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https://stat.ethz.ch/pipermail/r-help/2008-April/160603.html | 1,627,334,097,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046152144.92/warc/CC-MAIN-20210726183622-20210726213622-00435.warc.gz | 530,790,720 | 2,708 | [R] quasi-random sequences
Stas Kolenikov skolenik at gmail.com
Sun Apr 27 01:10:44 CEST 2008
```You might want to shuffle coordinates independently to get rid of the
diagonals. Otherwise what quasi-random sequence guarantee are upper
boundaries on the coverage errors, but not anything nice-looking and
irregular. Sobol' sequences, even though they are theoretically
superior to some others (e.g., Halton sequences more popular among
economists), are especially nasty in producing bands and bricks on the
low dimensional plots.
Among statisticians, Art Owen from Stanford is almost the only one
interested in this sort of stuff (referred to as quasi-Monte Carlo, in
his field(s)). You might have better luck on a physics list with a
question like yours.
On Sat, Apr 26, 2008 at 5:22 AM, baptiste Auguié <ba208 at exeter.ac.uk> wrote:
> Dear list useRs,
>
> I have to generate a random set of coordinates (x,y) in [-1 ; 1]^2
> for say, N points. At each of these points is drawn a circle (later
> on, an ellipse) of random size, as in:
>
>
> > N <- 100
> >
> > positions <- matrix(rnorm(2 * N, mean = 0 , sd= 0.5), nrow=N)
> > sizes<-rnorm(N, mean = 0 , sd= 1)
> > plot(positions,type="p",cex=sizes)
>
>
> My problem is to avoid collisions (overlap, really) between the
> points. I would like some random pattern, but with a minimum
> exclusion distance. In looking up "Numerical recipes in C", I found
> out about some Sobol quasi-random sequences, which one can call from
> the gsl package,
>
>
> > library(gsl)
> >
> > g <- qrng_alloc(type="sobol",dim=2)
> > qrng_get(g,n= N) ->xy
> >
> > plot((xy),t="p",cex=0.5)
>
> but this does not look very random: I clearly see some pattern
> (diagonals, etc...), and even the non-overlapping condition is not
> impressive.
>
> One (painful) way I can foresee is to check the distance between each
> symbol and the others, and move the overlapping ones in a recursive
> manner. Before delving into this, I wanted to check I'm not
> overlooking something in the rgl quasi-random sequences, or missing a
> more obvious way to generate such patterns. Perhaps solving an
> electrostatic problem with a potential both attractive at long
> distances and repulsive at short distances is a better way? I have a
> vague recollection of hearing that somewhere to position points
> evenly on a sphere.
>
--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I don't check Gmail account regularly.
``` | 701 | 2,488 | {"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-2021-31 | latest | en | 0.913343 |
http://physics.stackexchange.com/questions/tagged/kinematics?sort=unanswered&pagesize=15 | 1,469,322,405,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257823805.20/warc/CC-MAIN-20160723071023-00294-ip-10-185-27-174.ec2.internal.warc.gz | 197,127,713 | 27,307 | # Tagged Questions
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32 views | 1,953 | 8,633 | {"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} | 2.890625 | 3 | CC-MAIN-2016-30 | latest | en | 0.901131 |
http://thelogician.net/FUTURE-LOGIC/Actual-Propositions-5.htm | 1,718,751,109,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861794.76/warc/CC-MAIN-20240618203026-20240618233026-00524.warc.gz | 28,455,191 | 32,722 | CHAPTER 5.PROPOSITIONS.
1.Terms and Copula.
Logic looks upon sentences as attempts to record or predict reality, which may or may not be correct. For this reason, it calls thempropositions, to stress their fallibility. Logic develops by scrutiny of ordinary thought and language, but also sets especially rigid structural standards in order to be able to develop systematically.
Looking at many propositions, we see that irrespective of their particular contents, they appear to share certain ‘forms’. Our job is to analyze each form, how it is structured, what it means and implies, what are its interrelationships with other propositions, and how it can be known to be true.
Our study begins with one form shared by many propositions, ‘S is P’. Propositions of this sort are characterized ascategorical, meaning that they are unconditional. We call ‘S’ thesubject; ‘is’, thecopula; and ‘P’ thepredicate. The subject and predicate are both calledterms. The copula relates the terms together in a certain way. We may view the subject as our center of interest, while the predication (copula and predicate) provides us with additional information concerning it.
Note well how the terms are treated as ‘variables’, while other features such as the copula (so far) are kept ‘constant’, like in algebra. In this way, we can theoretically concentrate on the properties of a kind of proposition, without regard to the specific ‘values’ which might take the place of the symbols S and P. Form is released from content.
We owe this artifice to Aristotle’s genius. In one stroke, it made possible the development of a science of logic, because the study of relations and processes was thereby greatly facilitated, as we shall see.
We will concentrate mainly on categoricals calledclassificatory. Here, the subject and predicate are classes, and their copula informs us that they contain members in common. Typically, in a general proposition, the subject is a species and the predicate a genus; for example, ‘trees are plants’. Other forms will be dealt with eventually.
2.Polarity and Quantity.
Propositions may be distinguished by thepolarityof their copula. Thus, ‘S is P’ is said to have apositivecopula; ‘S is not P’, anegativeone. (Polarity is traditionally also known as ‘quality’, note, but since this word has other meanings it will be avoided here.)
We could view ‘is’ and ‘is not’ as two distinct relations (which happen to be contradictory), or as respectively the presence and absence of the same relation of ‘being’ (so that ‘is-not’ means ‘not-is’); logically, these viewpoints are equivalent.
The characterization of propositions as affirmations or denials has accordingly two senses, one absolute and the other relative. Normally, an assertion with a positive copula is called affirmative, and that with a negative copula is called denying; but also, we say of either polarity that it affirms itself and denies the other.
Another relevant distinction between propositions refers to theirquantity. This primarily concerns the subject, clarifying how much of it we intend by our statement. The quantity is often left tacit in everyday discourse, but for the purposes of science, we have to be more explicit.
If S is a specific, recognizable individual, we use the designation ‘this S’, and the proposition is said to besingular(and indicative). Any proposition which is not singular may be calledplural. If S refers to the whole class, we say ‘all S’, and the proposition is calledgeneralor universal. If S is a loose reference to some unspecified member(s) of the class, we say ‘some S’, and the proposition is calledparticular.
Other quantifiers define ‘some’ more precisely. Thus, ‘a few’ or ‘many’ mean, a small or large number; ‘few’ or ‘most’ mean, a minority or majority, a small or large proportion. These for most purposes have the same logical properties as particulars, though the latter two sometimes require special treatment.
By combining these different features, the various polarities and quantities, we obtain the following list of classificatory propositions. These are traditionally assigned symbols as shown to facilitate treatment (from the Latin wordsAffIRmo and nEGO, which serve as mnemonics).
A All S are P E No S is P R This S is P G This S is not P I Some S are P O Some S are not P
The other quantities are also applicable to the two polarities, of course, as in ‘Few or Most S are or are not P’, but have not been traditionally symbolized.
All such propositions are calledactual, because they suggest the relation they describe as taking place in the present. In that case, they imply that the units which their terms referred to do exist, i.e. that there are S’s and P’s in the world at the time concerned. This claim is open to debate, but will be taken for granted for now — later, we will clarify the issues involved, and look into the implications of not making such an assumption.
3.Distribution.
Plural propositions normally refer us to their class memberseach one singly; the plural is simply a shorthand statement of a number of independent singulars. Each individual, subsumed by the subject, and included in the all or some enumeration, is separately and equally related to the predicate. The predication is intended to be ‘dispensively’ applied; meaning severally, not jointly or collectively.
Thus, ‘All S are P’ or ‘Some S are P’, here means ‘S1 is P’, ‘S2 is P’, ‘S3 is P’, … and so on; ‘No S is P’ or ‘Some S are not P’ here means ‘S1 is not P’, ‘S2 is not P’, …etc. — until every S, this one, that one, and the others, which are included by the quantity have been listed.
The doctrine of distribution is that if all the members of a class are covered, the term is called ‘distributive’; otherwise it is not.
This means that the subjects of universals,AandE, are distributive; whereas those of particulars,IandO, are not, since the instances involved are not fully enumerated. With regard to singulars,RandG, they are effectively distributive, insofar as they point to unique subjects.
What of the distribution of predicates? The predicates of negatives,E,G, andO, are distributive, because P is altogether absent from the cases of S concerned ; while in affirmatives,A,R, andI, the predicates are undistributive, since things other than the cases of S concerned might be P.
These properties can be illustrated by means of Euler diagrams, named after the Swiss logician who invented them. In these, S and P are represented by the areas of circles, which overlap or fail to overlap to varying degrees. The reader is invited to explore these analogies. (Very similar are Venn diagrams, named after another logician; the latter differ in that they stress the areas outside the circles, the areas of nonS or nonP.)
Diagram 5.1Euler Circles.
InApropositions, the S circle is wholly within the P circle, and smaller or equal in size to it. InE, the circles are apart, whatever their relative sizes. InIpropositions, the two circles at least partly intersect, whether each covers only a part of the other’s area, or S is wholly embraced by P, or P by S, or they both cover one and the same area. InO, the two circles at least partly do not overlap, whether each only covers only a part of the other’s area, or neither covers any part of the other’s area.
The forms in current use, listed above, are so designed that we can specify alternate quantities for the predicate, if necessary, simply by making an additional statement, in which the original predicate is subject and the original subject is predicate, with the appropriate distributions.
As a result of the distribution doctrine, there have been attempts to invent forms which quantify the predicate, but they have not aroused much interest, being artificial to our normal ways of thinking.
4.Permutation.
Classification is a special outlook, but one we can use to develop Logic with efficiently, because it allows us to standardize statements. Classification is more mathematical in nature, and so easier of treatment, than other relations. The process of rewording a proposition, so that its terms are overlapping classes, is called ‘permutation’.
Note that, in formal logic, the word ‘universal’ is used in a quantitative sense, to apply to general propositions, which address the totality of a class. But in philosophy, a ‘universal’ is understood as the common factor, resemblance, similarity, which led us or allowed us to group certain units into a class; in this sense every term is a universal for its members, and even a particular proposition contains universals, except that they happen to be only partially addressed.
Likewise, the word ‘particular’ refers to less than general propositions, in formal logic; whereas, in philosophy, it is understood to mean concrete individuals, as distinct from abstract essences. Normally, the context makes clear what sense of each word we intend.
a.The equivocation of the word ‘universal’ is not entirely an historical accident. A proposition may have a ‘quality as such’ as its subject, and only incidentally imply a quantifiable subject-class. Thus, for example, ‘greenness is a (kind of) color’ and ‘all green things are colored’ do not mean quite the same, though their truths are related.
Propositions which have as their subject a quality as such, a universal in the philosophical sense, are virtually singular in format. To be quantified, their subject must be reworded somewhat. This is called permutation of the subject.
b.As Logic has developed, it has come to focus especially on the classificatory sense of ‘is’, because attribution, and other relations, can be reduced to it. Colloquially, the ‘is’ copula first suggests that the subject has a certain attribute, viz. the predicate, as in ‘trees are green’. But attribution is a more complex and qualitative relational format than classification, requiring more philosophical analysis.
Many propositions which normally are thought without the classifying ‘is’ copula, can be restructured to fit into it, while more or less retaining the same meaning. Thus, in our example, we would shift from the sense ‘trees have greenness’ to the sense ‘trees are greenness-having-things’. This is called permutation of the predicate.
Most logical processing of categoricals assumes that the statements involved have been permuted into classificatory form. Note well that permutation merelyconcealsthe previously intended relationship in a new term, it does not annul or replace it. The difficult relation is once-removed, put out of the way; it is not defined. | 2,275 | 10,603 | {"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} | 3.1875 | 3 | CC-MAIN-2024-26 | latest | en | 0.954545 |
https://www.bartleby.com/questions-and-answers/merkel-inc.-has-a-monopoly-in-producing-coconut-oil.-draw-a-graph-to-show-the-profit-maximization-by/420063a6-0ecc-4589-999c-1fbe9c0e8dac | 1,581,910,782,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875141653.66/warc/CC-MAIN-20200217030027-20200217060027-00350.warc.gz | 680,246,389 | 29,046 | # Merkel, Inc. has a monopoly in producing coconut oil. Draw a graph to show the profit maximization by Merkel, Inc. Label the profit maximizing quantity, QM. Show that Merkel, Inc. is earning negative economic profit [that is, economic loss]. Label the loss either by shading or by using the letters to define the area.Make sure all the curves, axes and lines are labeled appropriately.Suppose that the coconut oil is produced in a perfectly competitive market. Use the graph you drew for part a) to show the profit maximizing quantity [label it Qc] produced by the perfectly competitive industry.Compare the competitive price with the monopoly price. Does the competitive industry earn loss or the profit situation is different now? Explain.Use the profit situation [loss or economic profit as drawn] to explain the long run adjustment by the firms in perfect competition.
Question
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• Merkel, Inc. has a monopoly in producing coconut oil.
1. Draw a graph to show the profit maximization by Merkel, Inc. Label the profit maximizing quantity, QM. Show that Merkel, Inc. is earning negative economic profit [that is, economic loss]. Label the loss either by shading or by using the letters to define the area.
Make sure all the curves, axes and lines are labeled appropriately.
1. Suppose that the coconut oil is produced in a perfectly competitive market. Use the graph you drew for part a) to show the profit maximizing quantity [label it Qc] produced by the perfectly competitive industry.
2. Compare the competitive price with the monopoly price. Does the competitive industry earn loss or the profit situation is different now? Explain.
3. Use the profit situation [loss or economic profit as drawn] to explain the long run adjustment by the firms in perfect competition.
check_circle
Step 1
1.
Monopoly:
In a monopoly market, profit maximization will occur at where the marginal revenue and marginal cost intersect each other.
Monopoly firm earns the negative profit, if price is less than the average cost.
Step 2
Figure -1 shows the negati...
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https://dataz4s.com/statistics/bias/ | 1,638,970,157,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363510.40/warc/CC-MAIN-20211208114112-20211208144112-00391.warc.gz | 268,333,607 | 15,000 | +34 616 71 29 85 carsten@dataz4s.com
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# Bias
In statistical analysis we intent to avoid bias, as bias lead to results that are not representative for the population we are studying. To reduce bias, we would wish to apply a probability sampling if resources allow for it.
## Sampling frame bias
Sampling bias is typically understood as inappropriate methods applied for the selecting of a certain type of sample. We use the wrong methods for the choosing of a sample. Sampling frame can be inappropriate and/or not representative of the population.
Example 1: Say we wish to understand certain conditions among our colleagues. We could draw a list of all employees and then select staffs from this list. This list is the sampling frame. The sample frame is the subset of the population, or the whole of the population, that we wish to study.
Example 2: Say we wish to study certain conditions among Norwegian adults and that we have legal access to a list of cell phone numbers of Norwegian citizens. It could turn out that a relatively large proportion of the Norwegian pensioners do not have cell phones. That means that the sample frame is incorrect, as there will be a so-called undercoverage of the pensioners in the sample.
Example 3: When a media, say that an online and printed magazine makes an opinion poll among their subscribers and take the results as representative for the whole country.
For example: A Spanish media publishes an article saying: “Spanish citizens prefer cheeseburgers rather than paella”. For the sake of this example, say that this media is called “Spanish Cheeseburger Lovers”.
Loosely stated: They have run a poll among cheeseburger lovers asking if they prefer cheeseburgers rather than paella. This sampling frame is obviously not representative for the whole of the Spanish population.
## Response bias
How do the individuals in the sample respond to the survey? That depends on how the questions, the poll or the survey is introduced to them. Problems related to this relation are called response bias.
## Voluntary response bias
Reality shows, fan culture programs, call-in programs, mail-in surveys and other surveys in which there is a cost to participate usually are typically used by participants with strong views.
They are willing to pay and to participate in order to get their “voice out”. These kinds of surveys are typically over-covered with people who feel passionate about their views and under-covered with people who have different opinions but who are less passionate about them.
Another example of voluntary response bias are the polls for which everyone can vote or express their opinion the number of times they wish.
## Non-response bias
“Oh, one more of those salespersons calling. I really can’t take the time”. Maybe, this reaction rings a bell (for me it does (sorry!)). This is one of the mayor problems in polling: the difficulty in getting people to participate. There is no way that we can get these people’s opinions reflected in the survey, and therefore any poll or survey can contain non-response bias.
## Questionnaire bias
One question can be asked in different ways:
• Do you believe that it is reasonable to add some extra tax on meat and in this way contribute to the critical global climate situation?
• Do you believe meat consumption should be punished adding more tax to the prices, assuring extra income for the state?
The way a question is asked influences the response. In this case the persons with a less passionate feeling about the meat-taxing issue might be influenced on one way or the other through the way the question is asked. This is questionnaire bias.
## Incorrect response bias
In statistics we work with datapoints, but we should always bear in mind that there is a quality to each point. The datapoint can be completely wrong compared to the context!
The datapoint can be a yes, when it is actually a no. Or it can be 10 when it is actually 5. Questions can be answered in a non-truthful way. There can be many reasons for the individuals not to answering truthfully, and this is called incorrect bias.
## Size bias
Size bias occur when a certain subgroup of a population is incorrectly represented as to its’ number of individuals in the sample. It can be over- or under-represented.
Example: What is the mean size as to number of employees in start-up companies based in Malaga, Spain?
Say we go to Malaga Startup Greenhouse office facilities where “a great proportion” of Malaga start-ups are housed within their first years of their start-up. We go to the entrance door and ask people who enter about the size of the company they work in.
Say that the situation is that 3 companies have +20 workers (+60 employees) and 15 companies have less than 3 workers (less than 45).
Chances are that half of the workers that we ask will answer that they are more than 15 workers. So, I might end up with a wrong conclusion stating that most of the Malaga startups have more than 15 workers. This is an example of size bias.
Or the marathon example: I feel intimidated whereas other runners are passing by me all the time. My sample size, in this case, include only the runners passing by me, because I don’t see the ones that don’t pass me. This is another of size bias.
## Bias learning resources
#### Carsten Grube
Freelance Data Analyst
p
p
p
##### ANOVA & the F-distribution
+34 616 71 29 85
Call me
Spain: Ctra. 404, km 2, 29100 Coín, Malaga
...........
Denmark: c/o Musvitvej 4, 3660 Stenløse
Drop me a line
What are you working on just now? Can I help you, and can you help me? | 1,210 | 5,631 | {"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-2021-49 | latest | en | 0.939445 |
https://www.supercalendar.com/days-until/28-july/ | 1,685,599,481,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647614.56/warc/CC-MAIN-20230601042457-20230601072457-00013.warc.gz | 1,085,064,713 | 3,997 | # Days Until July 28, 2023
## Calculation Process
The days difference between June 01, 2023 and July 28, 2023 is calculated as follows:
Step 1: Calculate the number of days from the start of the year to each date.
1. For June 01, 2023:
• Days from start of the year 2023 to June 01, 2023: 152 days
2. For July 28, 2023:
• Days from start of the year 2023 to July 28, 2023: 209 days
Step 2: Subtract the two results tofind the difference.
1. Difference = Days in later date - Days in earlier date
2. Difference = 209 - 152
3. Difference = 57 days
How many days are between June 01, 2023 and July 28, 2023?
Ans: There are 57 days between those two dates.
How many weeks are between June 01, 2023 and July 28, 2023?
Ans: There are 8 weeks between those two dates.
How many months are between June 01, 2023 and July 28, 2023?
Ans: There are 1 months between those two dates.
How many years are between June 01, 2023 and July 28, 2023?
Ans: There are 0 years between those two dates.
## 28 July
July 28th is an important day for different countries around the world. Here are some significant events that have happened on this day:
• World Hepatitis Day: Established by the World Health Organization (WHO), this day aims to raise awareness about the viral hepatitis and reduce the stigma that surrounds the disease. Hepatitis is a liver inflammation caused by a virus or liver damage, which can become chronic and cause serious complications.
• Birthday of Beatrix Potter: The beloved English author and illustrator, best known for her children's books, such as "The Tale of Peter Rabbit," was born on July 28th, 1866. Her stories have been translated into many languages and have enchanted generations of children worldwide.
• Peruvian Independence Day: Peru celebrates its independence from Spain on July 28th, 1821. The country's rich cultural heritage, diverse geography, and vibrant festivals attract tourists from all over the world.
• First public demonstration of the telegraph: On July 28th, 1837, British inventor Charles Wheatstone and scientist William Fothergill Cooke gave the first public demonstration of their electric telegraph between Euston and Camden Town in London. The device used a system of wires and needles to send messages over long distances, revolutionizing communication.
July 28th is also the birth date of several notable individuals, such as:
• Jacqueline Kennedy Onassis, American first lady and style icon
• Jim Davis, American cartoonist and creator of the comic strip "Garfield"
• Barbara La Marr, American silent film actress and screenwriter
• Ricardo Montalbán, Mexican-American actor known for his roles in "Fantasy Island" and "Star Trek"
Whether you're celebrating World Hepatitis Day, enjoying the works of Beatrix Potter, visiting Peru, sending instant messages, or remembering the legacies of great people, July 28th marks an important date in history. | 696 | 2,914 | {"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} | 3.84375 | 4 | CC-MAIN-2023-23 | latest | en | 0.977606 |
https://www.queryhome.com/puzzle/22409/double-decker-passengers-upper-lower-deck-group-passengers | 1,542,374,737,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039743046.43/warc/CC-MAIN-20181116132301-20181116154301-00546.warc.gz | 967,827,534 | 30,732 | # Double Decker bus can have 80 passengers 35 in upper and 40 in lower deck. how many ways can a group of 80 passengers...
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A double Decker bus can accommodate 80 passengers 35 in upper deck and 40 in lower deck. In how many ways can a group of 80 passengers be accommodated if 5 refuse to sit in the lower deck and 10 refuse to sit in the upper deck
posted Aug 1, 2017
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http://openstudy.com/updates/55929398e4b0e2e1a96258ac | 1,477,261,805,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719437.30/warc/CC-MAIN-20161020183839-00132-ip-10-171-6-4.ec2.internal.warc.gz | 197,335,634 | 14,716 | ## anonymous one year ago *Area of the base equals* a)8 pi square units b)16 pi square units c) 64 pi square units
1. anonymous
2. anonymous
3. anonymous
@elic2k15
4. anonymous
@UsukiDoll
5. anonymous
@math1234
6. UsukiDoll
I'm juggling one question back in forth.. so if I'm slow to reply sorry in advanced. Anyway we are given a cylinder |dw:1435669876398:dw|
7. anonymous
It's okay
8. UsukiDoll
the formula for area of the base of a cylinder is A = pi(r^2)
9. anonymous
Okay. But every time I put it into the calculator it shows: either 39.4384 or 50.24
10. UsukiDoll
I know.. we don't calculate the pi part.. leave it as is. so if r = 4 what is r^2?
11. UsukiDoll
looking at the choices... I think it doesn't want you to calculate the pi.. it's just finding the r and then squaring it
12. anonymous
Well then it's just 16
13. anonymous
So it's B?
14. UsukiDoll
A=pi(4^2) A=pi(16) =16 pi yeah
15. anonymous
Thanks. So would it be about the same thing for this problem?
16. anonymous
A cylinder has a volume of 245 pi cubic units and a height of 5 units. The diameter of the cylinder is a) 7 units b) 14 units c) 49 units
17. UsukiDoll
I think we need the diameter of the cylinder formula.
18. UsukiDoll
yeah we need a different formula for that.
19. UsukiDoll
$\large V = \pi r^2h$
20. UsukiDoll
so given height is 5 units volume is 245 pi cubic units . Looks like we're solve for r and then the diameter is twice the radius (d=2r) .. AHA! We need to find the radius first
21. anonymous
Yes
22. UsukiDoll
ok let V = 245, and h = 5
23. anonymous
V r h = � or 2 =
24. anonymous
Well that didn't come out right
25. anonymous
:(
26. UsukiDoll
$\large 245 = \pi r^2(5)$
27. anonymous
What's "large"?
28. UsukiDoll
that's to make the font large
29. UsukiDoll
oh are you trying to use the equation tool? right click show math as -> tex command and it will have this code or text you can copy and paste. And then click on the equation tool and paste.
30. anonymous
Oh
31. UsukiDoll
so we are solving for r that would mean that r needs to be by itself
32. UsukiDoll
our first goal is to have r^2 by itself .. and then afterwards we can take the square root
33. anonymous
$V = \pi r2h$
34. anonymous
r is squared
35. UsukiDoll
yeah it should have that ^ that carrot sign
36. UsukiDoll
$\large V = \pi r^2h$
37. UsukiDoll
anyway back to this $\large 245 = \pi r^2(5)$ we need r^2 by itself so what do we need to do?
38. UsukiDoll
should we add both sides? subtract both sides? multiply both sides? or.. divide both sides by 5pi
39. anonymous
divide both sides by 5 pi
40. UsukiDoll
yes. $\large \frac{245}{5 \pi} = r^2$
41. UsukiDoll
now we take the square root of both sides
42. anonymous
So 49 = ?
43. anonymous
Umm
44. UsukiDoll
we're not done.. we need to take the square root on both sides
45. UsukiDoll
UH OH! I need to refresh my screen is crazy
46. anonymous
kk
47. anonymous
48. anonymous
I neded to digest a little
49. UsukiDoll
ok so taking the square root of both sides $\large \sqrt{ \frac{245}{5 \pi} }= \sqrt{r^2}$ what is the square root of r^2
50. UsukiDoll
we need to take the square root of r^2 so we can have r
51. UsukiDoll
then once we have our r we can get the diameter. which is d =2r
52. anonymous
r=2.5
53. UsukiDoll
that's not a choice for answers that would've yielded d = 5.. that's not right
54. anonymous
No wait. 5 was the height not the diameter
55. anonymous
56. UsukiDoll
wait a minute we are solving for r.
57. UsukiDoll
we have already plugged in V and h... now we need to take the square root of both sides. We're almost there
58. anonymous
I was thinking that the diameter is 7
59. anonymous
cus 7 squared is 49
60. UsukiDoll
$\large \sqrt{ \frac{245}{5 \pi} }= \sqrt{r^2}$ becomes ??? what is the square root of r^2
61. anonymous
49 times 3.14 = 153.86
62. anonymous
Umm
63. anonymous
7
64. UsukiDoll
once we find r we can find the diameter which is d = 2r
65. UsukiDoll
What? ok no substituting we are solving for r we need the square root of r^2 .
66. UsukiDoll
I want an r by itself
67. UsukiDoll
we have square rooted both sides.. which is correct. Now we just need the square root of r^2 Then we have this $\[\[\large \sqrt{ \frac{245}{5 \pi} }= r$ \]
68. UsukiDoll
now the diameter is d=2r so d = 2( That whole square root)
69. UsukiDoll
$\large \sqrt{r^2} \rightarrow r^{\frac{2}{2}} \rightarrow r^1 \rightarrow r$
70. UsukiDoll
so now our $d=2(\sqrt{\frac{245}{5 \pi}})$
71. UsukiDoll
so we just need 245 divided by 5 pi... take the square root of that result and multiply by 2
72. anonymous
7.9
73. UsukiDoll
yes. so our diameter is 7.9 kind of a dangerous number because we can round up to 8
74. UsukiDoll
7 units would be the closest to the answer.. though the real answer is 7.9
75. anonymous
Okay. Look I'm sorry if I aggravated you. It's been a long couple of weeks and I'm really tired
76. anonymous
Thanks for the help. I really appreciate it
77. UsukiDoll
it's ok ... I'm also tired.. in fact it's almost 4 in the morning. I need zzz's before my dad get suspicious again.
78. UsukiDoll
that's why I had my latex wrong... r to the first power is just r if it was r^0 that would've been 1. But I should always take the advice of never do math while tired.
79. anonymous
Yeah I can connect with that
80. UsukiDoll
I have to go sleep. night
81. anonymous
Really. Wow it's 9:55 AM here
82. anonymous
well alright
83. anonymous
I live in Florida btw | 1,740 | 5,553 | {"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} | 3.890625 | 4 | CC-MAIN-2016-44 | longest | en | 0.828924 |
https://de.mathworks.com/matlabcentral/cody/problems/95-given-two-strings-find-the-maximum-overlap/solutions/735097 | 1,606,659,200,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141198409.43/warc/CC-MAIN-20201129123729-20201129153729-00549.warc.gz | 262,215,220 | 17,177 | Cody
Problem 95. Given two strings, find the maximum overlap
Solution 735097
Submitted on 14 Sep 2015 by Jean-Yves Tinevez
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
Test Suite
Test Status Code Input and Output
1 Pass
%% s1 = [1 2 3 4 5]; s2 = [5 4 3 2]; s3_correct = [1 2 3 4 5 4 3 2]; assert(isequal(overlap(s1,s2),s3_correct))
2 Pass
%% s1 = [1 0 1 7 7 7 6]; s2 = [1 0 1 0 1]; s3_correct = [1 0 1 0 1 7 7 7 6]; assert(isequal(overlap(s1,s2),s3_correct))
3 Pass
%% s1 = [3 1 4 1 5 9 2 6 5 3 5]; s2 = [9 2 6 5]; s3_correct = [3 1 4 1 5 9 2 6 5 3 5]; assert(isequal(overlap(s1,s2),s3_correct))
4 Pass
%% s1 = 1:100; s2 = [50 51]; s3_correct = s1; assert(isequal(overlap(s1,s2),s3_correct))
5 Pass
%% s1 = 90:10:200; s2 = 10:10:120; s3_correct = 10:10:200; assert(isequal(overlap(s1,s2),s3_correct))
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Start Hunting! | 414 | 1,006 | {"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-2020-50 | latest | en | 0.746994 |
https://www.physicsforums.com/threads/union-and-intersection-of-empty-collection.762940/ | 1,531,880,059,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589980.6/warc/CC-MAIN-20180718002426-20180718022426-00243.warc.gz | 957,534,258 | 14,890 | # Union and Intersection of Empty Collection
1. Jul 23, 2014
### Greg Bernhardt
Definition/Summary
A Topological Space can be defined as a non empty set X along with a class of sets, called a topology on X which is closed under (1) arbitrary unions (2) finite intersections. It can be assumed that this will always include X and p (the empty set), but understanding the reason for this can be quite difficult.
Equations
Let
X be the universe
P be the empty collection
Q be the collection of compliments of P
p the empty set
U = Union
I = Intersection
C = Compliment
Briefly, p is included as the union of the empty collection and X is included as the intersection of the empty collection. It's the latter of these that causes conceptual difficulties. How can the intersection of a collection with nothing in it be the whole universe?
If we first accept that as a simple accumulation of elements it's easy to grasp that U(P) = p. Now we can use De Morgan's laws to calculate I(P). Normally when we deal with these laws we have a non empty collection of sets. So, the collection of compliments is also a non empty collection. In our case here though, there are no sets to have compliments of, so there are no compliments, so Q = P and thus U(Q) = U(P) = p. Now, by De Morgan:
The compliment of the union of a collection = The intersection of the collection of compliments.
So, C(U(P)) = I(Q)
But, Q = P, so I(Q) = I(P)
Also, C(U(P)) = C(p) = X
Thus I(P) = X
Extended explanation
This is basically the key point that makes sense out of the logic of this situation. If you accept that U(P) = p and you get that Q = P, the result necessarily follows.
Another way of thinking about this involves returning to the ideas of basic set logic. Given a universe X, then any sub set A can be seen as a condition on the elements of X. EG: Consider the universe of all people visiting a fair ground. P1 = the collection containing C1 = {people taller than 130cm}, C2 = {people older than 13}, ...Cn = {people with no heart condition} ... etc. These are the conditions on a particularly dangerous fair ground ride. The intersection of this collection of sets/conditions is I(P1) = {people allowed to go on ride 1}, that is, only those people who satisfy all of the conditions. Now consider another ride, that's very safe and has no conditions of entry. This collection of conditions, P2, is empty and the intersection of this collection is I(P2) = {people allowed to go on ride 2} = X, that is, everyone.
* This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks! | 631 | 2,635 | {"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} | 3.8125 | 4 | CC-MAIN-2018-30 | latest | en | 0.942611 |
http://betterlesson.com/lesson/resource/2102173/how-high-can-you-count-table-docx | 1,488,269,636,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501174154.34/warc/CC-MAIN-20170219104614-00322-ip-10-171-10-108.ec2.internal.warc.gz | 33,739,206 | 21,539 | ## How high can you count table.docx - Section 2: Investigation
How high can you count table.docx
How high can you count table.docx
# How High Can You Count?
Unit 2: Scale of the Universe: Making Sense of Numbers
Lesson 2 of 21
## Big Idea: Simple patterns can help us make sense of very large values.
Print Lesson
3 teachers like this lesson
Standards:
Subject(s):
Math, Scalars, Number Sense and Operations, scientific notation, large numbers, Number Sense
60 minutes
### Shaun Errichiello
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Environment: Urban | 301 | 1,265 | {"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-2017-09 | latest | en | 0.785305 |
https://quick-advices.com/how-many-glasses-of-water-is-in-33-oz/ | 1,686,274,481,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224655244.74/warc/CC-MAIN-20230609000217-20230609030217-00453.warc.gz | 517,294,183 | 44,392 | # How many glasses of water is in 33 oz?
## How many glasses of water is in 33 oz?
33 oz = 4.125 cups You may also be interested to know that 1 cup is 12.5 percent of an ounce.
### Is 33.8 fl oz of water enough?
A new article published in the Harvard Health Letter recommends drinking 30 to 50 ounces a day, an amount equal to about four to six glasses of water.
#### How many 32 oz bottles does it take to make a gallon?
There are four 32 oz bottles in a gallon. To find the answer yourself, take 128 ounces, which is the number of ounces in a gallon, and divide it by 32 ounces in a water bottle. 128 divided by 32 equals 4, so there are four 32 ounce bottles in a gallon.
How many glasses of water are in 32 ounces?
The answer, which is four, tells you that there are 4 cups in 32 ounces. You can also reverse the equation to figure out how many ounces there are in any given number of cups. For this, you would simply need to multiply the number of cups by eight. For example, if you have 6 cups, you would multiply 6 by 8.
How much is 33.8 ounces of water?
There are 4 water bottles in 33.8 fl oz equals a gallon. To figure out the number of water bottles that will count as a gallon, you need to get fluid oz value.
## How many cups make 32 ounces?
32 oz = 4 cups You may also be interested to know that 1 cup is 12.5 percent of an ounce.
### Is it bad to chug 32 oz of water?
If a person is not thirsty and his or her urine is pale yellow, that person is likely drinking enough water. Consuming a 32-ounce drink of water at once can throw off your body’s electrolyte balance, negatively impacting your health.
#### Is 32 oz half a gallon?
The answer is simple there are 64 fl oz in half a gallon and 128 fl oz in 1 full gallon .
How many servings is 32 ounces?
32 ounces. Do the math. That is a little over five 6 0z. servings.
How many oz of water should I drink a day?
The National Academies of Science, Engineering and Medicine recommends that men drink about 3.7 liters (about 125 ounces) a day and women drink 2.7 liters (about 91 ounces). “Those amounts include the water that’s in our food,” says Dr. Sukol. “So it doesn’t mean that you have to drink that many ounces of water.
## What size is 32 ounces?
Overview: Glass & Plastic Container Size Conversion Chart
Container Size Dram Ounce
8 oz. 64 8
12 oz. 96 12
16 oz. 128 16
32 oz. 256 32
### How many fluid ounces is 32 ounces?
How Many Ounces are in a Fluid Ounce?
Volume in Fluid Ounces: Weight in Ounces of:
Water Cooking Oil
30 fl oz 31.3 oz 27.54 oz
31 fl oz 32.34 oz 28.46 oz
32 fl oz 33.38 oz 29.38 oz | 704 | 2,601 | {"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-2023-23 | latest | en | 0.955614 |
http://www.algebra.com/algebra/homework/Finance/Finance.faq.question.298676.html | 1,369,300,635,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368703057881/warc/CC-MAIN-20130516111737-00002-ip-10-60-113-184.ec2.internal.warc.gz | 313,975,385 | 4,326 | # SOLUTION: An equivalent form of this equation is? a/(b-10)=a/3
Algebra -> Algebra -> Finance -> SOLUTION: An equivalent form of this equation is? a/(b-10)=a/3 Log On
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Algebra in Finance Solvers Lessons Answers archive Quiz In Depth
Click here to see ALL problems on Finance Question 298676: An equivalent form of this equation is? a/(b-10)=a/3Answer by user_dude2008(1861) (Show Source): You can put this solution on YOUR website!a/(b-10)=a/3 equivalent to 3a = a(b-10) | 182 | 667 | {"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-2013-20 | latest | en | 0.794386 |
https://community.splunk.com/t5/Splunk-Search/Is-this-the-actual-total-cost-of-Splunk/td-p/492952 | 1,701,192,950,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679099892.46/warc/CC-MAIN-20231128151412-20231128181412-00556.warc.gz | 220,028,209 | 39,060 | Splunk Search
Is this the actual total cost of Splunk?
Explorer
Hello all,
I will be contacting the sales team as well but for now I wanted to get some clearer idea of the actual cost breakdown for Splunk with anyone who may have firsthand knowledge.
On the Pricing Calculator page we can see that a 100 GB/day connection costs \$63 per GB and multiplying that by 12 for each month gives us \$756 shown as \$750 on the same page
Now using this if we multiply this by 30 for each day of the month and multiply that by 100 for the 100 GB, is it fair to assume the total cost (which includes service as it is the annual license) is at least \$2,250,000 per year.
Cost per GB/Day - 63
Days per Month - 30
Months per Year - 12
GB Used per day - 100
63*30*12*100 = 2268000
Please correct me if I have misinterpreted the breakdown as I need to present the estimated yearly costs for using Splunk to our team.
Thanks.
Tags (5)
1 Solution
SplunkTrust
Hi @mustafag1,
there an error in your calculation, the license is for 100 GB/day, and this means that you can consume until 100 GB for each day (and you can exceed 5 times in 30 solar days) , but the cost isn't for day is an annual cost, not a daily cost!
You can see in https://www.splunk.com/en_us/products/pricing/calculator.html that an annual subscription for 100 GB/day costs 690 \$/GB, this means 69K\$ for one year.
Probably these values aren't fully exact because in the above page there still the value of the perpetual license that is over, but the order of magnitude of the prize should be correct and my hint is to wait for the prize of the sales man.
Ciao.
Giuseppe
SplunkTrust
Hi @mustafag1,
there an error in your calculation, the license is for 100 GB/day, and this means that you can consume until 100 GB for each day (and you can exceed 5 times in 30 solar days) , but the cost isn't for day is an annual cost, not a daily cost!
You can see in https://www.splunk.com/en_us/products/pricing/calculator.html that an annual subscription for 100 GB/day costs 690 \$/GB, this means 69K\$ for one year.
Probably these values aren't fully exact because in the above page there still the value of the perpetual license that is over, but the order of magnitude of the prize should be correct and my hint is to wait for the prize of the sales man.
Ciao.
Giuseppe
Explorer
It seems that my mistake was multiplying the number of days. I did suspect that the 30 would be the overkill for the calculations.
Thanks!
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https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-1-section-1-4-angles-and-their-relationships-exercises-page-37/46 | 1,708,596,332,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473738.92/warc/CC-MAIN-20240222093910-20240222123910-00193.warc.gz | 804,785,477 | 12,171 | ## Elementary Geometry for College Students (6th Edition)
The difference between the measure of its supplement and the measure of its complement is $90^{\circ}$
Let $A$ be the supplement of $x$: $A = 180^{\circ}-x$ Let $B$ be the complement of $x$: $B = 90^{\circ}-x$ We can find the difference between $A$ and $B$: $A-B = (180^{\circ}-x)-(90^{\circ}-x)$ $A-B = 180^{\circ}-x-90^{\circ}+x$ $A-B = 180^{\circ}-90^{\circ}$ $A-B = 90^{\circ}$ The difference between the measure of its supplement and the measure of its complement is $90^{\circ}$ | 176 | 543 | {"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} | 4.125 | 4 | CC-MAIN-2024-10 | latest | en | 0.932395 |
https://www.acmicpc.net/problem/21883 | 1,660,516,068,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572077.62/warc/CC-MAIN-20220814204141-20220814234141-00021.warc.gz | 559,478,484 | 8,650 | 시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 512 MB743100.000%
## 문제
Gandalf and Saruman are playing a game. Gandalf has $n$ potions in a row, and Saruman has $m$ potions in a row. Each potion has a magical power, Gandalf's potions have powers $a_1, a_2, \ldots, a_n$, and Saruman's potions have powers $b_1, b_2, \ldots, b_m$. Initially both of them have no unit of mana.
Players take turns. Gandalf moves first.
At each turn player takes the leftmost potion he has, drinks it, and receives $x$ units of mana, where $x$ is the power of the taken potion. If player does not have any potion on his turn, he loses the game. After drinking the potion, player may use his magical powers to destroy some potions of his opponent. Destroying one potion costs one unit of mana.
Each player wants to win, and, furthermore, wants to finish the game with the maximum possible number of potions left. A player who is going to lose tries to minimize the number of potions of the opponent in the end of the game. Determine who is going to win and how many potions they have at the end of the game if both players play optimally.
## 입력
The first line contains two integers $n$ and $m$ --- the number of potions that Gandalf and Saruman have, respectively ($1 \le n, m \le 200$).
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ --- the powers on Gandalf's potions from left to right ($0 \le a_i \le 200$).
The third line contains $m$ integers $b_1, b_2, \ldots, b_m$ --- the powers on Saruman's potions from left to right ($0 \le b_i \le 200$).
## 출력
Print the name of the player who wins the game and the number of potions that the winning player has at the end of the game.
## 서브태스크
번호배점제한
15
$a_i = 0, b_i = 0$
210
$n, m \leq 5$
325
$n, m \leq 20$
435
$n, m \leq 100$
525
## 예제 입력 1
5 4
1 0 1 4 4
2 3 0 5
## 예제 출력 1
Gandalf 0
## 예제 입력 2
3 4
1 3 4
3 2 0 0
## 예제 출력 2
Saruman 2
## 예제 입력 3
9 9
2 0 1 2 1 1 2 1 2
1 2 1 1 1 0 1 2 2
## 예제 출력 3
Gandalf 1
## 채점 및 기타 정보
• 예제는 채점하지 않는다. | 681 | 2,004 | {"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": 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} | 2.984375 | 3 | CC-MAIN-2022-33 | latest | en | 0.885524 |
https://questions.examside.com/past-years/jee/question/let-leftab-xc-x2right10sumlimitsi020-jee-main-mathematics-aipuwll1tndcf5ez | 1,723,436,065,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641028735.71/warc/CC-MAIN-20240812030550-20240812060550-00322.warc.gz | 371,607,086 | 50,742 | 1
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Let $\left(a+b x+c x^{2}\right)^{10}=\sum\limits_{i=0}^{20} p_{i} x^{i}, a, b, c \in \mathbb{N}$.
If $p_{1}=20$ and $p_{2}=210$, then $2(a+b+c)$ is equal to :
A
15
B
8
C
6
D
12
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
The coefficient of $$x^{5}$$ in the expansion of $$\left(2 x^{3}-\frac{1}{3 x^{2}}\right)^{5}$$ is :
A
$$\frac{26}{3}$$
B
$$\frac{80}{9}$$
C
9
D
8
3
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Fractional part of the number $$\frac{4^{2022}}{15}$$ is equal to
A
$$\frac{8}{15}$$
B
$$\frac{4}{15}$$
C
$$\frac{1}{15}$$
D
$$\frac{14}{15}$$
4
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If $$\frac{1}{n+1}{ }^{n} \mathrm{C}_{n}+\frac{1}{n}{ }^{n} \mathrm{C}_{n-1}+\ldots+\frac{1}{2}{ }^{n} \mathrm{C}_{1}+{ }^{n} \mathrm{C}_{0}=\frac{1023}{10}$$ then $$n$$ is equal to :
A
9
B
6
C
7
D
8
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Class 12
© ExamGOAL 2024 | 544 | 1,213 | {"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} | 2.875 | 3 | CC-MAIN-2024-33 | latest | en | 0.525926 |
https://forums.studentdoctor.net/threads/what-is-composite-score.460518/ | 1,495,947,308,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463609598.5/warc/CC-MAIN-20170528043426-20170528063426-00269.warc.gz | 940,999,573 | 22,490 | # What is composite score?
Discussion in 'PCAT Discussions' started by misswash82, Oct 21, 2007.
1. SDN is made possible through member donations, sponsorships, and our volunteers. Learn about SDN's nonprofit mission.
1. ### misswash82 5+ Year Member
103
0
Oct 21, 2007
I was thinking the composite score was the avg of all the others, but I noticed that is not true. Someone received composite of 99 and had scores of 99, 97, 95, 99, and 85. They cannot be averaged to 99.
Could you explain what it means by composite score?
3. ### parabolicOne of many 2+ Year Member
168
0
Jan 30, 2007
The subtest percentile ranks are not averaged to get the composite percentile rank. However, the subtest scaled scores are averaged to get the composite scaled score.
So let's say your scaled composite is 450. That means that the average of the subtest scaled scores was 450. Then that score is compared to the composite scaled score of some range of test takers from 1998-2003, and you are given a percentile rank based on how your 450 compared to their scores. If your 450 is better than 99% of all takers, then your composite percentile rank will be 99%, even if your some of your subtest percentile ranks are <99%.
At least, I think that's how it goes!
4. ### AngelaCL 7+ Year Member
410
1
Oct 9, 2007
Generally people will do better on their composite than the average of all 5, because there aren't many people who are going to get 99% on every single section. So you can do lower on a section or two and still be in the top 1% of people overall. What I think is sort of weird is that I've seen people who have the same scores as me, but in different subjects, but our composite is different. For example, I got 90, 92, 96, 95, 69 - total of 442. I've seen other people with, say, 78, 85, 92, 93, 94, which also totals to 442, and they have a composite score of 97, where I got a 95. I didn't think to add up my scaled scores compared to theirs, so maybe that's the difference.
5. ### omnioneSDN PharmoderatorModerator Emeritus 5+ Year Member
Your scaled scores (the 3 digit number) are averaged and that number is compared to the standard group of PCAT test-takers between 1998 to 2003 to derive your composite percentile score. For example, a 400 average composite scaled score ranks would rank in the 50th percentile of all those standard test takers.
6. ### misswash82 5+ Year Member
103
0
Oct 21, 2007
You guys are great!!
7. ### rowerpharmP1 5+ Year Member
145
0
Sep 28, 2007
When schools look at the actual 400ish number... are they looking at a number that is not "equal" for all test forms?
8. ### omnioneSDN PharmoderatorModerator Emeritus 5+ Year Member
It depends on your interpretation. Harcourt designs it so that a 400 for one exam is the same as the next. However, the number of questions missed to get that 400 differs for each exam depending on the form's difficulty. In principle, it is the "equal" number that comes from adjusting for difficulty but "unequal" in terms of the number of questions missed. | 798 | 3,034 | {"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} | 3.15625 | 3 | CC-MAIN-2017-22 | longest | en | 0.968657 |
https://www.inchcalculator.com/convert/dyne-to-force-newton/ | 1,723,745,171,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641311225.98/warc/CC-MAIN-20240815173031-20240815203031-00376.warc.gz | 635,905,790 | 15,809 | # Dynes to Newtons Converter
Enter the force in dynes below to get the value converted to newtons.
## Result in Newtons:
1 dyn = 1.0E-5 N
Hint: use a scientific notation calculator to convert E notation to decimal
Do you want to convert newtons to dynes?
## How to Convert Dynes to Newtons
To convert a measurement in dynes to a measurement in newtons, divide the force by the following conversion ratio: 100,000 dynes/newton.
Since one newton is equal to 100,000 dynes, you can use this simple formula to convert:
newtons = dynes ÷ 100,000
The force in newtons is equal to the force in dynes divided by 100,000.
For example, here's how to convert 50,000 dynes to newtons using the formula above.
newtons = (50,000 dyn ÷ 100,000) = 0.5 N
## What Is a Dyne?
The dyne is the force needed to move one gram of mass at a rate of one centimeter per second squared.
The dyne is a centimeter-gram-second (CGS) unit of force. Dynes can be abbreviated as dyn; for example, 1 dyne can be written as 1 dyn.
Dynes can be expressed using the formula: 1 dyn = 1 gcm / s2
## What Is a Newton?
The newton is a unit to for measuring force equal to the force needed to move one kilogram of mass at a rate of one meter per second squared.[1]
The newton is the SI derived unit for force in the metric system. Newtons can be abbreviated as N; for example, 1 newton can be written as 1 N.
Newtons can be expressed using the formula: 1 N = 1 kgm / s2
## Dyne to Newton Conversion Table
Table showing various dyne measurements converted to newtons.
