-when-betting-heavy-favorites/ | 1,695,478,836,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506481.17/warc/CC-MAIN-20230923130827-20230923160827-00837.warc.gz | 637,207,840 | 14,215 | # What Is a Winning Percentage When Betting Heavy Favorites?
For most sports fans, seeing a big favorite win is always more exciting than a close game. After all, it usually means the game was in the bag from the very beginning. On the opposite end of the spectrum, a loss by a large favorite can be just as heartbreaking as one by a small underdog because it seems like the better odds should have tipped the balance in the bookie’s favor.
The truth is, betting heavy favorites in sports is extremely difficult. It’s all about understanding how to calculate a winning percentage when hitting the books with long odds. So let’s dive into the details to find out what makes a favorite so much more difficult to bet than an underdog, and how you can optimize your odds of making money when betting on these massive games.
## Odds Are Always A Double-Edged Sword
Before you start making money off these long shots, you need to understand the fundamentals of taking a gamble. The long odds in these situations are usually a sign that the bookmaker is trying to scare you off. They may tell you that betting a big favorite is a bad idea because it’s a sure thing and they’ll never pay off. But that’s not true at all!
It’s a well-known fact that bookmakers love to play with money, so if you’re seeing long odds on a game that means there’s someone trying to trick you into thinking it’s a bad bet. Remember, bookies thrive on fear and uncertainty, so they can make more money off of us irrational sports fans. That’s all the more reason not to fall for their tricks.
The good news is, even though it’s more difficult to bet on these massive favorites, they don’t always have to be a losing proposition. As long as you adhere to the fundamentals of betting and analysis, you can still make money off them. The key is in the little nuances that prove whether a team is capable of winning or losing a game. Let’s take a closer look.
## The Basics Of Calculating A Winning Percentage
First off, make sure you verify the accuracy of your winnings. Sometimes, unscrupulous bookmakers will take advantage of people who are not aware of the true score of a game. To prevent this, make sure you call their customer service department and ask for an official confirmation once the game has ended. Then, you can proceed to make another wager.
## Forming A Good Habits And Routine
To be able to successfully bet on these long shots, you need to develop good betting habits. If you’re used to winning at the casino, it might be hard to believe that you can lose money gambling, but it’s all about the odds. The more you bet, the more you’ll lose, so it’s logical that you’ll eventually wind up broke. It’s a known fact that gambling is not a way to make money; it’s a way to waste it. Similarly, if you’re used to betting on games with big favorites, it might be hard to believe that you can successfully place a wager on games with small favorites because, well, the odds are always in favor of the home team. This is where developing good habits and a routine come in handy. If you’re looking to place a bet on a specific game, stick to the same establishment and avoid changing booksies if you’re winning or losing. This will help you form a good record of what happens when you place a bet and will also help you verify the accuracy of your winnings or losses. When you establish these good habits and follow them strictly, you’ll be on your way to successfully betting on the favorites, which will eventually make you some money.
## Analyzing Past Performance
If you’re trying to make money off these long shots, it’s important to look at the past performance of the team in question. This way, you’ll be able to tell whether or not they’re capable of winning a game. While it’s always exciting to root for your favorite team, it’s critical to remember that they might not always be the best fit for winning a particular game. Sometimes, they’ll pull a rare upset and surprise everybody, but it’s rare. Looking at their historical performance is the only way to find out whether or not they’re capable of winning a particular game. This way, you won’t get emotionally attached to a team that you know is only capable of losing. That’s all the more reason to avoid betting on these games if you’re seeking to win money, as these are the types of games that you’ll inevitably lose.
## Proper Weighting Of The Odds
To begin with, the spread should be weighted in favor of the sportsbook. For example, a 7-point spread on a football game is usually a sign that the bookie is trying to trick you. That’s because the last thing they want is for you to win, since you’ll eventually come back and place another bet, and they’ll never pay off. This is why, in the case of a 7-point spread, they’ll often give you 5 points or less as a teaser or rebate. In the case of a 10-point spread, they’ll give you 7 points as a teaser or rebate.
As a general rule of thumb, always lean towards the underdogs. Seeing a big favorite win is always more exciting because it means more to the casual bettor. But if you want to be able to make money off these long shots, it’s important to understand the odds and properly weight them in your favor. Just know that it’s never a good idea to bet against the favorite in any sport, especially not in a game with long odds. | 1,155 | 5,348 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2023-40 | latest | en | 0.948512 |
https://www.coursehero.com/file/132810/ece159s-2004-qs04/ | 1,513,243,630,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948542031.37/warc/CC-MAIN-20171214074533-20171214094533-00091.warc.gz | 727,748,330 | 23,391 | ece159s_2004_qs04
ece159s_2004_qs04 - MAR-25-2004 12:16 erik P.01 University...
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Unformatted text preview: MAR-25-2004 12:16 erik P.01 University of Toronto ECE 159\$ - Electrical Fundamentals March 18lh 2004 Last Name: First Name: Student Number: Quiz 4 — Thevenin & Norton Equivalent Circuits, Nodal Analysis Question I [5 marks] Find the Norton equivalent of the circuit below with respect to the load RL . What value of RL maximizes the power delivered to the load? RL A B 2R T QQJV‘QJ‘J C:|(CM\B(- -' R A @ \$w~J -"“W '" ‘ | " RAMON LGQA \/ #:— élsg ‘ urnswidnon V’VAHA ; (3‘ ~~ as L \/ 7“BR ' i .— "l l = V’rH :"2_\/_ :,_>L W o i m R N r' n E: onLhwt C(cw‘A'l C9 F‘“;‘Q ETH: RN 0 1'0 Y A {K A "d V in? MAR-25-2004 12:16 erik P.02 University of Toronto ECE 159\$ - Electrical Fundamentals March 18th 2004 Question 2 [5 marks] For the circuit shown below, let I be the reference node. Using nodal analysis, find the current I and the potential at b. TOTAL P.02 ...
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ece159s_2004_qs04 - MAR-25-2004 12:16 erik P.01 University...
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Ask a homework question - tutors are online | 475 | 1,470 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2017-51 | latest | en | 0.679001 |
https://repl.it/@YatinBayya?tab=comments | 1,569,148,948,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514575484.57/warc/CC-MAIN-20190922094320-20190922120320-00095.warc.gz | 633,996,366 | 84,862 | Yatin
@YatinBayya (18) • Harvest Park Middle School
This is getting tense
@InfernoKay Good luck to you too!
@thec0mpletionist @raghavm Thanks, good luck to you guys also
hi im new at python
The Basics
This is an overview of the basics to help you boost your start with python. I won't go through everything of course but enough for you to start your first application. Make sure you selected Python 3 instead of Python 2.
Variables
Variables in python are just like the ones in math but you have to define them. You can store different types of data like the ones below...
Booleans - True/False
Strings- Text
Int/Integer - Numbers with no decimal
Double - Decimals
Long - Big Number
Short - Small Number
Byte- 0-8
This is how we define each one
``````var myBoolean = True
var myString = "A String"
var myInt= -34
var myDouble= 43.143
var myShort = 10
var myLong =34123
var myByte = 2``````
The variable names are in the middle which you will need to call it... and you can name the variables anything without any special characters(!, +, #, etc)
Note: True/False in booleans MUST be capitalized
Operators
Operators is math. Done! Ok, here are the different types...
Subtraction- - (It subtracts stuff)
Multiplication- is the star above the 8 key (It multiplies stuff)
Division- / (It divides stuff)
*Modulus- % (It finds the remainder of an equation)
Here is the syntax
``````var mathNumber = 42
As you can see my very AP math skills
Print Statements
The print statement is a very simple concept, all it does is display text in the terminal/console. In replit, you should see your program running on the side. Below is the syntax of the code for printing.
``print("Hello World")``
Whatever is in the quotes is printed so you can change it to "Creeper Aww Man" and it would work. We can also print variables like this (only if we have it defined)...
``print(myInt)``
To print variables along strings you can do...
``print("My Name is" + name)``
Input
Say you want to print What is your Name? and then print the user's name. To do this you would need to tell the computer you are getting there input.
``name = input("What is your name?")``
The code here makes a variable which you can use later to print or do something.
Note: the thing before the = sign is your variable name for pulling the data later.
If/Else Statements
What do we do when we want to check if data is equal to something... well if statements. This is the syntax to make if statements are...
``````if(age > 60):
else if(age == 9):
print("Greetings 9-year-old")
else:
print("Hello"+age+"year-old")``````
Note: Indentations (press tab key, NO SPACES) are REALLY important for the syntax. If it is wrong you program will crash. This is only when the line before has ":" which means it continues to the next line so you need to indent the things you want to execute when that statement is true.
Conclusion
This is a very small part of the programming world but I found some tutorials I think would help you out with your python coding.
Game making🎮
Website based Games/ Canvas Games
If you want to make games on the web I would recommend learning HTML/CSS and then start learning JS when you are confident with both HTML/CSS. After you are done learning JS I would suggest looking into Canvas Games (Google It) which there are a ton of tutorials for. This is the easiest way to game development. This can get you into game development in about a month or so if you are really dedicated.
Desktop/Pc Games
This genre is a bit complicated because of the variety of choices. You can do Python which is the easiest of which. But after you are thorough with the fundamentals, basics, and intermediate level programming, I recommend starting with PyGame which is a programming library(Existing Code that you can build upon) that helps you make games. Then they are harder languages for this like Java(Which Minecraft is made in) and C++(Which pretty much all games are made in). Remember this genre will take a year or so to master.
Apple Appstore
I recommend you to use an Apple device for this one, although possible in windows. This uses a programming language called Swift. This is made by apple and there are a ton of tutorials. The syntax is very similar to Java and C++ which I rather recommend you learn one of those before you go onto Swift.
The Google play store uses Java just like Desktop/Pc Games and learning this language you can do two genres in one go.
Pretty Much Everything
This is the path that I recommend, learn Unity which uses C#(Not to be confused with C++), for this learning C# is not necessary but recommended and search online for some Unity tutorials. The great part about this is that it will take a couple of months to master and this can be used for Websites, Xbox, Pc, Apple App Store, Google Play, Facebook Game Room, and much more. This is the most popular of which but it can be confusing at first so I recommend getting some programming experience before hopping on to this.
Good Luck with your game development and If this helps your question please select the checkmark next to this comment.
what did i do wrong
I am going to assume that you are trying to make a title as in a heading. What the title tag is not to make titles but to title the website which appears on the tab. To make a heading you need to do this
``````<html>
<title> HELLO WORLD!</title>
<body>
<h1>Hello World </h1>
</body>
</html>``````
Whatever you put in the body is the content of your website. And the H1 stands for heading 1. There are 6 levels of heading, h1 being the biggest and h6 being the smallest.
``````<h1>Hello World</h1>
<h2>Hello World</h2>
<h3>Hello World</h3>
<h4>Hello World</h4>
<h5>Hello World</h5>
<h6>Hello World</h6>``````
FYI: to add pargraphs which is achieved by doing html <p>CONTENT HERE</p>
I hope I was able to help if so select the checkmark next to my comment which would be greatly appreciated.
How do you change replit usernames?
@Zavexeon ok I will do so
Currently, the default libraries prevent you to automate the user's keyboard or mouse. Although this might be helpful, it guides you through the basics and eventually leads your question in chapter 18.
I hope that is helpful and good luck with your project. If this helps you I would appreciate if you would select this as the correct answer.
MUSIC HACKATHON: FAQ
Do the votes matter when you judge
error
@kiki2005 then you have some minor errors but I fixed it for you... I recommend to compare and contrast both and implement better syntax next time
``````global character
print("Please enter a number that fits with one of the below.")
print("3: Quit")
if c.isspace() != True:
character=0
character = character + 1
if character<=8:
print ("this password is too short")
if character>=24:
else:
point = 0
uppers = [x for x in password if x.isupper()]
uppernum = len(uppers)
lowers = [x for x in password if x.islower()]
lowernum = len(lowers)
point = point + length + (uppernum * 5) + (lowernum * 5)
print(point)``````
BAN ANM
Hopeflly he isnt hacking the people signed in with google cuz then he will have access to everything
hi im new at python
@ThanhTungTung My bad there is no else if there is only elif.
hi im new at python
@ThanhTungTung Your welcome. I am glad it helped it took me an hour to write it
I would buy a water bottle.
I mean a "non biased" \$5k challenge.
Make a rigged competition so Chandler can win something for the second time
Python Experts
I would say there is no such thing as learning a programming language fully. Even "experts" learn from a day to day basis and there are constantly new features and libraries to explore. By that you are meaning the fundlementals it really depends on how dedicated you are. It could be one day or one year. And your struggles right now will be the way you get better at programming :)
⛈Brainstorm ⛈What should we code?
@ebest Yes, you could add Unicodes but python accepts a certain range
🎵 MusiK-it (Bespoke musical tool) 🎵
posted to Challenge by YatinBayya
@abc3354 It is not played at the same time because the audio files are different lengths therefore the timing function must play one after one.
MUSIC HACKATHON: FAQ
@katyadee that is such a relief
@vedprad1 but when you say getElementByClassName() it is actually a list so you need to loop through it
error
``global character `` | 2,042 | 8,378 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2019-39 | longest | en | 0.881088 |
https://math.stackexchange.com/questions/1186672/role-of-group-actions-in-differential-geometry | 1,624,497,004,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488544264.91/warc/CC-MAIN-20210623225535-20210624015535-00190.warc.gz | 343,811,516 | 38,207 | # Role of Group actions in Differential Geometry
This is a rather soft question, my hope is to bring some order into the stuff I would like to learn about differential geometry -- here it is:
I was told over and over again that Geometry has to do with angles, length of curves, curvature etc.
However, most graduate textbooks on Differential Geometry start with smooth manifolds and keep studying them without every mentioning the presence of a Riemannian metric. And then there are group actions acting on smooth manifolds -- here I see the use of the word "Geometry" as well when results are obtained regarding the basic structure of the manifold, such as the way orbits are arranged, whether there are special orbits and how orbits smoothly collapse, whether these are certain bundles and so on.