Dynes Newtons
1 dyn 0.00001 N
2 dyn 0.00002 N
3 dyn 0.00003 N
4 dyn 0.00004 N
5 dyn 0.00005 N
6 dyn 0.00006 N
7 dyn 0.00007 N
8 dyn 0.00008 N
9 dyn 0.00009 N
10 dyn 0.0001 N
100 dyn 0.001 N
1,000 dyn 0.01 N
10,000 dyn 0.1 N
100,000 dyn 1 N
## References
1. Z. J. Jabbour and S. L. Yaniv, The Kilogram and Measurements of Mass and Force, Journal of Research of the National Institute of Standards and Technology, https://www.nist.gov/system/files/documents/calibrations/j61jab.pdf | 609 | 2,025 | {"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} | 3.890625 | 4 | CC-MAIN-2024-33 | latest | en | 0.775984 |
https://grvsuporte.com.br/12pitris/article.php?id=0ec205-kalman-filter-time-series | 1,627,227,918,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046151699.95/warc/CC-MAIN-20210725143345-20210725173345-00584.warc.gz | 301,374,292 | 8,559 | as our best guesses for $$x_1$$ and $$P_1$$ given our current state. $\begin{eqnarray*} Filter (following its name) is good in smoothing of noisy time series. \end{eqnarray*}$ Kalman filter time series prediction in python. Generic Description of the Ensemble Kalman Filter as Implemented in This Study a a An ensemble of N e forecasts is generated at discrete time t i by forward integration of each ensemble member e using the nonlinear dynamo model M between discrete times and t i (we assume without loss of generality that the last analysis was carried out at time ). INTRODUCTION Until now, Kalman filter still an appropriate tool for analyzing time series of position when the deformations are modeled as a linear dynamic system. Let’s see how this works using an example. Time series forecast with Kalman Filters in R-Cran. Since the states of the system are time-dependent, we need to subscript them with t. We will use θtto represent a column vector of the states. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. One can create a forecast easily with only one SPL command without tuning tons of parameters. x_{t}^{t-1} & = & \theta x_{t-1}^{t-1}\\ Ask Question Asked 8 years, 9 months ago. in a previous article, we have shown that Kalman filter can produce… Architettura Software & Python Projects for €30 - €250. Below is a simple plot of a kalman filtered version of a random walk (for now, we will use that as an estimate of a financial time series). signal-processing kalman-filter time-series … \end{eqnarray*}\], $Kalman filter for time series prediction. Registrati e fai offerte sui lavori gratuitamente. Ask Question Asked 2 years, 9 months ago. Given our new observation $$y_1$$, we can the update our guess based on this new information to get \[\begin{eqnarray*} The Kalman Filter Michael Rockinger August 26, 2004 The following section is heavily inspired by Thierry Roncalli™s book: fiApplications à la Finance et à l™EconomØtriefl, Volume 2fl, the book by Andrew Harvey: fiForecasting structural time series models and the Kalman –lterfl, Cambridge University Press, as I have time series from stock market and want to apply the Kalman Filter. Where does rayquaza spawn in pixelmon 2020, Blue merle great danes for sale in washington. I was recently given a task to impute some time series missing values for a prediction problem. Analysis of GPS Coordinates Time Series by Kalman Filter Bachir GOURINE, Abdelhalim NIATI, Achour BENYAHIA and Mokhfi BRAHIMI, Algeria 1. P_{t}^{t-1} & = & \theta^2 P_{t-1}^{t-1} + \tau^2. I read the samples about the setup of the Filter and they all work with some kind of matrizes. \tau^2\text{ is large} & \Rightarrow & \text{Trust the data} P_t^t & = & (1-K_t) P_t^{t-1} P_t^t & = & (1-K_t) P_t^{t-1} x_t^t & = & x_t^{t-1} + K_t(y_t-x_t^{t-1})\\ \sigma^2\text{ is large} & \Rightarrow & \text{Trust the system}\\ x_1^0 & = & \theta x_0^0\\ Il filtro di Kalman è un efficiente filtro ricorsivo che valuta lo stato di un sistema dinamico a partire da una serie di misure soggette a rumore. - kenluck2001/pySmooth Trova utilizzo come osservatore dello stato, come loop transfer recovery (LTR) e come sistema di identificazione parametrica. I need an unscented / kalman filter forecast of a time series. Some advantages to the kalman filter are that is is predictive and adaptive, as it looks forward with an estimate of the covariance and mean of the time series one step into the future and unlike a Neural Network, it does NOT require stationary data. Kalman filter gives the best estimate. Only the estimated state from the previous time step and current measurement is required to make a prediction for the current state. This is done using Kalman filters, but the numerous resources I could find in terms of papers, presentations etc were not especially helpful.$ Active 2 years, 9 months ago. I needed to reverse engineer the mathematics used by R in fitting ARIMA time series. x_{t}^{t-1} & = & \theta x_{t-1}^{t-1}\\ 137 − 142 in [5]. where $\begin{eqnarray*} \end{eqnarray*}$ I would like to apply Kalman smoothing to a series of data sampled at irregular time points. Given the new information $$y_t$$, we can then update our estimate to get . Kalman filter can predict the worldwide spread of coronavirus (COVID-19) and produce updated predictions based on reported data. Let’s make a brief review of Kalman filter in Splunk. A unique time series library in Python that consists of Kalman filters (discrete, extended, and unscented), online ARIMA, and time difference model. Learn more about kalman filter We start with an initial state $$x_0^0$$ and initial variance $$P_0^0$$. The one-step prediction is then In a linear state-space model we say that these st… From the technical point of … particle filter) –Optimal closed-form solution to the tracking problem (under the assumptions) •No algorithm can do better in a linear-Gaussian environment! K_t = \frac{P_t^{t-1}}{P_t^{t-1} + \sigma^2} In such situations, the use of the Kalman Filter, with its ability to incorporate time-varying coefficients and infer unobserved factors driving the evolution of observed yields, is often appropriate for the estimation of yield curve model parameters and the subsequent simulation and forecasting of yields, which are at the heart of insurance and pension analysis. P_1^0 & = & \theta^2 P_0^0 + \tau^2 \end{eqnarray*}\] Since that time, due in large part to advances in digital computing, the Kalman. 1. 5.2 The Kalman Filter | A Very Short Course on Time Series Analysis 5.2 The Kalman Filter FUN FACT: The Kalman filter was developed by Rudolf Kalman while he worked at the Research Institute for Advanced Study in Baltimore, MD. The basic one-dimensional Kalman filtering algorithm is as follows. Viewed 3k times 4 $\begingroup$ I have the information about the behaviour of 400 users across period of 1 months (30 days). x_1^0 & = & \theta x_0^0\\ Cerca lavori di Kalman filter time series python o assumi sulla piattaforma di lavoro freelance più grande al mondo con oltre 18 mln di lavori. We propose a Kalman filter for InSAR time series analysis (KFTS), an efficient method to rapidly update preexisting time series of displacement with data as they are made available, with limited computational cost. Per le sue caratteristiche intrinseche è un filtro ottimo per rumori e disturbi agenti su sistemi gaussiani a media nulla. I decided it wasn't particularly helpful to invent my own notation for the Kalman Filter, as I want you to be able to relate it to other research papers or texts. where we assume $$w_t\sim\mathcal{N}(0,\tau^2)$$ and $$v_t\sim\mathcal{N}(0,\sigma^2)$$. However, some of the basic principles can be made intelligible by a simpler approach involving only scalar time series2. This estimate tend to be more accurate than those based on a single measurement alone. The command dspadpt3 gives me some weird mask which I have no conlcusion about handling it. A unique time series library in Python that consists of Kalman filters (discrete, extended, and unscented), online ARIMA, and time difference model. If we look at the formula for the Kalman gain, itâs clear that if the measurement noise is high, so $$\sigma^2$$ is large, then the Kalman gain will be closer to $$0$$, and the influence of the new data point $$y_t$$ will be small. P_{t}^{t-1} & = & \theta^2 P_{t-1}^{t-1} + \tau^2. Kalman Filters are used in signal processing to estimate the underlying state of a process. The Kalman Filter is a state-space model that adjusts more quickly for shocks to a time series. \], A Very Short Course on Time Series Analysis. \end{eqnarray*}\], $\begin{eqnarray*} Kalman filter time series python. The kalman filter is one of those tools. The presentation in this lecture is to a large degree based on the treatment in [2] . Kalman Filter is an easy topic. Vorrei fare domanda Kalman smoothing per una serie di dati campionati in corrispondenza di tempi irregolari. There is a claim on Stack Exchange that "For irregular spaced time series it's easy to construct a Kalman filter", but I haven't been able to find any literature that specifically addresses this.. Kalman filter algorithm uses a series of measurements observed over time, containing noise and other inaccuracies, and produces estimates of unknown variables. x_1^1 & = & x_1^0 + K_1(y_1-x_1^0)\\ In this study, we developed a new image fusion model based on Kalman Filter method (Kalman, 1960; Welch and Bishop, 2006) for blending Landsat-8 Operational Land Imager (OLI) and MODIS images to produce a time-series of synthetic Landsat images and their uncertainty estimate, as well as to evaluate their applications for generation of vegetation indices. Extremely useful, yet, very difficult to understand conceptually because of the complex mathematical jargon. This section follows closely the notation utilised in both Cowpertwait et al and Pole et al. In this paper, by proposing to use both market data (futures prices) and analysts’ forecasts (expected prices) to calibrate a commodity pricing model, several related objectives are … The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory. The Kalman filter •Pros(compared to e.g. \end{eqnarray*}$, $\begin{eqnarray*} This is important to remember when tuning the Kalman filtering algorithm for specific applications. \end{eqnarray*}$, $\begin{eqnarray*} But this simplicity means the lack of flexibility. Let's begin by discussing all of the elements of the linear state-space model. I need an unscented / kalman filter forecast of a time series. Expectation–maximization algorithm should be implemented like a code I will give you. In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The output has to be a rolling predict step without incorporating the next measurement (a priori prediction). \[ If $$\sigma^2$$ is small, then the filtered value $$x_t^t$$ will be adjusted more in the direction of $$y_t$$. P_1^0 & = & \theta^2 P_0^0 + \tau^2 Active 8 years, 8 months ago. The Kalman filter is a uni-modal, recursive estimator. For example, the GPS receiver provides the location and velocity estimation, where location and velocity are the hidden variables and differential time of satellite's signals arrival are the measurements. For the sake of introducing the Kalman filter, letâs take a simple model sometimes referred to as the âlocal levelâ model, which has a state equation of. is the Kalman gain coefficient. The general idea is, \[\begin{eqnarray*} From here we compute FUN FACT: The Kalman filter was developed by Rudolf Kalman while he worked at the Research Institute for Advanced Study in Baltimore, MD. Normalizing Kalman Filters for Multivariate Time Series Analysis Emmanuel de Bézenac1y, Syama Sundar Rangapuram 2, Konstantinos Benidis , Michael Bohlke-Schneider 2, Richard Kurle3y, Lorenzo Stella, Hilaf Hasson2, Patrick Gallinari1, Tim Januschowski2 1Sorbonne Université, 2AWS AI Labs, 3Techincal University of Munich Correspondence to: emmanuel.de-bezenac@lip6.fr, … where $$K_1 = P_1^0/(P_1^0 + \sigma^2)$$. \[\begin{eqnarray*} \end{eqnarray*}$, $\begin{eqnarray*} How to apply Kalman filter on time series? In January 2015, currency markets underwent one of the biggest shocks ever endured, when the Swiss National Bank decided to … The Hodrick–Prescott filter (also known as Hodrick–Prescott decomposition) is a mathematical tool used in macroeconomics, especially in real business cycle theory, to remove the cyclical component of a time series from raw data.It is used to obtain a smoothed-curve representation of a time series, one that is more sensitive to long-term than to short-term fluctuations. Python has the TSFRESH package which is pretty well documented but I wanted to apply something using R. I opted for a model from statistics and control theory, called Kalman Smoothing which is available in the imputeTS package in R.. Viewed 8k times 3. It is a simple and useful tool for time series forecasting. For the general case, we want to produce a new estimate $$x_t$$ and we have the current state $$x_{t-1}^{t-1}$$ and variance $$P_{t-1}^{t-1}$$. \end{eqnarray*}$ P_1^1 & = & (1-K_1) P_1^0. P_1^1 & = & (1-K_1) P_1^0. This book, however, was exactly what was required, especially Chapter 3. Those working on the Neural Network tutorials, hopefully see a big advantage here. K_t = \frac{P_t^{t-1}}{P_t^{t-1} + \sigma^2} KFTS solves together for the evolution of phase change with time and for a parametrized model of ground deformation. x_1^1 & = & x_1^0 + K_1(y_1-x_1^0)\\ However, ... variables based on the series of measurements. x_t^t & = & x_t^{t-1} + K_t(y_t-x_t^{t-1})\\ The Kalman Recursions are usually established for multivariate time series applying matrix equations, see, e.g., pp. Can anybody point me to a well documented example, step-by-step on how to forecast a time series with Kalman Filters in R?
Non Profit Organization Philippines, Easy Crayfish Recipes, Where To Buy Live Crawfish In Washington State, Ice Machine Commercial, State Capitol Tours, Can Eucerin Lotion Be Used On Face, | 3,422 | 13,607 | {"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": 2, "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} | 2.765625 | 3 | CC-MAIN-2021-31 | latest | en | 0.890444 |
http://www.cs.utexas.edu/users/moore/acl2/v6-0/ACL2-AS-STANDALONE-PROGRAM.html | 1,477,702,946,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476990033880.51/warc/CC-MAIN-20161020190033-00330-ip-10-142-188-19.ec2.internal.warc.gz | 383,463,376 | 2,171 | ## ACL2-AS-STANDALONE-PROGRAM
Calling ACL2 from another program
```Major Section: ACL2-TUTORIAL
```
ACL2 is intended for interactive use. It is generally unrealistic to expect it to prove theorems fully automatically; see the-method, and see introduction-to-the-theorem-prover for a more detailed tutorial.
Nevertheless, here we describe an approach for how to call the ACL2 theorem prover noninteractively. These steps can of course be modified according to your needs. Here, we illustrate how to call ACL2 from another Lisp program (or an arbitrary program) to attempt to prove an arithmetic theorem.
=== STEP 1: ===
Build a suitable ACL2 image by starting ACL2 and then executing the following forms. In particular, these define a macro, `try-thm`, that causes ACL2 to exit with with an exit status indicating success or failure of a proof attempt.
```(include-book "arithmetic-5/top" :dir :system)
(defmacro try-thm (&rest args)
`(mv-let (erp val state)
(with-prover-time-limit 3 (thm ,@args))
(declare (ignore val))
(prog2\$ (if erp (exit 1) (exit 0)) state))))
(reset-prehistory) ; optional
:q
(save-exec "arith-acl2" "Included arithmetic-4/top")
```
If you prefer, above you can replace 3 by some other number of seconds as a time limit for the prover. Also, you can replace
```(with-prover-time-limit 3 (thm ,@args))
```
by
```(with-output :off :all (with-prover-time-limit 3 (thm ,@args)))
```
if you want to turn off output. It may be best to leave the output on, instead eliminating it in the calling program (see Step 3 below).
=== STEP 2: ===
Try a little test. In that same directory try this:
```echo '(try-thm (equal x x))' | ./arith-acl2
echo \$?
```
The exit status should be 0, indicating success. Now try this:
```echo '(try-thm (not (equal x x)))' | ./arith-acl2
echo \$?
```
The exit status should be 1, indicating failure.
=== STEP 3: ===
Create a shell script that automates Step 2, for example:
```#!/bin/sh
(echo "(try-thm \$1)" | ./arith-acl2) >& /dev/null
exit \$?
```
=== STEP 4: ===
Try your script from a Lisp program, if you like. Here is how you can do it in SBCL, for example. (Different Lisps have different ways to do this, as summarized in function `system-call` in ACL2 source file `acl2-init.lisp`.)
```(defun provable? (x)
(let ((status
(process-exit-code
(sb-ext:run-program "./try-thm.sh" (list (format nil "~s" x))
:output t :search t))))
(eql status 0)))
```
Then here is a log:
``` * (provable? '(equal x y))
NIL
* (provable? '(equal x x))
T
*
```
Certainly refinements are possible -- for example the above doesn't distinguish between unprovable and ill-formed input. But it's a start. | 731 | 2,658 | {"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-2016-44 | latest | en | 0.837989 |
http://www.questionpaper4exam.com/2014/09/ | 1,548,021,556,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583739170.35/warc/CC-MAIN-20190120204649-20190120230649-00159.warc.gz | 384,190,311 | 24,967 | ## ALGEBRA FORMULAS
(a+b)2 = (a2 +b2 +2ab)
(a-b)2 = (a2 + b2 – 2ab)
(a+b)2 + (a-b)2 = 2 (a2 + b2)
(a+b)2 – (a-b)2 = 4ab
(a2-b2) = (a+b) (a-b)
(a+b)3= a3 + b3 + 3ab (a+b)
(a-b)3 = a3 – b3 -3ab (a-b)
(a3+b3) = (a+b) (a2-ab+b2)
(a3-b3) = (a-b) (a2+ab+b2)
Arithmetic progression (A.P)
Series a, a+d, a+2d, a+3d,…….
First term = a
Difference = d
Then
nth term Tn = a + (n-1)d
sum of “n” term Sn = n/2 – (2a + (n-1)d)
sum of n term Sn = n/2 (a+L)
L = last term
Geometric progression (G.P)
a , ar, ar2,…….
First term = a
Difference = r
Then
nth term Tn = arn-1
sum of “n” terms Sn = a(rn – 1 )/ (r – 1)
## MENTAL MATH SHORTCUT TRICKS
Dear friends,
now in most of the competitive exam we are have to deal with math question which are easy to solve with tricks but many of candidate doesn't aware how to solve them easily.
now days competition are high in exam there are less vacancies and more number of registration in any kind of recruitment like ssc, upsc, banking, ibps, railways and many more
we are seen that cut off are very high now days because more number of candidates applied or given the exam.
Candidates are required to memories some basic concept of math. Math is the subject you can score more if you can hard work and practice regularly.
some of question that are always found in exam like percentage formulas , ratio ,algebra formulas, square roots, cube roots, simple interest, compound interest, work and time and many more
In these question we are to brush up only basic concept of mental math tricks . Work hard on these thing sure help you to get more mark in exams
we have prepare easy maths tricks on these percentage, work and time, algebra, and trigonometry tricks so, candidate are not only save time but get more mark in competitive exams
FOLLW THIS SIMPLE TRICKS FOR SSC, UPSC, BANKING, IBPS, RAILWAY, PCS etc for help in math
## SSC CGL 2014 ANSWER KEY
ssc that stands for staff selection commission a government organization that recruits candidates for various post in central government department throughout India. Ssc have been published recruitment under combined graduate level exam for various post under ministries of Indian department under group ‘c’ and group ‘b’ ministerial and non ministerial.
The exam of combined graduate level 2014 was been conducted in april / may 2014 but due to some malpractice in cgl 2013 exam cgl 2014 postponed. Now fresh dates have been given to hold ssc cgl 2014 tier 1.
The date of cgl 2014 now are 19 october and 26 october 2014. More than one million candidates are registered for exam. Competition are now more because more number of post in 2014.
### PATTERN OF SSC COMBINED GRADUATE LEVEL 2014
In the exam there are four parts of 200 marks. Each part consist of 50 mark. Four part are general awareness, reasoning abilities, mathematics aptitude and English comprehensive. There is negative mark of 0.25 for every wrong answer. If you left any question blank no mark are deduction from your score. So, candidate are advised be sure while marking your answer in the omr sheet.
Competition in ssc cgl 2014 are very high. So, candidates are have to work hard on their basic concept to get secured any post in this year cgl exam.
## OFFICIALLY ANSWER KEY OF CGL 2014 ON WWW.SSC.NIC.IN
Candidate those are waiting for the answer key of cgl 2014 now. They can find official answer key of cgl on www.ssc.nic.in
1. First log on www.ssc.nic.in
2. Second goes to latest news section
3. There you will find the answer key of various exam conducted by staff selection commission.
4. Answer key of all the set are their on the website
Officially answer key are update by ssc website after some day of cgl 2014.
But there are some coaching center they bring answer key by solving the paper.
After all the sum up we are advised the candidate to check their answer by officially answer key of ssc cgl.
## SSC CGL RE EXAM QUESTION PAPER GENERAL AWARENESS PART FOR PRACTICE
ON SEPT 21 2014 CGL TIER 2 ARE GOING TO BE HELD
FOR CANDIDATE ARE QUALIFIED IN TIER 1 DOWNLOAD GENERAL AWARENESS PART AND SOLVED IT FULL
## SSC QUESTION PAPER RE EXAM 2013 REASONING PART FOR PRACTICE
for those whose are preparing for tier 2 ssc cgl
## SSC CGL RE EXAM QUESTION PAPER FOR PRACTICE
Hi friend those are waiting for the ssc cgl tier 2 on 21 sept 2014 are now doing hard work on their basic concept of various type of question that are asked in ssc exam .
so, here we are provide re exam question paper in pdf format to practice.
PRACTICE IT AND SOLVED IT FULL AND SHARE IT WITH OTHER | 1,261 | 4,576 | {"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-2019-04 | latest | en | 0.908025 |
https://rcogenasia.com/electricity-generation/quick-answer-what-are-the-3-basic-types-of-electrical-circuits-quizlet.html | 1,643,207,475,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304954.18/warc/CC-MAIN-20220126131707-20220126161707-00272.warc.gz | 530,263,151 | 18,217 | # Quick Answer: What are the 3 basic types of electrical circuits quizlet?
Contents
## What are the 3 basic types of electrical circuits?
What are the 3 basic types of electrical circuits?
• electric circuit.
• electric power.
• parallel circuit.
• series circuit.
## What are the 3 basic units in electricity quizlet?
Voltage, current, and resistance (volts, amps, and ohms).
## What are the three main parts of an electrical circuit quizlet?
Parts of electric circuit, three basic parts : Energy source, electrical conductor, and a load.
## What are three circuits?
There are actually 5 main types of electrical circuits: Close circuit, open circuit, short circuit, series circuit, and parallel circuit. Each type of circuit is designed to create a conductive path of current or electricity.
## What are the 2 types of circuits?
Series and parallel circuits
• There are two types of circuit we can make, called series and parallel.
• If there are no branches then it’s a series circuit.
• If there are branches it’s a parallel circuit.
## What are the 3 components of electricity?
Three elements are basic to all circuits:
• Voltage source (such as a battery or gen- erator). A device that supplies the energy.
• Load (such as a resistor, motor, or. lamp). A device that uses energy from. the voltage source.
• Conductive pathway (such as an insu-
THIS IS INTERESTING: When copper sulphate solution is prepared it conducts electricity but solid copper sulphate does not why?
## What are the three elements of electricity?
What three elements are required to form an electrical circuit? A source of electrical energy, a load or resistance to use the electricity, and wire or conductors to connect the source to the load. DC circuits can take one of three forms or types.
## What are the 4 basic units of electricity?
Therefore, the 4 basic units of electricity are volts, amps, ohms, and watts.
## What are the three basic properties of circuits and or components?
Introduction. Electrical systems, also named circuits or networks, are designed as combinations of mainly three fundamental components: resistor, capacitor, and inductor. They are correspondingly defined by resistance, capacitance, and inductance—generally considered to be lumped-parameter properties.
## Which of the following parts are found in every electric circuit?
Every electric circuit, regardless of where it is or how large or small it is, has four basic parts: an energy source (AC or DC), a conductor (wire), an electrical load (device), and at least one controller (switch).
## What are fuses and breakers?
Fuses and circuit breakers are both designed to interrupt the flow of electricity. But they operate through different mechanisms. The fuse works as a piece of metal that melts down when overheated. While a circuit breaker works by operating a switching mechanism when an overflow of electricity is detected. | 612 | 2,921 | {"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-2022-05 | latest | en | 0.896423 |
http://nrich.maths.org/public/leg.php?code=-339&cl=4&cldcmpid=5498 | 1,477,318,521,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719638.55/warc/CC-MAIN-20161020183839-00012-ip-10-171-6-4.ec2.internal.warc.gz | 184,577,408 | 7,818 | # Search by Topic
#### Resources tagged with Practical Activity similar to Ding Dong Bell Interactive:
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### There are 31 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Practical Activity
### Ding Dong Bell Interactive
##### Stage: 5 Challenge Level:
Try ringing hand bells for yourself with interactive versions of Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the article 'Ding Dong Bell'.
### Enigma
##### Stage: 2, 3 and 4 Challenge Level:
This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.
### Making Maths: Celtic Knot Tiles
##### Stage: 2, 3 and 4 Challenge Level:
Make some celtic knot patterns using tiling techniques
### Well Balanced
##### Stage: 1, 2, 3, 4 and 5 Challenge Level:
Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.
### First Forward Into Logo 11: Sequences
##### Stage: 3, 4 and 5 Challenge Level:
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
### Proof Sorter - Sum of an AP
##### Stage: 5 Challenge Level:
Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing
### Plaited Origami Polyhedra
##### Stage: 2, 3 and 4 Challenge Level:
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
### Whirling Fibonacci Squares
##### Stage: 3 and 4
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
### First Forward Into Logo 9: Stars
##### Stage: 3, 4 and 5 Challenge Level:
Turn through bigger angles and draw stars with Logo.
### First Forward Into Logo 6: Variables and Procedures
##### Stage: 3, 4 and 5 Challenge Level:
Learn to write procedures and build them into Logo programs. Learn to use variables.
### First Forward Into Logo 4: Circles
##### Stage: 2, 3 and 4 Challenge Level:
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
### Turning the Place Over
##### Stage: 3, 4 and 5 Challenge Level:
As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?
### Which Solids Can We Make?
##### Stage: 4 Challenge Level:
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
### First Forward Into Logo 2: Polygons
##### Stage: 2, 3 and 4 Challenge Level:
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
### First Forward Into Logo 5: Pen Up, Pen Down
##### Stage: 2, 3 and 4 Challenge Level:
Learn about Pen Up and Pen Down in Logo
### First Forward Into Logo 8: More about Variables
##### Stage: 3, 4 and 5 Challenge Level:
Write a Logo program, putting in variables, and see the effect when you change the variables.
### Paper Folding - Models of the Platonic Solids
##### Stage: 2, 3 and 4
A description of how to make the five Platonic solids out of paper.
### Factors and Multiples Game
##### Stage: 2, 3 and 4 Challenge Level:
A game in which players take it in turns to choose a number. Can you block your opponent?
### The Best Card Trick?
##### Stage: 3 and 4 Challenge Level:
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
### First Forward Into Logo 7: Angles of Polygons
##### Stage: 3, 4 and 5 Challenge Level:
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
##### Stage: 3, 4 and 5
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
### First Forward Into Logo 10: Count up - Count Down
##### Stage: 3, 4 and 5 Challenge Level:
What happens when a procedure calls itself?
### First Forward Into Logo 12: Puzzling Sums
##### Stage: 3, 4 and 5 Challenge Level:
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
### Cool as Ice
##### Stage: 3 and 4 Challenge Level:
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
### Nine Colours
##### Stage: 3 and 4 Challenge Level:
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
### Fitting Flat Shapes
##### Stage: 5 Challenge Level:
How efficiently can various flat shapes be fitted together?
### Stonehenge
##### Stage: 5 Challenge Level:
Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.
### Tower of Hanoi
##### Stage: 4 Challenge Level:
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
### Gym Bag
##### Stage: 3 and 4 Challenge Level:
Can Jo make a gym bag for her trainers from the piece of fabric she has?
### Witch's Hat
##### Stage: 3 and 4 Challenge Level:
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat? | 1,355 | 5,736 | {"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} | 4.375 | 4 | CC-MAIN-2016-44 | longest | en | 0.844366 |
https://nbviewer.ipython.org/github/ipython/ipython/blob/rel-0.13.1/docs/examples/notebooks/sympy_quantum_computing.ipynb | 1,642,686,625,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301863.7/warc/CC-MAIN-20220120130236-20220120160236-00054.warc.gz | 477,229,030 | 5,334 | # Basic Symbolic Quantum Mechanics with SymPy¶
We first load the IPython extensions that enable LaTeX-based mathematical printing of SymPy objects, and then import the quantum computing libraries from SymPy.
In [1]:
%load_ext sympyprinting
In [2]:
from sympy import sqrt, symbols, Rational
from sympy import expand, Eq, Symbol, simplify, exp, sin
from sympy.physics.quantum import *
from sympy.physics.quantum.qubit import *
from sympy.physics.quantum.gate import *
from sympy.physics.quantum.grover import *
from sympy.physics.quantum.qft import QFT, IQFT, Fourier
from sympy.physics.quantum.circuitplot import circuit_plot
## Bras and Kets
Create symbolic states
In [3]:
phi, psi = Ket('phi'), Ket('psi')
alpha, beta = symbols('alpha beta', complex=True)
Create a superposition
In [4]:
state = alpha*psi + beta*phi; state
Out[4]:
$$\alpha {\left|\psi\right\rangle } + \beta {\left|\phi\right\rangle }$$
Dagger the superposition and multiply the original
In [5]:
ip = Dagger(state)*state; ip
Out[5]:
$$\left(\overline{\alpha} {\left\langle \psi\right|} + \overline{\beta} {\left\langle \phi\right|}\right) \left(\alpha {\left|\psi\right\rangle } + \beta {\left|\phi\right\rangle }\right)$$
Distribute
In [6]:
qapply(expand(ip))
Out[6]:
$$\alpha \overline{\alpha} \left\langle \psi \right. {\left|\psi\right\rangle } + \alpha \overline{\beta} \left\langle \phi \right. {\left|\psi\right\rangle } + \beta \overline{\alpha} \left\langle \psi \right. {\left|\phi\right\rangle } + \beta \overline{\beta} \left\langle \phi \right. {\left|\phi\right\rangle }$$
## Operators
Create symbolic operators
In [7]:
A = Operator('A')
B = Operator('B')
C = Operator('C')
Test commutativity
In [8]:
A*B == B*A
Out[8]:
False
Distribute A+B squared
In [9]:
expand((A+B)**2)
Out[9]:
$$A B + \left(A\right)^{2} + B A + \left(B\right)^{2}$$
Create a commutator
In [10]:
comm = Commutator(A,B); comm
Out[10]:
$$\left[A,B\right]$$
Carry out the commutator
In [11]:
comm.doit()
Out[11]:
$$A B - B A$$
Create a more fancy commutator
In [12]:
comm = Commutator(A*B,B+C); comm
Out[12]:
$$\left[A B,B + C\right]$$
Expand the commutator
In [13]:
comm.expand(commutator=True)
Out[13]:
$$\left[A,B\right] B + \left[A,C\right] B + A \left[B,C\right]$$
Carry out and expand the commutators
In [14]:
_.doit().expand()
Out[14]:
$$A B C + A \left(B\right)^{2} - B A B - C A B$$
Take the dagger
In [15]:
Dagger(_)
Out[15]:
$$- B^{\dagger} A^{\dagger} B^{\dagger} - B^{\dagger} A^{\dagger} C^{\dagger} + \left(B^{\dagger}\right)^{2} A^{\dagger} + C^{\dagger} B^{\dagger} A^{\dagger}$$ | 872 | 2,591 | {"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": 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} | 3.140625 | 3 | CC-MAIN-2022-05 | latest | en | 0.35396 |
https://www.sanfoundry.com/analog-circuits-questions-answers-halfwave-rectifier-1/ | 1,721,438,431,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514972.64/warc/CC-MAIN-20240719231533-20240720021533-00281.warc.gz | 848,494,260 | 20,579 | # Analog Circuits Questions and Answers – Halfwave Rectifier
This set of Analog Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Halfwave Rectifier”.
1. DC average current of a half wave rectifier output is ___________
(Where Im is the maximum peak current of input)
a) 2Im/ᴨ
b) Im/ᴨ
c) Im/2ᴨ
d) 1.414Im/ᴨ
View Answer
Answer: b
Explanation: Average DC current of half wave rectifier is Im/ᴨ . Since output of half wave rectifier contains only one half of the input. The average value is the half of the area of one half cycle of sine wave with peak Im. This is equal to Im/ᴨ.
Thus this is calculated by Area of graph of current/Perion.
IDC=1/2π∫idx between 0 to 2π.
This is equal to Im/ᴨ.
2. DC power output of half wave rectifier is equal to ____________
(Im is the peak current and RL is the load resistance)
a) (2Im2/ ᴨ2)RL
b) (Im2/2 ᴨ2)RL
c) (Im2/ ᴨ2)RL
d) (4Im2/ ᴨ2)RL
View Answer
Answer: c
Explanation: Average DC power of half wave rectifier output is (Im2/ ᴨ2)RL. Since power is VDC * IDC,
= Im/ᴨ x Vm/ᴨ = VmIm/ ᴨ2
We know Vm = Im RL. Therefore, power = (Im2/ ᴨ2)RL.
3. Ripple factor of half wave rectifier is _________
a) 1.414
b) 1.21
c) 1.3
d) 0.48
View Answer
Answer: b
Explanation: Ripple factor of a rectifier is the measure of the effectiveness of a power supply filter
in reducing the ripple voltage. It is calculated by taking ratio of RMS AC component of output voltage to DC component of output voltage.
r = √Irms2 – IDC2/IDC
For a half wave rectifier, it is 1.21.
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4. If input frequency is 50Hz then ripple frequency of half wave rectifier will be equal to __________
a) 100Hz
b) 50Hz
c) 25Hz
d) 500Hz
View Answer
Answer: b
Explanation: The ripple frequency of output and input is the same since one half cycle of input is passed and other half cycle is blocked. So effectively frequency is the same.
5. Transformer utilization factor of a half wave rectifier is equal to __________
a) 0.267
b) 0.287
c) 0.297
d) 0.256
View Answer
Answer: b
Explanation: Transformer utilization factor is the ratio of DC output power to the AC rating of the secondary winding. AC rating is the product of RMS voltage across winding and RMS current through the winding, expressed in volt-amp. This factor indicates the effectiveness of transformer usage by a rectifier. For half wave rectifier it is low and equal to 0.287.
Sanfoundry Certification Contest of the Month is Live. 100+ Subjects. Participate Now!
6. If peak voltage on a half wave rectifier circuit is 5V and diode cut-in voltage is 0.7, then peak inverse voltage on diode will be __________
a) 3.6V
b) 4.3V
c) 5V
d) 5.7V
View Answer
Answer: c
Explanation: PIV is the maximum reverse bias voltage that can be appeared across a diode in the circuit. If PIV rating of the diode is less than this value breakdown of diode may occur. For a half wave rectifier, PIV of diode is Vm. Therefore, PIV is 5V.
7. Efficiency of half wave rectifier is __________
a) 50%
b) 81.2%
c) 40.6%
d) 45.3%
View Answer
Answer: c
Explanation: Efficiency of a rectifier is a measure of the ability of a rectifier to convert input power into DC power. Mathematically it is equal to the ratio of DC output power to the total input power and efficiency = 40.6xRL/RF+RL%. Its maximum value is 40.6 %.
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8. In a half wave rectifier, the input sine wave is 200sin100 ᴨt Volts. The average output voltage is __________
a) 57.456V
b) 60.548V
c) 75.235V
d) 63.661V
View Answer
Answer: d
Explanation: The equation of sine wave is in the form Em sin wt.
Therefore, Em=200
Hence output voltage is Em/ᴨ. That is 200/ᴨ = 63.6619V.
9. In a half wave rectifier, the input sine wave is 200sin200 ᴨt Volts. If load resistance is of 1k then the average DC power output of half wave rectifier is __________
a) 3.25W
b) 4.05W
c) 5.02W
d) 6.25W
View Answer
Answer: b
Explanation: The equation of sine wave is in the form Em sin wt.
On comparing Em = 200
Power = Em2/ ᴨ2RL = 200/ ᴨ2x 1000.
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10. In a half wave rectifier, the input sine wave is 250sin100 ᴨt Volts. The output ripple frequency of rectifier will be __________
a) 100Hz
b) 200Hz
c) 50Hz
d) 25Hz
View Answer
Answer: c
Explanation: The equation of sine wave is in the form Em sin wt.
On comparing equation w = 100 ᴨ rad/s
We know w=2 ᴨ x frequency.
Therefore, frequency = 50 Hz.
Ripple frequency and input frequency are the same.
Sanfoundry Global Education & Learning Series – Analog Circuits.
To practice all areas of Analog Circuits, here is complete set of 1000+ Multiple Choice Questions and Answers.
If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]
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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.
Subscribe to his free Masterclasses at Youtube & discussions at Telegram SanfoundryClasses. | 1,586 | 5,381 | {"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-2024-30 | latest | en | 0.795235 |
https://math.stackexchange.com/questions/4220192/why-doesnt-pcalvin-wins-the-match-by-winning-2-more-games-than-his-opponent | 1,718,518,805,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861643.92/warc/CC-MAIN-20240616043719-20240616073719-00287.warc.gz | 341,877,085 | 36,348 | # Why doesn't P(Calvin wins the match by winning 2 more games than his opponent) = $P(C|W_1)P(W_1)+P(C|L_1)P(L_1) = (p)(p) + (1-q)(q)$?
Calvin and Hobbes play a match consisting of a series of games, where Calvin has probability $$p$$ of winning each game (independently). They play with a “win by two” rule: the first player to win two games more than his opponent wins the match. Find the probability that Calvin wins the match (in terms of $$p$$), in two different ways.
Blitzstein, Introduction to Probability (2019 2 edn), Chapter 2, Exercise 50, p 94.
## My attempt
Let event $$C$$ be "Calvin wins."
$$P(C) = P(C|W_1)P(W_1)+P(C|L_1)P(L_1) = (p)(p) + (1-q)(q)$$
This doesn't match the answer key, $$\frac{p^2}{p^2+q^2}$$.
I think the conceptual misunderstanding is $$P(C|W_1)$$, $$P(C|L_1)$$. For $$P(C|W_1)$$, my thinking is: if we interpret this problem as the gambler ruin's problem, $$i$$ is originally at 2, but given that $$W_1$$, we have that $$i=3$$. Thus, because C occurring corresponds to $$i=4$$, $$P(C|W_1) = \text{ (the probability that we move from } i=3 \text{ to } i = 4) = p$$ The same goes for $$P(C|L_1)$$: $$i$$ is originally at 2, but given that $$L_1$$, we have that $$i=1$$. Thus, because C not occurring corresponds to $$i=0$$, $$P(C|L_1) = 1 - P(C^c|L_1) = 1 -\text{ (the probability that we move from } i=1 \text{ to } i = 0) = 1-q$$
I know this is wrong because the gambler ruin's problem would interpret, for example, $$P(C|W_1) = p_{i+1}$$. When I first learned the gambler ruin's problem, this made sense. However, now that I'm actually doing a problem that's kind of related, I'm left questioning this: why can't we just $$P(C|W_1) = p^{n-i-1}$$, where $$n$$ represents the # of wins to win the series, $$i$$ is the original starting spot, and one represents winning the first game
And yet, I also don't think the gambler's ruin problem totally applies here; the biggest difference is that given $$W_1$$ or $$L_1$$, the important thing is that we are one spot away from the edge, so the probability of winning or losing one spot from the edge is either $$p$$ or $$q$$, whereas if we were at an $$i$$ in the "middle," $$i$$ can shift left, right, and back left, and left some more.
You are missing the chance that Calvin can win the first game, lose the second, and still win the match. Your conversion of $$P(C|W_1)P(W_1)$$ to $$p^2$$ says the only way Calvin can win given that he won the first game is to win the second as well. You should use the fact that the games are independent to say if Calvin wins the first game, either he wins the second and wins the match or he loses the second and has the same chance of winning the match as he started with. Similarly, if he loses the first game and wins the second he is back where he started.
• Ahhh. Thank you. I correctly redid the problem by solving it as a gambler ruin's problem. But, there's a second part to this problem which is to condition using the LOTP. How else can I condition $P(C)$? Commented Aug 9, 2021 at 5:33 | 921 | 3,026 | {"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": 31, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2024-26 | latest | en | 0.933775 |
https://hubpages.com/money/1116-Student-Loan-Consolidation-Rates | 1,544,905,149,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376827097.43/warc/CC-MAIN-20181215200626-20181215222626-00611.warc.gz | 634,266,777 | 25,396 | # Student Loan Consolidation Rates
Updated on September 14, 2015
## Student Loan Consolidation Rates
Are you looking for information on student loan consolidation rates or trying to figure out if this financing option is right for you? The purpose of a consolidation on student loans is to help individuals lower their payments by spreading them out over a longer time period, to make managing monthly bills easier and to hopefully get a better interest rate that is fixed. Determining if consolidating your student loans is in your best interest requires doing a little mathematics, looking over your financial paperwork and making a decision that you can pay a little extra each month over the minimum due to save money in the long run – to save on interest over the years.
Did you know that according to Wikipedia, that student loans average at about 7 percent a year? Be aware that if you are currently in school, student loan consolidation rates will not apply to you. These loans cannot be consolidated while attending classes.
## What Determines the Student Loan Consolidation Rates?
Federal student loan consolidation rates are determined by the average of the interest rates on all federal loans. The interest rate is then rounded up 1/8th of one percent. All forms of federal loans are allowed to be combined together; however if you have private student loans then they cannot be consolidated with your federal loans. To be eligible for a student loan consolidation, all loans must be in grace period or in satisfactory payment mode. Payments must be current and if you are currently several months behind or in default, you will need to rehabilitate your loans through one of programs available by the Department of Education. Visit ED.gov to have a representative help you get your loans back on track so that you will then be able to consolidate your student loans.
## Calculating Student Loan Consolidation Rates
Gather a pen and a piece of notebook paper and all of your financial records about your student loans. Make a two column list by putting the amount you owe for each federal student loan in the first column and each loan’s interest rate in the second column. Add all of your loan interest rates together and divide by the total of loans that you have. Use the example below for help.
Example: If you have three federal loans and one is 4.5 percent and the other two are 5 percent interest then the weighted average would be formulated by this: 4.5+ 5.0+ 5.0 divided by 3 = 4.83333. The 4.8333 would then be rounded up 1/8th of a percentage to give you your overall fixed interest rate for a consolidation of your federal loans.
## Student Loan Consolidation Rates - Pros and Cons
There are several advantages of consolidating your student loans. You will only have one payment per month to worry about. This is particularly useful if you have multiple lenders servicing your loans. Another advantage is that your payment is generally lowered. However, this can also be a disadvantage. Even though you now will have a lower payment, you will pay more money in interest in the long run due to a lengthier loan plan. A consolidated student loan plan is generally ten to thirty years but you can cut down the costs paid over the year if you pay extra each month. Another negative aspect to student loan consolidation rates is that your average may go up slightly and your terms can change; therefore, if you had certain loan perks before then you may lose them. Read your loan promissory notes carefully before you consolidate to ensure that you are making the right decision. Once your student loans are consolidated, they cannot be changed – ever.
## Student Loan Consolidation Rates - Do Options for Private Loans Exist?
Options for private student loan consolidation are slim; however, banks like Wells Fargo, Chase, NextStudent and Student Loan Network offer consolidating private student loans. They are currently the only four bank entities that will handle these types of loans for consolidation. Wells Fargo will consolidate private student loans from the amounts of \$5,000 all the way up to \$100,000. Chase allows individuals who have between \$7,500 and \$150,000 in private loans to consolidate. Unfortunately, private loans are consolidated under a variable APR based primarily on an individual’s credit FICO score and credit history, unlike federal student loans that have a fixed rate. Chase requires a co-signer to receive a lower interest rate on a private student loan consolidation. Approval generally takes a month and a half to process; therefore, do not delay if you need your loans consolidated immediately.
## References Used to Create this Hub: "Student Loan Consolidation Rates"
ChaseStudentLoans.com: “Chase Private Consolidation Loan”
WellsFargo.com: “Wells Fargo Student Loans - Consolidate Private Loans”
ED.gov: “Department of Education”
StudentAid.Edu.gov: “Loan Consolidation”
Wikipedia.com: "Student Loans in the United States"
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http://www.ques10.com/p/1617/heat-transfer-question-paper-may-2015-mechanical-1/ | 1,556,167,917,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578681624.79/warc/CC-MAIN-20190425034241-20190425060037-00042.warc.gz | 295,050,064 | 7,090 | Question Paper: Heat Transfer : Question Paper May 2015 - Mechanical Engineering (Semester 5) | Mumbai University (MU)
0
## Heat Transfer - May 2015
### Mechanical Engineering (Semester 5)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
### Solve any four:
1 (a) What is meant by film condensation and dropwise condensation? (5 marks)
1 (b) What is Fin? What are the various types of fins? (5 marks)
1 (c) Explain the number of transfer units (NTU). (5 marks)
1 (d) Define Thermal Diffusivity and state its significance. (5 marks)
2 (a) Derive the relation for heat transfer through fin with insulated tip. State the assumptions clearly. (10 marks)
2 (b) Explain the term 'Time Constant' of thermocouple. (3 marks)
2 (c) A copper wire of radius 0.5mm is insulated uniformly with plastic (k=0.5 W/m K) sheathing 1mm thick. The wire is exposed to atmosphere at 30°C and the outside surface coefficient is 8 W/m2 K. Find the maximum safe current carried by the wire so that no part of the insulated plastic is above 75°C. Also calculate critical thickness of insulation. For copper, thermal conductivity = 400 W/m K, specific electrical resistance=2 X10-8 ohm-m. (7 marks)
3 (a) Using dimensional analysis, derive an expression for forced convection:- Nu=Constant X(Re)mX (Pr)n. (8 marks)
3 (b) Air at atmospheric pressure and 207deg;C flows with 6 m/s velocity through main trunk duct of air condisioning system. The duct is rectangular in cross-section and measures 40cm × 80cm. Determine heat loss per meter length of duct corresponding to unit temperature difference.
The relevant thermo-physical properties of air are: v=15×10-6, α=7.7×10-2 m2/hr, k=0.026 W/m-deg-k.
Use Nu=0.023 (Re)0.8 × (Pr)0.4.
(8 marks)
3 (c) What is meant by Fouling in Heat Exchangers. (4 marks)
4 (a) Distinguish between specular and diffuse radiation. (4 marks)
4 (b) Prove that the total emissive power of black surface is π time the intensity of radiation. (6 marks)
4 (c) 16.5 kg/s of the product at 650°C (cp=3.55 kJ/kg K), in a chemical plant, are to be used to heat 20.5 kg/s of the incoming fluid from 100°C (cp=4.2 kJ/kg K). If the overall heat transfer coefficient is 0.95 kW/m2 K and the installed heat transfer surface is 44 m2, calculate the fluid outlet temperature for the counter flow and parallel flow arrangements. (10 marks)
5 (a) Derive the relationship between the effectiveness and the number of transfer units for a parallel flow heat exchanger. (10 marks)
5 (b) A thermocouple indicates a temperature of 800°C when placed in a pipeline where a hot gas is flowing at 870°C. If the convective heat transfer cofficient between the thermocouple and gas is 60 W/m2 K, find the duct wall temperature, ε (thermocouple)=0.5. (5 marks)
5 (c) A thin copper sphere with its internal surface highly oxydises, has a diameter of 20 cm. How small a hole must be made in the sphere to make an operating that will have an absorptivity of 0.9? (5 marks)
### Write a short note (Any Two):
6 (a) (i) Heisler chart. (4 marks)
6 (a) (ii) Importance of numerical methods. (4 marks)
6 (a) (iii Heat Pipe. (4 marks)
6 (b) Draw the boiling curve and identify the different boiling regimes. (5 marks)
6 (c) A 15 mm diameter mild steel sphere (k=42 W/m °C) is exposed to coding airflow at 20°C resulting in the convective coefficient h=120 W/m2 °C.
Determine the following:
i) Time required to cool the sphere from 550°C to 90°C
ii) Instantaneous heat transfer rate 2 minutes after the start of cooling.
For mild steel take: ρ=7850 kg/m3, c=475 J/kg °C, α=0.045 m2/h.
(7 marks) | 1,032 | 3,721 | {"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} | 3.28125 | 3 | CC-MAIN-2019-18 | latest | en | 0.853225 |
http://serc.carleton.edu/serc/site_guides/earthquake_activities.html?results_start=81 | 1,462,251,659,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860118790.25/warc/CC-MAIN-20160428161518-00171-ip-10-239-7-51.ec2.internal.warc.gz | 263,080,409 | 8,288 | SERC > Site Guides > Earthquakes > Earthquake Activities
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Getting to the Point: Exploring Tectonic Motion at Point Reyes National Seashore
Module by: Judy McIlrath, University of South Florida Cover Page by: Len Vacher and Denise Davis, University of South Florida
Spreadsheets Across the Curriculum module/Geology of National Parks course. Students use foundational math to calculate such earthquake-related numbers as fault displacement rate and earthquake recurrence interval associated with the San Andreas Fault at Point Reyes National Seashore.
Explaining Seismic Hazard Probabilities
Mary Savina, Carleton College
This activity asks students to explain earthquake hazard probabilities to a lay audience of citizens, government officials and others.
Developing student literacy on risk, resilience, and strategies for living with disaster uncertainty
Monica Gowan, Mayo Medical School
In this guided research and critical thinking activity, students prepare a research paper comprised of two parts: 1) a "state-of-the-science" review and synthesis of selected literature from risk and resilience research (provided) and 2) a brief critical appraisal of how current knowledge is (or could be) applied to building disaster resilience in a real-world scenario. Part 2 will be set in a student-selected hazard context (coastal hazards, flooding, or earthquake), employment sector (academia, government, private industry, services, non-profit), and geopolitical sphere of influence (e.g., Resilience to earthquake disaster in the student population at Universidad de Lima, Peru).
ConcepTest: EQ Recurrence Interval
Plate A moves 3 cm/yr past plate B. A typical earthquake along the plate boundary has 6 meters of slip. What is the recurrence interval of the earthquake? a. 0.2 years b. 2 years c. 200 years d. 2000 years
ConcepTest: EQ Locations in North America
Which of the locations on the map of North America below is most likely to experience a magnitude 6 or greater earthquake? a. b. c. d.
Plotting Earthquakes with Near Real-Time Data
Bill Slattery, Wright State University-Main Campus
Students access the United States Geological Survey National Earthquake Information Center at http://earthquake.usgs.gov/earthquakes/map/ and plot the longitude latitude and depth of earthquakes on a physiographic ...
ConcepTest: EQ Intensity and Distance
Following a shallow earthquake, twenty residents located througout the affected region were surveyed to guage the level of destruction. Their observations were quantified using the Modified Mercalli scale. Which of ...
ConcepTest: Divergent Boundary Sketch
The figure below was drawn by a student to show the relationship between earthquake epicenters (filled circles) and a divergent plate boundary (red line). The figure represents a boundary between two oceanic ...
ConcepTest: EQ and Convergent Boundary Sketch2
The figure below was drawn by a student to show the relationship between earthquake epicenters (filled circles) and a convergent plate boundary (red line). The figure represents a boundary between an oceanic plate ...
ConcepTest: EQ and Convergent Boundary Sketch
The figure below was drawn by a student to show the relationship between earthquake epicenters (filled circles) and a convergent plate boundary (red line). The figure represents a boundary between an oceanic plate ... | 753 | 3,601 | {"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} | 3.40625 | 3 | CC-MAIN-2016-18 | latest | en | 0.883072 |
https://www.aqua-calc.com/one-to-one/density/kilogram-per-cubic-decimeter/pound-per-cubic-millimeter/1 | 1,571,886,090,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987838289.72/warc/CC-MAIN-20191024012613-20191024040113-00105.warc.gz | 791,221,507 | 8,608 | # 1 kilogram per cubic decimeter in pounds per cubic millimeter
## kg/dm³ to lb/mm³ unit converter of density
1 kilogram per cubic decimeter [kg/dm³] = 2 × 10-6 pound per cubic millimeter [lb/mm³]
### kilograms per cubic decimeter to pounds per cubic millimeter density conversion cards
• 1
through
25
kilograms per cubic decimeter
• 1 kg/dm³ to lb/mm³ = 2 × 10-6 lb/mm³
• 2 kg/dm³ to lb/mm³ = 4 × 10-6 lb/mm³
• 3 kg/dm³ to lb/mm³ = 7 × 10-6 lb/mm³
• 4 kg/dm³ to lb/mm³ = 9 × 10-6 lb/mm³
• 5 kg/dm³ to lb/mm³ = 1.1 × 10-5 lb/mm³
• 6 kg/dm³ to lb/mm³ = 1.3 × 10-5 lb/mm³
• 7 kg/dm³ to lb/mm³ = 1.5 × 10-5 lb/mm³
• 8 kg/dm³ to lb/mm³ = 1.8 × 10-5 lb/mm³
• 9 kg/dm³ to lb/mm³ = 2 × 10-5 lb/mm³
• 10 kg/dm³ to lb/mm³ = 2.2 × 10-5 lb/mm³
• 11 kg/dm³ to lb/mm³ = 2.4 × 10-5 lb/mm³
• 12 kg/dm³ to lb/mm³ = 2.6 × 10-5 lb/mm³
• 13 kg/dm³ to lb/mm³ = 2.9 × 10-5 lb/mm³
• 14 kg/dm³ to lb/mm³ = 3.1 × 10-5 lb/mm³
• 15 kg/dm³ to lb/mm³ = 3.3 × 10-5 lb/mm³
• 16 kg/dm³ to lb/mm³ = 3.5 × 10-5 lb/mm³
• 17 kg/dm³ to lb/mm³ = 3.7 × 10-5 lb/mm³
• 18 kg/dm³ to lb/mm³ = 4 × 10-5 lb/mm³
• 19 kg/dm³ to lb/mm³ = 4.2 × 10-5 lb/mm³
• 20 kg/dm³ to lb/mm³ = 4.4 × 10-5 lb/mm³
• 21 kg/dm³ to lb/mm³ = 4.6 × 10-5 lb/mm³
• 22 kg/dm³ to lb/mm³ = 4.9 × 10-5 lb/mm³
• 23 kg/dm³ to lb/mm³ = 5.1 × 10-5 lb/mm³
• 24 kg/dm³ to lb/mm³ = 5.3 × 10-5 lb/mm³
• 25 kg/dm³ to lb/mm³ = 5.5 × 10-5 lb/mm³
• 26
through
50
kilograms per cubic decimeter
• 26 kg/dm³ to lb/mm³ = 5.7 × 10-5 lb/mm³
• 27 kg/dm³ to lb/mm³ = 6 × 10-5 lb/mm³
• 28 kg/dm³ to lb/mm³ = 6.2 × 10-5 lb/mm³
• 29 kg/dm³ to lb/mm³ = 6.4 × 10-5 lb/mm³
• 30 kg/dm³ to lb/mm³ = 6.6 × 10-5 lb/mm³
• 31 kg/dm³ to lb/mm³ = 6.8 × 10-5 lb/mm³
• 32 kg/dm³ to lb/mm³ = 7.1 × 10-5 lb/mm³
• 33 kg/dm³ to lb/mm³ = 7.3 × 10-5 lb/mm³
• 34 kg/dm³ to lb/mm³ = 7.5 × 10-5 lb/mm³
• 35 kg/dm³ to lb/mm³ = 7.7 × 10-5 lb/mm³
• 36 kg/dm³ to lb/mm³ = 7.9 × 10-5 lb/mm³
• 37 kg/dm³ to lb/mm³ = 8.2 × 10-5 lb/mm³
• 38 kg/dm³ to lb/mm³ = 8.4 × 10-5 lb/mm³
• 39 kg/dm³ to lb/mm³ = 8.6 × 10-5 lb/mm³
• 40 kg/dm³ to lb/mm³ = 8.8 × 10-5 lb/mm³
• 41 kg/dm³ to lb/mm³ = 9 × 10-5 lb/mm³
• 42 kg/dm³ to lb/mm³ = 9.3 × 10-5 lb/mm³
• 43 kg/dm³ to lb/mm³ = 9.5 × 10-5 lb/mm³
• 44 kg/dm³ to lb/mm³ = 9.7 × 10-5 lb/mm³
• 45 kg/dm³ to lb/mm³ = 9.9 × 10-5 lb/mm³
• 46 kg/dm³ to lb/mm³ = 0.000101 lb/mm³
• 47 kg/dm³ to lb/mm³ = 0.000104 lb/mm³
• 48 kg/dm³ to lb/mm³ = 0.000106 lb/mm³
• 49 kg/dm³ to lb/mm³ = 0.000108 lb/mm³
• 50 kg/dm³ to lb/mm³ = 0.00011 lb/mm³
• 51
through
75
kilograms per cubic decimeter
• 51 kg/dm³ to lb/mm³ = 0.000112 lb/mm³
• 52 kg/dm³ to lb/mm³ = 0.000115 lb/mm³
• 53 kg/dm³ to lb/mm³ = 0.000117 lb/mm³
• 54 kg/dm³ to lb/mm³ = 0.000119 lb/mm³
• 55 kg/dm³ to lb/mm³ = 0.000121 lb/mm³
• 56 kg/dm³ to lb/mm³ = 0.000123 lb/mm³
• 57 kg/dm³ to lb/mm³ = 0.000126 lb/mm³
• 58 kg/dm³ to lb/mm³ = 0.000128 lb/mm³
• 59 kg/dm³ to lb/mm³ = 0.00013 lb/mm³
• 60 kg/dm³ to lb/mm³ = 0.000132 lb/mm³
• 61 kg/dm³ to lb/mm³ = 0.000134 lb/mm³
• 62 kg/dm³ to lb/mm³ = 0.000137 lb/mm³
• 63 kg/dm³ to lb/mm³ = 0.000139 lb/mm³
• 64 kg/dm³ to lb/mm³ = 0.000141 lb/mm³
• 65 kg/dm³ to lb/mm³ = 0.000143 lb/mm³
• 66 kg/dm³ to lb/mm³ = 0.000146 lb/mm³
• 67 kg/dm³ to lb/mm³ = 0.000148 lb/mm³
• 68 kg/dm³ to lb/mm³ = 0.00015 lb/mm³
• 69 kg/dm³ to lb/mm³ = 0.000152 lb/mm³
• 70 kg/dm³ to lb/mm³ = 0.000154 lb/mm³
• 71 kg/dm³ to lb/mm³ = 0.000157 lb/mm³
• 72 kg/dm³ to lb/mm³ = 0.000159 lb/mm³
• 73 kg/dm³ to lb/mm³ = 0.000161 lb/mm³
• 74 kg/dm³ to lb/mm³ = 0.000163 lb/mm³
• 75 kg/dm³ to lb/mm³ = 0.000165 lb/mm³
• 76
through
100
kilograms per cubic decimeter
• 76 kg/dm³ to lb/mm³ = 0.000168 lb/mm³
• 77 kg/dm³ to lb/mm³ = 0.00017 lb/mm³
• 78 kg/dm³ to lb/mm³ = 0.000172 lb/mm³
• 79 kg/dm³ to lb/mm³ = 0.000174 lb/mm³
• 80 kg/dm³ to lb/mm³ = 0.000176 lb/mm³
• 81 kg/dm³ to lb/mm³ = 0.000179 lb/mm³
• 82 kg/dm³ to lb/mm³ = 0.000181 lb/mm³
• 83 kg/dm³ to lb/mm³ = 0.000183 lb/mm³
• 84 kg/dm³ to lb/mm³ = 0.000185 lb/mm³
• 85 kg/dm³ to lb/mm³ = 0.000187 lb/mm³
• 86 kg/dm³ to lb/mm³ = 0.00019 lb/mm³
• 87 kg/dm³ to lb/mm³ = 0.000192 lb/mm³
• 88 kg/dm³ to lb/mm³ = 0.000194 lb/mm³
• 89 kg/dm³ to lb/mm³ = 0.000196 lb/mm³
• 90 kg/dm³ to lb/mm³ = 0.000198 lb/mm³
• 91 kg/dm³ to lb/mm³ = 0.000201 lb/mm³
• 92 kg/dm³ to lb/mm³ = 0.000203 lb/mm³
• 93 kg/dm³ to lb/mm³ = 0.000205 lb/mm³
• 94 kg/dm³ to lb/mm³ = 0.000207 lb/mm³
• 95 kg/dm³ to lb/mm³ = 0.000209 lb/mm³
• 96 kg/dm³ to lb/mm³ = 0.000212 lb/mm³
• 97 kg/dm³ to lb/mm³ = 0.000214 lb/mm³
• 98 kg/dm³ to lb/mm³ = 0.000216 lb/mm³
• 99 kg/dm³ to lb/mm³ = 0.000218 lb/mm³
• 100 kg/dm³ to lb/mm³ = 0.00022 lb/mm³
#### Foods, Nutrients and Calories
LIVE KOMBUCHA, UPC: 853874004069 contain(s) 20 calories per 100 grams or ≈3.527 ounces [ price ]
PURE DARK and MILK CHOCOLATE, UPC: 708656000602 contain(s) 575 calories per 100 grams or ≈3.527 ounces [ price ]
#### Gravels, Substances and Oils
CaribSea, Freshwater, Super Naturals, Moonlight Sand weighs 1 521.75 kg/m³ (94.99975 lb/ft³) with specific gravity of 1.52175 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 ]
Chromic anhydride [CrO3] weighs 2 700 kg/m³ (168.55549 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-401B, liquid (R401B) with temperature in the range of -51.12°C (-60.016°F) to 68.34°C (155.012°F)
#### Weights and Measurements
A square millimeter per second (mm²/s) is a derived metric SI (System International) measurement unit of kinematic viscosity.
Dynamic viscosity is a measure of how resistive a fluid is to flow. Viscosity describes how thick a fluid is
oz/cm to lb/ft conversion table, oz/cm to lb/ft unit converter or convert between all units of linear density measurement.
#### Calculators
Calculate volume of a dodecahedron and its surface area | 2,830 | 5,963 | {"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} | 2.921875 | 3 | CC-MAIN-2019-43 | latest | en | 0.168144 |
https://wab.uib.no/sample/frmnorm.htm | 1,713,151,685,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816939.51/warc/CC-MAIN-20240415014252-20240415044252-00295.warc.gz | 542,007,249 | 15,237 | A1
## Summary
One reason for thinking the old notation wrong is that it is very unlikely that from every proposition p an infinite number of other propositions not-not-p, not-not-not-not-p, etc., should follow.
If only those signs which contain proper names were complex then propositions containing nothing but apparent variables would be simple. Then what about their denials?
The verb of a proposition cannot be „is true” or „is false”, but whatever is true or false must already contain the verb.
Deductions only proceed according to the laws of deduction, but these laws cannot justify the deduction.
One reason for supposing that not all propositions which have more than one argument are relational propositions is that if they were, the relations of judgement and inference would have to hold between an arbitrary number of things.
Every proposition which seems to be about a complex can be analysed into a proposition about its constituents and about the proposition which describes the complex perfectly; i.e., that proposition which is equivalent to saying the complex exists.
The idea that propositions are names of complexes suggests that whatever is not a proper name is a sign for a relation. Because spatial complexes1 consist of Things and Relations only and the idea of a complex is taken from space.
In a proposition convert all its indefinables into variables; there then remains a class of propositions which is not all propositions but a type.
A2 There are thus two ways in which signs are similar. The names Socrates and Plato are similar: they are both names. But whatever they have in common must not be introduced before Socrates and Plato are introduced. The same applies to subject-predicate form etc. Therefore, thing, proposition, subject-predicate form, etc., are not indefinables, i.e., types are not indefinables.
When we say A judges that etc., then we have to mention a whole proposition which A judges. It will not do either to mention only its constituents, or its constituents and form, but not in the proper order. This shows that a proposition itself must occur in the statement that it is judged; however, for instance, „not-p” may be explained. The question „What is negated” must have a meaning.
To understand a proposition p it is not enough to know that p implies ‚„p” is true’, but we must also know that ~p implies „p is false”. This shows the bipolarity of the proposition.
W-F = Wahr-Falsch
To every molecular function a WF scheme corresponds. Therefore we may use the WF scheme itself instead of the function. Now what the WF scheme does is, it correlates the letters W and F with each proposition. These two letters are the poles of atomic propositions. Then the scheme correlates another W and F to these poles. In this notation all that matters is the correlation of the outside poles to the pole of the atomic propositions. Therefore not-not-p is the same symbol as p. And therefore we shall never get two symbols for the same molecular function.
A3 The meaning of a proposition is the fact which actually corresponds to it.
As the ab functions of atomic propositions are bi-polar propositions again we can perform ab operations on them. We shall, by doing so, correlate two new outside poles via the old outside poles to the poles of the atomic propositions.
The symbolising fact in a-p-b is that, say2 a is on the left of p and b on the right of p; then the correlation of new poles is to be transitive, so that for instance if a new pole a in whatever way i.e. via whatever poles is correlated to the inside a, the symbol is not changed thereby. It is therefore possible to construct all possible ab functions by performing one ab operation repeatedly, and we can therefore talk of all ab functions as of all those functions which can be obtained by performing this ab operation repeatedly.
[Note by Bertrand Russell]
[NB. ab means the same as WF, which means true-false.]
Naming is like pointing. A function is like a line dividing points of a plane into right and left ones; then „p or not-p” has no meaning because it does not divide the plane.
But though a particular proposition „p or not-p” has no meaning, a general proposition „for all p's, p or not-p” has a meaning because this does not contain the nonsensical function „p or not-p” but the function „p or not-q” just as „for all x's xRx” contains the function „xRy”.
A4 A proposition is a standard to which all facts behave, with names it is otherwise; it is thus bi-polarity and sense comes in; just as one arrow behaves to another arrow by being in the same sense or the opposite, so a fact behaves to a proposition.
The form of a proposition has meaning in the following way. Consider a symbol „xRy”. To symbols of this form correspond couples of things whose names are respectively „x” and „y”. The things x y stand to one another in all sorts of relations, amongst others some stand in the relation R, and some not; just as I single out a particular thing by a particular name I single out all behaviours of the points x and y with respect to the relation R. I say that if an x stands in the relation R to a y the sign „x R y” is to be called true to the fact and otherwise false. This is a definition of sense.
In my theory p has the same meaning as not-p but opposite sense. The meaning is the fact. The proper theory of judgment must make it impossible to judge nonsense.
It is not strictly true to say that we understand a proposition p if we know that p is equivalent to „p is true” for this would be the case if accidentally both were true or false. What is wanted is the formal equivalence with respect to the forms of the proposition, i.e., all the general indefinables involved. The sense of an ab function of a proposition is a function of its sense. There are only unasserted propositions. ¦ Assertion is merely psychological. In not-p, p is exactly the same as if it stands alone; this point is absolutely fundamental. Among the facts which make „p or q” true there are also facts which make „p and q” true; if propositions have only meaning, we ought, in such a case, to say that these two propositions are identical, but in fact, their sense is different for we have introduced sense by talking of all p's and all q's. Consequently the molecular propositions will only be used in cases where there ab function stands under a generality sign or enters into another function such as „I believe that, etc.,” because then the sense enters.
A5 In „a judges pp cannot be replaced by a proper name. This appears if we substitute „a judges that p is true and not p is false”. The proposition „a judges p” consists of the proper name a, the proposition p with its 2 poles, and a being related to both of these poles in a certain way. This is obviously not a relation in the ordinary sense.
The ab notation makes it clear that not and or are dependent on one another and we can therefore not use them as simultaneous indefinables. <!> Same objections in the case of apparent variables to old indefinables, as in the case of molecular functions: The application of the ab notation to apparent-variable propositions becomes clear if we consider that, for instance, the proposition „for all x, φx” is to be true when φx is true for all x's and false when jx is false for some x's. We see that some and all occur simultaneously in the proper apparent variable notation.
A6 The Notation is:
for (x) φx ; a - (x) - a φ x b - (&Exist; x) - b
and
for (&Exist;x) φ x : a - (&Exist;x) - a φ x b - (x) - b
Old definitions now become tautologous.
In aRb it is not the complex that symbolises but the fact that the symbol a stands in a certain relation to the symbol b. Thus facts are symbolised by facts, or more correctly: that a certain thing is the case in the symbol says that a certain thing is the case in the world.
Judgment, question and command are all on the same level. What interests logic in them is only the unasserted proposition. Facts cannot be named.
A proposition cannot occur in itself. This is the fundamental truth of the theory of types.
Every proposition that says something about one thing is a subject-predicate proposition, and so on.
Therefore we can recognize a subject-predicate proposition if we know it contains only one name and one form, etc. This gives the construction of types. Hence the type of a proposition can be recognized by its symbol alone.
A7 What is essential in a correct apparent-variable notation is this:- (1) it must mention a type of propositions; (2) it must show which components of a proposition of this type are constants.
[Components are forms and constituents.]
Take (φ).φ!x. Then if we describe the kind of symbols, for which φ! stands and which, by the above, is enough to determine the type, then automatically „(φ).φ!x” cannot be fitted by this description, because it containsφ!x” and the description is to describe all that symbolizes in symbols of the φ! - kind. If the description is thus complete vicious circles can just as little occur as for instance in (φ).(x)φ (where (x)φ is a subject-predicate proposition).
B1
## First MS.
Indefinables are of two sorts: names, and forms. Propositions cannot consist of names alone; they cannot be classes of names. A name can not only occur in two different propositions, but can occur in the same way in both.
Propositions [which are symbols having reference to facts] are themselves facts: that this inkpot is on this table may express that I sit in this chair.
It can never express the common characteristic of two objects that we designate them by the same name but by two different ways of designation, for, since names are arbitrary, we might also choose different names, and where then would be the common element in the designations? Nevertheless one is always tempted, in a difficulty, to take refuge in different ways of designation.
Frege said „propositions are names”; Russell said „propositions correspond to complexes”. Both are false; and especially false is the statement „propositions are names of complexes”.
It is easy to suppose that only such symbols are complex as contain names of objects, and that accordingly „(&Exist;x,φ).φx” or „(&Exist;x,R,y).xRy” must be simple. It is then natural to call the first of these the name of a form, the second the name of a relation. But in that case what is the meaning of (e.g.) „˜(&Exist;x,y).xRy”? Can we put „not” before a name?
B2 The reason why „˜Socrates” means nothing is that „˜x” does not express a property of x.
There are positive and negative facts: if the proposition „this rose is not red” is true, then what it signifies is negative. But the occurrence of the word „not” does not indicate this unless we know that the signification of the proposition „this rose is red” (when it is true) is positive. It is only from both, the negation and the negated proposition, that we can conclude to a characteristic of the significance of the whole proposition. (We are not here speaking of negations of general propositions, i.e. of such as contain apparent variables. Negative facts only justify the negations of atomic propositions.)
Positive and negative facts there are, but not true and false facts.
If we overlook the fact that propositions have a sense which is independent of their truth or falsehood, it easily seems as if true and false were two equally justified relations between the sign and what is signified. (We might then say e.g. that „qsignifies in the true way what „not-qsignifies in the false way). But are not true and false in fact equally justified? Could we not express ourselves by means of false propositions just as well as hitherto with true ones, so long as we know that they are meant falsely? ¦ No! For a proposition is then true when it is as we assert in this proposition; and accordingly if by „q” we mean „not-q”, and it is as we mean to assert, then in the new interpretation „q” is actually true and not false. But it is important that we can mean the same by „q” as by „not-q”, for it shows that neither to the symbol „not” nor to the manner of its combination with „q” does a characteristic of the denotation of „q” correspond.
B4
## 2nd MS.
We must be able to understand propositions which we have never heard before. But every proposition is a new symbol. Hence we must have general indefinable symbols; these are unavoidable if propositions are not all indefinable.
Whatever corresponds in reality to compound propositions must not be more than what corresponds to their several atomic propositions.
Not only must logic not deal with [particular] things, but just as little with relations and predicates.
There are no propositions containing real variables.
What corresponds in reality to a proposition depends upon whether it is true or false. But we must be able to understand a proposition without knowing if it is true or false.
What we know when we understand a proposition is this: We know what is the case if the proposition is true, and what is the case if it is false. But we do not know [necessarily] whether it is true or false.
Propositions are not names.
We can never distinguish one logical type from another by attributing a property to members of the one which we deny to members of the other.
Symbols are not what they seem to be. In „aRb”, „R” looks like a substantive, but is not one. What symbolizes in „aRb” is that R occurs between a and b. Hence „R” is not the indefinable in „aRb”. Similarly in „φx”, „φ” looks like a substantive but is not one; in „˜p”, „˜” looks like „φ” but is not like it. This is the first thing that indicates that there may not be logical constants. A reason against them is the generality of logic: logic cannot treat a special set of things.
B5 Molecular propositions contain nothing beyond what is contained in their atoms; they add no material information above that contained in their atoms.
All that is essential about molecular functions is their T-F schema [i.e. the statement of the cases when they are true and the cases when they are false].
Alternative indefinability shows that the indefinables have not been reached.
Every proposition is essentially true-false: to understand it, we must know both what must be the case if it is true, and what must be the case if it is false. Thus a proposition has two poles, corresponding to the case of its truth and the case of its falsehood. We call this the sense of a proposition.
In regard to notation, it is important to note that not every feature of a symbol symbolizes. In two molecular functions which have the same T-F schema, what symbolizes must be the same. In „not-not-p”, „not-p” does not occur; for „not-not-p” is the same as ”p”, and therefore, if „not-p” occurred in „not-not-p”, it would occur in „p”.
Logical indefinables cannot be predicates or relations, because propositions, owing to sense, cannot have predicates or relations. Nor are „not” and „or”, like judgment, analogous to predicates or relations, because they do not introduce anything new.
Propositions are always complex even if they contain no names.
B6 A proposition must be understood when all its indefinables are understood. The indefinables in „aRb” are introduced as follows:
„a” is indefinable;
„b” is indefinable;
Whatever „x” and „y” may mean, „xRy” says something indefinable about their meanings.
A complex symbol must never be introduced as a single indefinable. (Thus e.g. no proposition is indefinable.) For if one of its parts occurs also in another connection, it must there be re-introduced. And would it then mean the same?
The ways by which we introduce our indefinables must permit us to construct all propositions that have sense from these indefinables alone. It is easy to introduce „all” and „some” in a way that will make the construction of (say) „(x,y).xRy” possible from „all” and „xRyas introduced before.
B7
## 3rd MS.
An analogy for the theory of truth: Consider a black patch on white paper; then we can describe the form of the patch by mentioning, for each point of the surface, whether it is white or black. To the fact that a point is black corresponds a positive fact, to the fact that a point is white (not black) corresponds a negative fact. If I designate a point of the surface (one of Frege's „truth-values”), this is as if I set up an assumption to be decided upon. But in order to be able to say of a point that it is black or that it is white, I must first know when a point is to be called black and when it is to be called white. In order to be able to say that „p” is true (or false), I must first have determined under what circumstances I call a proposition true, and thereby I determine the sense of a proposition. The point in which the analogy fails is this: I can indicate a point of the paper that is white and black, but to a proposition without sense nothing corresponds, for it does not designate a thing (truth-value), whose properties might be called „false” or „true”; the verb of a proposition is not „is true” or „is false”, as Frege believes, but what is true must already contain the verb.
The comparison of language and reality is like that of retinal image and visual image: to the blind spot nothing in the visual image seems to correspond, and thereby the boundaries of the blind spot determine the visual image - as true negations of atomic propositions determine reality.
B8 Logical inferences can, it is true, be made in accordance with Frege's or Russell's laws of deduction, but this cannot justify the inference; and therefore they are not primitive propositions of logic. If p follows from q, it can also be inferred from q, and the „manner of deduction” is indifferent.
Those symbols which are called propositions in which „variables occur” are in reality not propositions at all, but only schemes of propositions, which only become propositions when we replace the variables by constants. There is no proposition which is expressed by „x = x”, for „x” has no signification; but there is a proposition „(x).x = x” and propositions such as „Socrates = Socrates” etc.
In books on logic, no variables ought to occur, but only the general propositions which justify the use of variables. It follows that the so-called definitions of logic are not definitions, but only schemes of definitions, and instead of these we ought to put general propositions; and similarly the so-called primitive ideas (Urzeichen) of logic are not primitive ideas, but the schemes of them. The mistaken idea that there are things called facts or complexes and relations easily leads to the opinion that there must be a relation of questioning to the facts, and then the question arises whether a relation can hold between an arbitrary number of things, since a fact can follow from arbitrary cases. It is a fact that the proposition which e.g. expresses that q follows from p and p⊂q is this: p.p⊂q.⊂p.q.q.
B9 At a pinch, one is tempted to interpret „not-p” as „everything else, only not p”. That from a single fact p an infinity of others, not-not-p etc., follow, is hardly credible. Man possesses an innate capacity for constructing symbols with which some sense can be expressed, without having the slightest idea what each word signifies. The best example of this is mathematics, for man has until lately used the symbols for numbers without knowing what they signify or that they signify nothing.
Russell's „complexes” were to have the useful property of being compounded, and were to combine with this the agreeable property that they could be treated like „simples”. But this alone made them unserviceable as logical types, since there would have been significance in asserting, of a simple, that it was complex. But a property cannot be a logical type.
Every statement about apparent complexes can be resolved into the logical sum of a statement about the constituents and a statement about the proposition which describes the complex completely. How, in each case, the resolution is to be made, is an important question, but its answer is not unconditionally necessary for the construction of logic.
B10 That „or” and „not” etc. are not relations in the same sense as „right” and „left” etc., is obvious to the plain man. The possibility of cross-definitions in the old logical indefinables shows, of itself, that these are not the right indefinables, and, even more conclusively, that they do not denote relations.
If we change a constituent a of a proposition φ(a) into a variable, then there is a class
˜p {(&Exist;x).φ(x) = p}.
This class in general still depends upon what, by an arbitrary convention, we mean by „j(x)”. But if we change into variables all those symbols whose significance was arbitrarily determined, there is still such a class. But this is now not dependent upon any convention, but only upon the nature of the symbol „j(x)”. It corresponds to a logical type.
Types can never be distinguished from each other by saying (as is often done) that one has these but the other has that properties, for this presupposes that there is a meaning in asserting all these properties of both types. But from this it follows that, at best, these properties may be types, but certainly not the objects of which they are asserted.
B11 At a pinch, we are always inclined to explanations of logical functions of propositions which aim at introducing into the function either only the constituents of these propositions, or only their forms, etc. etc.; and we overlook that ordinary language would not contain the whole propositions if it did not need them: However, e.g., „not-p” may be explained, there must always be a meaning given to the question „what is denied?”
The very possibility of Frege's explanations of „not-p” and „if p then q”, from which it follows that not-not-p denotes the same as p, makes it probable that there is some method of designation in which „not-not-p” corresponds to the same symbol as „p”. But if this method of designation suffices for logic, it must be the right one.
Names are points, propositions arrows - they have sense. The sense of a proposition is determined by the two poles true and false. The form of a proposition is like a straight line, which divides all points of a plane into right and left. The line does this automatically, the form of proposition only by convention.
B12 Just as little as we are concerned, in logic, with the relation of a name to its meaning, just so little are we concerned with the relation of a proposition to reality, but we want to know the meaning of names and the sense of propositions - as we introduce an indefinable concept „A” by saying: „‚A’ denotes something indefinable”, so we introduce e.g. the form of propositions aRb by saying: „For all meanings of „x” and „y”, „xRy” expresses something indefinable about x and y”.
In place of every proposition „p”, let us write „abp”. Let every correlation of propositions to each other or of names to propositions be effected by a correlation of their poles „a” and „b”. Let this correlation be transitive. Then accordingly „a-ab-bp” is the same symbol as „abp”. Let n propositions be given. I then call a „class of poles” of these propositions every class of n members, of which each is a pole of one of the n propositions, so that one member corresponds to each proposition. I then correlate with each class of poles one of two poles (a and b). The sense of the symbolizing fact thus constructed I cannot define, but I know it.
If p = not-not-p etc., this shows that the traditional method of symbolism is wrong, since it allows a plurality of symbols with the same sense; and thence it follows that, in analyzing such propositions, we must not be guided by Russell's method of symbolizing.
B13 It is to be remembered that names are not things, but classes: „A” is the same letter as „A”. This has the most important consequences for every symbolic language.
Neither the sense nor the meaning of a proposition is a thing. These words are incomplete symbols.
It is impossible to dispense with propositions in which the same argument occurs in different positions. It is obviously useless to replace φ(a,a) by φ(a,b).a = b.
Since the ab-functions of p are again bi-polar propositions, we can form ab-functions of them, and so on. In this way a series of propositions will arise, in which in general the symbolizing facts will be the same in several members. If now we find an ab-function of such a kind that by repeated application of it every ab-function can be generated, then we can introduce the totality of ab-functions as the totality of those that are generated by application of this function. Such a function is ˜pv˜q.
B14 It is easy to suppose a contradiction in the fact that on the one hand every possible complex proposition is a simple ab-function of simple propositions, and that on the other hand the repeated application of one ab-function suffices to generate all these propositions. If e.g. an affirmation can be generated by double negation, is negation in any sense contained in affirmation? Does „p” deny „not-p” or assert „p”, or both? And how do matters stand with the definition of „⊃” by „v” and „·”, or of „v” by „·” and „⊃”? And how e.g. shall we introduce p|q (i.e. ˜pv˜q), if not by saying that this expression says something indefinable about all arguments p and q? But the ab-functions must be introduced as follows: The function p|q is merely a mechanical instrument for constructing all possible symbols of ab-functions. The symbols arising by repeated application of the symbol „¦” do not contain the symbol „p¦q”. We need a rule according to which we can form all symbols of ab-functions, in order to be able to speak of the class of them; and we now speak of them e.g. as those symbols of functions which can be generated by repeated application of the operation „¦”. And we say now: For all p's and q's, „p¦q” says something indefinable about the sense of those simple propositions which are contained in p and q.
B15 The assertion-sign is logically quite without significance. It only shows, in Frege and Whitehead and Russell, that these authors hold the propositions so indicated to be true. „¦-” therefore belongs as little to the proposition as (say) the number of the proposition. A proposition cannot possibly assert of itself that it is true.
Every right theory of judgment must make it impossible for me to judge that this table penholders the book. Russell's theory does not satisfy this requirement.
It is clear that we understand propositions without knowing whether they are true or false. But we can only know the meaning of a proposition when we know if it is true or false. What we understand is the sense of the proposition.
The assumption of the existence of logical objects makes it appear remarkable that in the sciences propositions of the form „pvq”, „pq”, etc. are only then not provisional when „v” and ”⊃” stand within the scope of a generality-sign [apparent variable].
B16
## 4th MS.
If we formed all possible atomic propositions, the world would be completely described if we declared the truth or falsehood of each. [I doubt this.]
The chief characteristic of my theory is that, in it, p has the same meaning as not-p.
A false theory of relations makes it easily seem as if the relation of fact and constituent were the same as that of fact and fact which follows from it. But the similarity of the two may be expressed thus: φa.⊃.φ,a a = a.
If a word creates a world so that in it the principles of logic are true, it thereby creates a world in which the whole of mathematics holds; and similarly it could not create a world in which a proposition was true, without creating its constituents.
Signs of the form „pv˜p” are senseless, but not the proposition „(p).p v ˜p”. If I know that this rose is either red or not red, I know nothing. The same holds of all ab-functions.
To understand a proposition means to know what is the case if it is true. Hence we can understand it without knowing if it is true. We understand it when we understand its constituents and forms. If we know the meaning of „a” and „b”, and if we know what „xRy” means for all x's and y's, then we also understand „aRb”.
I understand the proposition „aRb” when I know that either the fact that aRb or the fact that not aRb corresponds to it; but this is not to be confused with the false opinion that I understand „aRb” when I know that „aRb or not-aRb” is the case.
B17 But the form of a proposition symbolizes in the following way: Let us consider symbols of the form „xRy”; to these correspond primarily pairs of objects, of which one has the name „x”, the other the name „y”. The x's and y's stand in various relations to each other, among others the relation R holds between some, but not between others. I now determine the sense of „xRy” by laying down: when the facts behave in regard to „xRy” so that the meaning of „x” stands in the relation R to the meaning of „y”, then I say that they [the facts] are „of like sense” [„gleichsinnig”] with the proposition „xRy”; otherwise, „of opposite sense” [entgegengesetzt”]; I correlate the facts to the symbol „xRyby thus dividing them into those of like sense and those of opposite sense. To this correlation corresponds the correlation of name and meaning. Both are psychological. Thus I understand the form „xRy” when I know that it discriminates the behaviour of x and y according as these stand in the relation R or not. In this way I extract from all possible relations the relation R, as, by a name, I extract its meaning from among all possible things.
Strictly speaking, it is incorrect to say: We understand the proposition p when we know that ‚„p” is true’ = p; for this would naturally always be the case if accidentally the propositions to right and left of the symbol „=” were both true or both false. We require not only an equivalence, but a formal equivalence, which is bound up with the introduction of the form of p.
The sense of an ab-function of p is a function of the sense of p.
B18 The ab-functions use the discrimination of facts, which their arguments bring forth, in order to generate new discriminations.
Only facts can express sense, a class of names cannot. This is easily shown.
There is no thing which is the form of a proposition, and no name which is the name of a form. Accordingly we can also not say that a relation which in certain cases holds between things holds sometimes between forms and things. This goes against Russell's theory of judgment.
It is very easy to forget that, tho. the propositions of a form can be either true or false, each one of these propositions can only be either true or false, not both.
Among the facts which make „p or q” true, there are some which make „p and q” true; but the class which makes „p or q” true is different from the class which makes „p and q” true; and only this is what matters. For we introduce this class, as it were, when we introduce ab-functions.
A very natural objection to the way in which I have introduced e.g. propositions of the form xRy is that by it propositions such as (&Exist;x,y).xRy and similar ones are not explained, which yet obviously have in common with aRb what cRd has in common with aRb. But when we introduced propositions of the form xRy we mentioned no one particular proposition of this form; and we only need to introduce (&Exist;x,y).φ(x,y) for all φ's in any way which makes the sense of these propositions dependent on the sense of all propositions of the form φ(a,b), and thereby the justification of our procedure is proved.
B19 The indefinables of logic must be independent of each other. If an indefinable is introduced, it must be introduced in all combinations in which it can occur. We cannot therefore introduce it first for one combination, then for another; e.g., if the form xRy has been introduced, it must henceforth be understood in propositions of the form aRb just in the same way as in propositions such as (&Exist;x,y). xRy and others. We must not introduce it first for one class of cases, then for the other; for it would remain doubtful if its meaning was the same in both cases, and there would be no ground for using the same manner of combining symbols in both cases. In short, for the introduction of indefinable symbols and combinations of symbols the same holds, mutatis mutandis, that Frege has said for the introduction of symbols by definitions.
It is a priori likely that the introduction of atomic propositions is fundamental for the understanding of all other kinds of propositions. In fact the understanding of general propositions obviously depends on that of atomic propositions.
Cross-definability in the realm of general propositions leads to the quite similar questions to those in the realm of ab-functions.
B20 When we say „A believes p”, this sounds, it is true, as if here we could substitute a proper name for „p”; but we can see that here a sense, not a meaning, is concerned, if we say „A believes that ‚p’ is true”; and in order to make the direction of p even more explicit, we might say „A believes that ‚p’ is true and ‚not-p’ is false”. Here the bi-polarity of p is expressed, and it seems that we shall only be able to express the proposition „A believes p” correctly by the ab-notation; say by making „A” have a relation to the poles „a” and „b” of a-p-b.
The epistemological questions concerning the nature of judgment and belief cannot be solved without a correct apprehension of the form of the proposition.
The ab-notation shows the dependence of or and not, and thereby that they are not to be employed as simultaneous indefinables.
Not: „The complex sign ‚aRb’” says that a stands in the relation R to b; but that ‚a’ stands in a certain relation to ‚b’ says that aRb.
In philosophy there are no deductions: it is purely descriptive.
Philosophy gives no pictures of reality.
Philosophy can neither confirm nor confute scientific investigation.
B21 Philosophy consists of logic and metaphysics: logic is its basis.
Epistemology is the philosophy of psychology.
Distrust of grammar is the first requisite for philosophizing.
Propositions can never be indefinables, for they are always complex. That also words like „ambulo” are complex appears in the fact that their root with a different termination gives a different sense.
Only the doctrine of general indefinables permits us to understand the nature of functions. Neglect of this doctrine leads to an impenetrable thicket.
Philosophy is the doctrine of the logical form of scientific propositions (not only of primitive propositions).
The word „philosophy” ought always to designate something over or under, but not beside, the natural sciences.
Judgment, command and question all stand on the same level; but all have in common the propositional form, which does interests us.
The structure of the proposition must be recognized, the rest comes of itself. But ordinary language conceals the structure of the proposition: in it, relations look like predicates, predicates like names, etc.
Facts cannot be named.
B22 It is easy to suppose that „individual”, „particular”, „complex” etc. are primitive ideas of logic. Russell e.g. says „individual” and „matrix” are „primitive ideas”. This error presumably is to be explained by the fact that, by employment of variables instead of the generality-sign, it comes to seem as if logic dealt with things which have been deprived of all properties except thing-hood, and with propositions deprived of all properties except complexity. We forget that the indefinables of symbols [Urbilder von Zeichen] only occur under the generality-sign, never outside it.
Just as people used to struggle to bring all propositions into the subject-predicate form, so now it is natural to conceive every proposition as expressing a relation, which is just as incorrect. What is justified in this desire is fully satisfied by Russell's theory of manufactured relations.
One of the most natural attempts at solution consists in regarding „not-p” as „the opposite of p”, where then „opposite” would be the indefinable relation. But it is easy to see that every such attempt to replace the ab-functions by descriptions must fail.
B23 The false assumption that propositions are names leads us to believe that there must be logical objects: for the meanings of logical propositions will have to be such things.
A correct explanation of logical propositions must give them a unique position as against all other propositions.
No proposition can say anything about itself, because the symbol of the proposition cannot be contained in itself; this must be the basis of the theory of logical types.
Every proposition which says something indefinable about a thing is a subject-predicate proposition; every proposition which says something indefinable about two things expresses a dual relation between these things, and so on. Thus every proposition which contains only one name and one indefinable form is a subject-predicate proposition, and so on. An indefinable simple symbol can only be a name, and therefore we can know, by the symbol of an atomic proposition, whether it is a subject-predicate proposition.
B24 I. Bi-polarity of propositions: sense and meaning, truth and falsehood.
II. Analysis of atomic propositions: general indefinables, predicates, etc.
III. Analysis of molecular propositions: ab-functions.
IV. Analysis of general propositions.
V. Principles of symbolism: what symbolizes in a symbol. Facts for facts.
VI. Types.
B25
This is the symbol for
˜p v ˜q
B26
1 you for instance imagine every fact as a spatial complex.
2 This is quite arbitrary but if we such have fixed on which sides the poles have to stand we must of course stick to our convention. If for instance „apb” says p then bpa says nothing. (It does not say ˜p.) But a-apb-b is the same symbol as apb the ab function vanishes automatically for here the new poles are related to the same side of p as the old ones. The question is always: how are the new poles correlated to p compared with the way the old poles are correlated to p. | 8,525 | 38,312 | {"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} | 2.734375 | 3 | CC-MAIN-2024-18 | latest | en | 0.9493 |
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### In the Playground
##### Age 5 to 11 Challenge Level:
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
### Planning a School Trip
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You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.
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What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?
### Meaningful Statistics
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Statistics problems at primary level that may require resilience.
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Statistics problems for inquiring primary learners.
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### The Hair Colour Game
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### Helicopters
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Design and test a paper helicopter. What is the best design? | 518 | 2,435 | {"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} | 3.640625 | 4 | CC-MAIN-2019-30 | latest | en | 0.85933 |
https://cypherpunks.venona.com/date/1995/02/msg00041.html | 1,516,178,796,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886860.29/warc/CC-MAIN-20180117082758-20180117102758-00123.warc.gz | 642,988,498 | 3,549 | # Re: Lucky primes & omlets on my face...
```-----BEGIN PGP SIGNED MESSAGE-----
From: Nathan Zook <[email protected]>
> Recall: x^p = x mod p therefore, x^(p-1) = 1 mod p. So what we need is:
> (x^e)^d = x^ed = x^(p-1)*i+1 = x mod p.
This would only be true for prime p, but with RSA we are dealing with
composite moduli. What we want is ed=1 mod phi(n), where
phi(n)=(p-1)(q-1). (Actually you want to use (p-1)(q-1)/gcd((p-1),(q-1)).
I forget what that is called.)
Conceptually, I gather you are setting e = 0x10001, then finding its
multiplicative inverse d mod phi(n) (or mod p-1 in your example). Then
you are looking for other possible values for d. I am a little unclear
on what the interval would be between suitable values of d. I think it
would be phi(n)/gcd as above, or p-1 in your example, but I am not sure.
> Let's try this again.
>
> Let 2*x be the target number of bits in the modulous.
>
> Let n be a large random number with x+2 digits.
> Let n1 be the next multiple of 0x10001.
> Let t2 be n1 mod 8, t3 be n1 mod 9, t5 be n1 mod 25, t7 be n1 mod 49.
>
> Loop:
> For i = 2 to 7
> If n1 = 1 mod i and (n1-1)/i + 1 is not a multiple of {2,3,5,7}
> If (n1-1)/i + 1 is prime.
> {
> Let k = 0's in n1/0x10001.
> If k is in range, save and exit.
> }
> EndIf
> EndIf
> Next
> n1 += 0x10001;
> EndLoop
>
> Recall: x^p = x mod p therefore, x^(p-1) = 1 mod p. So what we need is:
> (x^e)^d = x^ed = x^(p-1)*i+1 = x mod p.
>
> ie: ed = (p-1)*i+1
> or: (ed - 1) / i + 1 = p
>
> Now 0x10001 inverts easily, it is just n1/0x10001. By keeping track of
> various quantities, we can eliminate all multiprecision divisions except
> for the original one needed to get n1 and the t's, and doing increments
I still don't follow this. Is k claimed to be d? Where do we verify
that ed=1 mod (p-1)? ed would be n1, right? When you said "If (n1-1)/i
+ 1 is prime" did you mean "is p"? I really don't think this whole thing
works.
Let me tell you what I tried. I inverted e to get a correct d. Then I
looked at different d's to find one with lots of 0's. This turned out
to be useless! The reasons is that PGP does not use d. It uses the
Chinese Remainder Theorem to do its exponentiation. The two
exponentiations it does use exponents d mod (p-1) and d mod (q-1).
Adding multiples of phi to d does not change these values (since it is
a multiple of both p-1 and q-1).
Now one thing you could do is to use in place of d mod (p-1),
(d mod (p-1)) + k*(p-1) where we choose k to minimize the sum of the number
of bits and the number of 1 bits in this expression. Unfortunately the
PGP data structures do not store d mod (p-1), it is constructed on the
fly when you do a decryption. So there is no where to save a
pre-computed optimal value for the two exponents used in the CRT
exponentiations. So, this was a good idea, but the implementation does
not fit into the current structure very well.
Hal
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=EHVe
-----END PGP SIGNATURE-----
``` | 1,102 | 3,164 | {"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} | 3.921875 | 4 | CC-MAIN-2018-05 | latest | en | 0.861034 |
https://www.enotes.com/homework-help/please-use-integration-find-center-mass-rectangle-455327 | 1,685,913,897,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224650264.9/warc/CC-MAIN-20230604193207-20230604223207-00319.warc.gz | 831,044,721 | 17,640 | Find the center of mass of the rectangle `(1,-3)(4,-3)(4,5)(1,5)`
Expert Answers
The center of mass of the rectangle with vertexes (1, -3), (4, -3), (4, 5) and (1, 5) has to be determined. Assuming the material that the rectangle is made of has a uniform density, the center of mass of the rectangle lies at the intersection of its diagonals.
This is the intersection of the liens between (1, -3) and (4, 5) and between (4, -3) and (1, 5)
The line between (1, -3) and (4, 5) is (y +3)/(x - 1) = (8/3)
=> 3y + 9 = 8x - 8
=> y = (8x -17)/3
The line between (4, -3) and (1, 5) is (y +3)/(x - 4) = (8/-3)
=> -3y - 9 = 8x - 32
=> y = (8x - 23)/(-3)
(8x -17)/3 = (8x - 23)/(-3)
=> 8x - 17 = 23 - 8x
=> 16x = 40
=> x = 2.5
y = 1
The center of mass is (2.5, 1)
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Approved by eNotes Editorial Team | 371 | 976 | {"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} | 4.09375 | 4 | CC-MAIN-2023-23 | latest | en | 0.934348 |
https://beta.mapleprimes.com/products/Maple?page=1855 | 1,653,415,466,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662573189.78/warc/CC-MAIN-20220524173011-20220524203011-00353.warc.gz | 173,412,798 | 27,495 | ## How to solve this problem with Maple...
I need help to solve this problem in maple. :) "Use as many columns of matrix A as possible to construct a matrix B, with the property that the equation Bx=0 has only the trivial solution. Solve Bx=0 to verify you work.." Martix A: A:=matrix([[8,-3,0,-7,2],[-9,4,5,11,-7],[6,-2,2,-4,4],[5,-1.7.0.10]]);
## Plotting during procedure execution...
I was using a procedure for linear systems solution (Gauss-Seidel) and in way to obtain information about the solution convergence I would like to obtain a graph during the procedure execution by Maple that may be ploted in a Maplet window. Does anyone have some suggestion on as I can make this? I am very grateful to anyone who may help.
solve({a1*alpha+b1 *beta=a1^2*alpha+2*a1*a2*gamma+a2^2*gamma*delta/beta,a2*alpha+b2* beta=a1^2*beta+2*a1*a2*delta+a2^2* (beta*gamma-delta*(alpha-delta))/beta, a1*gamma+b1*delta=a1*b1*alpha+a1*b2*gamma+a2*b1*gamma+a2 *b2*gamma*delta/beta,a2*gamma+b2*delta=a1*b1*beta+a1*b2* delta+a2*b1*delta+a2*b2*(beta*gamma-delta*(alpha-delta))/ beta, a1*gamma*delta/beta+b1*(beta*gamma-delta*(alpha-delta))/ beta=b1^2*alpha+2*b1*b2*gamma+b2^2*gamma*delta/beta,a2* gamma*delta/beta+b2*(beta*gamma-delta*(alpha-delta))/ beta=b1^2*beta+2*b1*b2*delta+b2^2*(beta*gamma-delta*( alpha-delta))/beta},{a1,a2,b1,b2}); Warning, computation interrupted
## Old-timer techniques
by: Maple
So you think you really want to know what Maple does? Are you really sure? Well, here is how old-timers do it. [I do not claim that this is either the best or the modern way to do it, just that this is how people with over 10 years of Maple experience do it].
## How to solve this integral?...
I know these two integrals: int(sin(x)/x,x=0..infinity)=Pi/2 and int((sin(x)/x)^2,x=0..infinity)=Pi/2, so I want to know the answer to this integral int((sin(x)/x)^n,x=0..infinity), here n is a positive integer. Only assume(n>0) and additionally(n, integer) and then enter the above statement, Maple could not give an answer. Then I want to know whether there is an exact symbolic result of the integral and if so, how can I get it in Maple. 3x...
## Cross Product Symbol...
I have a question regarding a symbol for cross product. I just uploaded the file referenced at the bottom of this post, and when I viewed it in the file manager it looks different enought from the original file that anyone kind enought to help me will have to download the file. thanks View 2292_CrossProductSymbol.mw on MapleNet or Download 2292_CrossProductSymbol.mw
## Optimize coefficients in a polynomial...
Does anyone have a good idea on how to do this? I have two polynomials alpha := x -> sum('a[k]*x^k','k'=0..N); and beta := x -> sum('b[k]*x^k','k'=0..N);. where N is some constant. I then create a third polynomial g := x -> beta(alpha(x))^2; Then I integrate g(x) from some point to an other point, say -1 to 2: d_tot := int(g(x), x=-1..2); The result is now a 'polynomial' of the indexes a[i] and b[i] from alpha and beta. So far so good but here I'm stuck. Next I would like to choose the indexes a[i] and b[i] for all i=0..N in order to minimize d_tot. Therefore I want Maple to see the a[i]'s and b[i]'s as variables and not coefficients so I can do some manipulations (for instance try minimize(d_tot)).
## To contain Momentum in the Kinetic Energy express...
I am currently working on kinetics area. We have for Kinetic Energy KE = 1/2*m*v^2 and for momentum P= m*v. I need to check for the presence of 'm*v' term in the kinetic Energy expression and want to express Kinetic energy in terms of momentum. That is KE= 1/2*m*v^2 should be expressed as 1/2*P*v after checking for the presence of m*v. The momentum expression should be contained in the formula foe Kinetic energy. Anyone please help me on this Siva
## fsolve...
I am trying to numerically solve the equation (1+j/365)^365=1.1 using command: fsolve((1+j/365)^365=1.1,j); or fsolve((1+j/365)^365=1.1,j,0...1); both cause Maple a lot of problems...cycling. I lost patience. Anyone know how to get the answer?
## output from dsolve...
I have used the dsolve feature and solved a normal ODE. The problem ariss from evaluating that result for different y(x) values. I get the y(x) attached to some message regarding a table. The ODE was y'=-400t*y(t). After solving the diff eq, I evaluated y(t) at t=0 and I got a nice answer, which I defined as t[0]. A few lines later I attempted to use t[0] in a simple subtraction step but got 19.7table[....]... where 19.7 was the correct answer but the subsequent phrase table referred to earlier y(t) evaluation. So, even though t[0] gives a nice answer it can't be used for any calculations. How do I rectify this problem?
## String vibration HELP!...
Hi, Again I'm hearing voices! I have beat myself to death and have found the end of the internet in my search for help on the solutions to String deflection problems: I need to find u(x,t) for the following: Initial velocity = 0, a small k = 0.01, L=1 c^2 = 1 Problem 1 k*(sin(2*Pi*x) ; #Problem 2 k*(sin(Pi*x)-1/3*sin(Pi*3*x)); The second problem is a homework problem. The first is a problem I want to do to see how this works, but I can't grasp the idea. The problems are from the 9th Ed of Kreyszig AEM. (Great for proofs, short on examples)
## Help Understanding Maple Program...
I'm working through an example program. It seems to be working correctly. However, I would like to know why this procedure produces a Maplet ? Any other insight into this procedure you can provide would also be helpful. thanks, View 285_dicegame.mw on MapleNet or Download 285_dicegame.mw
View file details | 1,601 | 5,641 | {"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} | 3.34375 | 3 | CC-MAIN-2022-21 | latest | en | 0.821493 |
https://www.dataunitconverter.com/kilobit-per-second-to-yobibyte-per-minute | 1,716,985,945,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059239.72/warc/CC-MAIN-20240529103929-20240529133929-00061.warc.gz | 615,040,534 | 17,238 | # kbps to YiB/Min → CONVERT Kilobits per Second to Yobibytes per Minute
expand_more
info 1 kbps is equal to 0.000000000000000000006203854594147707558 YiB/Min
S = Second, M = Minute, H = Hour, D = Day
Sec
Min
Hr
Day
Sec
Min
Hr
Day
## Kilobits per Second (kbps) Versus Yobibytes per Minute (YiB/Min) - Comparison
Kilobits per Second and Yobibytes per Minute are units of digital information used to measure storage capacity and data transfer rate.
Kilobits per Second is a "decimal" unit where as Yobibytes per Minute is a "binary" unit. One Kilobit is equal to 1000 bits. One Yobibyte is equal to 1024^8 bytes. There are 9,671,406,556,917,033,397,649.408 Kilobit in one Yobibyte. Find more details on below table.
Kilobits per Second (kbps) Yobibytes per Minute (YiB/Min)
Kilobits per Second (kbps) is a unit of measurement for data transfer bandwidth. It measures the number of Kilobits that can be transferred in one Second. Yobibytes per Minute (YiB/Min) is a unit of measurement for data transfer bandwidth. It measures the number of Yobibytes that can be transferred in one Minute.
## Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min) Conversion - Formula & Steps
The kbps to YiB/Min Calculator Tool provides a convenient solution for effortlessly converting data rates from Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min). Let's delve into a thorough analysis of the formula and steps involved.
Outlined below is a comprehensive overview of the key attributes associated with both the source (Kilobit) and target (Yobibyte) data units.
Source Data Unit Target Data Unit
Equal to 1000 bits
(Decimal Unit)
Equal to 1024^8 bytes
(Binary Unit)
The conversion from Data per Second to Minute can be calculated as below.
x 60
x 60
x 24
Data
per
Second
Data
per
Minute
Data
per
Hour
Data
per
Day
÷ 60
÷ 60
÷ 24
The formula for converting the Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min) can be expressed as follows:
diamond CONVERSION FORMULA YiB/Min = kbps x 1000 ÷ (8x10248) x 60
Now, let's apply the aforementioned formula and explore the manual conversion process from Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min). To streamline the calculation further, we can simplify the formula for added convenience.
FORMULA
Yobibytes per Minute = Kilobits per Second x 1000 ÷ (8x10248) x 60
STEP 1
Yobibytes per Minute = Kilobits per Second x 1000 ÷ (8x1024x1024x1024x1024x1024x1024x1024x1024) x 60
STEP 2
Yobibytes per Minute = Kilobits per Second x 1000 ÷ 9671406556917033397649408 x 60
STEP 3
Yobibytes per Minute = Kilobits per Second x 0.0000000000000000000001033975765691284593 x 60
STEP 4
Yobibytes per Minute = Kilobits per Second x 0.000000000000000000006203854594147707558
Example : By applying the previously mentioned formula and steps, the conversion from 1 Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min) can be processed as outlined below.
1. = 1 x 1000 ÷ (8x10248) x 60
2. = 1 x 1000 ÷ (8x1024x1024x1024x1024x1024x1024x1024x1024) x 60
3. = 1 x 1000 ÷ 9671406556917033397649408 x 60
4. = 1 x 0.0000000000000000000001033975765691284593 x 60
5. = 1 x 0.000000000000000000006203854594147707558
6. = 0.000000000000000000006203854594147707558
7. i.e. 1 kbps is equal to 0.000000000000000000006203854594147707558 YiB/Min.
Note : Result rounded off to 40 decimal positions.
You can employ the formula and steps mentioned above to convert Kilobits per Second to Yobibytes per Minute using any of the programming language such as Java, Python, or Powershell.
### Unit Definitions
#### What is Kilobit ?
A Kilobit (kb or kbit) is a decimal unit of digital information that is equal to 1000 bits. It is commonly used to express data transfer speeds, such as the speed of an internet connection and to measure the size of a file. In the context of data storage and memory, the binary-based unit of Kibibit (Kibit) is used instead.
arrow_downward
#### What is Yobibyte ?
A Yobibyte (YiB) is a binary unit of digital information that is equal to 1,208,925,819,614,629,174,706,176 bytes (or 9,671,406,556,917,033,397,649,408 bits) and is defined by the International Electro technical Commission(IEC). The prefix 'yibi' is derived from the binary number system and it is used to distinguish it from the decimal-based 'yottabyte' (YB). It is widely used in the field of computing as it more accurately represents the storage size of high end servers and data storage arrays.
## Excel Formula to convert from Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min)
Apply the formula as shown below to convert from 1 Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min).
A B C
1 Kilobits per Second (kbps) Yobibytes per Minute (YiB/Min)
2 1 =A2 * 0.0000000000000000000001033975765691284593 * 60
3
If you want to perform bulk conversion locally in your system, then download and make use of above Excel template.
## Python Code for Kilobits per Second (kbps) to Yobibytes per Minute (YiB/Min) Conversion
You can use below code to convert any value in Kilobits per Second (kbps) to Kilobits per Second (kbps) in Python.
kilobitsperSecond = int(input("Enter Kilobits per Second: "))
yobibytesperMinute = kilobitsperSecond * 1000 / (8*1024*1024*1024*1024*1024*1024*1024*1024) * 60
print("{} Kilobits per Second = {} Yobibytes per Minute".format(kilobitsperSecond,yobibytesperMinute))
The first line of code will prompt the user to enter the Kilobits per Second (kbps) as an input. The value of Yobibytes per Minute (YiB/Min) is calculated on the next line, and the code in third line will display the result.