I guess my question is the following: Is the study of group actions on smooth manifolds "more fundamental" than Riemannian geometry, or can one reduce any group action on a manifold to the presence of a (unique?) Riemannian metric on $M$ and study that metric instead? If not, are there "geometric" aspects of a smooth manifold that one cannot frame in terms of a group action?
(Maybe I should add that this question is motivated in the context of real (as opposed to complex) smooth manifolds)
Riemannian geometry can be interpreted as the study of $O_n$-structures. A choice of Riemannian metric is equivalent to a choice of $O_n$-structure. | 313 | 1,448 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2021-25 | latest | en | 0.952219 |
https://justaaa.com/physics/249785-the-junction-rules-states-that-at-a-junction | 1,718,357,797,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861545.42/warc/CC-MAIN-20240614075213-20240614105213-00737.warc.gz | 308,148,004 | 10,628 | Question
# The junction rules states that at a junction between several wires in a circuit, the total...
The junction rules states that at a junction between several wires in a circuit, the total current going into the junction equals the total current leaving the junction. Discuss what might happen if the rule were not true, for instance, if the current going into the junction were larger than the current leaving the junction. Explain your answer.
The sum of all the currents entering any junction point is equal to the sum of all the currents leaving that junction point.
If the rule wasn't satisfied then charge would build up at the junction points, violating basic fundamental steady-state assumption.Also the distribution of charges would have been impossible to calculate leading to a great mishap.Also some charges would have been lost leading to the discontinuous or complete stoppage of electrical current till we again general emf.The process would have been unable to attain a regular steady current.
#### Earn Coins
Coins can be redeemed for fabulous gifts. | 201 | 1,080 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-26 | latest | en | 0.96556 |
https://forums.techguy.org/threads/stupid-things-to-consider.326262/ | 1,627,569,225,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153860.57/warc/CC-MAIN-20210729140649-20210729170649-00077.warc.gz | 265,494,232 | 23,243 | # Stupid Things to Consider,
#### Hulk701
Banned
When it is late at night and I cant get to sleep I often consider stupid things.
Like this one:
Ways to Make the Roman Alphabet Simpler
Take the letter c. There is either a soft c or a hard c, but neither has any purpose because the soft c can be replaced by the letter s, and the hard c can be replaced by the letter k.
Now we come to q. The letter q has no purpose in our language at all because it can just as easily be replaced by the letters kw.
And x. There is no purpose to the letter x. You can say everything with the letters ecks as you can with the letter x. So get rid of it, we dont need it.
So there are three letters gone. Now lets look at how we can simplify words. First, why do we have so many double letters, when we need only one. Why do we spell hell with two lls rather than one? Or even the word spell?
Hell, I dont know. How about silent letters? Why do they exist if they are silent? Why not get rid of them all together. Especially that e on the end of all the French words weve stolen from their language. Give 'em back to the French, we don't need 'em.
Well you have a choice. You can either list your own silly conundrums or help solve some of mine. Im goen to bed
..
#### LuckyStrike
When I am trying to sleep and need to wind down, I think about "what if" questions.
What if the temperature were to drop 2 degrees per hour? What would the world look like in 8 hours?, 16 hours?, 32 hours?, 64 hours? etc, etc.
What if the temperature were to increase 2 degrees per hour? What would the world look like in ... so on and so forth.
What if starting April 1, 1944 we had an additional 1000 each of B-17's, B-24's, B-25's, B-26's, P-51's, P-38's, P-47's flying one sortie per day? Plus 2000 of each? Plus 5000 of each? An additional airborne division? 500 additional LST's? etc, etc. How would the course of the war have changed?
What if I had \$1000 and one acre of farm land? \$2000 and two acres........\$100,000 and 100 acres? etc, etc. When could I retire?
Heh, it worked, I'm getting drowsy.
#### MSM Hobbes
hulk - good! Funny thing is, I do pronounce as many of them poor, forgotten, ignored, and shunned so called "silent" letters in so many words. For example, the word sword... there IS a "w" there, right? Well, it does get its due mention when I speak this word. What is fun is when teaching children how to talk. For some reason, the woman did not really appreciate my style... strange.
As to what rattles through my mind, in a non-XXX rated fashion, well, there is that part that still buggers me when I contemplate what if you took a pie, divide it in half, and then that half in half, and then the following half by another half, and so on... Another way to say this is if you divide a number by 2, and then divide that number by 2, and so on and so on, you will never ever ever reach zero... yea, you'll get close, but never reach it. So, how can you touch something - if you approach it via that thinking, you can never actually reach out and feel it, yet, we can... hmmmm....
FWIW, if interested, look up a fella by the name of Zeno of Elea. And for those of yas that do take that challenge, notice how a certain Cheshire cat from a famous book about the adventures by a gal named Alice has a part in this story...
#### moonmist
Some people have wayyyyyyyyyyy to much time on their hands
#### MSM Hobbes
moonmist said:
Some people have wayyyyyyyyyyy to much time on their hands
Ohhhhhh, my dear, you bring up one of my fav subjects to contemplate when the night is dark, the stars are flickering, and your brain is awash with thoughts of the cosmos... Time? Well, what really is time? Some arbitrary concept postulated by humans to denote a meaning of temporal positions? Where a mind can experience complete synchronization with a past, a present, and a future now... and as the now that I am experiencing is the end of my lunch, I must get ready for another conference call and then a meeting.
#### moonmist
MSM Hobbes said:
Ohhhhhh, my dear, you bring up one of my fav subjects to contemplate when the night is dark, the stars are flickering, and your brain is awash with thoughts of the cosmos... Time? Well, what really is time? Some arbitrary concept postulated by humans to denote a meaning of temporal positions? Where a mind can experience complete synchronization with a past, a present, and a future now... and as the now that I am experiencing is the end of my lunch, I must get ready for another conference call and then a meeting.
the only thing i can answer to that is.......... I love you..........
#### MSM Hobbes
hobbes fur gets a redish tint to it now...
#### moonmist
MSM Hobbes said:
hobbes fur gets a redish tint to it now...
Looks good on ya !!
When I cant sleep I try to think of life in 5 dimentions; height, width, depth, time and emotion. I attempt to connect the five and try and prove emotion as a location and not a state of mind. (confusing? Thats the point ) After awhile of pondering this my mind gets tired and I can go to sleep
#### AKA Arizona
When I am tierd the voices in my head are very very quiet then they start getting louder & louder & louder I yell to them to SHUT UP then we all fall asleep,...........
PhSyyyyc................. my last interview sounded alot like that he was a nut case, he killed his brother the voices said to do it it must have been God. real wack job, he went strait to the 5th floor in a jacket.....
Actually, I start building things in my mind using vector graphs to keep things strait usually a bigger garage for my toys.....................
#### gotrootdude
What if, we insert ribonucleic acid strands into nanotubes for delivery of RNA interference? Why not use counterweighting on the bottoms of large ships to make them waveproof? Why can't we ionize steel store shelves with a small corona discharge device so that they don't get dusty? Instead of rail guns and laser rifles, why can't we combine the two and have rail guns where the projectile has a form of volatile rear coating with a cusp shape where a laser can be aimed at the rear of in order to further increase it's velocity? Why do schools teach kids sexual education instead of leaving it to the parents, don't people realize that those sex ed classes just put thoughts into sex crazed teenager's heads? Why should there be a "no child left behind" policy? Why do I need a tax EIN in order to subcontract for a international company? Why is it cheaper to ship to canada when you call the item a gift? Why do people press recycling when the true solution to pollution is dillution? What if I bend the plexiglass in that direction so that the mirrored side produces this effect?
Is the universe a product of the collision of dimensional membranes layered on top each other and vibrating so that collisions between membranes result in the creation of matter/time/space? If so what happens with matter being believed to be the product of 12 or more dimensions with the 11th and 12th dimension curled into itself in a tesseract-like manner? Whatever happened to physicist who believed gluons created strong interactions holding together time-space?
What if people think I think too much?
Oh, I forgot, what is the equation for computing frequency changes between musical notes? I used to have it memorized...
I'm not tired at all right now.. I do most of my project thinking when I'm half asleep.. Sleepiness increases creativeness.
Sometimes instead of counting sheep, I memorize product nomenclatures, read a mercks manual, mod something into something else, notate musical scale in my head, calculate lottery probabilities, research buying and selling prices, etc..
The one problem I have with falling asleep, is that often, I'm not sure of the barrier between when I'm asleep and when I'm awake.. I often wake up not knowing when I fell asleep, and having the feeling that I'd never been asleep. I often work on problems in my sleep and have been known to make myself a snack, use the bathroom, use the PC, etc, while I am asleep.. My wife says I even hold conversations in foriegn languages in my sleep.
....gotrootdude, put down your triple expresso latte, put down the Meta-Physics text book, take a deep breath, sit down and relax. Your brain is working way too hard way too fast.
How do you come up with some of that Gotrootdude? Do you have a background in Physics and Math-theory?
#### MSM Hobbes
gotrootdude:
Is the universe a product of the collision of dimensional membranes layered on top each other and vibrating so that collisions between membranes result in the creation of matter/time/space? If so what happens with matter being believed to be the product of 12 or more dimensions with the 11th and 12th dimension curled into itself in a tesseract-like manner? Whatever happened to physicist who believed gluons created strong interactions holding together time-space?
btw, while the string theory and the attraction of dark matter both have legs, gluons - oh, yea,,, talk to me!!!
gotrootdude:
What if people think I think too much?
Those that think about others thinking too much are not thinking about themselves enough - they're all goobers, let 'em! Mindless drones...
ps: omega, meta-physics is where its at! esp. if you throw in some Eastern & even native cultural concepts, beliefs, and religions into that mix.... yeeeeeha!!!
lol, used to be interested in that stuff but all I ever had to show for it was headaches
#### Moby
gotrootdude said:
What if, we insert ribonucleic acid strands into nanotubes for delivery of RNA interference? Why not use counterweighting on the bottoms of large ships to make them waveproof? Why can't we ionize steel store shelves with a small corona discharge device so that they don't get dusty? Instead of rail guns and laser rifles, why can't we combine the two and have rail guns where the projectile has a form of volatile rear coating with a cusp shape where a laser can be aimed at the rear of in order to further increase it's velocity? Why do schools teach kids sexual education instead of leaving it to the parents, don't people realize that those sex ed classes just put thoughts into sex crazed teenager's heads? Why should there be a "no child left behind" policy? Why do I need a tax EIN in order to subcontract for a international company? Why is it cheaper to ship to canada when you call the item a gift? Why do people press recycling when the true solution to pollution is dillution? What if I bend the plexiglass in that direction so that the mirrored side produces this effect?
Is the universe a product of the collision of dimensional membranes layered on top each other and vibrating so that collisions between membranes result in the creation of matter/time/space? If so what happens with matter being believed to be the product of 12 or more dimensions with the 11th and 12th dimension curled into itself in a tesseract-like manner? Whatever happened to physicist who believed gluons created strong interactions holding together time-space?
What if people think I think too much?
Oh, I forgot, what is the equation for computing frequency changes between musical notes? I used to have it memorized...
I'm not tired at all right now.. I do most of my project thinking when I'm half asleep.. Sleepiness increases creativeness.
Sometimes instead of counting sheep, I memorize product nomenclatures, read a mercks manual, mod something into something else, notate musical scale in my head, calculate lottery probabilities, research buying and selling prices, etc..
The one problem I have with falling asleep, is that often, I'm not sure of the barrier between when I'm asleep and when I'm awake.. I often wake up not knowing when I fell asleep, and having the feeling that I'd never been asleep. I often work on problems in my sleep and have been known to make myself a snack, use the bathroom, use the PC, etc, while I am asleep.. My wife says I even hold conversations in foriegn languages in my sleep.
I'm almost at the same spot as you Gotrootdude. I just need to figure out how worms move and why cheese used to be milk and I'll be right with you.
As Seen On | 2,886 | 12,274 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2021-31 | latest | en | 0.955722 |
http://math.stackexchange.com/questions/412663/absorbing-probability-and-martingale | 1,466,956,537,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783395346.72/warc/CC-MAIN-20160624154955-00155-ip-10-164-35-72.ec2.internal.warc.gz | 200,732,782 | 16,862 | Absorbing probability and Martingale
This is a problem from the book "Markov chains". Let $(X_n)_{n\ge 0}$ be a Markov chain on $I$ and let $A$ be an absorbing set in $I$. Set $$T=\inf\{n\ge 0 : X_n \in A\}$$ and $$h_i = \mathbb{P}_i(X_n \in A \text{ for some } n \ge 0) = \mathbb{P}_i(T<\infty)$$ Show that $M_n = h(X_n)$ is a martingale.
This is my solution: \begin{align*} E[M_{n+1} \mid \mathcal{F}_n] = E[h(X_{n+1}) \mid \mathcal{F}_n] &= \sum_{j \in I} p_{X_n,j}h(j) \\ &= h(X_n) \text{ (First step analysis)}\\ &= M_n \end{align*} Am I correct or not? I'm afraid I missed something. Thanks!
-
Some notions first. To show that $h(X_n)$ is a martingale it is just sufficient to check whether $$\mathsf E[h(X_{n+1})|X_n] = h(X_n) \iff \mathsf E_x[h(X_1)] = h(x) \iff h(x) = Ph(x) \tag{1}$$ since $(X_n)$ is a Markov process. Here $P$ is a transition operator $$Pf(x):=\mathsf E_x[f(X_1)] = \sum_{y\in I}p_{x,y}f(y).$$ and all functions satisfying $Pf=f$ are called harmonic. As a result, $(1)$ shows that $f$ is harmonic if and only if $f(X_n)$ is a martingale.
So, your step is right where you get $$\mathsf E[M_{n+1}|\mathscr F_n] = \sum_{y\in I}p_{X_n,y}h(y)$$ is correct. To show that the latter is $h(X_n)$, just use the formula $$h(x) = 1_A(x)+1_{A^c}(x)Ph(x). \tag{2}$$ In general, $(2)$ describes the hitting probability for any set $A$ and then $h(X_n)$ is a supermartingale in general. It is a martingale provided $A$ is absorbing. | 548 | 1,449 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2016-26 | latest | en | 0.722176 |
https://www.midasoft.com/bridge-library/soilstructureusingnonlinearanalysis | 1,725,849,741,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651053.52/warc/CC-MAIN-20240909004517-20240909034517-00488.warc.gz | 845,985,427 | 22,825 | # Soil Structure Interaction during Earthquake using Boundary Nonlinear Analysis
#### Author: MIDASoft
##### Publish Date: 21 May, 2024
Summary: The blog explains the importance of soil-structure interaction during the seismic design of bridges, along with current practices. Want to know how easily boundary nonlinear time history analysis can be used to simulate nonlinear soil behavior during earthquakes using Midas? Read to discover it.
## What is Nonlinear Analysis?
Before delving into nonlinearity, let's first see what a simple linear analysis entails. A linear analysis is an analysis where the stiffness of the structure remains constant throughout the process; the stiffness matrix remains the same. Consequently, a linear correlation between applied forces and deformations is observed.
On the other hand, a nonlinear analysis involves applied forces and displacements showing a nonlinear relationship; the stiffness of the system is not constant throughout the analysis.
Nonlinear analysis can be categorized mainly into three: geometric, material, and boundary nonlinear analysis. In this blog, my primary focus will be on boundary nonlinear analysis, where the stiffness of the boundary changes concerning time or loading.
Fig 1. Nonlinearity types
Most of the formulas in soil mechanics are derived assuming soil to be an elastic material. However, in reality, soil P-Y curves are not linear, and their slope changes with loading. Thus, we can conclude that soil is nonlinear.
Current Scenario:
Engineers use different methods for seismic analysis of bridges. Linear analysis includes response spectrum and linear time history analysis, while Nonlinear Seismic Analysis includes Pushover Analysis and Nonlinear Time History Analysis.
Many engineers prefer to simplify their approach and rely on linear analysis, such as response spectrum. However, in any linear analysis, the nonlinear behavior of the soil is not accounted for. Typically, only the initial stiffness of the soil is considered for analysis, treating it as a linear spring, which tends to yield slightly conservative results in most cases.
Let's explore this further, Imagine a man pushing a wall. As he applies more force, the wall either yields or topples, reducing the force he experiences due to decreased reaction from the wall. Now, think of the scenario where the wall is not moving; as force increases, more reactions are exerted onto the man.
The same is true for soil. During response spectrum analysis, the forces in the structure will increase since the soil is considered linear and does not yield. However, incorporating nonlinear soil behavior allows for more realistic and often more economical seismic designs.
How to Consider Nonlinear Soil Behavior during Seismic Analysis?
Now, let's address the core question: How to simulate it? Using boundary nonlinear time history analysis.
During a Boundary Nonlinear Time History Analysis, the equations of motion for the structure are solved numerically considering the change in stiffness of the structure (Nonlinear Soil behavior) concerning loading for each time step.
In other words, a certain portion of the structure is considered nonlinear during time history analysis, in this case, the entire structure as linear except for the soil whose stiffness changes with applied load.
One of the primary challenges engineers encounter during nonlinear time history analysis is the scarcity of earthquake data, often necessitating the scaling of earthquakes.
Simulation using Midas
Currently, in Midas Civil, the multi-linear springs are converted to linear springs during any seismic analysis like Eigen Value, Response Spectrum and Time History (both linear and nonlinear), leading to slightly conservative results in most cases.
For example, when a bilinear curve, as shown in the figure, is used to simulate soil, the software considers only the initial curve and treats the spring as linear with a stiffness of 2000 kN/m.
We can use the General Link feature in Midas to simulate the exact soil stiffness as a workaround.
A general link is considered a dynamic boundary nonlinear element; a nonlinear seismic time history analysis can generate results considering the soil behavior. For any linear analysis, these links exhibit a linear behavior.
Consider a straightforward three-span bridge to compare the outcomes of linear and nonlinear time history analyses, aiming to grasp the impact of soil-structure interaction during seismic assessments. Nonlinear soil behavior is replicated by establishing general links connecting the substructure node to a fixed support, representing the stiffness of the soil continuum. Time history analysis is then conducted to replicate seismic loading.
Figure 2: Sample Bridge Model with General Links simulating Nonlinear Soil Behavior
Figure 3: Sample model - Nonlinear time history bending moment results.
Figure 4: Sample model - Linear Time History
Upon reviewing the results, linear time history analysis yields 1743.33 kNm, while nonlinear time history analysis produces 1253.9 kNm — 28% lower than the former. This discrepancy arises primarily because linear analysis assumes the soil to be elastic, thus offering greater stiffness to the substructure, leading to increased forces. Conversely, in boundary nonlinear time history analysis, the soil yields, resulting in reduced substructure stiffness and consequently lower seismic forces.
To sum up, bridges are longer and more complicated than ever before, and incorporating the dynamic nature of the soil is imperative to ensure resilient, safe, and economically viable seismic designs. By leveraging simulation techniques such as boundary nonlinear time history analysis, engineers can accurately capture the nonlinear behavior of soil and its impact on structural integrity.
If you want to explore further, Click on the downloadable materials and follow the step-by-step process to consider nonlinear soil behavior during Boundary Nonlinear Analysis. You can also access the model sample file and spring stiffness verification for a better understanding.
About the Author: Rohit Joseph is a structural engineer with over two years of experience at Midas IT, where he works as a Technical Support Engineer. He holds a Master’s degree in Structural Engineering from NIT Surat. Rohit collaborates with bridge engineers worldwide, offering expert assistance with technical queries related to bridge engineering and Midas software. | 1,187 | 6,504 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2024-38 | latest | en | 0.924086 |
https://www.aqua-calc.com/page/density-table/substance/caribsea-coma-and-blank-marine-coma-and-blank-aragonite-coma-and-blank-aragamax-blank-sugar-sized-blank-sand | 1,708,791,954,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474541.96/warc/CC-MAIN-20240224144416-20240224174416-00757.warc.gz | 641,410,033 | 9,446 | # CaribSea, Marine, Aragonite, Aragamax Sugar-Sized Sand
## CaribSea, Marine, Aragonite, ...60 weighs 1.5378 g/cm³ (0.8889 oz/in³)
• CaribSea, Marine, Aragonite, Aragamax Sugar-Sized Sand weighs 1.54 gram per cubic centimeter or 1 537.8 kilogram per cubic meter, i.e. density of caribSea, Marine, Aragonite, Aragamax Sugar-Sized Sand is equal to 1 537.8 kg/m³. In Imperial or US customary measurement system, the density is equal to 96 pound per cubic foot [lb/ft³], or 0.89 ounce per cubic inch [oz/inch³] .
• CaribSea, Marine, Aragonite, Aragamax Sugar-Sized Sand weighs 1 537.8 kg/m³ (96.00172 lb/ft³) with specific gravity of 1.5378 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 ]
### CaribSea, Marine, Aragonite, Aragamax Sugar-Sized Sand density values, grouped by weight and shown as value of density, unit of density
23.73 gr/cm³ 23 731.88 gr/dm³ 672 012.02 gr/ft³ 388.9 gr/in³ 23 731 880.75 gr/m³ 0.02 gr/mm³ 18 144 324.58 gr/yd³ 23 731.88 gr/l 5 932.97 gr/metric c 355.98 gr/metric tbsp 118.66 gr/metric tsp 23.73 gr/ml 5 614.68 gr/US c 701.75 gr/fl.oz 89 834.94 gr/US gal 11 229.37 gr/pt 22 458.74 gr/US qt 350.92 gr/US tbsp 116.97 gr/US tsp
1.54 g/cm³ 1 537.8 g/dm³ 43 545.65 g/ft³ 25.2 g/in³ 1 537 800 g/m³ 0 g/mm³ 1 175 732.46 g/yd³ 1 537.8 g/l 384.45 g/metric c 23.07 g/metric tbsp 7.69 g/metric tsp 1.54 g/ml 363.83 g/US c 45.47 g/fl.oz 5 821.21 g/US gal 727.65 g/pt 1 455.3 g/US qt 22.74 g/tbsp 7.58 g/tsp
0 kg/cm³ 1.54 kg/dm³ 43.55 kg/ft³ 0.03 kg/in³ 1 537.8 kg/m³ 1.54 × 10-6 kg/mm³ 1 175.73 kg/yd³ 1.54 kg/l 0.38 kg/metric c 0.02 kg/metric tbsp 0.01 kg/metric tsp 0 kg/ml 0.36 kg/US c 0.05 kg/fl.oz 5.82 kg/US gal 0.73 kg/pt 1.46 kg/US qt 0.02 kg/tbsp 0.01 kg/tsp
1.51 × 10-6 long tn/cm³ 0 long tn/dm³ 0.04 long tn/ft³ 2.48 × 10-5 long tn/in³ 1.51 long tn/m³ 1.51 × 10-9 long tn/mm³ 1.16 long tn/yd³ 0 long tn/l 0 long tn/metric c 2.27 × 10-5 long tn/metric tbsp 7.57 × 10-6 long tn/metric tsp 1.51 × 10-6 long tn/ml 0 long tn/US c 4.81 × 10-5 long tn/fl.oz 0.01 long tn/US gal 0 long tn/pt 0 long tn/US qt 2.24 × 10-5 long tn/US tbsp 7.46 × 10-6 long tn/US tsp
1 537 800 µg/cm³ 1 537 800 000 µg/dm³ 43 545 646 701.48 µg/ft³ 25 200 027.02 µg/in³ 1 537 800 000 000 µg/m³ 1 537.8 µg/mm³ 1 175 732 460 632.4 µg/yd³ 1 537 800 000 µg/l 384 450 000 µg/metric c 23 067 000 µg/metric tbsp 7 689 000 µg/metric tsp 1 537 800 µg/ml 363 825 390.86 µg/US c 45 478 173.82 µg/fl.oz 5 821 206 235.28 µg/US gal 727 650 780.18 µg/pt 1 455 301 560.36 µg/US qt 22 739 086.91 µg/tbsp 7 579 695.62 µg/tsp
1 537.8 mg/cm³ 1 537 800 mg/dm³ 43 545 646.7 mg/ft³ 25 200.03 mg/in³ 1 537 800 000 mg/m³ 1.54 mg/mm³ 1 175 732 460.63 mg/yd³ 1 537 800 mg/l 384 450 mg/metric c 23 067 mg/metric tbsp 7 689 mg/metric tsp 1 537.8 mg/ml 363 825.39 mg/US c 45 472.75 mg/fl.oz 5 821 206.25 mg/US gal 727 650.78 mg/pt 1 455 301.56 mg/US qt 22 739.09 mg/tbsp 7 579.7 mg/tsp
0.05 oz/cm³ 54.24 oz/dm³ 1 536.03 oz/ft³ 0.89 oz/in³ 54 244.3 oz/m³ 5.42 × 10-5 oz/mm³ 41 472.74 oz/yd³ 54.24 oz/l 13.56 oz/metric c 0.81 oz/metric tbsp 0.27 oz/metric tsp 0.05 oz/ml 12.83 oz/US c 1.72 oz/fl.oz 205.34 oz/US gal 25.67 oz/pt 51.33 oz/US qt 0.8 oz/tbsp 0.27 oz/tsp
0.99 dwt/cm³ 988.83 dwt/dm³ 28 000.5 dwt/ft³ 16.2 dwt/in³ 988 828.36 dwt/m³ 0 dwt/mm³ 756 013.53 dwt/yd³ 988.83 dwt/l 247.21 dwt/metric c 14.83 dwt/metric tbsp 4.94 dwt/metric tsp 0.99 dwt/ml 233.95 dwt/US c 29.24 dwt/fl.oz 3 743.12 dwt/US gal 467.89 dwt/pt 935.78 dwt/US qt 14.62 dwt/US tbsp 4.87 dwt/US tsp
0 lb/cm³ 3.39 lb/dm³ 96 lb/ft³ 0.06 lb/in³ 3 390.27 lb/m³ 3.39 × 10-6 lb/mm³ 2 592.05 lb/yd³ 3.39 lb/l 0.85 lb/metric c 0.05 lb/metric tbsp 0.02 lb/metric tsp 0 lb/ml 0.8 lb/US c 0.11 lb/fl.oz 12.83 lb/US gal 1.6 lb/pt 3.21 lb/US qt 0.05 lb/tbsp 0.02 lb/tsp
1.7 × 10-6 short tn/cm³ 0 short tn/dm³ 0.05 short tn/ft³ 2.78 × 10-5 short tn/in³ 1.7 short tn/m³ 1.7 × 10-9 short tn/mm³ 1.3 short tn/yd³ 0 short tn/l 0 short tn/metric c 2.54 × 10-5 short tn/metric tbsp 8.48 × 10-6 short tn/metric tsp 1.7 × 10-6 short tn/ml 0 short tn/US c 5.38 × 10-5 short tn/fl.oz 0.01 short tn/US gal 0 short tn/pt 0 short tn/US qt 2.51 × 10-5 short tn/US tbsp 8.36 × 10-6 short tn/US tsp
0 sl/cm³ 0.11 sl/dm³ 2.98 sl/ft³ 0 sl/in³ 105.37 sl/m³ 1.05 × 10-7 sl/mm³ 80.56 sl/yd³ 0.11 sl/l 0.03 sl/metric c 0 sl/metric tbsp 0 sl/metric tsp 0 sl/ml 0.02 sl/US c 0 sl/fl.oz 0.4 sl/US gal 0.05 sl/pt 0.1 sl/US qt 0 sl/tbsp 0 sl/tsp
0 st/cm³ 0.24 st/dm³ 6.86 st/ft³ 0 st/in³ 242.16 st/m³ 2.42 × 10-7 st/mm³ 185.15 st/yd³ 0.24 st/l 0.06 st/metric c 0 st/metric tbsp 0 st/metric tsp 0 st/ml 0.06 st/US c 0.01 st/fl.oz 0.92 st/US gal 0.11 st/pt 0.23 st/US qt 0 st/US tbsp 0 st/US tsp
1.54 × 10-6 t/cm³ 0 t/dm³ 0.04 t/ft³ 2.52 × 10-5 t/in³ 1.54 t/m³ 1.54 × 10-9 t/mm³ 1.18 t/yd³ 0 t/l 0 t/metric c 2.31 × 10-5 t/metric tbsp 7.69 × 10-6 t/metric tsp 1.54 × 10-6 t/ml 0 t/US c 4.55 × 10-5 t/fl.oz 0.01 t/US gal 0 t/pt 0 t/US qt 2.27 × 10-5 t/tbsp 7.58 × 10-6 t/tsp
0.05 oz t/cm³ 49.44 oz t/dm³ 1 400.03 oz t/ft³ 0.81 oz t/in³ 49 441.42 oz t/m³ 4.94 × 10-5 oz t/mm³ 37 800.68 oz t/yd³ 49.44 oz t/l 12.36 oz t/metric c 0.74 oz t/metric tbsp 0.25 oz t/metric tsp 0.05 oz t/ml 11.7 oz t/US c 1.46 oz t/fl.oz 187.16 oz t/US gal 23.39 oz t/pt 46.79 oz t/US qt 0.73 oz t/US tbsp 0.24 oz t/US tsp