## Frequently Asked Questions - FAQs
#### How many Yobibytes(YiB) are there in a Kilobit(kbit)?expand_more
There are 0.0000000000000000000001033975765691284593 Yobibytes in a Kilobit.
#### What is the formula to convert Kilobit(kbit) to Yobibyte(YiB)?expand_more
Use the formula YiB = kbit x 1000 / (8x10248) to convert Kilobit to Yobibyte.
#### How many Kilobits(kbit) are there in a Yobibyte(YiB)?expand_more
There are 9671406556917033397649.408 Kilobits in a Yobibyte.
#### What is the formula to convert Yobibyte(YiB) to Kilobit(kbit)?expand_more
Use the formula kbit = YiB x (8x10248) / 1000 to convert Yobibyte to Kilobit.
#### Which is bigger, Yobibyte(YiB) or Kilobit(kbit)?expand_more
Yobibyte is bigger than Kilobit. One Yobibyte contains 9671406556917033397649.408 Kilobits.
## Similar Conversions & Calculators
All below conversions basically referring to the same calculation. | 2,053 | 6,518 | {"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} | 2.921875 | 3 | CC-MAIN-2024-22 | latest | en | 0.761293 |
https://www.coursehero.com/tutors-problems/Finance/8228945-ABCs-current-capital-structure-of-60-percent-equity-30-percent-debt/ | 1,548,290,218,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547584431529.98/warc/CC-MAIN-20190123234228-20190124020228-00171.warc.gz | 741,664,767 | 21,511 | View the step-by-step solution to:
# ABC's current capital structure of 60 percent equity, 30 percent debt, and 10 percent preferred stock is considered optimal.
ABC's current capital structure of 60 percent equity, 30 percent debt,
and 10 percent preferred stock is considered optimal. This year ABC expects
to have earnings after tax of \$4 million and pay dividends based on its 40%
dividend pay-out ratio.
ABC just paid a dividend of \$2.00. Dividends have been growing at an annual
compound rate of 7 percent a year and are expected to continue growing at
that rate. The current market price of ABC stock is \$35 and up to \$2 million
in new equity can be raised for a flotation cost of 10 percent. If more than
\$2 million is sold then the flotation cost will be 15 percent.
Up to \$2 million in debt can be sold at par with a coupon rate of 10
percent. An additional \$3 million in debt can be sold at par with a coupon
rate of 11%. Any additional debt will carry a 12 percent coupon rate and be
sold at par.
ABC can sell an unlimited amount of preferred stock at a pre-tax cost of
11.5%.
ABC’s marginal tax rate is 40% and it has an opportunity to invest in the
following capital projects. Which one(s) should be accepted? What is ABC’s
optimal capital budget? (Please draw MCC and IOS curves when answering this
question.)
Project \$ IRR
A 2,000,000 0.135
B 2,500,000 0.125
C 1,500,000 0.12
D 1,250,000 0.115
E 1,000,000 0.11
F 750,000 0.105
G 500,000 0.1
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http://research.stlouisfed.org/fred2/series/A640RZ2Q224SBEA?rid=53 | 1,430,867,266,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1430457008123.23/warc/CC-MAIN-20150501051008-00041-ip-10-235-10-82.ec2.internal.warc.gz | 165,394,548 | 20,031 | # Contributions to percent change in real exports of goods: Capital goods, except automotive
2015:Q1: -3.02 Percentage Points at Annual Rate (+ see more)
Quarterly, Seasonally Adjusted Annual Rate, A640RZ2Q224SBEA, Updated: 2015-04-29 9:19 AM CDT
Click and drag in the plot area or select dates: Select date: 1yr | 5yr | 10yr | Max to
BEA Account Code: A640RZ2
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(a) Contributions to percent change in real exports of goods: Capital goods, except automotive, Percentage Points at Annual Rate, Seasonally Adjusted Annual Rate (A640RZ2Q224SBEA)
BEA Account Code: A640RZ2
Contributions to percent change in real exports of goods: Capital goods, except automotive
Integer Period Range: to copy to all
Create your own data transformation: [+]
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Use a formula to modify and combine data series into a single line. For example, invert an exchange rate a by using formula 1/a, or calculate the spread between 2 interest rates a and b by using formula a - b.
Use the assigned data series variables above (e.g. a, b, ...) together with operators {+, -, *, /, ^}, braces {(,)}, and constants {e.g. 2, 1.5} to create your own formula {e.g. 1/a, a-b, (a+b)/2, (a/(a+b+c))*100}. The default formula 'a' displays only the first data series added to this line. You may also add data series to this line before entering a formula.
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``` US. Bureau of Economic Analysis, Contributions to percent change in real exports of goods: Capital goods, except automotive [A640RZ2Q224SBEA], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/A640RZ2Q224SBEA/, May 5, 2015. ```
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https://www.safaribooksonline.com/library/view/digital-logic-design/9781107027534/chap3.xhtml | 1,521,381,999,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257645775.16/warc/CC-MAIN-20180318130245-20180318150245-00042.warc.gz | 851,020,999 | 15,966 | ## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.
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CHAPTER 3 Sequences and Series
In this chapter, we consider three important types of sequences: arithmetic sequences, geometric sequences, and the harmonic sequence. In an arithmetic sequence, the difference between consecutive elements is constant. In a geometric sequence, the ratio between consecutive elements is constant. The harmonic sequence is simply the sequence (1, , , … ).
Given a sequence (x0, x1, … ), we may wish to define a new sequence that consists of the partial sums
The sequence (y0, y1, … ) of partial sums is a series.
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https://orderyourpaper.com/bus5110-managerial-accounting-accounting-homework-help/ | 1,669,625,597,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710488.2/warc/CC-MAIN-20221128070816-20221128100816-00436.warc.gz | 486,528,927 | 14,335 | # Bus5110 – managerial accounting | Accounting homework help
A manufacturing company is evaluating two options for new equipment to introduce a new product to its suite of goods. The details for each option are provided below:
Option 1
· \$65,000 for equipment with useful life of 7 years and no salvage value.
· Maintenance costs are expected to be \$2,700 per year and increase by 3% in Year 6 and remain at that rate.
· Materials in Year 1 are estimated to be \$15,000 but remain constant at \$10,000 per year for the remaining years.
· Labor is estimated to start at \$70,000 in Year 1, increasing by 3% each year after.
Revenues are estimated to be:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
75,000
100,000
125,000
150,000
150,000
150,000
Option 2
· \$85,000 for equipment with useful life of 7 years and a \$13,000 salvage value
· Maintenance costs are expected to be \$3,500 per year and increase by 3% in Year 6 and remain at that rate.
· Materials in Year 1 are estimated to be \$20,000 but remain constant at \$15,000 per year for the remaining years.
· Labor is estimated to start at \$60,000 in Year 1, increasing by 3% each year after.
Revenues are estimated to be:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
80,000
95,000
130,000
140,000
150,000
160,000
The company’s required rate of return is 8%.
Management has turned to its finance and accounting department to perform analyses and make a recommendation on which option to choose. They have requested that the four main capital budgeting calculations be done: NPV, IRR, Payback Period, and ARR for each option.
For this assignment, compute all required amounts and explain how the computations were performed. Evaluate the results for each option and explain what the results mean. Based on your analysis, recommend which option the company should pursue.
Superior papers will:
· Perform all calculations correctly.
· Articulate how the calculations were performed, including from where values used in the calculations were obtained.
· Evaluate the results computed and explain the meaning of the results, including why certain measurements are more accurate than others.
· Recommend which option to pursue, supported by well-thought-out rationale, and considering any other factors that could impact the recommendation.
Be sure to use APA formatting in your paper. Purdue University’s Online Writing Lab (OWL) is a free website that provides excellent information and resources for understanding and using the APA format and style. The OWL website can be accessed here: https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_style_introduction.html
This assignment will be assessed using the BUS 5110 Unit 6 Written Assignment rubric. | 656 | 2,774 | {"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-2022-49 | latest | en | 0.929529 |
https://recetaseco.com/how-many-cubic-inches-is-a-5-liter-engine/ | 1,656,340,420,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103334753.21/warc/CC-MAIN-20220627134424-20220627164424-00330.warc.gz | 539,950,703 | 15,441 | # How Many Cubic Inches Is A 5 Liter Engine?
Engine Size ChartLiters (L)Cubic Centimeters (CC)Cubic Inches (cid)5.04,9833045.04,9993055.05,0323075.25,212318
## How many cubic inches does it take to make a liter?
For conversions reference, 1 Liter = 61.02 cubic inches (C.I.D.).
## How many liters are there in 1 cubic?
1 cubic meter is 1000 liters.
## Is 1 liter or 1 cubic meter bigger?
Cubic meters (m3) and liters (L) are two metric units of volume. A cubic meter is a much larger unit than a liter. One cubic meter is 1000 liters!
## What liter is a 454?
For many years the 454 (7.4-liter) V8 was the top choice from GM, while Ford had the mighty 460 (7.5-liter) V8.
## Is a 6.2 A big block?
The 6.2L engine could be described as a 6.2L big-block modular. Most big-block engines have more than 400 cubic inches of displacement and they weigh more. And the small-block engines have a smaller displacement. The 6.2L engine, though, fits into a 4.02-inch bore.
## How do you convert engine displacement?
Engine displacement is determined by calculating the engine cylinder bore area multiplied by the stroke of the crankshaft, and then multiplied by the number of cylinders. This will result in the overall volume of air displaced by the engine.
## How do you calculate cubic inches?
To calculate a volume in cubic inches, start by taking measurements of the length, width, and height. When measuring, find the length, width, and height in inches. Then, multiply the dimensions of each side together to find the volume in cubic inches.
## How many square inches are in a liter?
Liter to Square inch Calculator
1 liter = 15.5 in2 0.0164 liter
2 liter = 24.6048 in2 0.0463 liter
3 liter = 32.2414 in2 0.0851 liter
4 liter = 39.0576 in2 0.1311 liter
5 liter = 45.3224 in2 0.1832 liter
## How do you calculate litter?
Dividing the volume (in cubic centimeters) of the shape by 1,000 will give you the volume in liters (L). . So, a fish tank that is 40.64 cm long, 25.4 cm wide, and 20.32 tall has a volume of 20.975 L.
## How do you measure soil in litres?
For example the planter has a diameter of 30 centimetres and it is 26 centimetres high, then the calculation is as follows: 30 x 30 x 26 cm / 1800 = 13 litres. In short, you multiply the diameter by the diameter and then you multiply this by the height. You then divide this by 1800.
## How many liters are in a mole?
Molar volume at STP can be used to convert from moles to gas volume and from gas volume to moles. The equality of 1mol=22.4L is the basis for the conversion factor. Many metals react with acids to produce hydrogen gas.
## What does m3 mean in math?
more A volume that is made by a cube that is 1 meter on each side. Its symbol is m3. It is equal to 1000 (one thousand) liters.
## How many litres is a square meter of water?
A cubic metre equals 1,000 litres of water.
## Is cm3 same as L?
A liter is a unit of volume equal to 1,000 cubic centimeters.
## What car came with a 572?
For 2022, the COPO Camaro is available with a gigantic 572-cubic-inch (9.4-liter) big-block V-8, which Chevy says “channels the spirit of the original 1969 COPO Camaro.” Chevy didn’t reveal horsepower figures for the 572, but said that it uses a cast-iron block with aluminum heads, a forged steel crankshaft and
## What liter is a 572 big-block?
Chevrolet said it had a big announcement planned for today and now we know what it meant by “big.” The 2022 edition of the COPO Camaro, a non-street-legal car exclusively designed for drag racing, will be available with a 9.4-litre big-block V8 engine. That’s 572 cubic inches if you prefer U.S. measurements.
## What is a 632 engine?
The ZZ632/1000 is a 632-cubic-inch V-8 delivering 1,004 horsepower. 2021-10-20. DETROIT – Chevrolet Performance today introduced the ZZ632/1000* crate engine — the largest and most powerful crate engine in the brand’s history. The naturally aspirated 632-cubic-inch V-8 produces 1,004 horsepower and 876 lb-ft of torque.
## What does LS stand for?
In a car engine, LS stands for luxury sport, meaning it is majorly used in high-end cars that offer great performance like the Chevrolet. In a Chevy, the LS engine is the main V8 mainly used in General Motors’ line of rear-wheel-drive cars.
## What is an LS9 engine?
Being one of a handful of GM engines assembled by hand, the LS9 is part of GM’s fourth-generation V8 Small Block engine family and is notorious for being the automaker’s most powerful production engine. It was produced for the sixth-generation Corvette ZR1 — the flagship of the Corvette lineup. 6.2L LS9 Engine Vitals.
## Is a Chevy 5.3 a LS engine?
The cheapest of the LS engine family is the 5.3L truck engine since it came in most of the trucks and SUVs that Chevrolet has produced.
## How many liters is a 632 big block?
10.35 liters
WORLD PRODUCTS MERLIN 632 SPECIFICATIONS
Engine Type OHV V-8; iron block (four-bolt main caps) with aluminum heads
Displacement 632 cubic inches (10.35 liters)
Bore x Stroke (inches) 4.600 x 4.750
Compression Ratio 10.4:1
## What is a Chevy 6.0 in cubic inches?
The Chevy 6.0 engine is a 364.4 cubic inch 6.0L with a bore and stroke of 4 x 3.625. It’s a V8 that comes in cast iron or aluminum depending on make and model and has been rated at around 341 horsepower.
## What is the horsepower of a 6.2 liter Chevy engine?
The 6.2 liter LS3 V8 engine is currently produced by Chevrolet Performance as a crate engine, offering a peak output of 430 horsepower at 5900 RPM. Between 2007 and 2017, the LS3 was used in high-performance vehicles, such as the Camaro and Corvette, among others.
## How do you calculate volume of a tank?
The formula of volume of the rectangular tank is given as, V = l × b × h where “l” is the length of the base, “b” is the breadth of the base, “h” is the height of the tank and “V” is the volume of the rectangular tank.
## How do you calculate volume of water?
Multiply length (L) by width (W) to get area (A). Multiply area by height (H) to get volume (V). Multiply volume by 7.48 gallons per cubic foot to get capacity (C).
## How do you calculate cubic volume?
To find the volume of a box, simply multiply length, width, and height — and you’re good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters.
## How do you calculate tank capacity in litres?
2) calculate volume of rectangular water tank multiply Length, breadth and their height, as Volume = 2m × 1m × 0.5m = 1m3, 3) you get volume of water rectangular tank it can hold 1 cubic metre, multiply the answer by 1000 as 1×1000= 1000 liters, the result 1000 is rectangular water tank capacity in liters.
## What is L * W * H?
Length x Width x Height. (LxWxH)
## How do I calculate how much soil I need?
To estimate soil volume for any area, all you need is a tape measure. “The basic formula is simple: Length x Width x Height = Volume,” says Michael Dean, co-founder of Pool Research. Then divide the number of cubic feet by 27. So one cubic yard = 27 cubic feet = 1,728 cubic inches.
## How do I calculate how much dirt I need?
Length in feet x Width in feet x Depth in feet (inches divided by 12). Take the total and divide by 27 (the amount of cubic feet in a yard). The final figure will be the estimated amount of cubic yards required.
## How do you calculate potting mix?
• rectangular – e.g. raised bed soil containers. volume of rectangular cuboid: volume = depth * length * width.
• round. volume of a cylinder: volume = π * R² * depth , where R is a radius.
• flower pot in the shape of truncated cone.
## How many moles is 1l of water?
The density of water is 1g/cc, so if you do dimensional analysis, you can find that in 1 L of water, there is 55.56 mol.
## What does m3 mean in water?
The water meter records how much water you use in cubic metres (m3). One cubic metre equals 1000 litres – that’s enough for either 13 baths, 14 washing machine loads, 28 showers, 33 dishwasher loads or 111 toilet flushes!
## What does 5 m3 look like?
What that means is that five cubic meters of volume are a cuboid that is (in the case on the picture) one meter wide, two meters tall and two and a half meters long. 5 cubic meters equal precisely 176 cubic feet.
## What is m3 gas?
Cubic Meter or m3 (Volumetric Quantity Of Natural Gas)
Cubic meters are a unit of volume. 1 m3 of natural gas is equal to: 35.315 cubic feet of natural gas. 35,300 BTU.
## How many litres of water are in 1 cubic meter of concrete?
Typically, 1m3 of concrete is made up of 350Kg of cement, 700Kg of sand, 1,200Kg of chippings and 150 Litres of water.
## How many liters of water are in a square foot?
Therefore, one cubic foot is equal to 28.317 liters of volume. | 2,350 | 8,736 | {"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} | 3.609375 | 4 | CC-MAIN-2022-27 | latest | en | 0.863992 |
https://studylib.net/doc/6856675/phys-212biot | 1,657,091,558,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104668059.88/warc/CC-MAIN-20220706060502-20220706090502-00717.warc.gz | 591,170,621 | 11,946 | # PHYS 212Biot
```PHYS 212
Ch-29: Biot-Savart Law
Practice for Test
A current-length element i
produces a differential magnetic field
the page there. Its value is given by Biot-Savart law as follows:
at point P, directed into
Show that the magnetic field at C due to a circular arc of wire is given by the following equation.
1. (P8) In Fig. 29-39, two semicircular arcs have radii R2 = 7.80 cm and R1 = 3.15 cm, carry current i =
0.281 A, and share the same center of curvature C. What are the (a) magnitude and (b) direction
(into or out of the page) of the net magnetic field at C?
2. (P 64) In Fig. 29-76, a closed loop carries current i = 200 mA. The loop consists of two radial
straight wires and two concentric circular arcs of radii 2.00 m and 4.00 m. The angle θ is π/4 rad.
What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at
the center of curvature P?
``` | 274 | 915 | {"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} | 3.25 | 3 | CC-MAIN-2022-27 | latest | en | 0.894625 |
https://solve-variable.com/solve-variable/logarithms/least-common-multiple-of.html | 1,680,167,710,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949107.48/warc/CC-MAIN-20230330070451-20230330100451-00677.warc.gz | 604,168,704 | 11,643 | Free Algebra Tutorials!
Try the Free Math Solver or Scroll down to Tutorials!
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Author Message
Roiman
Registered: 30.05.2006
From: Weert, Limburg, The Netherlands
Posted: Saturday 30th of Dec 09:05 Hello math wizards, I need some urgent help. I have a set of math problems that I need to solve and I am hopelessly lost. I don’t know where to begin or how to go about and this paper is due next week. Kindly let me know if you are good in angle complements or if there is a good site which can assist me.
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Mibxrus
Registered: 19.10.2002 | 702 | 2,609 | {"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} | 2.609375 | 3 | CC-MAIN-2023-14 | latest | en | 0.89131 |
https://gmatclub.com/forum/antarctica-receives-more-solar-radiation-than-does-any-other-74602.html?fl=similar | 1,495,767,243,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608622.82/warc/CC-MAIN-20170526013116-20170526033116-00113.warc.gz | 751,149,164 | 47,737 | Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
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07 Jan 2009, 22:16
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Antarctica receives more solar radiation than does any other place on Earth, yet the temperatures are so cold and the ice cap is reflective, so that little polar ice melts during the summer; otherwise, the water levels of the oceans would rise 250 feet and engulf most of the world's great cities.
A. is reflective, so that little polar ice melts during the summer; otherwise,
B. is so reflective that little of the polar ice melts during the summer; were it not to do so,
C. so reflective that little polar ice melts during the summer, or else
D. reflective, so that little of the polar ice melts during the summer, or
E. reflects so that little of the polar ice melts during the summer; if it did
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07 Jan 2009, 23:09
keeping parallelism:
"..temperatures are so cold.." ==> ice is so.. ==> B
Also, the phrase "little ice" sounds improper and thus A and C are eliminated. D, E are eliminated for not being parallel
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08 Jan 2009, 18:05
What s wrong with C ? Anyway , what does "it" refer to in B ?
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08 Jan 2009, 21:27
Antarctica receives more solar radiation than does any other place on Earth, yet the temperatures are so cold and the ice cap is reflective, so that little polar ice melts during the summer; otherwise, the water levels of the oceans would rise 250 feet and engulf most of the world's great cities.
A. is reflective, so that little polar ice melts during the summer; otherwise,
B. is so reflective that little of the polar ice melts during the summer; were it not to do so,
C. so reflective that little polar ice melts during the summer, or else
D. reflective, so that little of the polar ice melts during the summer, or
E. reflects so that little of the polar ice melts during the summer; if it did
A: needs "so" to make parallel.
B: correct "is + so"
C: "is" is missing.
D: main verb "is" missing.
E: main verb "is" missing.
so B.
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10 Jan 2009, 14:33
OA is B
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10 Jan 2009, 14:38
richardLee wrote:
What s wrong with C ? Anyway , what does "it" refer to in B ?
"the ice cap so reflective"
is not correct
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10 Jan 2009, 16:46
B is most appropriate.
Would the level of this question be <500 or 500-600 or 600-700?
Antarctica receives more solar radiation than does any other place on Earth, yet the temperatures are so cold and the ice cap is reflective, so that little polar ice melts during the summer; otherwise, the water levels of the oceans would rise 250 feet and engulf most of the world's great cities.
A. is reflective, so that little polar ice melts during the summer; otherwise,
B. is so reflective that little of the polar ice melts during the summer; were it not to do so,
C. so reflective that little polar ice melts during the summer, or else
D. reflective, so that little of the polar ice melts during the summer, or
E. reflects so that little of the polar ice melts during the summer; if it did
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tusharvk
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06 May 2009, 12:33
why in B, "were it not to do so" has to be in reverse order?
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16 Sep 2009, 13:55
I have a serious problem with B. "Were it not to do" what? Melt? Be white and reflective? What does "it" refer to? Antartica? The ice caps. Can someone vouch the source of this question?
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16 Nov 2009, 04:20
mendelay wrote:
I have a serious problem with B. "Were it not to do" what? Melt? Be white and reflective? What does "it" refer to? Antartica? The ice caps. Can someone vouch the source of this question?
"Were it not to do so" is actually introducing a hypothetical situation, which is apt in this situation.
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16 Nov 2009, 10:14
tusharvk wrote:
B is most appropriate.
Would the level of this question be <500 or 500-600 or 600-700?
Antarctica receives more solar radiation than does any other place on Earth, yet the temperatures are so cold and the ice cap is reflective, so that little polar ice melts during the summer; otherwise, the water levels of the oceans would rise 250 feet and engulf most of the world's great cities.
A. is reflective, so that little polar ice melts during the summer; otherwise,
B. is so reflective that little of the polar ice melts during the summer; were it not to do so,
C. so reflective that little polar ice melts during the summer, or else
D. reflective, so that little of the polar ice melts during the summer, or
E. reflects so that little of the polar ice melts during the summer; if it did
My guess is 500-600. As long as you are familiar with the idiom "so X that" it is very straightforward.
Re: Antarctica [#permalink] 16 Nov 2009, 10:14
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Author: Glenn Clemens
Subject: A2/Trig #29
Can someone with a statistics background help me out with question 29 (82video game players, ages normally distributed with mean 17 and std d 3; werethere 15 players over the age of 20?). Yes, in an ideal normal distribution (which I don't think you'll see with 82data points), 15.9% of the scores should be more than 1 sigma above themean. But in a sample from a normal, doesn't this become an expected value?In the given problem, we would EXPECT about 13 players to be 20 years orolder, but there could be more or there could be fewer. Assume the 82 players were randomly sampled from a larger population whoseages are normally distributed with the given mean and std d. If I use abinomial distribution with n = 82 and p = 0.159, I get a 9.6% chance thatthere will be exactly 15 players over the age of 20 and a 32% chance thatthere will be 15 or more players over the age of 20. What then is theappropriate answer to "Determine if there were 15 players in this study overthe age of 20."? Probably not but we can't be even close to sure.I do not like the wording of this question. But my probability andstatistics education is a loooong time in the past. I'd appreciate a second(third, fourth, . . . dozenth) opinion. Glenn Clemens
``` | 351 | 1,320 | {"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-2018-17 | latest | en | 0.960765 |
https://www.nomidl.com/computer-vision/computer-vision-for-beginners-part-3/ | 1,718,424,714,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861583.78/warc/CC-MAIN-20240615031115-20240615061115-00050.warc.gz | 833,681,907 | 26,711 | ### Computer Vision for Beginners – Part 3
You may be already familiar with the word ‘contour.’ I’ve used this term several times in previous posts. A contour line is a curved line representing values. It is a very simple type of map that outlines the changes in an area, typically separating the different landforms.
But then you may ask this. The terms ‘edges’ and ‘contours’ are often used interchangeably, which can become confusing. The difference between the two is that edges have sharp angles while contours have curved or jagged lines. Edges are the most local region of a figure while contours are the boundaries of a figure. Edges are points whose values change significantly compared to their neighboring points. Contours, on the other hand, are closed curves which are obtained from edges and depicting a boundary of figures.
Contour detection can be implemented by the function cv2.findContours() in OpenCV and there are two important parameters here. Mode is the way of finding contours, and method is the approximation method for the detection.
The mode CV_RETR_CCOMP retrieves all of the contours and organizes them into a two-level hierarchy. At the top level, there are external boundaries of the components. At the second level, there are boundaries of the holes. If there is another contour inside a hole of a connected component, it is still put at the top level.
CV_CHAIN_APPROX_NONE stores absolutely all the contour points. That is, any 2 subsequent points (x1, y1) and (x2, y2) of the contour will be either horizontal, vertical or diagonal neighbors, that is, max(abs(x1-x2), abs(y2-y1)) == 1.
The returned contour is a list of points consisting of the contour lines. With the selected contour line, cv2.drawContours() will depict the bounding line along with the points as shown above.
## Extracting the Largest Contour in the image
The contours detected are returned as a list of continuous coordinates that form the shape of the object. Using these coordinates and the built-in python’s max() function we can retrieve the largest contour in the list. The max() function takes in as input the contours list along with a key parameter which refers to the single argument function used to customize the sort order. The function is applied to each item on the iterable. For retrieving the largest contour we use the key cv2.contourArea which is a function that returns the area of a contour. It is applied to each contour in the list and then the max() function returns the largest contour based on its area.
## Sorting Contours in terms of size
The max() function will only return the largest contour in the list. To compare all of the contours in the list another built-in python function sorted() can be used. sorted() function also takes in the optional key parameter which we use as before for returning the area of each contour. Then the contours are sorted based on area and the resultant list is returned. We also specify the order of sort reverse = True i.e in descending order of area size.
## Drawing a rectangle around the contour
Bounding rectangles are often used to highlight the regions of interest in the image. If this region of interest is a detected contour of a shape in the image, we can enclose it within a rectangle. There are two types of bounding rectangles that you may draw:
• Straight Bounding Rectangle
• Rotated Rectangle
For both types of bounding rectangles, their vertices are calculated using the coordinates in the contour list.
## Straight Bounding Rectangle
A straight bounding rectangle is simply an upright rectangle that does not take into account the rotation of the object. Its vertices can be calculated using the cv2.boundingRect() function which calculates the vertices for the minimal up-right rectangle possible using the extreme coordinates in the contour list. The coordinates can then be drawn as rectangle using cv2.rectangle() function.
## Function Syntax:
x, y, w, h = cv2.boundingRect(array)
## Parameters:
array – It is the Input gray-scale image or 2D point set from which the bounding rectangle is to be created
## Returns:
• x – It is X-coordinate of the top-left corner
• y – It is Y-coordinate of the top-left corner
• w – It is the width of the rectangle
• h – It is the height of the rectangle
## Image Moments
Image moments are like the weighted average of the pixel intensities in the image, they help you to calculate some features like the center of mass of the object, area of the object, etc. We can get the image moment of this contour by using the function cv2.moments() which gives us a dictionary of various properties to use.
## Function Syntax:
retval = cv.moments(array)
## Parameters:
array – Single-channel, 8-bit or floating-point 2D array
## Returns:
retval – A python dictionary containing different moments properties
The values returned represent different kinds of image movements including raw moments, central moments, scale/rotation invariant moments, and so on. For more information on image moments and how they are calculated you can read this Wikipedia article. Below we will discuss how some of the image moments returned can be used to analyze the contours detected.
## Find the center of a contour
The image moments calculated above can be used to find the centroid of the object in the image. The coordinate of the Centroid is given by two relations the central image moments, Cx=M10/M00 and Cy=M01/M00.
Now we can repeat the process for the rest of the contours detected in the image and draw a circle using cv2.circle() to indicate the centroids on the image.
## Finding Contour Area
Area for a contour can be found using two methods. One is using the function cv.contourArea() as we have done before for sorting and retrieving the largest contour.
Another method is to get the ‘m00’ moment which contains the area of the contour.
## Drawing Convex Hull
Convex Hull is another way to draw the contour onto the image. The function cv2.convexHull() checks a curve for convexity defects and corrects it. Convex curves are curves which are bulged out. And if it is bulged inside (Concave), it is called defects.
Function Syntax:
hull = cv2.convexHull(points, hull, clockwise, returnPoints)
## Parameters:
• points – Input 2D point set. This is a single contour.
• clockwise – Orientation flag. If it is true, the output convex hull is oriented clockwise. Otherwise, it is oriented counter-clockwise. The assumed coordinate system has its X axis pointing to the right, and its Y axis pointing upwards.
• returnPoints – Operation flag. In case of a matrix, when the flag is true, the function returns convex hull points. Otherwise, it returns indices of the convex hull points. By default it is True.
## Returns:
• hull – Output convex hull. It is either an integer vector of indices or vector of points. In the first case, the hull elements are 0-based indices of the convex hull points in the original array (since the set of convex hull points is a subset of the original point set). In the second case, hull elements are the convex hull points themselves. | 1,560 | 7,123 | {"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-2024-26 | latest | en | 0.905206 |
http://www.kushima.org/?p=50577 | 1,713,961,132,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819273.90/warc/CC-MAIN-20240424112049-20240424142049-00077.warc.gz | 46,903,925 | 13,412 | # Math Goodies
An experiment is a situation involving chance or probability that leads to results called outcomes.
An outcome is the result of a single trial of an experiment.
An event is one or more outcomes of an experiment.
Probability is the measure of how likely an event is.
In order to measure probabilities, mathematicians have devised the following formula for finding the probability of an event.
(Probability of an Event) = (the number of ways Event a can occur) / (the total number of possible Outcomes) | 105 | 517 | {"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} | 2.609375 | 3 | CC-MAIN-2024-18 | latest | en | 0.954384 |
http://www.hellenicaworld.com/Science/Mathematics/en/BakhshaliManuscript.html | 1,632,800,341,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780060201.9/warc/CC-MAIN-20210928032425-20210928062425-00053.warc.gz | 85,386,941 | 9,375 | ### - Art Gallery -
The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan). It is perhaps "the oldest extant manuscript in Indian mathematics."[4] For some portions a carbon-date was proposed of AD 224–383 while for other portions a carbon-date as late as AD 885–993 in a recent study, but the dating has been criticised by specialists on methodological grounds (Plofker et al. 2017[1] and Houben 2018 §3[2]). The manuscript contains the earliest known Indian use of a zero symbol.[5][6] It is written in Sanskrit with significant influence of local dialects.[4]
Discovery
The manuscript was unearthed from a field in 1881,[7] by a peasant in the village of Bakhshali, which is near Mardan, now in Khyber Pakhtunkhwa, Pakistan.[4] The first research on the manuscript was done by A. F. R. Hoernlé.[4][8] After his death, it was examined by G. R. Kaye, who edited the work and published it as a book in 1927.[9]
The extant manuscript is incomplete, consisting of seventy leaves of birch bark,[4][7] whose intended order is not known.[4] It is in the Bodleian Library at the University of Oxford[4][7] (MS. Sansk. d. 14), and is said to be too fragile to be examined by scholars.
Contents
The numerals used in the Bakhshali manuscript, dated to sometime between the 3rd and 7th century AD.
The manuscript is a compendium of rules and illustrative examples. Each example is stated as a problem, the solution is described, and it is verified that the problem has been solved. The sample problems are in verse and the commentary is in prose associated with calculations. The problems involve arithmetic, algebra and geometry, including mensuration. The topics covered include fractions, square roots, arithmetic and geometric progressions, solutions of simple equations, simultaneous linear equations, quadratic equations and indeterminate equations of the second degree.[9][10]
Composition
The manuscript is written in an earlier form of Śāradā script, a script which is known for having been in use mainly from the 8th to the 12th century in the northwestern part of India, such as Kashmir and neighbouring regions.[4] The language of the manuscript,[a] though intended to be Sanskrit, was significantly influenced in its phonetics and morphology by a local dialect or dialects, and some of the resultant linguistic peculiarities of the text are shared with Buddhist Hybrid Sanskrit. The overlying dialects, though sharing affinities with Apabhraṃśa and with Old Kashmiri, have not been identified precisely.[11] It is probable that most of the rules and examples had been originally composed in Sanskrit, while one of the sections was written entirely in a dialect.[12] It is possible that the manuscript might be a compilation of fragments from different works composed in a number of language varieties.[11] Hayashi admits that some of the irregularities are due to errors by scribes or may be orthographical.[13]
A colophon to one of the sections states that it was written by a brahmin identified as "the son of Chajaka", a "king of calculators," for the use of Vasiṣṭha's son Hasika. The brahmin might have been the author of the commentary as well as the scribe of the manuscript.[10] Near the colophon appears a broken word rtikāvati, which has been interpreted as the place Mārtikāvata mentioned by Varāhamihira as being in northwestern India (along with Takṣaśilā, Gandhāra etc.), the supposed place where the manuscript might have been written.[4]
Mathematics
The manuscript is a compilation of mathematical rules and examples (in verse), and prose commentaries on these verses.[4] Typically, a rule is given, with one or more examples, where each example is followed by a "statement" (nyāsa / sthāpanā) of the example's numerical information in tabular form, then a computation that works out the example by following the rule step-by-step while quoting it, and finally a verification to confirm that the solution satisfies the problem.[4] This is a style similar to that of Bhāskara I's commentary on the gaṇita (mathematics) chapter of the Āryabhaṭīya, including the emphasis on verification that became obsolete in later works.[4]
The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers (profit and loss), measurement such as of the fineness of gold, etc.[7]
Mathematical context
Scholar Takao Hayashi has compared the text of the manuscript with several Sanskrit texts.[4] He mentions that a passage is a verbatim quote from Mahabharata. He discusses similar passages in Ramayana, Vayupurana, Lokaprakasha of Kshemendra etc. Some of the mathematical rules also appear in Aryabhatiya of Aryabhatta, Aryabhatiyabhashya of Bhaskara I, Patiganita and Trairashika of Sridhara, Ganitasarasamgraha of Mahavira, and Lilavati and Bijaganita of Bhaskara II. An unnamed manuscript, later than Thakkar Pheru, in the Patan Jain library, a compilation of mathematical rules from various sources resembles the Bakhshali manuscript, contains data in an example which are strikingly similar.
Numerals and zero
Bakhshali manuscript, detail of the numeral "zero".
The Bakhshali manuscript uses numerals with a place-value system, using a dot as a place holder for zero.[14] The dot symbol came to be called the shunya-bindu (literally, the dot of the empty place). References to the concept are found in Subandhu's Vasavadatta, which has been dated between 385 and 465 by the scholar Maan Singh.[15]
Prior to the 2017 carbon dating – which, however, has in the meantime been discounted, see below under Date – a 9th-century inscription of zero on the wall of a temple in Gwalior, Madhya Pradesh, was thought to be the oldest Indian use of a zero symbol.[6]
Date
In 2017, three samples from the manuscript were thought to come from three different centuries, from AD 224–383, 680–779, and 885–993, on the basis of a study involving radiocarbon dating. If the dates were accepted, it is not known how fragments from different centuries came to be packaged together.[5][16][6]
A detailed reconsideration of all relevant evidence regarding the date of the Bakhshali manuscript, led Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk to conclude the following: "We express regret that the Bodleian Library kept their carbon-dating findings embargoed for many months, and then chose a newspaper press-release and YouTube as media for a first communication of these technical and historical matters. The Library thus bypassed standard academic channels that would have permitted serious collegial discussion and peer review prior to public announcements. ... we urge the investigators to consider the importance of reconciling their findings with historical knowledge and inferences obtained by other means. It should not be hastily assumed that the apparent implications of results from physical tests must be valid even if the conclusions they suggest appear historically absurd."[1]
Referring to the detailed reconsideration of the evidence by Kim Plofker et al., Jan Houben remarked: "If the finding that samples of the same manuscript would be centuries apart is not based on mistakes in the procedure of sampling etc., or if the manuscript was at the moment it was written upon not partly consisting of older, recycled pages, there are still some factors that have evidently been overlooked by the Bodleian research team: the well-known divergence in exposure to cosmic radiation at different altitudes and the possible variation in background radiation due to the presence of certain minerals in exposed, mountainous rock have nowhere been taken into account. Among the variables of carbon dates, variation in script and linguistic variation, the first is the most objective but still much in need of calibration for relatively recent, historical dates."[2]
Prior to the proposed radiocarbon dates of the 2017 study, most scholars agreed that the physical manuscript was a copy of a more ancient text, whose date had to be estimated partly on the basis of its content. Hoernlé thought that the manuscript was from the 9th century, but the original was from the 3rd or 4th century.[b] Indian scholars assigned it an earlier date. Datta assigned it to the "early centuries of the Christian era".[9] Channabasappa dated it to AD 200–400, on the grounds that it uses mathematical terminology different from that of Aryabhata.[18] Hayashi noted some similarities between the manuscript and Bhaskara I's work (AD 629), and said that it was "not much later than Bhaskara I".[4] To settle the date of the Bakhshali manuscript, language use and especially palaeography are other major parameters to be taken into account. In this context Jan Houben observed: "In view of the strong normativity of linguistic usage within the dimension “sanskrit - approximative sanskrit” it is difficult to derive a linear chronological difference from the observed linguistic variation. Also writing is a normative activity and moreover dependent on some amount of individual variation from scribe to scribe. However, writing has been much less subject either to the intensive study of early scripts by later generation scribes or to the conscious reintroduction of archaisms in later forms of writing (something we see in language, most famously the studied archaizing “Vedic” language use in parts of the Mahābhārata and in the Bhāgavatapurāṇa). We therefore have to take quite seriously the judgement of palaeographists such as Richard Salomon who observed that, what he teleologically called “Proto-Śāradā,” “first emerged around the middle of the seventh century” (Salomon 1998: 40). This excludes the earlier dates attributed to manuscript folios on which a fully developed form of Śāradā appears. The “hardest” evidence to judge the date of a manuscript such as the Bakhshali and its sections would therefore be the palaeographic evidence. Other evidence, including the laboratory results of radiocarbon dating, is to be interpreted in the light of the results reached by careful palaeographic study."[2]
Birch bark manuscript
Bakhshali approximation
Indian mathematics
Zero (number)
Notes
Variously described either as an "irregular Sanskrit" (Kaye 2004, p. 11), or as the so-called Gāthā dialect, the literary form of the Northwestern Prakrit, which combined elements of Sanskrit and Prakrit and whose use as a literary language predated the adoption of Classical Sanskrit for this purpose.(Hoernle 1887, p. 10)
G. R. Kaye, on the other hand, thought in 1927 that the work was composed in the 12th century,[4][9] but this was discounted in recent scholarship. G. G. Joseph wrote, "It is particularly unfortunate that Kaye is still quoted as an authority on Indian mathematics."[17]
References
Plofker, Kim, Agathe Keller, Takao Hayashi, Clemency Montelle, and Dominik Wujastyk. 2017. “The Bakhshālī Manuscript: A Response to the Bodleian Library’s Radiocarbon Dating.” History of Science in South Asia, 5.1: 134-150. https://journals.library.ualberta.ca/hssa/index.php/hssa/article/view/22
Jan E.M. Houben “Linguistic Paradox and Diglossia: on the emergence of Sanskrit and Sanskritic language in Ancient India.” De Gruyter Open Linguistics (Topical Issue on Historical Sociolinguistic Philology, ed. by Chiara Barbati and Christian Gastgeber.) OPLI – Vol. 4, issue 1: 1-18. DOI: https://doi.org/10.1515/opli-2018-0001
All the pages have been photographed which are available in the book by Hayashi
Takao Hayashi (2008), "Bakhshālī Manuscript", in Helaine Selin (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, 1, Springer, pp. B1–B3, ISBN 9781402045592
Devlin, Hannah (2017-09-13). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. ISSN 0261-3077. Retrieved 2017-09-14.
"Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.
John Newsome Crossley; Anthony Wah-Cheung Lun; Kangshen Shen; Shen Kangsheng (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press. ISBN 0-19-853936-3.
Hoernle 1887.
Bibhutibhusan Datta (1929). "Book Review: G. R. Kaye, The Bakhshâlî Manuscript—A Study in Mediaeval Mathematics, 1927". 35 (4). Bull. Amer. Math. Soc.: 579–580.
Plofker, Kim (2009), Mathematics in India, Princeton University Pres, p. 158, ISBN 978-0-691-12067-6
Hayashi 1995, p. 54.
Section VII 11, corresponding to folio 46v.(Hayashi 1995, p. 54)
Hayashi 1995, p. 26.
Pearce, Ian (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Retrieved 2007-07-24.
Singh, Maan (1993). Subandhu, New Delhi: Sahitya Akademi, ISBN 81-7201-509-7, pp. 9–11.
Mason, Robyn (2017-09-14). "Oxford Radiocarbon Accelerator Unit dates the world's oldest recorded origin of the zero symbol". School of Archaeology, University of Oxford. Archived from the original on 2017-09-14. Retrieved 2017-09-14.
Joseph, G. G. (2000), The Crest of the Peacock, non-European roots of Mathematics, Princeton University Press, pp. 215–216
E. F. Robinson (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Archived from the original on 9 August 2007. Retrieved 2007-07-24.
Bibliography
Hayashi, Takao (1995). The Bakhshālī manuscript: an ancient Indian mathematical treatise. Groningen Oriental studies. Groningen: Egbert Forsten. ISBN 978-90-6980-087-5.
Hoernle, Augustus (1887), On the Bakshali manuscript, Vienna: Alfred Hölder (Editor of the Court and of the University)
Kaye, George Rusby (2004) [1927]. The Bakhshālī manuscripts: a study in medieval mathematics. New Delhi: Aditya Prakashan. ISBN 978-81-7742-058-6.
Plofker, Kim; Agathe Keller; Takao Hayashi; Clemency Montelle; and Dominik Wujastyk. "The Bakhshālī Manuscript: A Response to the Bodleian Library’s Radiocarbon Dating" History of Science in South Asia, 5.1: 134-150. doi:10.18732/H2XT07
Sarasvati, Svami Satya Prakash; Jyotishmati, Usha (1979), The Bakhshali Manuscript: An Ancient Treatise of Indian Arithmetic (PDF), Allahabad: Dr. Ratna Kumari Svadhyaya Sansthan, archived from the original (PDF) on 2014-06-20, retrieved 2016-01-19 with complete text in Devanagari, 110 pages
M N Channabasappa (1976). "On the square root formula in the Bakhshali manuscript" (PDF). Indian J. History Sci. 11 (2): 112–124.
David H. Bailey, Jonathan Borwein (2011). "A Quartically Convergent Square Root Algorithm: An Exercise in Forensic Paleo-Mathematics" (PDF).
The Bakhshali manuscript
6 – The Bakhshali manuscript
Hoernle: On the Bakhshali Manuscript, 1887, archive.org
"A Big Zero: Research uncovers the date of the Bakhshali Manuscript", YouTube video, University of Oxford
[1] | 3,781 | 15,057 | {"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-2021-39 | latest | en | 0.968669 |
http://www.daiden.in/books/matrix-partial-orders-shorted-operators-and-applications-series-in-algebra | 1,563,675,536,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526818.17/warc/CC-MAIN-20190721020230-20190721042230-00172.warc.gz | 196,387,407 | 9,234 | > > New PDF release: Matrix Partial Orders, Shorted Operators and Applications
# New PDF release: Matrix Partial Orders, Shorted Operators and Applications
By Sujit Kumar Mitra
ISBN-10: 9812838449
ISBN-13: 9789812838445
The current monograph on matrix partial orders, the 1st in this subject, makes a special presentation of many partial orders on matrices that experience involved mathematicians for his or her attractiveness and utilized scientists for his or her wide-ranging program capability. apart from the Löwner order, the partial orders thought of are fairly new and got here into being within the past due Nineteen Seventies. After a close creation to generalized inverses and decompositions, the 3 simple partial orders specifically, the minus, the pointy and the megastar and the corresponding one-sided orders are offered utilizing a number of generalized inverses. The authors then provide a unified idea of some of these partial orders in addition to research the parallel sums and shorted matrices, the latter being studied at nice size. Partial orders of converted matrices are a brand new addition. eventually, functions are given in data and electric community conception.
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Additional resources for Matrix Partial Orders, Shorted Operators and Applications (Series in Algebra)
Example text
Further, T R must satisfy I = QQ−1 = QPT. As QP is a square matrix, we have R T = (QP)−1 . Thus, every χ-inverse must be of the form P(QP)−1 P−1 L . −1 −1 −1 −1 Conversely, A(P(QP) PL )A = PQP(QP) PL PQ = PQ = A −1 −1 and C(P(QP)−1 P−1 PL −1 L ) = C(P) = C(A), for each PL . So, P(QP) is a χ-inverse of A. Proof of (iii) is similar to proof of (ii). (iv) follows form (ii) and (iii). 5. Let A be an n × n matrix such that ρ(A) = ρ(A2 ). Let A = Pdiag(C, 0) P−1 , where P and C are non-singular. 28 Matrix Partial Orders, Shorted Operators and Applications (i) The class of all A− χ is given by P C−1 L P−1 ; where L is arbitrary.
N ). Then the spectral decomposition A = UΛU of A can also be written as n λi Ui Ui . 42. The above decomposition is in general not unique (unless all eigen-values are distinct). However, if µ1 , . . , µs (s ≤ n) are distinct eigen-vectors of A, then by appropriate pooling of the eigen-values we can write s µi Vi Vi , where Vi Vi = I , Vi Vj = 0 and I = U= Vi Vi . i=1 This decomposition is unique in the sense that the orthogonal projectors Vi Vi are unique. 43. (Spectral Decomposition of a Hermitian Matrix) Let A be an n×n matrix over C.
Then A is rangehermitian if and only if there exists a unitary matrix U such that A = Udiag(T, 0)U , where T is non-singular. 30. A matrix A over C is said to be simple if all its eigenvalues are distinct. A is said to be semi-simple, if the algebraic multiplicity for each of its distinct eigen-values equals its geometric multiplicity. 31. (Spectral Decomposition of a Semi-Simple Matrix) Let A be an n×n matrix over C. Then A is semi-simple if and only if there exist matrices E1 , . . , Es of order n × n and distinct complex numbers λ1 , . | 1,004 | 4,045 | {"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-2019-30 | latest | en | 0.916496 |
http://www.coyoteblog.com/coyote_blog/2009/10?doing_wp_cron=1412238596.9653038978576660156250 | 1,412,238,598,000,000,000 | text/html | crawl-data/CC-MAIN-2014-41/segments/1412037663739.33/warc/CC-MAIN-20140930004103-00274-ip-10-234-18-248.ec2.internal.warc.gz | 516,070,870 | 30,111 | Archive for October 2009
## The Cost of Solar
I had wanted to dig into the costs of a Florida solar facility that Obama recently visited. Fortunately Ronald Bailey does it for us:
Now let's do a rough calculation of the costs of DeSoto Solar versus conventional power sources. According to the Electric Power Research Insitute, a modern 1,000 megawatt coal plant without carbon capture technology would cost about \$2.8 billion to build. Adding carbon capture would boost the cost to as much as \$4.7 billion.
The 25 megawatt DeSoto facility cost \$150 million. Scaling it up to 1,000 megawatts would cost \$6 billion. But coal power plants operate 90 percent of the time snd solar only 30 percent, so in order to get the equivalent amount of electricity out of solar plant would mean tripling the capital cost for a total of about \$18 billion. In other words, building a solar power plant costs between 4- and 6-times more than conventional, or even carbon capture, power. Even worse, a scaled up DeSoto-style plant costs 18-times more than a natural gas plant.
## Agriculture Is Cheap When You Have Serfs to do the Work
Tom Nelson has a pretty funny set of articles on the White House vegetable garden. Michelle Obama told a group of kids it only cost \$180. Tom links a variety of videos and articles showing:
• Five NPS workers digging in the garden, with a tractor, tiller, and hand tools.
• A job posting for a college grad for the position of "White House Farmer."
• A job description of an assistant White House chef who currently overseas the garden.
Farming is cheap if the serfs (ie US citizens) provide all the labor and equipment for free.
## What A Freaking Mess
It takes eleven pages just to summarize the new 1990-page House government health care bill. Here is the summary.
The implications for my business is staggering. I have already mentioned in the previous post that it imposes an 8% tax on wages on my business -- a business where 50% of revenues go to wages and margins are in the 6-7% range. You do the math.
Worse for us is that nearly all our competitors are ma and pa companies with less than \$500,000 in wages a year, meaning that our competitors will be exempt from these taxes, giving them an automatic 4% cost advantage over our company. Great.
Twelve seconds after this thing passes, I will be on my phone to my attorney to figure out if it is possible to break my company into multiple corporations that all fall under the 500,000 wage limit. The paperwork and administration for this would be a huge hassle, but it can't be as high as 4% of sales.
Beyond this, I have not seen the detail yet, but the old House bill imposed enormous record-keeping obligations on businesses. Basically, I would have to know at all times exactly what kind of medical insurance policy every one of my employees has. Barf.
## Do Consumers Get Excited About Sales They Don't Qualify For?
Tiffany's is (hypothetically) handing out coupons for 50% off diamond necklaces. This generates a lot of press, but you do not get a coupon. Are you, without a coupon, more likely to buy a necklace anyway given all the publicity? Or is your behavior unchanged, because you received no inventive? Or are you perhaps less likely to buy, with the full retail price you would be paying now seeming higher as compared to the 50% off others are getting?
This issue seems to be at the heart of the conflict between the Obama administration and Edmunds.com (what is it about this administration and picking battles with media companies?) In their analysis, Edmunds said that only about 250,000 of the auto sales during the cash-for-clunkers period were incremental. The White House says they are underestimating, because even people who did not qualify for the program bought more cars because of the program:
The White House said [totally great car-buying, car-selling, and all-around-awesome-info site for every goddamn great and awful car website] Edmunds based its analysis on the "implausible" assumption that "the market for cars that didn't qualify for cash for clunkers was completely unaffected by this program. In other words, all the other cars were being sold on Mars, while the rest of the country was caught up in the excitement of the cash for clunkers program."...
Edmunds stands by its analysis.
"Instead of shooting the messenger, government officials should take heart from the core message of the analysis: The fundamentals of the auto marketplace are improving faster than the current sales numbers suggest," [Edmunds jefe Jeremy] Anwyl wrote.
The central issue, Anwyl said, "is how many of these sales would have occurred anyway. Apparently, the \$24,000 figure caught many by surprise. It shouldn't have. The truth is that consumer incentive programs are always hugely expensive when calculated by incremental sales -- always in the tens of thousands of dollars."
Edmunds rejected the White House suggestion that people got caught up in the excitement of the program and bought cars, even if they didn't qualify. And it discarded the notion that automakers boosted production solely because of the program.
"No manufacturer increases production, a decision with long-term consequences, based on the 30-day sales blip triggered by an event like cash for clunkers," Edmunds wrote.
Its an interesting question. I would tend to come down on Edmunds' side from my own experience running promotions, but it is not totally cut and dried. I can think of at least two examples where a discount to person A yields more sales to person B, but neither are really applicable here
• Example 1: Ladies night. Cheap drinks for the ladies bring in male customers, on the theory that that are looking for bars with, frankly, lots of drunk women
• Example 2: Kids eat free. Restaurants have programs with discounted or free kids meals to get their parent's business
I think one could actually make the argument that people who did not get the clunker discount would be less likely to buy, as its really hard to buy something for X when you know all the people around you are getting it for (X-\$3000)**. This isn't an absolute rule - after all, people fly all the time next to folks who paid more or less for the same service. But I do think it is a psychological issue that would tend to offset the general excitement around the program. In the end, we won't have to guess, once we get sales data for the rest of the year and we can see if clunkers merely moved sales forward a few months or generated incremental sales.
** As shown here, cash for clunkers amounted to about a \$3000 subsidy per buyer, above and beyond the blue book value of the car turned in.