0 troy/cm³ 4.12 troy/dm³ 116.67 troy/ft³ 0.07 troy/in³ 4 120.12 troy/m³ 4.12 × 10-6 troy/mm³ 3 150.06 troy/yd³ 4.12 troy/l 1.03 troy/metric c 0.06 troy/metric tbsp 0.02 troy/metric tsp 0 troy/ml 0.97 troy/US c 0.12 troy/fl.oz 15.6 troy/US gal 1.95 troy/pt 3.9 troy/US qt 0.06 troy/US tbsp 0.02 troy/US tsp
CaribSea, Marine, Aragonite, Aragamax Sugar-Sized Sand density values in 285 units of density, in the form of a matrix
Density = weight ÷ volumemicrogram (µg)milligram (mg)gram (g)kilogram (kg)tonne (t)ounce (oz)pound (lb)volume unitgrain (gr)slug (sl)short ton (short tn)long ton (long tn)stone (st)troy ounce (oz t)troy pound (troy)pennyweight (dwt)
cubic millimeter1 537.81.54<0.01<0.01<0.01<0.01<0.01cubic millimeter0.02<0.01<0.01<0.01<0.01<0.01<0.01<0.01
cubic centimeter1 537 8001 537.81.54<0.01<0.010.05<0.01cubic centimeter23.73<0.01<0.01<0.01<0.010.05<0.010.99
cubic decimeter1 537 800 0001 537 8001 537.81.54<0.0154.243.39cubic decimeter23 731.880.11<0.01<0.010.2449.444.12988.83
cubic meter1 537 800 000 0001 537 800 0001 537 8001 537.81.5454 244.33 390.27cubic meter23 731 880.75105.371.71.51242.1649 441.424 120.12988 828.36
milliliter1 537 8001 537.81.54<0.01<0.010.05<0.01milliliter23.73<0.01<0.01<0.01<0.010.05<0.010.99
liter1 537 800 0001 537 8001 537.81.54<0.0154.243.39liter23 731.880.11<0.01<0.010.2449.444.12988.83
metric teaspoon7 689 0007 6897.690.01<0.010.270.02metric teaspoon118.66<0.01<0.01<0.01<0.010.250.024.94
metric tablespoon23 067 00023 06723.070.02<0.010.810.05metric tablespoon355.98<0.01<0.01<0.01<0.010.740.0614.83
metric cup384 450 000384 450384.450.38<0.0113.560.85metric cup5 932.970.03<0.01<0.010.0612.361.03247.21
cubic inch25 200 027.0225 200.0325.20.03<0.010.890.06cubic inch388.9<0.01<0.01<0.01<0.010.810.0716.2
cubic foot43 545 646 701.4843 545 646.743 545.6543.550.041 536.0396cubic foot672 012.022.980.050.046.861 400.03116.6728 000.5
cubic yard1 175 732 460 632.41 175 732 460.631 175 732.461 175.731.1841 472.742 592.05cubic yard18 144 324.5880.561.31.16185.1537 800.683 150.06756 013.53
US teaspoon7 579 695.627 579.77.580.01<0.010.270.02US teaspoon116.97<0.01<0.01<0.01<0.010.240.024.87
US tablespoon22 739 086.9122 739.0922.740.02<0.010.80.05US tablespoon350.92<0.01<0.01<0.01<0.010.730.0614.62
US fluid ounce45 478 173.8245 472.7545.470.05<0.011.720.11US fluid ounce701.75<0.01<0.01<0.010.011.460.1229.24
US cup363 825 390.86363 825.39363.830.36<0.0112.830.8US cup5 614.680.02<0.01<0.010.0611.70.97233.95
US pint727 650 780.18727 650.78727.650.73<0.0125.671.6US pint11 229.370.05<0.01<0.010.1123.391.95467.89
US quart1 455 301 560.361 455 301.561 455.31.46<0.0151.333.21US quart22 458.740.1<0.01<0.010.2346.793.9935.78
US gallon5 821 206 235.285 821 206.255 821.215.820.01205.3412.83US gallon89 834.940.40.010.010.92187.1615.63 743.12
#### Foods, Nutrients and Calories
KROGER, YELLOW POPCORN, UPC: 011110914538 weigh(s) 8 grams per metric cup or 0.3 ounce per US cup, and contain(s) 367 calories per 100 grams (≈3.53 ounces) [ weight to volume | volume to weight | price | density ]
13383 foods that contain Vitamin E (alpha-tocopherol). List of these foods starting with the highest contents of Vitamin E (alpha-tocopherol) and the lowest contents of Vitamin E (alpha-tocopherol), and Recommended Dietary Allowances (RDAs) for Vitamin E (Alpha-Tocopherol)
#### Gravels, Substances and Oils
CaribSea, Freshwater, Eco-Complete Planted, Black weighs 865 kg/m³ (54.00019 lb/ft³) with specific gravity of 0.865 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 ]
Chromium(III) fluoride, anhydrous [CrF3] weighs 3 800 kg/m³ (237.22625 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ]
Volume to weightweight to volume and cost conversions for Safflower oil with temperature in the range of 10°C (50°F) to 140°C (284°F)
#### Weights and Measurements
A cubic micrometer (µm³) is a derived metric SI (System International) measurement unit of volume with sides equal to one micrometer or micron (1μm)
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.
mil² to fur² conversion table, mil² to fur² unit converter or convert between all units of area measurement.
#### Calculators
Oils, fuels, refrigerants: compute volume by weight and temperature | 4,535 | 9,992 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2024-10 | latest | en | 0.325827 |
https://math.answers.com/Q/What_is_the_LCM_of_140_and_77 | 1,695,704,731,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510149.21/warc/CC-MAIN-20230926043538-20230926073538-00814.warc.gz | 441,714,636 | 45,299 | 0
# What is the LCM of 140 and 77?
Updated: 8/20/2019
Wiki User
11y ago
LCM x GCD = 140 x 77 140 = 2 x 2 x 5 x 7
77 = 7 x 11
GCD = 7
LCM = 140 x 77 / 7 = 140 x 11 = 1540
Wiki User
11y ago
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The LCM is 77.
The LCM is 77.
### What is the LCM of 77 and 11?
The Least Common Multiple (LCM) of 77 and 11 is 77.
### What is the LCM 140 and 28?
LCM 140 and 28 is 140.
The LCM is 140.
The LCM is 140.
The LCM is 140.
The LCM is: 140
### What is the LCM for 35 70 and 140?
The LCM of 35, 70, and 140 is 140.
The LCM is 140.
The LCM is 140. | 326 | 825 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2023-40 | latest | en | 0.900814 |
http://digilib.stikom-db.ac.id/gdl42/gdl.php?mod=browse&op=read&id=gdlhub-gdl-qiulinshen-3028 | 1,674,794,999,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764494936.89/warc/CC-MAIN-20230127033656-20230127063656-00827.warc.gz | 10,867,613 | 4,036 | Path: Top -> Journal -> Telkomnika -> 2015 -> Vol 13, No 2: June
Design and Simulation of Small Space Parallel Parking Fuzzy Controller
Design and Simulation of Small Space Parallel Parking Fuzzy Controller
Journal from gdlhub / 2016-11-16 06:38:12
Oleh : Qiulin Sheng, Jie Min, Xing Zhang, Zhengwen Zhang, Yi Li, Guangya Liu, Telkomnika
Dibuat : 2015-06-01, dengan 1 file
Keyword : Parallel Parking, Fuzzy Control, Matlab Simulation
Based on the nonlinearity and time-variation of automatic parking path tracking control system, we use fuzzy control theories and methods to explore the control rules to improve fuzzy controllers and design an automobile steering controller. Then we build the simulation experiment platform of an automobile in Simulink to simulate the reversing settings of parallel parking. This paper adopts the Mamdani control rules; the membership function is the Gauss function. This paper verifies the fuzzy controller's kinematic model and the advantages of fuzzy control rules. Simulation results show that the design of the controller allows the automobile to stop into the parking space smaller than the space obtained by planning path, and automatic parking becomes possible in the parking plot. The control system is characterized by small tracking error, fast response and high reliability.
Deskripsi Alternatif :
Based on the nonlinearity and time-variation of automatic parking path tracking control system, we use fuzzy control theories and methods to explore the control rules to improve fuzzy controllers and design an automobile steering controller. Then we build the simulation experiment platform of an automobile in Simulink to simulate the reversing settings of parallel parking. This paper adopts the Mamdani control rules; the membership function is the Gauss function. This paper verifies the fuzzy controller's kinematic model and the advantages of fuzzy control rules. Simulation results show that the design of the controller allows the automobile to stop into the parking space smaller than the space obtained by planning path, and automatic parking becomes possible in the parking plot. The control system is characterized by small tracking error, fast response and high reliability.
PropertiNilai Properti
ID Publishergdlhub
OrganisasiTelkomnika
Nama KontakHerti Yani, S.Kom
AlamatJln. Jenderal Sudirman
KotaJambi
DaerahJambi
NegaraIndonesia
Telepon0741-35095
Fax0741-35093
E-mail CKOelibrarystikom@gmail.com
Print ...
Kontributor... | 531 | 2,492 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2023-06 | longest | en | 0.816106 |
http://scindeks.ceon.rs/article.aspx?query=RELAKW%26and%26GUM&page=1&sort=1&stype=0&backurl=%2FRelated.aspx%3Fartak%3DGUM | 1,652,748,595,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662515466.5/warc/CC-MAIN-20220516235937-20220517025937-00380.warc.gz | 56,500,464 | 12,144 | ## Akcije
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2014, vol. 69, br. 3, str. 549-554
Dva postupka procene merne nesigurnosti rezultata merenja fazne razlike metodom tri voltmetra
Ključne reči: fazna razlika; metoda tri voltmetra; merna nesigurnost; GUM; Dodatak 1 GUM
Sažetak
U radu je prikazan postupak merenja fazne razlike izmenu dva sinusna električna napona koristeći metodu tri voltmetra. Merna nesigurnost rezultata merenja fazne razlike procenjena je na dva načina: u skladu sa Uputstvom za izražavanje nesigurnosti u merenju (GUM) i u skladu sa Dodatkom 1 GUM - Prenos raspodela korišćenjem metode Monte Karlo. Upoređeni su dobijeni rezultati za mernu nesigurnost.
Reference *** (2000) 3458A Multimeter: Users guide. Agilent *** Calibration and measurement capabilities: CMC. http://kcdb.bipm.org/appendixc/EM/DE/EM_DE *** (1995) Guide to the expression of uncertainty in measurement. Switzerland: ISO, BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML *** (2008) ISO IEC GUIDE 98-3/Suppl.1: Uncertainty of measurement Part 3: Guide to the expression of uncertainty in measurement (GUM:1995) Supplement 1: Propagation of distributions using a Monte Carlo method *** (2008) GUIDE OIML G 1-100: Evaluation of measurement data: Guide to the expression of uncertainty in measurement. OIML *** (2008) ISO IEC GUIDE 98-3: Uncertainty of measurement: Guide to the expression of uncertainty in measurement. Part 3, (GUM:1995) *** (2008) JCGM 200:2008 International vocabulary of metrology: Basic and general concepts and associated terms. VIM, 3rd edition Callegaro, L., D`Elia, V. (2001) Automated system for inductance realization traceable to AC resistance with a three-voltmeter method. IEEE Transactions on Instrumentation and Measurement, 50(6): 1630-1633 Clarke, K.K., Hess, D.T. (1990) Phase measurement, traceability, and verification theory and practice. IEEE Transactions on Instrumentation and Measurement, 39(1): 52-55 Joint Committee for Guides in Metrology (2006) Evaluation of measurement data, supplement 1 to the 'Guide to the expression of uncertainty in measurement': Propagation of distributions using a Monte Carlo method. Nacrt Joint Committee for Guides in Metrology (2006) Evaluation of measurement data, supplement 1 to the 'Guide to the expression of uncertainty in measurement': Propagation of distributions using a Monte Carlo method. Nacrt Mohns, E., Kahmann, M. (2007) Heterodyne Measurement System (HMS) for Determining Phase Angles. IEEE Transactions on Instrumentation and Measurement, 56(2): 505-508 Ramm, G., Moser, H., Braun, A. (1999) A new scheme for generating and measuring active, reactive, and apparent power at power frequencies with uncertainties of 2.5×10/sup -6/. IEEE Transactions on Instrumentation and Measurement, 48(2): 422-426 Svenson, S. (1999) Power measurement techniques for non-sinusoidal conditions. Goteborg, Sweden: Chalmers university of technology, Doctoral thesis for the degree of PhD Webster, J., ed. (1999) The measurement, instrumentation and sensors handbook. CRC Press, poglavlje 41 | 952 | 3,243 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2022-21 | latest | en | 0.180069 |
https://assignment-help.co/2022/07/04/marketing-algorithms-and-data-brokers/ | 1,695,385,752,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506399.24/warc/CC-MAIN-20230922102329-20230922132329-00490.warc.gz | 142,913,329 | 13,314 | # Marketing algorithms and data brokers
## Definition and the use of an algorithm
The algorithm refers to a procedural formula for solving scientific problems. In many instances, the difficulties are built on executing a sequence of defined actions. For instance, a computer program is an example logarithm. In computer science and mathematics, the term algorithm is used to describe a simple technique for solving repetitive issues. They are variedly employed throughout the IT context and in the search engine domains. The encryption algorithm can alter data based on specified actions (Moran par. 2). (Moran par. 2). The military uses secret algorithms in the encryption and decoding of data. The algorithm is utilized for security since it promotes enhanced security. Besides, a person without the access key cannot complete the data decryption.
## The use of the algorithm to marketers or consumers today
The algorithm is helpful for automating marketing plan, which can be found here. In the area of marketing, automation has emerged as the single most essential factor that helps to improve marketing strategy as well as client services (Roetzer par. 2). Within the context of automated marketing, the algorithm has been performing an important function. The optimization of a marketing strategy through the use of marketing automation software helps to make the most of the opportunities presented by marketing campaigns. In addition to this, it customises the experiences that its consumers have with the products and services that it offers. Algorithms that are based on computers have the speed and understanding that are necessary for marketers and customers to communicate at the appropriate time (Villasenor par. 5). In this scenario, the collection of instructional content that was coded by people is carried out by computers that are both quick and effective.The application of algorithms can give a computerised system control in a way that contributes to the manipulation of marketing information. The system is able to function with only minimal supervision from the humans. The execution of complex algorithms can vary due to a number of factors, the most important of which being the magnitude of the data being entered (Moran par. 4). For example, the operation of a sorting algorithm on an integer set that has already been sorted is typically more efficient than the operation on an integer set that has been generated at random.
## Data brokers
One of the popular data brokers is the Aboutthedata.com, which provides vital data necessary for the everyday operation of enterprises. They supply companies with the data that personalize and share their experiences with the customers, therefore boosting their market shares. Through the current modern technology, the Aboutthedata.com gives business organizations with the appropriate data that would assist them realize practical benefits. The corporation offers “about us” data to other companies and this typically enables other organizations to establish their privacy policy and marketing plans. The primary components of the data include the company’s address, what they offer, phone number, email, and the number of years they have been functioning in the industry (Bachman par. 3). (Bachman par. 3). The analytical methods done by the Aboutthedata.com develop modeled insights employed in the essential data to infer information about the companies. These bits of information are employed in directing potential clients into buying products from the company.
## The company’s practices
The business model of a data broker corporation violates individuals’ rights to both their privacy and the safety of their personal information. The practise of data brokering, such as that done by Aboutthedata.com, is therefore undesirable and should be avoided. The business enterprise is responsible for the collection, analysis, and packaging of some of the most sensitive data as well as personal information before offering it as a commodity to other businesses. Their customers include government agencies and advertisers, both of which are examples of businesses that could potentially exploit the information in an unethical manner. Without the original owner’s knowledge, the information is processed and made available for sale (Moran par. 2). The information being mined, as well as its volume and type, are the only things that shift over time. The content itself is unaltered. Human rights are being violated by the business practises of data brokerage firms, which is especially problematic given that these firms operate with virtually no supervision from the relevant authority. visit for more https://academic-master.com
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No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system. | 1,296 | 6,821 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2023-40 | longest | en | 0.950478 |
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Net Worth Calculator in Excel
Why should you calculate your net worth?
An individual’s net worth is defined as the difference between the assets they own and the liabilities they owe. Thus, it lets you know if he is building on assets and if his financial health is in good shape. It also tells you how much liquidity or cash you have. Lastly, it indicates whether you are controlling the interest rate on your assets and liabilities.
Assets can include land and houses, cash, stocks, vehicles, mutual funds, provident funds, art, gold, jewelry, electronics, or other consumer durables. You must take depreciation into account when calculating the market value of your electronics, automobiles, or other consumer durables.
The passive It will include any outstanding balances on mortgages, automobiles, and other consumer durables. It will also include outstanding credit cards and other loans you may have taken from friends and family. The difference between the assets and liabilities gives you the net worth. Does it grow every year? A growth in your net worth indicates that you are financially sound. Therefore, net worth is a useful tool to determine whether or not you are progressing financially.
You should also make sure you have enough cash to cover sudden expenses like an emergency and expensive hospitalization. The general rule of thumb for asset management is that about 25% of your income should be used to build assets and about 20% should be liquid assets.
Another important aspect that a net worth calculation provides is the interest rate mismatch on your assets and liabilities. If you’re paying a higher interest rate on your liabilities, then you’re better off paying off the debts by breaking down your assets.
You should check your net worth each year and compare it to last year’s performance. That way, you have control over managing your net worth. Details of your assets and corresponding values can be entered into an Excel spreadsheet and the value of total assets can be calculated using a ‘sum’ formula. Similarly, the descriptions and values of the liabilities can be entered in parallel columns and the total of the liabilities can be recalculated using the ‘sum’ formula. Then using the formula ‘=total_assets-total_libilites’ you can easily find your net worth. With the formula ‘=today()’ you can display the date of your net worth calculation. At the top of the worksheet, you can merge and wrap some cells to give your worksheet a title called ‘NET WORTH CALCULATOR’. Of course, the worksheet tab can also be renamed to ‘networth’.
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Có thể bạn quan tâm: | 791 | 3,886 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2023-06 | latest | en | 0.949023 |
https://bookdown.org/kevin_davisross/applied-stochastic-processes/pp-mc-intro.html | 1,726,780,416,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652067.20/warc/CC-MAIN-20240919194038-20240919224038-00078.warc.gz | 123,138,959 | 7,179 | Introduction to Markov Chains
In each of the following, briefly explain why $$\{X_n\}$$ is a Markov chain, specify its transition matrix, and draw a state diagram.
1. Rihanna has three umbrellas, some at her office and some at home. If she is leaving home in the morning (or leaving work at night) and it is raining, she will take an umbrella if there is one there (otherwise, she gets wet). Assume that, independent of the past, it rains on each trip with probability 0.2.
Let $$X_n$$ be the number of umbrellas at her current location.
2. Consider a retail store that sells a particular item (say a TV). Each day they experience customer demand of 0 units of the item with probability 0.6, 1 unit with probability 0.3, and 2 units with probability 0.1 (provided enough units are on the shelf), independently from day to day. The shelf space in the store has room for at most 5 units of the item. If at the end of the day there are fewer than 2 units left then the store restocks the shelf so that it has a total of 5 units on it at the start of the next day.
Let $$X_n$$ be the number of units on the shelf at the end of day $$n$$, before restocking.
3. Consider the following simplified model for the spread of a disease in a population of 5 people. Each person either has the disease or not. In each time period, 2 of the 5 people are selected uniformly at random, and interact. If one of the two people selected has the disease and the other does not, then the disease is transmitted to the healthy person with probability 0.1. Otherwise, no transmission of the disease occurs.
Let $$X_n$$ denote the number of people who have the disease at the end of the $$n$$th time period (after any disease transmission occurs). | 412 | 1,729 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2024-38 | latest | en | 0.943491 |
https://physics.stackexchange.com/questions/178346/newtons-law-of-cooling-for-the-heat-equation-boundary-condition | 1,713,698,162,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817765.59/warc/CC-MAIN-20240421101951-20240421131951-00592.warc.gz | 409,607,312 | 40,277 | # Newton's law of cooling for the heat equation boundary condition
Newton's law of cooling says the temperature of an object satisfies
$$\frac{dT}{dt} = -k(T(t) - T_0),\tag{1}$$
where $T_0$ is the surrounding temperature. See these HTML notes for example.
Now if $u(x,t)$ denotes the temperature of a laterally insulated bar at a point $x$ and time $t$, then heat equation says
$$\frac{\partial u}{\partial t} = \alpha\, \frac{\partial^2 u}{\partial x^2}$$
If the left end $x = 0$ is exposed to an environment at temperature $T_0$, all mathematical physics books say that Newton's law of cooling is
$$-c \frac{\partial u}{\partial x}(0,t) = -k( u(0,t) - T_0), \tag{2}$$
where $c$ is a constant. See Problem 5 in this Google book preview of Boundary Value Problems: and Partial Differential Equations by David Powers. See also page 131 of the same book. (Three pages before the problem 5, where Newton's law of cooling first appears.)
However, according to Newton's law of cooling (1), we get $$\frac{\partial u}{\partial t}(0,t) = -k( u(0,t) - T_0),$$
By the heat equation, $\frac{\partial u}{\partial t} = \alpha\, \frac{\partial^2 u}{\partial x^2}$, we conclude that
$$\alpha \frac{\partial^2 u}{\partial x^2}(0,t) = -k( u(0,t) - T_0).\tag{3}$$
This boundary condition is not the same as (2). Why is (3) not correct?
• Unlike your equation (2), your equation (3) is not a boundary condition. Apr 26, 2015 at 16:47
• @AmeyJoshi Why? By definition, a "boundary condition" is a condition on the boundary required of the function. By this definition, (3) is certainly a "boundary condition". Apr 26, 2015 at 17:42
• Part of the problem here is your source for (1). It's not wrong per se, but it uses a very simplified heat transfer model. In that case, $k$ is not conductivity used in (2), it's more like the heat transfer coefficient, $c$. It's treating the object as lumped (constant temperature) rather than resolving heat transfer within it, as the subsequent equations you've used do. That's also why they've used the notation for ODEs ($d/dt$) rather than PDEs ($\partial/\partial t$). Apr 28, 2015 at 5:56
• @user3823992, you should elaborate this a little in an answer; it will be more to the point than the existing answer, I think.
– Ilja
Apr 23, 2016 at 19:26
Newton's law of cooling actually comes from the more general equation for heat $Q$ transferred between a system (temeperature $T$) and it's surroundings(temperature $T_0$): $$\frac{dQ}{dt} = -hA(T-T_0)$$ where $A$ is the area through which heat transfer occurs (see, for example, here). For an ordinary macroscopic object, where $dQ = mc\ dT$, we get the conventional Newton's law of cooling in terms of temperature: $$mc\frac{dT}{dt} = -hA(T-T_0)$$ For the case of the conducting bar however, from Fourier's law: $$\frac{1}{A}\frac{dQ}{dt} = -k\frac{\partial u}{\partial x}$$ The boundary condition is therefore: $$-k\frac{\partial u(0, t)}{\partial x} = -h(u(0, t) - T_0)$$
• But, this still does not answer "why" --- why can't you use the formula $dQ = mc dT$ for the case of the bar to conclude equation (3)? That is, assume you did not know about Fourier's law. What would prevent you from using the formula $dQ = mc dT$ to deduce the formula $\partial u/\partial t (0,t) = -k(u(0,t) - T_0)$? Would you not think this formula was valid if you were not told to use Fourier's law instead? Apr 28, 2015 at 12:30
• At the boundary, there is an incoming heat (by conduction) $Q_1$ and heat transfer to the surroundings $Q_2$ per unit time. On considering a segment of length $dx$ at the boundary, we see that the net heat entering the region is in fact $dQ = Q_1 - Q_2 = Q(dx) - Q(0)$. It is this that contributes to the change in temperature - not the heat loss to the surroundings alone. This change is given by $\frac{\partial Q}{\partial x}dx$ while $dQ = mc\dot{T} = \rho Ac dx \dot{T}$. Thus, we get $\dot{T} = \frac{1}{\rho Ac} \frac{\partial Q}{\partial x}$. Thus is equivalent to the heat equation...
• ...with the missing piece of what $Q$ actually is being given by Fourier's law. | 1,210 | 4,074 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2024-18 | latest | en | 0.902907 |
http://www.cplusplus.com/forum/beginner/97913/ | 1,500,979,525,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549425144.89/warc/CC-MAIN-20170725102459-20170725122459-00548.warc.gz | 395,015,413 | 4,809 | ### Debugging issue regarding fractions
The code below is designed to add, subtract, multiply, and divide fractions created in the class Rational. The class definition is in a header file and is fine. Also, int main() was supplied, and must not be changed. The two problems found are:
1. the output of the functions (i.e. what x equals) is always constant, being equal to the second fraction (i.e. "d").