## Congrats to the Obama Administration...
... for taking one of the few governments in Latin America that actually is trying to respect its democratic Constitution and forcing them to disavow the protections in its Constitution against elected officials attempting to hold onto power and reinstate a strongman friend of Hugo Chavez.
From start to finish I have been unable to understand the Obama Administrations policy in Honduras. I just refuse to believe he is actively working as an agent for totalitarianism, so the best explanation I can come up with is that he made an ignorant mistake in his early reactions to the Zelaya and has since doubled down on the mistake rather than admitting it and reversing himself. This theory is consistent with John Kerry's attempts to hide the evidence of the administration's mistake, not to mention Hillary Clinton's personality at State.
In a foreign policy career that so far has been marked by a marked softness, it is amazing to me that the one place Obama has decided he is going to demonstrate his cojones internationally is in helping a wannabee dictator return to power in a democratic nation.
Earlier posts here and here.
## Jeff Flake Rocks
I really like our AZ Congressman Jeff Flake -- the libertarian goodness of Ron Paul without the weirdness and connections to racism. This is pretty funny, from his site (ht: Radley Balko)
Washington, D.C., Oct 28 - Republican Congressman Jeff Flake, who represents Arizona's Sixth District, today released the following statement regarding his vote against H.Res.784, a bill "honoring the 2560th anniversary of the birth of Confucius and recognizing his invaluable contributions to philosophy and social and political thought."
"He who spends time passing trivial legislation may find himself out of time to read healthcare bill," said Flake.
## My New #1 Reason I Hate This Recession...
...because nearly every day I get another letter from some near-bankrupt city, state, county, or other taxing authority which says basically:
"we have this vague, non-fact based hypothesis that your company owes us a lot of taxes you are not paying. To avoid the determination that you owe us lots more money for some unproven or unspecified reason, you must send us approximately a two-inch stack of information that it will take from 8-10 hours to prepare, including..."
The most recent of these just came from the state of Michigan. There are several taxes that I don't pay because they clearly do not apply to me, but I just got a letter saying basically they will assume I owe them unless I fill out a four page form and send them a bunch of detailed financial information.
RRRRRRRRR.
## Bank Failures in Perspective
Bank failures in the last coupe of years, in terms of institutions as well as assets, are still well below the S&L crisis of the 1980's. So what justifies the current nationalization of the banking sector and the short-circuiting of institutional failures and the subsequent creation of moral hazard. Via Carpe Diem.
## Moral Hazard Continued at GMAC
GMAC, the former lending arm of General Motors Co., is in talks with the Treasury Department for a third injection of taxpayer aid, a further sign of the U.S. government's entrenchment in the U.S. auto industry.
The Treasury Department mandated earlier this year that GMAC Financial Services raise an additional \$11.5 billion in capital after undergoing a "stress test" along with 18 other banks. While other banks deemed undercapitalized have been able to raise funds from private investors, GMAC has been forced to go back to the government.
Maybe the reason no one but Obama will give GMAC any money is that they know that every time GMAC gets any money, it simply starts shoveling it at every car buyer who walks within shouting distance of a dealership and can fog a mirror.
Immediately after GMAC became eligible for TARP money, GM reduced to zero the interest rate"¦ on certain models. ...
GMAC has begun making loans to borrowers with credit scores as low as 621, a significant relaxation of the 700 minimum score the company adopted just three months ago as it struggled to survive. America's median credit score is 723"¦
GMAC is a giant ponzi scheme to subsidize car sales. Ponzi schemes last only so long as there is a sucker to keep putting in money. No private funds are that dumb, but fortunately for GMAC there is the Obama administration.
## Window Repair Jobs
Tyler Cowen links to a good article that gets at the fallacy that suddenly obsoleting our energy infrastructure and having to rebuild it will be of net economic benefit.
Optimistically treating European Commission partially funded data, we find that for every renewable energy job that the State manages to finance, Spain's experience cited by President Obama as a model reveals with high confidence, by two different methods, that the U.S. should expect a loss of at least 2.2 jobs on average, or about 9 jobs lost for every 4 created, to which we have to add those jobs that non-subsidized investments with the same resources would have created
Includes 1 million euros in government subsidies per wind job created.
In my mind, the green jobs mantra is a result of the CO2 abatement case becoming fatally weak, with supporters of legislation casting about for other justificaitons. From the very beginning, many of the most passionate folks are on the AGW bandwagon not because they really understand the science, but because the theory provided justification for a range of government actions (reduced growth, limited technology, reduced energy use, reduction in global trade -- even vegetarianism) that they supported long before AGW made the news.
Update: A quick note on a theme I harp on a lot - nameplate capacity for wind and solar is really, really misleading. In Spain in the study cited, wind operates at 19% of nameplate over the course of a year and solar operates at 8% (figure 3). The actual CO2 reduction is even worse, because, particularly for wind, fossil-fuel fired turbines have to be spinning on hot backup for when wind suddenly dies. Germany, the largest wind user in the word, found only 1,000MW of reduced fossil fuel plant needs from every 24,000 MW of wind capacity.
## Product Safety
Don Boudreaux has a nice summary of the problems with a lot of product safety problems.
You write as if "safe" is an objectively determinable and unique fact, such as whether or not your newspaper's paid circulation exceeds 500,000 or whether or not your sister is pregnant. But "safe" is not objective in this way. Because no product is 100 percent certain never to cause even the slightest harm (or 100 percent certain to cause harm), the question "Is this product safe?" has no correct single answer. It has correct answers as varied as the number of that product's potential users. No product is "safe" or "unsafe" in the abstract.
Perhaps your tolerance for risk is higher than mine. Perhaps the pleasure I get from using a product is less than yours. If so, should I be permitted to prevent you from using that product because, for me, the product is insufficiently safe? My evaluation of the product's safety is correct only for me, not for you. And matters don't change if I'm a government official.
## Aarrrggghhh
I find myself stuck in a Flagstaff city council meeting. I am listening to a truly irritating public comment. She is currently pounding on absentee landlords (apparently a large number of Flagstaff residents, as many as 50%, rent from out-of-town landlords. She just said basically that these landlords should get no consideration in such and such ordinance because they contribute nothing to the city but a thin sliver of property taxes.
Well, my guess is that "thin sliver" of property taxes pretty much funds all the schools, but I really wanted to stand up and ask - what about the capital they have invested in the city? Obviously half of the town is unable to construct their own house and have housing by the grace of these evil out of town landowners who have invested capital in the city to build out the housing stock.
## We Have Clearly Run Out of Real Law Enforcement Challenges
Via the AZ Republic, the excepting of which will probably bring in all kinds of spam code into this post no matter how hard I try to get rid of it:
Arizona wildlife officials are investigating the shooting death of a prairie dog in southern Arizona.
Apparently the state is irritated because this prairie dog was brought to the state as part of a program to bring more plague-infested nuisance rodents onto our land - on purpose!
The prairie dog was one of more than 100 transported from New Mexico in October 2008 in hopes of reintroducing the indigenous species to southern Arizona.
## Health Insurance Mandates
One of the reasons for substantial variation in the cost of health insurance between the states is the variations in state "must-cover" health insurance mandates. New York and Massachusetts, both known to have among the most extensive requirements, not coincidentally have the highest average premium costs.
I found this study the other day - it was put together by a health insurance group and is certainly self-serving; but since it is just a summary of existing law, I don't see any reason why it wouldn't be mostly accurate.
Here is one example table from the report -- it is the type of specialist care that must be covered in each state. They also have much longer tables on the individual procedures that must be covered:
Gotta make sure that "naturopaths" are covered, don't we? You can picture the process of specialists marching into state capitals and making their pitch that their profession needs to be covered.
You can get a feeling for what goes on with one example. One procedure, "Port Wine Stain Elimination," caught my eye. I assumed this was removal of some type of birthmark, but I was curious and looked it up. I got this study near the top of the Google search, and in this link you can see the political process of mandates in a nutshell. Here is the abstract (emphasis added)
background. Port-wine stains are congenital vascular malformations that can be disfiguring and may lead to psychosocial as well as medical complications. The 585-nm pulsed dye laser is very effective in treating port-wine stains. Laser treatment is often viewed by insurance companies as a "cosmetic procedure" and not "medically necessary." Consequently many patients are denied coverage for treatment of their disfiguring birthmarks.
objective. To determine variability of insurance coverage for laser treatment of port-wine stains from state to state. Natural history, progression, and potential complications of port-wine stains arc reviewed and rationale for consistent insurance coverage for laser treatment of port-wine stains is given.
methods. A questionnaire was mailed to 40 dermatologic surgeons in 22 states and the District of Columbia. We reviewed the literature regarding port-wine stains and their potential complications, and health care policy guidelines regarding "medical necessity" and "cosmetic procedures."
results. Insurance coverage for laser treatment of port-wine stains varies from state to state.
conclusion. Based on current health care policy guidelines, laser treatment of port-wine stains should be regarded, and covered, as a medical necessity by all insurance providers.
In other words, the study surveyed a bunch of cosmetic surgeons. They were asked "should an expensive procedure you provide be covered by insurance." They all answered "Hell YES!" Anyone want to bet whether the funding for the study came from the company that makes the laser equipment?
But today, they now have to run to 50 state houses (well, 48 since they have been successful in 2). In the future, they will just run to Congress. And we know how good Congress is at saying no to special interests.
Postscript: I would normally assume this is obvious, but after years of blogging I know that I must add that I have nothing against those with port wine stains, I am thrilled that a technology exists today to remove them, but I don't want to pay for it in my policy.
Postscript #2: I am willing to bet that the Venn diagram of the 4 states offering "naturopath" coverage and the 3 states offering "Pastoral Counselors" don't overlap.
Postscript #3: What does a naturopath (whose tools include homeopathy) charge an insurance company for a remedy consisting of at most one molecule of active ingredient in a glass of pure but well shaken water? Speaking of homeopathy, this is classically funny.
## Government Strongarm Tactics in the Chrysler Bankrupcy
This is an interesting video from the State Treasurer of Indiana about his state's experience as a secured creditor of Chrysler, and how their legal claims were pushed aside as the Administration moved more politically-favored constituencies (e.g the UAW) ahead of the secured creditors in line.
One side issue here. Early in the video he explains that the State of Indiana held a lot of Chrysler bonds because Chrysler is a big employer and they try to support companies with a big footprint in the state.
Isn't that terrible risk management policy, closely akin to Enron employees putting all of their savings in Enron stock? If Chrysler goes down, this means loss of investment returns in key retirement funds at the same time there is a large loss of tax money that will likely be the source of replacement funds.
## Cost of Climate Change Legislation
This video doesn't touch much on the science of global warming, but does make an eloquent case about the true cost of CO2 abatement legislation.
## Yeah, But....
From the AZ Republic, on the yet-again-revived public option:
Health-care legislation heading for the Senate floor will give millions of Americans the option of purchasing government-run insurance coverage, Majority Leader Harry Reid announced Monday, although he stopped short of claiming the 60 votes needed to pass a plan steeped in controversy. Reid, D-Nev., said individual states would have the choice of opting out of the program. Details of how it would work were still sketchy, but states would get a year after the 2013 phase-in of the new health-care plan to decide whether to participate.
And federal taxes for citizens of opt-out states will be reduced, right? No way. This opt-out is a joke. Its a bit like saying that every individual has the right to opt out of public education in favor of a private school. Sure they do -- they don't have to attend the public school, but they have to pay for it anyway in their taxes.
Update: Sorry, the AZ Republic has made it almost freaking impossible to excerpt from their online articles without bringing over a load of cr*p code.
## Fortunately, Pregnant Women Can Easily Get A Big Mac
I liked TJIC's response to the story of the pregnant woman who could not find any available supplies of the government-provided flu vaccine:
Man, it's a good thing that the flu vaccine isn't being left in the hands of the free market "“ we might have the same horrible production and distribution bottlenecks that we run into with Coke, pizza, books, and pajamas "“ you can't find those things anywhere.
And, hey, on the bright side, socialized medicine is coming!
## Fox, Meet Henhouse
Via Maggies Farm and a commenter on TigerHawk:
During consideration of H.R. 3126, legislation to establish a Consumer Financial Protection Agency (CFPA), Democrats on the House Financial Services Committee voted to pass an amendment offered by Rep. Maxine Waters (D-CA) that will make ACORN eligible to play a role in setting regulations for financial institutions.The Waters amendment adds to the CFPA Oversight Board 5 representatives from the fields of "consumer protection, fair lending and civil rights, representatives of depository institutions that primarily serve underserved communities, or representatives of communities that have been significantly impacted by higher-priced mortgages" to join Federal banking regulators in advising the Director on the consistency of proposed regulations, and strategies and policies that the Director should undertake to enforce its rules.
By making representatives of ACORN and other consumer activist organizations eligible to serve on the Oversight Board, the amendment creates a potentially enormous government sanctioned conflict of interest. ACORN-type organizations will have an advisory role on regulating the very financial institutions from which they receive millions of dollars annually in direct corporate contributions and benefit from other financial partnerships and arrangements. These are the same organizations that pressured banks to make subprime mortgage loans and thus bear a major responsibility for the collapse of the housing market.
In light of recent evidence linking ACORN to possible criminal activity, Democrats took an unprecedented step today to give ACORN a potential role alongside bank regulators in overseeing financial institutions. This is contrary to recent actions taken by the Senate and House to block federal funds to ACORN.
ACORN was an important actor in the housing bubble, responsible for numerous lawsuits and other political pressure to force banks to lend to borrowers who by objective standards did not have the income or credit history to sustain mortgage payments. It would be interesting to see how many mortgages ACORN was involved with have gone belly up. But now, as part of the "solution" to the financial crisis, we will put ACORN in charge.
## The Gods Must be Crazy
I hardly know what to do with this. When this is a pressing enough gender issue to demand NOW's attention, perhaps it is time to declare victory and move on to weightier topics.
A couple of weeks ago, President Obama had members of his cabinet, as well as members of congress, including Flake, over to the White House for a game of hoops.
They were all men.
Sounds like the boys had some fun but If you ask the "Debby Downers" from women advocacy groups like the National Organization for Women, the games lack of estrogen is unacceptable.
"Relationships get built in those more informal settings," NOW President Terry O'Neill told ABC News, "and the relationships have a huge impact on the influence an individual has. We know what happens when we segregated whether it by race or whether it by gender -- you end up with 1st class citizens and you end up with 2nd class citizens."
Fortunately we have moved beyond quotas. Not.
"It's extremely important, now especially, for the president to have as many women as men in his closest circle of advisors. ... If women had been at the heads of the companies on Wall Street instead of these masters of the universe then we might not be in the predicament that we're in today," O'Neill says. "[The ratio of women to men] needs to be 50/50. Women are 52 percent of the voting public so obviously there needs to be 50/50 of any Cabinet."
I will be counting the men at the next baby shower.
## Reminder: Nov. 10 Phoenix Climate Presentation
I will be making a free presentation in Phoenix on climate change and the science behind the skeptic's case. It is free to the public, and in answer to numerous inquiries, it is not sponsored or paid for by any organization and I am not promoting a book or any commercial product. This is simply my personal hobby and style of activism (e.g. cerebral lecture rather than circling around carrying a sign).
But here is the really interesting coincidence: It turns out Al Gore will be making the keynote address at the Greenbuild Conference in Phoenix on the next day (Nov 11). Those who would like to be immunized in advance against his silliness should come to my presentation the night before.
The web site and directions for the presentation are hereNov 10 Climate Lecture Brochure (pdf). We have a pretty large auditorium, so everyone is welcome. Feel free to send the link or brochure to your friends in the area.
Update: I can see the local climate is already reacting to Gore's visit, as we get an early dose of the Gore effect:
Temperatures in the Valley are expected to fall more than 20 degrees to the 60s by midweek, according to the National Weather Service.
## A Total Crock
Since the New York Times has pretty much become the official media outlet of this administration, I presume that this article represents a new trial balloon in selling government health care. The pitch this time -- its good for small businesses! (via Maggies Farm)
President Obama, in his Saturday radio address, said the Democrats' health insurance overhaul would help small businesses and stimulate the economy by providing relief from "the crushing costs of health care "” costs that have forced too many small businesses to cut benefits, shed jobs, or shut their doors for good."....
The House speaker, Nancy Pelosi of California, said the sharp rise in premiums for small businesses offered the latest evidence that Congress must act swiftly on health care legislation.
"This underlines the urgent need for health insurance reform, including a public option," she said in an interview. "We need to have competition for the insurance companies to keep premiums down."
I am only now getting through the 1500 pages of this bill (putting me ahead of Ms. Pelosi in reading it, I am sure), but the last House bill would have been a disaster for my company, increasing taxes on wages by up to 8% and imposing a record-keeping burden that was just horrific.
The NYT and the Democrats are apparently trying to set up a mini-class war within bussinesses, snidely saying these companies have more negotiating leverage. Sure. But what they have even more of is the leverage to shape federal legislation to their benefit. However worse a deal my company may get in free insurance markets due to being small is nothing compared to how much worse of a deal we will get from Congress by being small.
If they really wanted to cut costs for small businesses, they would strip out all the national and state coverage mandates for things like aromatherapy that raise costs so much and let me shop for insurance across state lines. That would be real competition. Unfortunately, all Pelosi means by competition is throwing Amtrak into the mix to compete with the airlines. Yeah, that will do the trick.
## Classic Government
This is just so typical. In response to demands for transparency, the Norwegian government starts publishing ... tons of private data about its citizens. I wonder how much detail they put online about how the government spends the tax money? Via maggies farm.
## We're Going To Fund Health Care Reform By Cutting the Insurance Company Profits
I am not sure anyone has actually said this, but that has certainly been the implication, right? Obama & Pelosi spends a lot of time accusing insurance companies of having profits that are too high, so I have to believe his intention is to reap cost savings by cutting into them.
I have blogged about this before, but Carpe Diem also picks up this thread, observing that health insurance companies are #86 on the list of US industries in terms of profit margins, with a ROS of 3.3%. As Mark Perry points out, this gives them a profit of about \$100 per individual policy. Not really a very promising source of savings, is it? But it is very scary for any industry that makes more than 3.3% profits, knowing that the Administration thinks they are making too much money and has shown a willingness to slice into profits it thinks to be excessive.
## The Corporate State
From Henry Payne:
Rent-seeking is the new venture capital model, Kleiner Perkins managing partner Ray Lane explained to an electric car-conference here Wednesday.
In an extraordinary speech, Lane laid out how market socialism can guarantee profits for politically connected VC firms like Kleiner -- far more preferable to the old model of "throwing a dart at a dart board," as Lane has put it. While Silicon Valley-based Kleiner made its reputation as a financier of tech startups like Netscape, Lane confided that they are inherently risky ventures in uncertain, fast-moving markets.
By contrast, Lane expressed admiration for communist governments like China and market-socialist economies like France where government determines new markets, thus providing a more certain investment climate for rent-seekers. With Kleiner partner Al Gore lobbying for federal mandates from wind to electric cars, Kleiner would be assured of a return on otherwise risky investments like Fisker Automotive, a California electric car company. | 6,550 | 31,488 | {"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-2014-41 | latest | en | 0.920963 |
https://socratic.org/questions/how-do-you-find-excluded-values-for-rational-expressions#631143 | 1,685,559,269,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224647409.17/warc/CC-MAIN-20230531182033-20230531212033-00515.warc.gz | 585,023,418 | 5,772 | # How do you find excluded values for rational expressions?
Jun 17, 2018
See below
#### Explanation:
Let our general rational expression be $f \frac{x}{g} \left(x\right)$
This expression is defined where $g \left(x\right) \ne 0$
[Since we cannot divide by 0]
Hence, the excluded values are where $g \left(x\right) = 0$
Hope this helps! | 98 | 342 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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} | 3.40625 | 3 | CC-MAIN-2023-23 | latest | en | 0.747965 |
http://www.math-only-math.com/worksheet-on-metric-measures.html | 1,537,822,505,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267160754.91/warc/CC-MAIN-20180924205029-20180924225429-00342.warc.gz | 362,369,133 | 7,513 | # Worksheet on Metric Measures
Practice the questions given in the worksheet on metric measures as we know it is very important for us to know how to convert smaller units into bigger units and bigger units into smaller units.
I. Convert 145 kilometres into following units.
(i) metres
(ii) centimetres
(iii) hectometres
II. Convert 4567 metres into the following units.
(i) hectometres
(ii) kilometres
(iii) millimetres
III. Convert 25 litres into the following units.
(i) centilitres
(ii) millilitres
(iii) decalitres
IV. Convert 6250 grams into the following units.
(i) decagrams
(ii) kilograms
(iii) milligrams
V. Convert 4538 decilitres into the following units.
(i) litres
(ii) decalitres
(iii) hectolitres
VI. Convert 6 g 7 dg 9 cg 2 mg into mg
VII. Convert 9 l 5 dl 8 cl 4 ml into ml.
VIII. Convert 5 km 8 hm 7 dam into dam.
IX. Fill in the blanks.
(i) 20 cm = _____________ mm
(ii) 2525 cg = _____________ g
(iii) 2000 l = _____________ kl
(iv) 23 kg = _____________ dag
(v) 25 hm = _____________ m
(vi) 307 dg = _____________ dag
(vii) 3000 hl = _____________ kl
(viii) 5207 m = _____________ km
X. Fill in the boxes.
(i) 8 km = ____ m
(ii) 4.325 kg = ____ g
(iii) 20.325 kl = ____ hl
(iv) ____ mm = 2m
(v) ____ dag = 5 kg
(vi) ____ mm = 25 cm
(vii) 25382 mg = ____ g ____ mg
(viii) 5405 l = ____ kl ____ l
(ix) 2496 mm = ____ m ____ dm ____ cm ____ mm
(x) 5949 ml = ____ l ____ dl ____ cl ____ ml
(xi) 9 kg 5 hg 2 dag 3 g = ______ g
(xii) 6 m 2 dm 4 cm 9 mm = ______ mm
(xiii) 2 l 5 dl 9 cl 5 ml = ______ ml
(xiv) 8 m 9 dm 3 cm = ______ cm
`
Answers for the worksheet on metric measures are given below.
I. (i) 145000 m
(ii) 14500000 cm
(iii) 1450 hm
II. (i) 45670 hm
(ii) 4.567 km
(iii) 4567000 mm
III. (i) 2500 cl
(ii) 25000 ml
(iii) 2.5 dal
IV. (i) 625 dam
(ii) 250 g
(iii) 6250000 mg
V. (i) 453.8 l
(ii) 45.38 dal
(iii) 4.538 hl
VI. 6792 mg
VII. 9584 ml.
VIII. 587 dam.
IX. (i) 200
(ii) 25.25
(iii) 2
(iv) 2300
(v) 2500
(vi) 3.07
(vii) 300
(viii) 5.207
X. (i) 8000
(ii) 4325
(iii) 203.25
(iv) 2000
(v) 500
(vi) 250
(vii) 25, 382
(viii) 5, 405
(ix) 2, 4, 9, 6
(x) 5, 9, 4, 9
(xi) 9523
(xii) 6249
(xiii) 2595
(xiv) 893 | 875 | 2,221 | {"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-2018-39 | latest | en | 0.502113 |
http://python-forum.org/viewtopic.php?f=27&t=3687&p=44927&sid=5b001aa801e03264dfa1ca4f950acaa4 | 1,500,648,183,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549423785.29/warc/CC-MAIN-20170721142410-20170721162410-00645.warc.gz | 257,784,620 | 6,842 | ## Find the sum of all the multiples of 3 or 5 below 1000.
For questions about problems on the Project Euler web site. No spoilers. Please include the question number in the subject line of your post.
### Find the sum of all the multiples of 3 or 5 below 1000.
removed for spoilers
Last edited by mrlog101 on Thu May 30, 2013 2:01 pm, edited 1 time in total.
mrlog101
Posts: 3
Joined: Wed May 29, 2013 4:12 pm
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
Hello
Your result is right (if 1000 is included in the sum) and I have seen no mistake in your code
you also have the result with :
Code: Select all
`sum(set(range(0,1001,3)+range(0,1001,5)))`
Regards
MichelFJM
Posts: 19
Joined: Wed May 22, 2013 1:41 pm
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
Well the website I got the task from says it's incorrect, so I've either misunderstood the question or something else... I can't see what though.
The question is at http://projecteuler.net/problem=1 if you want to see and try to put the answer in.
mrlog101
Posts: 3
Joined: Wed May 29, 2013 4:12 pm
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
1000 is not below 1000.
Last edited by stranac on Thu May 30, 2013 2:00 pm, edited 2 times in total.
Reason: Moved topic to Project Euler
Friendship is magic!
R.I.P. Tracy M. You will be missed.
stranac
Posts: 1790
Joined: Thu Feb 07, 2013 3:42 pm
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
Oh right... well that was stupid of me.
mrlog101
Posts: 3
Joined: Wed May 29, 2013 4:12 pm
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
Quicker approach:
Code: Select all
`3 * 333 * 167 + 5 * 100 * 201 - 15 * 33 * 67`
codingismycraft
Posts: 6
Joined: Fri May 23, 2014 3:25 pm
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
codingismycraft wrote:Quicker approach:
Code: Select all
`3 * 333 * 167 + 5 * 100 * 201 - 15 * 33 * 67`
Agreed but in my book you still fail the exercise, because you are not explaining why you get there so the poor future programmer that lacks you genius and has to maintain your code may not understand how you got here. There are usually two outcomes: you code gets enshrined to the point that no-one dares rewriting the application to any extent(*), or someone rewrites your code badly, and introduces numerous obscure bugs that plague the applications for years.
(*) I know an application somewhere that runs on a farm of Linux servers, but the core is on a Windows computer (likely XP) because it was written using the IBM C++ Compiler for Windows and OS/2, using its proprietary string library (STL was unheard of when the application was initially written).
This forum has been moved to http://python-forum.io/. See you there.
Ofnuts
Posts: 2659
Joined: Thu May 14, 2015 9:46 am
Location: Paris, France, EU, Earth, Solar system, Milky Way, Local Cluster, Universe #32987440940987
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
Ofnuts wrote:
codingismycraft wrote:Quicker approach:
Code: Select all
`3 * 333 * 167 + 5 * 100 * 201 - 15 * 33 * 67`
Agreed but in my book you still fail the exercise, because you are not explaining why you get there so the poor future programmer that lacks you genius and has to maintain your code may not understand how you got here. There are usually two outcomes: you code gets enshrined to the point that no-one dares rewriting the application to any extent(*), or someone rewrites your code badly, and introduces numerous obscure bugs that plague the applications for years.
(*) I know an application somewhere that runs on a farm of Linux servers, but the core is on a Windows computer (likely XP) because it was written using the IBM C++ Compiler for Windows and OS/2, using its proprietary string library (STL was unheard of when the application was initially written).
OK.. Quick documentation of this approach:
Sum of multiples of 3 that are less than 1000:
SUM_3 = 3 * ( 1 + 2 + ... + 333)
Sum of multiples of 5 that are less than 1000:
SUM_5 = 5 * ( 1 + 2 + ... + 200)
Using the formula:
1 + 2 + ... + n = n * ( n-1) / 2
We have:
SUM_3 = 3 * 333 * 334 / 2 = 3 * 333 * 167
SUM_5 = 5 * 200 * 201 / 2 = 5 * 100 * 201
C = SUM_3 + SUM_5
Multiples of both 3 and 5 are encountered twice in C, so we need
to subtract it from it. We can find their total by calculating
the SUM_15 (exactly as we did for SUM_3 and SUM_5):
SUM_15 = 15 * ( 1 + 2 + ... + 66)
or
SUM_15 = 15 * 66 * 67 / 2 = 15 * 33 * 67
So:
Sum = SUM_3 + SUM_5 - SUM_15
codingismycraft
Posts: 6
Joined: Fri May 23, 2014 3:25 pm
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
codingismycraft wrote:[
Sum of multiples of 5 that are less than 1000:
SUM_5 = 5 * ( 1 + 2 + ... + 200)
That includes 1000, when it shouldn't, doesn't it?
This forum has been moved to http://python-forum.io/. See you there.
Ofnuts
Posts: 2659
Joined: Thu May 14, 2015 9:46 am
Location: Paris, France, EU, Earth, Solar system, Milky Way, Local Cluster, Universe #32987440940987
### Re: Find the sum of all the multiples of 3 or 5 below 1000.
Ofnuts wrote:
codingismycraft wrote:[
Sum of multiples of 5 that are less than 1000:
SUM_5 = 5 * ( 1 + 2 + ... + 200)
That includes 1000, when it shouldn't, doesn't it?
Yes, it is inclusive as the other solution that was presented before.
Obviously to make it non inclusive we take the sum for
SUM_5 = 5 * ( 1 + 2 + ... + 199)
and
SUM_15 = 15 * ( 1 + 2 + ... + 65)
codingismycraft
Posts: 6
Joined: Fri May 23, 2014 3:25 pm | 1,705 | 5,571 | {"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-2017-30 | latest | en | 0.875782 |
https://discourse.mcneel.com/t/calculate-high-and-low-points-on-surfaces/70314 | 1,709,314,414,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475422.71/warc/CC-MAIN-20240301161412-20240301191412-00005.warc.gz | 204,729,844 | 9,757 | # Calculate high and low points on surfaces
I have two surfaces/landscapes that are lying in the same space, and I want to calculate which points that are above and which are below in a grid. In other words: which point of the grid is above and which is below. Is there a definition for that or maybe an example?
As you can see on the image there’s a grid on both surfaces, and I can easily make a contour line of the grids if it’s easier for the definition to work with curves.
1 Like
interesting problem!
I am not sure if when you say grid you mean a grid on the surface or on the xy plane. This is the first case but it should be easy to modify to the second.
over.gh (14.9 KB)
That’s amazing! That’s what I meant; points in a grid on the surfaces. The end goal is to calculate the volume that is subtracted (from the green on your image to the top surface) and the volume that is added (the yellow to the bottom layer). The way I figured that I could do it is by.
1: drawing lines between the two surfaces grids (listing the lengths of the added/subtracted would be handy).
2: making a rectangular pipe on the line (that I know how to do).
3: calculate the separate volumes.
It’s basically how much soil is added and how much is subtracted from two specific landscape surfaces.
There might be a better way, but that’s what I came up with…
Hi Fengal,
If you turn both surfaces into solid objects by projecting their edges down to a common horizontal plane anywhere below the lowest point on either surface, you can, provided the bottom faces are identical sizes, simply subtract the Rhino volume of one from the volume of the other to get the difference.
Sorry, but I am not at my Rhino computer so I can’t illustrate this.
Regards
Jeremy
I think that this is a totally different animal.
You just create volumes with boundaries the two surfaces and the boundary of the property (in this case I used a bbox but you can extrude the site boundary)
and add/ subtract them by checking if they’re over or under the old landscape.
volume.gh (16.7 KB)
EDIT:
Sorry!!! I mixed the area with the volume components in my hurry!!!
here is the correct way:
volume.gh (19.0 KB)
Wow, thank you, this is really helpful.
My classmate who works with the same project figured out another way to do it, however, we can’t figure out how to differentiate between subtracted and added volumes. Do you perhaps see a solution?AddSub.gh (56.1 KB)
Not unless you internalize your geometry! (right click on surface components —>internalize)
also: ctrl-shift-q takes an image of your canvas so you can share it easily
Ah, sorry. This should be itAddSub2.gh (51.2 KB)
:
Ok, somehow managed to do something similar but with the surfaces instead of solids. Will try solids. Thanks.
Ah, sorry. This should be itAddSub2.gh (51.2 KB)
Another trick is that Plane Closest Point will give you distance in positive if it is above or negative if it is below. Additionally, Pufferfish has a Point Surface Side component if you want to check that out also.
Point Surface Side.gh (12.0 KB)
That’s handy. Thanks. I will try to figure out how to use it to calculate the two volumes.
How did you edit the colors of your Grasshopper UI?
Now you’re asking the real questions!
1 Like
Yes or just simply change any of these fields in script editor component.
https://developer.rhino3d.com/wip/api/grasshopper/html/T_Grasshopper_GUI_Canvas_GH_Skin.htm
Or go to File>Special Folders > Settings Folder and open the file grasshopper_gui.xml in note pad, edit any of the color values and save.
1. Be brave.
2. Press ctrl-alt-defeat.
3. Open attached (talk and walk and this (and that)).
Tarrain_PriorAfter_Compare_V1.3dm (290.3 KB)
Tarrain_PriorAfter_Compare_V1.gh (127.6 KB)
It looks advanced but I can’t figure out how to use it.
Other than using code (rather ordinary these days) … it’s not advanced at all: one should operate with meshes instead of nurbs for some sort of acceptable response [“interactive” so to speak].
As it is:
1. If one of the input Breps is null … C# aborts.
2. You should use a suitable pair: terrain prior (OEM) and terrain after that have exactly the same projected inner and outer loops … meaning that the bool diff on these projected Breps (BrepFaces to be exact) is null. That’s the primitive test for “equality” used here. BTW: If the result is not null … C# stops playing ball (see info panel).
3. You should use valid Breps (with one BrepFace) that have no 2 (or more) points that share the same x.y coordinates. This means terrains with no negative slope.
Anyway - just for the record - post some test pairs of yours here. Avoid at any cost internalizing Breps (use a Rhino file). | 1,126 | 4,700 | {"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} | 3.421875 | 3 | CC-MAIN-2024-10 | latest | en | 0.947823 |
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# Memory-less Processes
#### January 10th, 2017
Today we will investigate a very interesting property of the exponential distribution. Often used to model waiting times, the exponential distribution has a probability density function of
$$P(x) = \lambda e^{-\lambda x}$$
It has an expected value of $\frac{1}{\lambda}$. If we use this model for a waiting time for a bus, then we expect to wait $\frac{1}{\lambda}$ minutes (for our model, we will use minutes, but it really doesn’t matter).
### I. Expected Value
We start by computing the expected value. Let $T$ have a distribution of $$P(T) = \lambda e^{-\lambda T}$$
We compute the expected value of $T$, $\langle T\rangle$ via
$$\langle T\rangle = \int_{T_{\text{min}}}^{T_{\text{max}}}T\cdot P(T) \text{d}T$$
We could wait a minimum of 0 minutes (the bus is there when we arrive), and could wait at most, well, infinity, because the bus may break and never arrive. The exponential distribution is defined for $T\in[0,\infty)$, so our integral becomes
$$\langle T\rangle = \int_{0}^{\infty}T\lambda e^{-\lambda T} \text{d}T$$
$$= -Te^{-\lambda T}+\int e^{-\lambda T}\text{d}T\hspace{4mm}|_{T=0}^{T=\infty}$$
$$= -Te^{-\lambda T}-\frac{1}{\lambda}e^{-\lambda T}\hspace{4mm}|_{T=0}^{T=\infty}$$
$$= 0 – (-\frac{1}{\lambda}) = \frac{1}{\lambda}$$
### II. Conditional Distributions Intro
Now we will examine a conditional distribution. This sounds confusing, but it’s a pretty easy concept to understand. Let’s say you have a red ball and a yellow ball, and you pick a ball from a hat, then pick the other ball out of the hat. What’s the probability that you pick the red ball second? Hopefully it’s obvious that it’s 50%. Well, what if I tell you that you pick the yellow ball first, now, what’s the probability that you pick the red ball second given that you pick the yellow ball first? 100%. This is what a conditional distribution is; the probability of some event occurring, given some prior knowledge.
In our case, our event is the probability that we wait $T$ minutes, and the knowledge we are given is that we’ve already waited $W$ minutes. Let’s say you are waiting for a bus, how long do you expect until the next bus comes given that you have already waited $W$ minutes and no bus has arrived?
We will use Bayes’ Theorem, which states that the probability of $A$ given $B$, or $P(A|B)$, can be expressed as
$$P(A|B) = \frac{P(A\hspace{1mm}\text{and}\hspace{1mm}B)}{P(B)}$$
### III. Conditional Distribution Calculations
In our case, we want the probability that we wait $T$ minutes given we’ve waited $W$ minutes already. It is very important to understand how to interpret the information given. By waiting $W$ minutes, we know that $T\geq W$. We know nothing else, other than the fact that $T$ must be greater than or equal to $W$, since we have already waited that long. Therefore,
$$P(B) = P(T\geq W) = \int_{W}^{\infty} \lambda e^{-\lambda T}\text{d}T$$
$$= -e^{-\lambda T}\hspace{4mm}|_{T=W}^{T=\infty}$$
$$= e^{-\lambda W}$$
Now, we need to calculate $P(A\hspace{1mm}\text{and}\hspace{1mm}B)$. But in fact, we don’t, we already know it! The probability that we wait $T$ minutes AND $T\geq W$ is just the probability that we wait $T$ minutes for $T\geq W$ and 0 for $T<W$.
Therefore, we have
$$P(T|T\geq W) = \frac{e^{-\lambda T}}{e^{-\lambda W}} \hspace{5mm} T\geq W$$
$$= e^{-\lambda (T-W)}\hspace{5mm} T\geq W$$
### IV. Conditional Expected Value
So, how long do we expect to wait, given that we’ve already waited $W$ minutes? The expected value can be calculated the same way as before.
$$\langle T|T\geq W\rangle = \int_{W}^{\infty}T\cdot P(T|T\geq W) \text{d}T$$
$$= \int_{W}^{\infty}T\lambda \frac{e^{-\lambda T}}{e^{-\lambda W}}\text{d}T$$
$$= e^{\lambda W}\int_{W}^{\infty}T\lambda e^{-\lambda T}\text{d}T$$
$$= e^{\lambda W}\cdot (-Te^{-\lambda T}-\frac{1}{\lambda}e^{-\lambda T}\hspace{4mm}|_{T=W}^{T=\infty})$$
$$= e^{\lambda W}\cdot (We^{-\lambda W}+ \frac{e^{-\lambda W}}{\lambda})$$
$$= W + \frac{1}{\lambda}$$
This shows that we expect to wait $W + \frac{1}{\lambda}$ minutes. What’s significant about this? Well, given no information, we expected to wait $\frac{1}{\lambda}$ minutes. Given we’ve already waited $W$ minutes, we now expect to wait $W + \frac{1}{\lambda}$ minutes. This means that we simply expect to wait another $\frac{1}{\lambda}$ minutes. No matter how long we have already waited, we are no more likely to encounter a bus any quicker than if we hadn’t been waiting. Pretty interesting, I think.
That’s all folks. Thanks for reading! | 1,424 | 4,591 | {"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": 2, "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} | 3.984375 | 4 | CC-MAIN-2018-13 | latest | en | 0.796188 |
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# Problem 42595. UICBioE240 problem 1.1
Solution 2961427
Submitted on 18 Sep 2020
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Fail
x = [1 2 3; 1 2 3; 1 2 3]; y_correct = [1 2 3; 1 2 3]; assert(isequal(your_fcn_name(x),y_correct))
Output argument "ans" (and maybe others) not assigned during call to "your_fcn_name". Error in Test1 (line 3) assert(isequal(your_fcn_name(x),y_correct))
2 Fail
x = [1;9;8]; y_correct = [1;8]; assert(isequal(your_fcn_name(x),y_correct))
Output argument "ans" (and maybe others) not assigned during call to "your_fcn_name". Error in Test2 (line 3) assert(isequal(your_fcn_name(x),y_correct))
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• ## Related Books
0 answersPost by Terry Kim on October 20, 2015why are we adding df and variances when we are actually calculating the DIFFERENCE? H(null): mu_(x-y) = 0 here it is 0 because it is the differencebut I don't get why we add the dfs and variances if its S_(x-y) isn't it also should be sqrt(s^2_(x)-s^2(y))?? 0 answersPost by Professor Son on November 12, 2014Just for students who happen to have a class with me, I don't emphasize s-pool a lot because typically it's more conservative to assume that they are separate. If you take a more advanced statistics class, you could learn about hypothesis testing that allows us to infer whether we can pool standard deviations together. 0 answersPost by Professor Son on November 12, 2014In the section about s-pool, I accidentally refer to SE as "sample error" but what I meant to say was "standard error."
### Confidence Intervals for the Difference of Two Independent Means
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
• Intro 0:00
• One Mean vs. Two Means 1:17
• One Mean vs. Two Means
• Notation 2:41
• A Sample! A Set!