2. The first fraction in all functions following addition() is "1/8", or , in general "1/[denominator of d]".
Here is the code in question
``123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116`` ``````void Rational::printRational() // prints a single fraction { cout << numerator << "/" << denominator; } void Rational::printRationalAsDouble() // prints a fraction as a decimal { double function = static_cast (numerator)/static_cast (denominator); cout << function; } Rational Rational::addition(Rational y) // adds fractions { int numerSum; numerSum = (numerator * y.getDenominator()) + (denominator * y.getNumerator()); if (denominator <= y.getDenominator()) { denominator = y.getDenominator(); } return y; } Rational Rational::subtraction(Rational y) // subtracts fractions { int numerDifference; numerDifference = (numerator * y.getDenominator()) - (denominator * y.getNumerator()); if (y.getDenominator() >= denominator) { y.setDenominator(denominator); } return y; } Rational Rational::multiplication(Rational y) // multiples fractions { int numerProduct; int numerProduct2; numerProduct = (numerator * y.getNumerator()); numerProduct2 = (denominator * y.getDenominator()); return y; } Rational Rational::division(Rational y) // divides fractions { int numerQuotient; int numerQuotient2; numerQuotient = (numerator * y.getDenominator()); numerQuotient2 = (denominator * y.getNumerator()); return y; } int main() { Rational c( 3, 6 ); Rational d( 7, 9 ); Rational x; // creates three rational objects c.reduction(); d.reduction(); c.printRational(); // prints rational object c cout << " + "; d.printRational(); // prints rational object d x = c.addition( d ); // adds object c and d; sets the value to x --------------------------------- cout << " = "; x.printRational(); // prints rational object x cout << '\n'; x.printRational(); // prints rational object x cout << " = "; x.printRationalAsDouble(); // prints rational object x as double cout << "\n\n"; c.printRational(); // prints rational object c cout << " - "; d.printRational(); // prints rational object d x = c.subtraction( d ); // subtracts object c and d ------------------------------------------ cout << " = "; x.printRational(); // prints rational object x cout << '\n'; x.printRational(); // prints rational object x cout << " = "; x.printRationalAsDouble(); // prints rational object x as double cout << "\n\n"; c.printRational(); // prints rational object c cout << " x "; d.printRational(); // prints rational object d x = c.multiplication( d ); // multiplies object c and d ---------------------------------------- cout << " = "; x.printRational(); // prints rational object x cout << '\n'; x.printRational(); // prints rational object x cout << " = "; x.printRationalAsDouble(); // prints rational object x as double cout << "\n\n"; c.printRational(); // prints rational object c cout << " / "; d.printRational(); // prints rational object d x = c.division( d ); // divides object c and d ------------------------------------------------- cout << " = "; x.printRational(); // prints rational object x cout << '\n'; x.printRational(); // prints rational object x cout << " = "; x.printRationalAsDouble(); // prints rational object x as double cout << endl; system("pause"); return 0; }``````
Any and all help will be welcomed.
This function
``12345678910`` ``````Rational Rational::addition(Rational y) // adds fractions { int numerSum; numerSum = (numerator * y.getDenominator()) + (denominator * y.getNumerator()); if (denominator <= y.getDenominator()) { denominator = y.getDenominator(); } return y; }``````
has no any sense. The function gets as an argument an object of type Rational and returns the same object without any changes of it. So what you will pass to the function as an argument the same will be returned by the function.
Apart from this as far as I know denominator of the sum is calculated as a product of two denominators.
Last edited on
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http://openstudy.com/updates/51391466e4b01c4790d0f99c | 1,519,488,628,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891815843.84/warc/CC-MAIN-20180224152306-20180224172306-00554.warc.gz | 266,426,711 | 12,524 | • SWAG
1. Set up a linear system consisting of two equations. Assume you will talk for a minimum of 600 minutes. The first equation would be for the Talks-A-Lot Company. The total cost, y, equals the base fee plus cost per minute times the number of minutes exceeding 600 minutes. The second equation would be set up just like the first, only you need to use the information for the Chat-Away Company.
Mathematics
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Not the answer you are looking for? Search for more explanations. | 335 | 1,331 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-09 | latest | en | 0.429977 |
http://forums.wolfram.com/mathgroup/archive/2010/Oct/msg00116.html | 1,579,545,745,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250599718.13/warc/CC-MAIN-20200120165335-20200120194335-00435.warc.gz | 70,113,547 | 7,989 | Re: PSE Example 8.6 via Reduce
• To: mathgroup at smc.vnet.net
• Subject: [mg112881] Re: PSE Example 8.6 via Reduce
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Tue, 5 Oct 2010 05:31:34 -0400 (EDT)
```Eduardo Cavazos wrote:
> On Sep 26, 1:44 am, Eduardo Cavazos <wayo.cava... at gmail.com> wrote:
>
>> Here's example 8.6 from PSE [1]:
>>
>> http://i.imgur.com/HJLqs.png
>>
>> Here I'll be working with the "exercise" portion of the example; i.e.
>> the case where there is friction between point A and point B.
>>
>> Use Reduce on the set of equations which describe the system between
>> point A and point B:
>>
>> http://i.imgur.com/PLWza.png
>>
>> The result shows that vB is about 12.9.
>>
>> Now use Reduce on the set of equations which describe the system
>> between point B and point C. Also, plug in our value of 'vB' manually:
>>
>> http://i.imgur.com/rujUz.png
>>
>>
>> Above I solved the problem in "piecemeal" fashion; first I used Reduce
>> on the system from A to B and used the result from that to work with
>> the system from B to C, also using Reduce.
>>
>> I don't have alot of experience with Reduce, but it seems like, in
>> theory, I should be able to throw the whole set of equations at Reduce
>> in one step, instead of in two steps. However, when I try to do so,
>> Mathematica seems to have trouble with it (at least on this system;
>> Pentium M with about 1.5GB RAM). So something along the lines of:
>>
>> http://i.imgur.com/2swfE.png
>>
>> So my questions are... Is this too much for Reduce to handle? Would
>> you recommend the piecemeal method instead?
>
> In particular, the trouble is that the computation ran over 3 hours
> without completing. When I split up the problem, each piece takes a
> few seconds.
>
> Ed
I do not know if you will get serious responses if you provide the code
you used. But I rather suspect you will not get such responses in the
absence of said code.
Daniel Lichtblau
Wolfram Research
```
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• Next by thread: Re: PSE Example 8.6 via Reduce | 629 | 2,185 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2020-05 | longest | en | 0.91952 |
http://lists.w3.org/Archives/Public/www-math/2000Apr/0024.html | 1,519,305,414,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891814105.6/warc/CC-MAIN-20180222120939-20180222140939-00567.warc.gz | 211,796,765 | 3,737 | Re: re Optimisation / Sparse Matrices (plain text)
From: Leonardo B. Lopes <leo@iems.nwu.edu>
Date: Tue, 11 Apr 2000 12:05:39 -0500 (CDT)
Message-ID: <Pine.GSO.4.04.10004111143560.21586-100000@leontief.iems.nwu.edu>
```Thank You for your help. I downloaded the current Open Math standard and I
am in the process of studying it. I have an important concern: Are these
standards going to be appropriate for communicating huge objects
(matrices, etc...)? As I read this material, I realize that my
applications requirements are a little different, and I am trying to
decide if MathML/Openmath is the way to proceed with my research.
Also, are there any optimization people involved in these discussions? I
would really appreciate if one of you could get in touch.
Thanks,
Leo.
On Mon, 10 Apr 2000, Stan Devitt wrote:
> Apologies, I meant to send this as plain text.
>
>
>
> There is provision for extensions that handle such things.
> It is through the csymbol element. For example, a
> sparse matrix representation could be defined so that
> For example, you could write:
>
> <apply><csymbol definitionURL=".../SparseMatrix">SparseMatrix</csymbol>
> <vector><cn>5</cn><cn>5</cn><cn>
> <vector><cn>1</cn><cn>1</cn><cn> 3.232432423</cn></vector>
> <vector><cn>1</cn><cn>2</cn><cn> 3.01</cn></vector>
> <vector><cn>1</cn><cn>5</cn><cn> 3.43543453</cn></vector>
> </apply>
>
> to mean a 5 by 5 sparse matrix with the a[i,j] specified for selected
> coordinates. Column defined matrices could be handled in a similar
> manner.
>
> The presentation is handled via XSLT and can range from something
> as simple as listing the non-zero table entries, c/w coordinates, through
> to generating an actual matrix.
>
> What is needed is an agreed apon vocabulary and then
> references to those definitions. Building such a vocabulary
> is one of the goals of the OpenMath project. The MathML content
> definitions match (or will shortly) a specific collection of those
> definitions. Both groups are tracking changes closely.
>
> Stan Devitt
>
>
>
========================================================================
Leonardo B. Lopes leo@iems.nwu.edu
Ph.D. Student (847)491-8470
IEMS - Northwestern University http://www.iems.nwu.edu/~leo
```
Received on Tuesday, 11 April 2000 13:05:42 UTC
This archive was generated by hypermail 2.3.1 : Tuesday, 6 January 2015 21:27:29 UTC | 669 | 2,492 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2018-09 | latest | en | 0.82852 |
http://mathhomeworkanswers.org/224918/find-angle | 1,488,229,879,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501173761.96/warc/CC-MAIN-20170219104613-00309-ip-10-171-10-108.ec2.internal.warc.gz | 168,960,508 | 11,728 | In a equilateral triangle ABC ,P is any point inside the triangle such that APsquare =BPsquare +ABsquare. Find angle BPC.(There is construction).
If AP^2=BP^2+AB^2, then angle B is a right angle. But that would put P outside the triangle.
Also, since BP is not zero length then AP must be longer than AB, which is the length of each side of the triangle, a. P cannot be inside the triangle because there is no line longer than the side of the triangle which is also inside the triangle. The greatest distance from A is a (AB or AC).
If P is outside the triangle then as long as B is a right angle, angle BPC can have any size less than 150 degrees, because CPB=90-ABC=90-60=30 degrees and BPC+BCP=180-CBP=180-(90-ABC)=180-(90-60)=180-30=150.
But if AB^2=AP^2+PB^2 then P is inside the triangle.
If AB is the diameter of a circle then the midpoint of AB is O the centre of the circle. Draw a circle with radius AO. It will pass through vertices A and B. P can be any point on the circle inside the triangle. Because P can move about on the circle there is no fixed angle for BPC.
answered Aug 8, 2016 by Top Rated User (425,700 points) | 308 | 1,140 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2017-09 | latest | en | 0.906768 |
https://gbee.edu.vn/7-3-polar-coordinates-calculus-volume-2-5iuazj61/ | 1,723,599,814,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641086966.85/warc/CC-MAIN-20240813235205-20240814025205-00152.warc.gz | 229,316,243 | 19,177 | ### Learning Objectives
• 7.3.1 Locate points in a plane by using polar coordinates.
• 7.3.2 Convert points between rectangular and polar coordinates.
• 7.3.3 Sketch polar curves from given equations.
• 7.3.4 Convert equations between rectangular and polar coordinates.
• 7.3.5 Identify symmetry in polar curves and equations.
The rectangular coordinate system (or Cartesian plane) provides a means of mapping points to ordered pairs and ordered pairs to points. This is called a one-to-one mapping from points in the plane to ordered pairs. The polar coordinate system provides an alternative method of mapping points to ordered pairs. In this section we see that in some circumstances, polar coordinates can be more useful than rectangular coordinates.
### Defining Polar Coordinates
To find the coordinates of a point in the polar coordinate system, consider Figure 7.27. The point has Cartesian coordinates The line segment connecting the origin to the point measures the distance from the origin to and has length The angle between the positive -axis and the line segment has measure This observation suggests a natural correspondence between the coordinate pair and the values and This correspondence is the basis of the polar coordinate system. Note that every point in the Cartesian plane has two values (hence the term ordered pair) associated with it. In the polar coordinate system, each point also has two values associated with it: and
Using right-triangle trigonometry, the following equations are true for the point
Furthermore,
Each point in the Cartesian coordinate system can therefore be represented as an ordered pair in the polar coordinate system. The first coordinate is called the radial coordinate and the second coordinate is called the angular coordinate. Every point in the plane can be represented in this form.
Note that the equation has an infinite number of solutions for any ordered pair However, if we restrict the solutions to values between and then we can assign a unique solution to the quadrant in which the original point is located. Then the corresponding value of r is positive, so
### Theorem 7.4
#### Converting Points between Coordinate Systems
Given a point in the plane with Cartesian coordinates and polar coordinates the following conversion formulas hold true:
These formulas can be used to convert from rectangular to polar or from polar to rectangular coordinates.
### Example 7.10
#### Converting between Rectangular and Polar Coordinates
Convert each of the following points into polar coordinates.
Convert each of the following points into rectangular coordinates.
#### Solution
1. Use and in Equation 7.8:
Therefore this point can be represented as in polar coordinates.
2. Use and in Equation 7.8:
Therefore this point can be represented as in polar coordinates.
3. Use and in Equation 7.8:
Direct application of the second equation leads to division by zero. Graphing the point on the rectangular coordinate system reveals that the point is located on the positive y-axis. The angle between the positive x-axis and the positive y-axis is Therefore this point can be represented as in polar coordinates.
4. Use and in Equation 7.8:
Therefore this point can be represented as in polar coordinates.
5. Use and in Equation 7.7:
Therefore this point can be represented as in rectangular coordinates.
6. Use and in Equation 7.7:
Therefore this point can be represented as in rectangular coordinates.
7. Use and in Equation 7.7:
Therefore this point can be represented as in rectangular coordinates.
### Checkpoint 7.10
Convert into polar coordinates and into rectangular coordinates.
The polar representation of a point is not unique. For example, the polar coordinates and both represent the point in the rectangular system. Also, the value of can be negative. Therefore, the point with polar coordinates also represents the point in the rectangular system, as we can see by using Equation 7.8:
Every point in the plane has an infinite number of representations in polar coordinates. However, each point in the plane has only one representation in the rectangular coordinate system.
Note that the polar representation of a point in the plane also has a visual interpretation. In particular, is the directed distance that the point lies from the origin, and measures the angle that the line segment from the origin to the point makes with the positive -axis. Positive angles are measured in a counterclockwise direction and negative angles are measured in a clockwise direction. The polar coordinate system appears in the following figure.
The line segment starting from the center of the graph going to the right (called the positive x-axis in the Cartesian system) is the polar axis. The center point is the pole, or origin, of the coordinate system, and corresponds to The innermost circle shown in Figure 7.28 contains all points a distance of 1 unit from the pole, and is represented by the equation Then is the set of points 2 units from the pole, and so on. The line segments emanating from the pole correspond to fixed angles. To plot a point in the polar coordinate system, start with the angle. If the angle is positive, then measure the angle from the polar axis in a counterclockwise direction. If it is negative, then measure it clockwise. If the value of is positive, move that distance along the terminal ray of the angle. If it is negative, move along the ray that is opposite the terminal ray of the given angle.
### Example 7.11
#### Plotting Points in the Polar Plane
Plot each of the following points on the polar plane.
#### Solution
The three points are plotted in the following figure.
### Checkpoint 7.11
Plot and on the polar plane.
### Polar Curves
Now that we know how to plot points in the polar coordinate system, we can discuss how to plot curves. In the rectangular coordinate system, we can graph a function and create a curve in the Cartesian plane. In a similar fashion, we can graph a curve that is generated by a function
The general idea behind graphing a function in polar coordinates is the same as graphing a function in rectangular coordinates. Start with a list of values for the independent variable in this case) and calculate the corresponding values of the dependent variable This process generates a list of ordered pairs, which can be plotted in the polar coordinate system. Finally, connect the points, and take advantage of any patterns that may appear. The function may be periodic, for example, which indicates that only a limited number of values for the independent variable are needed.
### Problem-Solving Strategy
#### Problem-Solving Strategy: Plotting a Curve in Polar Coordinates
1. Create a table with two columns. The first column is for and the second column is for
2. Create a list of values for
3. Calculate the corresponding values for each
4. Plot each ordered pair on the coordinate axes.
5. Connect the points and look for a pattern.
### Example 7.12
#### Graphing a Function in Polar Coordinates
Graph the curve defined by the function Identify the curve and rewrite the equation in rectangular coordinates.
#### Solution
Because the function is a multiple of a sine function, it is periodic with period so use values for between 0 and The result of steps 1–3 appear in the following table. Figure 7.30 shows the graph based on this table.
0 0 0 0
This is the graph of a circle. The equation can be converted into rectangular coordinates by first multiplying both sides by This gives the equation Next use the facts that and This gives To put this equation into standard form, subtract from both sides of the equation and complete the square:
This is the equation of a circle with radius 2 and center in the rectangular coordinate system.
### Checkpoint 7.12
Create a graph of the curve defined by the function
The graph in Example 7.12 was that of a circle. The equation of the circle can be transformed into rectangular coordinates using the coordinate transformation formulas in Equation 7.8. Example 7.14 gives some more examples of functions for transforming from polar to rectangular coordinates.
### Example 7.13
#### Transforming Polar Equations to Rectangular Coordinates
Rewrite each of the following equations in rectangular coordinates and identify the graph.
#### Solution
1. Take the tangent of both sides. This gives Since we can replace the left-hand side of this equation by This gives which can be rewritten as This is the equation of a straight line passing through the origin with slope In general, any polar equation of the form represents a straight line through the pole with slope equal to
2. First, square both sides of the equation. This gives Next replace with This gives the equation which is the equation of a circle centered at the origin with radius 3. In general, any polar equation of the form where k is a positive constant represents a circle of radius k centered at the origin. (Note: when squaring both sides of an equation it is possible to introduce new points unintentionally. This should always be taken into consideration. However, in this case we do not introduce new points. For example, is the same point as
3. Multiply both sides of the equation by This leads to Next use the formulas
This gives
To put this equation into standard form, first move the variables from the right-hand side of the equation to the left-hand side, then complete the square.
This is the equation of a circle with center at and radius 5. Notice that the circle passes through the origin since the center is 5 units away.
### Checkpoint 7.13
Rewrite the equation in rectangular coordinates and identify its graph.
We have now seen several examples of drawing graphs of curves defined by polar equations. A summary of some common curves is given in the tables below. In each equation, a and b are arbitrary constants.
A cardioid is a special case of a limaçon (pronounced “lee-mah-son”), in which or The rose is a very interesting curve. Notice that the graph of has four petals. However, the graph of has three petals as shown.
If the coefficient of is even, the graph has twice as many petals as the coefficient. If the coefficient of is odd, then the number of petals equals the coefficient. You are encouraged to explore why this happens. Even more interesting graphs emerge when the coefficient of is not an integer. For example, if it is rational, then the curve is closed; that is, it eventually ends where it started (Figure 7.34(a)). However, if the coefficient is irrational, then the curve never closes (Figure 7.34(b)). Although it may appear that the curve is closed, a closer examination reveals that the petals just above the positive x axis are slightly thicker. This is because the petal does not quite match up with the starting point.
### Example 7.14
#### Chapter Opener: Describing a Spiral
Recall the chambered nautilus introduced in the chapter opener. This creature displays a spiral when half the outer shell is cut away. It is possible to describe a spiral using rectangular coordinates. Figure 7.35 shows a spiral in rectangular coordinates. How can we describe this curve mathematically?
#### Solution
As the point P travels around the spiral in a counterclockwise direction, its distance d from the origin increases. Assume that the distance d is a constant multiple k of the angle that the line segment OP makes with the positive x-axis. Therefore where is the origin. Now use the distance formula and some trigonometry:
Although this equation describes the spiral, it is not possible to solve it directly for either x or y. However, if we use polar coordinates, the equation becomes much simpler. In particular, and is the second coordinate. Therefore the equation for the spiral becomes Note that when we also have so the spiral emanates from the origin. We can remove this restriction by adding a constant to the equation. Then the equation for the spiral becomes for arbitrary constants and This is referred to as an Archimedean spiral, after the Greek mathematician Archimedes.
Another type of spiral is the logarithmic spiral, described by the function A graph of the function is given in Figure 7.36. This spiral describes the shell shape of the chambered nautilus.
Suppose a curve is described in the polar coordinate system via the function Since we have conversion formulas from polar to rectangular coordinates given by
it is possible to rewrite these formulas using the function
This step gives a parameterization of the curve in rectangular coordinates using as the parameter. For example, the spiral formula from Figure 7.31 becomes
Letting range from to generates the entire spiral.
### Symmetry in Polar Coordinates
When studying symmetry of functions in rectangular coordinates (i.e., in the form we talk about symmetry with respect to the y-axis and symmetry with respect to the origin. In particular, if for all in the domain of then is an even function and its graph is symmetric with respect to the y-axis. If for all in the domain of then is an odd function and its graph is symmetric with respect to the origin. By determining which types of symmetry a graph exhibits, we can learn more about the shape and appearance of the graph. Symmetry can also reveal other properties of the function that generates the graph. Symmetry in polar curves works in a similar fashion.
### Theorem 7.5
#### Symmetry in Polar Curves and Equations
Consider a curve generated by the function in polar coordinates.
1. The curve is symmetric about the polar axis if for every point on the graph, the point is also on the graph. Similarly, the equation is unchanged by replacing with
2. The curve is symmetric about the pole if for every point on the graph, the point is also on the graph. Similarly, the equation is unchanged when replacing with or with
3. The curve is symmetric about the vertical line if for every point on the graph, the point is also on the graph. Similarly, the equation is unchanged when is replaced by
The following table shows examples of each type of symmetry.
### Example 7.15
#### Using Symmetry to Graph a Polar Equation
Find the symmetry of the rose defined by the equation and create a graph.
#### Solution
Suppose the point is on the graph of
1. To test for symmetry about the polar axis, first try replacing with This gives Since this changes the original equation, this test is not satisfied. However, returning to the original equation and replacing with and with yields
Multiplying both sides of this equation by gives which is the original equation. This demonstrates that the graph is symmetric with respect to the polar axis.
2. To test for symmetry with respect to the pole, first replace with which yields Multiplying both sides by −1 gives which does not agree with the original equation. Therefore the equation does not pass the test for this symmetry. However, returning to the original equation and replacing with gives
Since this agrees with the original equation, the graph is symmetric about the pole.
3. To test for symmetry with respect to the vertical line first replace both with and with
Multiplying both sides of this equation by gives which is the original equation. Therefore the graph is symmetric about the vertical line
This graph has symmetry with respect to the polar axis, the origin, and the vertical line going through the pole. To graph the function, tabulate values of between 0 and and then reflect the resulting graph.
This gives one petal of the rose, as shown in the following graph.
Reflecting this image into the other three quadrants gives the entire graph as shown.
### Checkpoint 7.14
Determine the symmetry of the graph determined by the equation and create a graph.
### Section 7.3 Exercises
In the following exercises, plot the point whose polar coordinates are given by first constructing the angle and then marking off the distance r along the ray.
For the following exercises, consider the polar graph below. Give two sets of polar coordinates for each point.
Coordinates of point A.
Coordinates of point B.
Coordinates of point C.
Coordinates of point D.
For the following exercises, the rectangular coordinates of a point are given. Find two sets of polar coordinates for the point in Round to three decimal places.
For the following exercises, find rectangular coordinates for the given point in polar coordinates.
For the following exercises, determine whether the graphs of the polar equation are symmetric with respect to the -axis, the -axis, or the origin.
For the following exercises, describe the graph of each polar equation. Confirm each description by converting into a rectangular equation.
For the following exercises, convert the rectangular equation to polar form and sketch its graph.
For the following exercises, convert the rectangular equation to polar form and sketch its graph.
For the following exercises, convert the polar equation to rectangular form and sketch its graph.
For the following exercises, sketch a graph of the polar equation and identify any symmetry.
[T] The graph of is called a strophoid. Use a graphing utility to sketch the graph, and, from the graph, determine the asymptote.
[T] Use a graphing utility and sketch the graph of
[T] Use a graphing utility to graph
[T] Use technology to graph
[T] Use technology to plot (use the interval
Without using technology, sketch the polar curve
[T] Use a graphing utility to plot for
[T] Use technology to plot for
[T] There is a curve known as the “Black Hole.” Use technology to plot for
[T] Use the results of the preceding two problems to explore the graphs of and for
You are watching: 7.3 Polar Coordinates – Calculus Volume 2. Info created by GBee English Center selection and synthesis along with other related topics. | 3,624 | 17,879 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.78125 | 5 | CC-MAIN-2024-33 | latest | en | 0.890315 |
http://research.stlouisfed.org/fred2/series/A34JTI?rid=95 | 1,430,017,498,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1429246652296.40/warc/CC-MAIN-20150417045732-00253-ip-10-235-10-82.ec2.internal.warc.gz | 229,525,557 | 19,614 | # Value of Manufacturers' Total Inventories for Durable Goods Industries: Computers and Electronic Products: Defense Search and Navigation Equipment
2015-02: 3,276 Million of Dollars (+ see more)
Monthly, End of Period, Seasonally Adjusted, A34JTI, Updated: 2015-04-02 9:26 AM CDT
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Name: Email: | 490 | 1,990 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2015-18 | longest | en | 0.800702 |
https://stackoverflow.com/questions/33284713/parsing-variable-names-from-cell-content?noredirect=1 | 1,585,892,755,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370510287.30/warc/CC-MAIN-20200403030659-20200403060659-00536.warc.gz | 684,415,002 | 31,879 | # Parsing variable names from cell content
I learned from this question that I can declare variables in Excel by naming cells. Now I'm wondering whether it'd be possible to parse text in a cell to call this variable. Say I name cell A1 "var1", and assign it the value `0.5`, and cell A2 "var2" with the value `0.75`. Then I want to do the following:
`````` B C D
1 var1 10 =B1*C1
2 var2 10 =B2*C2
3 var2 10 =B3*C3
4 var2 10 =parse(B4)*C4
5 var1 10 =CELL(B5)*C5
6 var1 10 =VALUE(B6)*C6
``````
that is, multiply the values in column `D` by either `var1` or `var2`, which is read from the same row in column `C`. Rows 4, 5, and 6 show some unsuccessful attempts of what I have in mind.
Use the `INDIRECT` function. In cell `D6` the formula you want is `=INDIRECT(B6)*C6`.
Note that in Excel 2010 or later, you can't use `var1` as a cell name, because it looks like a cell reference. You would have to use something like `_var1` or `variable1` instead.