• Mean of X, Mean of Y, and Difference of Two Means
• SE of X
• SE of Y
• Sampling Distribution of the Difference between Two Means (SDoD) 7:48
• Sampling Distribution of the Difference between Two Means (SDoD)
• Rules of the SDoD (similar to CLT!) 15:00
• Mean for the SDoD Null Hypothesis
• Standard Error
• When can We Construct a CI for the Difference between Two Means? 21:28
• Three Conditions
• Finding CI 23:56
• One Mean CI
• Two Means CI
• Finding t 29:16
• Finding t
• Interpreting CI 30:25
• Interpreting CI
• Better Estimate of s (s pool) 34:15
• Better Estimate of s (s pool)
• Example 1: Confidence Intervals 42:32
• Example 2: SE of the Difference 52:36
### Transcription: Confidence Intervals for the Difference of Two Independent Means
Hi and welcome to www.educator.com.0000
Today we are going to talk about confidence intervals for the difference of two independent means.0002
It is pretty important that there are for independent means because later we are going to go to non-independent or error means.0007
We have been talking about how to find confidence intervals and hypothesis testing for one mean.0013
We are going to talk about what that means for how we go about doing that for two means.0023
We are going to talk about what two means means?0029
We are going to talk a little bit about mu notation and we are going to talk about sampling distribution of the difference between two means.0032
I am going to shorten this, this is just means this is not like official or anything as SDOD0041
because it is long to say assembling distribution of the difference between two means, but that is what I mean.0048
We will talk about the rules of the SDOD and those are going to be very similar to the CLT (the central limit theorem) with just a few differences.0055
Finally, we all set it all up so that we can find and interpret the confidence interval.0066
One mean versus two means.0075
So far we have only looked at how to compare one mean against some population, but that is not usually how scientific studies go.0081
Most scientific studies involve comparisons.0091
Comparisons either between different kinds of water samples or language acquisition for babies versus babies who did not.0093
Scores from the control group versus the experimental group.0102
In science we are often comparing two different sets of the two different samples.0106
Two means really means two samples.0112
Here in the one mean scenarios we have one sample and we compare that to an idea in hypothesis testing0120
or we use that one sample in order to derive the potential population means.0132
But now we are going to be using two different means.0140
What do we do with those two means?0143
Do we just do the one sample thing two times or is there a different way?0145
Two means is a different story.0155
They are related but different story.0159
In order to talk about two means and two samples, we have to talk about some new notation.0162
This is totally arbitrary that we use x and y.0170
You could use j and k or m and n, whatever you want.0176
X and y is the generic variables that we use.0182
Feel free to use your favorite letters.0189
One sample will just be called x and all of its members in the sample will be x sub 1, x sub 2, x sub 3.0191
When we say x sub I, we are talking about all of these little guys.0203
The other sample we do not just call it x as well because we will get confused.0208
We cannot call it x2 because x sub 2 has a meaning.0216
What we call it is y.0221
Y sub i now means all of these guys.0224
We could keep them separate.0229
In fact this x and y is going to follow us from here on out.0232
For instance when we talk about the mean of x we call it the x bar.0236
What would be the mean of y?0241
Maybe y bar right.0243
That makes sense.0246
And if you call this b, this will be b bar.0247
It just follows you.0253
That is going to be x bar - y bar.0264
Now you could also do y bar - x bar, it does not matter.0267
But definitely mean by the difference between two means.0271
We could talk about the standard error of all whole bunch of x bars, standard error of x, standard error of y.0274
You could also talk about the variance of x and the variance of y.0285
You can have all kinds of thing they need something to denote that they are little different.0292
That standard error of x sort and another way you could write it is that we are not just talking about standard error.0298
When we say standard error, you need to keep in mind if we double-click on it that means the standard deviation of a whole bunch of means.0312
Standard deviation of a whole bunch of x bars.0322
Sometimes we do not have sigma so we cannot get this value.0328
We might have to estimate sigma from s and that would be s sub x bar.0334
If we wanted to know how to get this that would just be s sub x.0345
Notice that is different from this, but this is the standard error and this is the actual standard deviation of your sample ÷ √n.0353
Not just n the n of your sample x.0367
In this way we could perfectly denote that we are talking about the standard error of the x, the standard deviation of the x, and the n(x).0372
You could do the same thing with y.0387
The standard error of y, if you had sigma, you can just call it sigma sub y bar because it is the standard deviation of a whole bunch of y bars.0390
Or if you do not have sigma you could estimate sigma and use s sub y bar.0402
Instead of just getting the standard deviation of x we would get the standard deviation of y and divide that by √n Sub y.0411
It makes everything a little more complicated because now I have to write sub x and sub y after everything.0423
But it is not hard because the formula if you look remains exactly the same.0430
The only thing that is different now is that we just add a little pointer to say we are talking0438
about the standard deviation of our x sample or standard deviation of our y sample.0446
Even this looks a little more complicated, deep down at the heart of the structure it is still the standard error equals standard deviation of the sample ÷√n.0452
Let us talk about what this means, the sampling distribution of the difference between two means.0466
When we talk about the population right now we do not know anything about the population.0480
We do not know if it is uniform, the mean, standard deviation.0491
Let us call this one x and this one y.0500
From this x population and this y population we are going to draw out samples and0507
create the sampling distribution and that is the SDOM (the sampling distribution of the mean).0514
Here is a whole bunch of x bars and here is a whole bunch of y bars.0522
Thanks to the central limit theorem if we have big enough n and all that stuff then we know that we could assume normality.0530
Here we know a little bit more than we know about the population.0540
We know that in the SDOM, the standard error, I will write s from here because0545
we are basically going to assume real life examples when we do not have the population standard deviation.0557
The only time we get that is like in problems given to you in statistics textbook.0565
We will call it s sub x bar and that can be the standard deviation of x/√n sub x.0570
We know those things and we also know the standard error of y and that is going to be the standard deviation of y ÷ √n sub y.0585
Because of that you do not write s sub y again because that would not make sense that0601
the standard error would equal the standard error over into something else.0607
That would not quite make sense.0612
You want to make sure that you keep this s special and different because standard error0614
is talking about entirely different idea than the standard deviation.0621
Now that we have two SDOM if we just decided to do this then we would not need to know anything new about creating a confidence interval of two means.0625
You what just create two separate confidence intervals like you consider that x bar,0638
consider that y bar, construct a 95% confidence interval for both of these guys.0644
You are done.0649
Actually what we want is not a sampling distribution of two means and get two sampling distributions.0650
We would like one sampling distribution of the difference between two means.0661
That is what I am going to call SDOD.0668
Here is what you have to imagine, in order to get the SDOM what we had to do is go to the population and draw out samples of size n and plot the means.0671
Do that millions and millions of times.0682
That is what we had to do here.0685
We also have to do that here, we want the entire population of y pulled out samples and plotted the means until we got this distribution of means.0687
Imagine pulling out a mean from here randomly and then finding the difference of those means and plotting that difference down here.0699
Do that over and over again.0715
You would start to get a distribution of the difference of these two means.0718
You would get a distribution of a whole bunch of x bar - y bar.0727
That is what this distribution looks like and that distribution looks normal.0734
This is actually one of the principle of probability distributions that we have covered before.0742
I think we have covered it in binomial distributions.0747
I know this is not a binomial distribution but the same principles apply here where if you draw from two normally distributed population0749
and subtract those from each other you will get a normal distribution down here.0764
We have this thing and what we now want to find is not just the mu sub x bar or mu sub y bar, that is not what we want to find.0769
What we want to find is something like the mu of x bar - y bar because this is our x bar - y bar and we want to find the mu of that.0783
Not only that but we also want to find the standard error of this thing.0796
I think we can figure out what that y might be.0800
At least the notation for it, that would be the standard error.0807
Standard error always have these x bar and y bar things.0812
This is how you notate the standard deviation of x bar - y bar and that is called0817
the standard error of the difference and that is a shortcut way of saying x bar - y bar.0829
We could just say of the difference.0837
You can think of this as the sampling distribution of a whole bunch of differences of means.0839
In order to find this, again it draws back on probability principles but actually let us go to variance first.0845
If we talk about the variance of this distribution that is going to be the variance of x bar + the variance of y bar.0856
If you go back to your probability principles you will see why.0869
This from this we could actually figure out standard error by square rooting both sides.0874
We are just building on all the things we have learned so far.0881
We know population.0888
We know how to do the SDOM.0889
We are going to use two SDOM in order to create a sampling distribution of differences.0891
Let us talk about the rules of the SDOD and these are going to be very, very similar to the CLT.0898
The first thing is this, if SDOM for x and SDOM for y are both normal then the SDOD is going to be normal too.0909
Think about when these are normal?0919
These are normal if your population is normal.0922
That is one case where it is normal.0924
This is also normal when n is large.0927
In certain cases, you can assume that the SDOM is normal, and if both of these have met those conditions,0929
then you can assume that the SDOD is normal too.0939
We have conditions where we can assume it is normal and they are not crazy.0942
There are things we have learned.0949
It is always shape, center, spread.0953
What about the mean for the SDOD?0956
That is going to be characterized by mu sub x bar - y bar.0959
That is the idea.0972
Let us consider the null hypothesis and in the null hypothesis usually the idea is they are not different like nothing stands out.0975
Y does not stand out from x and x does not stand out from y.0987
That means we are saying very similar.0991
If that is the case we are saying is that when we take x bar – y bar and do it over and over again, on average, the difference should be 0.0994
Sometimes the difference will be positive.1009
Sometimes the difference will be negative.1012
But if x and y are roughly the same then we should actually get a difference of 0 on average.1014
For the null hypothesis that is 0.1022
The so what would be the alternative hypothesis?1027
Something like the mean of the SDOD is not 0.1031
This is in the case where x and y assume to be same.1037
That is always with the null hypothesis.1051
They assume to be the same.1055
They are not significantly different from each other.1056
That is the mean of the SDOD.1058
In order to calculate standard error, you have to know whether these are independent samples or not.1064
Remember to go back to sampling, independent samples is where you know that these two1073
come from different populations and the picking one does not change the probabilities of picking the other.1079
As long as these are independent samples, then you can use these ideas of the standard error.1089
As we said before, it is easier when I think about the variance of the SDOD first because that rule is quite easy.1096
The variance of SDOD, so the variance is going to be just the variance of the SDOM + the variance of the SDOM for the other guy.1105
And notice that these are the x bars and the y bars.1121
These are for the SDOM they are not for the populations nor the samples.1131
From here what you can do is sort of justice derive the standard error formula.1137
We can just square root both sides.1149
If you wanted to just get standard error, then it would just be the square root of adding each of these variances together.1153
Let us say you double-click on this guy, what is inside of him?1168
He is like a stand in for just the more detailed idea of s sub x / n sub x.1175
Remember when we talk about standard error we are talking about standard error = s / √n.1193
The variance of the SDOM =s2 /n.1205
If you imagine squaring this you would get s/n but we need the variance.1210
We need to add the variances together before you square root them.1220
Here we have the variance of y / n sub y.1224
You could write it either like this or like this.1235
They mean the same thing.1240
They are perfectly equivalent.1242
You do have to remember that when you have this all under the square root sign,1244
the square root sign acts like a parentheses so you have to do all of this before you square root.1253
That is standard error.1261
I know it looks a little complicated, but they are just all the principles we learned before,1265
but now we have to remember does it come from x or does come from y distributions.1273
That is one of the few things you have to ask yourself whenever we deal with two samples.1279
Now that we know the revised CLT for this sampling distribution of the differences,1287
now we need to ask when can we construct a confidence interval for the difference between two means?1298
Actually these conditions are very similar to the conditions that must be met when we construct an SDOM.1306
There are a couple of differences because we are dealing with two samples.1314
The three conditions have to be met.1318
All three of these have to be checked.1321
One is independence, the notion of independence.1323
The first is this, the two samples we are randomly and independently selected from two different populations.1329
That is the first thing you have to meet before you can construct this confidence interval.1340
The second thing is this, this is the assumption for normality.1348
How do we know that the SDOD is normal.1355
It needs to be reasonable to assume that both populations that the sample comes from the population are normal or your sample size is sufficiently large.1358
These are the same ones that apply to the CLT.1372
This is the case where we can assume normality for the SDOM but also the SDOD.1376
In number 3, in the case of sample surveys the population size should be at least 10 times larger than the sample size for each sample.1384
The only reason for this is we talked before about replacement, a sampling with replacement versus sampling not with replacement.1397
Well, whenever you are doing a sample you are technically not having replacement1409
but if your population is large enough then this condition actually makes it so that you could assume that it works pretty much like with replacement.1413
If you have many people then it does not matter.1427
That is the replacement rule.1430
Finally, we could get to actually finding the confidence interval.1433
Here is the deal, with confidence interval let us just review how we used to do it for one mean.1444
One mean confidence interval.1450
Back in the day when we did one mean and life was nice and what we would do is often take the SDOM1455
and assume that the x bar, the sample mean is at the center of it and then we construct something like 95% confidence interval.1466
These are .025 because if this is 95% and symmetrical there is 5% leftover but it needs to be divided on both sides.1484
What we did was we found these boundary values by using this idea, this middle + or – how many standard errors you are away.1496
We used either t or z.1525
I’m just going to use t from now on because usually we are not given the standard deviation of the population × the standard error.1529
That was the basic idea from before and that would give us this value, as well as this value.1530
We could say we have 95% confidence that the population mean falls in between these boundaries.1537
That is for one mean.1545
In this case, we are not going to be calculating using the SDOM anymore.1549
We are going to use the SDOD.1560
If this mean is going to be x bar, this sample mean then you can probably assume that1562
it might be something as simple as a difference between the two means.1575
That is what we assume to be the center of the SDOD.1580
Just like before, whatever level of confidence you need.1583
If it is 99% you have 1% left over on the side.1593
You have to divide that 1% in half so .5% for the side and .5% for that side.1598
In this case, let us just keep the 95%.1603
What we need to do is find these borders.1611
What we can to just use the exact same idea again.1618
We could use that exact same idea because we can find the standard error of this distribution.1624
We know what that is.1629
Let me write this out.1631
We will write s sub x bar.1640
We can actually just translate these ideas into something like this.1645
That would be taking this, adding or subtracting how many jumps away you are, like the distance you are away.1652
That would be something like x bar - y bar but instead of just having x in the middle we have this thing in the middle.1661
+ or – the t remains the same, t distributions but we have to talk about how to find degrees of freedom for this guy.1670
The new SE, but now this is the SE of the difference.1680
How do we write that?1691
X bar - y bar + or - the t × s sub x bar = y bar.1694
If we wanted to we could take all that out into the square root of variance of the SDOM for x and variance of SDOM for y.1707
We could unpack all of this if we need to but this is the basic idea of the confidence interval of two means.1719
In order to do this I want you to notice something.1727
Here we need to find t and because we need to find t we need to find degrees of freedom1732
but not just any all degrees of freedom because right now we have 2 degrees of freedom.1740
Degrees of freedom for x and degrees of freedom for y.1744
We need a degrees of freedom for the difference.1747
That is what we need.1751
Let us figure out how to do that.1753
We need to find degrees of freedom.1756
We know how to find degrees of freedom for x, that is straightforward.1760
That is n sub x -1 and degrees of freedom for y is just going to be n sub y -1.1764
Life is good.1771
Life is easy.1772
How do we find the degrees of freedom for the difference between x and y?1773
That is actually going to just be the degrees of freedom for x + degrees of freedom for y.1778
If we want to unpack this, if you think about double-clicking on this and get that.1792
N sub x - 1 + n sub y -1.1797
I am just putting that parentheses as you could see the natural groupings but obviously you could1804
do them in any order because you could just do them straight across this adding and subtracting.1810
They all have the same order of operation.1816
That is degrees of freedom and once you have that then you can easily find the t.1820
Look it up in the back of your book or you can do it in Excel.1830
Let us interpret confidence interval.1833
We have the confidence interval let us think about how to say what we have found.1837
I am just going to briefly draw that picture again because this picture anchors my thinking.1844
Here is our difference of means.1852
When you look at this t, think of this as the difference of two means.1858
I guess I could write DOTM but that would just be DOM.1863
Here what we found, if we find something like a 95% confidence interval that means we have found these boundaries.1869
We say something like this.1887
The actual difference of the two means of the real population, of the population x and y.1891
The real population that they come from should be within this interval 95% of the time or something like1919
we have 95% confidence that the actual difference between means of the population of x and population of y should be within this interval.1939
That comes from that notion that this is created from the SDOM.1950
Remember the SDOM, the CLT says that their means or the means of the population.1955
We are getting the population means drop down to the SDOM and from the SDOM we get this.1962
Because of that we could actually make a conclusion that goes back to the population.1970
Let us think about if 0 is not in between here.1980
Remember the null hypothesis when we think about two means is going to be something like this.1987
That the mu sub x bar – y bar is going to be equal to 0.1993
This is going to mean that on average when you subtract these two things the average is going to be 0.1998
There is going to be no difference on average.2004
The alternative hypothesis should then be the mean of these differences should not be 0.2006
They are different.2015
If 0 is not within this confidence interval then we have very little reason to suspect that this would be true.2016
It is a very little reason to think that this null hypothesis is true.2026
We could also say that if we do not find 0 in our confidence interval that we might in my hypothesis testing be able to also reject the null hypothesis.2030
But we will get to that later.2040
I just wanted to show you this because the confidence interval here is very tightly linked to the hypothesis testing part.2042
They are like two side of the same coin.2050
That universe is fairly straightforward but I feel like I need to cover one other thing because sometimes this is emphasized in some books.2052
Some teachers emphasize this over other teachers and so I'm going to talk to you about SPOOL because this will come up.2065
One of the things I hope you noticed was that in order to find our estimate of SDOM,2076
in order to find the SDOD sample error what we did was we took the variance of one SDOM2085
and added that to the variance of the other SDOM and square root the whole thing.2106
Let me just write that here.2110
The s sub x bar - y bar is the square root of one the variances + the variance of the other SDOM.2111
Here what we did was let us just treat them separately and then combine them together.2129
That is what we did.2137
Although this is an okay way of doing it, in doing this we are assuming that they might have different standard deviations.2138
The two different populations might have two different standard deviations.2154
Normally, that is a reasonable assumption to make.2159
Very few populations have the exact standard deviation.2162
For the vast majority of time because we just assumed if you come from two different population you probably have two different standard deviations.2166
This is pretty reasonable to do like 98% of the time.2177
The vast majority of time.2182
But it is actually is not as good as the estimate of this value then, if you had just used up a POOL version of the standard deviation.2184
Here is what I mean.2198
Now we are saying, we are going to create the standard deviation of x.2198
You are going to be what we used to create the standard deviation of y.2206
Just of not make that explicit.2210
I am going to write this out so that you could actually see the variance of x and the variance of y.2213
We use x to create this guy and we use y to create that guy and they remain separate.2228
This is going to take a little reasoning.2235
Think back if you have more data then your estimate of the population standard deviation is better, more data more accurate.2239
Would not it be nice if we took all the guys from the x pool and all the guys from the y pull and put them together.2253
Together let us estimate the standard deviation.2262
Would not that be nice?2267
Then we will have more data and more data should give us a more accurate estimate of the population.2268
You can do that but only in the case that you have reason to think that the population of x has a similar standard deviation to the population of y.2278
If you have a reason to think they are both normally distributed.2293
Let us say something like this.2299
If you have reason to believe that the population x and y have similar standard deviation2303
then you can pull samples together to estimate standard deviation.2324
You can pull them together and that is going to be called spull.2347
There are very few populations that you can do this for.2351
One thing something like height of males and females, height tends to be normally distributed and we know that.2357
Height of Asians and Latinos or something, but there are a lot of examples that come to mind where you could do this.2365
That is why some teachers do not emphasize it but I know that some others do so.2374
That is why I want to definitely go over it.2378
How do you get spull and where does it come in?2380
Here is the thing, in order to find Spull, what we would do is we would substitute in spull for s sub x and s sub y.2384
Instead of two separate estimates of standard deviations use Spull.2396
We will be using Spull2.2408
How do we find Spull2?2411
In order to find Spull2, what you would do is you would add up all of the sum of squares.2415
The sum of squares of x and sum of squares of y, add them together and then divide by the sum of all the degrees of freedom.2432
If I double-click on this, this would mean the sum of squares of x + the sum of squares of y ÷ degrees of freedom x + degrees of freedom y.2442
This is what you need only to do in order to find Spull and then what you would do is substitute in s(x)2 and s sub y2.2457
That is the deal.2469
In the examples that are going to follow, I am not going to use Spull because there is very little reason usually to assume that we can use Spull.2471
And but a lot of times you might hear this phrase assumption of homogeneity of variance.2483
If you could assume that these guys have a similar variance, if you can assume2490
they have similar homogeneous variance then you can use Spull.2502
For the most part, for the vast majority of time you cannot assume homogenous variance.2508
Because of that we will often use this one.2514
However, I should say that some teachers do want you to be able to calculate both.2517
That is the only thing.2525
Finally I should just say one thing.2528
Usually this works just as well as pull.2531
It is just that there are sometimes we get more of a benefit from using this one.2536
If worse comes to worse, and after the statistics class you are only remember this one.2543
If not all you are pretty good to go.2548
Let us go on to some examples.2551
A random sample of American college students was collected to examine quantitative literacy.2556
How good they are in reasoning about quantitative ideas.2562
The survey sampled 1,000 students from four-year institutions, this was the mean and standard deviation.2565
800 from two-year institutions, here is the mean and standard deviations.2571
Are the conditions for confidence intervals met?2576
Also construct a 95% confidence interval and interpret it.2581
Let us think about the confidence interval requirements.2586
First is independent random samples.2593
It does say random sample right and these are independent populations.2596
There are very few people going to both of them at the same time.2606
First one, check.2609
Second one, can we assume normality either because of the large n or because we know that both these populations are originally normally distributed?2612
Well, they have pretty large n, so I am going to say number 2 check.2622
Number 3, is this sample roughly sampling with replacement?2627
And although 1000 students seem a lot, there are a lot of college students.2635
I am pretty sure that this meets that qualification as well.2640
Go ahead and construct the 95% confidence interval.2643
Well, it helped to start off with the drawing of SDOD just to anchor my thinking.2648
And this mu sub x bar - y bar we could assume that this is x bar - y bar.2656
That is what we do with confidence intervals.2667
We use what we have from the samples to figure out what the population might be.2670
We want to construct a 95% confidence interval.2678
That is going to be .025 and then maybe it will help us to figure out the degrees of freedom so that we will know the t value to use.2685
Let us figure out degrees of freedom.2703
It is going to be the degrees of freedom for x and I will call x the four-year university guys and the degrees of freedom for y the two-year university guys.2706
That is going to be 999 + 799 and so it is going to be 1800 - 2 = 1798.2718
We have quite large degrees of freedom and let us find the t for this place.2747
We need to find is this and this.2755
Let us find the t first.2760
This is the raw score, this is the t, and let me delete some of the stuff.2765
I will just put x bar - y bar in there and we can find that later.2772
The t is going to be the boundaries for this guy and the boundaries for this guy.2782
What is our t value?2788
You can look it up in the back of your book or you could do it in Excel.2790
Here we want to put in the t in because we have the probability and remember this one2799
wants two tailed probability .05 and the degrees of freedom which is 1798 = 1.896.2806
We will put 1.961 just to distinguish it.2819
Let us write down our confidence interval formula and see what we can do.2831
Confidence interval is going to be x bar - y bar.2838
The middle of this guy + or - t × standard error of this guy.2844
That is going to be s sub x bar - y bar.2854
It would be probably helpful to find this thing.2858
X bar - y bar.2862
X bar - y bar that is going to be 330 – 310.2868
Let us also try to figure out the standard error of SDOD which is s sub x bar - y bar.2883
What I'm trying to do is find this guy.2911
In order to find that guy let us think about the formula.2918
I'm just writing this for myself.2921
The square root of the variance of x bar + the variance of y bar .2925
We do not have the variance of x bar and y bar.2937
Let us think about how to find the variance of x bar.2943
The variance of x bar is going to be s sub s2 ÷ n sub x.2947
The variance of y bar is going to be the variance of y2 ÷ n sub y.2959
I wanted to write all these things out just because I need to get to a place where finally I can put in s.2977
Finally, I can do that.2986
This is s sub x and this is s sub y.2988
I can put in 1112 ÷ n sub x which is 1000 and I could put in the standard deviation of y2 ÷ 800.2990
I have these two things and what I need to do is go back up here and add these and square root them.3017
Square root this + this.3028
I know that this equal that.3034
We have our standard error, which is 4.49 and this is 20 + or - 1.961.3038
Now I could do this.3064
I will going to take that in my calculator as well.3066
The confidence interval for the high boundary is going to be 20 + 1.961 × 4.493069
and the confidence interval for the low boundary is going to be that same thing.3085
I am just going to change that into subtraction.3097
11.20.3101
Let me move this over.3105
It is going to be 28.8.3110
Let me get the low end first.3117
The confidence interval is from about 11.2 through 28.8.3121
We have to interpret it.3127
This is the hardest part for a lot of people.3130
We have to say something like this.3133
The true difference between the population means 95% of the time is going to fall in between these two numbers.3136
Or we have 95% confidence that the true difference between the two population means fall in between these two numbers.3146
Let us go to example 2.3154
This will be our last example.3157
If the sample size of both samples are the same, what would be the simplified formula for standard error of the difference?3159
If in addition, the standard deviation of both samples are the same, what would be the simplified formula for standard error of the difference?3167
This is just asking depending on how similar the two examples are can we simplify a formula for standard error.3175
We can.3183
Let us write the actual formula out so that would just x bar – y bar = square root of the variance of x bar + variance of y bar.3184
If we double-click on these guys that would give the variance of x / n sub x + the variance of y / n sub y.3207
It is asking, what if the sample size for both samples are the same?3223
What would be the simplified formula?3230
That is saying that if n sub x = n sub y then what would be this?3231
We can get the variance of x + variance of y / n.3240
Because the n for each of them should be the same.3251
This would make it a lot simpler.3254
If in addition a standard deviation of both samples are the same right then this would mean that3260
because the standard deviation is the same then the variances are the same.3272
That would be that case.3276
If in addition this was the case, then you would just get 2 × s2 whatever the equal variances /n.3279
That would make it a simple formula.3294
That would make life a lot easier but that is not always the case.3298
If it is you know that it will be simple for you.3303
That is it for the confidence intervals for the difference between two means.3307
Thank you for using www.educator.com.3312 | 9,013 | 36,433 | {"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-2017-47 | latest | en | 0.893372 |
https://oeis.org/A016760 | 1,624,511,958,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488551052.94/warc/CC-MAIN-20210624045834-20210624075834-00372.warc.gz | 402,136,007 | 3,947 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
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A016760 a(n) = (2*n+1)^8. 3
1, 6561, 390625, 5764801, 43046721, 214358881, 815730721, 2562890625, 6975757441, 16983563041, 37822859361, 78310985281, 152587890625, 282429536481, 500246412961, 852891037441, 1406408618241, 2251875390625, 3512479453921, 5352009260481, 7984925229121, 11688200277601 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(n) = A016756(n)^2. - Michel Marcus, Dec 26 2016 G.f.: -(1+6552*x +331612*x^2 +2485288*x^3 +4675014*x^4 +2485288*x^5 +331612*x^6 +6552*x^7 +x^8)/(x-1)^9 . - R. J. Mathar, Jul 07 2017 Sum_{n>=0} 1/a(n) = 17*Pi^8/161280 (A300710). - Amiram Eldar, Oct 11 2020 Product_{n>=1} (1 - 1/a(n)) = Pi*cosh(Pi/2)*(cos(Pi/sqrt(2)) + cosh(Pi/sqrt(2)))/32. - Amiram Eldar, Jan 28 2021 MATHEMATICA Table[(2*n+1)^8, {n, 0, 30)] (* G. C. Greubel, Sep 15 2018 *) PROG (MAGMA) [(2*n+1)^8: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011 (Maxima) A016760(n):=(2*n+1)^8\$ makelist(A016760(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */ (PARI) vector(30, n, n--; (2*n+1)^8) \\ G. C. Greubel, Sep 15 2018 CROSSREFS Cf. A016756, A300710. Sequence in context: A017500 A017632 A209510 * A203652 A016772 A059980 Adjacent sequences: A016757 A016758 A016759 * A016761 A016762 A016763 KEYWORD nonn,easy AUTHOR STATUS approved
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Last modified June 24 01:07 EDT 2021. Contains 345404 sequences. (Running on oeis4.) | 761 | 1,954 | {"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} | 3.109375 | 3 | CC-MAIN-2021-25 | latest | en | 0.499214 |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/507/2/j/ | 1,696,344,828,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511106.1/warc/CC-MAIN-20231003124522-20231003154522-00190.warc.gz | 942,069,962 | 52,755 | # Properties
Label 507.2.j Level $507$ Weight $2$ Character orbit 507.j Rep. character $\chi_{507}(316,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $54$ Newform subspaces $9$ Sturm bound $121$ Trace bound $10$
# Related objects
## Defining parameters
Level: $$N$$ $$=$$ $$507 = 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 507.j (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$9$$ Sturm bound: $$121$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$2$$, $$5$$
## Dimensions
The following table gives the dimensions of various subspaces of $$M_{2}(507, [\chi])$$.
Total New Old
Modular forms 150 54 96
Cusp forms 94 54 40
Eisenstein series 56 0 56
## Trace form
$$54 q - q^{3} + 30 q^{4} + 3 q^{7} - 27 q^{9} + O(q^{10})$$ $$54 q - q^{3} + 30 q^{4} + 3 q^{7} - 27 q^{9} - 4 q^{10} + 6 q^{11} + 12 q^{12} - 8 q^{14} - 6 q^{15} - 20 q^{16} - 4 q^{17} - 6 q^{19} - 12 q^{20} + 8 q^{22} - 10 q^{23} - 34 q^{25} + 2 q^{27} - 6 q^{28} + 14 q^{29} - 4 q^{30} + 6 q^{33} + 10 q^{35} + 30 q^{36} + 8 q^{38} - 24 q^{40} + 12 q^{41} - 13 q^{43} - 6 q^{45} + 4 q^{48} + 24 q^{49} + 8 q^{51} - 56 q^{53} - 12 q^{56} + 6 q^{59} + 17 q^{61} - 16 q^{62} - 3 q^{63} - 32 q^{64} - 8 q^{66} - 15 q^{67} + 24 q^{68} + 2 q^{69} + 18 q^{71} + 12 q^{74} - q^{75} + 12 q^{76} + 20 q^{77} - 2 q^{79} + 24 q^{80} - 27 q^{81} - 20 q^{82} - 6 q^{84} - 2 q^{87} - 24 q^{88} - 12 q^{89} + 8 q^{90} - 32 q^{92} - 3 q^{93} + 12 q^{94} - 32 q^{95} + 9 q^{97} + O(q^{100})$$
## Decomposition of $$S_{2}^{\mathrm{new}}(507, [\chi])$$ into newform subspaces
Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
507.2.j.a $2$ $4.048$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$1$$ $$0$$ $$-6$$ $$q+(-1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
507.2.j.b $2$ $4.048$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$3$$ $$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+\cdots$$
507.2.j.c $2$ $4.048$ $$\Q(\sqrt{-3})$$ None $$3$$ $$1$$ $$0$$ $$6$$ $$q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
507.2.j.d $4$ $4.048$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
507.2.j.e $4$ $4.048$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
507.2.j.f $8$ $4.048$ $$\Q(\zeta_{24})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+(1-\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{4}+\cdots$$
507.2.j.g $8$ $4.048$ 8.0.1731891456.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2+3\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$$
507.2.j.h $12$ $4.048$ 12.0.$$\cdots$$.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$
507.2.j.i $12$ $4.048$ 12.0.$$\cdots$$.1 None $$0$$ $$6$$ $$0$$ $$0$$ $$q+(-\beta _{1}+\beta _{8}+2\beta _{11})q^{2}+\beta _{7}q^{3}+\cdots$$
## Decomposition of $$S_{2}^{\mathrm{old}}(507, [\chi])$$ into lower level spaces
$$S_{2}^{\mathrm{old}}(507, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 2}$$ | 1,676 | 3,378 | {"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} | 2.625 | 3 | CC-MAIN-2023-40 | latest | en | 0.341203 |
http://bootmath.com/if-fx-0-for-all-x-in-mathbbq-is-f-constant.html | 1,534,539,861,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221212910.25/warc/CC-MAIN-20180817202237-20180817222237-00393.warc.gz | 70,173,213 | 6,252 | # If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
• Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
#### Solutions Collecting From Web of "If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?"
[I use a construction given by Rooij and Schikhof in A second course on real functions, Example 13.2.]
Let $\Omega$ be the collection of all continuous functions $\omega : \mathbb{R} \to (0, + \infty)$ having the following property: for all $a<b \in \mathbb{R}$, $$\left| \frac{1}{b-a} \int_a^b \omega(x) dx \right| \leq 4 \omega(a).$$
Let $\alpha_1,\beta_1,\alpha_2,\beta_2,\dots$ be pairwise distinct real numbers. Then the authors show that one can construct $\omega_1,\omega_2, \dots \in \Omega$ such that for each $n \in \mathbb{N}$ we have, writing $f_n:= \omega_1+ \cdots + \omega_n$:
$$f_n \leq \left( \frac{n}{n+1} \right)^2, \ \ f_n(\alpha_i) \geq \left( \frac{n-1}{n} \right)^2, \ \ f_n(\beta_i) < \frac{n}{n+1} \cdot \frac{i}{i+1}.$$
Afterward, they show that $\displaystyle F(x):= \sum\limits_{i \geq 1} \int_0^x \omega_i(t)dt$ is well-defined and differentiable with $F'(x)= \sum\limits_{i \geq 1} \omega_i(x)$. In particular, because $F'(x)= \lim\limits_{n \geq + \infty} f_n(x)$, we have $$F'(\alpha_i)=1, \ \ F'(\beta_i) \leq \frac{i}{i+1}.$$
Let $f$ denote the function given by the construction above with $\{\alpha_1,\alpha_2,\dots \}= \mathbb{Q}$ and $\{\beta_1= \sqrt{2}, \beta_2, \dots \}$. Let $g$ denote the function given by the consruction above with $\{A_1= \sqrt{2},A_2, \dots\}= \mathbb{Q} \cup \{\sqrt{2} \}$ and $\{B_1, B_2, \dots\}$.
Let $G:=f-g$. Then $G'(q)=0$ for all $q \in \mathbb{Q}$ and $G'(\sqrt{2}) \leq \frac{1}{2}-1=- \frac{1}{2} <0$. In particular, from the mean value theorem, we deduce that $G$ is not constant since its derivate does not vanish everywhere.
For your second question, it is a consequence of Darboux’s theorem that a function is constant if its derivative vanish on $\mathbb{R} \backslash \mathbb{Q}$.
Indeed, $f'(\mathbb{R})$ has to be an interval $I$, but $f'(\mathbb{R} \backslash \mathbb{Q})= \{0\}$, so $I$ is in fact countable: necessarily, $I$ is the singleton $\{0\}$, that is $f’$ vanish everywhere. Now, it may be deduced that $f$ is constant from the mean value theorem.
It’s false, you can find an answer here. (French)
The proposed function is
$$g(x)= \inf\{d(x,E_k)^{1/k}: k\in \mathbb{N}\}$$
where $E_k$ is the closed discrete set $\{p/2^k : p\in \mathbb{Z}\}$ | 935 | 2,530 | {"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} | 3.859375 | 4 | CC-MAIN-2018-34 | latest | en | 0.640152 |
https://uk.mathworks.com/help/ident/ug/represent-nonlinear-dynamics-using-matlab-file-for-grey-box-estimation.html | 1,716,242,538,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058313.71/warc/CC-MAIN-20240520204005-20240520234005-00775.warc.gz | 550,034,822 | 22,855 | # Represent Nonlinear Dynamics Using MATLAB File for Grey-Box Estimation
This example shows how to construct, estimate and analyze nonlinear grey-box models.
Nonlinear grey-box (idnlgrey) models are suitable for estimating parameters of systems that are described by nonlinear state-space structures in continuous or discrete time. You can use both idgrey (linear grey-box model) and idnlgrey objects to model linear systems. However, you can only use idnlgrey to represent nonlinear dynamics. To learn about linear grey-box modeling using idgrey, see Building Structured and User-Defined Models Using System Identification Toolbox.
In this example, you model the dynamics of a linear DC motor using the idnlgrey object.
Figure 1: Schematic diagram of a DC-motor.
If you ignore the disturbances and choose y(1) as the angular position [rad] and y(2) as the angular velocity [rad/s] of the motor, you can set up a linear state-space structure of the following form (see Ljung, L. System Identification: Theory for the User, Upper Saddle River, NJ, Prentice-Hall PTR, 1999, 2nd ed., p. 95-97 for the derivation):
d | 0 1 | | 0 |
-- x(t) = | | x(t) + | | u(t)
dt | 0 -1/tau | | k/tau |
| 1 0 |
y(t) = | | x(t)
| 0 1 |
tau is the time-constant of the motor in [s] and k is the static gain from the input to the angular velocity in [rad/(V*s)]. See Ljung (1999) for how tau and k relate to the physical parameters of the motor.
1. Load the DC motor data.
2. Represent the estimation data as an iddata object.
z = iddata(y, u, 0.1, 'Name', 'DC-motor');
3. Specify input and output signal names, start time and time units.
z.InputName = 'Voltage';
z.InputUnit = 'V';
z.OutputName = {'Angular position', 'Angular velocity'};
z.Tstart = 0;
z.TimeUnit = 's';
4. Plot the data.
The data is shown in two plot windows.
figure('Name', [z.Name ': Voltage input -> Angular position output']);
plot(z(:, 1, 1)); % Plot first input-output pair (Voltage -> Angular position).
figure('Name', [z.Name ': Voltage input -> Angular velocity output']);
plot(z(:, 2, 1)); % Plot second input-output pair (Voltage -> Angular velocity).
Figure 2: Input-output data from a DC-motor.
### Linear Modeling of the DC-Motor
1. Represent the DC motor structure in a function.
In this example, you use a MATLAB® file, but you can also use C MEX-files (to gain computational speed), P-files or function handles. For more information, see Creating IDNLGREY Model Files.
The DC-motor function is called dcmotor_m.m and is shown below.
function [dx, y] = dcmotor_m(t, x, u, tau, k, varargin)
% Output equations.
y = [x(1); ... % Angular position.
x(2) ... % Angular velocity.
];
% State equations.
dx = [x(2); ... % Angular velocity.
-(1/tau)*x(2)+(k/tau)*u(1) ... % Angular acceleration.
];
The file must always be structured to return the following:
Output arguments:
• dx is the vector of state derivatives in continuous-time case, and state update values in the discrete-time case.
• y is the output equation
Input arguments:
• The first three input arguments must be: t (time), x (state vector, [] for static systems), u (input vector, [] for time-series).
• Ordered list of parameters follow. The parameters can be scalars, column vectors, or 2-dimensional matrices.
• varargin for the auxiliary input arguments
2. Represent the DC motor dynamics using an idnlgrey object.
The model describes how the inputs generate the outputs using the state equation(s).
FileName = 'dcmotor_m'; % File describing the model structure.
Order = [2 1 2]; % Model orders [ny nu nx].
Parameters = [1; 0.28]; % Initial parameters. Np = 2.
InitialStates = [0; 0]; % Initial initial states.
Ts = 0; % Time-continuous system.
nlgr = idnlgrey(FileName, Order, Parameters, InitialStates, Ts, ...
'Name', 'DC-motor');
In practice, there are disturbances that affect the outputs. An idnlgrey model does not explicitly model the disturbances, but assumes that these are just added to the output(s). Thus, idnlgrey models are equivalent to Output-Error (OE) models. Without a noise model, past outputs do not influence prediction of future outputs, which means that predicted output for any prediction horizon k coincide with simulated outputs.
3. Specify input and output names, and units.
set(nlgr, 'InputName', 'Voltage', 'InputUnit', 'V', ...
'OutputName', {'Angular position', 'Angular velocity'}, ...
'TimeUnit', 's');
4. Specify names and units of the initial states and parameters.
nlgr = setinit(nlgr, 'Name', {'Angular position' 'Angular velocity'});
nlgr = setpar(nlgr, 'Name', {'Time-constant' 'Static gain'});
nlgr = setpar(nlgr, 'Unit', {'s' 'rad/(V*s)'});
You can also use setinit and setpar to assign values, minima, maxima, and estimation status for all initial states or parameters simultaneously.
5. View the initial model.
a. Get basic information about the model.
The DC-motor has 2 (initial) states and 2 model parameters.
size(nlgr)
Nonlinear grey-box model with 2 outputs, 1 inputs, 2 states and 2 parameters (2 free).
b. View the initial states and parameters.
Both the initial states and parameters are structure arrays. The fields specify the properties of an individual initial state or parameter. Type help idnlgrey.InitialStates and help idnlgrey.Parameters for more information.
nlgr.InitialStates(1)
nlgr.Parameters(2)
ans =
struct with fields:
Name: 'Angular position'
Value: 0
Minimum: -Inf
Maximum: Inf
Fixed: 1
ans =
struct with fields:
Name: 'Static gain'
Value: 0.2800
Minimum: -Inf
Maximum: Inf
Fixed: 0
c. Retrieve information for all initial states or model parameters in one call.
For example, obtain information on initial states that are fixed (not estimated) and the minima of all model parameters.
getinit(nlgr, 'Fixed')
getpar(nlgr, 'Min')
ans =
2x1 cell array
{[1]}
{[1]}
ans =
2x1 cell array
{[-Inf]}
{[-Inf]}
d. Obtain basic information about the object:
nlgr
nlgr =
Continuous-time nonlinear grey-box model defined by 'dcmotor_m' (MATLAB file):
dx/dt = F(t, u(t), x(t), p1, p2)
y(t) = H(t, u(t), x(t), p1, p2) + e(t)
with 1 input(s), 2 state(s), 2 output(s), and 2 free parameter(s) (out of 2).
Name: DC-motor
Status:
Created by direct construction or transformation. Not estimated.
Use get to obtain more information about the model properties. The idnlgrey object shares many properties of parametric linear model objects.
get(nlgr)
FileName: 'dcmotor_m'
Order: [1x1 struct]
Parameters: [2x1 struct]
InitialStates: [2x1 struct]
FileArgument: {}
SimulationOptions: [1x1 struct]
TimeVariable: 't'
NoiseVariance: [2x2 double]
InputName: {'Voltage'}
InputUnit: {'V'}
InputGroup: [1x1 struct]
OutputName: {2x1 cell}
OutputUnit: {2x1 cell}
OutputGroup: [1x1 struct]
Notes: [0x1 string]
UserData: []
Name: 'DC-motor'
Ts: 0
TimeUnit: 'seconds'
Report: [1x1 idresults.nlgreyest]
### Performance Evaluation of the Initial DC-Motor Model
Before estimating the parameters tau and k, simulate the output of the system with the parameter guesses using the default differential equation solver (a Runge-Kutta 45 solver with adaptive step length adjustment). The simulation options are specified using the "SimulationOptions" model property.
1. Set the absolute and relative error tolerances to small values (1e-6 and 1e-5, respectively).
nlgr.SimulationOptions.AbsTol = 1e-6;
nlgr.SimulationOptions.RelTol = 1e-5;
2. Compare the simulated output with the measured data.
compare displays both measured and simulated outputs of one or more models, whereas predict, called with the same input arguments, displays the simulated outputs.
The simulated and measured outputs are shown in a plot window.
compare(z, nlgr);
Figure 3: Comparison between measured outputs and the simulated outputs of the initial DC-motor model.
### Parameter Estimation
Estimate the parameters and initial states using nlgreyest, which is a prediction error minimization method for nonlinear grey box models. The estimation options, such as the choice of estimation progress display, are specified using the "nlgreyestOptions" option set.
nlgr = setinit(nlgr, 'Fixed', {false false}); % Estimate the initial states.
opt = nlgreyestOptions('Display', 'on');
nlgr = nlgreyest(z, nlgr, opt);
### Performance Evaluation of the Estimated DC-Motor Model
1. Review the information about the estimation process.
This information is stored in the Report property of the idnlgrey object. The property also contains information about how the model was estimated, such as solver and search method, data set, and why the estimation was terminated.
nlgr.Report
fprintf('\n\nThe search termination condition:\n')
nlgr.Report.Termination
ans =
Status: 'Estimated using NLGREYEST'
Method: 'Solver: ode45; Search: lsqnonlin'
Fit: [1x1 struct]
Parameters: [1x1 struct]
OptionsUsed: [1x1 idoptions.nlgreyest]
RandState: []
DataUsed: [1x1 struct]
Termination: [1x1 struct]
The search termination condition:
ans =
struct with fields:
WhyStop: 'Change in cost was less than the specified tolerance.'
Iterations: 5
FirstOrderOptimality: 1.4014e-04
FcnCount: 6
Algorithm: 'trust-region-reflective'
2. Evaluate the model quality by comparing simulated and measured outputs.
The fits are 98% and 84%, which indicate that the estimated model captures the dynamics of the DC motor well.
compare(z, nlgr);
Figure 4: Comparison between measured outputs and the simulated outputs of the estimated IDNLGREY DC-motor model.
3. Compare the performance of the idnlgrey model with a second-order ARX model.
na = [2 2; 2 2];
nb = [2; 2];
nk = [1; 1];
dcarx = arx(z, [na nb nk]);
compare(z, nlgr, dcarx);
Figure 5: Comparison between measured outputs and the simulated outputs of the estimated IDNLGREY and ARX DC-motor models.
4. Check the prediction errors.
The prediction errors obtained are small and are centered around zero (non-biased).
pe(z, nlgr);
Figure 6: Prediction errors obtained with the estimated IDNLGREY DC-motor model.
5. Check the residuals ("leftovers").
Residuals indicate what is left unexplained by the model and are small for good model quality. Use the resid command to view the correlations among the residuals. The first column of plots shows the autocorrelations of the residuals for the two outputs. The second column shows the cross-correlation of these residuals with the input "Voltage". The correlations are within acceptable bounds (blue region).
figure('Name',[nlgr.Name ': residuals of estimated model']);
resid(z,nlgr);
Figure 7: Residuals obtained with the estimated IDNLGREY DC-motor model.
6. Plot the step response.
A unit input step results in an angular position showing a ramp-type behavior and to an angular velocity that stabilizes at a constant level.
figure('Name', [nlgr.Name ': step response of estimated model']);
step(nlgr);
Figure 8: Step response with the estimated IDNLGREY DC-motor model.
7. Examine the model covariance.
You can assess the quality of the estimated model to some extent by looking at the estimated covariance matrix and the estimated noise variance. A "small" value of the (i, i) diagonal element of the covariance matrix indicates that the i:th model parameter is important for explaining the system dynamics when using the chosen model structure. Small noise variance (covariance for multi-output systems) elements are also a good indication that the model captures the estimation data in a good way.
getcov(nlgr)
nlgr.NoiseVariance
ans =
1.0e-04 *
0.1573 0.0021
0.0021 0.0008
ans =
0.0010 -0.0000
-0.0000 0.0110
For more information about the estimated model, use present to display the initial states and estimated parameter values, and estimated uncertainty (standard deviation) for the parameters.
present(nlgr);
nlgr =
Continuous-time nonlinear grey-box model defined by 'dcmotor_m' (MATLAB file):
dx/dt = F(t, u(t), x(t), p1, p2)
y(t) = H(t, u(t), x(t), p1, p2) + e(t)
with 1 input(s), 2 state(s), 2 output(s), and 2 free parameter(s) (out of 2).
Inputs:
u(1) Voltage(t) [V]
States: Initial value
x(1) Angular position(t) [rad] xinit@exp1 0.0302675 (estimated) in [-Inf, Inf]
x(2) Angular velocity(t) [rad/s] xinit@exp1 -0.133777 (estimated) in [-Inf, Inf]
Outputs:
Parameters: Value Standard Deviation
p1 Time-constant [s] 0.243649 0.00396671 (estimated) in [-Inf, Inf]
p2 Static gain [rad/(V*s)] 0.249644 0.000284486 (estimated) in [-Inf, Inf]
Name: DC-motor
Status:
Termination condition: Change in cost was less than the specified tolerance..
Number of iterations: 5, Number of function evaluations: 6
Estimated using Solver: ode45; Search: lsqnonlin on time domain data "DC-motor".
Fit to estimation data: [98.34;84.47]%
FPE: 0.001096, MSE: 0.1187
### Conclusions
This example illustrates the basic tools for performing nonlinear grey-box modeling. See the other nonlinear grey-box examples to learn about:
• Using nonlinear grey-box models in more advanced modeling situations, such as building nonlinear continuous- and discrete-time, time-series and static models.
• Writing and using C MEX model-files.
• Handling nonscalar parameters.
• Impact of certain algorithm choices.
For more information on identification of dynamic systems with System Identification Toolbox, visit the System Identification Toolbox product information page. | 3,449 | 13,616 | {"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} | 3.34375 | 3 | CC-MAIN-2024-22 | latest | en | 0.752559 |
https://math.answers.com/Q/What_is_the_answer_of_one_half_plus_one_fourth | 1,653,578,693,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662606992.69/warc/CC-MAIN-20220526131456-20220526161456-00591.warc.gz | 447,193,057 | 38,103 | 0
# What is the answer of one half plus one fourth?
Wiki User
2011-11-27 02:09:03
1/2 +1/4 = ?
Take LCM of 2, 4 which is 4
so 1/2 = 2/4
therefore 2/4 + 1/4 = 3/4
Ans 3/4
Wiki User
2011-11-27 02:09:03
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853 Reviews | 124 | 267 | {"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-2022-21 | latest | en | 0.822297 |
http://bestwoodworkingplansblog.com/log-furniture-plans-japanese-woodworking-plans.html | 1,558,291,697,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255092.55/warc/CC-MAIN-20190519181530-20190519203530-00126.warc.gz | 25,502,062 | 12,165 | Begin by cutting off a 10-in. length of the board and setting it aside. Rip the remaining 38-in. board to 6 in. wide and cut five evenly spaced saw kerfs 5/8 in. deep along one face. Crosscut the slotted board into four 9-in. pieces and glue them into a block, being careful not to slop glue into the saw kerfs (you can clean them out with a knife before the glue dries). Saw a 15-degree angle on one end and screw the plywood piece under the angled end of the block.
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#### How do you divide 11-3/8-in. (or any other mathematically difficult number) into equal parts without dividing fractions? Simple. Angle your tape across the workpiece until it reads an easily-divisible dimension and make your marks with the tape angled. For example, say you want to divide an 11-3/8-in. board into three equal parts. Angle the tape until it reads 12-in., and then make marks at “4” and “8”. Plus: More measuring tips and tricks.
```We cut the supports 16 in. long, but you can place the second shelf at whatever height you like. Screw the end supports to the walls at each end. Use drywall anchors if you can’t hit a stud. Then mark the position of the middle supports onto the top and bottom shelves with a square and drill 5/32-in. clearance holes through the shelves. Drive 1-5/8-in. screws through the shelf into the supports. You can apply this same concept to garage storage. See how to build double-decker garage storage shelves here.
```
Pocket screws create a solid, simple-to-make joint. Because of the size and visibility of the hole, it’s usually located in areas that are concealed or rarely seen (though special plugs can be used to fill the holes.) Craig Sommerfeld, founder of The Kreg Tool Company, is credited with popularizing pocket screw joinery in the 1980s. The company today is the leader in creating the jigs, clamps and screws used to create pocket screw joints. Learn how to use a pocket screw jig in woodworking projects.
You can also make one for elders and put it in your garden or terrace or anywhere in the house. Elders can use it to relax and kids can use it to play or sleep. Although this is a really beautiful piece of woodwork, it is not that easy to make. Only someone with good woodworking skill can think of making this swing set. Also, I couldn’t find a good tutorial that illustrates the process of building a wooden boat-shaped swing set. Most Probably, I will write one when I build mine.But if you really want this swing set like right now, I would suggest you hire a good woodworker, who can build something similar. Or just search the internet and maybe you get lucky enough to find a tutorial for this. Good luck either way.
Clamping up four mitered corners is tricky. You can buy specialty clamps for this, but I make my own. Here’s how to do it. Start with a long 1×4, as it’s easier (and safer) to clamp for making the angled cuts than a short piece. Mark out the blocks, and then drill a 1-in. diameter hole in the center of each one. The hole prevents the blocks from getting glued to your project. Cut 45-degree angles tangent to the hole, and then cut the blocks free from the long board. We’ll walk you through how to make one for your home shop.
Drill four 5/8-in.-dia. 1/2-in.-deep holes on the large disc?inside the traced circle?then use 5/8-in. dowel centers to transfer the hole locations to the underside of the small disc. Drill four 1/2-in.-deep holes on the underside of the small disc and a 1/2-in.-deep hole in the center of the top for the dowel handle. Glue in the dowels to join the discs, and glue in the handle. We drilled a wood ball for a handle knob, but a screw-on ceramic knob also provides a comfortable, attractive grip.
To corral shelf-dwelling books or DVDs that like to wander, cut 3/4-in.-thick hardwood pieces into 6-in. x 6-in. squares. Use a band saw or jigsaw to cut a slot along one edge (with the grain) that’s a smidgen wider than the shelf thickness. Stop the notch 3/4 in. from the other edge. Finish the bookend and slide it on the shelf. Want to build the shelves, too? We’ve got complete plans for great-looking shelves here.
### I mix a lot of epoxy in small batches, but I’ve seldom had the right size container on hand. I solved this problem by drilling 1-1/2-in. holes in 2×4 scraps with a Forstner bit. The resulting shallow “cups” allow easy mixing without the risk of spilling. When the holes are used up, I just make a new mixing board. — Bill Wells. Save your takeout utensils to use in the shop!
The items you’ll need for this project include wood board, power drill, tape measure, adhesive, etc. Read the tutorial for details. Follow the steps properly to make a nice and strong wall rack. This rack makes use of magnets to hold metal items. The tutorial explains the procedure for building this beautiful wall rack. Make sure to use only high quality items for any woodworking project. Use the rack only to hang items that are not too heavy for the magnet to hold. Also, be careful while working around this wall rack and beware of the knives falling off the rack.
As you can see in the image, this shelf goes on both sides of the corner wall. It looks beautiful and can be used to organize books, trophies, pictures frames and many other things. The strength and design of the shelf depends on how properly you build it. First time workers definitely need some guidance to help them with the process. Therefore, I am including this basic video that I found on YouTube that demonstrates the process of making corner wall wooden shelves.
Drill four 5/8-in.-dia. 1/2-in.-deep holes on the large disc?inside the traced circle?then use 5/8-in. dowel centers to transfer the hole locations to the underside of the small disc. Drill four 1/2-in.-deep holes on the underside of the small disc and a 1/2-in.-deep hole in the center of the top for the dowel handle. Glue in the dowels to join the discs, and glue in the handle. We drilled a wood ball for a handle knob, but a screw-on ceramic knob also provides a comfortable, attractive grip.
### Commonly used woodworking tools included axes, adzes, chisels, pull saws, and bow drills. Mortise and tenon joints are attested from the earliest Predynastic period. These joints were strengthened using pegs, dowels and leather or cord lashings. Animal glue came to be used only in the New Kingdom period.[3] Ancient Egyptians invented the art of veneering and used varnishes for finishing, though the composition of these varnishes is unknown. Although different native acacias were used, as was the wood from the local sycamore and tamarisk trees, deforestation in the Nile valley resulted in the need for the importation of wood, notably cedar, but also Aleppo pine, boxwood and oak, starting from the Second Dynasty.[4]
Woodworking was essential to the Romans. It provided, sometimes the only, material for buildings, transportation, tools, and household items. Wood also provided pipes, dye, waterproofing materials, and energy for heat.[5]:1Although most examples of Roman woodworking have been lost,[5]:2 the literary record preserved much of the contemporary knowledge. Vitruvius dedicates an entire chapter of his De architectura to timber, preserving many details.[6] Pliny, while not a botanist, dedicated six books of his Natural History to trees and woody plants, providing a wealth of information on trees and their uses.[7]
You can also make one for elders and put it in your garden or terrace or anywhere in the house. Elders can use it to relax and kids can use it to play or sleep. Although this is a really beautiful piece of woodwork, it is not that easy to make. Only someone with good woodworking skill can think of making this swing set. Also, I couldn’t find a good tutorial that illustrates the process of building a wooden boat-shaped swing set. Most Probably, I will write one when I build mine.But if you really want this swing set like right now, I would suggest you hire a good woodworker, who can build something similar. Or just search the internet and maybe you get lucky enough to find a tutorial for this. Good luck either way.
Use whatever image hosting service you like and post the link to /r/woodworking. The key here is it needs to be apparent that you've built the entry, and you follow the photo requirements listed in the contest rules. Submissions of finished photos only will not be accepted for entry. <-- I can't emphasize this enough, you absolutely need more than 2-3 photos for a valid submission. I will no longer accept entries that have albums that go from rough stock to 90% complete in one jump.
Old doors laid across sawhorses make great temporary workbenches, but they take up a lot of space when you’re not using them. Instead of full-size doors, I use bifold doors with hinges so I can fold them up when I’m done working. They’re also easier to haul around in the pickup for on-the-road jobs. — Harry Steele. Here are 12 more simple workbenches you can build.
The engineering involved in building this garden bench is pretty simple, and we have provided some links to get a full cut list and plans with photos to help you along the way. Additionally, to the stock lumber, you will need wood screws, barrel locks, and hinges to complete the table. A miter saw or hand saw is also extremely helpful for cutting down your stock to the correct angle and length.
Always nice to see project ideas. Yet, to make a living while woodworking all projects need to be scaled up so that one can actually earn enough to survive and compete against the flood of Chinese imports and others. Substitute products made from plastic, metal or wood are a common place and normally cheaper due to mass production and human rights violations. Politicians don’t care about the disappearance of many of America’s Cottage Industries and most consumers don’t care as well.
With two varieties, red and white, oak is known to be easy to work with and relatively strong. However, furniture makers often opt for white oak over red oak for its attractive figure and moisture-resistance.[12] Depending on the kind needed, oak can probably be found at a local home center or a lumberyard for a bit pricier than other hardwoods.[12][13]
I am sharing here a link to the detailed tutorial written by Pete at diypete.com, who shares the step by step process for making a wonderful barrel coffee table from scratch. He also tells you what items you’ll need for this project and where to find them. For example, you can buy an old whiskey barrel online or from a local whiskey store for a few bucks, if you haven’t already got one.
With two varieties, red and white, oak is known to be easy to work with and relatively strong. However, furniture makers often opt for white oak over red oak for its attractive figure and moisture-resistance.[12] Depending on the kind needed, oak can probably be found at a local home center or a lumberyard for a bit pricier than other hardwoods.[12][13]
Here’s an easier way to stain or seal chairs, lattice or anything with numerous tight recesses. Pour the stain into a clean, empty spray bottle (\$3). Spray the stain onto the project and wipe up the excess with a brush or rag. The sprayer will squirt stain into all those tight, hard-to-reach cracks and joints. — Valrie Schuster. Learn more about staining wood.
Tired of waiting for finish to dry on one side before finishing the other side? You can purchase standoffs, but it’s also really easy to make them yourself. Simply drive 2-in. drywall screws through 2-in. x 2-in. squares of 3/4-in. thick stock. The screw points will leave a divot in the finish that can be touched up later, but I always let the back side of my project rest on the screws while the finish dries. — Matt Boley. Plus: Check out these 32 other handy hints for frugal shop rats.
This is definitely going to be one of the easiest woodworking projects you’ll be reading about today. So why not just get started? The tutorial link is given below. Just do exactly what they are saying in the tutorial and you will end up making a beautiful wooden doormat just like the one in the image above. They are using pine wood to build this doormat. You can choose any wood material that best suits your budget.
Hardwoods, botanically known as angiosperms, are deciduous and shed their leaves annually with temperature changes.[8] Softwoods come from trees botanically known as gymnosperms, which are coniferous, cone-bearing, and stay green year round.[8] Although a general pattern, softwoods are not necessarily always “softer” than hardwoods, and vice versa.[9]
Having swing in your own home, yard or garden can be so de-stressing and be relaxing a thing to enjoy, that doesn’t matter you have a big yard or patio, or vacant porch. Kids will surely fall in love with this swing porch and love playing on a breezy day. Even, adults also do relax and enjoy a quite morning coffee, or just being embraced by the sun in the swing.
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Particleboard is a manufactured wood product composed of sawdust, wood chips or wood shavings mixed with a resin. This concoction is layered, compressed, subjected to heat and cut to shape, resulting in a sheet material that can be used for a variety of things. It’s often used as shelving or as an underlayment for carpet. Plastic laminate may be applied to both sides to create a product that can be used to create everything from furniture to cabinets to wall paneling. Head into IKEA and you’ll find acres of particleboard.
Woodworking was essential to the Romans. It provided, sometimes the only, material for buildings, transportation, tools, and household items. Wood also provided pipes, dye, waterproofing materials, and energy for heat.[5]:1Although most examples of Roman woodworking have been lost,[5]:2 the literary record preserved much of the contemporary knowledge. Vitruvius dedicates an entire chapter of his De architectura to timber, preserving many details.[6] Pliny, while not a botanist, dedicated six books of his Natural History to trees and woody plants, providing a wealth of information on trees and their uses.[7]
For your kitchen, it can work as a knife rack. It gives you easy access to all essential tools while saving space. In addition, it adds a nice visual appeal to your kitchen wall. You can customize your wall rack with different materials, designs and styles. I am here sharing the source link to the step by step tutorial about how to make a rustic wall knife rack.
Some tools required to build a picture frame are a table saw, miter saw, measuring tape, wood glue etc. A table saw with a backing board and miter gauge can be used to get the right angle and lengths of picture frame every time. You can use builders square to arrange the final cut pieces before nailing, screwing or gluing. Check out the video tutorial below for more details.
I am sharing here a link to the detailed tutorial written by Pete at diypete.com, who shares the step by step process for making a wonderful barrel coffee table from scratch. He also tells you what items you’ll need for this project and where to find them. For example, you can buy an old whiskey barrel online or from a local whiskey store for a few bucks, if you haven’t already got one.
```I built my first platform bed by following the steps mentioned in the tutorial and the end result was everything I expected. It was as beautiful as comfortable and strong. It only cost me around \$60 to build this one from the scratch. And if I can build it, anyone can. What you need is a little bit of woodworking experience and a lot of confidence. Collect the items as suggested in the video and start working now.
```
Sanding concave molding doesn’t have to be difficult. Find a deep socket that fits the contour of your molding. Wrap a piece of sand- paper around the socket and hold it in place with your fingers. Your sanding will be uniform and the delicate edges of the molding won’t round over. — Eric and Cheryl Weltlich. In this video, Travis talks about his favorite sanding tips.
# And the fact is that you can make your own patio chair with several old but still good pallets. Here we are providing a tutorial that everybody can follow easily – it is very well-written and also self-explanatory, which is great for those who are a beginner at woodworking and have never completed a DIY project before. As you don’t need to be a professional woodworker or a handyman to complete this project, so it is not a difficult task – all you need is a bit of determination!
Always nice to see project ideas. Yet, to make a living while woodworking all projects need to be scaled up so that one can actually earn enough to survive and compete against the flood of Chinese imports and others. Substitute products made from plastic, metal or wood are a common place and normally cheaper due to mass production and human rights violations. Politicians don’t care about the disappearance of many of America’s Cottage Industries and most consumers don’t care as well.
Woodworking was essential to the Romans. It provided, sometimes the only, material for buildings, transportation, tools, and household items. Wood also provided pipes, dye, waterproofing materials, and energy for heat.[5]:1Although most examples of Roman woodworking have been lost,[5]:2 the literary record preserved much of the contemporary knowledge. Vitruvius dedicates an entire chapter of his De architectura to timber, preserving many details.[6] Pliny, while not a botanist, dedicated six books of his Natural History to trees and woody plants, providing a wealth of information on trees and their uses.[7]
##### Some tools required to build a picture frame are a table saw, miter saw, measuring tape, wood glue etc. A table saw with a backing board and miter gauge can be used to get the right angle and lengths of picture frame every time. You can use builders square to arrange the final cut pieces before nailing, screwing or gluing. Check out the video tutorial below for more details.
As you can see in the image, this shelf goes on both sides of the corner wall. It looks beautiful and can be used to organize books, trophies, pictures frames and many other things. The strength and design of the shelf depends on how properly you build it. First time workers definitely need some guidance to help them with the process. Therefore, I am including this basic video that I found on YouTube that demonstrates the process of making corner wall wooden shelves.