• Great, thank you! And thanks for the hint about `var1` as well, while I was only using this as an example here and not in my actual application, it's still good to know. – Nils Gudat Oct 22 '15 at 15:36
You can use the `INDIRECT()` command to query both a range and a named range. Try `=INDIRECT("myVar1")*C6` | 413 | 1,304 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2020-16 | latest | en | 0.895392 |
https://arpitbhayani.me/competitive-programming-solutions/spoj/kuruk14 | 1,585,963,283,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370519111.47/warc/CC-MAIN-20200404011558-20200404041558-00350.warc.gz | 358,441,568 | 106,213 | # KURUK14 spoj Solution - Correct, Optimal and Working
``````/*
* KURUK14.cpp
*
* Created on: Jun 21, 2014
* Author: Arpit Bhayani
*/
#include <cstdio>
#include <cstdlib>
#include <iostream>
using namespace std;
#define DEBUG 0
#define gc getchar
#define ll long long
void scanint(ll int &x) {
register ll int c = gc();
x = 0;
for (; (c < 48 || c > 57); c = gc())
;
for (; c > 47 && c < 58; c = gc()) {
x = (x << 1) + (x << 3) + c - 48;
}
}
int i = 0;
char ch;
while ((ch = getchar()) != '\n') {
str[i++] = ch;
}
str[i] = '\0';
return i;
}
int main(int argc, char * argv[]) {
int t;
scanf("%d", &t);
while (t--) {
int n, x;
scanf("%d", &n);
int * array = (int *) calloc(n, sizeof(int));
for (int i = 0; i < n; i++) {
scanf("%d", &x);
if (array[x] == 0) {
array[x] = 1;
} else if (array[x] == 1 && array[n - 1 - x] == 0) {
array[n - 1 - x] = 1;
}
}
int i = 0;
for (i = 0; i < n; i++) {
if (array[i] == 0) {
break;
}
}
if (i == n) {
printf("YES\n");
} else {
printf("NO\n");
}
free(array);
}
return 0;
}
`````` | 391 | 1,031 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2020-16 | longest | en | 0.223883 |
https://www.teachoo.com/4815/727/Example-34---Evaluate-integral-sin4-x---sin4-x---cos4-x-dx/category/Examples/ | 1,685,646,962,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648000.54/warc/CC-MAIN-20230601175345-20230601205345-00101.warc.gz | 1,104,413,467 | 36,963 | Examples
Chapter 7 Class 12 Integrals
Serial order wise
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
### Transcript
Example 32 Evaluate β«_0^(π/2)βsin^4β‘π₯/(sin^4β‘π₯ + cos^4β‘π₯ ) ππ₯ Let I =β«_0^((π )/2)βγ(γπ ππγ^4 π₯)/γγπ ππγ^4 π₯γβ‘γ+ γπππ γ^4 π₯γ ππ₯γ β΄ I =β«_0^((π )/2)βsin^4β‘(π/2 β π₯)/(γγπ ππγ^4 π₯γβ‘γ (π/2 β π₯) γ+ γγπππ γ^4 π₯γβ‘(π/2 β π₯) ) ππ₯ I = β«_0^((π )/2)β(γπππ γ^4 π₯)/γγπππ γ^4 π₯γβ‘γ+γπ ππγ^4 π₯γ ππ₯ Using the property P4 β«_0^πβγπ(π₯)ππ₯=γ β«_0^πβπ(πβπ₯)ππ₯ Using :- sin (π/2βπ)=cosβ‘π & cos (π/2βπ)=sinβ‘π Adding (1) and (2) i.e. (1) + (2) I + I = β«_0^((π )/2)β(γπ ππγ^4 π₯)/(γπ ππγ^4 π₯ +γπππ γ^4 π₯) ππ₯+β«_0^(π/2)βγ(πππ π₯)/(γπ ππγ^4 π₯ +γπππ γ^4 π₯).γ ππ₯ 2I = β«_0^((π )/2)βγ(γπ ππγ^4 π₯ + γπππ γ^4 π₯)/(γπ ππγ^4 π₯ +γπππ γ^4 π₯).γ ππ₯ 2I = β«_0^((π )/2)βππ₯" " 2I = [π₯]_0^(π/2) 2I = [π/2β0] I = π/(2 Γ 2) β΄ π = π
/π | 1,125 | 1,388 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2023-23 | longest | en | 0.353044 |
https://catchsomeair.us/and-relationship/what-is-the-relationship-among-electric-force-charge-and-distance.php | 1,563,633,727,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526517.67/warc/CC-MAIN-20190720132039-20190720154039-00201.warc.gz | 352,477,668 | 9,839 | # What is the relationship among electric force charge and distance
### Comparing electric force and gravitational force (practice) | Khan Academy
Practice: Relationship between electric force, charge, and distance analyzing the electric and gravitational interaction between a proton and an alpha particle. only really need to do the Qs, to see the charge (Q1 multiplied by Q2) E=k( Q1Q1/r^2), describe the relationship between electric force, charge, and distance. Forces between two electrically-charged objects can be extremely large. Metals are good conductors of electric charge, while plastics, wood, and rubber are not. When the ground connection is removed, the conductor will have a charge opposite in sign to that r is the distance between the charges.
The magnitude of the force and the distance between the two balloons is said to be inversely related.
### Electric charge and Coulomb's law
Coulomb's Law Equation The quantitative expression for the effect of these three variables on electric force is known as Coulomb's law.
Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects. In equation form, Coulomb's law can be stated as where Q1 represents the quantity of charge on object 1 in CoulombsQ2 represents the quantity of charge on object 2 in Coulombsand d represents the distance of separation between the two objects in meters.
The symbol k is a proportionality constant known as the Coulomb's law constant. The value of this constant is dependent upon the medium that the charged objects are immersed in.
In the case of air, the value is approximately 9. If the charged objects are present in water, the value of k can be reduced by as much as a factor of It is worthwhile to point out that the units on k are such that when substituted into the equation the units on charge Coulombs and the units on distance meters will be canceled, leaving a Newton as the unit of force. The Coulomb's law equation provides an accurate description of the force between two objects whenever the objects act as point charges.
A charged conducting sphere interacts with other charged objects as though all of its charge were located at its center. While the charge is uniformly spread across the surface of the sphere, the center of charge can be considered to be the center of the sphere. The sphere acts as a point charge with its excess charge located at its center. Since Coulomb's law applies to point charges, the distance d in the equation is the distance between the centers of charge for both objects not the distance between their nearest surfaces.
The symbols Q1 and Q2 in the Coulomb's law equation represent the quantities of charge on the two interacting objects. The sign on the charge is simply representative of whether the object has an excess of electrons a negatively charged object or a shortage of electrons a positively charged object.
While the practice is not recommended, there is certainly no harm in doing so.
This is consistent with the concept that oppositely charged objects have an attractive interaction and like charged objects have a repulsive interaction. If the charge of one of the objects is doubled, and the distance separating the objects is doubled, then what is the new force? The electrostatic force is directly related to the product of the charges and inversely related to the square of the separation distance. Doubling one of the charges would serve to double the force. Doubling the distance would serve to reduce the force by a factor of four.
The combined affect of these two variations would be to decrease the force by a factor of two - changing it from 0. If the charge of both of the objects is doubled and the distance separating the objects is doubled, then what is the new force? Doubling both of the charges would serve to quadruple the force. The combined affect of these two variations would be to not change the force at all; it remains as 0.
If the charge of one of the objects is increased by a factor of four, and the distance separating the objects is doubled, then what is the new force? Quadrupling one of the charges would serve to quadruple the force. The combined affect of these two variations would be to not alter the force at all; it would remain as 0.
There are three ways that objects can be given a net charge. Charging by friction - this is useful for charging insulators. If you rub one material with another say, a plastic ruler with a piece of paper towelelectrons have a tendency to be transferred from one material to the other.
For example, rubbing glass with silk or saran wrap generally leaves the glass with a positive charge; rubbing PVC rod with fur generally gives the rod a negative charge.
### Relationship between electric force, charge, and distance (practice) | Khan Academy
Charging by conduction - useful for charging metals and other conductors. If a charged object touches a conductor, some charge will be transferred between the object and the conductor, charging the conductor with the same sign as the charge on the object.
Charging by induction - also useful for charging metals and other conductors. Again, a charged object is used, but this time it is only brought close to the conductor, and does not touch it. If the conductor is connected to ground ground is basically anything neutral that can give up electrons to, or take electrons from, an objectelectrons will either flow on to it or away from it.
When the ground connection is removedthe conductor will have a charge opposite in sign to that of the charged object. An example of induction using a negatively charged object and an initially-uncharged conductor for example, a metal ball on a plastic handle. Electrons on the conductor will be repelled from the area nearest the charged object.
The electrons on the conductor want to get as far away from the negatively-charged object as possible, so some of them flow to ground. This leaves the conductor with a deficit of electrons.
## Inverse Square Law
The conductor is now positively charged. A practical application involving the transfer of charge is in how laser printers and photocopiers work. This is a good web page that gives a nice description of how a photocopier works: University of Delaware Why is static electricity more apparent in winter?
You notice static electricity much more in winter with clothes in a dryer, or taking a sweater off, or getting a shock when you touch something after walking on carpet than in summer because the air is much drier in winter than summer. Dry air is a relatively good electrical insulator, so if something is charged the charge tends to stay. In more humid conditions, such as you find on a typical summer day, water molecules, which are polarized, can quickly remove charge from a charged object.
Try this at home See if you can charge something at home using friction. I got good results by rubbing a Bic pen with a piece of paper towel. To test the charge, you can use a narrow stream of water from a faucet; if the object attracts the stream when it's brought close, you know it's charged.
## CHAPTER 22
All you need to do is to find something to rub - try anything made out of hard plastic or rubber. You also need to find something to rub the object with - potential candidates are things like paper towel, wool, silk, and saran wrap or other plastic.
Coulomb's law The force exerted by one charge q on another charge Q is given by Coulomb's law: Remember that force is a vector, so when more than one charge exerts a force on another charge, the net force on that charge is the vector sum of the individual forces. | 1,580 | 7,817 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2019-30 | latest | en | 0.950957 |
https://community.smartsheet.com/discussion/63746/help-with-if-and-formulas | 1,718,623,927,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861701.67/warc/CC-MAIN-20240617091230-20240617121230-00751.warc.gz | 160,341,089 | 107,000 | # Help with IF(AND) formulas
Options
✭✭✭✭✭
edited 12/09/19
= IF[Instructor 1 Last Name]@row = "" - AND [Instructor Status]@row = "U.S. Instructor" - I need it to count as 1. Otherwise, 0.
What I've written above is what I want to do. Below is the formula, which gives me the dreaded #UNPARSEABLE.
=IF(AND([INSTRUCTOR 1 LAST NAME]@row=””, [INSTRUCTOR 1 STATUS]@row=”U.S. Instructor”, 1, 0))
After I can get this straightened out, then it becomes more complicated.
Then I need to check that Instructor 2's LAST NAME does not equal Instructor 1's LAST Name.
Then I need to check that Instructor 3's LAST NAME does not equal Instructor 1 & 2's LAST NAMES
Finally, I'll need to check that Instructor 4's LAST NAME does not equal Instructor 1, 2, & 3's LAST NAMES.
Sometimes we have a group of instructors who go to teach in one location. Sometimes we only have 1 instructor who will teach at least 2 courses. (Even though there are 2 courses taught, we only count it as 1 instructor even though his name will appear twice for this trip.)
I need a count of instructors who go to teach each quarter, and I need to know if they are Nationals or if they are U.S. Instructors.
All names columns are TEXT only. (My brain is slowly frying....) Thanks for any help!!
Tags:
• ✭✭✭✭✭✭
Options
The initial formula is simply an issue of a misplaced closing parenthesis. You need to move one from the end of the formula to close out the AND statement.
=IF(AND([INSTRUCTOR 1 LAST NAME]@row=””, [INSTRUCTOR 1 STATUS]@row=”U.S. Instructor”), 1, 0)
.
That should get you started. Next comment will approach the additional name criteria.
• ✭✭✭✭✭✭
Options
Ok. So the absolute easiest way to figure out how many unique names you have in the last name columns is to duplicate the last name columns (or move the columns themselves) so that they are next to each other. Then you can use a very basic
=COUNT(DISTINCT([First Last Name Column]@row:[Last Last Name Column]@row))
.
This will tell you how many unique names are within that range. So if you have 4 instructors, it will return 4. If you have 4 courses but one instructor taught two of them, then it will return 3 since you only have 3 unique names within the range.
• ✭✭✭✭✭✭
Options
I am also noticing that a lot of the " marks are slanted which means you probably constructed your formula in a word processor like Microsoft Word or Google Docs. Word processors tend to substitute straight quotes with slanted quotes, and those quotes will cause your formula to be unparseable as well.
• ✭✭✭✭✭✭
Options
I noticed that and just forgot to mention it. Thanks, Mike!
• ✭✭✭✭✭✭
Options
You bet!
• ✭✭✭✭✭
Options
Thank you SO VERY MUCH! Everything you posted worked! So very grateful. Now I can surface "numbers" to the dashboard. Blessings!
• ✭✭✭✭✭✭
Options
• ✭✭✭✭✭
Options
Thank you! I had no idea. Very good tip! | 814 | 2,877 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2024-26 | latest | en | 0.891961 |
http://stackoverflow.com/questions/9553354/how-do-i-get-the-precision-of-a-floating-point-number-in-javascript | 1,419,653,897,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1419447550279.98/warc/CC-MAIN-20141224185910-00018-ip-10-231-17-201.ec2.internal.warc.gz | 96,096,413 | 18,150 | # How do I get the precision of a floating point number in Javascript?
Basically, what i would like to have is the opposite of Number.prototype.toPrecision(), meaning that when i have number, what decimal precision does it currently have? E.g.
``````(12.3456).getPrecision() // 4
``````
-
`15 - Math.ceil(Math.log(x) / Math.log(10))` – Ignacio Vazquez-Abrams Mar 4 '12 at 8:12
possible dup of: stackoverflow.com/questions/1458633/… – alfasin Mar 4 '12 at 8:17
`x = 12.3456; var precision = String(x).replace('.', '').length - x.toFixed().length;` – blackpla9ue Mar 4 '12 at 8:20
@alfasin don't think so. In this case the OP doesn't want to restrict to a given precision, they just want to count the number of decimal places – JaredPar Mar 4 '12 at 8:23
One possible solution (depends on the application):
``````var precision = (12.3456 + "").split(".")[1].length;
``````
-
If by "precision" you mean "decimal places", then that's impossible because floats are binary. They don't have decimal places, and most values that have a small number of decimal places have recurring digits in binary, and when they're translated back to decimal that doesn't necessarily yield the original decimal number.
Any code that works with the "decimal places" of a float is liable to produce unexpected results on some numbers.
-
Ok, good to know. Anyway, i'm only dealing with how decimal numbers are shown, so changing them to string an splitting with '.' seems to be thee answer. – JussiR Mar 4 '12 at 11:00
There is no native function to determine the number of decimals. What you can do is convert the number to string and then count the offset off the decimal delimiter `.`:
``````Number.prototype.getPrecision = function() {
var s = this + "",
d = s.indexOf('.') + 1;
return !d ? 0 : s.length - d;
};
(123).getPrecision() === 0;
(123.0).getPrecision() === 0;
(123.12345).getPrecision() === 5;
(1e3).getPrecision() === 0;
(1e-3).getPrecision() === 3;
``````
But it's in the nature of floats to fool you. `1` may just as well be represented by `0.00000000989` or something. I'm not sure how well the above actually performs in real life applications.
-
Try the following
``````function countDecimalPlaces(number) {
var str = "" + number;
var index = str.indexOf('.');
if (index >= 0) {
return str.length - index - 1;
} else {
return 0;
}
}
``````
- | 642 | 2,355 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2014-52 | latest | en | 0.776114 |
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