#### This self-clamping table saw fence takes only seconds to put on and lets you crank the blade into the fence to create both angled cuts along board edges and extremely thin rip or rabbet cuts. With a hand- or jigsaw, cut pieces from a 1×4, making the inside width of the “L” a hair under the thickness of your saw’s fence. Drill 5/16-in. holes in the L-blocks and plywood fence and join them with two 1/4-in. x 3-in. countersunk machine screws, washers and Wing-Nuts. As always, use extra caution when you’re sawing without a blade guard. Our thanks for this new sawing angle to professional furniture maker George Vondriska. Check out these 16 genius tool hacks you need to know!
Luckily, we have also managed to find a detailed video tutorial of the Barn door project that illustrates the process of building a Barn door of your own. The steps and instructions in the video tutorial are different from the source links listed above. Actually, you can make different types of designs for your Barn door depending on which one you can afford easily and DIY on your own.
Another wooden item that I love very much is a beautiful mobile holder. You can see one in the image below. These things are not only beautiful, but they can comfortably hold any sized mobile and ensure proper safety. Another amazing thing is that they can be built in many shapes and sizes, as and how you need it. You can see some more examples at the source below
Another wooden item that I love very much is a beautiful mobile holder. You can see one in the image below. These things are not only beautiful, but they can comfortably hold any sized mobile and ensure proper safety. Another amazing thing is that they can be built in many shapes and sizes, as and how you need it. You can see some more examples at the source below
There’s a lot of space above the shelf in most closets. Even though it’s a little hard to reach, it’s a great place to store seldom-used items. Make use of this wasted space by adding a second shelf above the existing one. Buy enough closet shelving material to match the length of the existing shelf plus enough for two end supports and middle supports over each bracket. Twelve-inch-wide shelving is available in various lengths and finishes at home centers and lumberyards.
The tutorial that I am sharing here was written by someone who built this pallet art just to improve the value of a property they wanted to sell fast and they succeed in it. So you can imagine how wonderful this item must look like. I am assuming you do not just want to make this beautiful pallet art so that you can also sell your property easily. Well, whatever your reasons are, this beauty is able to attract anyone who visits your house.
The video explains the step by step process of making a nice wooden phone stand from scratch. My first wooden holder was not the best one, but it was good enough to motivate me to make more. I now possess 10 mobile wooden stands in different shapes and styles. And if I can make this, you too can make one yourself. Search the internet for more mobile holder ideas and start making one now.
Use whatever image hosting service you like and post the link to /r/woodworking. The key here is it needs to be apparent that you've built the entry, and you follow the photo requirements listed in the contest rules. Submissions of finished photos only will not be accepted for entry. <-- I can't emphasize this enough, you absolutely need more than 2-3 photos for a valid submission. I will no longer accept entries that have albums that go from rough stock to 90% complete in one jump.
Another awesome thing about this coffee table is that it is also has a storage unit. So you can store drinks, and other stuff in the half barrel of your table and then close or open it whenever you need. Pete has also constructed a video for this tutorial for which you can find the link below. It illustrates the same process in a video guide that shows you the exact process to be followed while building this whiskey barrel coffee table.
###### By video tutorial, you will get step by step process instructions of making a nice wooden folding sling chair from scratch. However, my first wooden chair was not the best one, but it was good enough to motivate me to make some more folding chairs like this one. If I can make this, you too can make one yourself. You can browse the internet for more folding sling chairs ideas and start making one now.
The owners, webmasters, administrators, authors and editors, expressly disclaim all and any liability to any person, whether a user of this website or not, in respect of anything and of the consequences of anything done or omitted to be done by any such person in reliance, whether whole or partial, upon the whole or any part of the contents of this website. Please exercise caution when working with any tools or machinery. Follow common safety rules and precautions as outlined in any manuals related to the equipment being used. If advice or other expert assistance is required, the services of a competent professional person should be sought.
I am sharing here a link to the detailed tutorial written by Pete at diypete.com, who shares the step by step process for making a wonderful barrel coffee table from scratch. He also tells you what items you’ll need for this project and where to find them. For example, you can buy an old whiskey barrel online or from a local whiskey store for a few bucks, if you haven’t already got one. | 5,480 | 25,178 | {"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-2019-22 | latest | en | 0.922534 |
http://www.ncsu.edu/labwrite/res/tablevsgraph/res-tablevsgraph.html | 1,440,817,644,000,000,000 | text/html | crawl-data/CC-MAIN-2015-35/segments/1440644064167.28/warc/CC-MAIN-20150827025424-00128-ip-10-171-96-226.ec2.internal.warc.gz | 610,228,268 | 4,903 | # Tables vs. Graphs
## Tabular Versus Visual Display of Data
An initial decision that has to be made about your data is whether it should be displayed in a table or a graph. Though there are no hard rules, there are general guidelines you can use to make this determination. Questions to ask yourself:
• Are the independent and dependent variables qualitative or quantitative?
• What is the total number of data points to be shown?
• Is there more than one independent variable?
• Are you trying to represent the statistical distribution of the data?
• How important is it to be able to see individual values?
• How important is it to understand the overall trend?
With these questions in mind, here are some examples:
Table 1. Oxygen requirement for species of Streptomyces Organism Optimal Growth Condition Streptomyces hardaur Aerobic S. huesis Anaerobic S. rainiour Anaerobic S. colorious Aerobic
When both your independent and dependent variables are qualitative, there will not be a suitable graph format to put it in. Symbols representing the different levels of the qualitative dependent variable can be substituted for words, however. In this example, a filled circle could represent Aerobic and a circle outline could represent Anaerobic.
Table 2. Impact failure threshold of 1018 cold rolled steel Temperature (deg C) Mean Impact Energy (joules) 20 70.4 100 77.3
Figure 1.
With only two values in Table 2, it does not make much sense to provide a graph since the data can be easily interpreted from the table data. The display of the exact values for each data point in Figure 1 reinforces the lack of the necessity of a graph. Two data points can also be successfully described in the main text without a table. They should be included in a table only if required by the instructor.
Table 3. Impact failure threshold of 1018 cold rolled steel Temperature (deg C) Mean Impact Energy (joules) -150 1.4 0 62.2 20 70.4 100 77.3
Figure 2.
With four data points, a table for the data is usually called for. You would show these four points as a graph if it was important to show the rate of change between each pair of points (e.g., the slope of the line). Rate of change can be hard to visualize directly from numbers.
Table 4. Impact failure threshold of 1018 steel Temperature (deg C) Mean Impact Energy (joules) Cold Rolled Annealed -195 1.4 0.8 0 62.2 50.5 20 70.4 202.7 100 77.3 231.0
Figure 3.
When a second independent variable is introduced (i.e., the two types of 1018 steel), a graph is usually called for in order to understand the relationship between the two sets of data.
Table 5. Impact failure threshold of 1018 cold rolled steel Temperature (deg C) Impact Energy (joules) Mean Standard Deviation -195 1.4 0.55 0 62.2 20.79 20 70.4 14.45 100 77.3 4.32
Figure 4.
When the statistical properties of an independent variable are described, a graph is usually called for. In Figure 4, the visual representation of the error bars on the graph helps to clarify the precision of data collected at each temperature.
Figure 5.
Finally, when you have over 6-10 data points, you almost always represent the data in a graph. Individuals cannot simultaneously manage more than this amount of data in memory at one time and a graph provides a compact method of synthesizing all of the data into a single image. In Figure 5, over 700 data points are summarized on the graph. If particular data values are important for your results, then these numbers can be listed on the graph, in a table, or in the main text.
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# Hilbert–Huang transform
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### Hilbert–Huang transform
The Hilbert–Huang transform (HHT) is a way to decompose a signal into so-called intrinsic mode functions (IMF), and obtain instantaneous frequency data. It is designed to work well for data that is nonstationary and nonlinear. In contrast to other common transforms like the Fourier transform, the HHT is more like an algorithm (an empirical approach) that can be applied to a data set, rather than a theoretical tool.
## Contents
• Introduction 1
• Introduction to EMD and IMF 1.1
• Introduction to HSA 1.2
• Techniques 2
• The empirical mode decomposition (EMD) 2.1
• The stoppage criteria of the sifting process 2.2
• Hilbert spectral analysis 2.3
• Current applications 3
• Limitations 4
• References 6
## Introduction
The Hilbert–Huang transform (HHT), a NASA designated name, was proposed by Huang et al. (1996, 1998, 1999, 2003, 2012). It is the result of the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA). The HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions, and uses the HSA method to obtain instantaneous frequency data. The HHT provides a new method of analyzing nonstationary and nonlinear time series data.
### Introduction to EMD and IMF
The fundamental part of the HHT is the empirical mode decomposition (EMD) method. Using the EMD method, any complicated data set can be decomposed into a finite and often small number of components, which are intrinsic mode functions (IMF). An IMF represents a generally simple oscillatory mode as a counterpart to the simple harmonic function. By definition, an IMF is any function with the same number of extrema and zero crossings, whose envelopes are symmetric with respect to zero. This definition guarantees a well-behaved Hilbert transform of the IMF. This decomposition method operating in the time domain is adaptive and highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it can be applied to nonlinear and nonstationary processes.
### Introduction to HSA
Hilbert spectral analysis (HSA) is a method for examining each IMF's instantaneous frequency as functions of time. The final result is a frequency-time distribution of signal amplitude (or energy), designated as the Hilbert spectrum, which permits the identification of localized features.
## Techniques
### The empirical mode decomposition (EMD)
The EMD method is a necessary step to reduce any given data into a collection of intrinsic mode functions (IMF) to which the Hilbert spectral analysis can be applied. An IMF is defined as a function that satisfies the following requirements:
1. In the whole data set, the number of extrema and the number of zero-crossings must either be equal or differ at most by one.
2. At any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero.
Therefore, an IMF represents a simple oscillatory mode as a counterpart to the simple harmonic function, but it is much more general: instead of constant amplitude and frequency in a simple harmonic component, an IMF can have variable amplitude and frequency along the time axis.
The procedure of extracting an IMF is called sifting. The sifting process is as follows:
1. Identify all the local extrema in the test data.
2. Connect all the local maxima by a cubic spline line as the upper envelope.
3. Repeat the procedure for the local minima to produce the lower envelope.
The upper and lower envelopes should cover all the data between them. Their mean is m1. The difference between the data and m1 is the first component h1:
X(t)-m_1=h_1.\,
Ideally, h1 should satisfy the definition of an IMF, since the construction of h1 described above should have made it symmetric and having all maxima positive and all minima negative. After the first round of sifting, a crest may become a local maximum. New extrema generated in this way actually reveal the proper modes lost in the initial examination. In the subsequent sifting process, h1 can only be treated as a proto-IMF. In the next step, h1 is treated as data:
h_{1}-m_{11}=h_{11}.\,
After repeated sifting up to k times, h1 becomes an IMF, that is
h_{1(k-1)}-m_{1k}=h_{1k}.\,
Then, h1k is designated as the first IMF component of the data:
c_1=h_{1k}.\,
### The stoppage criteria of the sifting process
The stoppage criterion determines the number of sifting steps to produce an IMF. Two different stoppage criteria have been used traditionally:
• 1. The first criterion is proposed by Huang et al. (1998). It similar to the Cauchy convergence test, and we define a sum of the difference, SD, as
SD_k=\frac{\sum_{t=0}^{T}|h_{k-1}(t)-h_k(t)|^2}{\sum_{t=0}^{T} h_{k-1}^2 (t)}.\,
Then the sifting process stops when SD is smaller than a pre-given value.
• 2. A second criterion is based on the so-called S-number, which is defined as the number of consecutive siftings for which the number of zero-crossings and extrema are equal or at most differing by one. Specifically, an S-number is pre-selected. The sifting process will stop only if, for S consecutive siftings, the numbers of zero-crossings and extrema stay the same, and are equal or at most differ by one.
Once a stoppage criterion is selected, the first IMF, c1, can be obtained. Overall, c1 should contain the finest scale or the shortest period component of the signal. We can, then, separate c1 from the rest of the data by X(t)-c_1=r_1.\, Since the residue, r1, still contains longer period variations in the data, it is treated as the new data and subjected to the same sifting process as described above.
This procedure can be repeated for all the subsequent rj's, and the result is
r_{n-1}-c_n=r_n.\,
The sifting process finally stops when the residue, rn, becomes a monotonic function from which no more IMF can be extracted. From the above equations, we can induce that
X(t)=\sum_{j=1}^n c_j+r_n.\,
Thus, a decomposition of the data into n-empirical modes is achieved. The components of the EMD are usually physically meaningful, for the characteristic scales are defined by the physical data. Flandrin et al. (2003) and Wu and Huang (2004) have shown that the EMD is equivalent to a dyadic filter bank.
### Hilbert spectral analysis
Having obtained the intrinsic mode function components, the instantaneous frequency can be computed using the Hilbert Transform. After performing the Hilbert transform on each IMF component, the original data can be expressed as the real part, Real, in the following form:
X(t)=\text{Real}{\sum_{j=1}^n a_j(t)e^{i\int\omega_j(t)dt}}.\,
## Current applications
• Biomedical applications: Huang et al. [1999b] analyzed the pulmonary arterial pressure on conscious and unrestrained rats. Pachori (2008) has used EMD for discrimination of seizure and seizure-free EEG signals.
• Neuroscience: Pigorini et al. [2011] analyzed Human EEG response to Transcranial Magnetic Stimulation; Liang et al. [2005] analyzed the visual evoked potentials of macaque performing visual spatial attention task.
• Chemistry and chemical engineering: Phillips et al. [2003] investigated a conformational change in Brownian dynamics(BD) and molecular dynamics(MD) simulations using a comparative analysis of HHT and wavelet methods. Wiley et al. [2004] used HHT to investigate the effect of reversible digitally filtered molecular dynamics(RDFMD) which can enhance or suppress specific frequencies of motion. Montesinos et al. [2002] applied HHT to signals obtained from BWR neuron stability.
• Financial applications: Huang et al. [2003b] applied HHT to nonstationary financial time series and used a weekly mortgage rate data.
• Image processing: Hariharan et al. [2006] applied EMD to image fusion and enhancement. Chang et al. [2009] applied an improved EMD to iris recognition, which reported a 100% faster in computational speed without losing accuracy than the original EMD.
• Meteorological and atmospheric applications: Salisbury and Wimbush [2002], using Southern Oscillation Index(SOI) data, applied the HHT technique to determine whether the SOI data are sufficiently noise free that useful predictions can be made and whether future El Nino southern oscillation(ENSO) events can be predicted from SOI data. Pan et al. [2002] used HHT to analyze satellite scatterometer wind data over the northwestern Pacific and compared the results to vector empirical orthogonal function(VEOF) results.
• Ocean engineering:Schlurmann [2002] introduced the application of HHT to characterize nonlinear water waves from two different perspectives, using laboratory experiments. Veltcheva [2002] applied HHT to wave data from nearshore sea. Larsen et al. [2004] used HHT to characterize the underwater electromagnetic environment and identify transient manmade electromagnetic disturbances.
• Seismic studies: Huang et al. [2001] used HHT to develop a spectral representation of earthquake data. Chen et al. [2002a] used HHT to determined the dispersion curves of seismic surface waves and compared their results to Fourier-based time-frequency analysis. Shen et al. [2003] applied HHT to ground motion and compared the HHT result with the Fourier spectrum.
• Solar physics: Nakariakov et al. [2010] used EMD to demonstrate the triangular shape of quasi-periodic pulsations detected in the hard X-ray and microwave emission generated in solar flares. Barnhart and Eichinger [2010] used HHT to extract the periodic components within sunspot data, including the 11-year Schwabe, 22-year Hale, and ~100-year Gleissberg cycles. They compared their results with traditional Fourier analysis.
• Structural applications: Quek et al. [2003] illustrate the feasibility of the HHT as a signal processing tool for locating an anomaly in the form of a crack, delamination, or stiffness loss in beams and plates based on physically acquired propagating wave signals. Using HHT, Li et al. [2003] analyzed the results of a pseudodynamic test of two rectangular reinforced concrete bridge columns.
• Health monitoring: Pines and Salvino [2002] applied HHT in structural health monitoring. Yang et al. [2004] used HHT for damage detection, applying EMD to extract damage spikes due to sudden changes in structural stiffness. Yu et al. [2003] used HHT for fault diagnosis of roller bearings. Parey and Pachori (2012) have applied EMD for gear fault diagnosis.
• System identification: Chen and Xu [2002] explored the possibility of using HHT to identify the modal damping ratios of a structure with closely spaced modal frequencies and compared their results to FFT. Xu et al. [2003] compared the modal frequencies and damping ratios in various time increments and different winds for one of the tallest composite buildings in the world.
• Speech recognition: Huang and Pan [2006] have used the HHT for speech pitch determination.[1]
## Limitations
Chen and Feng [2003] proposed a technique to improve the HHT procedure.[2] The authors noted that the EMD is limited in distinguishing different components in narrow-band signals. The narrow band may contain either (a) components that have adjacent frequencies or (b) components that are not adjacent in frequency but for which one of the components has a much higher energy intensity than the other components. The improved technique is based on beating-phenomenon waves.
Datig and Schlurmann [2004] [3] conducted a comprehensive study on the performance and limitations of HHT with particular applications to irregular waves. The authors did extensive investigation into the spline interpolation. The authors discussed using additional points, both forward and backward, to determine better envelopes. They also performed a parametric study on the proposed improvement and showed significant improvement in the overall EMD computations. The authors noted that HHT is capable of differentiating between time-variant components from any given data. Their study also showed that HHT was able to distinguish between riding and carrier waves.
Huang and Zu [2008] [4] reviewed applications of the Hilbert–Huang transformation emphasizing that the HHT theoretical basis is purely empirical, and noting that "one of the main drawbacks of EMD is mode mixing". They also outline outstanding open problems with HHT, which include: End effects of the EMD, Spline problems, Best IMF selection and uniqueness. Although the ensemble EMD (EEMD) may help mitigate the latter.
In the US, where patents on algorithms are permitted, the HHT is heavily encumbered by patents in almost all of its domains of possible application .
## References
1. ^ Huang, H.; Pan, J. (2006). "Speech pitch determination based on Hilbert-Huang transform" (pdf). Signal Processing 86 (4): 792–803.
2. ^ Chen, Y.; Feng M.Q. (2003). "A technique to improve the empirical mode decomposition in the Hilbert-Huang transform". Earthquake Engineering and Engineering Vibration 2 (1): 75–85.
3. ^ Dätig, Marcus; Schlurmann, Torsten. "Performance and limitations of the Hilbert–Huang transformation (HHT) with an application to irregular water waves". Ocean Engineering 31 (14-15): 1783–1834.
4. ^ Huang, N. E.; Wu Z. (2008). "A review on Hilbert-Huang transform: Method and its applications to geophysical studies,". Rev. Geophys. 46.
• Ditommaso, R.; Mucciarelli, M.; Parolai, S.; Picozzi, M. (2012). "Monitoring the Structural Dynamic Response of a Masonry Tower: Comparing Classical and Time-Frequency Analyses" (pdf). Bulletin of Earthquake Engineering 10 (4): 1221–1235.
• Barnhart, B. L.; Eichinger, W. E. (2011). "Analysis of Sunspot Variability Using the Hilbert-Huang Transform". Solar Physics 269 (2): 439–449.
• Nakariakov, V. M. et al. (2010). "Oscillatory processes in solar flares". Plasma Physics and Controlled Fusion 52 (12): 124009.
• Boudraa, A.O.; Cexus, J.C. (2007). "EMD-Based Signal Filtering" (pdf). IEEE Transactions on Instrumentation and Measurement 56 (6): 2196–2202.
• Huang, N. E.; Shen, Z.; Long, S. R.; Wu, M. C.; Shih, H. H.; Zheng, Q.; Yen, N. C.; Tung, C. C.; Liu, H. H. (1998). "The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis" (pdf). Proceedings of the Royal Society of London A 454 (1971): 903–995.
• Huang, N. E.; Wu Z. (2008). "A review on Hilbert-Huang transform: Method and its applications to geophysical studies,". Rev. Geophys. 46.
• Huang, N. E.; Attoh-Okine, N. O. (2005). The Hilbert-Huang Transform in Engineering. CRC Taylor & Francis.
• Huang, N. E.; Shen, S. S. P. (2005). Hilbert-Huang Transform and its Applications. London: World Scientific.
• Flandrin, P.; Rilling, G.; Gonçalves, P. (2003). "Empirical Mode Decomposition as a Filterbank" (pdf). IEEE Signal Processing Letters 11 (2): 112–114.
• Huang, N. E.; Long, S. R.; Shen, Z. (1996). "The Mechanism for Frequency Downshift in Nonlinear Wave Evolution". Advances in Applied Mechanics 32: 59–111.
• Huang, N. E.; Shen, Z.; Long, R. S. (1999). "A New View of Nonlinear Water Waves — The Hilbert Spectrum" (pdf). Annual Review of Fluid Mechanics 31: 417–457.
• Huang, N. E.; Wu, M. L.; Long, S. R.; Shen, S. S.; W. D. Qu, W. D.; Gloersen, P.; Fan, K. L. (2003). "A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis" (pdf). Proceedings of the Royal Society of London A 459 (2037): 2317–2345.
• Wu, Z.; Huang, N. E. (2004). "A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method" (pdf). Proceedings of the Royal Society of London A 460 (2046): 1597–1611.
• Hariharan H.; Gribok, A.; Abidi, M. A.; Koschan, A. (2006). "Image Fusion and Enhancement via Empirical Mode Decomposition" (pdf). Journal of Pattern Recognition Research 1 (1): 16–31.
• Chang, J. C.; Huang, M. Y.; Lee, J. C.; Chang, C. P.; Tu, T. M. (2009). "Iris Recognition with an Improved Empirical Mode Decomposition Method". Optical Engineering 48 (4): 047007–047007–15.
• Parey, A.; Pachori, R.B. (2012). "Variable cosine windowing of intrinsic mode functions:
Application to gear fault diagnosis". Measurement 45 (3): 415–426.
• Pigorini, A.; Casali, A.G.; Casarotto, S.; Ferrarelli, F.; Baselli, G.; Mariotti, M.; Massimini, M.; Rosanova, M.C.E. (2011). "Time-frequency spectral analysis of TMS-evoked EEG oscillations by means of Hilbert-Huang transform". J Neurosci Methods 198 (2): 236–245.
• Pachori, R.B. (2008). "Discrimination between ictal and seizure-free EEG signals using empirical mode decomposition",". Research Letters in Signal Processing 2008 (Article ID 293056).
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a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department. | 4,417 | 18,357 | {"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} | 3.078125 | 3 | CC-MAIN-2020-45 | latest | en | 0.815962 |
https://www.enotes.com/homework-help/there-an-easy-way-find-volume-surface-area-all-244407 | 1,606,293,569,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141181482.18/warc/CC-MAIN-20201125071137-20201125101137-00554.warc.gz | 634,488,211 | 18,907 | # Is there an easy way to find volume and surface area of all prisms, pyramids, cones, cylinders, and spheres?
The surface area and volume of solids like prisms, pyramids, cones, cylinders, and spheres can be determined by using the following formulae. Only the required values for the variables in the formulae need to substituted with the values available.
Prism:
Volume = Area of the base * height = length* width* height
Surface area = 2*( length* width + length* height + width* height)
Pyramid:
Volume = (1/3)*Surface area of base * height
Surface area = (1/2)*perimeter of base * slant height
Cone:
Volume = (1/3)*pi*r^2*h
Surface area = pi*r*l + pi*r^2 , here l is the slant height
Cylinder:
Volume = area of base * height = pi*r^2*h
Surface Area = 2*pi*r^2 + 2*pi*r*h
Sphere:
Volume =( 4/3)* pi*r^3
Surface Area = 4*pi*r^2
Approved by eNotes Editorial Team
Posted on | 250 | 894 | {"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} | 3.515625 | 4 | CC-MAIN-2020-50 | longest | en | 0.759639 |
https://code.ashish.me/100-algorithms/014-array-conversion | 1,709,397,335,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475833.51/warc/CC-MAIN-20240302152131-20240302182131-00001.warc.gz | 185,731,966 | 4,097 | ### 014 Array Conversion
/**
*
* Ashish Patel
* e: ashishsushilPatel@gmail.com
* w: https://ashish.me
*
*/
/* Given an array of 2k integers (for some integer k), perform the following operations until the array contains only one element:
On the 1st, 3rd, 5th, etc. iterations (1-based) replace each pair of consecutive elements with their sum;
On the 2nd, 4th, 6th, etc. iterations replace each pair of consecutive elements with their product. After the algorithm has finished, there will be a single element left in the array. Return that element.
Example
For inputArray = [1, 2, 3, 4, 5, 6, 7, 8], the output should be arrayConversion(inputArray) = 186.
We have [1, 2, 3, 4, 5, 6, 7, 8] -> [3, 7, 11, 15] -> [21, 165] -> [186], so the answer is 186.
*/
function arrayConversion(values) {
let isOdd = true
while(values.length !== 1){
values = calculateSumOrProduct(values, isOdd)
isOdd = !isOdd
}
return values
}
function calculateSumOrProduct(array, isOdd){
let calculatedArray = []
if(isOdd){
for (let index = 0; index < array.length; index+=2) {
calculatedArray.push(array[index] + array[index+1])
}
} else {
for (let index = 0; index < array.length; index+=2) {
calculatedArray.push(array[index] * array[index+1])
}
}
return calculatedArray
}
test('array Conversion', () => {
expect(arrayConversion([1, 2, 3, 4, 5, 6, 7, 8])).toEqual([186])
});
Created 2019-12-07T17:35:15+05:30 · Edit | 439 | 1,399 | {"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} | 3.234375 | 3 | CC-MAIN-2024-10 | latest | en | 0.575431 |
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The key is the researchers are not comparing ALL items the FB has to the SK.
They are ONLY comparing items that were bought by the random shoppers.
These items could be frequent items and are cheaper at FB.
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FoodBasket supermarket cost 5% less than ShopperKing supermarket but the shoppers will not save money by shopping at FodBasket because shoppers who shop regularly at a supermarket are given discount and in this case the shoppers were picked at random.
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14 Sep 2010, 09:56
IMO A
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14 Sep 2010, 19:40
A it is.
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15 Sep 2010, 21:05
how do u eliminate C ??
i also liked A, but C also seems fine.
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15 Sep 2010, 21:20
sushma0805 wrote:
how do u eliminate C ??
i also liked A, but C also seems fine.
We are trying to prove that ShopperKing's shoppers won't save money by shopping at FoodBasket.
So factors other than price are irrelevant
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Re: CR3 [#permalink] 15 Sep 2010, 21:20
Display posts from previous: Sort by | 1,174 | 3,819 | {"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} | 3.59375 | 4 | CC-MAIN-2017-43 | latest | en | 0.891313 |
https://www.esaral.com/q/find-the-second-order-derivatives-of-the-function-30120 | 1,713,914,424,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818835.29/warc/CC-MAIN-20240423223805-20240424013805-00349.warc.gz | 675,995,701 | 11,301 | # Find the second order derivatives of the function.
Question:
Find the second order derivatives of the function.
$\log (\log x)$
Solution:
Let $y=\log (\log x)$
Then,
$\frac{d y}{d x}=\frac{d}{d x}[\log (\log x)]=\frac{1}{\log x} \cdot \frac{d}{d x}(\log x)=\frac{1}{x \log x}=(x \log x)^{-1}$
$\therefore \frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left[(x \log x)^{-1}\right]=(-1) \cdot(x \log x)^{-2} \cdot \frac{d}{d x}(x \log x)$\
$=\frac{-1}{(x \log x)^{2}} \cdot\left[\log x \cdot \frac{d}{d x}(x)+x \cdot \frac{d}{d x}(\log x)\right]$
$=\frac{-1}{(x \log x)^{2}} \cdot\left[\log x \cdot 1+x \cdot \frac{1}{x}\right]=\frac{-(1+\log x)}{(x \log x)^{2}}$ | 286 | 664 | {"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} | 4.40625 | 4 | CC-MAIN-2024-18 | latest | en | 0.360617 |
https://solutionlibrary.com/business/finance/forward-and-futures-jj5m | 1,611,403,434,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703537796.45/warc/CC-MAIN-20210123094754-20210123124754-00717.warc.gz | 570,294,860 | 4,134 | # Forward and Futures
During the summer you had to spend some time with your uncle, who is a wheat farmer. Your uncle, knowing you are studying for an MBA at Harvard, asked your help. He is afraid that the price of wheat will fall, which will have a severe impact on his profits. Thus he asks you to compute the 1yr forward price of wheat. He tells you that its current price is \$3.4 per bushel and interest rates are at 4%. However, he also says that it is relatively expensive to store wheat for one year. Assume that this cost, which must be paid upfront, runs at about \$0.1 per bushel. What is the 1yr forward price of wheat? | 151 | 632 | {"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-2021-04 | latest | en | 0.990677 |
http://nrich.maths.org/public/leg.php?code=32&cl=2&cldcmpid=2467 | 1,506,008,796,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818687833.62/warc/CC-MAIN-20170921153438-20170921173438-00163.warc.gz | 263,491,484 | 9,992 | # Search by Topic
#### Resources tagged with Multiplication & division similar to St Ives:
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### There are 164 results
Broad Topics > Calculations and Numerical Methods > Multiplication & division
##### Stage: 3 Challenge Level:
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
### Two Many
##### Stage: 3 Challenge Level:
What is the least square number which commences with six two's?
### Largest Number
##### Stage: 3 Challenge Level:
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
### Slippy Numbers
##### Stage: 3 Challenge Level:
The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.
### Like Powers
##### Stage: 3 Challenge Level:
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
### Diggits
##### Stage: 3 Challenge Level:
Can you find what the last two digits of the number $4^{1999}$ are?
### Clever Santa
##### Stage: 2 Challenge Level:
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
### Long Multiplication
##### Stage: 3 Challenge Level:
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
### Divide it Out
##### Stage: 2 Challenge Level:
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
### Eminit
##### Stage: 3 Challenge Level:
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
##### Stage: 3 Challenge Level:
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
### Cows and Sheep
##### Stage: 2 Challenge Level:
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
### Difficulties with Division
##### Stage: 1 and 2
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
### Always, Sometimes or Never? Number
##### Stage: 2 Challenge Level:
Are these statements always true, sometimes true or never true?
##### Stage: 3 Challenge Level:
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
### Round and Round and Round
##### Stage: 3 Challenge Level:
Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?
### As Easy as 1,2,3
##### Stage: 3 Challenge Level:
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
### Ordering Cards
##### Stage: 1 and 2 Challenge Level:
This problem is designed to help children to learn, and to use, the two and three times tables.
### A One in Seven Chance
##### Stage: 3 Challenge Level:
What is the remainder when 2^{164}is divided by 7?
### Learning Times Tables
##### Stage: 1 and 2 Challenge Level:
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
### I'm Eight
##### Stage: 1, 2, 3 and 4 Challenge Level:
Find a great variety of ways of asking questions which make 8.
### Which Is Quicker?
##### Stage: 2 Challenge Level:
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
### Square Subtraction
##### Stage: 2 Challenge Level:
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
### What Two ...?
##### Stage: 2 Short Challenge Level:
56 406 is the product of two consecutive numbers. What are these two numbers?
### X Marks the Spot
##### Stage: 3 Challenge Level:
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
### Remainders
##### Stage: 2 Challenge Level:
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
### 1, 2, 3, 4, 5
##### Stage: 2 Challenge Level:
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
### Sending Cards
##### Stage: 2 Challenge Level:
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
### Napier's Bones
##### Stage: 2 Challenge Level:
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
### All the Digits
##### Stage: 2 Challenge Level:
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
### Penta Post
##### Stage: 2 Challenge Level:
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
### Clock Face
##### Stage: 2 Challenge Level:
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
### Pies
##### Stage: 2 Challenge Level:
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
### Tom's Number
##### Stage: 2 Challenge Level:
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
### Practice Run
##### Stage: 2 Challenge Level:
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
### Zios and Zepts
##### Stage: 2 Challenge Level:
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
##### Stage: 2 Challenge Level:
Use the information to work out how many gifts there are in each pile.
### Integrated Product Sudoku
##### Stage: 3 and 4 Challenge Level:
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
### Machines
##### Stage: 2 Challenge Level:
What is happening at each box in these machines?
### Factor-multiple Chains
##### Stage: 2 Challenge Level:
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
### Highest and Lowest
##### Stage: 2 Challenge Level:
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
### What's My Weight?
##### Stage: 2 Short Challenge Level:
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
### Repeaters
##### Stage: 3 Challenge Level:
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
### What's in the Box?
##### Stage: 2 Challenge Level:
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
### Sept03 Sept03 Sept03
##### Stage: 2 Challenge Level:
This number has 903 digits. What is the sum of all 903 digits?
### Current Playing with Number Upper Primary Teacher
##### Stage: 2 Challenge Level:
Resources to support understanding of multiplication and division through playing with number.
### Jumping
##### Stage: 2 Challenge Level:
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
### Escape from the Castle
##### Stage: 2 Challenge Level:
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out? | 2,201 | 9,150 | {"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} | 4.15625 | 4 | CC-MAIN-2017-39 | latest | en | 0.839688 |
https://ca.answers.yahoo.com/question/index?qid=20200330005827AAvv0aZ | 1,590,421,876,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347388758.12/warc/CC-MAIN-20200525130036-20200525160036-00427.warc.gz | 275,204,150 | 20,832 | Sydnei asked in Science & MathematicsMathematics · 2 months ago
# Optimization Problem?
Find the dimensions of the rectangle of maximum area that can be formed from a 50-in piece of wire.
What are the dimensions and maximum area?
Relevance
• Philip
Lv 6
2 months ago
Let (length,width) of rectangle = (x,y).
Perimeter of rectangle = 2(x+y) = 50 and y = 25-x.
Area of rectangle = f(x) = x(25-x) = 25x - x^2.
f'(x) = 25 - 2x.
f''(x) = -2.
An extremum occurs wherever f'(x) = 0.
f'(x) = 0 for x = (25/2).
f''(x) = -2, < 0, ---> extremum is a maximum.
f(25/2) = (25/2)[2(25/2) -1(25/2)] = (25/2)^2 = (625/4) = 156.25.
The rectangle is actually a square of side length (25/2).
• Philip
Lv 6
2 months agoReport
Sadly, I must reject your criticism until you present valid proof that I did, in fact, make several
mistakes. Where your thumbs point is of little concern to me.
• ted s
Lv 7
2 months ago
it is well known that the figure is a square
• rotchm
Lv 7
2 months ago
Let x & y be the width & length resp.
You Are given that 2x+2y = 50, right?
And the area is A = xy, right?
From the first eqs, solve for y. So you have y = y(x). Plug this y(x) into the second eqs. You now have the area A(x) solely as a fct of x. What is this function A(x) ?
Answer that & we will proceed.
• Philip
Lv 6
2 months agoReport
Congratulations. I did exactly that which you did and proceeded without your permission. I felt,
unlike you, no need to explain length & width & how area of a rectangle is calculated as if my fellow participants were totally ignorant children. | 487 | 1,574 | {"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} | 3.765625 | 4 | CC-MAIN-2020-24 | latest | en | 0.91011 |
https://math.answers.com/Q/What_is_the_percentage_of_75_out_go_85 | 1,718,582,557,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861674.39/warc/CC-MAIN-20240616233956-20240617023956-00208.warc.gz | 355,117,815 | 47,284 | 0
# What is the percentage of 75 out go 85?
Updated: 9/23/2023
Wiki User
11y ago
percentage of 75 out of 85 = 88.24%
= 75/85 * 100%
= 0.8824 * 100%
= 88.24%
Wiki User
11y ago
Earn +20 pts
Q: What is the percentage of 75 out go 85? | 98 | 241 | {"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-2024-26 | latest | en | 0.884717 |
https://wiki.projecttopics.org/math/ | 1,696,284,325,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511021.4/warc/CC-MAIN-20231002200740-20231002230740-00669.warc.gz | 667,186,422 | 7,954 | Wiki » Math
# Math
Dive into the 'Math' category to unravel the intricacies of numbers and equations. Whether it's about transforming fractions into decimals, or the other way around, this space provides comprehensive guides to help you. It's a great resource for students, educators, or anyone looking to refresh their math skills or satisfy their numerical curiosity.
## 5/9 as a decimal
Welcome! Today, we take a close look at fractions. Our task? To convert 5/9 into a decimal. Don't worry, we'll break it down, step by step. With this guide, you'll have it down in no time. So let's get started! Before diving in, let's understand these terms. A fraction is a part of a whole....
Math / How-To
04.06.23
9
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## 5/16 as a decimal
We aim to convert the fraction 5/16 into a decimal. That's our target. First, we need to know what these terms mean. A fraction is a part of a whole. A decimal is a way to write a number that is not an entire number. Every fraction is a division problem. It's simple math. The number on top, the 5,...
Math / How-To
04.06.23
9
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## 9/16 as a decimal
In math, we use fractions and decimals a lot. They help us talk about parts of a whole. A fraction like 9/16 splits an entire into 16 parts. We then take 9 of those parts. Decimals are different. They are a way to write fractions with a base of 10. So, the fraction 9/16 and the decimal 0.5625 are...
Math / How-To
04.06.23
10
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## 0.8125 as a fraction
Decimals and fractions are close pals in math. They often depict the same values but in varied ways. For instance, the decimal .8125 can also be represented as a fraction. First, recognize what a decimal is. It's a way to show a whole unit that's been split into even parts....
Math / How-To
04.06.23
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## 0.6875 as a fraction
The path from decimals to fractions can be bumpy. But don't worry! We have a roadmap. Our target? .6875. Before we start, it's good to know our number. The decimal .6875 has four digits after the decimal point. That's a hint! The key to moving from decimals to fractions is knowing place value....
Math / How-To
04.06.23
12
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## 0.4375 as a fraction
Hello there! Want to turn .4375 into a fraction? Don't worry, we'll guide you. Get ready to learn and have fun! You'll be a pro in no time. First, let's identify the place value of .4375. In our case, '4375' is in the ten-thousandths place. Next, write .4375 at 4375/10000....
Math / How-To
04.06.23
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## 2.4 as a fraction
Today, we tackled 2.4. Can we make it a fraction? Let's find out. Step one is easy. Just spot the '4' in 2.4. It's in the tenths place. Simple, isn't it? In step two, we frame 2.4 as 24/10. The whole number '2' moves to the tens place, making it '24'. The decimal gets shifted....
Math
04.06.23
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## 0.16 as a fraction
Hello math enthusiasts! Today, we're converting 0.16 as a fraction. It's a simple task. No worries. Let's jump right in. To start, look at 0.16. The '16' sits in the hundredths place. This knowledge is key for the upcoming steps. Next, we express 0.16 as 16/100. The '16' becomes our numerator, and...
Math / How-To
03.06.23
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0
## 0.35 as a fraction
Decimals and fractions seem entirely unique. But they're not. This guide helps you see that. So, let's start with 0.35. First, spot the decimal places. Here, '35' is in the hundredths place. This knowledge is key. Now, write 0.35 as 35/100. That's your fraction. Keep in mind that 35 and 100 are...
Math / How-To
03.06.23
10
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## 0.9 as a fraction
Decimals and fractions are buddies. They both tell us about parts of a whole. We're dealing with 0.9 here. It's less than 1, but more than 0. In the world of fractions, how can we write it? That's our focus. To start, note that 0.9 is a simple decimal. When we write it as a fraction, we look at...
Math / How-To
03.06.23
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0 | 1,107 | 3,810 | {"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} | 4.6875 | 5 | CC-MAIN-2023-40 | latest | en | 0.921351 |
https://www.mrexcel.com/board/tags/google-spreadsheets/ | 1,696,364,109,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511220.71/warc/CC-MAIN-20231003192425-20231003222425-00664.warc.gz | 973,832,419 | 13,677 | Hi, I have a google spreadsheet and all the columns are continuously updating based on the website values. Is there a way to record the highest value that a cell had during all this time/for a particular period? It is like recording the last 24 hour high for financial markets. Thanks
2. ### Date diff with multiple conditions
Hi, Currently I am computing the date difference in days using this formula (which works): =if(and(ISNUMBER(W2),ISNUMBER(H2)),W2-R2,"") However, I would like to restrain the output and only consider values between 5 and 150. So I would like the function to say If W2 isnumber and if H2...
3. ### Is it possible to build such a application using Microsoft Excel or should I stick to googlesheets?
For a personal project, I am trying to build an application for data collection. This is the idea for the application 1. The user enters data into the spreadsheet template using either an android mobile phone or chrome browser 2. Each week, the user creates a new spreadsheet from the...
4. ### Google Sheets SUM + CountIfs formula not working
I'm using Google Sheets and am trying to get this formula to work to give the me the following count: Count when Column T = Kenneth AND Column U = (Pending OR Contacted) AND Column W has a date that falls between the dates shown in B14 and B15. This is what I have so far...
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Hey guys, I'm running an email script which works fine but only want it to run through the last row with data in it. I don't need it or want it to run if there is no data obviously. How do I reflect that in the example script below? For example, say there are only 3 rows of data in my sheet...
6. ### Small Bug Fix to a Multi If Formula
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Hi, So, I'm creating a gantt chart in google spreadsheets and need to have bars fill in specific colors based on the start date, estimated completion date, todays date, and the tasks progress. In other words, I need the time between the start date and estimated completion date to be gray. As...
Hello all, This is technically not an Excel question but about Google spreadsheets because I know how to do this on Excel but it won't work on Google spreadsheets. I need to count all total instances of the word "Freelance" in a column A with a corresponding value of "London" in a column B...
Hello all, I have used quite a few COUNTIFS formulas in Excel that do not translate into Google spreadsheets. I was wondering if anyone would know how to translate the following formula into Google spreadsheets...
10. ### Can I identify a specific permutation of responses to a survey and display it?
I very much appreciate any and all help in accomplishing this objective as follows: I have an online survey which has 9 list box questions. The only options for each question is "A" or "B". When the form is submitted I will have one row with some "9 column permutation" of "A's" and "B's". Each...
Hi, Anyone heard of a decent way to import spreadsheet data from Google Spreadsheets into an excel document so the resulting excel spreadsheet has live updatable google spreadsheet data? Regards Steve Flavel Pharmacist from Queensland, Australia
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http://www.slidesearchengine.com/slide/midterm-review-1 | 1,500,706,244,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549423903.35/warc/CC-MAIN-20170722062617-20170722082617-00076.warc.gz | 544,721,145 | 8,023 | # midterm review 1
40 %
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Published on November 2, 2007
Author: Brainy007
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CS248 Midterm Review: CS248 Midterm Review Michael Green and Sean Walker (based on the work of previous TAs) CS248 Midterm: CS248 Midterm Mon, November 1, 7-9 pm, Gates B01 Mostly “short answer” questions Keep your answers short and sweet! Covers lectures up to Tuesday, Oct 26 plus taxonomy from start of last lecture Review session slides available from class website Exam is closed book, closed notes Raster Displays, Resolution, Perception: Raster Displays, Resolution, Perception CRTs 3 phosphors for “red”, “green”, and “blue” Triads and shadow mask Measures of spatial resolution physical vs. addressable resolution Human spatial frequency sensitivity: Human spatial frequency sensitivity Sensitivity highest in fovea Frequency sensitivity Phase sensitivity (Vernier acuity) Temporal sensitivity Flicker (50-70Hz) Perceived motion 12 Hz = cartoons, 24 Hz = film, 60 Hz = video Raster Displays, Resolution, Perception: Raster Displays, Resolution, Perception Human intensity sensitivity Response to intensity is nonlinear Gamma in cameras, CRTs Gamma correction Raster Displays, Resolution, Perception: Raster Displays, Resolution, Perception Sample (easy) question: A scene is photographed with a TV camera with gamma=0.5 and displayed on a CRT with gamma=2.4. If we want system gamma to be 1.0, we should do gamma correction with what exponent? Color: Color Perception of color Humans are trichromat Three cones sensitive to “red”, “green”, and “blue” Overlapping response curves Know their general shapes! Color matching Color matching experiment Color spaces: Color spaces Linear colorspaces , , space (perceptual stimulus) R, G, B space X, Y, Z space Non-linear colorspaces HSV Spectral locus Gamut of reproducible colors Color: Color Sample questions: 1. Circle those colors that are not reproducible with a single monochromatic light Red Yellow Blue Magenta White Green Color: Color Sample questions: 2. If you had a special CRT that could produce pure spectral colors, how many spectral colors would you need to represent a normal RGB color gamut? How about the spectral locus? Sampling and Antialiasing: Sampling and Antialiasing The sampling and reconstruction pipeline: Prefiltering Sampling Resampling Reconstruction Aliasing in the frequency domain Filtering and convolution Duality: F(x)*G(x) <=> F(w)G(w) Sampling and Antialiasing: Sampling and Antialiasing Prefiltering vs. postfiltering Desirable filters for antialiasing Box, pyramid, gaussian, sinc Methods of antialiasing Supersampling: regular vs. stochastic Analytical antialiasing Sampling and Antialiasing: Sampling and Antialiasing Sample questions: What is the result of convolving a 1-D box filter with itself? Which of the following would affect your choice of a reconstruction filter? pixel shape choice of prefilter actual size of display Rasterization: Rasterization Rasterization of lines DDA, incremental algorithm Rasterization of polygons Only pixels in the polygon Supersampling Patterns: understand its effect on the image Rasterization: Rasterization Sample question: If you rasterized this line using DDA, which pixels would get turned on? Digital Compositing: Digital Compositing What is compositing? The compositing approximation Conditions for validity Compositing algebra: Compositing algebra Digital Compositing: Digital Compositing Sample question: You are doing the special effects for a movie, and need to composite a computer generated object over a live background. Why should you use an 8-bit alpha matte rather than a binary (1-bit) matte, even if the computer-generated object is fully opaque? Transformations: Transformations Homogeneous coordinates – why? Matrices rotation, translation, scale, shear in 2D, 3D Know the form of each kind Geometric properties preserved/changed by each kind Composing transformations multiply matrices in reverse order Transformations: Transformations Sample questions Compute the 2D transform that translates an object centered at (-3,4) to the origin, then rotates it by +45o, then translates it to (10,5). What sequence of transforms would cause the triangle to change as shown below ? GOOD LUCK AND HAPPY HALLOWEEN!: GOOD LUCK AND HAPPY HALLOWEEN!
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View Test Prep - Midterm review (1) from MBAB 5P02 at Brock University. | 1,373 | 5,708 | {"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} | 2.609375 | 3 | CC-MAIN-2017-30 | longest | en | 0.785457 |
https://termaviation.com/what-is-mac-in-aviation/ | 1,713,157,082,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816942.33/warc/CC-MAIN-20240415045222-20240415075222-00053.warc.gz | 521,580,955 | 43,822 | # What is MAC in Aviation? (Mean Aerodynamic Chord)
In the field of aviation, there are numerous terms and concepts that pilots, engineers, and enthusiasts must be familiar with. One such term is the mean aerodynamic chord (MAC), which plays a crucial role in the design and performance of aircraft. The mean aerodynamic chord, often represented by its abbreviation MAC, is a fundamental parameter that helps determine the stability and control characteristics of an aircraft.
## Understanding the Mean Aerodynamic Chord
The mean aerodynamic chord is a measurement used to simplify the complex shape of an aircraft wing into a single average chord length. This average chord length represents the wing geometry over its entire span, and it is crucial for various important calculations and design considerations. The MAC is determined by dividing the wing area by the wing span.
The MAC is typically measured from the leading edge of the wing to a point where the chord length reaches 0.25 units. This point is usually found near the wing’s mid-section. However, it’s important to note that the MAC may vary depending on the specific aircraft design and manufacturer’s specifications.
## The Importance of the Mean Aerodynamic Chord
Knowing the MAC is essential for various aspects of aircraft design and operation. Here are some key reasons why the mean aerodynamic chord is important:
1. Stability and Control: The MAC is crucial for determining the stability and control characteristics of an aircraft. It helps in assessing the aircraft’s pitch stability, yaw stability, and roll control effectiveness. Understanding the MAC allows engineers to design and optimize the aircraft’s control surfaces, such as the ailerons, elevators, and rudder, to ensure proper maneuverability and stability.
2. Wing Loading: The MAC is also utilized in determining the wing loading of an aircraft. Wing loading refers to the weight carried by each unit of wing area. It is an important parameter for assessing the aircraft’s performance, such as its ability to climb, maneuver, and operate at different speeds. By knowing the MAC and wing area, engineers can calculate the wing loading and make design decisions accordingly.
3. Center of Gravity: The MAC plays a crucial role in determining the aircraft’s center of gravity (CG). The CG refers to the point on an aircraft where its weight is assumed to be concentrated. It is essential to maintain the CG within specified limits to ensure the aircraft’s stability and controllability. The MAC provides a reference point for calculating the CG location and making adjustments to achieve the desired balance.
Considering the significance of the MAC in aircraft design and operation, it is crucial to accurately determine its value. Different types of aircraft may have different MAC values, and variations may even exist within aircraft of the same type but different models or configurations. Manufacturers typically provide MAC values and specifications in the aircraft’s technical documentation.
## The Mean Aerodynamic Chord in Aircraft Design
When designing an aircraft, engineers consider the MAC as a critical parameter. Here are some key considerations related to the mean aerodynamic chord in aircraft design:
1. Wing Shape and Performance: The MAC helps in determining the optimal wing shape and size for a given aircraft design. By analyzing the MAC in conjunction with other factors like wing sweep, aspect ratio, and airfoil selection, engineers can optimize the wing’s aerodynamic performance. This includes minimizing drag, maximizing lift, and enhancing efficiency during different flight phases.
2. Control Surface Sizing: Control surfaces, such as ailerons, elevators, and rudder, are designed based on the MAC to ensure optimal control and maneuverability. The control surface dimensions, including their span, hinge line, and deflection range, are determined by considering the MAC and the desired aircraft characteristics. This enables the pilots to have precise control over the aircraft during various flight conditions.
3. Stability and Maneuverability: The MAC is directly linked to an aircraft’s stability and maneuverability. By positioning the MAC at the appropriate location along the wing, engineers can optimize stability and control characteristics. This involves evaluating the longitudinal, lateral, and directional stability requirements and adjusting the wing design accordingly. Achieving the desired balance between stability and maneuverability contributes to a safe and predictable flight experience.
The mean aerodynamic chord is a fundamental concept in aviation that influences various aspects of aircraft design, performance, and handling. Its accurate determination and consideration are crucial for ensuring safe and efficient flight operations. Whether it’s calculating wing loading, designing control surfaces, or assessing stability characteristics, the MAC remains a key parameter in the aviation industry.
For More: What is GP in Aviation? (Glide Path) | 922 | 5,055 | {"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-2024-18 | longest | en | 0.942618 |
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When a light beam emerges from water into air, the average light speed A. remains the same. B. decreases. C. increases.
When a light beam emerges from water into air, the average light speed increases.
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When a light beam emerges from water into air, the average light speed increases.
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Home | Contact | Blog | About | Terms | Privacy | © Purple Inc. | 1,592 | 5,308 | {"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} | 2.609375 | 3 | CC-MAIN-2020-05 | latest | en | 0.91334 |
https://economics.stackexchange.com/questions/30606/why-is-consumer-surplus-the-area-under-the-curve | 1,719,046,568,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862310.25/warc/CC-MAIN-20240622081408-20240622111408-00865.warc.gz | 183,566,772 | 39,947 | # Why is consumer surplus the area under the curve?
So I understand that the definition of consumer surplus is the difference between what the consumer pays and what the consumer would have been willing to pay. I just don't understand why the consumer surplus is the area of the triangle, as shown in the diagram. Is it representing all the possible consumer surpluses?
Imagine that there are $$n$$ consumers in the market. You sort them by their willingness to pay from high to low. So the first consumer is willing to pay very high, and so on. Let's say the willingness to pay (sorted) is 12, 10, 9, 7, 5, 4, 2. This is represented by the downward-sloping demand curve.
Let's say the price is \$8. The first consumer's surplus is $$12-8 = 4$$. The second consumer's surplus is $$10-8 = 2$$. The third consumer's surplus is $$9-8 = 1$$. The fourth consumer onward wouldn't buy the item, since their willingness to pay is lower than the price. Their surpluses are all zero. They are the ones on the right of the equilibrium quantity. The sum of the consumers' surplus is 4 + 2 + 1 = 7, which is given by the area under the demand curve and above the price the consumer pays. Hope that helps! • +1 This is a good explanation of consumer surplus for a case in which each consumer buys at most one item (or unit of the good), but the price they are willing to pay differs. It should be noted however that consumer surplus can also arise, even for consumers with identical willingness to pay, if the number of items each is willing to pay for is greater when the price is lower - say 1 item each at price \$12, 2 at \$10, 3 at \$8. Commented Aug 22, 2019 at 14:54
Using almost 50 million individual-level observations [...], we estimate that in 2015 the UberX service generated about \$2.9billion in consumer surplus in the four U.S. cities included in our analysis. For each dollar spent by consumers, about \$1.60 of consumer surplus is generated. Back-of-the-envelope calculations suggest that the overall consumer surplus generated by the UberX service in the United States in 2015 was \\$6.8 billion. | 506 | 2,103 | {"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": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2024-26 | latest | en | 0.96088 |
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The existence is an ergodic and complete phase space
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The existence is an ergodic and complete phase space
The whole existence is a multidimensional phase space [1]. Phase space denotes to an abstract space that records all possible states of a system. Each possible state corresponds to one unique point. The abstract phase space approach does away with the traditional location, velocity, energy and momentum involved with individual particles (or, for instance, galaxies), thus allowing us to understand the existence (not just our universe) as a whole.
Phase spaces are widely used in analytical mechanics. For an example of a very simple phase space, take a look at the phase space diagrams for a 1D oscillator [2]. Undamped and damped oscillators produce nice phase space curves (on the right) in two dimensions (position, velocity) that capture the essentials of the physical system. It's certainly overkill when you're dealing with such a simple system, but when your system has more degrees of freedom (more dimensions), it becomes truly useful. For instance, if you're dealing with a three dimensional oscillator, your phase space becomes six dimensional. While this sounds daunting, but it actually simplifies the mathematics: all the relevant physical quantities can be calculated as simple multidimensional volume and surface integrals or partial differentials without even thinking about the actual physical configuration. Writing the explicit non-phase space equations in the traditional way you learnt in school, by calculating forces, velocities and accelerations, is much more complicated and eventually becomes impossible. Yes, multidimensional volume integrals are easier.
Now, it is my belief that the phase space of the existence is ergodic [3] and the phase space structure is complete [4]. In non-mathematical terms that means that there are no "empty spaces" in the phase space and that every point of the phase space will be visited at least once. Now you see the power of the phase space approach. Without considering individual creatures, humans, galaxies or stars, it can be deduced that in such a system, every possible scenario will become reality at some point or another.
You will live every possible life (e.g. in one universe your friend here is you), all the possible variations of the earth exist (e.g. one with Mount Everest and one without it), there exists an improbable universe where all the galaxies have clustered right next to each other, and so on. Now, of course, this can't be sequential. We can't first have an earth with Mount Everest and then another earth without it.
The logical conclusions is that they have to exist in parallel. Hence, when the existence is exploring every possible point in the phase space, it generates an infinite number of parallel universes where the alternatives are explored. Satisfying ergodicity this way is possible, because the universes do not have to communicate with each other - in fact, satisfying the ergodicity requirement dictates that the parallel universes CANNOT communicate with each other.
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Agreed.
2. ### Factor y = -3x^2 - 2x + 5
When I need to solve a quadratic, I simply solve it by completing the square (unless, of course, it's already a perfect square trinomial). No formula to memorize, no factoring, just the same procedure every time. :smile: | 80 | 280 | {"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-2022-05 | latest | en | 0.900516 |
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Request time (0.022 seconds) [cached] - Completion Score 300000
1 yard equals how many inches?0.03 1 yard is how many inches0.02 1 inch equals how many yards0.2 how many inches make 1 yard0.46
one yard equals how many inches 1/2 yard equals how many inches 5/8 yard equals how many inches 1 4 yard equals how many inches 1/8 yard equals how many inches
10 results & 5 related queries
### 1 yard equals how many inches? - Answers
Yard32.4 Inch16.9 Foot (unit)6.8 Imperial units0.8 Length0.2 10.2 Unit of measurement0.1 Algebra0.1 Geometry0.1 Yard (sailing)0.1 Arithmetic0.1 Distance0.1 Richmond Shipyards0.1 Neil Diamond0.1 Foot0.1 Mathematics0.1 Home Improvement (TV series)0.1 Louis Farrakhan0.1 One half0.1 Calculus0.1
### 2 yards 1 foot equals how many inches? - Answers
Answers 84 inches2 yard foot = 7 feet7 feet = 84 inches
Yard30.5 Foot (unit)22.3 Inch20 Square foot0.6 Length0.3 Algebra0.2 Yard (sailing)0.2 Foot0.1 Distance0.1 Geometry0.1 Arithmetic0.1 10.1 Unit of measurement0.1 United States Postal Service0.1 Mathematics0.1 Home Improvement (TV series)0.1 Ultraviolet0.1 Calculus0.1 Louis Farrakhan0.1 Triangle0
### One yard equals how many inches? - Answers
One yard equals how many inches? - Answers yard = 3 feet, foot = 12 inches so yard = 3 12 = 36 inches
Yard28.1 Inch21.9 Foot (unit)10.4 Centimetre1 Fraction (mathematics)0.3 Length0.3 Yard (sailing)0.2 Algebra0.2 10.1 Geometry0.1 Distance0.1 Arithmetic0.1 Unit of measurement0.1 Foot0.1 One half0.1 Mathematics0.1 Neil Diamond0.1 Triangle0.1 Mole (unit)0.1 Home Improvement (TV series)0.1
### 1 yard equals how many feet? - Answers
Yard30.8 Foot (unit)27.7 Square yard2.3 Inch2.3 Square foot2 Cubic yard1 Imperial units0.9 Algebra0.4 Cubic foot0.3 Length0.3 Distance0.2 Geometry0.2 10.2 Triangle0.1 Rubik's Cube0.1 Mathematics0.1 Arithmetic0.1 Yard (sailing)0.1 Unit of measurement0.1 Beowulf0.1
### 1 yard has how many inches? - Answers
There are 3 feet in one yard , and 12 inches So yard =36 inches
Inch29 Yard26.9 Foot (unit)6 Meterstick1.2 Yard (sailing)0.3 10.2 Length0.2 Unit of measurement0.2 Mathematics0.1 Geometry0.1 Algebra0.1 Arithmetic0.1 Distance0.1 Ultraviolet0.1 Home Improvement (TV series)0.1 Gram0.1 Whitney Houston0.1 Foot0.1 Triangle0 One half0
### One half of a yard equals how many inches? - Answers
One half of a yard equals how many inches? - Answers yard =36 inches /2 yard 18 inches
Yard30.4 Inch15.3 Foot (unit)5.1 Imperial units0.7 Fraction (mathematics)0.4 One half0.3 Length0.2 Yard (sailing)0.2 Arithmetic0.1 Distance0.1 10.1 Unit of measurement0.1 Mathematics0.1 Home Improvement (TV series)0.1 Whitney Houston0.1 Calculus0.1 Corrosion0 Onion0 Multiplication algorithm0 Yard (land)0
### 44 inches equals how many yards? - Answers
Answers There are 22 yards in 44 inches 44 inches x yard /36 inches = .22 yards yards = 36 inches
Inch41.1 Yard17.1 Centimetre7.4 Foot (unit)5.9 Millimetre1.5 Rope0.6 Screw0.5 Mile0.5 Textile0.4 Yard (sailing)0.4 Square foot0.4 Dimensional analysis0.4 Acre0.3 United States customary units0.3 Cubic yard0.2 Length0.1 Gallon0.1 Unit of measurement0.1 Bolt (fastener)0.1 Arithmetic0.1
### 1 yd 1 ft equals how many inches? - Answers
Answers There are 12 inches & in one foot. There are 3 feet in one yard . Therefore, yard
Yard36.8 Foot (unit)14.8 Inch11.2 Cubic yard1.9 Square yard0.4 Mile0.4 Square inch0.3 3D rotation group0.3 Algebra0.3 10.2 Length0.2 Geometry0.1 Triangular prism0.1 Arithmetic0.1 Mathematics0.1 Unit of measurement0.1 Distance0.1 United States customary units0.1 Dodecagonal prism0.1 Ultraviolet0.1
### If 1 yard is equal to 3 ft how many inches is in 1 yard? - Answers
F BIf 1 yard is equal to 3 ft how many inches is in 1 yard? - Answers 36 inches 12 inches = foot 36 inches = 3 feet = 1yard
Yard27.5 Inch17.8 Foot (unit)17.7 Square foot0.4 Imperial units0.4 Length0.3 Algebra0.2 Cant (road/rail)0.2 10.1 Distance0.1 Mathematics0.1 Geometry0.1 Tea0.1 Yard (sailing)0.1 Arithmetic0.1 Triangle0.1 Rigel0.1 Home Improvement (TV series)0.1 Unit of measurement0.1 Equality (mathematics)0.1 | 1,370 | 4,124 | {"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 | 0.845003 |
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# Paul Berglund
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https://mycalcu.com/4-micrometers-to-meters | 1,701,482,003,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100309.57/warc/CC-MAIN-20231202010506-20231202040506-00676.warc.gz | 455,813,814 | 7,823 | # 4 micrometers to meters
4 micrometers to meters calculator converts 4 micrometers into meters quickly.
How many meters made 4 micrometers?
You can convert 4 micrometers into meters by dividing 4 by 1,000,000.
## Convert 4 μm to m
What is the value of 4 micrometers in meters?
4 micrometers is equal to 4.0E-6 m.
## 4 MICRO METERS Conversion to Other Lengths
Meters 4e-06 Millimeters 0.004 Feet 1.31234e-05 Centimeters 0.0004 Inches 0.00015748 Yards 4.37445e-06 Kilometers 4e-09 Miles 2.48602e-09
## Relevant Calculators
4 micrometers to m calculator converts 4 micrometers into other units as well like km, mm, inches, yards, and more.
micrometers m
4.00 micrometers 4.0E-6 m
4.01 micrometers 4.0E-6 m
4.02 micrometers 4.0E-6 m
4.03 micrometers 4.0E-6 m
4.04 micrometers 4.0E-6 m
4.05 micrometers 4.0E-6 m
4.06 micrometers 4.0E-6 m
4.07 micrometers 4.0E-6 m
4.08 micrometers 4.0E-6 m
4.09 micrometers 4.0E-6 m
4.10 micrometers 4.0E-6 m
4.11 micrometers 4.0E-6 m
4.12 micrometers 4.0E-6 m
4.13 micrometers 4.0E-6 m
4.14 micrometers 4.0E-6 m
4.15 micrometers 4.0E-6 m
4.16 micrometers 4.0E-6 m
4.17 micrometers 4.0E-6 m
4.18 micrometers 4.0E-6 m
4.19 micrometers 4.0E-6 m
4.20 micrometers 4.0E-6 m
4.21 micrometers 4.0E-6 m
4.22 micrometers 4.0E-6 m
4.23 micrometers 4.0E-6 m
4.24 micrometers 4.0E-6 m
4.25 micrometers 4.0E-6 m
4.26 micrometers 4.0E-6 m
4.27 micrometers 4.0E-6 m
4.28 micrometers 4.0E-6 m
4.29 micrometers 4.0E-6 m
4.30 micrometers 4.0E-6 m
4.31 micrometers 4.0E-6 m
4.32 micrometers 4.0E-6 m
4.33 micrometers 4.0E-6 m
4.34 micrometers 4.0E-6 m
4.35 micrometers 4.0E-6 m
4.36 micrometers 4.0E-6 m
4.37 micrometers 4.0E-6 m
4.38 micrometers 4.0E-6 m
4.39 micrometers 4.0E-6 m
4.40 micrometers 4.0E-6 m
4.41 micrometers 4.0E-6 m
4.42 micrometers 4.0E-6 m
4.43 micrometers 4.0E-6 m
4.44 micrometers 4.0E-6 m
4.45 micrometers 4.0E-6 m
4.46 micrometers 4.0E-6 m
4.47 micrometers 4.0E-6 m
4.48 micrometers 4.0E-6 m
4.49 micrometers 4.0E-6 m
4.50 micrometers 5.0E-6 m
4.51 micrometers 5.0E-6 m
4.52 micrometers 5.0E-6 m
4.53 micrometers 5.0E-6 m
4.54 micrometers 5.0E-6 m
4.55 micrometers 5.0E-6 m
4.56 micrometers 5.0E-6 m
4.57 micrometers 5.0E-6 m
4.58 micrometers 5.0E-6 m
4.59 micrometers 5.0E-6 m
4.60 micrometers 5.0E-6 m
4.61 micrometers 5.0E-6 m
4.62 micrometers 5.0E-6 m
4.63 micrometers 5.0E-6 m
4.64 micrometers 5.0E-6 m
4.65 micrometers 5.0E-6 m
4.66 micrometers 5.0E-6 m
4.67 micrometers 5.0E-6 m
4.68 micrometers 5.0E-6 m
4.69 micrometers 5.0E-6 m
4.70 micrometers 5.0E-6 m
4.71 micrometers 5.0E-6 m
4.72 micrometers 5.0E-6 m
4.73 micrometers 5.0E-6 m
4.74 micrometers 5.0E-6 m
4.75 micrometers 5.0E-6 m
4.76 micrometers 5.0E-6 m
4.77 micrometers 5.0E-6 m
4.78 micrometers 5.0E-6 m
4.79 micrometers 5.0E-6 m
4.80 micrometers 5.0E-6 m
4.81 micrometers 5.0E-6 m
4.82 micrometers 5.0E-6 m
4.83 micrometers 5.0E-6 m
4.84 micrometers 5.0E-6 m
4.85 micrometers 5.0E-6 m
4.86 micrometers 5.0E-6 m
4.87 micrometers 5.0E-6 m
4.88 micrometers 5.0E-6 m
4.89 micrometers 5.0E-6 m
4.90 micrometers 5.0E-6 m
4.91 micrometers 5.0E-6 m
4.92 micrometers 5.0E-6 m
4.93 micrometers 5.0E-6 m
4.94 micrometers 5.0E-6 m
4.95 micrometers 5.0E-6 m
4.96 micrometers 5.0E-6 m
4.97 micrometers 5.0E-6 m
4.98 micrometers 5.0E-6 m
4.99 micrometers 5.0E-6 m
## More Calculations
5 micrometers to meters 4.1 micrometers to meters 4.2 micrometers to meters 4.3 micrometers to meters 4.4 micrometers to meters 4.5 micrometers to meters 4.6 micrometers to meters 4.7 micrometers to meters 4.8 micrometers to meters 4.9 micrometers to meters | 1,805 | 3,545 | {"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-2023-50 | latest | en | 0.335485 |
https://ricardolevinsmorales.com/att-uverse-cat5-wiring-diagram/ | 1,656,771,359,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104141372.60/warc/CC-MAIN-20220702131941-20220702161941-00766.warc.gz | 519,122,365 | 45,349 | # Att Uverse Cat5 Wiring Diagram
Variety of att uverse cat5 wiring diagram. A wiring diagram is a streamlined conventional pictorial representation of an electrical circuit. It shows the elements of the circuit as streamlined shapes, as well as the power and also signal links between the tools.
A wiring diagram normally gives details regarding the family member setting as well as plan of gadgets as well as terminals on the tools, to assist in building or servicing the device. This differs a schematic layout, where the setup of the elements’ affiliations on the diagram usually does not represent the parts’ physical locations in the finished device. A photographic diagram would show a lot more detail of the physical look, whereas a wiring diagram utilizes an extra symbolic symbols to highlight affiliations over physical appearance.
A wiring diagram is frequently utilized to troubleshoot problems and to earn certain that the links have been made which whatever is present.
## att uverse cat5 wiring diagram
Wiring Diagram Pictures Detail:
• Name: att uverse cat5 wiring diagram – Att Uverse Wiring Diagram Efcaviation Inside 2 Requirements 6
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Wiring Diagram Sheets Detail:
• Name: att uverse cat5 wiring diagram – cat5 home wiring diagram save u verse home wiring diagram fresh att rh kobecityinfo cat 5 wiring diagram 568b cat 5 wiring diagram rj45
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Variety of att uverse cat5 wiring diagram. Click on the image to enlarge, and then save it to your computer by right clicking on the image.
A Beginner s Overview to Circuit Diagrams
A first look at a circuit representation may be complex, yet if you could read a metro map, you can review schematics. The objective is the very same: getting from factor A to point B. Literally, a circuit is the path that permits electricity to circulation.
The Language of Wiring
First, let s take a look at several of terms that you will have to know:
Voltage: Determined in volts (V), voltage is the pressure or pressure of electrical energy. This is typically supplied by a battery (such as a 9V battery) or mains electrical energy, the electrical outlets in your home run at 120V. Electrical outlets in various other countries run at a various voltage, which is why you require a converter when traveling.
Current: Existing is the flow of electrical energy, or more particularly, the circulation of electrons. It is measured in Amperes (Amps), and can only move when a voltage supply is connected.
Resistance: Measured in Ohms (R or O), resistance defines how conveniently electrons could stream via a material. Products such as gold or copper, are called conductors, as they easily permit circulation of movement (low resistance). Plastic, timber, and also air are examples of insulators, preventing the activity of electrons (high resistance).
DC (Straight Current). DC is a continuous flow of present in one direction. DC can stream not just via conductors, however semi-conductors, insulators, as well as even a vacuum.
A/C (Alternating Present). In Air Conditioning, the circulation of existing periodically alternates in between 2 instructions, frequently forming a sine wave. The regularity of Air Conditioner is measured in Hertz (Hz), and also is generally 60 Hz for electrical energy in domestic and service objectives.
The Schematics
Completing an electrical engineering degree and after that getting a job in the field means you will certainly see a lot a great deal a lot of these schematics. It s vital to recognize exactly what is going on with these.
Beginning to make good sense? These are the basics as well as may also seem noticeable or user-friendly to you, such as the wires and if they are attached. Whenever you identify your specific area of electric engineering, you may see more intricate representations and also symbols. You ll discover likewise that different countries utilize different icons. Of the 2 symbols for resistors above, the initial one is used in the U.S., while the second is utilized in Europe. You will certainly additionally learn more about the various icons made use of for buttons, various other power products, inductors, meters, lamps, LEDs, transistors, antennas, as well as much a lot more. | 934 | 4,376 | {"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-2022-27 | longest | en | 0.84127 |
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×
Find v(t) for t > 0 for the circuit of Figure P 9.8-5
ISBN: 9781118477502 422
Solution for problem P9.8-5 Chapter 9.8
Introduction to Electric Circuits | 9th Edition
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Problem P9.8-5
Find v(t) for t > 0 for the circuit of Figure P 9.8-5.
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STA3032 MODULE 1 ARTICLE I. 1.1-1.3.5 1) 1.1 Descriptive Statistics a) Population parameters- “a numerical summary concerning the complete collection of subjects” i) Notated by Greek characters b) Sample statistics- “a numerical summary concerning a subset of the population, from which we try to draw inference about the population parameter” i) Notated by the...
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https://buy-essay.com/answered-essay-vollmer-manufacturing-makes-three-components-for-sale-to-refrigeration-companies-the-components-are-processed-on-two-machines-a-shaper-and-a-grinder-the-times-in-minutes-required/ | 1,674,877,494,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499470.19/warc/CC-MAIN-20230128023233-20230128053233-00181.warc.gz | 170,366,093 | 12,900 | # Answered Essay: Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows.
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows.
Machine Component Shaper Grinder 1 6 4 2 4 5 3 4 2
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are \$8, \$6, and \$9, respectively.
a. Provide the mathematical formulation for this problem. Carefully define your decision variables, objective function, model constraints, and non-negativity statement.
Decision variables:
Let
A = units of component 1 manufactured
B = units of component 2 manufactured
C = units of component 3 manufactured
Objective function:
Objective function is to maximize the profits
Max Z = 8A + 6B + 9C
Constraints:
6A + 4B + 4C <= 7200 (Shaper machine available minutes)
4A + 5B + 2C <= 6600 (Grinder machine available minutes)
C <= 200 (No more than 200 units of component 3 can be sold)
B <= 1000 (Component 2 can be sold up to 1000 units)
A <= 1000 (Component 1 can be sold up to 1000 units)
A>=600 (company already has orders for 600 units of component 1 )
A,B,C>= 0 (Non-negativity costraints)
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# Screwed my GMAT
Author Message
Joined: 15 Dec 2012
Posts: 54
Kudos [?]: 9 [0], given: 14
GMAT 1: 700 Q48 V38
### Show Tags
06 Sep 2013, 09:09
Hey Guys
Trust you all are good
I wrote my GMAT and screwed it very badly... Scored meager 600... Q42 V28...
Please guide me how should i prepare for the next attempt.
I look forward to hear from you guys
Thanks
Kudos [?]: 9 [0], given: 14
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4491
Kudos [?]: 8758 [0], given: 105
### Show Tags
06 Sep 2013, 10:22
diehardmbafan wrote:
Hey Guys
Trust you all are good
I wrote my GMAT and screwed it very badly... Scored meager 600... Q42 V28...
Please guide me how should i prepare for the next attempt.
I look forward to hear from you guys
Thanks
Dear diehardmbafan,
I'm happy to help.
Here's a three-month study plan designed for someone who struggles with GMAT Verbal:
http://magoosh.com/gmat/2012/3-month-gm ... l-focused/
Here's a discussion of the best resources for GMAT prep.
http://magoosh.com/gmat/2013/best-gmat- ... rces-2013/
Here's a practice RC question:
http://gmat.magoosh.com/questions/2721
Here's a practice CR question:
http://gmat.magoosh.com/questions/3129
Here's a practice SC question:
http://gmat.magoosh.com/questions/3218
For each one of those, when you submit your answer, the next page will have both a video explanation and a text explanation. Each one of Magoosh's 1000+ practice questions has it's own video & text explanations, available as soon as you answer the question, for accelerated learning.
Let me know if you have any question.
Mike
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Kudos [?]: 8758 [0], given: 105
Re: Screwed my GMAT [#permalink] 06 Sep 2013, 10:22
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# PROBABILITY AND STATISTICS MULTIPLE CHOICE TEST
Probability and Statistics Quizzes | Study
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Probability - Multiple Choice - ProProfs Quiz
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40 MULTIPLE CHOICE QUESTIONS IN BASIC STATISTICS
MULTIPLE CHOICE QUESTIONS In the following multiple choice questions, circle the correct answer. 1. A numerical value used as a summary measure for a sample, such as sample mean, is known as a a. population parameter b.[PDF]
Examination 110 – Probability and Statistics Examination
The Probability and Statistics Examination consists of 45 multiple-choice test questions. The test is a three-hour examination based on material usually covered in undergraduate mathematics courses in math- ematical probability and statistics.[PDF]
STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE
STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS 1. If two events (both with probability greater than 0) are mutually exclusive, then: Suppose the probability of a positive test result is if someone has the disease, but the probability is only that someone has the disease if his or her test result was positive. A
AP Statistics Practice Test - Statistics and Probability
This is a practice test for the multiple-choice section of the Advanced Placement Statistics Exam. Each question is followed by five possible answers. Choose the response that best answers the question. To start the test, tap the "Begin test" button. * AP and Advanced Placement Program are[PDF]
Exam 1 Practice Questions I - MIT OpenCourseWare
A multiple choice exam has 4 choices for each question. A student has studied enough so that the probability they will know the answer to a question is 0.5, the probability that they will be able to eliminate one choice is 0, otherwise all 4 choices seem equally plausible.
To Engineer is Human: Guessing on Multiple Choice Tests
Aug 02, 2013The mean is n*p and the variance is sqrt[ n * p *(1- p)], where n is the number of trials and p is the probability of the desired outcome. In our example multiple-choice test, whether you guess randomly or choose 'C' every time, you would expect, Author: Alohonyai
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https://iitutor.com/simplified-circle-drawing-for-high-school-students/ | 1,716,712,553,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058872.68/warc/CC-MAIN-20240526074314-20240526104314-00104.warc.gz | 263,252,129 | 28,140 | Simplified Circle Drawing for High School Students
Hey there, high school math whizzes! Ready to dive into the wonderful world of circle drawing circle? I’m your friendly math tutor, and today, we will make drawing circles a piece of cake. Let’s turn those complex equations into fun and creative sketches. So, buckle up and let’s get started!
Why Circle Drawing Matter (And They Do!)
Before we jump into drawing, let’s talk about why circles are a big deal. From the wheels on your skateboard to the orbits of planets, circles are everywhere. Understanding how to draw them is like having a superpower—it opens doors to some cool stuff. So, get ready to see circles in a whole new light!
The Basics of Circle Equations: No Jargon Zone
Alright, let’s lay the groundwork. Circle equations can sound intimidating, but fear not! We’re keeping it straightforward. I’ll break down the elements for you, making sure you understand the basics before we dive into the drawing fun.
Visualizing Circles: Let’s Get Creative
Now, let’s spice things up a bit. Visualizing circles is key to mastering the art of drawing them. We’ll explore some nifty techniques using real-world examples and interactive tools. Prepare to see circles in ways you never thought possible.
Step-by-Step Circle Drawing: Time to Sketch!
Now, grab your pencils because here comes the fun part! I’ll guide you through a step-by-step process of drawing circles from equations. We’re starting with the easy stuff and gradually levelling up. By the end of this section, you’ll be the Picasso of circle drawing.
First, the Basics of Circle Drawing
We’ll start with the fundamental techniques. How to find the centre, how to figure out the radius—simple, bite-sized lessons that build your confidence.
As we progress, we’ll tackle more complex scenarios. I’ll share tricks to handle those equations that might look like a puzzle.
Real-Life Examples
We’re not just drawing circles for the sake of it. I’ll show you how these skills translate into real-life situations. Trust me; math is cooler than you think!
Practical Exercises: Hands-On Fun
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Circle Drawing in the Wild
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Mistakes Welcome!
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Tips and Tricks for Success: Math Hacks 101
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Drawing with Confidence
Confidence is half the battle. I’ll share strategies to boost your confidence so you can easily tackle any circle equation.
Common Pitfalls to Avoid
We’ll navigate the common mistakes together. Spoiler alert: I’ve made them, too, so no judgment here.
But wait, there’s more! Drawing circles goes beyond the classroom. Whether you’re into art, technology, or science, your circle-drawing skills can open doors to exciting possibilities.
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Science Connections
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Conclusion: You Did It!
Congratulations, high school math champ! You’ve successfully navigated the world of circle drawing. Remember, math is not just about numbers; it’s a tool that empowers you to understand and create the world around you.
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https://www.physicsforums.com/threads/two-blocks-and-a-pulley-friction-problem.892369/ | 1,566,355,399,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027315750.62/warc/CC-MAIN-20190821022901-20190821044901-00180.warc.gz | 924,557,035 | 17,614 | Two Blocks and a Pulley Friction Problem
joemost12
1. Homework Statement
System comprised blocks, a light frictionless pulley and connecting ropes (see diagram). The 9.0kg block is on a perfectly smooth horizontal table. The surfaces of the 12kg block are rough, with μk = .2 between the two blocks. If the 5.0 kg block accelerates downward when it is released, find its acceleration
Fairly certain my solution is correct, just would love a second opinion!
Diagram:
http://i.imgur.com/6k5Im7W.png
2. Homework Equations
3. The Attempt at a Solution
So for the 12kg Block my reasoining for its forces was:
Fnet = Ffriction - T1 = Ma = 0
Fnormal = (12kg)(9.8 m/s^2 _ = 117.6
ForceFriction = (.2)(11.6) = 23.52 N
Then for the 9 KG block:
Fnet = T2 - ForceFriction
T2 - 23.52N = Ma
T2 - 23.52N = (9kg)a
23.52-T2 = (9 kg) a
Then finally for the hanging 5.0 KG block:
T2 - Fg = ma
T2 - (5)(9.8) = (5)a
T2 - 49N = 5(a)
Then I simply solved the system of equations to find the value of A
Set two equations for the 9kg and the 5kg block in terms of a
(T2 - 49N)/5 kg = (23.52N - T2)/9kg
Solving to find that T2 = 39.9
Then simply plug that value back into T2 - 49N = 5a
a = 1.82 m/s^2
Related Introductory Physics Homework Help News on Phys.org
Mentor
Looks good.
joemost12
Looks good.
Great. Thanks
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# Manual Reference Pages - GMX-VANHOVE (1)
### NAME
gmx-vanhove - Compute Van Hove displacement and correlation functions
Synopsis
Description
Options
### SYNOPSIS
gmx vanhove [-f [<.xtc/.trr/...>]] [-s [<.tpr/.tpb/...>]]
[-n [<.ndx>]] [-om [<.xpm>]] [-or [<.xvg>]]
[-ot [<.xvg>]] [-nice <int>] [-b <time>] [-e <time>]
[-dt <time>] [-[no]w] [-xvg <enum>] [-sqrt <real>]
[-fm <int>] [-rmax <real>] [-rbin <real>] [-mmax <real>]
[-nlevels <int>] [-nr <int>] [-fr <int>] [-rt <real>]
[-ft <int>]
### DESCRIPTION
gmx vanhove computes the Van Hove correlation function. The Van Hove G(r,t) is the probability that a particle that is at r_0 at time zero can be found at position r_0+r at time t. gmx vanhove determines G not for a vector r, but for the length of r. Thus it gives the probability that a particle moves a distance of r in time t. Jumps across the periodic boundaries are removed. Corrections are made for scaling due to isotropic or anisotropic pressure coupling.
With option -om the whole matrix can be written as a function of t and r or as a function of sqrt(t) and r (option -sqrt).
With option -or the Van Hove function is plotted for one or more values of t. Option -nr sets the number of times, option -fr the number spacing between the times. The binwidth is set with option -rbin. The number of bins is determined automatically.
With option -ot the integral up to a certain distance (option -rt) is plotted as a function of time.
For all frames that are read the coordinates of the selected particles are stored in memory. Therefore the program may use a lot of memory. For options -om and -ot the program may be slow. This is because the calculation scales as the number of frames times -fm or -ft. Note that with the -dt option the memory usage and calculation time can be reduced.
### OPTIONS
Options to specify input and output files:
-f [<.xtc/.trr/...>] (traj.xtc) (Input)
Trajectory: xtc trr cpt trj gro g96 pdb tng
-s [<.tpr/.tpb/...>] (topol.tpr) (Input)
Structure+mass(db): tpr tpb tpa gro g96 pdb brk ent
-n [<.ndx>] (index.ndx) (Input, Optional)
Index file
-om [<.xpm>] (vanhove.xpm) (Output, Optional)
X PixMap compatible matrix file
-or [<.xvg>] (vanhove_r.xvg) (Output, Optional)
xvgr/xmgr file
-ot [<.xvg>] (vanhove_t.xvg) (Output, Optional)
xvgr/xmgr file
Other options:
-nice <int> (19)
Set the nicelevel
-b <time> (0)
First frame (ps) to read from trajectory
-e <time> (0)
Last frame (ps) to read from trajectory
-dt <time> (0)
Only use frame when t MOD dt = first time (ps)
-[no]w (no)
View output .xvg, .xpm, .eps and .pdb files
-xvg <enum> (xmgrace)
xvg plot formatting: xmgrace, xmgr, none
-sqrt <real> (0)
Use sqrt(t) on the matrix axis which binspacing in sqrt(ps)
-fm <int> (0)
Number of frames in the matrix, 0 is plot all
-rmax <real> (2)
Maximum r in the matrix (nm)
-rbin <real> (0.01)
Binwidth in the matrix and for -or (nm)
-mmax <real> (0)
Maximum density in the matrix, 0 is calculate (1/nm)
-nlevels <int> (81)
Number of levels in the matrix
-nr <int> (1)
Number of curves for the -or output
-fr <int> (0)
Frame spacing for the -or output
-rt <real> (0)
Integration limit for the -ot output (nm)
-ft <int> (0)
Number of frames in the -ot output, 0 is plot all | 1,010 | 3,330 | {"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-2018-34 | latest | en | 0.740939 |
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# How Much Is It Worth to Use Facebook? It Depends
People do not, of course, have to pay to use Facebook. It’s free. The company’s revenues come mostly from advertising.
But in light of recent controversies, there have been discussions, at least outside of Facebook, about changing the business model. 1 What if people had to pay to use it? How much would they be willing to spend? Any answers would tell us something important about the value of social media in general.
I recently conducted a pilot experiment to obtain some preliminary answers. Using Amazon’s Mechanical Turk, I tried to find out, from 400 Facebook users, exactly how much the platform is worth.
More specifically, I asked 200 Facebook users a simple question: “Suppose that you had to pay for the use of Facebook. How much would you be willing to pay, at most, per month?”
I asked 200 other Facebook users a different question: “Suppose that you are being offered money to stop using Facebook. How much would you have to be paid per month, at a minimum, to make it worth your while to stop using Facebook?”
According to standard economic theory, the two questions should produce the same answers. But they didn’t — not close.
For the first question, the median answer was just \$1 per month. The average was \$7.38. Nearly half of participants (46 percent) said that they would pay \$0 if Facebook tried to charge them a fee.
For the second question, the median answer was a whopping \$59 per month. The average amount people would demand to leave Facebook was \$74.99.
What’s going on here?
Behavioral economists, led by Nobel Prize winner Richard Thaler, have drawn attention to the “endowment effect,” which means that most people would demand a lot more to give up a good than they would be willing to pay to get it in the first instance. For example, people might be willing to pay \$5 for a coffee mug with their college’s insignia on it — but if they are given such a mug, and are asked how much they would demand to sell it, they might say \$10.
My pilot study finds an endowment effect, but it’s unusually high. That tells us something important not just about Facebook but also other goods provided by modern technology. The critical point is that we are now used to getting those goods for free.
With that point in mind, return to my first question. Having had to pay nothing for Facebook, people dislike the idea of a monthly fee. When almost half said that they are willing to pay \$0, they are giving a protest answer, announcing: “If you are going to start charging me, well, then, forget about it!”
Those who said that they would pay only a small monthly amount (say, \$10) might well have been thinking that Facebook is worth more than that, but registering their displeasure at the idea of suddenly having to buy something that has long been provided gratis.
What about the high numbers for the second question? Many of the subjects undoubtedly enjoy Facebook, and they resent the very idea that “someone” is trying to pay them to stop using the platform. They demand a lot of money to give up what they have.
As it happens, Professor Eric Brynjolfsson and doctoral student Avinash Gannamaneni of the Massachusetts Institute of Technology, along with Felix Eggers of the University of Groningen, recently tried to value use of Facebook by asking consumers if they would prefer: (a) to maintain access to the platform or (2) to give it up for one month in response to a specified payment.
This is called a “discrete choice experiment.” It does not ask people (as I did) how much they would pay for some good or how much they would demand to give up some good, but instead to choose between two identified options and to specify the one they value more.
In controlling for various confounding factors, Brynjolfsson and his collaborators used highly sophisticated methods. They also used a large, nationally representative sample. Interestingly, the median answer was in the vicinity of \$40 to \$50 to give up Facebook for a month (slightly below the median answer to my second question).
Brynjolfsson and his collaborators conclude that digital goods, including social media, are producing large, monetizable benefits that are not included in conventional measures of well-being, such as gross domestic product.
That conclusion seems right, but we need to add two qualifications. The first is that whatever numbers we generate will be an artifact of the particular method we use — and they might be a poor approximation of the actual value of digital goods.
The second is that we need better measures of the effects of such goods on people’s well-being. People might be willing to pay \$10 each month for the right to use Facebook, or demand \$60 to give up that right. But what are the effects on their actual experience? Are they enjoying life more, or less, or the same?
We are just beginning to get answers to these questions, and the results are mixed. We need to learn much more.
This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.
1. Over the last year, I have served as a consultant to Facebook on several occasions, but not in connection with any of the issues and experiments discussed here.
To contact the author of this story:
Cass Sunstein at csunstein1@bloomberg.net
To contact the editor responsible for this story:
Katy Roberts at kroberts29@bloomberg.net
Before it's here, it's on the Bloomberg Terminal. | 1,164 | 5,512 | {"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-2018-22 | latest | en | 0.978123 |
http://www.shellsec.com/news/28027.html | 1,490,519,614,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218189198.71/warc/CC-MAIN-20170322212949-00326-ip-10-233-31-227.ec2.internal.warc.gz | 711,056,274 | 12,011 | # Simulating movement with ES6 generators
## Motivation
One particularly good example to infinite collections and ES6 generators is movement simulation. This requires a possibly complex calculation of the points along the path, and you need to take care of a few additional cases like collision detection and eventual termination. In a traditional way, you might use a while-loop that takes care of all the necessary parts. This results in an intermingled function that does many things. Using ES6 generators, you can nicely separate the different concerns, making the code easier to understand and maintain.
This post is intended only to give an example on how to use infinite collections for a more complex use case. It is not meant to give a thorough guide on every aspect of movement simulation.
### Typical parts
There are a few typical building blocks when you want to calculate movement. You might want to
• calculate the series of points that forms the path
• control when to terminate (for example collision detection)
• protect against infinite loops
• emit the points at a lower resolution for display
## Example
Live demo and full source are available.
For an example to this post, I’ll use a simple gravitational simulation. The user can hover over the canvas to set the initial velocity of a rock, then the path is calculated based on the gravitational pull of three planets. If the rock crashes into a planet or the infinite loop protection kicks in (after 3000 points) then the simulation terminates. Also because there is no need to have subpixel-level precision, only the points that moves at least a pixel are emitted.
### Using a while-loop
Without using an infinite collection, you might use a while-loop. In this function, all concerns are mixed, and it is quite hard to reuse this function.
``const generatePath = (vx, vy, gravityFn) => { // Contains the results const result = []; const vc = 0.1; // The current position and velocity let position = { x: 150, y: 150 } let velocity = { x: vx, y: vy } // How many points we've calculated so far let numPoints = 0; // Does the ball crashed to a planet? const isNotCrashed = () => { return holes.every((hole) => { return dist(hole, position) >= 3.5; }) }; // Keeps track of the last outputted position so that we know when we need to output another one let lastPosition = undefined; // Run until not crashed and not limited while (numPoints++ < 3000 && isNotCrashed()) { // Calculate the next position const { ax, ay } = gravityFn(position); velocity = { x: velocity.x + ax, y: velocity.y + ay } position = { x: position.x + velocity.x * vc, y: position.y + velocity.y * vc } // Calculate whether we should output a new point const shouldDraw = !lastPosition || dist(lastPosition, position) >= 1; if (shouldDraw) { lastPosition = position; result.push(position); } } return result; }``
### Using an infinite collection
If you are using an infinite collection, then the different parts can be separated. The path calculation does not need to know about neither stop conditions nor display resolution. It just emits the path infinitely.
``const pathGenerator = function*(vx, vy, gravityFn) { const vc = 0.1; let position = { x: 150, y: 150 } let velocity = { x: vx, y: vy } while (true) { const { ax, ay } = gravityFn(position); velocity = { x: velocity.x + ax, y: velocity.y + ay } position = { x: position.x + velocity.x * vc, y: position.y + velocity.y * vc } yield position; } }``
Using the generator function from above, we can then fit the other parts in:
• limit the number of points, so that it never results in an infinite loop
• lower the display resolution
The first part uses the limit operation. The order is important; if you put it to a later stage, it can easily result in an infinite loop, which we aim to prevent. 3000 is an arbitrary number, the exact value is not that important.
The stop condition is implemented using takeWhile . It is somewhat similar to the filter , but terminates once the predicate is false. It ensures that the simulation finishes when the trajectile is crashed into a planet.
Resolution conversion is done with a simple filter . It stores the last emitted point internally, and compare the stream to see if is displaced by at least a pixel. If not, then the point is filtered out.
This example uses the gentoo library, but you can use any others you like that provides these functions.
``const newPath = gentoo.chain(pathGen) .limit(3000) .takeWhile((point) => { return holes.every((hole) => { return dist(hole, point) >= 3.5; }) }) .filter((() => { let lastPoint = undefined; return (point) => { const result = !lastPoint || dist(lastPoint, point) >= 1; if (result) { lastPoint = point; } return result; } })()) .value()``
## Closing remarks
Infinite collections are useful only in a handful of situations and I’ve found that path calculation is a great example. They allow better separation, readability, and cleaner code overall over the traditional while-loop way, all without sacrificing performance. | 1,230 | 5,217 | {"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-2017-13 | longest | en | 0.885104 |
http://www.expertsmind.com/library/how-you-determined-which-improvement-option-to-recommend-51311242.aspx | 1,604,152,384,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107918164.98/warc/CC-MAIN-20201031121940-20201031151940-00249.warc.gz | 125,138,815 | 11,692 | ### How you determined which improvement option to recommend
Assignment Help Mechanical Engineering
##### Reference no: EM131311242
Using the Arena Simulation from the class lecture given by Dr. Eseonu, identify the best combination of system improvements as measured by the increase in average monthly profit per dollar invested. You may not spend more than \$4000 on changes. (Learning Outcome #2)
List the improvement options you tested and the increase in profit per dollar invested for each option tested.
Write a brief explanation of how you determined which improvement option to recommend.
Include a printed copy of the output sheet from Arena that shows the average number of good units produced in a month for the baseline (starting system) and for your final system with your recommended set of improvements.
#### Determine the total power dissipated from the disks
The paint on the rotating disk is worn off by dust in the air, exposing the base metal, which has an emissivity of s = 0.10. Determine the total power dissipated from the di
#### What is the ratio of the maximum tensile normal stress
A uniform cantilever beam with triangular cross section is loaded only due to its own weight (a load uniformly distributed along the length). What is the ratio of the maximu
#### Consider a cylindrical specimen of a steel alloy
Consider a cylindrical specimen of a steel alloy 8.0 mm (0.3150 in.) in diameter and 89 mm (3.504 in.) long that is pulled in tension. Determine its elongation when a load of
#### The wind mean energy velocity
A wind turbine with a diameter of 100 ft operates during a 24-h period in which the wind velocity may be approximated by half a sine wave as V(theta)=V(m)sin(pi*theta/24), whe
#### How many sectors should be present on the encoder disk
What is the minimum bit size that is required for each encoder output buffer? If the motion sensor used is an absolute encoder, how many tracks and how many sectors should b
#### Determine the air exit temperature
Air with a mass flow rate of 1.5 kg/sec and temperature of 400 K flows through a horizontal duct of an air heater. If 36 kJ/sec of heat is added to the flow, determine the air
#### Will careful storage beforehand prevent microcracking
If installation of a roll of fiber requires several hot and humid days to complete, will careful storage beforehand prevent microcracking? The mass diffusivity of water vapo
#### Find the hysteresis-damping constant of the structure
A load of 5000 N resulted in a static displacement of 0.05 m in a composite structure. A harmonic force of amplitude 1000 N is found to cause a resonant amplitude of 0.1 m. | 575 | 2,660 | {"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-2020-45 | latest | en | 0.904902 |
https://essaynexus.com/micro-economics-3/ | 1,680,084,569,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948965.80/warc/CC-MAIN-20230329085436-20230329115436-00190.warc.gz | 287,189,138 | 42,382 | ## MICRO ECONOMICS
We have been using the same set of data (Data Set One) in the notes to illustrate production and costs. I have provided Data Set One in both tables below. When costs were calculated in the notes, fixed costs were \$200. By using the term fixed costs economists are only referring to the fact that a firm must pay this expense no matter how much output it produces or sells. An example of a fixed cost could be the rent a small store pays on the space it rents. The rent will be the same for the duration of the lease, no matter if the store sells I item or 500 items. It is helpful to know what will happen to costs if the price of the variable or fixed resource changes.
PROBLEM ONE – Using the information in data set one, which I have included in the table below, recalculate total cost, fixed cost, variable cost, marginal cost, average total cost, average variable cost and average fixed costs if the price of the fixed input (the small stores rent) is not \$200 but \$220. A new lease may have caused the rent to increase. I have created Table 1 for you to put your answers in. Assume the price of the variable input, labor, is still \$50 per unit. When fixed costs change which other costs will increase? Compare the costs you calculate for table one to the costs calculated in the notes in chapter 7 to find the answer.
TABLE ONE FOR ANSWERS TO PROBLEM ONE
Units of Labor Total Product (output) FC VC TC MC ATC AVC AFC 0 0 1 3 2 7 3 12 4 16 5 19 6 21
Problem Two – Using the information in data set one, which I have included in the table below, recalculate total cost, fixed cost, variable cost, marginal cost, average total cost, average variable cost and average fixed costs if the price of the variable input (which is labor in this example) is not \$50 but \$55. I have created Table 2 for you to put your answers in. Assume that fixed costs remain at \$220. When the price of a variable input changes which other costs will increase? Compare the costs you calculate for table two to the costs calculated in table one to find your answers.
TABLE TWO FOR ANSWERS TO PROBLEM TWO
Units of Labor Total Product (output) FC VC TC MC ATC AVC AFC 0 0 1 3 2 7 3 12 4 16 5 19 6 21
Do you need a customized paper? Place an order with us! | 562 | 2,284 | {"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-2023-14 | latest | en | 0.899341 |
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# Understanding the Kelly Criterion
Kelly Criterion is a formula that can help traders and investors determine the optimal position size for a given trade, based on their trading edge and risk tolerance. It was developed by John L. Kelly Jr. in the 1950s, and has been used by traders and investors ever since. In this blog post, we will discuss how the Kelly % is calculated and how it can be used in day trading and investing.
The Kelly % Formula
The Kelly % formula is relatively simple, but it requires some input data to be accurate. Here is the formula:
Kelly % = (W – (1 – W)) / R
Where:
W = Winning probability
R = Win/Loss ratio
Let’s break down each component of the formula:
Winning Probability (W): This is the probability of your trade being profitable. It can be calculated by analyzing historical data, technical indicators, or fundamental analysis. In other words, it’s the percentage of time you expect to make money on a particular trade.
Win/Loss Ratio (R): This is the ratio of the average win to the average loss. For example, if your average win is \$200 and your average loss is \$100, then your win/loss ratio would be 2:1. You can calculate this ratio by analyzing historical data, or by tracking your trades over time.
Once you have calculated W and R, you can use the formula to determine the Kelly %, which represents the percentage of your trading account that you should risk on a particular trade.
How to Use the Kelly % in Day Trading and Investing
The Kelly % can be a useful tool for day traders and investors to determine their position size. However, it’s important to note that it’s not a one-size-fits-all solution, and traders and investors should always consider their own risk tolerance and trading goals.
Here are the steps to use the Kelly % in day trading and investing:
Step 1: Calculate your winning probability (W) and win/loss ratio (R) for a particular trade.
Step 2: Plug in the values of W and R into the Kelly % formula.
Step 3: Determine the position size that corresponds to the Kelly %, based on the total capital in your trading account.
For example, if your winning probability is 60% and your win/loss ratio is 2:1, your Kelly % would be:
Kelly % = (0.6 - 0.4) / 2
Kelly % = 0.1
Assuming you have \$10,000 in your trading account, your position size would be 10% of your account balance:
Position size = Kelly % * Account balance
Position size = 0.1 * \$10,000
Position size = \$1,000
This means you should risk \$1,000 on this trade, based on the Kelly % formula.
Conclusion
The Kelly % is a useful formula for day traders and investors to determine their position size, based on their trading edge and risk tolerance. However, it’s important to note that the Kelly % is not a guarantee of success, and traders and investors should always consider their own trading goals and risk management strategies. By using the Kelly % formula in combination with other trading tools and strategies, traders and investors can make more informed trading decisions and manage their risk more effectively.
## Recent Posts
See All
The Day something might have changed.
It was just an ordinary day, much like any other. I woke up, made breakfast, and headed off to work. But something felt off. I couldn't quite put my finger on it, but everything seemed different someh
bottom of page | 751 | 3,373 | {"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-2024-18 | longest | en | 0.924823 |
http://www.ques10.com/p/20229/renewable-energy-sources-question-paper-dec-2016-1/ | 1,558,330,737,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255562.23/warc/CC-MAIN-20190520041753-20190520063753-00291.warc.gz | 321,424,176 | 7,773 | Question Paper: Renewable Energy Sources : Question Paper Dec 2016 - Mechanical Engineering (Semester 8) | Mumbai University (MU)
0
## Renewable Energy Sources - Dec 2016
### Mechanical Engineering (Semester 8)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.
### Write short notes on any four of the following: Q.1(a,b,c,d)
1(a) Solar pond(5 marks) 1(b) Wind energy site selection(5 marks) 1(c) Mini and Micro hydel plants(5 marks) 1(d) OTEC plant(5 marks) 2(a) What is importance of renewable energy sources? What is the present energy scenario in India?(10 marks) 2(b) Describe different vertical axis wind turbines.(10 marks) 3(a) Using Kleins recommendation find daily global Radiation "Ho" for November 26 at Mumbai(19° 07'N, 72° 51 'E) if average sunshine hours is 9.8(10 marks) 3(b) Explain KVIC gobar gas plant in detail.(10 marks) 4(a) Calculate the variation of day length Over a Year (on 19th of each month of year 2016) of the following location and plot the same on graph and make your comments. Location Delhi (28° 35'N, 77° 42'E)(10 marks) 4(b) Explain with neat sketch any one wave energy conversion device.(6 marks) 4(c) What is solar declination angle.(4 marks) 5(a) Calculate the initial temperature and heat content per sq. Km above 40°C of an aquifer of thickness 0.5 km, depth 3km, porosity 5% under sediments of density 2700 kg/m3, specific heat capacity 840 J/kg.K, temperature gradient 30°C/km. Suggest the use of heat, if average surface temperature is 10°C, Also find the time constant for useful heat extraction with pumped water extraction of 100 ltr/skm2. What is the thermal power extracted initially and after 10 years?(10 marks) 5(b) What are gasifiers? Explain with neat sketch.(6 marks) 5(c) What is bentz coefficient(4 marks)
### Write a short note any four Q6.(a,b,c,d,e)
6(a) Fuel Cell(5 marks) 6(b) Limitation of Tidal energy(5 marks) 6(c) Community biogas plant(5 marks) 6(d) Appliction of Wind energy.(5 marks) 6(e) Energy Plantation.(5 marks) | 599 | 2,142 | {"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} | 2.734375 | 3 | CC-MAIN-2019-22 | latest | en | 0.779194 |
https://studyhippo.com/econ-160-final/ | 1,540,059,831,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583513009.81/warc/CC-MAIN-20181020163619-20181020185119-00356.warc.gz | 784,813,494 | 22,320 | ## Econ 160 Final
Explicit costs are payments the firm makes for
inputs such as wages and salaries to its employees, whereas implicit costs are non-expenditure costs that occur through the use of self owned resources such as foregone income.
The explicit costs of going to college include
tuition costs and the cost of books, whereas the implicit costs include foregone income.
Accounting profit equals sales revenue minus explicit costs
True
A normal profit is considered a cost because
this is the amount required to ensure continued supply of the product.
Wendy’s builds a new restaurant.
long-run adjustment
Harley-Davidson Corporation hires 200 more production workers.
short-run adjustment
A farmer increases the amount of fertilizer used on his corn crop.
short-run adjustment
An Alcoa aluminum plant adds a third shift of workers.
short-run adjustment
Complete the following table by calculating marginal product and average product from the data given. (Equations)
MC=∆TVC/∆Q
TC=TFC+TVC
ATC=TC/Q therefore TC=ATC(Q)
AFC=TFC/Q therefore TFC=AFC(Q)
AVC=TVC/Q therefore TVC=AVC(Q)
ATC=AFC+AVC
Advertising expenditures
variable cost
Fuel
variable cost
Interest on company-issued bonds
fixed cost
Shipping charges
variable cost
Payments for raw materials
variable cost
Real estate taxes
fixed cost
Executive salaries
fixed cost
Insurance premiums
fixed cost
Wage payments
variable cost
Depreciation and obsolescence charges
fixed cost
Sales taxes
variable cost
Rental payments on leased office machinery
fixed cost
Which of the following statements is true regarding the costs associated with owning and operating an automobile?
Fixed costs include insurance and variable costs include gasoline.
You are considering whether to drive your car or fly 1,000 miles to Florida for spring break. In making your decision you should consider
the variable cost of the trip, the opportunity cost of time, and the need for transportation in Florida.
Long-run average total cost falls as the firm realizes _____ and later rises when the firm experiences ______.
economies of scale, diseconomies of scale
The minimum efficient scale is the
smallest level of output needed to attain all economies of scale and minimum long-run average total cost.
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